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This study analyzed the performance of a single pressure, direct thermally fired heat pump cycle patented by Albert Einstein in 1927. The cycle uses ammonia, water, and butane as working fluids which were modeled using ideal gas and ideal solution assumptions and Raoult's law for the prediction of vapor-liquid equilibrium. Through the use of thermodynamic analysis, the study determined the operating parameters and their effect on the system performance. The major conclusions from the results of this work are as follows.

Perhaps the most important conclusion of this study is that the potential COP of the cycle is quite high relative to the ammonia-water-hydrogen single pressure cycles widely used. Current ammonia-water-hydrogen cycles have measured COP's around 0.1, and the COP's calculated for Einstein's cycle were as high as 0.4. For a three temperature heat pump system operating in the range of the temperatures chosen for this analysis, the ideal COP was calculated to be around 1.23. While the ideal cycle itself has an inherently low COP, the COP of the Einstein cycle is relatively high. However, the model used many idealizing assumptions.

Another important conclusion of this study is the dependence of the temperature lift from the evaporator to the condenser on the system pressure. Due to the nature of Raoult's law prediction of vapor liquid equilibrium, the ammonia-butane system's condensing and evaporating temperatures are constrained between the two pure component saturation temperatures at the system pressure. This fixes the lowest evaporator temperature and the highest condenser temperature for a particular pressure. Fortunately, an evaporator temperature below freezing can be obtained with the reasonably high condenser temperature of 107 F.

While the lift of the cycle is constrained by the system pressure, the driving potential of the cycle (the difference between the generator and condenser temperatures) is only limited by materials. However, it was shown that while increasing the generator heat transfer rate does increase the evaporator capacity, the system's performance was independent of the generator temperature. This means that the cycle can supply refrigeration with low temperature generator heat (i.e. industrial waste heat). This study showed the cycle to operate with generator temperatures as low as 170 F.

The last conclusion comes from examining experimental data on the ammonia-butane mixture found in the literature search (Kay & Fisch, 1958). This data shows that the minimum bubble point temperature is actually below both pure component saturation temperatures (Figure 4-1). While the data are for much higher pressures than used in the Einstein cycle, a similar shape is expected at lower pressures. If this were the case, then the maximum temperature lift at a particular pressure could be higher than the difference between the pure component saturation temperatures. Due to this real fluid mixture property, a lower evaporator temperature could be obtained with the same fixed condenser temperature.

Figure 4-1: Experimental Data for the Ammonia-Butane System


The real ammonia-butane data give rise to the first recommendation of modeling the cycle with a non-ideal mixture property model which will study this possible increased temperature lift. There are many equations of state which account for non-ideal effects and could be applied to this mixture. Furthermore, REFPROP, a software package which can now be interfaced with EES and is designed to handle mixtures in a non-ideal manner should be available by summer of 1997 (NIST, 1997).

While more nearly modeling the ammonia-water-butane system is certainly desirable, the inherent lift limitation in the system suggests another recommendation. Since the lift is dependent on the saturation temperatures of the pure components, a fluid pair with a greater difference in pure component saturation temperatures will give a higher temperature lift and may perform better. In a separate patent, Einstein discloses a very similar cycle which uses ammonia-water-methyl bromide instead. In any case, other working fluid sets for the cycle should be investigated.

In this study, the second law of thermodynamics was used to obtain the ideal COP of the system. Further studies could utilize a more complete second law analysis in order to determine the entropy generations of each process and their degradation effects on the systems performance. In this manner, the most performance impairing processes could be isolated and improvements to the cycle could be focused.

The heat exchangers in this study were modeled using a zero pinch idealization. In reality the heat exchangers would have some non-zero pinch, and the model should accurately reflect this.