Head Equation for the Expander/Turbine

[silentsound]

Please elaborate the HEAD ESTIMATION EQUATION for the expansion of the gas through Expander/turbine?
The similar equation for the compressor is in attachment;
Can some body help me similar equation for the TURBINE/EXPANDER??? Any reference please?
Regards

 

[EmmanuelTop]

For expansion work, you need to know the following parameters:

1) Fluid flow rate
2) Isentropic enthalpy change of the fluid
3) Expander efficiency

Multiplying these 3 gives you the actual extracted power.
See the thread

http://www.eng-tips.com/viewthread.cfm?qid=377170

and the attachment.

Dejan IVANOVIC
Process Engineer, MSChE

 

[EmmanuelTop]

The term "head" is pretty much meaningless for expansion process.

Dejan IVANOVIC
Process Engineer, MSChE

 

[silentsound]

Thanks EmmanuelTop,
I have to convert the Pressure ratio in maps in to head term to be used in Aspen Hysys as it takes only head instead of pressure ratio

 

[silentsound]

I am looking for head drop equation?

 

[EmmanuelTop]

What kind of data you have to plug in the simulator? Elaborate more on the problem. We can see here only what you post, we have absolutely no idea of anything else.

Dejan IVANOVIC
Process Engineer, MSChE

 

[silentsound]

I have to plug in the data for volume flowrate vs head and volume flow rate vs efficiency, in series. to calculate the steady and dynamic response of the Gas turbine. I have data of mass flow rate versus pressure ratio which needs to be converted to volume flow rate versus head?

 

[georgeverghese]

You have data on mass flow vs p2/p3 for a given speed of the turbine, but what about T2 (after the combustion operation)? T2 will depend on how much fuel is injected into the combustion chamber.

 

[apetri]

as suggested by others to simulate dynamic response of the Gas turbine you would need additional data and a different software,
with your software you can possibly solve a turbine from a thermodynamic point of view on specific points (I do something equivalent in Excel with Prode library) but analysis of dynamic response would require more data and more complex models,
there are specific software tools or perhaps you may define a procedure in Matlab or a similar tool..

 

[silentsound]

Dear Guys,
Yes I have turbine inlet and turbine outlet temperature. The inlet flow rate and gas composition is defined.MY problem is well defined and degree of freedom is zero at the moment. The solution is there.
The Only question at the moment is to plug the series of volume flow rate vs head. And for head estimation I need an equation? Please specify this equation????

 

[apetri]

not sure why you need head (Prode requires dP) but...
can't you convert by taking in account density ?
Make sure about the units for head

 

[silentsound]

To include performance maps of the turbine/expander in to my model. So that the number of inputs reduces to speed specification only.
My modeling tool require performance map data in terms of volume flow rate vs head for different speeds. For this purpose I require head equation as a function of pressure ratio.
The similar equation for the compressor is;
H = {k/k-1}[ZRT][(p2/p1)^(k-1/k) -1] please see the attachment for full equation of compressor.
If you have similar equation for turbine please specify???

 

[apetri]

the gas law is good in both cases, but...
why do you wish to enter that value ?

 

[silentsound]

Aperti,
to reduce the number of inputs which results in more better control during dynamic modelling.
But how gas law helps me to estimate the HEAD for expander????
Have you seen the compressor head equation in attachment of my last reply? I need similar equation.

 

[apetri]

for compressors and expanders,
if you have (see your previous post) a series (dP vs. flow) of operating points, use these (with proper conversions, taking in account density, when required) as inputs in your software

 

[silentsound]

The tool requires series (flow vs head) instead of flow vs Pressure ratio
I have to convert the available Pressure ratio in to head?
For which I require head as a function of Pressure ratio?

 

[georgeverghese]

If you run a separate simulation for an expander, and plug in the values you know so far with a simple thermo model (SRK or PR), the output from the simulator should state what the head is.

It is also possible to do this calc manually to get an approximate value for head; see Perry Chem Engg Handbook, 6th edn, chapter on process machinery, expanders subsection. This subsection is retained in the 7th edn also at page 29-46.

 

[silentsound]

Hi georgeverghese,
Many thanks for the reference.
The equation available in the Perry's 6th or 7th edition is quite generic and does not account the k = cp/cv.
Also the separate simulation of expander to estimate the head and then use it in gas turbine is last option in my mind as data is quite lengthy.

 

[georgeverghese]

The k value is indirectly implied in the temp drop for the expansion in the equation in Perry - in this case it is mostly N2, and pressure drop is not very high, so the k value is constant throughout the expansion.

If you are running on Pro II, using a controller unit operation will speed up the trial and error for isentropic efficiency. The same facility would be possible with the adjust operation in Hysis.