Is the specified mechanical efficiency equation wrong ?

[caskandavor]

First of all, thank you very much for your work, I have been working on scroll compressors for a few months now and PDSim has been very helpful.

I tried to get into the source code the understand the model better. I think I may have found a mistake. I believe that the mechanical losses are wrong when selecting specified mechanical efficiency. I enclosed two screenshots where I explain why I believe there has been a mistake.
For the expression of Wdot_mech, I have put the expression that should be (in my opinion) be correct.

If you still believe the equation used in the code is correct, I would very much appreciate an explanation.

Thank you again and happy new year !

[ibell]

I think the formula is indeed wrong, but not in the way you write.

First, let's agree about how to define the mechanical efficiency. I would say it is the indicated power divided by the total mechanical power which is the indicated power plus the mechanical losses. Thus:

$$\eta_{me} = \frac{W_{pv}}{W_{pv}+W_{mech}}$$

and solving for mechanical losses, you have

$$ W_{mech} = W_{pv}*(1/\eta_{mech}-1)$$

[ibell]

What do you think?

[davideziviani]

Actually in our development version at Herrick we fixed this issue, but forgot to commit

[caskandavor]

@ibell Thank you for your answer. I agree with what you wrote and it's actually how I corrected it in the code (since $W_{mech}$ is only computed afterwards we indeed need to use $W_{pv}$ ).

There is however something else that I believe might be erroneous. It is the way Wdot (Power of Compressor) is defined:

Here it is said that self.Qamb is positive if heat is being added to the lumped mass. If we consider this equation to be a conservation equation on the refrigerant, it makes sense (if heat is lost to ambient, self.Qamb is negative so we need to provide this work in addition to the enthalpy change of the gas). However this is not consistent with the way self.Qamb is defined:

The heat lost to the ambient is modeled with Newton's law of cooling $Q_{amb}=h_{shell}\cdot A_{shell}\cdot(T_{shell}-T_{amb})$, which will be positive if heat is being lost from the lumped mass.

When the residuals for the overall energy balance are computed, the sign of Qamb is flipped, and so is the convention for heat transfer signs (Qamb is positive if heat is being removed)

For this reason, I tried to flip the sign of self.Qamb in the first screenshot equation and align myself with the last convention (Qamb is positive when heat is being removed). I did a quick study comparing the before and after this modification in the code. Both cases have the exact same parameters, each plot is obtained by running over 3 increasing values of HTC (the heat transfer coefficient inside the scroll compressor), but h_shell is kept constant (please note that the values of HTC on the x-axis are not the values, just the number of the run).

As you can see, with the un-modified equation, the higher the heat transfer coefficient, the lower Power of compressor Wdot is, which does not seem resonable. Also, while the evolution of the electrical power and the gas power have the same evolution, the "power of compressor" has a different one, which seems odd to me.

With the modified equation, the latter effect is removed, and the curves now follow the same trend. However there still is the problem that the power consumption decreases as the HTC increases and the heat losses increases coincidentally. This does not make physical sense to me. I expect the power consumption to increase as the heat lost to the ambient increases as we have to compensate for it. To be more clear, here is a Sankey diagram I made to describe what I think should be the power flow, using the traditional convention that heat is positive when added to the control volume:

What do you think about this ?

Thanks again and sorry for the long comment.

[XD1001]

My thought is that the you may mis-interpret the meaning of variables. "Wdot" should be the energy received by the refrigerant from the compressor instead of "power of the compressor" and does not involved in calculations of the total power input of the compressor. Please notice that in both figures (modified and un-modified), the Wdot_mechanical and Wdot_pv were not affected by the Wdot value at all. If the heat transfer increases while the total power input is constant, the energy received by the refrigerant will decrease, which explains the trend you observed in the left sub-figure. Therefore, judging the sign of Qamb in different equations may be misleading.

[caskandavor]

@xinding1207 Agreed, Wdot is indeed not involved in the calculation of the total power input (hence the fact that despite changing the equation from one figure to the other, the Wdot_electrical and Wdot_pv remain the same). I also agree that the sign of Qamb can be different depending on the equation and the control volume studied and that it could lead to errors.
However, the sub left figure is obtained with the code un-modified, and it shows that the power of the compressor Wdot (which I agree, given its definition, is the energy received by the refrigerant from the compressor) decreases as the heat transfer increases. Note that the heat transfer to the ambient is positive, and from the convention in the code, it means that heat is lost. If heat is lost, the power given to the refrigerant should increase to compensate the heat loss.

As you can see in the previous comment, in the code, different conventions are used in different parts of the code for Qamb.
I simply believe that the one used to compute Wdot is not correct.

Also, since we've established that Wdot has no influence on the total power input Wdot_electrical and Wdot_pv, let's forget about it altogether for my next point. We can see that Wdot_electrical and Wdot_pv also decrease as the heat transfer with the ambient increases and heat is being lost. That should be the other way around for the reasons stated before.

I am still trying to figure that out, I will keep you updated. Please do comment if you have an idea or see a flaw in my reasoning !

[caskandavor]

One thing that I had not taken into account is the parameter suction_fraction, which is the fraction of the motor losses going in the suction gas. For now, it was set to 1, so all the losses from the motor were heating the gas. Redrawing a sankey diagram:

The way I see things, Wdot ( $W_{comp}$ ) is or should just be another way to write the total power input (so $W_{el}$ ) since Qamb represents all the losses anyway!

[ibell]

It could be helpful to read the paper about PDSim, that might clear up some of these points.

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