AMBROSE'S BLOG: April 2012

Overall view of an engineering process.
The study of process engineering is an attempt to combine all forms of physical processing into a small number of basic operations, which are called unit operations. Food processes may seem bewildering in their diversity, but careful analysis will show that these complicated and differing processes can be broken down into a small number of unit operations. For example, consider heating of which innumerable instances occur in every food industry. There are many reasons for heating and cooling - for example, the baking of bread, the freezing of meat, the tempering of oils.

But in process engineering, the prime considerations are firstly, the extent of the heating or cooling that is required and secondly, the conditions under which this must be accomplished. Thus, this physical process qualifies to be called a unit operation. It is called 'heat transfer'.

The essential concept is therefore to divide physical food processes into basic unit operations, each of which stands alone and depends on coherent physical principles. For example, heat transfer is a unit operation and the fundamental physical principle underlying it is that heat energy will be transferred spontaneously from hotter to colder bodies.

Because of the dependence of the unit operation on a physical principle, or a small group of associated principles, quantitative relationships in the form of mathematical equations can be built to describe them. The equations can be used to follow what is happening in the process, and to control and modify the process if required.

Important unit operations in the food industry are fluid flow, heat transfer, drying, evaporation, contact equilibrium processes (which include distillation, extraction, gas absorption, crystallization, and membrane processes), mechanical separations (which include filtration, centrifugation, sedimentation and sieving), size reduction and mixing.

These unit operations, and in particular the basic principles on which they depend, are the subject of this book, rather than the equipment used or the materials being processed.

Two very important laws which all unit operations obey are the laws of conservation of mass and energy.

Conservation of Mass and Energy

The law of conservation of mass states that mass can neither be created nor destroyed. Thus in a processing plant, the total mass of material entering the plant must equal the total mass of material leaving the plant, less any accumulation left in the plant. If there is no accumulation, then the simple rule holds that "what goes in must come out". Similarly all material entering a unit operation must in due course leave.

For example, if milk is being fed into a centrifuge to separate it into skim milk and cream, under the law of conservation of mass the total number of kilograms of material (milk) entering the centrifuge per minute must equal the total number of kilograms of material (skim milk and cream) that leave the centrifuge per minute.

Similarly, the law of conservation of mass applies to each component in the entering materials. For example, considering the butter fat in the milk entering the centrifuge, the weight of butter fat entering the centrifuge per minute must be equal to the weight of butter fat leaving the centrifuge per minute. A similar relationship will hold for the other components, proteins, milk sugars and so on.

The law of conservation of energy states that energy can neither be created nor destroyed. The total energy in the materials entering the processing plant, plus the energy added in the plant, must equal the total energy leaving the plant.

This is a more complex concept than the conservation of mass, as energy can take various forms such as kinetic energy, potential energy, heat energy, chemical energy, electrical energy and so on.
During processing, some of these forms of energy can be converted from one to another. Mechanical energy in a fluid can be converted through friction into heat energy. Chemical energy in food is converted by the human body into mechanical energy.

Note that it is the sum total of all these forms of energy that is conserved.

For example, consider the pasteurizing process for milk, in which milk is pumped through a heat exchanger and is first heated and then cooled. The energy can be considered either over the whole plant or only as it affects the milk. For total plant energy, the balance must include: the conversion in the pump of electrical energy to kinetic and heat energy, the kinetic and potential energies of the milk entering and leaving the plant and the various kinds of energy in the heating and cooling sections,as well as the exiting heat, kinetic and potential energies.
To the food technologist, the energies affecting the product are the most important. In the case of the pasteurizer, the energy affecting the product is the heat energy in the milk. Heat energy is added to the milk by the pump and by the hot water passing through the heat exchanger. Cooling water then removes part of the heat energy and some of the heat energy is also lost to the surroundings.

The heat energy leaving in the milk must equal the heat energy in the milk entering the pasteurizer plus or minus any heat added or taken away in the plant.
Heat energy leaving in milk = initial heat energy
                                          + heat energy added by pump
                                          + heat energy added in heating section
                                          - heat energy taken out in cooling section
                                          - heat energy lost to surroundings.
The law of conservation of energy can also apply to part of a process. For example, considering the heating section of the heat exchanger in the pasteurizer, the heat lost by the hot water must be equal to the sum of the heat gained by the milk and the heat lost from the heat exchanger to its surroundings.

From these laws of conservation of mass and energy, a balance sheet for materials and for energy can be drawn up at all times for a unit operation. These are called material balances and energy balances.

Overall View of an Engineering Process

Using a material balance and an energy balance, a food engineering process can be viewed overall or as a series of units. Each unit is a unit operation. The unit operation can be represented by a box as shown in Fig. 1.1.

Fig. 1.1 Unit operation

Into the box go the raw materials and energy, out of the box come the desired products, by-products, wastes and energy. The equipment within the box will enable the required changes to be made with as little waste of materials and energy as possible. In other words, the desired products are required to be maximized and the undesired by-products and wastes minimized. Control over the process is exercised by regulating the flow of energy, or of materials, or of both.

2.0 HEAT TRANSFER APPLICATIONS

2.1 REFRIGERATION, CHILLING AND FREEZING

Refrigeration Cycle

Performance Characteristics

Refrigerants

Mechanical Equipment

The Refrigeration Evaporator

Chilling

Freezing

Cold Storage
Rates of decay and of deterioration in foodstuffs depend on temperature. At suitable low temperatures, changes in the food can be reduced to economically acceptable levels. The growth and metabolism of micro-organisms is slowed down and if the temperature is low enough, growth of all microorganisms virtually ceases. Enzyme activity and chemical reaction rates (of fat oxidation, for example) are also very much reduced at these temperatures. To reach temperatures low enough for deterioration virtually to cease, most of the water in the food must be frozen. The effect of chilling is only to slow down deterioration changes.

In studying chilling and freezing, it is necessary to look first at the methods for obtaining low temperatures, i.e. refrigeration systems, and then at the coupling of these to the food products in chilling and freezing.

Refrigeration Cycle

The basis of mechanical refrigeration is the fact that at different pressures the saturation (or the condensing) temperatures of vapours are different as clearly shown on the appropriate vapour-pressure/temperature curve. As the pressure increases condensing temperatures also increase. This fact is applied in a cyclic process, which is illustrated in Fig. 6.8.

Figure 6.8 Mechanical refrigeration circuit

The process can be followed on the pressure-enthalpy (P/H) chart shown on Fig. 6.9.

Description: Figure 6.9 Temperature/enthalpy chart

Figure 6.9 Pressure/enthalpy chart

This is a thermodynamic diagram that looks very complicated at first sight but which in fact can make calculations straightforward and simple. For the present purposes the most convenient such chart is the one shown with pressure as the vertical axis (for convenience on a logarithmic scale) and enthalpy on the horizontal axis. On such a diagram, the properties of the particular refrigerant can be plotted, including the interphase equilibrium lines such as the saturated vapour line, which are important as refrigeration depends on evaporation and condensation. Figure 6.9 is a skeleton diagram and Appendix 11 gives charts for two common refrigerants, refrigerant 134a, tetrafluoroethane (in Appendix 11a), and ammonia (in 11b); others for common refrigerants can be found in the ASHRAE Guide and Data Books.
To start with the evaporator; in this the pressure above the refrigerant is low enough so that evaporation of the refrigerant liquid to a gas occurs at some suitable low temperature determined by the requirements of the product. This temperature might be, for example -18°C in which case the corresponding pressures would be for ammonia 229 kPa absolute and for tetrafluoroethane (also known as refrigerant 134a) 144 kPa. Evaporation then occurs and this extracts the latent heat of vaporization for the refrigerant from the surroundings of the evaporator and it does this at the appropriate low temperature. This process of heat extraction at low temperature represents the useful part of the refrigerator. On the pressure/enthalpy chart this is represented by ab at constant pressure (the evaporation pressure) in which 1 kg of refrigerant takes in (H_b - H_a) kJ . The low pressure necessary for the evaporation at the required temperature is maintained by the suction of the compressor.
The remainder of the process cycle is included merely so that the refrigerant may be returned to the evaporator to continue the cycle. First, the vapour is sucked into a compressor which is essentially a gas pump and which increases its pressure to exhaust it at the higher pressure to the condensers. This is represented by the line bc which follows an adiabatic compression line, a line of constant entropy (the reasons for this must be sought in a book on refrigeration) and work equivalent to (H_c - H_b) kJ kg^-1 has to be performed on the refrigerant to effect the compression. The higher pressure might be, for example, 1150 kPa (pressures are absolute pressures) for ammonia, or 772 kPa for refrigerant 134a, and it is determined by the temperature at which cooling water or air is available to cool the condensers.
To complete the cycle, the refrigerant must be condensed, giving up its latent heat of vaporization to some cooling medium. This is carried out in a condenser, which is a heat exchanger cooled generally by water or air. Condensation is shown on Fig. 6.9 along the horizontal line (at the constant condenser pressure), at first cd cooling the gas and then continuing along de until the refrigerant is completely condensed at point e. The total heat given out in this from refrigerant to condenser water is (H_c - H_e) = (H_c - H_a) kJ kg^-1. The condensing temperature, corresponding to the above high pressures, is about 30°C and so in this example cooling water at about 20°C, could be used, leaving sufficient temperature difference to accomplish the heat exchange in equipment of economic size.
This process of evaporation at a low pressure and corresponding low temperature, followed by compression, followed by condensation at around atmospheric temperature and corresponding high pressure, is the refrigeration cycle. The high-pressure liquid then passes through a nozzle from the condenser or high-pressure receiver vessel to the evaporator at low pressure, and so the cycle continues. Expansion through the expansion valve nozzle is at constant enthalpy and so it follows the vertical line ea with no enthalpy added to or subtracted from the refrigerant. This line at constant enthalpy from point e explains why the point a is where it is on the pressure line, corresponding to the evaporation (suction) pressure.
By adjusting the high and low pressures, the condensing and evaporating temperatures can be selected as required. The high pressure is determined: by the available cooling-water temperature, by the cost of this cooling water and by the cost of condensing equipment. The evaporating pressure is determined by either the low temperature that is required for the product or by the rate of cooling or freezing that has to be provided. Low evaporating temperatures mean higher power requirements for compression and greater volumes of low-pressure vapours to be handled therefore larger compressors, so that the compression is more expensive. It must also be remembered that, in actual operation, temperature differences must be provided to operate both the evaporator and the condenser. There must be lower pressures than those that correspond to the evaporating coil temperature in the compressor suction line, and higher pressures in the compressor discharge than those that correspond to the condenser temperature.
Overall, the energy side of the refrigeration cycle can therefore be summed up:

heat taken in from surroundings at the (low) evaporator temperature and pressure (H_b - H_a),

heat equivalent to the work done by the compressor (H_c - H_b) and

heat rejected at the (high) compressor pressure and temperature (H_c - H_e).
A useful measure is the ratio of the heat taken in at the evaporator (the useful refrigeration), (H_b - H_a) , to the energy put in by the compressor which must be paid for (H_c– H_b). This ratio is called the coefficient of performance (COP).
The unit commonly used to measure refrigerating effect is the ton of refrigeration = 3.52 kW. It arises from the quantity of energy to freeze 2000 lb of water in one day (2000 lb is called 1 short ton).
So far we have been talking of the theoretical cycle. Real cycles differ by, for example, pressure drops in piping, superheating of vapour to the compressor and non-adiabatic compression, but these are relatively minor. Approximations quite good enough for our purposes can be based on the theoretical cycle. If necessary, allowances can be included for particular inefficiencies.
The refrigerant vapour has to be compressed so it can continue round the cycle and be condensed. From the refrigeration demand, the weight of refrigerant required to be circulated can be calculated; each kg s^-1 extracts so many J s^-1 according to the value of (H_b - H_a). From the volume of this refrigerant, the compressor displacement can be calculated, as the compressor has to handle this volume. Because the compressor piston cannot entirely displace all of the working volume of the cylinder, there must be a clearance volume; and because of inefficiencies in valves and ports, the actual amount of refrigerant vapour taken in is less than the theoretical. The ratio of these, actual amount taken in, to the theoretical compressor displacement, is called the volumetric efficiency of the compressor. Both mechanical and volumetric efficiencies can be measured, or taken from manufacturer's data, and they depend on the actual detail of the equipment used.
Consideration of the data from the thermo-dynamic chart and of the refrigeration cycle enables quite extensive calculations to be made about the operation.

Performance Characteristics

Variations in load and in the evaporating or condensing temperatures are often encountered when considering refrigeration systems. Their effects can be predicted by relating them to the basic cycle.
If the heat load increases in the cold store, then the temperature tends to rise and this increases the amount of refrigerant boiling off. If the compressor cannot move this, then the pressure on the suction side of the compressor increases and so the evaporating temperature increases tending to reduce the evaporation rate and correct the situation. However, the effect is to lift the temperature in the cold space and if this is to be prevented additional compressor capacity is required.
As the evaporating pressure, and resultant temperature, change, so the volume of vapour per kilogram of refrigerant changes. If the pressure decreases, this volume increases, and therefore the refrigerating effect, which is substantially determined by the rate of circulation of refrigerant, must also decrease. Therefore if a compressor is required to work from a lower suction pressure its capacity is reduced, and conversely. So at high suction pressures giving high circulation rates, the driving motors may become overloaded because of the substantial increase in quantity of refrigerant circulated in unit time.
Changes in the condenser pressure have relatively little effect on the quantity of refrigerant circulated. However, changes in the condenser pressure and also decreases in suction pressure, have quite a substantial effect on the power consumed per ton of refrigeration. Therefore for an economical plant, it is important to keep the suction pressure as high as possible, compatible with the product requirement for low temperature or rapid freezing, and the condenser pressure as low as possible compatible with the available cooling water or air temperature.

Refrigerants

Although in theory a considerable number of fluids might be used in mechanical refrigeration, and historically quite a number including cold air and carbon dioxide have been, those actually in use today are only a very small number. Substantially they include only ammonia, which is used in many large industrial systems, and approved members of a family of halogenated hydrocarbons containing differing proportions of fluorine and chosen according to the particular refrigeration duty required. The reasons for this very small group of practical refrigerants are many.
Important reasons are:

actual vapour pressure/temperature curve for the refrigerant which determines the pressures between which the system must operate for any particular pair of evaporator and condenser temperatures,

refrigerating effect per cubic metre of refrigerant pumped around the system which in turn governs the size of compressors and piping, and the stability and cost of the refrigerant itself.
Ammonia is in most ways the best refrigerant from the mechanical point of view, but its great problem is its toxicity. The thermodynamic chart for ammonia, refrigerant 717 is given in Appendix 11(b).
In working spaces, such as encountered in air conditioning, the halogenated hydrocarbons (often known, after the commercial name, as Freons) are very often used because of safety considerations. They are also used in domestic refrigerators. Environmental problems, in particular due to the effects of any chlorine derivatives and their long lives in the upper atmosphere, have militated heavily, in recent years, against some formerly common halogenated hydrocarbons. Only a very restricted selection has been judged safe. A thermodynamic chart for refrigerant 134a (the reasons for the numbering system are obscure, ammonia being refrigerant 717), the commonest of the safe halogenated hydrocarbon refrigerants, is given in Appendix 11(a). Other charts are available in references such as those provided by the refrigerant manufacturers and in books such as the ASHRAE Guide and Data Books.

Mechanical Equipment

Compressors are just basically vapour pumps and much the same types as shown in Fig. 4.3 for liquid pumps are encountered. Their design is highly specialized, particular problems arising from the lower density and viscosity of vapours when compared with liquids. The earliest designs were reciprocating machines with pistons moving horizontally or vertically, at first in large cylinders and at modest speeds, and then increasingly at higher speeds in smaller cylinders. An important aspect in compressor choice is the compression ratio, being the ratio of the absolute pressure of discharge from the compressor, to the inlet suction pressure. Reciprocating compressors can work effectively at quite high compression ratios (up to 6 or 7 to 1). Higher overall compression ratios are best handled by putting two or more compressors in series and so sharing the overall compression ratio between them.
For smaller compression ratios and for handling the large volumes of vapours encountered at low temperatures and pressures, rotary vane compressors are often used, and for even larger volumes, centrifugal compressors, often with many stages, can be used. A recent popular development is the screw compressor, analogous to a gear pump, which has considerable flexibility. Small systems are often "hermetic", implying that the motor and compressor are sealed into one casing with the refrigerant circulating through both. This avoids rotating seals through which refrigerant can leak. The familiar and very dependable units in household refrigerators are almost universally of this type.

Refrigeration Evaporator

The evaporator is the only part of the refrigeration equipment that enters directly into food processing operations. Heat passes from the food to the heat-transfer medium, which may be air or liquid, thence to the evaporator and so to the refrigerant. Thermal coupling is in some cases direct, as in a plate freezer. In this, the food to be frozen is placed directly on or between plates, within which the refrigerant circulates. Another familiar example of direct thermal coupling is the chilled slab in a shop display.
Generally, however, the heat transfer medium is air, which moves either by forced or natural circulation between the heat source, the food and the walls warmed by outside air, and the heat sink which is the evaporator. Sometimes the medium is liquid such as in the case of immersion freezing in propylene glycol or in alcohol-water mixtures. Then there are some cases in which the refrigerant is, in effect, the medium such as immersion or spray with liquid nitrogen. Sometimes there is also a further intermediate heat-transfer medium, so as to provide better control, or convenience, or safety. An example is in some milk chillers, where the basic refrigerant is ammonia; this cools glycol, which is pumped through a heat exchanger where it cools the milk. A sketch of some types of evaporator system is given in Fig. 6.10.

Figure 6.10 Refrigeration evaporators

In the freezer or chiller, the heat transfer rates both from the food and to the evaporator, depend upon fluid or gas velocities and upon temperature differences. The values for the respective heat transfer coefficients can be estimated by use of the standard heat transfer relationships. Typical values that occur in freezing equipment are given in Table 6.3.

TABLE 6.3
EXPECTED SURFACE HEAT TRANSFER COEFFICIENTS (h_s)

	J m^-2 s^-1 °C^-1
Still-air freezing (including radiation to coils)	9
Still-air freezing (no radiation)	6
Air-blast freezing 3 m s^-1	18
Air-blast freezing 5 m s^-1	30
Liquid-immersion freezing	600
Plate freezing	120

Temperature differences across evaporators are generally of the order 3 - 10°C. The calculations for heat transfer can be carried out using the methods which have been discussed in other sections, including their relationship to freezing and freezing times, as the evaporators are just refrigerant-to-air heat exchangers.
The evaporator surfaces are often extended by the use of metal fins that are bonded to the evaporator pipe surface. The reason for this construction is that the relatively high metal conductance, compared with the much lower surface conductance from the metal surface to the air, maintains the fin surface substantially at the coil temperature. A slight rise in temperature along the fin can be accounted for by including in calculations a fin efficiency factor. The effective evaporator area is then calculated by the relationship
A = A_p+ A_s (6.5)
where A is the equivalent total evaporator surface area, A_p is the coil surface area, called the primary surface, A_s is the fin surface area, called the secondary surface and  (phi) is the fin efficiency.
Values of  lie between 65% and 95% in the usual designs, as shown for example in DKV Arbeitsblatt 2-02, 1950.

Chilling

Chilling of foods is a process by which their temperature is reduced to the desired holding temperature just above the freezing point of food, usually in the region of -2 to 2°C
Many commercial chillers operate at higher temperatures, up to 10-12°C. The effect of chilling is only to slow down deterioration changes and the reactions are temperature dependent. So the time and temperature of holding the chilled food determine the storage life of the food.
Rates of chilling are governed by the laws of heat transfer which have been described in previous sections. It is an example of unsteady-state heat transfer by convection to the surface of the food and by conduction within the food itself. The medium of heat exchange is generally air, which extracts heat from the food and then gives it up to refrigerant in the evaporator. As explained in the heat-transfer section, rates of convection heat transfer from the surface of food and to the evaporator are much greater if the air is in movement, being roughly proportional to v^0.8.
To calculate chilling rates it is therefore necessary to evaluate:
(a) surface heat transfer coefficient,
(b) resistance offered to heat flow by any packaging material that may be placed round the food,
(c) appropriate unsteady state heat conduction equation.
Although the shapes of most foodstuffs are not regular, they often approximate the shapes of slabs, bricks, spheres and cylinders.

Freezing

Water makes up a substantial proportion of almost all foodstuffs and so freezing has a marked physical effect on the food. Because of the presence of substances dissolved in the water, food does not freeze at one temperature but rather over a range of temperatures. At temperatures just below the freezing point of water, crystals that are almost pure ice form in the food and so the remaining solutions become more concentrated. Even at low temperatures some water remains unfrozen, in very concentrated solutions.
In the freezing process, added to chilling is the removal of the latent heat of freezing. This latent heat has to be removed from any water that is present. Since the latent heat of freezing of water is 335 kJ kg^-1, this represents the most substantial thermal quantity entering into the process. There may be other latent heats, for example the heats of solidification of fats which may be present, and heats of solution of salts, but these are of smaller magnitude than the latent heat of freezing of water. Also the fats themselves are seldom present in foods in as great a proportion as water.
Because of the latent-heat-removal requirement, the normal unsteady-state equations cannot be applied to the freezing of foodstuffs. The coefficients of heat transfer can be estimated by the following equation:

Cold Storage

For cold storage, the requirement for refrigeration comes from the need to remove the heat:

coming into the store from the external surroundings through insulation

from sources within the store such as motors, lights and people (each worker contributing something of the order of 0.5 kW)

from the foodstuffs.

Heat penetrating the walls can be estimated, knowing the overall heat-transfer coefficients including the surface terms and the conductances of the insulation, which may include several different materials. The other heat sources require to be considered and summed. Detailed calculations can be quite complicated but for many purposes simple methods give a reasonable estimate.

2.2 THERMAL PROCESSING

Thermal Death Time

Equivalent Killing Power at Other Temperatures

Pasteurization

Thermal processing implies the controlled use of heat to increase, or reduce depending on circumstances, the rates of reactions in foods.
A common example is the retorting of canned foods to effect sterilization. The object of sterilization is to destroy all microorganisms, that is, bacteria, yeasts and moulds, in the food material to prevent decomposition of the food, which makes it unattractive or inedible. Also, sterilization prevents any pathogenic (disease-producing) organisms from surviving and being eaten with the food. Pathogenic toxins may be produced during storage of the food if certain organisms are still viable. Microorganisms are destroyed by heat, but the amount of heating required for the killing of different organisms varies. Also, many bacteria can exist in two forms, the vegetative or growing form and the spore or dormant form. The spores are much harder to destroy by heat treatment than are the vegetative forms.

Studies of the microorganisms that occur in foods, have led to the selection of certain types of bacteria as indicator organisms. These are the most difficult to kill, in their spore forms, of the types of bacteria which are likely to be troublesome in foods.

A frequently used indicator organism is Clostridium botulinum. This particular organism is a very important food poisoning organism as it produces a deadly toxin and also its spores are amongst the most heat resistant. Processes for the heat treatment of foodstuffs are therefore examined with respect to the effect they would have on the spores of C. botulinum. If the heat process would not destroy this organism then it is not adequate. As C. botulinum is a very dangerous organism, a selected strain of a non-pathogenic organism of similar heat resistance is often used for testing purposes.

Thermal Death Time

It has been found that microorganisms, including C. botulinum, are destroyed by heat at rates which depend on the temperature, higher temperatures killing spores more quickly. At any given temperature, the spores are killed at different times, some spores being apparently more resistant to heat than other spores. If a graph is drawn, the number of surviving spores against time of holding at any chosen temperature, it is found experimentally that the number of surviving spores fall asymptotically to zero. Methods of handling process kinetics are well developed and if the standard methods are applied to such results, it is found that thermal death of microorganisms follows, for practical purposes, what is called a first-order process at a constant temperature (see for example Earle and Earle, 2003).
This implies that the fractional destruction in any fixed time interval, is constant. It is thus not possible, in theory at least, to take the time when all of the organisms are actually destroyed. Instead it is practicable, and very useful, to consider the time needed for a particular fraction of the organisms to be killed.
The rates of destruction can in this way be related to:
(1) The numbers of viable organisms in the initial container or batch of containers.
(2) The number of viable organisms which can safely be allowed to survive.
Of course the surviving number must be small indeed, very much less than one, to ensure adequate safety. However, this concept, which includes the admissibility of survival numbers of much less than one per container, has been found to be very useful. From such considerations, the ratio of the initial to the final number of surviving organisms becomes the criterion that determines adequate treatment. A combination of historical reasons and extensive practical experience has led to this number being set, for C. botulinum, at 10¹²:1. For other organisms, and under other circumstances, it may well be different.
The results of experiments to determine the times needed to reduce actual spore counts from 10¹² to 1 (the lower, open, circles) or to 0 (the upper, closed, circles) are shown in Fig. 6.4.

Figure 6.4. Thermal death time curve for Clostridium botulinum
Based on research results from the American Can Company

In this graph, these times are plotted against the different temperatures and it shows that when the logarithms of these times are plotted against temperatures, the resulting graph is a straight line. The mean times on this graph are called thermal death times for the corresponding temperatures. Note that these thermal death times do not represent complete sterilization, but a mathematical concept which can be considered as effective sterilization, which is in fact a survival ratio of 1:10¹², and which has been found adequate for safety

Any canning process must be considered then from the standpoint of effective sterilization. This is done by combining the thermal death time data with the time-temperature relationships at the point in the can that heats slowest. Generally, this point is on the axis of the can and somewhere close to the geometric centre. Using either the unsteady-state heating curves or experimental measurements with a thermocouple at the slowest heating point in a can, the temperature-time graph for the can under the chosen conditions can be plotted. This curve has then to be evaluated in terms of its effectiveness in destroying C. botulinum or any other critical organism, such as thermophilic spore formers, which are important in industry. In this way the engineering data, which provides the temperatures within the container as the process is carried out, are combined with kinetic data to evaluate the effect of processing on the product.
Considering Fig. 6.4, the standard reference temperature is generally selected as 121.1°C (250 °F), and the relative time (in minutes) required to sterilize, effectively, any selected organism at 121°C is spoken of as the F value of that organism. In our example, reading from Fig. 6.4, the F value is about 2.8 min. For any process that is different from a steady holding at 121°C, our standard process, the actual attained F values can be worked out by stepwise integration. If the total F value so found is below 2.8 min, then sterilization is not sufficient; if above 2.8 min, the heat treatment is more drastic than it needs to be.

Equivalent Killing Power at Other Temperatures

The other factor that must be determined, so that the equivalent killing powers at temperatures different from 121°C can be evaluated, is the dependence of thermal death time on temperature. Experimentally, it has been found that if the logarithm of t, the thermal death time, is plotted against the temperature, a straight-line relationship is obtained. This is shown in Fig. 6.4 and more explicitly in Fig. 6.5.

Figure 6.5 Thermal death time/temperature relationships

EXAMPLE 6.5. Time/Temperature in a can during sterilisation
In a retort, the temperatures in the slowest heating region of a can of food were measured and were found to be shown as in Fig. 6.6. Is the retorting adequate, if F for the process is 2.8 min and z is 10°C?

Figure 6.6 Time/Temperature curve for can processing

Approximate stepped temperature increments are drawn on the curve giving the equivalent holding times and temperatures as shown in Table 6.2. The corresponding F values are calculated for each temperature step.

TABLE 6.2

Temperature T (°C)	Time t (min)	(121 - T)	10^-(^121-T)/10	t x 10^-(^121-T)/10
80	11	41	7.9 x 10^-5	0.00087
90	8	31	7.9 x 10^-4	0.0063
95	6	26	2.5 x 10^-3	0.015
100	10	21	7.9 x 10^-3	0.079
105	12	16	2.5 x 10^-2	0.30
108	6	13	5.0 x 10^-2	0.30
109	8	12	6.3 x 10^-2	0.50
110	17	11	7.9 x 10^-2	1.34
107	2	14	4.0 x 10^-2	0.08
100	2	21	7.9 x 10^-3	0.016
90	2	31	7.9 x 10^-4	0.0016
80	8	41	7.9 x 10^-5	0.0006
70	6	51	7.9 x 10^-6	0.00005
			Total	2.64

The above results show that the F value for the process = 2.64 so that the retorting time is not quite adequate. This could be corrected by a further 2 min at 110°C (and proceeding as above, this would add 2 x 10^-(^121-110)/10 = 0.16, to 2.64, making 2.8).
From the example, it may be seen that the very sharp decrease of thermal death times with higher temperatures means that holding times at the lower temperatures contribute little to the sterilization. Very long times at temperatures below 90°C would be needed to make any appreciable difference to F, and in fact it can often be the holding time at the highest temperature which virtually determines the F value of the whole process. Calculations can be shortened by neglecting those temperatures that make no significant contribution, although, in each case, both the number of steps taken and also their relative contributions should be checked to ensure accuracy in the overall integration.
It is possible to choose values of F and of z to suit specific requirements and organisms that may be suspected of giving trouble. The choice and specification of these is a whole subject in itself and will not be further discussed. From an engineering viewpoint a specification is set, as indicated above, with an F value and a z value, and then the process conditions are designed to accomplish this.
The discussion on sterilization is designed to show, in an elementary way, how heat-transfer calculations can be applied and not as a detailed treatment of the topic. This can be found in appropriate books such as Stumbo (1973), Earle and Earle (2003).

Pasteurization

Pasteurization is a heat treatment applied to foods, which is less drastic than sterilization, but which is sufficient to inactivate particular disease-producing organisms of importance in a specific foodstuff. Pasteurization inactivates most viable vegetative forms of microorganisms but not heat-resistant spores. Originally, pasteurization was evolved to inactivate bovine tuberculosis in milk. Numbers of viable organisms are reduced by ratios of the order of 10¹⁵:1. As well as the application to inactivate bacteria, pasteurization may be considered in relation to enzymes present in the food, which can be inactivated by heat. The same general relationships as were discussed under sterilization apply to pasteurization. A combination of temperature and time must be used that is sufficient to inactivate the particular species of bacteria or enzyme under consideration. Fortunately, most of the pathogenic organisms, which can be transmitted from food to the person who eats it, are not very resistant to heat.
The most common application is pasteurization of liquid milk. In the case of milk, the pathogenic organism that is of classical importance is Mycobacterium tuberculosis, and the time/temperature curve for the inactivation of this bacillus is shown in Fig. 6.7.

Figure 6.7 Pasteurization curves for milk

This curve can be applied to determine the necessary holding time and temperature in the same way as with the sterilization thermal death curves. However, the times involved are very much shorter, and controlled rapid heating in continuous heat exchangers simplifies the calculations so that only the holding period is really important. For example, 30 min at 62.8°C in the older pasteurizing plants and 15 sec at 71.7°C in the so-called high temperature/short time (HTST) process are sufficient. An even faster process using a temperature of 126.7°C for 4 sec is claimed to be sufficient. The most generally used equipment is the plate heat exchanger and rates of heat transfer to accomplish this pasteurization can be calculated by the methods explained previously.
An enzyme present in milk, phosphatase, is destroyed under somewhat the same time-temperature conditions as the M. tuberculosis and, since chemical tests for the enzyme can be carried out simply, its presence is used as an indicator of inadequate heat treatment. In this case, the presence or absence of phosphatase is of no significance so far as the storage properties or suitability for human consumption are concerned.
Enzymes are of importance in deterioration processes of fruit juices, fruits and vegetables. If time-temperature relationships, such as those that are shown in Fig. 6.7 for phosphatase, can be determined for these enzymes, heat processes to destroy them can be designed. Most often this is done by steam heating, indirectly for fruit juices and directly for vegetables when the process is known as blanching.
The processes for sterilization and pasteurization illustrate very well the application of heat transfer as a unit operation in food processing. The temperatures and times required are determined and then the heat transfer equipment is designed using the equations developed for heat-transfer operations.

EXAMPLE 6.6. Pasteurisation of milk
A pasteurization heating process for milk was found, taking measurements and times, to consist essentially of three heating stages being 2 min at 64°C, 3 min at 65°C and 2 min at 66°C. Does this process meet the standard pasteurization requirements for the milk, as indicated in Fig. 6.7, and if not what adjustment needs to be made to the period of holding at 66°C?
From Fig. 6.7, pasteurization times t_T can be read off the UK pasteurisation standard, and from and these and the given times, rates and fractional extents of pasteurization can be calculated:
    At 64°C,        t₆₄ = 15.7 min
     so 2 min is    2    = 0.13
                      15.7
     At 65°C,        t₆₅ = 9.2 min
     so 3 min is   3     = 0.33
                9.2
     At 66°C,        t₆₆ = 5.4 min
     so 2 min is    2 = 0.37
               5.4
Total pasteurization extent = (0.13 + 0.33 + 0.37) = 0.83.

Pasteurization remaining to be accomplished = (1 - 0.83) = 0.17.
At 66°C this would be obtained from (0.17 x 5.4) min holding = 0.92 min.
So an additional 0.92 min (or approximately 1 min) at 66°C would be needed to meet the specification.

2.3HEAT TRANSFER APPLICATIONS

Heat exchangers

Continuous-flow Heat Exchangers

Jacketed Pans

Heating Coils Immersed in Liquids

Scraped Surface Heat Exchangers

Plate Heat Exchangers

The principles of heat transfer are widely used in food processing in many items of equipment. It seems appropriate to discuss these under the various applications that are commonly encountered in nearly every food factory.

HEAT EXCHANGERS

In a heat exchanger, heat energy is transferred from one body or fluid stream to another. In the design of heat exchange equipment, heat transfer equations are applied to calculate this transfer of energy so as to carry it out efficiently and under controlled conditions. The equipment goes under many names, such as boilers, pasteurizers, jacketed pans, freezers, air heaters, cookers, ovens and so on. The range is too great to list completely. Heat exchangers are found widely scattered throughout the food process industry.

Continuous-flow Heat Exchangers

It is very often convenient to use heat exchangers in which one or both of the materials that are exchanging heat are fluids, flowing continuously through the equipment and acquiring or giving up heat in passing.
One of the fluids is usually passed through pipes or tubes, and the other fluid stream is passed round or across these. At any point in the equipment, the local temperature differences and the heat transfer coefficients control the rate of heat exchange.
The fluids can flow in the same direction through the equipment, this is called parallel flow; they can flow in opposite directions, called counter flow; they can flow at right angles to each other, called cross flow. Various combinations of these directions of flow can occur in different parts of the exchanger. Most actual heat exchangers of this type have a mixed flow pattern, but it is often possible to treat them from the point of view of the predominant flow pattern. Examples of these exchangers are illustrated in Figure 6.1.

Figure 6.1 Heat exchangers

In parallel flow, at the entry to the heat exchanger, there is the maximum temperature difference between the coldest and the hottest stream, but at the exit the two streams can only approach each other's temperature. In a counter flow exchanger, leaving streams can approach the temperatures of the entering stream of the other component and so counter flow exchangers are often preferred.
Applying the basic overall heat-transfer equation for the the heat exchanger heat transfer:
q = UA T
uncertainty at once arises as to the value to be chosen for T, even knowing the temperatures in the entering and leaving streams.
Consider a heat exchanger in which one fluid is effectively at a constant temperature, T_b as illustrated in Fig. 6.1(d). Constant temperature in one component can result either from a very high flow rate of this component compared with the other component, or from the component being a vapour such as steam or ammonia condensing at a high rate, or from a boiling liquid. The heat-transfer coefficients are assumed to be independent of temperature.
The rate of mass flow of the fluid that is changing temperature is G kg s^-1, its specific heat is c_p J kg^-1 °C^-1. Over a small length of path of area dA, the mean temperature of the fluid is T and the temperature drop is dT. The constant temperature fluid has a temperature T_b. The overall heat transfer coefficient is U J m^-2 s^-1°C^-1.
Therefore the heat balance over the short length is:
               c_pGdT = U(T - T_b)dA
Therefore U/)c_pG) dA = dT/(T –T_b)
If this is integrated over the length of the tube in which the area changes from A = 0 to A = A, and T changes from T₁ to T₂, we have:
          U/(cpG) A = ln[(T₁ – T_b)/(T₂ - T_b)]               (where ln = log_e)
                          = ln (T₁/ T₂)
      in which T₁ = (T₁ – T_b) and T₂ = (T₂ - T_b)
therefore       c_pG = UA/ ln (T₁/ T₂)
From the overall equation, the total heat transferred per unit time is given by
                       q = UAT_m
where T_m is the mean temperature difference, but the total heat transferred per unit is also:
                       q = c_pG(T₁ –T₂)
                  so q = UAT_m = c_pG(T₁ –T₂) = UA/ ln (T₁/ T₂)] x (T₁ –T₂)
but (T₁ –T₂) can be written (T₁ – T_b) - (T₂ - T_b)
         so (T₁ –T₂) = (T₁ - T₂)
therefore UAT_m = UA(T₁ - T₂) / ln (T₁/ T₂)                                                 (6.1)
so that
                 T_m  = (T₁ - T₂) / ln (T₁/ T₂)                                                      (6.2)
where T_m is called the log mean temperature difference.
In other words, the rate of heat transfer can be calculated using the heat transfer coefficient, the total area, and the log mean temperature difference. This same result can be shown to hold for parallel flow and counter flow heat exchangers in which both fluids change their temperatures.
The analysis of cross-flow heat exchangers is not so simple, but for these also the use of the log mean temperature difference gives a good approximation to the actual conditions if one stream does not change very much in temperature.

EXAMPLE 6.1. Cooling of milk in a pipe heat exchanger
Milk is flowing into a pipe cooler and passes through a tube of 2.5 cm internal diameter at a rate of 0.4 kg s^-1. Its initial temperature is 49°C and it is wished to cool it to 18°C using a stirred bath of constant 10°C water round the pipe. What length of pipe would be required? Assume an overall coefficient of heat transfer from the bath to the milk of 900 J m^-2 s^-1 °C^-1, and that the specific heat of milk is 3890 J kg^-1 °C^-1.
Now
                      q = c_pG (T₁ –T₂)
                         = 3890 x 0.4 x (49 - 18)
                         = 48,240 J s^-1
Also                       q = UAT_m
                 T_m = [(49 - 10) - (18 –10)] / ln[(49 -10)1(18 - 10)]
                         = 19.6°C.
Therefore 48,240 = 900 x A x l9.6
                      A = 2.73 m²
                but A = DL
where L is the length of pipe of diameter D
               Now D = 0.025 m.
                      L = 2.73/( x 0.025)
                         = 34.8 m
This can be extended to the situation where there are two fluids flowing, one the cooled fluid and the other the heated fluid. Working from the mass flow rates (kg s^-1) and the specific heats of the two fluids, the terminal temperatures can normally be calculated and these can then be used to determine T_m and so, from the heat-transfer coefficients, the necessary heat-transfer surface.

EXAMPLE 6.2. Water chilling in a counter flow heat exchanger
In a counter flow heat exchanger, water is being chilled by a sodium chloride brine. If the rate of flow of the brine is 1.8 kg s^-1 and that of the water is 1.05 kg s^-1, estimate the temperature to which the water is cooled if the brine enters at -8°C and leaves at 10°C, and if the water enters the exchanger at 32°C. If the area of the heat-transfer surface of this exchanger is 55 m², what is the overall heat-transfer coefficient? Take the specific heats to be 3.38 and 4.18 kJ kg^-1°C^-1 for the brine and the water respectively.
With heat exchangers a small sketch is often helpful:

Description: FIG. 6.2. Diagrammatic heat exchanger

Figure 6.2. Diagrammatic heat exchanger

Figure 6.2 shows three temperatures are known and the fourth T_w2 (= T''₂ say on Fig 6.2) can be found from the heat balance:
By heat balance, heat loss in brine = heat gain in water
1.8 x 3.38 x [10 - (-8)] = 1.05 x 4.18 x (32 - T_w2)
            Therefore T_w2 = 7°C.
And for counterflow
                                  T₁ = [32 - 10] = 22°C and T₂ = [7 - (-8)] = 15°C.
           Therefore T_m = (22 - 15)/ln(22/15)
                                 = 7/0.382
                                 = 18.3°C.

For the heat exchanger
                              q = heat exchanged between fluids = heat lost by brine = heat gain to water
                                 = heat passed across heat transfer surface
                                 = UAT_m
Therefore
          3.38 x 1.8 x 18 = U x 55 x 18.3
                              U = 0.11 kJ m^-2 °C^-1
                                 = 110 J m^-2 °C^-1
Parallel flow situations can be worked out similarly, making appropriate adjustments.
In some cases, heat-exchanger problems cannot be solved so easily; for example, if the heat transfer coefficients have to be calculated from the basic equations of heat transfer which depend on flow rates and temperatures of the fluids, and the temperatures themselves depend on the heat-transfer coefficients. The easiest way to proceed then is to make sensible estimates and to go through the calculations. If the final results are coherent, then the estimates were reasonable. If not, then make better estimates, on the basis of the results, and go through a new set of calculations; and if necessary repeat again until consistent results are obtained. For those with multiple heat exchangers to design, computer programmes are available.

Jacketed Pans

In a jacketed pan, the liquid to be heated is contained in a vessel, which may also be provided with an agitator to keep the liquid on the move across the heat-transfer surface, as shown in Fig. 6.3(a).

Figure 6.3. Heat exchange equipment

The source of heat is commonly steam condensing in the vessel jacket. Practical considerations of importance are:
1. There is the minimum of air with the steam in the jacket.
2. The steam is not superheated as part of the surface must then be used as a de-superheater over which low gas heat-transfer coefficients apply rather than high condensing coefficients.
3. Steam trapping to remove condensate and air is adequate.
The action of the agitator and its ability to keep the fluid moved across the heat transfer surface are important. Some overall heat transfer coefficients are shown in Table 6.1. Save for boiling water, which agitates itself, mechanical agitation is assumed. Where there is no agitation, coefficients may be halved.

TABLE 6.1
SOME OVERALL HEAT TRANSFER COEFFICIENTS IN JACKETED PANS

Condensing fluid	Heated fluid	Pan material	Heat transfer coefficients J m^-2 s^-1 °C^-1
Steam	Thin liquid	Cast-iron	1800
Steam	Thick liquid	Cast-iron	900
Steam	Paste	Stainless steel	300
Steam	Water, boiling	Copper	1800

EXAMPLE 6.3. Steam required to heat pea soup in jacketed pan
Estimate the steam requirement as you start to heat 50 kg of pea soup in a jacketed pan, if the initial temperature of the soup is 18°C and the steam used is at 100 kPa gauge. The pan has a heating surface of 1 m² and the overall heat transfer coefficient is assumed to be 300 J m^-2 s^-1 °C^-1.

From steam tables (Appendix 8), saturation temperature of steam at 100 kPa gauge = 120°C and latent heat =  = 2202 kJ kg^-1.
                                           q = UA T
                                      = 300 x 1 x (120 - 18)
                                  = 3.06 x 10⁴ J s^-1
Therefore amount of steam
                = q/ = (3.06 x 10⁴)/(2.202 x 10⁶)
                    = 1.4 x 10^-2 kg s^-1
        = 1.4 x 10^-2 x 3.6 x 10³
              = 50 kg h^-1.
This result applies only to the beginning of heating; as the temperature rises less steam will be consumed as T decreases.
The overall heating process can be considered by using the analysis that led up to eqn. (5.6). A stirred vessel to which heat enters from a heating surface with a surface heat transfer coefficient which controls the heat flow, follows the same heating or cooling path as does a solid body of high internal heat conductivity with a defined surface heating area and surface heat transfer coefficient.

EXAMPLE 6.4. Time to heat pea soup in a jacketed pan
In the heating of the pan in Example 6.3, estimate the time needed to bring the stirred pea soup up to a temperature of 90°C, assuming the specific heat is 3.95 kJ kg^-1 °C^-1.
From eqn. (5.6) (T₂ - T_a)/(T₁– T_a) = exp(-h_sAt/cV )
                                         T_a = 120°C (temperature of heating medium)
                                         T₁ = 18°C (initial soup temperature)
                                       T₂ = 90°C (soup temperature at end of time t)
                           h_s = 300 J m^-2 s^-1 °C^-1
                  A = 1 m², c = 3.95 kJ kg^-1 °C^-1.
                          V = 50 kg
Therefore                          t = -3.95 x 10³ x 50 x   ln (90 - 120) / (18 - 120)
                                300 x 1
                               = (-658) x (-1.22) s
         = 803 s
           = 13.4 min.

Heating Coils Immersed in Liquids

In some food processes, quick heating is required in the pan, for example, in the boiling of jam. In this case, a helical coil may be fitted inside the pan and steam admitted to the coil as shown in Fig. 6.3(b). This can give greater heat transfer rates than jacketed pans, because there can be a greater heat transfer surface and also the heat transfer coefficients are higher for coils than for the pan walls. Examples of the overall heat transfer coefficient U are quoted as:

300-1400 for sugar and molasses solutions heated with steam using a copper coil,

1800 for milk in a coil heated with water outside,

3600 for a boiling aqueous solution heated with steam in the coil.
with the units in these coefficients being J m^-2 s^-1 °C^-1.

Scraped Surface Heat Exchangers

One type of heat exchanger, that finds considerable use in the food processing industry particularly for products of higher viscosity, consists of a jacketed cylinder with an internal cylinder concentric to the first and fitted with scraper blades, as illustrated in Fig. 6.3(c). The blades rotate, causing the fluid to flow through the annular space between the cylinders with the outer heat transfer surface constantly scraped. Coefficients of heat transfer vary with speeds of rotation but they are of the order of 900-4000 J m^-2 s^-1 °C^-1. These machines are used in the freezing of ice cream and in the cooling of fats during margarine manufacture.

Plate Heat Exchangers

A popular heat exchanger for fluids of low viscosity, such as milk, is the plate heat exchanger, where heating and cooling fluids flow through alternate tortuous passages between vertical plates as illustrated in Fig. 6.3(d). The plates are clamped together, separated by spacing gaskets, and the heating and cooling fluids are arranged so that they flow between alternate plates. Suitable gaskets and channels control the flow and allow parallel or counter current flow in any desired number of passes. A substantial advantage of this type of heat exchanger is that it offers a large transfer surface that is readily accessible for cleaning. The banks of plates are arranged so that they may be taken apart easily. Overall heat transfer coefficients are of the order of 2400-6000 J m^-2 s^-1 °C^-1.

2.4 DRYING

DRYING EQUIPMENT

Tray Dryers

Tunnel Dryers

Roller or Drum Dryers

Fluidized Bed Dryers

Spray Dryers

Pneumatic Dryers

Rotary Dryers

Trough Dryers

Bin Dryers

Belt Dryers

Vacuum Dryers

Freeze Dryers

In an industry so diversified and extensive as the food industry, it would be expected that a great number of different types of dryer would be in use. This is the case and the total range of equipment is much too wide to be described in any introductory book such as this. The principles of drying may be applied to any type of dryer, but it should help the understanding of these principles if a few common types of dryers are described.

The major problem in calculations on real dryers is that conditions change as the drying air and the drying solids move along the dryer in a continuous dryer, or change with time in the batch dryer. Such implications take them beyond the scope of the present book, but the principles of mass and heat balances are the basis and the analysis is not difficult once the fundamental principles of drying are understood. Obtaining adequate data may be the difficult part.

Tray Dryers

In tray dryers, the food is spread out, generally quite thinly, on trays in which the drying takes place. Heating may be by an air current sweeping across the trays, by conduction from heated trays or heated shelves on which the trays lie, or by radiation from heated surfaces. Most tray dryers are heated by air, which also removes the moist vapours.

Tunnel Dryers

These may be regarded as developments of the tray dryer, in which the trays on trolleys move through a tunnel where the heat is applied and the vapours removed. In most cases, air is used in tunnel drying and the material can move through the dryer either parallel or counter current to the air flow. Sometimes the dryers are compartmented, and cross-flow may also be used.

Roller or Drum Dryers

In these the food is spread over the surface of a heated drum. The drum rotates, with the food being applied to the drum at one part of the cycle. The food remains on the drum surface for the greater part of the rotation, during which time the drying takes place, and is then scraped off. Drum drying may be regarded as conduction drying.

Fluidized Bed Dryers

In a fluidized bed dryer, the food material is maintained suspended against gravity in an upward-flowing air stream. There may also be a horizontal air flow helping to convey the food through the dryer. Heat is transferred from the air to the food material, mostly by convection.

Spray Dryers

In a spray dryer, liquid or fine solid material in a slurry is sprayed in the form of a fine droplet dispersion into a current of heated air. Air and solids may move in parallel or counterflow. Drying occurs very rapidly, so that this process is very useful for materials that are damaged by exposure to heat for any appreciable length of time. The dryer body is large so that the particles can settle, as they dry, without touching the walls on which they might otherwise stick. Commercial dryers can be very large of the order of 10 m diameter and 20 m high.

Pneumatic Dryers

In a pneumatic dryer, the solid food particles are conveyed rapidly in an air stream, the velocity and turbulence of the stream maintaining the particles in suspension. Heated air accomplishes the drying and often some form of classifying device is included in the equipment. In the classifier, the dried material is separated, the dry material passes out as product and the moist remainder is recirculated for further drying.

Rotary Dryers

The foodstuff is contained in a horizontal inclined cylinder through which it travels, being heated either by air flow through the cylinder, or by conduction of heat from the cylinder walls. In some cases, the cylinder rotates and in others the cylinder is stationary and a paddle or screw rotates within the cylinder conveying the material through.

Trough Dryers

The materials to be dried are contained in a trough-shaped conveyor belt, made from mesh, and air is blown through the bed of material. The movement of the conveyor continually turns over the material, exposing fresh surfaces to the hot air.

Bin Dryers

In bin dryers, the foodstuff is contained in a bin with a perforated bottom through which warm air is blown vertically upwards, passing through the material and so drying it.

Belt Dryers

The food is spread as a thin layer on a horizontal mesh or solid belt and air passes through or over the material. In most cases the belt is moving, though in some designs the belt is stationary and the material is transported by scrapers.

Vacuum Dryers

Batch vacuum dryers are substantially the same as tray dryers, except that they operate under a vacuum, and heat transfer is largely by conduction or by radiation. The trays are enclosed in a large cabinet, which is evacuated. The water vapour produced is generally condensed, so that the vacuum pumps have only to deal with non-condensible gases. Another type consists of an evacuated chamber containing a roller dryer.

Freeze Dryers

The material is held on shelves or belts in a chamber that is under high vacuum. In most cases, the food is frozen before being loaded into the dryer. Heat is transferred to the food by conduction or radiation and the vapour is removed by vacuum pump and then condensed. In one process, given the name accelerated freeze drying, heat transfer is by conduction; sheets of expanded metal are inserted between the foodstuffs and heated plates to improve heat transfer to the uneven surfaces, and moisture removal. The pieces of food are shaped so as to present the largest possible flat surface to the expanded metal and the plates to obtain good heat transfer. A refrigerated condenser may be used to condense the water vapour.

Various types of dryers are illustrated in Fig. 7.8:

Figure 7.8 Dryers

2.5EVAPORATION

EVAPORATION EQUIPMENT

Open Pans

Horizontal-tube Evaporators

Vertical-tube Evaporators

Plate Evaporators

Long-tube Evaporators

Forced-circulation Evaporators

Evaporation for Heat-sensitive Liquids

Open Pans

The most elementary form of evaporator consists of an open pan in which the liquid is boiled. Heat can be supplied through a steam jacket or through coils, and scrapers or paddles may be fitted to provide agitation. Such evaporators are simple and low in capital cost, but they are expensive in their running cost as heat economy is poor.

Horizontal-tube Evaporators

The horizontal-tube evaporator is a development of the open pan, in which the pan is closed in, generally in a vertical cylinder. The heating tubes are arranged in a horizontal bundle immersed in the liquid at the bottom of the cylinder. Liquid circulation is rather poor in this type of evaporator.

Vertical-tube Evaporators

By using vertical, rather than horizontal tubes, the natural circulation of the heated liquid can be made to give good heat transfer. The standard evaporator, shown in Fig. 8.1, is an example of this type. Recirculation of the liquid is through a large “downcomer” so that the liquors rise through the vertical tubes about 5-8 cm diameter, boil in the space just above the upper tube plate and recirculate through the downcomers. The hydrostatic head reduces boiling on the lower tubes, which are covered by the circulating liquid. The length to diameter ratio of the tubes is of the order of 15:1. The basket evaporator shown in Fig. 8.4(a) is a variant of the calandria evaporator in which the steam chest is contained in a basket suspended in the lower part of the evaporator, and recirculation occurs through the annular space round the basket.

Description: FIG. 8.4 Evaporators (a) basket type (b) long tube (c) forced circulation

Figure 8.4 Evaporators (a) basket type (b) long tube (c) forced circulation

Plate Evaporators

The plate heat exchanger can be adapted for use as an evaporator. The spacings can be increased between the plates and appropriate passages provided so that the much larger volume of the vapours, when compared with the liquid, can be accommodated. Plate evaporators can provide good heat transfer and also ease of cleaning.

Long tube Evaporators

Tall slender vertical tubes may be used for evaporators as shown in Fig. 8.4(b). The tubes, which may have a length to diameter ratio of the order of 100:1, pass vertically upward inside the steam chest. The liquid may either pass down through the tubes, called a falling- ilm evaporator, or be carried up by the evaporating liquor in which case it is called a climbing-film evaporator. Evaporation occurs on the walls of the tubes. Because circulation rates are high and the surface films are thin, good conditions are obtained for the concentration of heat sensitive liquids due to high heat transfer rates and short heating times.
Generally, the liquid is not recirculated, and if sufficient evaporation does not occur in one pass, the liquid is fed to another pass. In the climbing-film evaporator, as the liquid boils on the inside of the tube slugs of vapour form and this vapour carries up the remaining liquid which continues to boil. Tube diameters are of the order of 2.5 to 5 cm, contact times may be as low as 5-10 sec. Overall heat- transfer coefficients may be up to five times as great as from a heated surface immersed in a boiling liquid. In the falling-film type, the tube diameters are rather greater, about 8 cm, and these are specifically suitable for viscous liquids.

Forced circulation Evaporators

The heat transfer coefficients from condensing steam are high, so that the major resistance to heat flow in an evaporator is usually in the liquid film. Tubes are generally made of metals with a high thermal conductivity, though scale formation may occur on the tubes which reduce the tube conductance.
The liquid-film coefficients can be increased by improving the circulation of the liquid and by increasing its velocity of flow across the heating surfaces. Pumps, or impellers, can be fitted in the liquid circuit to help with this. Using pump circulation, the heat exchange surface can be divorced from the boiling and separating sections of the evaporator, as shown in Fig.8.4(c). Alternatively, impeller blades may be inserted into flow passages such as the downcomer of a calandria- type evaporator. Forced circulation is used particularly with viscous liquids: it may also be worth consideration for expensive heat exchange surfaces when these are required because of corrosion or hygiene requirements. In this case it pays to obtain the greatest possible heat flow through each square metre of heat exchange surface.
Also under the heading of forced-circulation evaporators are various scraped surface and agitated film evaporators. In one type the material to be evaporated passes down over the interior walls of a heated cylinder and it is scraped by rotating scraper blades to maintain a thin film, high heat transfer and a short and controlled residence time exposed to heat.

Evaporation for Heat-sensitive Liquids

Many food products with volatile flavour constituents retain more of these if they are evaporated under conditions favouring short contact times with the hot surfaces. This can be achieved for solutions of low viscosity by climbing- and falling-film evaporators, either tubular or plate types. As the viscosity increases, for example at higher concentrations, mechanical transport across heated surfaces is used to advantage. Methods include mechanically scraped surfaces, and the flow of the solutions over heated spinning surfaces. Under such conditions residence times can be fractions of a minute and when combined with a working vacuum as low as can reasonably be maintained, volatiles retention can be maximized.

3.0 OTHER OPERATIONS
3.1FILTRATION

Constant-rate Filtration

Constant-pressure Filtration

Filter-cake Compressibility

Filtration Equipment

Plate and frame filter press

Rotary filters

Centrifugal filters

Air filters

In another class of mechanical separations, placing a screen in the flow through which they cannot pass imposes virtually total restraint on the particles above a given size. The fluid in this case is subject to a force that moves it past the retained particles. This is called filtration. The particles suspended in the fluid, which will not pass through the apertures, are retained and build up into what is called a filter cake. Sometimes it is the fluid, the filtrate, that is the product, in other cases the filter cake.
The fine apertures necessary for filtration are provided by fabric filter cloths, by meshes and screens of plastics or metals, or by beds of solid particles. In some cases, a thin preliminary coat of cake, or of other fine particles, is put on the cloth prior to the main filtration process. This preliminary coating is put on in order to have sufficiently fine pores on the filter and it is known as a pre-coat.

The analysis of filtration is largely a question of studying the flow system. The fluid passes through the filter medium, which offers resistance to its passage, under the influence of a force which is the pressure differential across the filter. Thus, we can write the familiar equation:

rate of filtration = driving force/resistance
Resistance arises from the filter cloth, mesh, or bed, and to this is added the resistance of the filter cake as it accumulates. The filter-cake resistance is obtained by multiplying the specific resistance of the filter cake, that is its resistance per unit thickness, by the thickness of the cake. The resistances of the filter material and pre-coat are combined into a single resistance called the filter resistance. It is convenient to express the filter resistance in terms of a fictitious thickness of filter cake. This thickness is multiplied by the specific resistance of the filter cake to give the filter resistance. Thus the overall equation giving the volumetric rate of flow dV/dt is:
              dV/dt = (AP)/R
As the total resistance is proportional to the viscosity of the fluid, we can write:
                   R = r(L_c + L)
where R is the resistance to flow through the filter,  is the viscosity of the fluid, r is the specific resistance of the filter cake, L_c is the thickness of the filter cake and L is the fictitious equivalent thickness of the filter cloth and pre-coat, A is the filter area, and P is the pressure drop across the filter.
If the rate of flow of the liquid and its solid content are known and assuming that all solids are retained on the filter, the thickness of the filter cake can be expressed by:
                  L_c = wV/A
where w is the fractional solid content per unit volume of liquid, V is the volume of fluid that has passed through the filter and A is the area of filter surface on which the cake forms.
The resistance can then be written
                   R = r[w(V/A) + L)                                                                                 (10.11)
and the equation for flow through the filter, under the driving force of the pressure drop is then:
              dV/dt = AP/r[w(V/A) + L]                                                                       (10.12)
Equation (10.12) may be regarded as the fundamental equation for filtration. It expresses the rate of filtration in terms of quantities that can be measured, found from tables, or in some cases estimated. It can be used to predict the performance of large-scale filters on the basis of laboratory or pilot scale tests. Two applications of eqn. (10.12) are filtration at a constant flow rate and filtration under constant pressure.

Constant-rate Filtration

In the early stages of a filtration cycle, it frequently happens that the filter resistance is large relative to the resistance of the filter cake because the cake is thin. Under these circumstances, the resistance offered to the flow is virtually constant and so filtration proceeds at a more or less constant rate. Equation (10.12) can then be integrated to give the quantity of liquid passed through the filter in a given time. The terms on the right-hand side of eqn.(10.12) are constant so that integration is very simple:

dV/Adt = V/At = P/r[w(V/A) + L]
or P = V/At x r[w(V/A) + L] (10.13)
From eqn. (10.13) the pressure drop required for any desired flow rate can be found. Also, if a series of runs is carried out under different pressures, the results can be used to determine the resistance of the filter cake.

Constant-pressure Filtration

Once the initial cake has been built up, and this is true of the greater part of many practical filtration operations, flow occurs under a constant-pressure differential. Under these conditions, the term P in eqn. (10.12) is constant and so
r[w(V/A) + L]dV = APdt
and integration from V = 0 at t = 0, to V = V at t = t
   r[w(V²/2A) + LV] = APt and rewriting this
               tA/V = rw/2P] x (V/A) + rL/P
          t / (V/A) =   rw/2P] x (V/A) + rL/P                                                         (10.14)
Equation (10.14) is useful because it covers a situation that is frequently found in a practical filtration plant. It can be used to predict the performance of filtration plant on the basis of experimental results. If a test is carried out using constant pressure, collecting and measuring the filtrate at measured time intervals, a filtration graph can be plotted of t/(V/A) against (V/A) and from the statement of eqn. (10.14) it can be seen that this graph should be a straight line. The slope of this line will correspond to rw/2P and the intercept on the t/(V/A) axis will give the value of rL/P. Since, in general, , w, P and A are known or can be measured, the values of the slope and intercept on this graph enable L and r to be calculated.

EXAMPLE 10.6. Volume of filtrate from a filter press
A filtration test was carried out, with a particular product slurry, on a laboratory filter press under a constant pressure of 340 kPa and volumes of filtrate were collected as follows:

Filtrate volume (kg)	20	40	60	80
Time (min)	8	26	54.5	93

The area of the laboratory filter was 0.186 m². In a plant scale filter, it is desired to filter a slurry containing the same material, but at 50% greater concentration than that used for the test, and under a pressure of 270 kPa. Estimate the quantity of filtrate that would pass through in 1 hour if the area of the filter is 9.3 m².

From the experimental data:

V (kg)	20	40	60	80
t (s)	480	1560	3270	5580
V/A (kg/m²)	107.5	215	323	430
t/(V/A) (s m² kg^-1)	4.47	7.26	10.12	12.98

These values of t/(V/A) are plotted against the corresponding values of V/A in Fig. 10.7. From the graph, we find that the slope of the line is 0.0265, and the intercept 1.6.

FIG. 10.7 Filtration Graph

Then substituting in eqn. (10.14) we have
            t/(V/A) = 0.0265(V/A) + 1.6.
To fit the desired conditions for the plant filter, the constants in this equation will have to be modified. If all of the factors in eqn. (10.14) except those which are varied in the problem are combined into constants, K and K', we can write
             t/(V/A) = (w/P)Kx(V/A) + K'/P                                      (a)
In the laboratory experiment w = w₁, and P = P₁
                K = (0.0265P₁ /w₁) and K' = 1.6P₁
For the new plant condition, w = w₂ and P = P₂, so that, substituting in the eqn.(a) above, we then have for the plant filter, under the given conditions:
           t/(V/A) = (0.0265 P₁/w₁)(w₂/P₂)(V/A) + (1.6P₁)(1/P₂)
and since from these conditions
       P₁/P₂ = 340/270
and       w₂/w₁ = 150/100,
           t/(V/A) = 0.0265(340/270)(150/100)(V/A) + 1.6(340/270)
                 = 0.05(V/A) + 2.0
               t = 0.5(V/A)² + 2.0(V/A).
To find the volume that passes the filter in 1 h which is 3600 s, that is to find V for t = 3600.
           3600 = 0.05(V/A)² + 2.0(V/A)
and solving this quadratic equation, we find that V/A = 250 kg m^-2
and so the slurry passing through 9.3 m² in 1 h would be:
                     = 250 x 9.3
                     = 2325 kg.

Filter-cake Compressibility

With some filter cakes, the specific resistance varies with the pressure drop across it. This is because the cake becomes denser under the higher pressure and so provides fewer and smaller passages for flow. The effect is spoken of as the compressibility of the cake. Soft and flocculent materials provide highly compressible filter cakes, whereas hard granular materials, such as sugar and salt crystals, are little affected by pressure. To allow for cake compressibility the empirical relationship has been proposed:
r = r'P^s
where r is the specific resistance of the cake under pressure P, P is the pressure drop across the filter, r' is the specific resistance of the cake under a pressure drop of 1 atm and s is a constant for the material, called its compressibility.
This expression for r can be inserted into the filtration equations, such as eqn. (10.14), and values for r' and s can be determined by carrying out experimental runs under various pressures.

Filtration Equipment

The basic requirements for filtration equipment are:

mechanical support for the filter medium,

flow accesses to and from the filter medium and

provision for removing excess filter cake.
In some instances, washing of the filter cake to remove traces of the solution may be necessary. Pressure can be provided on the upstream side of the filter, or a vacuum can be drawn downstream, or both can be used to drive the wash fluid through.

Description: FIG. 10.8 Filtration equipment: (a) plate and frame press (b) centrifugal filter

FIG. 10.8 Filtration equipment: (a) plate and frame press (b) rotary vacuum filter (c) centrifugal filter

Plate and frame filter press
In the plate and frame filter press, a cloth or mesh is spread out over plates which support the cloth along ridges but at the same time leave a free area, as large as possible, below the cloth for flow of the filtrate. This is illustrated in Fig. 10.8(a). The plates with their filter cloths may be horizontal, but they are more usually hung vertically with a number of plates operated in parallel to give sufficient area.
Filter cake builds up on the upstream side of the cloth, that is the side away from the plate. In the early stages of the filtration cycle, the pressure drop across the cloth is small and filtration proceeds at more or less a constant rate. As the cake increases, the process becomes more and more a constant-pressure one and this is the case throughout most of the cycle. When the available space between successive frames is filled with cake, the press has to be dismantled and the cake scraped off and cleaned, after which a further cycle can be initiated.
The plate and frame filter press is cheap but it is difficult to mechanize to any great extent. Variants of the plate and frame press have been developed which allow easier discharging of the filter cake. For example, the plates, which may be rectangular or circular, are supported on a central hollow shaft for the filtrate and the whole assembly enclosed in a pressure tank containing the slurry. Filtration can be done under pressure or vacuum. The advantage of vacuum filtration is that the pressure drop can be maintained whilst the cake is still under atmospheric pressure and so can be removed easily. The disadvantages are the greater costs of maintaining a given pressure drop by applying a vacuum and the limitation on the vacuum to about 80 kPa maximum. In pressure filtration, the pressure driving force is limited only by the economics of attaining the pressure and by the mechanical strength of the equipment.

Rotary filters
In rotary filters, the flow passes through a rotating cylindrical cloth from which the filter cake can be continuously scraped. Either pressure or vacuum can provide the driving force, but a particularly useful form is the rotary vacuum filter. In this, the cloth is supported on the periphery of a horizontal cylindrical drum that dips into a bath of the slurry. Vacuum is drawn in those segments of the drum surface on which the cake is building up. A suitable bearing applies the vacuum at the stage where the actual filtration commences and breaks the vacuum at the stage where the cake is being scraped off after filtration. Filtrate is removed through trunnion bearings. Rotary vacuum filters are expensive, but they do provide a considerable degree of mechanization and convenience. A rotary vacuum filter is illustrated diagrammatically in Fig. 10.8(b).

Centrifugal filters
Centrifugal force is used to provide the driving force in some filters. These machines are really centrifuges fitted with a perforated bowl that may also have filter cloth on it. Liquid is fed into the interior of the bowl and under the centrifugal forces, it passes out through the filter material. This is illustrated in Fig. 10.8(c).

Air filters

Filters are used quite extensively to remove suspended dust or particles from air streams. The air or gas moves through a fabric and the dust is left behind. These filters are particularly useful for the removal of fine particles. One type of bag filter consists of a number of vertical cylindrical cloth bags 15-30 cm in diameter, the air passing through the bags in parallel. Air bearing the dust enters the bags, usually at the bottom and the air passes out through the cloth. A familiar example of a bag filter for dust is to be found in the domestic vacuum cleaner. Some designs of bag filters provide for the mechanical removal of the accumulated dust. For removal of particles less than 5 m diameter in modern air sterilization units, paper filters and packed tubular filters are used. These cover the range of sizes of bacterial cells and spores.

3.2 MIXING EQUIPMENT

Liquid Mixers

Powder and Particle Mixers

Dough and Paste Mixers

Many forms of mixers have been produced from time to time but over the years a considerable degree of standardization of mixing equipment has been reached in different branches of the food industry. Possibly the easiest way in which to classify mixers is to divide them according to whether they mix liquids, dry powders, or thick pastes.

Liquid Mixers

For the deliberate mixing of liquids, the propeller mixer is probably the most common and the most satisfactory. In using propeller mixers, it is important to avoid regular flow patterns such as an even swirl round a cylindrical tank, which may accomplish very little mixing. To break up these streamline patterns, baffles are often fitted, or the propeller may be mounted asymmetrically.

Various baffles can be used and the placing of these can make very considerable differences to the mixing performances. It is tempting to relate the amount of power consumed by a mixer to the amount of mixing produced, but there is no necessary connection and very inefficient mixers can consume large amounts of power.

Powder and Particle Mixers

The essential feature in these mixers is to displace parts of the mixture with respect to other parts. The ribbon blender, for example, shown in Fig. 12.2(a) consists of a trough in which rotates a shaft with two open helical screws attached to it, one screw being right-handed and the other left-handed. As the shaft rotates sections of the powder move in opposite directions and so particles are vigorously displaced relative to each other.

Description: FIG.12.2 Mixers (a) ribbon blender, (b) double-cone mixer

Figure 12.2 Mixers (a) ribbon blender, (b) double-cone mixer

A commonly used blender for powders is the double-cone blender in which two cones are mounted with their open ends fastened together and they are rotated about an axis through their common base. This mixer is shown in Fig. 12.2(b).

Dough and Paste Mixers

Dough and pastes are mixed in machines that have, of necessity, to be heavy and powerful. Because of the large power requirements, it is particularly desirable that these machines mix with reasonable efficiency, as the power is dissipated in the form of heat, which may cause substantial heating of the product. Such machines may require jacketing of the mixer to remove as much heat as possible with cooling water.
Perhaps the most commonly used mixer for these very heavy materials is the kneader which employs two contra-rotating arms of special shape, which fold and shear the material across a cusp, or division, in the bottom of the mixer. The arms are of so-called sigmoid shape as indicated in Fig. 12.3.

Figure 12.3 Kneader

They rotate at differential speeds, often in the ratio of nearly 3:2. Developments of this machine include types with multiple sigmoid blades along extended troughs, in which the blades are given a forward twist and the material makes its way continuously through the machine.

Another type of machine employs very heavy contra-rotating paddles, whilst a modern continuous mixer consists of an interrupted screw which oscillates with both rotary and reciprocating motion between pegs in an enclosing cylinder. The important principle in these machines is that the material has to be divided and folded and also displaced, so that fresh surfaces recombine as often as possible.

3.4 SIZE REDUCTION

Grinding and cutting.

Energy Used in Grinding

New Surface Formed by Grinding

Grinding equipment.

Crushers

Hammer mills

Fixed-head mills

Plate mills

Roller mills

Miscellaneous milling equipment

Cutters

Raw materials often occur in sizes that are too large to be used and, therefore, they must be reduced in size. This size-reduction operation can be divided into two major categories depending on whether the material is a solid or a liquid. If it is solid, the operations are called grinding and cutting, if it is liquid, emulsification or atomization. All depend on the reaction to shearing forces within solids and liquids.

GRINDING AND CUTTING

Grinding and cutting reduce the size of solid materials by mechanical action, dividing them into smaller particles. Perhaps the most extensive application of grinding in the food industry is in the milling of grains to make flour, but it is used in many other processes, such as in the grinding of corn for manufacture of corn starch, the grinding of sugar and the milling of dried foods, such as vegetables.

Cutting is used to break down large pieces of food into smaller pieces suitable for further processing, such as in the preparation of meat for retail sales and in the preparation of processed meats and processed vegetables.

In the grinding process, materials are reduced in size by fracturing them. The mechanism of fracture is not fully understood, but in the process, the material is stressed by the action of mechanical moving parts in the grinding machine and initially the stress is absorbed internally by the material as strain energy. When the local strain energy exceeds a critical level, which is a function of the material, fracture occurs along lines of weakness and the stored energy is released. Some of the energy is taken up in the creation of new surface, but the greater part of it is dissipated as heat. Time also plays a part in the fracturing process and it appears that material will fracture at lower stress concentrations if these can be maintained for longer periods. Grinding is, therefore, achieved by mechanical stress followed by rupture and the energy required depends upon the hardness of the material and also upon the tendency of the material to crack - its friability.
The force applied may be compression, impact, or shear, and both the magnitude of the force and the time of application affect the extent of grinding achieved. For efficient grinding, the energy applied to the material should exceed, by as small a margin as possible, the minimum energy needed to rupture the material . Excess energy is lost as heat and this loss should be kept as low as practicable.
The important factors to be studied in the grinding process are the amount of energy used and the amount of new surface formed by grinding.

Energy Used in Grinding

Grinding is a very inefficient process and it is important to use energy as efficiently as possible. Unfortunately, it is not easy to calculate the minimum energy required for a given reduction process, but some theories have been advanced which are useful.
These theories depend upon the basic assumption that the energy required to produce a change dL in a particle of a typical size dimension L is a simple power function of L:
dE/dL = KLⁿ                                                                                                             (11.1)
where dE is the differential energy required, dL is the change in a typical dimension, L is the magnitude of a typical length dimension and K, n, are constants.
Kick assumed that the energy required to reduce a material in size was directly proportional to the size reduction ratio dL/L. This implies that n in eqn. (11.1) is equal to -1. If
                       K = K_Kf_c
where K_K is called Kick's constant and f_c is called the crushing strength of the material, we have:
                 dE/dL = K_Kf_cL^-1
which, on integration gives:

E = K_Kf_c log_e(L₁/L₂) (11.2)

Equation (11.2) is a statement of Kick's Law. It implies that the specific energy required to crush a material, for example from 10 cm down to 5 cm, is the same as the energy required to crush the same material from 5 mm to 2.5 mm.
Rittinger, on the other hand, assumed that the energy required for size reduction is directly proportional, not to the change in length dimensions, but to the change in surface area. This leads to a value of -2 for n in eqn. (11.1) as area is proportional to length squared. If we put:
K = K_Rfc
and so

dE/dL = K_Rf_cL_-2

where K_R is called Rittinger's constant, and integrate the resulting form of eqn. (11.1), we obtain:
E = K_Rf_c(1/L₂– 1/L₁) (11.3)
Equation (11.3) is known as Rittinger's Law. As the specific surface of a particle, the surface area per unit mass, is proportional to 1/L, eqn. (11.3) postulates that the energy required to reduce L for a mass of particles from 10 cm to 5 cm would be the same as that required to reduce, for example, the same mass of 5 mm particles down to 4.7 mm. This is a very much smaller reduction, in terms of energy per unit mass for the smaller particles, than that predicted by Kick's Law.
It has been found, experimentally, that for the grinding of coarse particles in which the increase in surface area per unit mass is relatively small, Kick's Law is a reasonable approximation. For the size reduction of fine powders, on the other hand, in which large areas of new surface are being created, Rittinger's Law fits the experimental data better.
Bond has suggested an intermediate course, in which he postulates that n is -3/2 and this leads to:
E = E_i (100/L₂)^1/2[1 - (1/q^1/2)] (11.4)
Bond defines the quantity E_i by this equation: L is measured in microns in eqn. (11.4) and so E_i is the amount of energy required to reduce unit mass of the material from an infinitely large particle size down to a particle size of 100 m. It is expressed in terms of q, the reduction ratio where q = L₁/L₂.
Note that all of these equations [eqns. (11.2), (11.3), and (11.4)] are dimensional equations and so if quoted values are to be used for the various constants, the dimensions must be expressed in appropriate units. In Bond's equation, if L is expressed in microns, this defines E_i and Bond calls this the Work Index.
The greatest use of these equations is in making comparisons between power requirements for various degrees of reduction.

EXAMPLE 11.1. Grinding of sugar
Sugar is ground from crystals of which it is acceptable that 80% pass a 500 m sieve(US Standard Sieve No.35), down to a size in which it is acceptable that 80% passes a 88 m (No.170) sieve, and a 5-horsepower motor is found just sufficient for the required throughput. If the requirements are changed such that the grinding is only down to 80% through a 125 m (No.120) sieve but the throughput is to be increased by 50% would the existing motor have sufficient power to operate the grinder? Assume Bond's equation.

Using the subscripts 1 for the first condition and 2 for the second, and letting m kg h^-1 be the initial throughput, then if x is the required power
Now 88m = 8.8 x 10^{-6m , 125}m = 125 x 10^{-6m , 500}m = 500 x 10^-6m
     E₁ = 5/m = E_i(100/88 x 10^-6)^1/2 [1 – (88/500)^1/2]
     E₂ = x/1.5m = E_i(100/125 x 10^-6)^1/2 [1 - (125/500)^1/2]

E₂/E₁ = x/(1.5 x 5) =    (88 x 10^-6)^1/2[1 - (125/500)^1/2]
                                  (125 x 10^-6)^1/2[1 – (88/500)^1/2]

x/(7.5) = 0.84 x (0.500/0.58)
          = 0.72
       x = 5.4 horsepower.
So the motor would be expected to have insufficient power to pass the 50% increased throughput, though it should be able to handle an increase of 40%.

New Surface Formed by Grinding

When a uniform particle is crushed, after the first crushing the size of the particles produced will vary a great deal from relatively coarse to fine and even to dust. As the grinding continues, the coarser particles will be further reduced but there will be less change in the size of the fine particles. Careful analysis has shown that there tends to be a certain size that increases in its relative proportions in the mixture and which soon becomes the predominant size fraction. For example, wheat after first crushing gives a wide range of particle sizes in the coarse flour, but after further grinding the predominant fraction soon becomes that passing a 250 m sieve and being retained on a 125 m sieve. This fraction tends to build up, however long the grinding continues, so long as the same type of machinery, rolls in this case, is employed.
The surface area of a fine particulate material is large and can be important. Most reactions are related to the surface area available, so the surface area can have a considerable bearing on the properties of the material. For example, wheat in the form of grains is relatively stable so long as it is kept dry, but if ground to a fine flour has such a large surface per unit mass that it becomes liable to explosive oxidation, as is all too well known in the milling industry. The surface area per unit mass is called the specific surface. To calculate this in a known mass of material it is necessary to know the particle-size distribution and, also the shape factor of the particles. The particle size gives one dimension that can be called the typical dimension, D_p, of a particle. This has now to be related to the surface area.
We can write, arbitrarily:
     V_p = pD_p³
and
      A_p= 6qD_p².
where V_p is the volume of the particle, A_p is the area of the particle surface, D_p is the typical dimension of the particle and p, q are factors which connect the particle geometries.(Note subscript p and factor p)
For example, for a cube, the volume is D_p³ and the surface area is 6D_p²; for a sphere the volume is (/6)D_p³ and the surface area is D_p² In each case the ratio of surface area to volume is 6/D_p.
A shape factor is now defined as q/p =  (lambda), so that for a cube or a sphere  = 1. It has been found, experimentally, that for many materials when ground, the shape factor of the resulting particles is approximately 1.75, which means that their surface area to volume ratio is nearly twice that for a cube or a sphere.
The ratio of surface area to volume is:
   A_p/V_p=( 6q/p)D_p = 6/D_p                                                              (11.5)

and so         A_p= 6q V_p/pD_{p = 6}V_P/D^P)
If there is a mass m of particles of density _p,the number of particles is m/_pVPeach of area A_p.
So total area     A_t = (m/_pV_P) x ( 6qV_p/pD_P) ₌6qm/_p pD_p
                        = 6m/D_p            (11.6)
where A_t is the total area of the mass of particles. Equation (11.6) can be combined with the results of sieve analysis to estimate the total surface area of a powder.

EXAMPLE 11.2. Surface area of salt crystals
In an analysis of ground salt using Tyler sieves, it was found that 38% of the total salt passed through a 7 mesh sieve and was caught on a 9 mesh sieve. For one of the finer fractions, 5% passed an 80 mesh sieve but was retained on a 115 mesh sieve. Estimate the surface areas of these two fractions in a 5 kg sample of the salt, if the density of salt is 1050 kg m^-3 and the shape factor () is 1.75.
Aperture of Tyler sieves, 7 mesh = 2.83 mm, 9 mesh = 2.00 mm, 80 mesh = 0.177 mm, 115 mesh = 0.125 mm.
Mean aperture 7 and 9 mesh      = 2.41 mm = 2.4 x 10^-3m
Mean aperture 80 and 115 mesh = 0.151 mm = 0.151 x 10^-3m
Now from Eqn. (11.6)
     A₁ = (6 x 1.75 x 0.38 x 5)/(1050 x 2.41 x 10^-3)
          = 7.88 m²
     A₂ = (6 x 1.75 x 0.05 x 5)/(1050 x 0.151 x 10^-3)
          = 16.6 m².

Grinding Equipment

Grinding equipment can be divided into two classes - crushers and grinders. In the first class the major action is compressive, whereas grinders combine shear and impact with compressive forces.

Crushers
Jaw and gyratory crushers are heavy equipment and are not used extensively in the food industry. In a jaw crusher, the material is fed in between two heavy jaws, one fixed and the other reciprocating, so as to work the material down into a narrower and narrower space, crushing it as it goes. The gyrator crusher consists of a truncated conical casing, inside which a crushing head rotates eccentrically. The crushing head is shaped as an inverted cone and the material being crushed is trapped between the outer fixed, and the inner gyrating, cones, and it is again forced into a narrower and narrower space during which time it is crushed. Jaw and gyratory crusher actions are illustrated in Fig. 11.1(a) and (b).

Description: FIG. 11.1 Crushers: (a) jaw, (b) gyratory

Figure 11.1 Crushers: (a) jaw, (b) gyratory

Crushing rolls consist of two horizontal heavy cylinders, mounted parallel to each other and close together. They rotate in opposite directions and the material to be crushed is trapped and nipped between them being crushed as it passes through. In some case, the rolls are both driven at the same speed. In other cases, they may be driven at differential speeds, or only one roll is driven. A major application is in the cane sugar industry, where several stages of rolls are used to crush the cane.

Hammer mills
In a hammer mill, swinging hammerheads are attached to a rotor that rotates at high speed inside a hardened casing. The principle is illustrated in Fig. 11.2(a).

Description: FIG. 11.2 Grinders: (a) hammer mill, (b) plate mill

Figure 11.2 Grinders: (a) hammer mill, (b) plate mill

The material is crushed and pulverized between the hammers and the casing and remains in the mill until it is fine enough to pass through a screen which forms the bottom of the casing. Both brittle and fibrous materials can be handled in hammer mills, though with fibrous material, projecting sections on the casing may be used to give a cutting action.

Fixed head mills
Various forms of mills are used in which the material is sheared between a fixed casing and a rotating head, often with only fine clearances between them. One type is a pin mill in which both the static and the moving plates have pins attached on the surface and the powder is sheared between the pins.

Plate mills
In plate mills the material is fed between two circular plates, one of them fixed and the other rotating. The feed comes in near the axis of rotation and is sheared and crushed as it makes its way to the edge of the plates, see Fig. 11.2(b). The plates can be mounted horizontally as in the traditional Buhr stone used for grinding corn, which has a fluted surface on the plates. The plates can be mounted vertically also. Developments of the plate mill have led to the colloid mill, which uses very fine clearances and very high speeds to produce particles of colloidal dimensions.

Roller mills
Roller mills are similar to roller crushers, but they have smooth or finely fluted rolls, and rotate at differential speeds. They are used very widely to grind flour. Because of their simple geometry, the maximum size of the particle that can pass between the rolls can be regulated. If the friction coefficient between the rolls and the feed material is known, the largest particle that will be nipped between the rolls can be calculated, knowing the geometry of the particles.

Miscellaneous milling equipment
The range of milling equipment is very wide. It includes ball mills, in which the material to be ground is enclosed in a horizontal cylinder or a cone and tumbled with a large number of steel balls, natural pebbles or artificial stones, which crush and break the material. Ball mills have limited applications in the food industry, but they are used for grinding food colouring materials.
The edge runner mill, which is basically a heavy broad wheel running round a circular trough, is used for grinding chocolate and confectionery.
Many types of milling equipment have come to be traditional in various industries and it is often claimed that they provide characteristic actions that are peculiarly suited to, and necessary for, the product.

Cutters

Cutting machinery is generally simple, consisting of rotating knives in various arrangements. A major problem often is to keep the knives sharp so that they cut rather than tear. An example is the bowl chopper in which a flat bowl containing the material revolves beneath a vertical rotating cutting knife.

3.5 PUMPS AND FANS

Positive Displacement Pumps

Jet pumps

Air-lift Pumps

Propeller Pumps and Fan

Centrifugal Pumps and Fans

In pumps and fans, mechanical energy from some other source is converted into pressure or velocity energy in a fluid. The food technologist is not generally much concerned with design details of pumps, but should know what classes of pump are used and something about their characteristics.
The efficiency of a pump is the ratio of the energy supplied by the motor to the increase in velocity and pressure energy given to the fluid.

Positive Displacement Pumps

In a positive displacement pump, the fluid is drawn into the pump and is then forced through the outlet. Types of positive displacement pumps include: reciprocating piston pumps; gear pumps in which the fluid is enmeshed in rotating gears and forced through the pump; rotary pumps in which rotating vanes draw in and discharge fluid through a system of valves. Positive displacement pumps can develop high-pressure heads but they cannot tolerate throttling or blockages in the discharge. These types of pumps are illustrated in Fig. 4.3 (a), (b) and (c).

Figure 4.3 Liquid pumps

Jet Pumps

In jet pumps, a high-velocity jet is produced in a Venturi nozzle, converting the energy of the fluid into velocity energy. This produces a low-pressure area causing the surrounding fluid to be drawn into the throat as shown diagrammatically in Fig. 4.3 (d) and the combined fluids are then discharged. Jet pumps are used for difficult materials that cannot be satisfactorily handled in a mechanical pump. They are also used as vacuum pumps. Jet pumps have relatively low efficiencies but they have no moving parts and therefore have a low initial cost. They can develop only low heads per stage.

Air-lift Pumps

If air or gas is introduced into a liquid it can be used to impart energy to the liquid as illustrated in Fig. 4.3 (e). The air or gas can be either provided from external sources or produced by boiling within the liquid. Examples of the air-lift principle are:

Air introduced into the fluid as shown in Fig. 4.3(e) to pump water from an artesian well.

Air introduced above a liquid in a pressure vessel and the pressure used to discharge the liquid.

Vapours produced in the column of a climbing film evaporator.

In the case of powdered solids, air blown up through a bed of powder to convey it in a "fluidized" form.
A special case of this is in the evaporator, where boiling of the liquid generates the gas (usually steam) and it is used to promote circulation. Air or gas can be used directly to provide pressure to blow a liquid from a container out to a region of lower pressure. Air-lift pumps and air blowing are inefficient, but they are convenient for materials which will not pass easily through the ports, valves and passages of other types of pumps.

Propeller Pumps and Fan

Propellers can be used to impart energy to fluids as shown in Fig. 4.3 (f). They are used extensively to mix the contents of tanks and in pipelines to mix and convey the fluid. Propeller fans are common and have high efficiencies.
They can only be used for low heads, in the case of fans only a few centimetres or so of water.

Centrifugal Pumps and Fans

The centrifugal pump converts rotational energy into velocity and pressure energy and is illustrated in Fig. 4.3(g). The fluid to be pumped is taken in at the centre of a bladed rotor and it then passes out along the spinning rotor, acquiring energy of rotation. This rotational energy is then converted into velocity and pressure energy at the periphery of the rotor. Centrifugal fans work on the same principles. These machines are very extensively used and centrifugal pumps can develop moderate heads of up to 20 m of water. They can deliver very large quantities of fluids with high efficiency. The theory of the centrifugal pump is rather complicated and will not be discussed. However, when considering a pump for a given application, the manufacturers will generally supply pump characteristic curves showing how the pump performs under various conditions of loading. These curves should be studied in order to match the pump to the duty required. Figure 4.4 shows some characteristic curves for a family of centrifugal pumps.

Figure 4.4 Characteristic curves for centrifugal pumps
Adapted from Coulson and Richardson, Chemical Engineering, 2nd Edition, 1973.

For a given centrifugal pump, the capacity of the pump varies with its rotational speed; the pressure developed by the pump varies as the square of the rotational speed; and the power required by the pump varies as the cube of the rotational speed. The same proportional relationships apply to centrifugal fans and these relationships are often called the "fan laws" in this context.

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Friday, 27 April 2012

FOOD ENGINEERING NOTES