Effect of the boundary layer on the base pressure in a two-dimensional flow with a Mach number M = 5

Abstract

New data on the base pressure in a two-dimensional flow with a Mach number M = 5 are obtained for a wide range of variation of the normalized boundary-layer thickness in the flow-separation cross section. The test results are compared with Tanner's theory, and a conclusion is made that this numerical model has to be corrected.Key words: supersonic flow, turbulent boundary layer, base pressure.Introduction. The dimensionless base pressure p b /p e of the body in a compressible flow has a strong effect on the near-wake structure. The problem of the near wake and, in particular, the base drag is discussed in numerous experimental and theoretical studies. A large list of papers on this topic can be found in the review [1] and monographs [2][3][4]. Various experiments and simplified numerical models are used to study the dependence of the base pressure of bodies with different configurations on the basic governing parameters, which is usually presented in the form p b /p e = f (M e , α, δ/(t/2) or δ * * /(t/2)), where M e is the free-stream Mach number, δ is the boundary-layer thickness, δ * * is the momentum thickness, t/2 is the half-height (radius) of the base cross section, and α is the angle of deviation of the body contour from the free-stream direction in the flow-separation cross section. The most extensively examined range is M e 3, δ/(t/2) 1; for this combination of parameters, the data available in the literature are sufficient to determine the base drag of bodies of simple geometry (cone, cone-cylinder, wedge, and step).In the range of high supersonic velocities (M e > 3), the measurements were performed either with a fixed ratio δ/(t/2), or the range of variation of the dimensionless boundary-layer thickness was varied within narrow limits corresponding to δ * * /(t/2) 1. The latter, in particular, does not allow us to determine the accuracy of taking into account the influence of this parameter on the base pressure in existing numerical models. Note that large values of δ/(t/2) are reached in some situations important for practice, e.g., in the flow around extended bodies or at low Reynolds numbers.It follows from the above-given information that the study of the boundary-layer effect on the base drag is still important. This problem is discussed in the present paper, which describes detailed measurements of the base pressure on the edge of a two-dimensional body in a supersonic flow with a Mach number M = 5 in a wide range of variation of the boundary-layer thickness at the exit, up to δ/(t/2) = 3.2. The experimental data obtained are used to test Tanner's numerical model [5][6][7], which, in contrast to other known numerical methods (see, e.g., [1][2][3][4]) claims that it can predict the base drag for bodies of different geometries for arbitrary values of M and δ/(t/2), and which was previously tested at lower Mach numbers.Setup, Models, and Measurement Technique. The base pressure was measured at the edge of a nozzle blade in the course of extensive studies of the flow structure formed by a block of ...

Numerical investigation of the effects of base size on supersonic flow through a sudden duct enlargement

“…A jet is referred to as over-expanded if θ > 1.0, correctly expanded if θ = 1.0, and under-expanded if θ < 1.0. In general, the jet is described in a detailed way, and complete information is given by presenting it in the form P b / P e = f ( M 1 , α , δ , H b , and P 0 ), where M 1 , α , δ , and H b are the incoming Mach number, flow angle, boundary layer thickness, and height of the base (base size), respectively [ 7 , 8 ]. The flow pattern is strongly influenced by the base size, particularly for small enlargements of the duct.…”