TWO- AND THREE-STAGE CASCADE REFRIGERATION SYSTEM By: Paul B. Reed

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1 INTRODUCTION Service Application Manual Mechanical refrigerating systems in most common use fall into three classes as far as the temperatures of the evaporators are concerned: 1. High temperatures, with evaporators from about 30 F to 60 F. The most common of these are used in air-conditioning, water cooling and some industrial processes. 2. Medium temperatures, with evaporators from about 5 F to 30 F. The vast majority of these are used in the preservation of fresh foods, ice-making, the cooling of beer, milk, flowers and many other products. 3. Low temperatures, with evaporators from about -20 F to 5 F. Most of these are used in the freezing and storage of frozen foods, ice-cream, and fruit juice concentrates. In addition to these more common applications, mechanical refrigeration is used in such specialized applications as bone banks, pharmaceutical and bacteriological storage, lens grinding, coolant cooling, aluminum storage, spot welding, and chemical and other industrial processes. ULTRA-LOW TEMPERATURES During World War II, low temperatures were found useful in aeronautical instrument testing, steel alloy treatment, blood plasma desiccation and similar purposes; and these war needs stimulated the development of what we now call "ultra-low" temperatures, with evaporators from -20 F down to as low as -200 F. There are many ultra-low temperature systems in use today with evaporator temperatures from - 40 F to -150 F. In research laboratories, temperatures within a fraction of a degree of absolute zero ( F or -273 C) have been attained, but not with ordinary, commercially available equipment, and the capacities of such extremely ultra-low temperature apparatus are very small. Evaporator temperatures down to about -150 F may be obtained with commercially available equipment of good design. Any service engineer with a good understanding of fundamental refrigeration principles, need not hesitate to work on ultra-low temperature equipment. There are several points however, that he must recognize: 1. He must thoroughly understand the basic fundamental principles of refrigeration; that is, the "theory." Guesswork may "get-by" with higher temperatures; but when dealing with ultra-low temperatures, he must know. 2. He must thoroughly understand the "why" of the design and operation of the various parts of the equipment such as the compressor, the expansion valve, the heat exchangers, the evaporator, and even of the condenser. Hit-or-miss valve changing, or adding refrigerant will not work in ultralow temperature equipment. 3. Losses must be reduced to the minimum. The Btu capacity at ultra-low temperatures is very low for a given size of equipment. As the evaporator temperatures go down, the capacity and efficiency of the compressor go down, and the cost of the equipment and the cost of operation to produce the refrigeration go up. Losses that would be disregarded in normal temperature equipment can double or triple the size and cost of the equipment and the cost of operation in ultra-low temperature applications. Avoidance of losses is therefore imperative. 1

2 HEAT LOAD Service Application Manual The heat leakage load to be removed per cubic foot of cabinet and the product load per pound of product is very high for ultra-low temperatures, for the temperature difference is far greater, and in fact is several times the corresponding loads at normal temperatures. In an 80 F room, the heat leakage for a cabinet with 2 inch insulation held at -100 F, is 4-1/2 times as great as for the same cabinet held at 40 F. In order to hold the same heat leakage, the insulation would have to be 4-1/2 times as thick, or 9 inches. The same applies to the product put in the cabinet. Reducing the temperature of a pound of aluminum from 80 F to -100 F requires 4-1/2 as much refrigeration as from 80 F to 40 F. In some installations it may be possible to first cool the product part of the way in a cabinet held at 0 F for example and then put it in the -100 F cabinet. In most instances this is not practical, for the cold product out of the zero cabinet condenses moisture from the air and becomes wet and icy. Introducing this water and ice into the -100 F introduces additional load and frost problems. The service loads in ultra-low temperature vary greatly, not only with the temperature, but with the frequency of opening, the type of cabinet (front or top opening), humidity of the room air, and other factors. In some ultra-low temperature installations, the service load may be much greater than all the other load factors combined. It must be estimated, for there are no formulas that apply to widely varying conditions. The estimate for the service load must necessarily be generous. In estimating heat loads for ultra-low temperatures, do not overlook lights and fan motors. The heat load from a small 25 watt light cannot be disregarded. PULL-DOWN The pull-down time is usually a very important factor, for it determines for example, the number of instruments that may be tested in the cabinet per day. The shorter the pull-down time demanded by the user, the greater must be the capacity of the evaporator, the condensing unit, and the corresponding accessories. A pull-down of one hour instead of two hours may double the capacity of the equipment. In estimating pull-down time, do not overlook the "lag" of the insulation itself. Eight or ten inches of insulation holds a considerable amount of heat, and it takes time to cool the insulation down. Reflective insulation such as aluminum foil or Ferro-Therm, or insulations of low density, such as silica aerogel (Santocel), are often used to reduce pull-down time due to insulation lag. VAPOR SEAL A good vapor seal is important for the insulation on a normal temperature cabinet or room, but for ultralow temperatures, the vapor seal of the insulation must, to all intents and purposes, be just about perfect. Moisture penetrates insulation chiefly because of the difference in vapor pressure of the moisture in the air on the two sides of the insulation. This difference in vapor pressure is about one-third greater in a F cabinet than in a 40 F cabinet, both in an 80 F room. EVAPORATORS The evaporators for ultra-low temperatures differ but little from those for higher temperatures. Plates (not the eutectic type) are used extensively, but finned coils are also used for some applications. Sometimes a combination of plates and finned coils are used. The heat load of ultra-low temperature cabinets is very large in comparison with the size of the cabinet; so the evaporator must be correspondingly large in order to handle the heat load. Thus, it is often a 2

3 problem to find space for the evaporator and still have as much usable space in the cabinet as is required. This necessitates making the cabinet larger, which in turn increases the heat leakage load, so that additional evaporator surface must be allowed for. In some ultra-low temperature cabinets, the entire inside of the cabinet, except the door, is lined with plates, and additional plates are used as shelves. In some cabinets, the additional evaporator capacity is obtained by using a fan to circulate the air in the cabinet more rapidly. This increases the rate of heat transfer per square foot of evaporator surface, and consequently increases the capacity of the evaporator. Ultra-low temperature cabinets used for testing airplane instruments are sometimes provided with vacuum pumps, so that a partial vacuum can be pumped on the cabinet to simulate high altitudes. In such cabinets it is important that the temperature of the cabinet be reduced about as low as desired, before the vacuum is pumped on the cabinet; otherwise, with little or no air in the cabinet, the rate of cooling is extremely slow. With no air in the cabinet, heat can pass from the cabinet walls and warm product to the cold evaporator by radiation only. Evaporators must be kept as clean and free of ice and frost as possible. A small amount of frost acts as an insulation to the evaporator. This slows the rate of heat absorption by the evaporator, and requires the evaporator to be operated colder in order to obtain the required temperature. EVAPORATOR TEMPERATURE Operating the evaporator colder means a lower suction pressure. A lower suction pressure means lower capacity and efficiency of the compressor; and this is particularly true with ultra-low temperatures, and the low suction pressures to obtain ultra-low temperatures. Usually the user specifies the ultra-low temperature that he wants in the cabinet. The refrigeration man's problem is to get that air temperature with as a high an evaporator and suction pressure as possible. That is, the temperature difference between the evaporator and the air must be as small as possible. Every degree that the temperature difference can be reduced means a big savings in size, capacity, and cost of the equipment, and in cost of the operation. A temperature difference of about 10 F between the evaporator and the cabinet air is about as low as is generally obtained, and it takes forced air circulation and a generously sized evaporator to do that. With gravity air circulation, 15 F is about the best that can be expected, and to get 15 F, the size of the evaporator must be generous. In cooling liquids, temperature differences of from 5 F to 10 F are normal, depending upon the type of liquid itself, rate that it is circulated, and the type of evaporator. In normal temperature refrigeration, it is not uncommon to skimp the size of the evaporator, although it is not good practice. Never skimp the evaporator of an ultra-low temperature installation. It is too expensive in the resulting increased size and capacity of the condensing unit to compensate for the undersize evaporator. CONDENSING TEMPERATURE The condensing temperature is the saturation temperature of the refrigerant corresponding to the discharge or "head" pressure. The lower the condensing temperature, the lower is the discharge pressure, and every refrigeration man knows that a high head pressure reduces the capacity and efficiency of the compressor, and increases the time and cost of operation. 3

4 Keeping the condensing temperature and pressure low is done in the same way as keeping the evaporator temperature and suction pressure high; that is, by keeping the temperature difference between the condenser and the surrounding air (or water in water-cooled condensers) as small as possible. This in turn is accomplished by using a condenser of generous size, keeping it clean, and passing a large amount of air (or water) over it. In ultra-low temperature work, everything is more critical than in normal temperature refrigeration. So the condensing temperature and head pressure must be kept as low as practically possible. Air-cooled condensers should be sized to maintain not more than a 30 F temperature difference between the room air and the temperature of the refrigerant. In the case of water-cooled condensers, the temperature difference should also be kept low. To do this may mean that a temperature rise of the water of only 10 can be permitted if the available cooling water is 75 F or over. The cost of water has a bearing on how low a head pressure can be maintained and consequently how much water must be used. In ultra-temperature work, it may often be more economical to use more water even at a high cost for the water, in order to maintain a low condensing temperature and pressure. COMPRESSION RATIO The compression ratio is a number obtained by dividing the discharge pressure by the suction pressure, both of these expressed in pounds per square inch absolute (psia). For Example: In a certain R-12 system, the head pressure is pounds per square inch gage (psig), corresponding to a condensing temperature of 94 F. The suction pressure is 1.3 psig, corresponding to an evaporator-temperature of -18 F. First, the gage pressures of and 1.3 must be converted to absolute pressures, by adding atmospheric pressure of 14.7 pounds per square inch to each of them. The head pressure of psig then becomes 121 psia, (pounds per square inch, absolute) and the suction pressure of 1.3 psig becomes 16 psia. The ratio of compression of this system is therefore or 7-9/16, or expressed decimally, Thus, the head pressure is about 7-1/2 times the suction pressure. The old rule "keep your head pressure low and your suction pressure high" is another way of saying that we should have a low ratio of compression. The higher the ratio of compression, the more difficult it is for the compressor to compress the suction gas and force it over into the condenser, so this takes more power. More important in low temperature work, the higher the ratio of compression, the greater are the losses in the compressor from slippage of gas past the pistons during the compression stroke; and during the suction stroke the greater will be the reexpansion of the compressed gas in the clearance space between the top of the piston and the underside of the valve plate, for at the top of the compression stroke, this gas must be greater than condenser pressure. As the piston goes downward on its suction stroke, this trapped high pressure gas re-expands, and its pressure gradually becomes less the farther down the piston goes. Finally, its pressure becomes low enough that it is less than that of the gas in the suction line. Until that time, no suction gas will enter the cylinder. If the pressure and amount of this trapped gas is high and the suction pressure is low, the piston may have to get almost to the bottom of the suction stroke before any suction gas can enter the cylinder, and only a small part of the cylinder is effective. Then the compressor would pump only a very small percentage of the gas that it could pump if the suction gas could start entering the cylinder near the top of 4

5 its downward suction stroke; that is, the volumetric efficiency of the compressor would be very low perhaps as low as ten or fifteen percent. The volumetric efficiency of the compressor is reduced by these losses. If the losses are excessive, the volumetric efficiency may be so low at ultra-low temperatures that the compressor "quits pumping", and it cannot obtain a lower suction pressure; or as we say, it "cannot pull the suction pressure down", and consequently cannot get the evaporator temperature any lower. If the ratio of compression is high, the compressor must be made with a high degree of precision, so as to avoid as much loss past the pistons and as much re-expansion from the clearance volume as possible. Thus, the compressor will be expensive to build, and a standard compressor cannot be used. In order to use ordinary commercially available compressors in ultra-low temperature work, the ratio of compression must be kept low. It is a good rule to keep compression ratios below 10. In ultra-low temperature work a compression ratio of 10 is the top limit; and if possible, the compression ratio should be kept below 7 or 8. Low compression ratios allow us to use commercially available compressors, with normal tolerances in manufacture, even in ultra-low temperature work, and still maintain reasonably good volumetric efficiencies. For Example: We wish to maintain a cabinet at -60 F. We can put in enough evaporator and air movement to maintain a temperature difference of 15 F. So the evaporator temperature will have to be -75 F. If we use R-22 and have no pressure drop through the evaporator and the suction line, the suction pressure at the compressor will be 18-1/2 inches vacuum or 5.6 psia. NOTE: Inches of vacuum can be converted to pounds per square inch absolute, by subtracting the inches of vacuum from 29.9, and then dividing by In this case, = 11.4; = 5.6 psia. In this example, we have cool condensing water available, so we can maintain an 80 F condensing temperature, which for R-22, corresponds to a head pressure of 145 psig or psia. Therefore, the compression ratio will be , or 28.5, which is about three times what it should be. With such a high ratio of compression, the volumetric efficiency of an ordinary compressor would be 10% or less, instead of a normal volumetric efficiency of about 60% to 70% and a compression ratio of around 5 or 6. Fortunately, it is not necessary to attempt to operate with such a high compression ratio, nor at such low volumetric efficiencies. The compression can be broken down into two steps or "stages," as they are more commonly called. There are two chief ways in which this is done compound-compression and the cascade method. COMPOUND-COMPRESSION In this method of two-staging, the -75 F evaporator is connected to the suction of a compressor of the size necessary, and this compressor is called the first stage or low stage compressor. 5

6 Instead of discharging this first stage compressor into a condenser, it discharges into the suction side of a second stage or high stage compressor of the right size. The first stage compressor compresses the R-22 from 18-1/2 inches of vacuum and discharges it at say 13.3 psig (28 psia) into the suction of the second stage, where it is recompressed from 13.3 psig to 145 psig (159.7 psia). The second stage compressor discharges into a condenser where it is condensed at 80 F into liquid R-22, which is then fed to the expansion valve, float valve or capillary tube and into the -75 F evaporator. The first stage of compression is from 18-1/2 inches of vacuum (5.6 psia to 13.3 psig (28 psia) so the ratio of compression for the first or low stage is or 5, which is a very acceptable ratio of compression at which the first stage compressor can operate efficiently at perhaps a volumetric efficiency of 60% or 70%, depending upon the design of the compressor and the precision with which it is constructed. The suction pressure of the second stage compressor is 13.3 psig (28 psia) and its discharge pressure 145 psig (159.7 psia) so the ratio of compression of the second stage is or 5.7. Again, this is an acceptable compression ratio, and the second stage compressor can also operate with a reasonably good volumetric efficiency of about 60% to 70%, depending upon its design and the precision used in its manufacture. By compound-compression, the compression ratio of 28.5 between the -75 F evaporator and the 80 F condenser has been broken up into a first stage with a compression ratio of 5, and a second stage with a compression ratio of 5.7, with a corresponding gain in efficiency in both compressors also a reduction in size of the overall equipment. Please note that by multiplying the two ratios of compression of 5 and 5.7 we get 28.5, so the product of the compression ratios of the compressors in compound-compression is the compression ratio that would have been required in one stage of compression. THE INTERSTAGE The 13.3 psig head pressure of the first stage, and which is also the suction pressure of the second stage, is sometimes known as the interstage. R-22 saturation temperature of the interstage, corresponding to 13.3 psig is -15 F. But certainly, the temperature of the interstage is not going to be -15 F. The first stage R-22 saturation temperature of the interstage, corresponding to 13.3 psig is -15 F. But certainly, the temperature of the interstage is not going to be -15 F. The first stage compressor does not work on the R-22 vapor at 18-1/2 in. vac., so that when it is discharged from the first stage compressor it will have in it not only the latent heat of the -75 F vapor but also the heat of compression. Although it is discharged at 13.3 psig, its temperature will be about 63 F or even higher, depending upon how much the -75 F gas is superheated when it enters the first stage compressor. That is, the discharge will be superheated about 78 F, from -15 F to 63 F, although it will be at 13.3 psig. If we feed this 63 F superheated gas directly into the suction of the second stage compressor, it will have so much superheat in it that it will overheat the second stage compressor, particularly the valves, and also tend to carbonize the oil. So we must cool the 63 F interstage before it goes to the second stage. We do not need to cool it to-15 F. In fact, it is better for it to be superheated somewhat to insure against slugging any liquid R-22 into the second stage compressor. Cooling the interstage to 0 F will allow 15 degrees of superheat to insure against liquid pumping, but it will also cool the interstage gas enough to keep from burning up the valves of the second stage compressor. 6

7 THE LIQUID COOLER One of the best ways to cool the interstage is shown in Figure 27F05. A second evaporator, called a Liquid Cooler, is provided, which serves two purposes; one, to cool the liquid R-22 before it goes to the main -75 F evaporator, and about which more will be said later; and second, to cool the interstage. This second purpose is served by feeding the outlet of the liquid cooler into the interstage. The cool gas from the liquid cooler will help to cool the interstage gas. In fact, we should overfeed the expansion valve of the liquid cooler, so that the vapor from the liquid cooler to the interstage is saturated and even contains some liquid R-22. When this liquid goes into the interstage, it is evaporated by the warm interstage gas and in doing so, absorbs its latent heat of vaporization. In this example, the valve should be so adjusted that the interstage gas entering the second stage compressor will be at approximately 0 F. Typical two-stage compound-compression system The 0 F interstage gas at 13.3 psig is compressed in the second stage compressor and fed into the condenser at 145 psig, which corresponds to a condensing temperature of 80 F. The compressed gas leaving the second stage compressor will be at about 153 F. If we had not cooled the interstage, the discharge temperature of the second stage would have been about 218 F. In the condenser, its superheat is first removed, cooling it to a saturated gas at 80 F. Then it loses its latent heat and changes to liquid R-22, still at 80 F. NET REFRIGERATING EFFECT In the receiver and liquid line, it may warm up some, but let us assume that it reaches the expansion valve at 80 F as a pure liquid. When it passes through the expansion valve (or float valve or capillary tube) its pressure drops from 145 psig to 18-1/2 inches of vacuum. This causes it to boil or vaporize and absorb its latent heat of vaporization. With a -75 F evaporator this is Btu for every pound of R-22 that is vaporized. But we do not get the full benefit of all of this latent heat of Btu per pound, for the 80 F liquid had to itself be cooled down to -75 F. This "uses up" some of the refrigerating ability or latent heat of vaporization of Btu per pound of R-22. The heat that must be removed from the one pound of 80 F liquid to cool it down to -75 F amounts to Btu, so the Btu must be subtracted from the Btu to get the actual amount of refrigeration that the one pound of 80 F liquid can do when fed into a -75 F evaporator. This is Btu 7

8 per pound, ( ) and is called the Net Refrigerating Effect, for it is the net amount of refrigerating effect that we actually get. The latent refrigerating ability of the R-22 was Btu per pound, but we only got to use Btu per pound of it just about 59%. If we did not have to use so much of the latent heat in cooling down the warm liquid from 80 F to -75 F, we could get a much greater net refrigerating effect for each pound of refrigerant. Then we would not have to evaporate as many pounds nor to pump as many pounds, and we could get greater refrigerating capacity from the compressor. In ultra-low temperature work we must reduce losses as much as practicable; we must squeeze all of the capacity out of the equipment that we can, for at best, the capacity of a compressor at these ultra-low temperatures is very low. This is where the liquid cooler, or as it is sometimes known, liquid sub-cooler, comes in. Several types of liquid coolers can be used, shell-and-tube, double tube, or, as we have shown in Figure 27F05, the shelland-coil type. The coil is fed by a thermostatic expansion valve on a branch from the main liquid line. Since the suction line from this coil is connected to the interstage at 13.3 psig, the temperature of the coil will be -15 F. The 80 F liquid at 145 psig is led through the -15 F liquid cooler and is there cooled to, let us say 0 F, but its pressure still stays at 145 psig. To cool a pound of R-22 from 0 F to -75 F requires that only Btu per pound be removed instead of from 80 F to -75 F. So now only Btu must be used of the Btu refrigerating ability in order to cool the liquid down to -75 F, so we have Btu of net refrigerating effect instead of 62.01, a gain of Btu or 38%. This is a direct gain of over 1/3 in the capacity of the first stage compressor. The gain is not all free, for the second stage compressor has to take the extra load. However, it does it at a higher suction pressure (13.3 psig) and consequently at a higher capacity and efficiency. In order to make the -75 F evaporator fully active which is extremely important there will be some "wasted" refrigeration in the suction line leaving the evaporator. Some of this can be used to further precool the 0 F liquid before it goes to the -75 F evaporator. This "wasted" refrigeration should be used sparingly, however. A little of it can be used economically, but any heating of the -75 F gas superheats it. Superheating the suction gas reduces its density (makes it "lighter") and consequently reduces the amount of gas by weight that the first stage compressor can pump; that is, superheating the suction gas reduces the compressor capacity. As said previously, we want the suction gas superheated enough to insure against liquid entering the compressor. We can afford to superheat the -75 F gas 15 or 20 degrees to do this, but there is no point in wasting compressor capacity through superheating more than is necessary. We should leave most of the job of cooling the liquid to the liquid cooler, where it can be done economically. WEIGHT OF R-22 CIRCULATED IN THE FIRST STAGE PER HOUR The sizes, or displacements of the two compressors can be estimated, without too much difficulty. Suppose in our example, that the cabinet imposes a load of 3,000 Btu per hour. The liquid is sub-cooled to 0 F, so its net refrigerating effect is Btu per pound. Dividing 3,000 by gives 35.0 lbs of R- 22 that must be circulated and evaporated in the -75 F evaporator per hour to produce 3,000 Btu of refrigeration per hour. 8

9 VOLUME OF R-22 CIRCULATED IN THE FIRST STAGE PER HOUR R-22 at a saturation temperature of -75 F but superheated to -60 F by the time it enters the first stage compressor, has a specific volume of 8.7 cubic feet per pound. This value can be obtained from the superheat tables or the pressure-enthalpy diagram for R-22. Then the first stage compressor must pump cubic feet of vapor per hour (35.0 x 8.7). This is 5.07 cu. ft. per minute. DISPLACEMENT OF FIRST STAGE COMPRESSOR A compressor with a displacement of 5.07 cfm would not be able to actually pump 5.07 cfm. Since we need 5.07 cfm and if we assume a volumetric efficiency of the compressor of 65%, the compressor displacement will be or 7.8 cfm. A four cylinder compressor with a bore of 2 inches and a stroke of 2 inches running at 535 rpm has displacement of over 7.8 cubic feet per minute, so it should be about right as the first stage compressor. VAPOR FROM THE LIQUID COOLER The vapor from the liquid cooler also feeds into the interstage, and we are overfeeding it so as to cool the interstage, so this extra gas will also have to be pumped by the second stage compressor. The liquid cooler is cooling the 35.0 pounds of 80 F liquid going to the -75 F evaporator, to 0 F ahead of the expansion valve, and this is a load of about 1,000 Btu per hour, including some heat leakage to the liquid cooler. The net refrigerating effect of R-22 from 80 F to -15 F is 69.1 Btu per pound. So the liquid cooler will put about another 14.5 pounds of refrigerant per hour into the interstage in addition to the 35.0 pounds per hour from the first stage compressor. Also, we are overfeeding the expansion valve on the liquid cooler, so as to cool the discharge gas from the first stage compressor from 63 F to 0 F. This will require 9.2 Btu for each of the 35.0 pounds of R-22 pumped by the first stage compressor, or a total of 4.9 pounds that the liquid cooler passes into the interstage and which must also of course be pumped by the second stage compressor. The second stage compressor will therefore have to pump 35.0 pounds from the first stage, 14.5 pounds from the liquid cooler and 4.9 pounds to cool the interstage, or a total of 54.4 pounds of R-22. TOTAL VOLUME OF R-22 TO BE PUMPED BY THE SECOND STAGE COMPRESSOR PER HOUR This 54.4 pounds of liquid, when vaporized to the 13.3 psig pressure and at the 0 F temperature, will have a volume of about 1.94 cubic feet per pound, so the volume of the 0 F R-22 at a pressure of 13.3 psig that the second stage compressor must pump is or cubic feet per hour. With a volumetric efficiency of 60%, the compressor displacement will have to be cubic feet per hour ( ) or 2.93 cubic feet per minute ( ). A four cylinder compressor with a bore of 1-7/16 inches and a stroke of 1-5/8 inches, running at 485 RPM will have this displacement, so would be suitable as the second stage compressor. MORE DENSE 0 F VAPOR CAN BE PUMPED THAN -60 F VAPOR, EVEN WITH SMALLER COMPRESSOR It will be noted that the second stage compressor with a displacement of 2.93 cfm, handles all of the gas from the first stage compressor having a displacement of 7.8 cfm which is almost three times as much. In addition, the second stage compressor is handling all of the gas from the liquid cooler, and the interstage cooling. The first stage compressor must have a displacement of 7.8 cfm to pump 35.0 pounds of R-22, while the second stage compressor with a little over one-third of the displacement of the first stage compressor, pumps 54.4 pounds of R-22 per hour. 9

10 The reason for this is of course, that the interstage gas, which is the second stage suction, is at a higher pressure and temperature and therefore much more dense, than the very low pressure, very light suction gas to the first stage compressor. The density of the second stage suction gas at 0 F is 5.15 pounds per cubic foot, compared to 1.94 pounds per cubic foot of the -60 F suction gas of the first stage. It is the pounds of R-22 pumped that counts, and because of the higher density of its suction gas, the second stage compressor can pump more pounds than the first stage compressor, despite its smaller size, and despite its lower volumetric efficiency due to its higher ratio of compression. THE CONDENSER The condenser must dispose of all of the heat taken from the ultra-low temperature cabinet, from the liquid cooler, and the heat of compression representing the work done on the gas by the two motors driving the compressors. The heat from the first stage, plus the heat from the liquid cooler is all in the suction gas to the second stage compressor. In that compressor is added the heat of compression of the second stage. There are 54.4 pounds of gas at a temperature of 0 F and at a pressure of 13.3 psig entering the second stage compressor and being compressed per hour. From the R-22 tables or chart we find that each pound of refrigerant has Btu of heat in it when it enters the second stage compressor. When it comes out of the second stage compressor and enters the condenser, it is at a temperature of 153 F and a pressure of 145 psig, and has a heat content of Btu per pound. So 19.2 Btu per pound has been added by the work done on it in compressing the gas. After the gas is cooled and condensed in the condenser, it leaves as a liquid at 80 F and still at the pressure of 145 psig. This liquid has in it Btu per pound. Since the Refrigerant enters the condenser with Btu/lb and leaves with Btu/lb, the condenser must have removed or Btu/ lb. The amount of refrigerant that the condenser must handle is 54.4 pounds per hour, so the condenser must remove or 4,908 Btu per hour; that is, the capacity of the condenser in our example must be 4,908 Btu per hour. Actually, a much larger condenser should be used, for one having a capacity of 5,070 Btu per hour, would be only large enough when the system got down to the desired temperatures. It would allow nothing extra for the pull-down. At least an additional 25% should be allowed, and preferably more, depending upon how rapid a pull-down is required. MOTORS The horsepower of the motors to drive the compressors can also be calculated from the amount of work that they must do to drive the compressors. Let us take the first stage of our example first. From the R-22 tables or diagram we find the -60 F suction gas, superheated from -75 F and at a pressure of 18-1/2 inches of vacuum has in it 98.2 Btu per pound. Also from the tables or diagram we find that when it leaves the first stage compressor at 13.3 psig and at a temperature of 63 F (but cooled to 0 F in the interstage) the R-22 has in it Btu per pound. Therefore, the difference ( ) 16.4 Btu per pound has been added in the compressor. This 16.4 Btu is called the Heat of Compression for it represents the heat added to the gas in compressing it. The first stage compressor is compressing 35.0 pounds of R-22 per hour, so the total amount of heat added to the first stage gas is ( ) or 574 Btu per hour or (574 60) 9.5 Btu per minute. 10

11 Heat is one form of energy, and we express it in Btu per hour, Btu per minute etc. Mechanical energy or work energy is another form of energy and we express it in horsepower (hp). Since energy can be changed from one form to another, we can express the heat energy in terms of work energy or horsepower. One Btu per minute is equivalent to horsepower so 9.5 Btu per minute is equivalent to.224 horsepower ( ) or under 1/4 hp. MECHANICAL EFFICIENCIES OF THE COMPRESSOR AND MOTOR The compressor is not 100% efficient; some energy is lost in friction, inertia, etc. If we assume a 75% mechanical efficiency for the compressor, then the motor driving the compressor will have to supply or.298, or under 1/3 hp to the compressor to drive it. But the motor itself is not 100% efficient either. In this size motor, a normal efficiency is about 65%, so the actual motor horsepower must be or.459, or under 1/2 hp. We can calculate the second stage in the same manner as follows: Heat of the 0 F suction gas, superheated from -15 F and at a pressure of 13.3 psig is Btu per pound. Heat of the 153 F discharge gas at a pressure of 145 psig is Btu per pound. The difference (heat of compression) is 19.2 Btu per pound. There are 54.4 pounds of R-22 pumped per hour by the second stage, so the total heat of compression is 1,044 Btu per hour ( ), or 17.4 Btu per min. (1,044 60). Converting 17.4 Btu per minute of heat to horsepower ( ), we get a "theoretical" horsepower of.410. Again, assuming a mechanical efficiency of 75% for the compressor, we get.546 hp ( ) to drive the compressor. Also assuming a motor efficiency of 65%, we get an actual motor horsepower of.84 ( ) or about a 7/8 hp motor for the second stage compressor. PULL-DOWN HORSEPOWER These motor sizes, 1/2 hp for the first stage, and 7/8 hp for the second stage would be sufficient when the first stage evaporator was -75 F with a 15 F superheat to the first stage compressor; with the liquid cooler at -15 F, with the interstage at 0 F, with the condensing temperature 80 F and the condensing pressure 145 psig; and with the liquid R-22 subcooled from 80 F to 0 F before reaching the expansion valve on the -75 F evaporator. That is, these motor sizes would be sufficient after the system was down to the operating temperatures and pressures. They would not be sufficient for the pull-down. Starting with a warm evaporator, a warm liquid cooler, and no sub-cooling of the liquid, the suction pressures would be quite high, and consequently the motor loads would be far greater than 1/2 hp and 7/8 hp. The motor sizes would have to be much greater than 1/2 hp and 7/8 8 hp, but how much greater they would have to be would depend on how long a time it would take to pull the load down to temperature, and this in turn would depend on whether the -60 F cabinet was started empty and pulled down to temperature or whether it was loaded with product first. 11

12 Motors 1 hp and above on refrigeration equipment will normally stand a continuous overload of 25% or even greater, and overloads of as much as 40% or 50% for a few minutes. These are allowed as safety factors and should not be relied upon for the pull-down for an ultra-low temperature system. To be on the safe side, the hp of the motors should be doubled at least to allow for the overloading during pull-down. Thus, on our example, we would probably use a 1 hp motor on the first stage and a 2 hp on the second stage. A single 3 hp could be used to drive both compressors, with the proper compressor pulley ratios to give the proper rpm for each of the two compressors for the required displacement. TWO-STAGE COMPRESSORS Some manufacturers have made two- stage compressors, with both stages built into the same compressor. For example, three of the cylinders can be used for the first stage, and one cylinder for the second stage with different bores or strokes or both, to obtain the necessary displacements of each stage. A somewhat better Btu capacity for the same horsepower can be obtained with both stages in the same compressor, for there is some gain in the overall mechanical efficiency of one compressor over two compressors. An ordinary four cylinder compressor cannot be used, as the three cylinders must have a separate discharge, and the one cylinder must have a separate suction and discharge. Moreover, the first stage discharge and the second stage suction must be available, so that the interstage can be cooled. Otherwise, the hot-gas from the first stage discharge, unless cooled, would burn up the valves and otherwise overheat the second stage. OTHER REFRIGERANTS Refrigerants differ as to boiling pressures, volume of both the liquid and vapor, and heat content. In our example, we used R-22. If we had used R-12 in order to refrigerate the -60 F cabinet (air temperature) with a -75 F evaporator, and with the condenser at 80 F, almost all of the above values would be changed. Table 27T11A shows the pressures, displacements, etc., for R-22, R-12, propane and Kulene 131 under these same conditions. This shows that R-12, although it can be used for such low temperatures, is not as suitable as some of the other refrigerants. It requires much lower suction pressures, the circulation of larger amounts of refrigerants, and much larger compressor displacements. Table 27T11A R-22 R-12 Propane Kulene 131 Cabinet Temperature F Evaporator Temperature F st Stage Suction pressure, psig (in. Hg) 18.5" 23" 17" 1.5" Displacement c.f.m Discharge pressure, psig Compression Ratio

13 Volumetric Efficiency % Pounds of refgn. pumped/hr Interstage Saturation Temperature F Pressure psig Superheat F nd stage Suction pressure, psig Displacement c.f.m Discharge pressure, psig Compression Ratio Volmetric Efficiency % Pounds of refgn. pumped/hr The horsepower required does not vary too greatly for the different refrigerants, and especially on small systems the horsepower required for the different refrigerants would not be as important a factor as displacement and suction and discharge pressures. CASCADE SYSTEMS In addition to the Compound-Compression method, which we have just described, there is another method of two-staging to reduce the high ratio of compression of 28.5 to 1 between the -75 F evaporator and the 80 F condenser. This other method is called the Cascade System. It involves the use of two separate and complete systems, one for the first stage and another for the second stage, as shown Figure 27F11. Two-Stage Cascade System 13

14 The evaporator is the same as for the compound-compression system and we will also assume that it is at -75 F, and that its load is 3,000 Btu per hour. Again, we will use R-22, and assume that the -75 F gas is superheated to -60 F before entering the first stage compressor, so the first stage suction pressure is 18.5" vacuum or 5.6 psia. As shown in Figure 27F11, the 0 F liquid comes directly from the first stage condenser; that is, the condensing temperature of the first stage is 0 F, so the condensing pressure is 24.1 psig or 38.8 psia. Therefore, the compression ratio is or 6.9. This is a higher compression ratio than the first stage with compound-compression; consequently, the volumetric efficiency of the first stage compressor will be less than the 65% we assumed for a compression ratio of 5 to 1. For the moment, we will also assume that R-22 liquid entering the expansion valve on the -75 F evaporator is 0 F. As far as the expansion valve, evaporator and the first stage compressor are concerned, they are identical with those of the first stage of the compound-compression system. However, in the cascade system, instead of pumping the discharge from the first stage compressor into the suction of the second stage compressor, we use the second stage to chill the first stage condenser down to 0 F. This is done as shown in Figure 27F11. The first stage condenser can be similar to an ordinary watercooled condenser; but instead of using water, R-22 at -10 F is circulated. It must be a few degrees lower than the condensing temperature of the first stage, so as to obtain a transfer of heat from the condensing gas of the first stage to the R-22 cooling it. We are assuming a 10 F temperature difference, which is about what we can obtain in practice. Actually, the -10 F R-22 is the evaporator temperature of the second stage, for the purpose of the second stage system is to reduce the condensing temperature and condensing pressure of the first stage so that the first stage compression ratio is low. It is not as low as the compound-compression example, but it is below the maximum of 10 to 1 that good practice requires. We could have kept the same compression ratio of 5 to 1 by cooling the first stage condenser to -15 F, for which the condensing pressure would have been 13.3 psig or 28 psia. Thus, the compression ratio would have become 5 to 1 (28 5.6). To do this, the second stage evaporator would have had to be - 25 F in order to allow the 10 F temperature difference. With the first stage condensing temperature being 0 F and the second stage evaporator being -10 F, the suction pressure of the second stage system is 16.6 psig or 31.3 psia. If we again assume a condensing temperature for the second stage, corresponding to a condensing pressure of 145 psig or psia, then the compression ratio of the second stage becomes 5.1 to 1 ( ). This is a little better than the 5.7 compression ratio for the second stage that we had in the compoundcompression example. Consequently, the volumetric efficiency of the cascade second stage compressor is somewhat higher than the 60% we assumed for the compound-compression second stage compressor. DISPLACEMENT Since the liquid temperature to the expansion valve is the same, 0 F, and the evaporator temperature is the same -75 F, as for the compound-compression first stage, the net refrigerating effect per pound is the same, Btu per pound. Also, since the load is the same, 3,000 Btu per hour, and the superheating of the suction gas is the same, 15 F, the pounds of R-22 pumped, 35.0 lbs. per hour and the volume of the gas, 5.07 cu. ft. per minute, are the same for the first stage cascade as for the first stage compoundcompression. 14

15 However, since one ratio of compression is higher, 6.9 for the cascade than for the compoundcompression 5, the volumetric efficiency of the compressor will be lower for the first stage cascade compressor than for the compound-compression. We assumed a volumetric efficiency of 65% based on a ratio of compression of 5 to 1. With a ratio of compression of 6.9, we can assume a volumetric efficiency of 60% for the first stage cascade compressor based on 6.9 to 1 compression ratio. Therefore, the displacement of the first stage cascade compressor must be or 8.4 cfm rather than 7.8 cfm for the first stage compound compression compressor. If we used the same four cylinder compressor with a bore of 2 inches and a stroke of 2 inches, we would have to run it 575 rpm instead of 535 rpm in order to get the 8.4 cfm displacement. In as much as the ratio of compression of the first stage cascade compressor is greater than for the compound-compression compressor, more work must be done on the gas to compress it, so the heat of compression will be greater. It will come from the compressor at 90 F instead of 63 F, and it will have Btu per pound in it instead of Btu per pound. Since 35.0 pounds of R-22 are pumped per hour, the total amount of heat put into the 0 F condenser will be or 4,147.5 Btu per hour. In the first stage condenser (with which is combined the second stage evaporator), the 90 F hot gas is cooled to 0 F and condensed to a liquid at 0 F. From the tables, we find that 0 F liquid R-22 at saturation has a heat content of Btu per pound, so the 35.0 pounds of R-22 per hour at 0 F still has or Btu per hour left in it. It must therefore have lost 4, or 3,775.4 Btu per hour in the condenser. This 3,775.4 Btu per hour lost by the compressed gas from the first stage, had to go somewhere. It was picked up by the -10 F evaporator of the second stage, so the Btu per hour is the load that the first stage passed on to the second stage. The combination first stage condenser and second stage evaporator should be well insulated so as to reduce the heat load as much as possible. Nevertheless, some heat will be absorbed from the room air; so let us assume that it will average about 200 Btu per hour. Then the total heat that the second stage evaporator must remove is 3, or 3,975.6 Btu per hour. SECOND STAGE With a -10 F evaporator, the heat of the saturated vapor is Btu per pound. At 80 F condensing, the heat of the liquid is Btu per pound, so the net refrigerating effect the second stage is or Btu per pound. With a load of 3,975.6 Btu per hour, 57.0 pounds (3, ) of R-22 must be circulated in the second stage per hour. There will be some superheating of the -10 F vapor before it gets to the second stage compressor. Let us assume that it is superheated 25 F, so that it enters the compressor at 15 F. The specific volume of -10 F R-22 vapor superheated to 15 F is 1.76 cu. ft. per lb., so the volume of vapor to be pumped is 1.76 x 57.0 or cu. ft. per hour. Let us assume that the volumetric efficiency of the second stage compressor, with a compression ratio of 5.1 to 1, is 65%. Then the actual displacement of the second stage compressor is or cu. ft. per hour or 2.5 cu. ft. per minute (cfm). This is somewhat less than the displacement of the second stage compressor in the compoundcompression example, which was 3.03 cfm. The reduction is partly due to the lower compression ratio and higher volumetric efficiency, but is mostly due to the lower specific volume of the suction vapor of 1.76 compared to

16 We could use the same compressor as before with a 1-7/16 " bore and 1-5/8 stroke, but we would need to run it at only 415 instead of 485 rpm. From the tables we find that the R-22 is discharged from the second stage compressor at 160 F with a heat content of 126 Btu per pound. Since 57.0 pounds per hour are pumped by the second stage, or 7,182.0 Btu of heat are put into the condenser of the second stage per hour. The 57.0 pounds of compressed gas is cooled to 80 F and condensed to an 80 F liquid in the condenser. The 80 F liquid has a heat content of Btu per pound, so the heat leaving the condenser in the liquid amounts to or 1,935 Btu per hour. The condenser must therefore remove the difference (7,182-1,953), or 5,229 Btu per hour, so a condenser of that rating must be used. MOTORS If we assume a mechanical efficiency of 75% for the compressors and 65% for the motors as we did in the example of compound-compression, and calculate motor sizes we find that the motor for the first stage cascade will be.6 hp, and for the second stage cascade 1 hp. In the compound-compression example, we allowed a large increase in motor horsepower for pull-down, for both stages must be started at the same time from a warm start. In the cascade system, we can start the second stage first and run it until the combination first stage condenser - second stage evaporator is about down to the normal operating temperatures of 0 F and - 10 F. Then the first stage can be started, and since its condensing temperature is already down, the pulldown load will not be as great as in the case of compound-compression. In this cascade example, we calculated a.6 hp motor, and we would probably find that a 3/4 hp motor would be large enough for the first stage, unless the pull-down is exceptionally long. For heavy, sustained pull-down loads, it might be advisable to use a 1 hp motor. Even though the second cascade stage is started warm, it does not have the first stage load on it at first. Nevertheless, the calculated one horsepower included no safety factor for overload, and there would be some overload during pull-down; so a 1-1/2 hp motor would be advisable. It will be seen that the displacement and horsepower for the cascade second stage is less than for the compound-compression second stage. The resulting savings in original cost may be offset, partially at least, by the additional cost of the combined first stage condenser-second stage evaporator. Also, the cascade type ordinarily cannot be made as compact as the compound-compression type. In the compound-compression type of two staging, the same refrigerant is circulated throughout both stages. The two stages of the cascade system are entirely separate, for the second stage is used to cool the condenser of the first stage. Consequently, the two cascade stages do not have to use the same refrigerant. This is a very great advantage for the cascade system, for a different refrigerant can be chosen for each stage, on the basis of refrigerant characteristics especially suitable for the range of temperatures and pressures of each stage. It is especially helpful from the practical standpoint to use in the first stage a refrigerant whose suction pressure is at or above atmospheric pressure (zero pounds gage). It is also helpful to use in the second stage, a refrigerant whose head pressure is 200 psig, or under, to avoid use of extra-heavy materials in the condenser, and to minimize leaks. 16