einstien refrigeration

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INTRODUCTION

The Vapor Compression Cycle

In ancient times, kings sent servants and camels to mountain tops to gather ice. The ice was insulated with dried grasses and hauled back down to a special place directly above the king's throne where air, cooled by the ice, would descend to provide comfort for the king. The practice of cooling with nature's ice persisted even after the first thermodynamic refrigeration cycles made their debut in the mid to late 1800's, but by the 1930's, vapor compression refrigeration cycles and a growing electricity infrastructure brought mechanical refrigeration to kings and servants alike.
Currently, electric motor driven vapor compression refrigeration cycles dominate air conditioning, heat pump, and refrigeration applications. The vapor compression cycle's principle of operation is relatively simple. A working fluid (i.e. ammonia) is boiled in an evaporator at a pressure and hence temperature, T_L, low enough to provide cooling (Figure 1-1). A work driven compressor (usually electrical work) then increases the pressure of the working fluid vapor allowing it to condense and reject heat at a temperature that of the surroundings, T_M. Having rejected its heat of condensation and condensed the working fluid liquid is then expanded (via an expansion valve) back into the evaporator where it can again provide cooling at a low temperature.

Figure 1-1: The Vapor-Compression Cycle

Direct Thermally Driven Heat Pumps

Vapor compression systems require work to power the compressor which is generally provided by electricity from thermally driven (usually combustion) central power plants. In contrast, direct thermally driven cycles eliminate the need for a central power plant. Instead of converting heat into work and then using work to pump heat through a temperature lift, they use heat to pump heat directly. Due to the following benefits, direct thermally driven heat pump cycles are receiving increasing attention:

• Improved electric utility load factor by reducing summer peak demand
• Increased gas utility load factor by increasing use in summer
• Efficient utilization of industrial waste heat
• Higher heating efficiency
• Environmentally benign working fluids

Figure 1-2: Thermally Driven Heat Pump All thermally driven heat pump cycles exchanging heat with only three temperature reservoirs can be represented by Figure 1-2. A high temperature reservoir at T_H delivers thermal energy, Q_H ,which enables the cycle to accept thermal energy, Q_L, from a low temperature reservoir at T_L. The sum of these two thermal energies, Q_M, are then dumped to a middle temperature reservoir at T_M.
Operating as a refrigerator, or air conditioner, the desired product, Q_L, is provided by Q_H which is the driving energy source. Thus, the efficiency of a three temperature thermally driven refrigerator, also known as the cooling coefficient of performance (COP), is defined as:

 (1-1) The first and second laws of thermodynamics written for the heat pump shown in Figure 1-2 operating reversibly are:

 (1-2)
 (1-3) Combining equations 1-2, and 1-3 with the definition of the cooling COP, equation 1-1, yields an expression for the reversible cooling COP in terms of the reservoir temperatures:

 (1-4) The COP of a reversible thermally driven refrigerator operating between three temperature reservoirs is a combination of the efficiency of a Carnot heat engine operating between T_H and T_M and the COP of a Carnot heat pump operating between T_L and T_M. Equation 1-4 provides the maximum possible COP for any three thermal energy reservoirs and is a good starting point in the analysis of direct thermally driven refrigeration cycles. Irreversibilities within the actual cycle will degrade this maximum possible COP to the actual COP.
Operating as a heater, a direct thermally driven heat pump utilizes thermal energy, Q_H, from a high temperature energy reservoir at T_H to enable the cycle to pull heat, Q_L, from a low temperature energy reservoir at T_L. The sum of these heats, Q_M, is then supplied to the space needing heat at T_M. Thus, the heating COP of a direct thermally driven heat pump cycle is:

 (1-5) Combining equations 1-2 and 1-3 with equation 1-5 yields the expression for the heating COP of a reversible direct thermally driven heat pump operating between three temperature reservoirs in terms of the reservoir temperatures:

 (1-6) The reversible COP of the heating cycle is a combination of the efficiency of a Carnot heat engine operating between T_H and T_L and the COP of a Carnot heat pump operating between T_L and T_M. As heaters, however, direct thermally driven cycles offer the advantage of providing the waste heat of the heat engine to the space needing heat.

Dual Pressure Direct Thermally Driven Heat Pumps

A dual pressure thermally driven heat pump is partially similar to the aforementioned vapor-compression cycle (Figure 1-1). Like the vapor-compression cycle, a working fluid (the refrigerant, i.e. ammonia) is throttled from a high temperature (T_M) and high pressure condenser to an evaporator where it is boiled at a pressure, and hence temperature, low enough to provide cooling, T_L (Figure 1-3). However, the vapor working fluid now enters an absorber where a second working fluid (the absorbent, e.g. water) in its liquid state absorbs the refrigerant vapor. The process of absorption creates heat, Q_M,absorber, which must be removed from the absorber usually to a thermal energy reservoir that has the same temperature, T_M, as the condenser.
Now the liquid mixture of refrigerant and absorbent is pumped to the pressure of the condenser into the generator. In the generator the thermal energy which drives the cycle, Q_H, is transferred from a reservoir (usually steam or combustion gases) at T_H. This causes the refrigerant fluid to separate from the liquid mixture as a nearly pure vapor where it can then be condensed (Q_M,condenser removed at T_M) and expanded into the evaporator. The remaining absorbent, still in the generator but with much less absorbed refrigerant, is expanded back into the absorber. While the cycle does require work for the pump, the majority of the energy is supplied thermally to the generator.

Figure 1-3: Dual Pressure Direct Thermally Driven Heat Pump

Single Pressure Direct Thermally Driven Heat Pumps

Another class of direct thermally driven cycles require no work or electricity because the entire cycle operates at a single pressure thus eliminating the need for a mechanical pump (work). Instead these more complex cycles use at least three working fluids which achieve low temperature evaporation and high temperature condensation by varying the partial pressure of the refrigerant. Along with the aforementioned advantages of conventional absorption cycles, they also have several other advantages:

• Silent operation
• Inexpensive equipment
• No moving parts
• High Reliability
• Portability

These advantages make them ideal for remote locations as well as for countries without electric utility infrastructures. They are also useful in any location where silent operation is essential.

The Ammonia-Water Hydrogen Cycle

The most familiar single pressure cycle is the ammonia-water-hydrogen cycle patented by Platen and Munters (1928). Refrigeration machines using this cycle have been in use since then and are recently receiving new attention. In the United States, these household refrigerators sold well during the 1920's and were driven by natural gas. Unfortunately, a fatal methyl chloride gas leak in Chicago, which was totally unrelated to the refrigerators, seriously marred the reputation of these machines and the vapor compression market has dominated since (Sands, 1993).
Single pressure cycle machines use three working fluids at a single pressure. They achieve cooling by lowering the partial pressure of the refrigerant thus allowing it to evaporate. In the ammonia-water-hydrogen cycle, ammonia is the refrigerant. The cycle is shown in Figure 1-4. The ammonia is driven (1) from its mixture with water (the absorbent) in the generator (5) by the application of heat, Q_G. Some of this heat drives the bubble pump, where the vaporized ammonia is used to lift the liquid mixture (now weak in refrigerant) back into the absorber (6). The nearly pure ammonia vapor enters the condenser (1). The nearly pure ammonia vapor is condensed at its saturation temperature for the system's total pressure. The condensed ammonia flows down into the evaporator (2).
The evaporator is perhaps the most interesting component of the system. Here the liquid ammonia is exposed to gaseous hydrogen which lowers the partial pressure on the liquid ammonia. This reduction in the partial pressure allows evaporation at ammonia's saturation temperature for its partial pressure in the evaporator, a temperature lower than that of the condenser. Thus, the evaporator is essentially equivalent to the expansion valve in a dual pressure cycle. The cool vapor mixture of ammonia and hydrogen (3) falls into the absorber. Here, water, bubble pumped from the generator (6), absorbs the vapor ammonia allowing the light hydrogen to rise back to the evaporator (4). Finally, the liquid ammonia-water mixture flows back into the generator (5) completing the cycle.

Figure 1-4: The Ammonia-Water-Hydrogen Cycle Since the 1920's, this cycle has been frequently used and perfected experimentally. Its uses include refrigerators in homes, campers, RV's, and hotel room mini bars, etc. An analytical model of the cycle predicts the COP of the cycle to be around 0.15 while experiments measure it to be as high as 0.2 (Kim, 1994).

Figure 1-5: The Einstein Refrigeration Cycle

The Einstein Cycle

The Platen and Munters single pressure cycle utilizes ammonia for the refrigerant and water for the absorbent. The water separates the ammonia from the inert gas, hydrogen. However, water's ability to absorb ammonia can be utilized in a completely different way. A recently uncovered U.S. patent by the famed Albert Einstein and Leo
Szilard issued on November 11, 1930 discloses another single pressure thermally driven refrigeration cycle which uses butane, ammonia, and water. In the Einstein cycle ammonia now acts as an inert gas to lower the partial pressure over the refrigerant, butane, and water later provides separation by absorbing the ammonia (see Figure 1-5).
Starting in the evaporator, liquid butane arrives from the condenser/absorber (component 6). In the evaporator (component 1), the partial pressure above the butane is greatly reduced by ammonia vapor flowing from the generator (component 29). With its partial pressure reduced, the butane evaporates near the saturation temperature of its partial pressure and cools itself, the ammonia, and the surroundings. The ammonia-butane vapor mixture leaves the evaporator and enters the pre-cooler (component 5) where it cools the hot vapor ammonia counter flowing from the generator. The now superheated ammonia-butane mixture flows out of the pre-cooler into the condenser/absorber which is being continuously cooled by the environment. Meanwhile, liquid water from the generator is sprayed into the condenser/absorber (35). With its great affinity for ammonia vapor, this sprayed water absorbs the vapor ammonia from the ammonia-butane mixture. This absorption of the ammonia vapor increases the partial pressure on the butane vapor to nearly the total pressure, allowing it now to condense at butane's saturation temperature for the total pressure (higher than butane's saturation temperature at the partial pressure of the evaporator). The butane and the ammonia water separate due to their respective density differences and the fact that ammonia-water is immiscible with butane at the condenser/absorber's temperature and pressure. Since liquid butane is less dense than liquid ammonia-water, it is the top liquid and is siphoned back to the evaporator. Meanwhile, the ammonia-water mixture leaves from the bottom of the condenser/absorber (27) and enters the solution heat exchanger (component 28). Here, the mixture is pre-heated before entering the generator (component 29).
Inside the generator, heat is applied to the strong ammonia-water solution driving off ammonia vapor where it rises under the influence of pressure created by the liquid head, h₁, and is carried to the evaporator (1). The remaining weak ammonia-water solution is pumped up to a reservoir (component 35) via a bubble pump (component 36). In the reservoir, any residual ammonia vapor from the bubble pump is sent to the condenser/absorber. The weak ammonia water solution falls to the solution heat exchanger where it gives up its heat to the strong ammonia-water solution leaving the condenser. Finally, the water is sprayed into the condenser/absorber (35).
While the overall pressure of the cycle is constant, there are slight pressure variations within the cycle necessary for fluid motion. These are due to height variations and are not large enough to significantly affect property evaluation.

Literature Review

Einstein Patent Review

Between 1927 and 1933, Albert Einstein and Leo Slizard published seventeen patents mostly in Germany; however, a few were published in the United Kingdom and one was published in the United States. One of the U.K. patents (number 282,428) is particularly interesting since it expounds upon the single pressure cycle patented in the U.S. and is the focus of this study.
The U.K. version was patented in 1928 on November 15, nearly two years before the U.S. version. It highlights four different single pressure refrigerators one of which appears in the U.S. patent. Two of these use methyl-bromide as the refrigerant while the other two use butane. All four use ammonia and water for separating the refrigerant at a constant total pressure.
In the U.K. patent, the first two cycles utilize methyl-bromide as the refrigerant. Since methyl-bromide is heavier than the ammonia-water mixture, the fluid arrangement in the condenser/absorber is different, with the ammonia-water being on top. Otherwise these two cycles operate similarly to the butane cycles, but offer alternative generator configurations. Methyl-bromide, however, is quite toxic.
The U.S. patent contains only the third of the four cycles presented in the U.K. patent. The fourth cycle in the U.K. patent is different from the U.S. patent (i.e. the pre-cooler has been removed, and the ammonia-butane vapor mixture is bubbled into the weak ammonia-water mixture in the condenser rather than the weak ammonia-water mixture being sprayed into the ammonia-butane vapor). Because of this latter change, the weak ammonia-water mixture is not sprayed into the condenser but simply flows in. Close examination of the fluid head pressures in the evaporator and condenser/absorber raises questions into the viability of this alternative cycle.

Cycle Models

Literature on the Einstein cycle is rare. A brief description of the cycle was made in Physics Today by George Alefeld (Alefeld, 1980), and a similar article found recently in Scientific American mentions it (Dannen, 1997). A search of the National Technical Information Service (NTIS) database resulted in one report from the Johns Hopkins University Applied Physics Laboratory by J.W. Follin and K. Yu titled "Evaluating the Einstein Refrigerator" (Follin, 1980).
In this report, Follin's only reference other than Einstein and himself is Alefeld (Alefeld, 1980). Follin investigated the Einstein cycle in order to determine if it could be powered by geothermal resources, solar energy, or co-generation systems. Making many simplifying assumptions such as ideal gas vapor behavior and perfect heat exchangers, Follin calculates a COP of 0.25. Follin recommended investigation of other working fluids for the Einstein cycle. However, no references have been found to any of this recommended work.
A previous study by the author, also using ideal mixture models, showed the Einstein cycle to have relatively promising COPs as high as 0.4 (Delano, 1997).
Further literature searches discovered two more items of interest. The first was another U.S. patent by Alexandre Rojey of France. He references the Einstein-Szilard U.S. patent but claims: "The device has however the major disadvantage of uneven running since ammonia condensation can be avoided only with difficulty under the pressure and temperature conditions prevailing in the evaporator. The evaporation of butane then greatly decreases and the exothermic condensation of ammonia converts the evaporator to a heat source rather than a cold source." (Rojey, 1984). Rojey's patent outlines a nearly identical refrigeration cycle which uses carbon dioxide as the inert fluid and suggests many absorbing and refrigerant fluids.
The second item discovered was a paper by B. Razi, T. Mediouni and M. Kaddioui, also of France. While the paper is entirely in French, a translation revealed that they did indeed analyze the Einstein Cycle. Razi et. al. were interested in powering the cycle with solar energy in Morocco and performed a simple analytical model to be used in their study. They modeled the cycle using iso-butane as well as n-butane and reported COP's of 0.19 and 0.13 respectively. They predicted iso-butane provided a higher COP due to its decreased heat of vaporization.
Papers on the Platen and Munters cycle are not rare at all. They obtained U.S. patent number 1,609,334 in 1922 and since then numerous papers and related patents have been published. The information presented here for this cycle was primarily obtained from two annual reports to the Gas Research Institute (Herold, 1991-1992, 1992-1993) and from Absorption Chillers and Heat Pumps (Herold, 1996 ).

Bubble Pumps

The most common applications of bubble pumps are electric drip and percolating coffee makers. Bubble pumps are also known as vapor lift pumps. While commonly used, literature on bubble pumps is nearly non-existent. However, since a bubble pump is really just a pipe containing two phase fluid flow, books and papers on two phase flow provide more than sufficient information for the analysis of a bubble pump. An extensive search revealed that the book which provides the best starting point for a bubble pump analysis was Two Phase Flow in Pipelines and Heat Exchangers (Chisholm, 1983). Chisholm provides the basic definitions and terminology, the flow patterns encountered in vertical pipes, and extensive references.
Absorption Chillers and Heat Pumps (Herold, 1996) provides a few references to papers which mention bubble pumps. The most recent, titled "Mathematical Modeling of a Steam-Injected Bubble Pump" (Hassoon, 1991), provides a theoretical model and experimental results for a bubble pump which utilizes injected steam for lift instead of vaporizing the liquid in the tube. Also referred to is an earlier paper in French titled "Coupling of an Absorption-Diffusion Refrigeration Machine and a Solar Flat-Plate Collector" (Bourseau, 1987). Bourseau provides a simulation of a solar driven bubble pump and reports flow rates for several different operating conditions but provides no information on his theoretical model.
Design information and experimental data for actual ammonia-water bubble pumps are presented in "A Boiler For Absorption Units of the Inert Gas Type Having a Wide Range of Input Power" (Lucas, 1967) and "A Device to Speed the Circulation of Water Solutions in Household Absorption Refrigerators" (Sellerio, 1951).
Similar to the bubble pump, the air lift pump utilizes the buoyancy of injected air to lift a slug of liquid up a tube. According to Hassoon, "the basic difference between the air lift and vapor lift pump is the phase change that takes place in the latter but not the former; otherwise, the pumping phenomenon and the flow regimes are of the same nature" (Hassoon, 1991). The amount of available literature on air lift pumps greatly surpasses that of the vapor lift pump.
While literature on air lift pumps exists as early as 1908, the first analysis using the basic principles of two phase flow was performed by Stenning and Martin in 1968. Kouremenos and Staicos analyzed the performance of a small air lift pump (tube diameters between 12 and 19 mm) in 1985, and Clark and Dabolt provided a general design equation for air lift pumps operating in slug flow in 1986.

Overview of Current Study

This study examines the single pressure direct driven heat pump cycle described in U.S. Patent No. 1,781,541 by Albert Einstein and Leo Szilard (the Einstein cycle). The Patel-Teja cubic equation of state, fitted to experimental data, is used for all fluid modeling (pure substances and mixtures). For the ammonia-butane mixture, the Patel-Teja equation of state predicts vapor-liquid-liquid equilibrium and azeotropic behavior at the pressures and temperatures in the evaporator. Experimental measurements on the ammonia-butane system verify this and the equation of state was fit to the experimental data (Wilding, 1996).
This study also develops general criteria for working fluids of the cycle. The three fluids were generalized as the refrigerant fluid, the inert fluid, and the absorbing fluid. The original cycle used butane, ammonia, and water, respectively. This study finds that while water is possibly the best absorbing fluid, viable alternatives exist for the refrigerant and absorbing fluids. Several of these alternative fluids are modeled with the Patel-Teja equation of state and are evaluated in the cycle.
Furthermore, a second law analysis of each process is performed, the effect of realistic pinch points in the heat exchangers are analyzed, and the bubble pump performance is predicted. Finally, using the analytical model as a guide, a conceptual demonstration prototype was built, charged with ammonia, water, and butane, and successfully operated