steam turbine pressure ratio Vs steam flow rate 1

[revata]

how does one calculate the pressure ratio (inlet to outlet steam pressure) when the steam flow through a given steam turbine is decreased?

 

[poetix99]

In a meaningful sense, the "pressure ratio" across the turbine is fixed, since the supply pressure and the exhaust pressure are (often) fixed.

A steam turbine can be thought of as a series of flow restrictions. In general the only restriction that varies is the inlet and/or first stage. The governing valve(s) open or close in order to admit more or less flow (in response to control signals). It is across the governing valves, and on the first stage that the pressure ratio changes the most as the amount of steam flow changes. (The last stage can also see significant variations in pressure ratio, when the exhaust pressure is fixed, as is usually the case.)

If the flow of steam is at the local sonic velocity (also referred to as "critical flow&quot at the first stage (or elsewhere), that is the easiest condition for which to relate steam flow to pressure, or pressure ratio, if the nozzle area is known.

In any case, a good text on the flow of compressible fluids (such as Ascher Shapiro's classic text) will give all of the necessary equations for sonic and sub-sonic compressible flow.

 

[davefitz]

poetic99 is mostly right, but some new operating mehtods are being used with the new, foreign made steam turbines.

If the pressure ratio is that measured by pressure transmitters truly monitoring only the turbine's process conditions and not any intervening valves, then poetix 99 is right. Newer steam turbines have loading procdures which utilize bypass valves, throttling of the intercept valevs, and proportioing flow at low loads bewteen HP and IP turbines that makes a mess of simple pressure ratios, if the pressure transmitters are also separated by valves.

 

[revata]

poetix 99 is correct if the supply and exhaust pressure are fixed and the steam flow is constant. However say for example a second hand (used) steam turbine were to be used in a plant which as a steam generation capacity that is 75% of the designed flow capapcity of the steam turbine. Would not the pressure drop across the steam turbine be reduced since the pressure drop is proportional to the square of the velocity which is now reduced due to the lower steam flow. All exit conditions are assumed to be the same for both cases. This is statment is based on considering the steam turbine as a series of flow restrictors as mentioned by poetix 99

 

[davefitz]

revata:
The principle that pressure drop is proportional to the square of the flow only holds for incompressible fluids. In the case of a steam turbine, it generates power by virtue of a transfer of kinetic energy from the gas molecules to the rotating blades, and the tubine geometry is carefully designed to maximize the efficiency of this transfer . This is maximized when the rfelative velocity of the blade to gas bulk flow is about 50% of soundspeed.

bottom line is that for a constant speed turbine with constant area Ai at blade row "i", the relationship between flow and pressure is :

W= KAiPi/ SQRT(Ti+460)
W= flow , lb/hr
K= proportional constant
Ai= flree flow area between blades at row i, ft2
Pi= pressure entering row i, psia
T= temperature entering row i, F

each succeeding row has a larger area A, so the pressure ration between any set of rows is a constant ratio ( aproximately), and this ratio slightly varies only as the ratio of specific heats Cp/Cv changes over large changes in process conditions.

regarding a new vs old turbine, as the turbine ages, the clearance between blades increases due to solid partical exfoiliation erosion, so A increases at the first few rows of blades. The area A decreases over time at teh middle of an old turbine due to build up of deposits.

 

[revata]

Davefitz, thanks for your comments on steam turbine pressure vs steam flow.

Does this mean that if you had a steam turbine with the following design conditions;
inlet steam pressure - 28 barg
inlet steam temperature - 370 deg. C
outlet steam pressure - 1 barg
steam flow rate - 24 TPH

Using the equation given by Davefitz, the corresponding inlet steam pressure would be 21 barg for a steam flow of 18 TPH. That is the inlet steam pressure is directly proportional to the steam flow rate provided all other conditions remain constant (incl steam temperature and outlet pressure).

 

[davefitz]

revata:

Ues, that is exactly right, as long as you are not considering any throttling of pressure across the inlet control valve. Considering only flow across the turbine stage , you have the right answer.

 

[revata]

davefitz
thanks for your help