Turbulent shear layer reattachment downstream of a backward-facing step in confined supersonic axisymmetric flow

Abstract

The reattachment of a supersonic jet with a turbulent boundary layer abruptly expanding into an axisymmetric parallel diffuser has been experimentally investigated using a surface-flow technique. Measurements were made in the started condition, where the blowing pressure is sufficiently high to establish an oblique shock system in the diffuser. The proposed reattachment criterion correlates present measurements in terms of the diffuser area ratio, and also those of other workers for unconfined flow in terms of the free stream Mach number after separation. As already reported for unconfined flow, it is found that disturbances downstream of reattachment do not affect the upstream region.

A note on turbulent shear-layer reattachment downstream of a backward-facing step in confined supersonic two-dimensional flow

“…As in the confined axisymmetric flow measurements reported by Mukerjee & Martin (1969), the wall static pressure distributions in two-dimensional flow for different 2, coincide in the region of steepest pressure rise, where reattachment occurs. I n this region the pressure is a linear function of distance from the sudden enlargement, the slope becoming independent of nozzle exit Reynolds number Re, = p,U,H/p, (where p, U and ,u are respectively fluid density, flow velocity and fluid viscosity) according to Sfeir (1966) when, as in the present case, where 4.9 x 105 6 Re, 6 6.85 x 105, the free shear layer is fully turbulent.…”

“…The apparatus, procedure and surface-flow technique used to determine the location of reattachment were otherwise as described by Mukerjee & Martin (1969) for axisymmetric flow, to which the reader is referred for a full description. Operation of the diffuser in the started condition needed for an oblique shock system also ensured flow symmetry in the diffuser; this was confirmed by equality of measured top and bottom wall static pressure distributions, whose accuracy was estimated to be within 3 yo.…”

“…Variation of R, with M,. 0, present work; +, Thomann (1959); Q, Sirieix (1960); a, Carrihre & Sirieix (1961); 0, Hastings (1963); A , Sfeir (1966).A, R, = 1-56M/,445; 13, R, = 6.0/Mf74(Mukerjee & Martin 1969).…”

“…I n a recent paper on turbulent shear-layer reattachment downstream of a backward-facing step in confined supersonic axisymmetric flow, Mukerjee & Martin (1969) proposed that the base pressure be evaluated from a reattachment criterion defined in terms of the initial stagnation pressure I?,. In the nomenclature of figure 1, which shows the conventional Korst-Chapman flow model for confined flow, where p is static pressure and subscripts 1, 2 and 3 denote the separating edge, the base region and the region downstream of reattachment respectively, while subscript T denotes dividing streamline reattachment, the reattachment criterion is This has the merit over the earlier proposals of Korst (1956), Nash (1962), McDonald (1964), Roberts (1964) and Sfeir (1966) of greater generality in its ability t o correlate both unconfined and confined flows, as Mukerjee & Martin (1969) have shown for the axisymmetric case, through its restriction to pressures upstream of reattachment. It, therefore, avoids reference to the non-uniform conditions which may arise downstream of reattachment in confined flows from the presence of reflected waves.…”

“…Martinand is equally valid for confined and unconfined flows over the range 1.75 < M2 < 4.4. Also included for comparison in figure 2 is the corresponding axisymmetric correlation ofMukerjee & Martin (1969) for 2-3 6 M2 < 5…”