Obtaining Time-Varying Pulsatile Gas Flow Rates With the Help of Dynamic Pressure Difference and Other Measurements for an Orifice-Plate Meter

Use of a conventional orifice-plate meter is typically restricted to measurements of steady flow rates. For any gas flowing within a duct in a pulsatile manner (i.e., large amplitude mass flow rate fluctuations relative to its steady-in-the-mean value), this paper proposes a new and effective approach for obtaining its time-varying mass flow rate at a specified cross section of an orifice meter. The approach requires time-varying (dynamic) pressure difference measurements across an orifice-plate meter, time-averaged mass flow rate measurements from a separate device (e.g., Coriolis meter), and a dynamic absolute pressure measurement. Steady-in-the-mean turbulent gas flows (Reynolds number ≫2300) with low mean Mach numbers (<0.2) exhibit effectively constant densities over long time-durations and are often made pulsatile by the presence of rotary or oscillatory devices that drive the flow (compressors, pumps, pulsators, etc.). In these pulsatile flows, both flow rate and pressure-difference fluctuation amplitudes at or near the device driver frequency (or its harmonics) are large relative to their steady mean values. The time-varying flow rate values are often affected by transient compressibility effects associated with acoustic waves. If fast Fourier transforms of the absolute pressure and pressure-difference measurements indicate that the predominant frequency is characterized by $fp$⁠, then the acoustic effects lead to a nonnegligible rate of change of stored mass (associated with density changes) over short time durations (∼ 1/$fP$⁠) and modest volumes of interest. As a result, for the same steady mean mass flow rate, the time variations (that resolve these density changes over short durations) of mass flow rates associated with pulsatile (and turbulent) gas flows are often different at different cross sections of the orifice meter (or duct). Together with the experimental measurements concurrently obtained from the three recommended devices, a suitable computational approach (as proposed and presented here) is a requirement for effectively converting the experimental information on time-varying pressure and pressure-difference values into the desired dynamic mass flow rate values. The mean mass flow rate measurement assists in eliminating variations in its predictions that arise from the use of turbulent flow simulation capabilities. Two independent verification approaches establish that the proposed measurement approach works well.