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Adding Uncontrolled Admission

Adding Uncontrolled Admission

(OP)
To make things simple lets say we have a two stage turbine.

The current configuration has only one steam source through the V1 valve gear. For discussion lets say the turbine inlet steam is 1000 psi at 900 deg and the turbine area is sized to flow 1,000,000 lbs/hr of steam (even though more stages are actually designed for efficiency stay with the two stage machine).
This configuration has a specific 1st stage shell pressure curve as a function of flow which is driven by the second stage area. So at a given flow i.e. 500,000 lbs/hr, the admission pressure to the second stage is at 700 psi. If the flow is increased to the full load, this shell pressure or second stage admission pressure will rise due to the resistance the second stage area provides.

Now for the question: A customer would like to introduce an admission inbetween the first and second stage for which he has 850,000 lbs/hr 850 psi 850 deg F steam available for this turbine AND another turbine that is fed from another steam source.

At a given load for the turbine we are looking at, how do we know how much steam will be pulled in from the admission line if there is no control valve. In this example lets say we want to operate near the 500,000 lb/hr load point with the corresponding stage pressure at 700 psi. My calculations say that with a 10" pipe, that the 850 psi steam flowing into the 750 psi shell, will pull all of the 850,000 lbs/hr that is supposed to feed both turbines, and starve the second turbine of steam or, trip the boiler offline because it cant supply steam fast enough to maintain the header pressure. Do i need to size the pipe such that it acts as an orifice and restricts the volume of steam? I know a control valve can accomplish this, but i can not find a valve to handle such a large pressure drop which maintaining the wide range of operation needed. Ideally i would like to only pull in 275,000 lbs/hr at all load points, whether the steam is going from the header line of 850 to the shell pressure of 500 or 800.

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