Calculating Steam turbine steam flow

At work we derive the steam flow entering the HP turbine stage of a

500MW steam turbine using the following equation:

Steam_flow = 735.7 x( 1st Stage steam pressure ) / Sqrt( 1st Stage steam Temp )

where 1st Stage pressure is in MPa absolute and 1st stage temp is in Deg K.

The calculated value agrees well with the measured feedwater flow into the steam drum.

However, not being from a thermodynamics background nobody can tell me how the equation is derived, it just always seems to have been always like that!

Can anyone direct me to information that explains how the steam flow through a turbine is proportional to the inlet pressure divided by square root of inlet temp ?

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This describes the "swallowing capacity" (my translation) or the turbine contant.

It can be derived from Stodala's cone rule. One derivation (which I don't think is complete, however) is in

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The general expression may be written as: m_dot^2=C_T^2*T/(p_i^2-p_o^2) under asssumption of an ideal gas.

As a Steam turbine expands to almost to vacuum and the inlet temperature is kept constant we can derive: m_dot=K_T*p_i

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Brian Elmegaard

Steam turbines are typically designed so the flow is predominantly controlled by a choked inlet nozzle. For a high pressure steam turbine the nozzle is typically a round or elliptical convergent/divergent supersonic nozzle. For axial gas turbines and low pressure steam turbines the nozzle might be an airfoil cascade.

derive the following equation for choked mass flow: w = A*Cd*Pt,in*sqrt{ k / (R*T) * [2/(k+1)]^[(k+1)/(k-1)] }

So for a choked device the flow is a function of: A - Area Cd - Discharge Coefficient (~1 for a well designed nozzle) Pt - Inlet Total Pressure Tt - Inlet Total Temperature R - Gas Constant k - Specific Heat Ratio

Obviously your equation assumes several of these parameters are constant and lumps them into the coefficient, 735.7.

Even if the nozzle is not fully choked most turbines behave choked and operate at nearly constant flow parameter, w*Pt*sqrt(k/(R*T))/A. This means that the only way to change the flow is to raise inlet pressure or reduce inlet temperature, and changing the back pressure has no effect on flow.

The flow of some gas turbines, and possibly some low pressure steam turbines may not be completely controlled by the nozzle. If the rotor "chokes" before the nozzle then the flow will be controlled by the rotor. This will cause a variation in flow parameter with the rotational speed of the engine. There's nothing inherently wrong with a turbine designed this way, but it's usually considered poor design practice because it adds difficulty to predicting flow, and may cause difficulty in matching compressor and turbine design points in a gas turbine engine.

Dave Parker Turbine Design Engineer West Palm Beach, FL

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