Steam turbine efficiency 1

[AndreChE]

I want to calculate a steam turbine efficiency. The expansion is from high pressure steam (104.4bar,468ºC) to 0.112 bar. I don't know how to calculate the exhaust steam quality and the efficiency. The isentropic expansion I can calculate but the real one I can't get it....

Can anybody help me?

AndreChE

 

[davefitz]

you have not provided enough information.

The efficiency of the steam turbine will be a function of whose turbine you bought as well as how you are operating it.

For example, there is an inlet throttling loss across the inlet valves , also , there are different exhaust losses depending on the design of the last 2 rows of blades. Individual stage efficiencies vary greatly today, since some major suppliers use 3Dcad-cam to design the blades and numerically controlled milling machines to cut teh most efficient blade geometries, but if you bought the turbine from a old technology company then these improvements were not included in your machine.

If you know the power output as well as the steam consumption you can directly calculate the efficiency

 

[AndreChE]

The steam consumption is 80t/h. The power output...should be calculated but I don't know how to calculate the steam quality in order to compare the isenthalpic expansion with the real one.

 

[katmar]

There is a very simple (and free) turbine steam consumption calculator available at

http://www.katmarsoftware.com

You could play with it and try various efficiencies (one of the program input requirements) until you match the actual steam outlet conditions. This would give you a rough idea of the actual efficiency.

regards
Harvey (Katmar)

 

[rmw]

Katmar,

I used your program in just that way to zero in on the efficiency of a 3 stage turbine just yesterday. I knew the mfg's stated water rate, and the steam inlet and exhaust conditions. I really appreciate that little program, and use it quite occasionally, as well as recommendint it to others.

rmw

 

[davefitz]

If you have the original mfr's data you can calcualte teh current efficiency as follows.

For a single turbine in one casing, the expansion line curve is based on 3 processes:
a) throttling loss across the inlet control valve
b) epxansion across the blades
c) exhaust loss

The original vendor data sheet probably states the performance with valves wide open ( VWO), so there is a likley 1/2 = 1% percent pressure drop across the inlet valves. On a H-S diagram, the H is constant and the S will increase due to the pressure drop of 1/2-1% of the inlet pressure.

The next step is to calculate the blade flow factor K1 or K2. For any turbine at constant speed, the relationship between the steam flow into the 1st row of blades and the P, T, and sv is :
W= K1*SQRT ( P / sv,i)
W= flow, mass/time
P=1st stage inlet abs press
sv,i= inlet specific volume, length^3/mass
K1= proportionality constant as requried for units chosen

A simpler approximation is :
W=K2*P/SQRT ( T, abs)
where T,abs is the absolute temp entering the 1st row of blades

Next step is plot on the H-S diag the expansion across the blades knowing the mfr's defined UEEP ( used energy end point)- this is the enthalpy of the steam rejected to the condenser, and includes the exhaust loss. Deduct from this enthalpy the mfr's exhaust loss ( they did give you the exhaust loss curve, didn't they?)and the result is the enthalpy leaving the last row of blades not corrected for exhaust loss. This endpoint ( Ho, So) and the 1st blade start point ( Hi, Si) can be connected with a straight line and this represents the stge effciiency of the blades tehy gave you. This can be anywhere from 82-95% efficient , depending on the technology used.

So ou now know the inlet flow factor , the stage efficiency , and you have the exhaust loss curve . To determine the off-design output and overall efficiency, do the following:
a) knowing the P and H entering the throttle valves, determine what the throttle valve outlet pressure must be in order to meet the relationship for the 1st stage flow faactor , define above. This is involves using the steam tables in an iterative manner. For a first guess, the pressure at the outlet of the throttle valve is roughly linearly proportional to the mass flow.
b) knowing the 1st stage inlet pressure,H and S, plot this point on the H-S diagram. The expansion process down to the condenser pressure will be a line that is exactly parrellel to the mfr design expansion plotted earlier.
c) the end point must have the exhaust loss deducted from it. This involves calculated the exhaust velocity at the current condenser pressure .

 

[AndreChE]

Katmar

Thank you for the tio and program but "my" turbine inlet steam pressure is above 100 bar...

 

[AndreChE]

I think anyone has really understood my question....

Is it possible or not, with calculations, to calculate the real turbine efficiency because the real problem is to know the exhaust steam quality, in order to know the real expansion (not isentropic). I know the final pressure but not the steam quality....

I think I don't have enough data to do it!!
With efficiency, I can calculate it...I want the opposite, the turbine efficiency.

I can calculate the ratio Energy to Turbine/Compressor Energy but...this is not the turbine real efficiency.

AndreChE

 

[DeltaCascade]

If I recall some work done last year correctly, its an iterative calculation where you guess quality and calculate entropy of outlet stream (condensate and sat steam), and keep guessing until you satisfy the isentopic expansion. Something like that... good luck

 

[davefitz]

You can calcualte the real turbine efficiency in several different ways.


If you use the ASME power test code PTC, you would monitor the the steam temp + Press at each extraction point and use the "enthalpy drop" method to compute the internal stage efficiency. If the extraction steam is 2-phase then you would also need to do a heat balance on the feedwater heater to get the extraction enthalpy.

You can arrive at teh enthalpy of the L-1 blade exhaust steam by performing an energy balance on the condenser , which would require measuring the flow and temperature of tehe circulating water, or you can conduct and overall energy balance of the steam turbine assuming you have accurate data on teh motive steam.

I suggest you read up on the ASME PTC.