A study of tip-leakage flow through orifice investigations
"Compressible fluid dynamics of flow through plain-faced long orifices was investigated with the hope of gaining insight into the fluid dynamics of tip leakage flow. The Reynolds number range investigated was greater than 10*. Measurements were made of the discharge coefficient as a function of back pressure ratio for a sharp-edged orifice and long orifices with an l/d from 1/2 to 8. The discharge coefficient measurements indicate the mass flow rate in an orifice with an l/d of approximately 2 is the largest and the flow rate in a sharp-edged orifice is the smallest for pressure ratios greater than 0.27. The mass flow rate in a sharp-edged orifice is largest for pressure ratios below 0.27. To visualize the flow in a long orifice and model centerline pressure variation, a water table study was performed. The results demonstrate that the flow separates from the sharp corner at the orifice entrance, it accelerates to a maximum Mach number, and then the pressure increases. For back pressures above 0.50, a pressure decrease follows the initial pressure increase. If the maximum Mach number is supersonic, oblique shocks will exist. At the higher back pressures that produce supersonic maximum Mach numbers (0.50 PB/P₀ < 0.70), the oblique shocks reflect from the centerline as ""Mach reflections"" and the flow is subsonic after the pressure increase. The maximum Mach number for a back pressure ratio of 0.50 is approximately 1.5. At lower back pressure ratios (PB/P₀ <0.70), the oblique shocks reflect from the centerline in a ""regular"" manner and the flow remains supersonic on the centerline once supersonic speeds are reached. The flow in a long orifice is relatively constant for all back pressure ratios below approximately 0.30. The maximum Mach number for pressure ratios below 0.30 is approximately 1.8.
One-dimensional analyses were used to model the flow in long orifices with maximum Mach numbers less than 1.3. Higher discharge coefficients of long orifices compared to sharp-edged orifices are due to pressure rises in the orifices caused by mixing and shock waves. These increases in the discharge coefficients are partly offset by friction and boundary layer blockage. For maximum Mach numbers greater than 1.3, the flow in long orifices is believed to become significantly two-dimensional because of supersonic effects."