I've got an issue about how to raise the condenser vacuum by reducing the exhaust steam temperatures, who come as the Temperature hot inlet of condenser. Is it really true, that if we can reduce the temperature of steam that will condense in condenser, so the vacuum of condenser will raise?
In my case, I've got turbin with its exhaust pressure design 64 mmHga. Exhaust Steam that coming to condenser is 47oC, and the condensor pressure is 85 mmHga. Can we decrease the pressure of condenser by reducing the temperature of the steam (maybe by using the hood spray system)?

There are a variety of possible reasons for getting 4-5 deg C higher than design conditions. Have you identified the cause ? After uncovering the real factor you'd be in a better position to decide on the desirable procedure to reduce temperatures and increase vacuum at the final surface condenser, if at all feasible.

The exhaust pressure is usually equal to the saturation pressure , based on a  saturation temperature equal to the the cooling water temperaure plus 12 C. If the cooling water temperature is too high ( as on a hot sumer day), then the condenser pressure will be high. You can prove this by plotting the exhasut saturation temperature vs the cooling water temperature , and the 2 lines should be parallel over the year, separated by about 12 C. The temperature difference will increase over 12C if you have fouling of the condenser tubes ( on the water side) or  if the circulating water pumps are not providing the full design circ water flowrate.

Another reason not often considered in condensers for causing a lack of correspondence between total pressure, and saturation pressure is superheat.  Yes, superheat coming from an inefficient or overloaded Boiler Feedpump Turbine (BFT) exhaust, or a high energy in-leakage coming from a defective trap or the like (valves(Safety Valves) left open, drain and dump valve seats defective) on a source capable of supplying high energy, like a stop valve drain, a feedwater heater extraction line drain, a reheater piping drain, etc. etc., and there are many possibilities.

Condensers, unlike feedwater heaters are ill-equipped to handle other than saturated or low quality steam.  Superheated steam vapor will blanket the condenser tubes and act like non-condensible fouling.  U-values for this sensible heat transfer are pathetically low because the renyolds numbers (velocities) are virtually laminar in this region.

So, check all drips and drains that dump to the condenser for abnormal conditions.

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