Compressibility Effect on Topology of Vortex Ring Formed by Vortex Breakdown in Closed Cylinder at Low-Mach-Numbers

A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation. Mach numbers, based on the bulk velocity and sound speed at the walls, of 1.5 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000. Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed. The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature. These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations. The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results.

Download Full-text

The compressible turbulent shear layer: an experimental study

Journal of Fluid Mechanics ◽

10.1017/s0022112088003325 ◽

1988 ◽

Vol 197 ◽

pp. 453-477 ◽

Cited By ~ 1066

Author(s):

Dimitri Papamoschou ◽

Anatol Roshko

Keyword(s):

Growth Rate ◽

Mach Number ◽

Shear Layer ◽

Large Scale ◽

Turbulent Shear ◽

Plane Shear ◽

Compressibility Effect ◽

Pressure Profiles ◽

Mach Numbers ◽

Convective Mach Number

The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. In this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic vaue of about 0.2 for supersonic convective Mach numbers.

Download Full-text