Vapor Compression Heat Pump Cycle with Evaporator and Condenser Temperature Inputs
Creators: name: Hirschey, Jason
Publisher: name: Zenodo
Year: 2022
Subjects: heat pump
vapor compression

description: A vapor compression HP model was written in MATLAB using Coolprop refrigerant data. The inputs are only the environmental temperatures around the condenser and evaporator. The code iteratively determines all other thermodynamic properties following several assumptions. Some constant properties were predefined in this model, and the compressor volumetric displacement and rotation speed were fixed at 2.5 cm<sup>3</sup> and 3,600 rpm, respectively. A 5°C approach temperature (<em>AT</em>) was chosen for both the evaporator and condenser; that is, the temperature of the refrigerant is 5°C higher or lower than the user-defined evaporator or condenser environment temperature, respectively. This approximates the temperature difference necessary in a real heat exchanger for these systems. Degrees of superheating and subcooling are defined. There are many standards for this <sup>7,8</sup>, which vary by application. For this model, a value of ~9.1°C for both superheating and subcooling was found to be stable. Future iterations of this model may use the standard degrees of superheating and subcooling for specific applications. The HP model is divided into each state along the vapor compression cycle: (1) compressor suction and evaporator outlet, (2) compressor discharge and condenser inlet, (3) mid-condenser (saturated vapor), (4) mid-condenser (saturated liquid), (5) condenser outlet and thermal expansion valve (TXV) inlet, (6) TXV outlet and evaporator inlet, and (7) mid-evaporator (saturated vapor). The model first defines all known properties based on the input temperatures and approach temperatures, and quality for states 3, 4, and 7. States 4 and 7 are fully defined with the thermodynamic state principle. These properties are then used to define the operating pressure for the other states. because there are no additional losses in this model, the pressure at state 7 defines the pressure for all states on the evaporator side: 1, 6, and 7. Likewise, the pressure at state 4 defines the pressure for all states on the condenser side: 2, 3, 4, and 5. Next, using the degrees of superheating and subcooling, states 1 and 5 are fully defined. Now that state 5 meets the state principle, its enthalpy is determined from refrigerant properties. In this ideal system, the enthalpy of state 6 is equal and thus, state 6 is fully defined. Furthermore, because the compressor is assumed isentropic, the entropy of state 2 is equal to state 1 and thus, all states are fully defined. Once all states are defined and meet the thermodynamic state principle, the model checks for consistency and continuity, and adjusts values slightly. Under normal operating conditions with a positive temperature lift where <em>T<sub>condenser</sub> &gt; T<sub>evaporator</sub></em>, this adjustment is small, if necessary. However, if the user inputs result in a negative temperature lift where <em>T<sub>condenser</sub> </em><em>≤ T<sub>evaporator</sub></em>, additional computations and iterations are necessary. This negative temperature lift scenario describes the external temperatures, around the evaporator and condenser. The internal temperature lift of the refrigerant in the HP must still be positive, however. To model this, a variable TXV throttling coefficient is calculated for small positive external lift, and The model checks if the user-defined evaporator and condenser temperatures satisfy the negative temperature lift scenario. If so, the model first solves each state using a small positive temperature lift. Once the system is solved, the TXV coefficient is determined from the pressure drop between states 5 and 6 using the equation . This TXV coefficient is held constant for calculation of the negative external lift andhis is representative of a variable TXV in the fully open position. The states are recalculated similar to the described process, except the approach temperatures are left undefined. Now, state 6 is used to define state 7, and the approach temperature is calculated between state 7 and the user-input evaporator temperature. Through the iteration of the model, this continues to shift the operating pressure on the condenser side until the model converges to a certain tolerance. The mass flow rate of refrigerant through the system is determined by calculating the refrigerant density at the compressor suction (state 1), and multiplying this with the constant volumetric displacement and compressor speed. The work is calculated by taking the difference in enthalpy between the compressor discharge and compressor suction, and multiplying the mass flow rate. This is an academic approach to solving compressor work and may not be representative of any real-world compressors, but since this analysis only addresses isentropic operation, this approach is valid. A 10-coefficient compressor map for work and mass flow may be implemented into future iterations of this model. The heat from the condenser side is calculated by taking the difference between the enthalpy at the compressor discharge and the TXV inlet. Again, this model assumes no losses, and the values at these states are thus valid to assume as representative of the ideal condenser heat exchanger. The heat from the evaporator is calculated by taking the difference between the enthalpy at the TXV outlet and the compressor suction.
description: {"references": ["Bell, I. H., Wronski, J., Quoilin, S. &amp; Lemort, V. Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Industrial &amp; Engineering Chemistry Research 53, 2498-2508, doi:10.1021/ie4033999 (2014)."]}