Calculations of orifice plates under supersonic conditions

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This post was last edited by wf927 on 2018-3-26 at 09:30. I recently encountered a problem related to the calculation of orifice plates; after reviewing many documents, I was unable to find a definitive answer. Therefore, I am seeking advice from experts. As is well known, orifice plates can be used for throttling and pressure reduction, similar to nozzles. The difference lies in the fact that for nozzles, the maximum flow velocity occurs at the smallest throat diameter, whereas for sharp-orifice throttling plates, the maximum flow velocity – and thus the lowest pressure – occurs behind the throttling orifice. As a result, when gas is throttled, due to the existence of critical pressure, the maximum flow rate at the throat diameter is limited by the speed of sound in the medium, resulting in a finite maximum flow velocity. This means that under the same upstream conditions and throat diameter, the flow rate through a nozzle does not increase as the downstream pressure continues to drop. Orifice plates, however, behave differently: once the downstream pressure reaches the speed-of-sound level, the flow rate increases as the pressure continues to decrease. This is different from the behavior of safety valves or nozzles. However, according to HG20570 and other documents, multi-stage orifice plates are used when the downstream pressure falls below the speed-of-sound level, in order to keep each stage of pressure drop within the critical range and avoid choked flow. This approach seems to contradict the actual flow characteristics of orifice plates. My question is: what is the fundamental reason for using multi-stage orifice plates rather than single-stage ones? How is the flow rate calculated after critical flow occurs during gas throttling using a single-stage orifice plate?