Question regarding rankine cycle

[tusharkhaire]

On what factors does the pressure in condenser of a rankine cycle depend?

The lesser the pressure in the condenser, the more expansion work will be done by the steam turbine. And depending on the pressure in the condenser, the temperature of the steam entering the condenser will depend. because lesser the pressure in the condenser, more will be the expansion work by turbine and hence lesser will be the temperature of the steam entering the condenser. And the pressure in the condenser must depend upon the temperature and amount of cooling water flowing through it. This is what i used to think.

But then i read in the textbook that the minimum temperature in the condenser is equal to the saturation pressure of the steam corresponding to the saturation temperature of the steam entering the condenser. So this got confusing. How the temperature of the steam leaving the turbine will decide the minimum possible pressure in the condenser?

Does'nt the temperature of the steam leaving the turbine itself is dependent on the pressure in the condenser? because that is why we would get greater work of turbine with lesser pressure in the condenser. please help me clear this concept.
THANK YOU !

 

[SteamKing]

You are getting ahead of yourself. The pressure in the condenser is the same as the exit pressure from the last stage of the LP turbine (more or less) because the steam system (turbines, piping, etc.) after the throttle is evacuated prior to use. There is no other pressure in the condenser except that provided by the exhausting steam from the turbine. For practical reasons (like controlling the erosion of turbine blades due to the formation of water droplets in the steam, the exhaust pressure from the turbine is a design point for the whole system.

 

[tusharkhaire]

Thanks a lot for your answer. It has cleared most of my doubt. But has raised new questions.
1) Just consider a simple rankine cycle having one turbine, a condenser, a pump and a boiler. The steam expands adiabatically in the turbine, work is done, and hence the temperature of exit steam from turbine is lesser. What factor decide this exit temperature? What changes i have to make in the cycle to reduce this exit temperature so that more work can be obtained from the turbine. Is there any theoretical lower limit to which this temperature can be reduced?

2)This is a sentence from my textbook..."The minimum absolute pressure of the condenser which can exist in a condenser is equal to the saturation pressure corresponding the the saturation temperature of the steam entering the condenser." Well... the saturation temperature of the steam entering the condenser is the same as the temperature of the steam entering the condenser. So why it is specified differently?

3)Further the book says that the actual pressure in the condenser is greater than the minimum pressure that can be obtained and that is because of the air leakage inside the condenser... but now because of the presence of air in the condenser the turbine should face a back pressure. And so the expansion of the steam will be less in the turbine and so now the exit temperature of the steam from turbine (or the temperature of steam entering the condenser) will be greater than the exit temperature in the absence of air leakage. So in this case it is the pressure inside the condenser that decides the exit temperature of steam leaving the turbine and not vice versa as stated by sentence in the above point.

I REQUEST YOU TO ANSWER ALL THREE POINTS. THANKS A LOT!

 

[SteamKing]

1. The theoretical lower limit for the turbine exhaust will be controlled by the temperature of the coolant circulating through the condenser. In order for heat transfer to take place, the exhaust steam must be at a higher temperature than the maximum expected temperature of the coolant.

2. I think this sentence is saying, in a roundabout way, that the steam conditions exiting the turbine are the same as those in the condenser, i.e., no losses are assumed between the turbine and condenser because of the close proximity of the two in steam plants. The statement as written is a bit of a tautology.

3. The lowest absolute pressure which is commonly found in steam plant condensers is 1.5" Hg. This corresponds I believe to a temp. of about 91F. A perfect system would be able to maintain these conditions as long as the coolant can be supplied with a temperature lower than 91F. Obviously, if air leaks into the condenser and raises the internal pressure to, say, 3" Hg abs., then the turbine will have to work against this higher pressure. I don't think you can take the statement in 2) as a guarantee that the cycle won't be affected by leaks in the condenser.

Steam plants are designed to work between certain turbine inlet conditions and certain turbine exhaust conditions. Obviously, if there is a crack in a steam pipe, a turbine casing, or a condenser shell, the system moves away from these design conditions.