as we are strating centrifugal pump with discharge valve close and can not start positive displacement comp. with disch. valve closed
You don't normally start compressors against a closed valve. Some compressors can handle this within their own controls that will dump the air automatically. If you need to control the discharge, it would be better to install a tank in line and control the discharge from the tank and not directly at the compressor.
I don't like the idea of dead-heading a pump that's not supposed to be dead-headed. I would check the manual for startup instructions, then contact the company representative and propose your solutions. This device may have a bypass loop, which is very useful for startup. If this device compresses flammable materials (methane, hydrogen) proceed with great caution, and hopefully with a couple of technicians who know this startup well.
You should probably be talking to a local factory representative for both the pump and the compressor and explain to them what you are trying to do. I am sure they would be happy to advise you. Sure beats damaging yourselves or others by doing this wrong.
I assume you are asking about a centrifugal compressor being driven by a gas turbine. You didn't state the service the compressor was in but it is possible in some services for the centrifugal compressor to add a load to the gas turbine's output shaft during the starting cycle. By having the valves closed, there is only the load from compressor wheels) and shaft being accelerated to operating speed. This would permit the gas turbine controls more lee way to get the turbine speed under control before adding significant load to the output shaft. Another consideration is the need to load the compressor in a manner that would get it past the surge point and into a stable operating regime. This can best be done with the compressor at operating speed and a fairly quick addition of load.
No, with no discharge flow, there's no suction flow the compressor will immediatley go into surge. However, if a Low-Flow recycle control is installed, upstream of the discharge valve (which should recycle back to the suction drum to prevent heat build-up), then the compressor will operate without surging and without lifting the discharge safety valve but the condition should be corrected ASAP. (A Centrifugal Compressor will normally be fitted with a Low flow recycle system taken off from the aftercooler discharge line for use during start-up but, if a sudden low flow condition occurs and the recycle doesn't have time to activate, a Low Flow alarm and trip system will shut down the machine). Also, starting a centrifugal pump against a closed discharge is quite common practice as long as it too has a low flow protection recycle back to the suction vessel. This Low flow recycle is common where the discharge has a liquid level or flow control valve installed and may close down during normal operation. This valve would be operating as a 'Split System' controller in conjunction with the Low-Flow recycle control valve. PD pumps without discharge pressure safety protection should NEVER be started against a closed discharge, the hydraulic pressure build up will be instantaneous with possible disastrous results or stalling of the pump.