Drag Measurement in Unsteady Compressible Flow

[摘要] Drag over a wide range of shapes is well established for steady flow conditions. Drag inunsteady flow, however, is for the most part not well understood. The research presentedherein examines the drag over cones in unsteady compressible flow. This was achievedby constraining cones, with half-vertex angles ranging from 15° to 30°, in a shock tubeand passing shock waves over them. The resulting drag was measured directly using astress wave drag balance (SWDB). Tests were run at shock Mach numbers between 1.12and 1.31 with corresponding post-shock Reynolds numbers between 2 × 105 and 6 × 105.The drag on the four cone geometries as well as one sphere geometry was modellednumerically. Density contours of the flow fields, obtained from the numericalsimulations were used to visualise the shock/model interactions and deduce the causes ofany variations in drag. It was thus proved that post-shock fluctuations are due to shockwave reflections off the shock tube walls and the model support. The maximum unsteadydrag values measured experimentally ranged from 53.5 N for the 15° cone at a Machnumber of 1.14 to 148.6 N for the 30° cone at a Mach number of 1.29. The drag obtainednumerically agreed well with experimental results, showing a maximum deviation inpeak drag of 9.6%. The drag forces on the conical models peaked as the shock wavereached the base of the cone whereas the drag on the sphere peaked just before the shockreached the equator of the sphere. The negative drag and large post-shock dragfluctuations on a sphere measured by Bredin (2002) were present in the numerical resultsand thus confirm that these features were not due to balance error. The large post-shockdrag fluctuations were also present on the cones. The unsteady drag was shown toincrease as both the shock wave Mach number and the cone angle were increased. Theratio of the maximum unsteady drag to the compressible steady state drag varied fromv4.4:1 to 9.8:1, while the ratio of the maximum unsteady drag to the incompressible steadystate drag varied from 8.3:1 to 22.2:1. The steady state drag values were shown to be ofthe same order of magnitude as the post shock unsteady drag. Further numerical work isrecommended to confirm that drag fluctuations are in fact due to shock reflections and tobetter establish the relationship between the unsteady drag and the cone angle.

[发布机构] University of the Witwatersrand