Develop head vs flow for a radial compressor 1

[akr768]

I have the characteristic curves such as head coefficient vs flow coefficient and flow coefficient vs compressor efficiency. I would like to develop a head (or deltaP) vs flow rate curve mathematically, ultimately determine the discharge pressure. The compressor is not an off-the-shelf item, so cannot rely on a vendor to provide this curve. The compressor is not fully operational yet to test for the characteristics. Is there a way to theoretically estimate pressure head vs flow curve? I know the RPM (10k-60k), flow rate (0.4-1.6 kg/s), pipe dimensions (0.75" to 1") and compressor inlet conditions (78 bar and 35 C), apart from the curves. I have used the following approach.

1. Used the axial velocity and rotor speed to determine the flow coefficient.
2. Used the empirical relation between head coefficient and flow coefficient to determine the appropriate value of head coefficient.
3. Used the head coefficient to determine the enthalpy, since the rotor speed is know.
4. Calculated the pressure head from enthalpy and then the discharge pressure.

Is this approach correct? Any help is appreciated. Thank you.

AKR

 

[rotw]

its not complicated. Considered a single compression stage curves, [label A] for a given curve point (fi1, tau) and (fi1, etap) on a constant speed curve (rpm), proceed as follows:
knowing the shaft speed rpm and diameter D2 you can calculate the peripheral speed U2.
knowing the peripheral speed U2 and diameter D2 and flow coefficient fi1 you can calculate actual inlet volume flow Q1.
knowing the peripheral speed U2 and head coefficient tau, you can calculate head H.
knowing the efficiency etap (polytropic, but its the same reasoning if isentropic) you can calculate polytopic head Hp.
this gives you a new point (Q1, Hp).
Go back to [label A] and proceed with next point on curve and repeat procedure.


Life is not about waiting for the storm to pass. It's about learning dance in the rain.

 

[rotw]

If you want to derive pressure or pressure ration vs. flow or need flow in mass flow unit, in general you will additionally need an equation of state.

Life is not about waiting for the storm to pass. It's about learning dance in the rain.

 

[akr768]

Thanks for your response, rotw.

Seems like my approach is right! Thanks for confirming it. And I do have the equation of state for the fluid. Given the inlet conditions and the calculated exit enthalpy, can the pressure head be used to determine the discharge pressure? Since I need two variables for gas phase to determine other properties. I assume that would be the case, since both variables denote the exit state.

 

[rotw]

Yes. In general, if you know the end points pressure and temperature you can calculate polytropic head and efficiency using Schultz or end point iterative nethod. In your case if you know the head and efficiency you can derive pressure (and temperature) via iterative or direct procedure too. Somehow which method you select all depends on the level of accuracy needed and departure from ideal gas behavior (example high pressure application, etc.). Either build your own automation tool for this or use some online tools; the later is rather more adequate for punctual calculation than multiple points typically needed in curve generation but can work too and would be the most precise.

Life is not about waiting for the storm to pass. It's about learning dance in the rain.

 

[akr768]

Thanks for your quick response again.

For now, I'm only interested in the head vs flow curve and the compressor discharge states - mainly to analyze the deltaP rise through the compressor as the inlet conditions or RPM or flow rates change. The polytropic efficiency may be required later, so I will keep your suggestions in mind.

 

[rotw]

The polytropic efficiency may be required later, so I will keep your suggestions in mind.

My comments in last post primarily apply to determining 'the compressor discharge states'.

Life is not about waiting for the storm to pass. It's about learning dance in the rain.

 

[akr768]

I already have the compressor efficiency information through the characteristic curves. I'm determining the discharge states using this efficiency data. So, I don't think I have to calculate the efficiency again. Please let me know if I misunderstood.

 

[rotw]

Like I said;
Quoted
In your case if you know the head and efficiency you can derive pressure (and temperature) via iterative or direct procedure too.
Unquoted
Starting from head and efficiency, to calculate what you call "the compressor discharge states", you either use a direct method (in short, use a formula) whereby you will have to scarify accuracy to a certain extent (for example you will have to consider the isentropic exponent to be constant across the compression process and set it equal to the one at inlet; and this was just one example). Either you use an iterative method. In all cases, you need an equation of state.

Life is not about waiting for the storm to pass. It's about learning dance in the rain.

 

[akr768]

Okay, thanks for the clarification.