On the critical conditions of safety valves: sound speed calculation
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When calculating safety valves, there is a determination of whether a condition is critical or subcritical; does reaching a critical state mean reaching the speed of sound? Is this determination formula related only to the pressure adiabatic coefficient? In other words, it can be understood that when the pressure difference reaches a certain level, a critical point is reached; it seems that this has nothing to do with the flow rate. However, the discharge volume of the safety valve is fixed, which means the flow rate remains constant. If we use the critical value criterion, the critical value corresponds to the speed of sound; in that case, the leakage rate becomes the speed of sound multiplied by the diameter of the pipe. Moreover, the sound speed is very high; even 0.3 times the sound speed amounts to 100 m/s. Where in a safety valve pipeline could there be a speed of 100 m/s? Additionally, this does not match the volume of flow released – how can this be understood?
The so-called critical and sonic speeds are not the same thing; what is actually referred to is choke flow, a condition in which the mass flow rate through the throat no longer increases as the pressure difference rises, but instead reaches a constant value. You can search for it on Baidu. The outlets of the vast majority of safety valves reach the critical point, as the back pressure is generally very low. As for a flow velocity of 100 m/s in the safety valve pipeline, this is quite normal; generally, the Mach number in the branch pipes can reach 0.7, while it should not exceed 0.5 in the main pipe
In essence, it is assumed that the flow velocity at the minimum throat diameter of the gas relief valve does not exceed the speed of sound; in other words, the maximum release rate remains constant regardless of the pressure difference. API 520 provides specific descriptions and calculation formulas for this. This determination is based on the relationship between the discharge pressure of the safety valve and the back pressure, in order to determine whether the extreme discharge condition can be achieved; accordingly, the appropriate calculation formula is selected. If the back pressure in the pipeline at the outlet of the safety valve is too high, the pressure difference across the valve during discharge is not sufficient to reach the extreme discharge condition, and as a result, the discharge capacity of the safety valve decreases.
This post was last edited by mustvictory on 2016-4-1 17:08. Yes, the concept of the mass flow rate no longer increasing is exactly what is meant by the speed of sound; you can find out more by searching on Baidu. Additionally, for a diameter of 100 m/s, we calculate the pipe diameter based on normal flow rates, not such high flow rates
The choke flow at the critical condition is the local speed of sound. See Laval nozzle