Modelling a scroll compressor with vapor injection can be a challenging task, but it is possible to do so using MATLAB. The basic steps involved in the modeling process are:
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Define the compressor geometry and operating conditions: Scroll compressor geometry includes the number of scrolls, the radius of the scrolls, and the tooth height. The operating conditions include suction pressure, discharge pressure and gas flow rate.
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Determine the thermodynamic properties of the refrigerant using an appropriate equation of state. For vapor injection, it is important to consider the refrigerant at two different states – the refrigerant state downstream of the economizer or evaporator and the refrigerant state entering the compressor, which is typically in a superheated state.
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Develop a model of the scroll compressor using the mass, energy and momentum conservation equations. There are different modeling approaches available such as isentropic, adiabatic and polytropic modelling. The most commonly used model is isentropic, due to its simplicity.
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Incorporate the vapor injection process into the model. This includes determining the mass flow rate, temperature and pressure of the vapor injection stream and accounting for the thermodynamic effects on the compressor performance.
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Simulate the model using MATLAB to obtain the compressor performance parameters such as suction and discharge temperatures and pressures, volumetric efficiency, mass flow rate, and so on.
Here is a sample MATLAB code for modeling a scroll compressor with vapor injection:
% Define the compressor geometry and operating conditions
n = 2; % Number of scrolls
rs = 0.05; % Radius of the scroll
th = 0.01; % Tooth height
P1 = 1.2; % Suction pressure (MPa)
P2 = 3; % Discharge pressure (MPa)
mdot = 0.1; % Mass flow rate of refrigerant (kg/s)
% Define the thermodynamic properties of the refrigerant
fluid = 'R134a';
T1 = 280; % Temperature downstream of evaporator (K)
T2 = 320; % Superheated temperature at compressor inlet (K)
h1 = refpropm('H','T',T1,'P',P1,fluid); % Enthalpy downstream of evaporator (J/kg)
h2 = refpropm('H','T',T2,'P',P1,fluid); % Enthalpy at compressor inlet (J/kg)
s1 = refpropm('S','T',T1,'P',P1,fluid); % Entropy downstream of evaporator (J/(kg.K))
% Model of the scroll compressor with vapor injection
phi = 0.5; % Volumetric efficiency
Tinj = 340; % Temperature of vapor injection (K)
mdotinj = phi*mdot*(h2-h1)/(refpropm('H','T',Tinj,'P',P1,fluid)-h2); % Mass flow rate of vapor injection (kg/s)
Tout = T1 + (T2-T1)/phi; % Discharge temperature
s2s = s1; % Isentropic entropy at discharge pressure
s2 = s1+(1/phi)*(refpropm('S','T',Tout,'P',P2,fluid)-refpropm('S','T',Tout,'P',P1,fluid))+(mdotinj/mdot)*refpropm('S','T',Tinj,'P',P1,fluid); % Actual entropy at discharge pressure
hs = refpropm('H','S',s2s,'P',P2,fluid); % Isentropic enthalpy at discharge pressure
hout = hs - phi*(hs-h2); % Actual enthalpy at discharge pressure
Wdot = mdot*(h2-hout); % Compressor power
Qdotinj = mdotinj*(refpropm('H','T',Tinj,'P',P1,fluid)-h1); % Vapor injection heat
% Outputs
disp(['Discharge temperature: ' num2str(Tout) ' K']);
disp(['Discharge pressure: ' num2str(P2) ' MPa']);
disp(['Mass flow rate: ' num2str(mdot) ' kg/s']);
disp(['Volumetric efficiency: ' num2str(phi)]);
disp(['Compressor power: ' num2str(Wdot/1000) ' kW']);
disp(['Vapor injection heat: ' num2str(Qdotinj/1000) ' kW']);
This code uses the REFPROP software to determine the thermodynamic properties of R134a refrigerant.