Efficiency of centrifugal compressor - Adiabatic walls vs CHT

Burken · May 11, 2018, 13:53

Hello!

I am currently writing my master thesis and have gotten into some problems understanding efficiency that I calculate from CFD-Post. The task is to perform CFD-simulations on a centrifugal compressor.

I have performed these simulations for two cases:

The first one is a conjugate heat transfer model, that allows for heat transfer between the fluids and the solids in the system.

The other case is the CHT model without its surrounding solids, and instead letting the outer walls of the fluids have adiabatic walls (impeller wheel is also modeled with adiabatic walls).

The problem I have is that the efficiency calculated for the two cases are almost the same (differs less than 1%). The efficiency that I calculate in CFD-Post is based on assumptions of an adiabatic and reversible process, meaning that the efficiency is isentropic.

Therefore the efficiency should be determined from the work ratio of the work at constant entropy over the actual work done on the compressor.

In terms of enthalpy this can be rewritten as:

$\eta_{isentropic} = \frac{W_{s}}{W_{actual}} = \frac{h_{2s}-h_{1}}{h_{2}-h_{1}}$

I won't derive the middle steps, but this efficiency can be written in terms of temperature ratio, pressure ratio and specific heat:

$\eta_{isentropic} = \frac{(P^0_2/P^0_1)^{(\frac{\gamma-1}{\gamma})}-1}{(T^0_2/T^0_1)-1},$

where $\gamma = \frac{c_p}{c_v}$ , subscript 1 and 2 denotes inlet and outlet, and superscript 0 denotes the total quantity.

Because of this, I believe that something is wrong if the efficiency calculated for the two cases (using the latter equation) are almost the same, since the CHT model allows heat transfer that will give contribution from heat transfer to the change in enthalphy.

The change of enthalpy is from what I have understand formulated as:

$\Delta h_{o} = \frac{W + \dot{q}}{\dot{m}}$ .

The compressor is considered an open system, letting matter travel in and out of it, so some kind of heat transfer will exist for both cases, but in the CHT model, the contribution from heat transfer between fluids and solids should also impact the efficiency.

Is it because of the equation for efficiency that I use only works for an adiabatic process, so I need another equation for the CHT case, or can it depend on something else that I've missed?

I hope you understand my problem and may have the answer that I'm looking for!

/Burken

May 11, 2018, 13:53	Efficiency of centrifugal compressor - Adiabatic walls vs CHT	#1
Burken New Member Johan Björk Join Date: Nov 2017 Posts: 9 Rep Power: 9	Hello! I am currently writing my master thesis and have gotten into some problems understanding efficiency that I calculate from CFD-Post. The task is to perform CFD-simulations on a centrifugal compressor. I have performed these simulations for two cases: The first one is a conjugate heat transfer model, that allows for heat transfer between the fluids and the solids in the system. The other case is the CHT model without its surrounding solids, and instead letting the outer walls of the fluids have adiabatic walls (impeller wheel is also modeled with adiabatic walls). The problem I have is that the efficiency calculated for the two cases are almost the same (differs less than 1%). The efficiency that I calculate in CFD-Post is based on assumptions of an adiabatic and reversible process, meaning that the efficiency is isentropic. Therefore the efficiency should be determined from the work ratio of the work at constant entropy over the actual work done on the compressor. In terms of enthalpy this can be rewritten as: $\eta_{isentropic} = \frac{W_{s}}{W_{actual}} = \frac{h_{2s}-h_{1}}{h_{2}-h_{1}}$ I won't derive the middle steps, but this efficiency can be written in terms of temperature ratio, pressure ratio and specific heat: $\eta_{isentropic} = \frac{(P^0_2/P^0_1)^{(\frac{\gamma-1}{\gamma})}-1}{(T^0_2/T^0_1)-1},$ where $\gamma = \frac{c_p}{c_v}$ , subscript 1 and 2 denotes inlet and outlet, and superscript 0 denotes the total quantity. Because of this, I believe that something is wrong if the efficiency calculated for the two cases (using the latter equation) are almost the same, since the CHT model allows heat transfer that will give contribution from heat transfer to the change in enthalphy. The change of enthalpy is from what I have understand formulated as: $\Delta h_{o} = \frac{W + \dot{q}}{\dot{m}}$ . The compressor is considered an open system, letting matter travel in and out of it, so some kind of heat transfer will exist for both cases, but in the CHT model, the contribution from heat transfer between fluids and solids should also impact the efficiency. Is it because of the equation for efficiency that I use only works for an adiabatic process, so I need another equation for the CHT case, or can it depend on something else that I've missed? I hope you understand my problem and may have the answer that I'm looking for! /Burken

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