# Steam Turbine thermodynamics

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1. Jan 14, 2017

### JohnPickerill

I have a thermodynamics question I'm having difficulty with...

I have a steam generator heated by a 39MW nuclear reactor that powers two 4.5MW turbine generators. It produces dry saturated steam at 330psig, and enters the turbine at those conditions. It exits the turbine to a condenser maintained at 28inHg vacuum. The feedwater enters the steam generator at 102F.
I'm trying to find the required mass flow rate of steam through the turbine to produce 4.5MW, but the answer I'm getting is unrealistically high and can't find the mistake. Was hoping to get a second set of eyes for help. Here's the calculations I'm using:

Enthalpy of feedwater entering steam generator = 70 BTU/lbm
Enthalpy of steam exiting steam generator = 1205 BTU/lbm
Therefore, the steam generator raises the enthalpy by 1135 BTU/lbm

At full power, the steam generator can produce the following steam flow:
39MW x lbm/1135BTU x 3.412BTU/W x 1000000W/MW = 117000 lbm/hr

Comparing that to the steam flow required by each 4.5MW turbine:
Enthalpy of steam entering turbine = 1205 BTU/lbm
Enthalpy of steam exiting turbine = 1106 BTU/lbm
Therefore, the turbine drops the enthalpy by 99 BTU/lbm

At full power, each turbine produces about 4.5MW of mechanical power, therefore each requires the following steam flow:
4.5MW x lbm/99BTU x 3.412BTU/W x 1000000W/MW = 155,000 lbm/hr
There are two turbines so total required steam flow = 310,000 lbm/hr.

So by my math is trying to say the turbines require over twice as much steam flow as what the steam generator is rated for. But this is an actual, built and operating 39MW nuclear power plant. What mistake did I make in my calculations or assumptions?

2. Jan 14, 2017

### anorlunda

You did not mention % moisture at the turbine exit. At 29 inches of mercury, saturated steam 1098 BTU/lbm, saturated water 51 BTU/lbm.

3. Jan 17, 2017

### Staff: Mentor

I agree with @anorlunda that, if the change in entropy of the steam were zero in the turbine, the steam would come out as a combination of liquid and vapor. In this case, the enthalpy of the exit stream would be less than 1105 BTU/lb, and that would lead to an even greater discrepancy. Maybe they expect you to assume that there is an increase in entropy, so that the steam comes out superheated and the exit enthalpy is higher.

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