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Instability and transition to turbulence in separated shear layer produced by laminar boundary layer separation from rearward-facing step, noting periodic spanwise structure
A correlation of new turbulent two-dimensional data and peak heating data for attaching free shear layers is presented for a 2.54-cm and 5.08-cm diam cylindrical leading-edge slab 25.4 cm long, and 7.62 and 10.16 cm wide. A 30.48 x 25.4 cm sharp leading-edge flat plate set at 15 and 20 deg is used to generate plane impinging shocks. The freestream Mach number is 6 and the freestream Reynolds number varies from 3,300,000 to 25,600,000/m. Peak heating is measured on silica-based epoxy models with a phase change coating technique. A comparison of the free shear layer data with the transition data of Birch and Keyes (1972) reveals that the shear layer data are turbulent at attachment. The trend of the data shows that peak heating is strongly affected by the state of development at attachment. As the free shear layers become more fully developed, the data approach the two-dimensional correlation. Persistence of transitional flow structures for supersonic free shear flows is pointed out.
The RPLUS2D code, capable of calculating high speed reacting flows, was adopted to design a compressible shear layer facility. In order to create reacting shear layers at high convective Mach numbers, hot air streams at supersonic speeds, rendered by converging-diverging nozzles, must be provided. A finite rate chemistry model is used to simulate the nozzle flows. Results are compared with one-dimensional solutions at chemical equilibrium. Additionally, a two equation turbulence model with compressibility effects was successfully incorporated with the RPLUS code. The model was applied to simulate a supersonic shear layer. Preliminary results show favorable comparisons with the experimental data.
The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =
The RPLUS2D code, capable of calculating high speed reacting flows, has been adopted to design a compressible shear layer facility. In order to create reacting shear layers at high convective Mach numbers, hot air streams at supersonic speeds, render by converging-diverging nozzles, must be provided. A finite rate chemistry model is used to simulate the nozzle flows. Results are compared with one-dimensional, chemically equilibrium solutions. Additionally, a two equation turbulence model with compressibility effects has been successfully incorporated with the RPLUS code. The model has been applied to simulate a supersonic shear layer. Preliminary results show favorable comparisons with the experimental data.
The primary aim of this research program was to investigate the mechanisms which cause the unsteady wall-pressure fluctuations in shock wave turbulent shear layer interactions. The secondary aim was to find means to reduce the magnitude of the fluctuating pressure loads by controlling the unsteady shock motion. The particular flow under study is the unsteady shock wave interaction formed in the reattachment zone of a separated supersonic flow. Similar flows are encountered in many practical situations, and they are associated with high levels of fluctuating wall pressure. The free shear layer is formed by the flow over a backward facing step, using an existing model, with the base pressure on the step adjusted so that there is no pressure discontinuity at the lip. The shear layer therefore develops in a zero pressure gradient. The primary advantage of this flow configuration is that the reattachment process can be studied in the absence of a separation shock. The mean flow data, and some preliminary hot-wire measurements of the mass-flux fluctuations were made by Baca and Settles, Baca, Williams and Bogdonoff, who showed that the shear layer became self-similar at about 17 delta(sub 0) downstream of the lip, and that it grew at a rate typical of the observed Mach number difference (about 1/3rd the incompressible growth rate). The turbulence measurements were later extended by Hayakawa, Smits and Bogdonoff under NASA Headquarters support.
A premixed propane-air flame is stabilized in a turbulent free shear layer formed at a rearward facing step. The mean and rms averages of the turbulent velocity flow field are determined by LDV for both reacting (equivalence ratio 0.57) and nonreacting flows (Reynolds number 15,000-37,000 based on step height). The effect of combustion is to shift the layer toward the recirculation zone and reduce the flame spread. For reacting flow, the growth rate is unchanged except very near the step. The probability density function of the velocity is bimodial near the origin of the reacting layer and single-peaked but often skewed elsewhere. Large-scale structures dominate the reacting shear layer. Measurements of their passing frequency from LDV are consistent with high-speed Schlieren movies of the reacting layer and indicate that the coalescence rate of the eddies in the shear layer is reduced by combustion.
The turbulent wake interacting with the rotating wall shear layer is investigated analytically and numerically. The turbulent wakes of the rotating blades in a compressor which are interacting with the rotating hub-wall boundary layer are analyzed. A modified version of the closure model of the pressure-strain correlation term in the Reynolds stress transport equation is developed to predict the effect of rotation, which is appreciable for the present flow because the thick hub-wall boundary layer is interacting with the rotor wake. It is noted that the Poisson type equation for the pressure-strain correlation has an extra rotation term when the entire flow field is rotating. This extra rotation term is modeled to accommodate the effect of rotation. In addition, the standard correction for the wall effect is incorporated for the utilized Reynolds stress closure model. The rotation-modified Reynolds stress closure model is used to predict the present flow, and the predictions are compared with the experimental data. The experimental data reveal that the characteristics of the three-dimensional turbulent wake interacting with the wall shear layer are considerably altered by the effects of the wall and the rotation. These features are predicted with good accuracy by the turbulence closure model developed.
A preliminary experimental study has been conducted to gain insight into the temporal and spatial contents of largescale structures in a convective Mach number = 0.51 high Reynolds number planar two-dimensional compressible free shear layer. Power spectra, coherence, and space-time correlations were obtained using single- and two-point pressure measurements. Both developing and fully developed regions of the flow were investigated. The passage frequency of structures were found to be 10-15 kHz in the developing region and 4-8 kHz in the fully developed region. The convective velocity obtained from the space-time correlation in the middle of the shear layer was close to the theoretical value but varied toward the edge of the shear layer. The structures were shown to be surprisingly three-dimensional even in this low compressibility level shear layer. The structures size and spacing were also determined and discussed.
The naturally occurring large scale motions in a single stream shear layer (that is initiated from a fully turbulent boundary layer) are made evident by the induced velocities in the entrainment region beyond the active shear layer. The distinctive attributes of these induced motions are particularly evident in the Michigan State Univerity Free Shear Flow Facility since the total test section length (3m) is nominally the same as the location of the first, fully formed, coherent motion, ca/x theta (0) = 400 (or 2.5 m). Hence, detailed studies of the induced motions can be executed. Individual coherent motions are identified by the induced velocity signatures and conditional-ensemble statistics are used to represent the irrotational field properties. Clusters of such motions exist; some of their properties are substantially different from the unconditionally averaged values.
A new mixing length model is presented for supersonic shear flows. In this model, the characteristic scale of the mixing region is not constant across the shear layer at each axial position but is determined locally by the lateral distance between the two points where flow moves sonic relative to the local point. Supersonic free shear layers at various Mach numbers were calculated by solving the compressible boundary layer equations with the new model. The results demonstrate the decrease of spreading rate with increasing Mach number and agree well with experimental data.
The problem of the transmission of sound in a duct with very thin shear layers at the walls is treated by an inner expansion method. The results show that the formulation of the problem of the transmission of sound in a duct with a shear layer at the wall converges, in the case of a vanishingly thin shear layer, to the formulation of the same problem when uniform flow is assumed and the wall boundary condition is that of continuity of particle displacement.
Numerical simulation of unsteady flow in an axisymmetric subsonic shear layer is accomplished by solving the time-dependent compressible Navier-Stokes equations. The objective of the effort is to investigate by numerical means the influence of various flow parameters on the shear layer behavior. The parameters investigated include the velocity ratio of two streams, total temperature, and nozzle lip thickness. The computations are performed on a CRAY-IS computer using McCormack's explicit finite difference scheme. The computed results generally show qualitative agreement with experimental data.
Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis was exact for all frequencies and was developed assuming a linear velocity profile in the shear layer. This assumption allowed the solution to be expressed in terms of parabolic cyclinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number gave expressions which correspond to solutions previously obtained for these limiting cases.
Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis is exact for all frequencies and is developed assuming a linear velocity profile in the shear layer. This assumption allows the solution to be expressed in terms of parabolic cylinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number give expressions which correspond to solutions previously obtained for these limiting cases.
Measurements of wall pressure fluctuations were made as part of an ongoing program to investigate the control of a turbulent, reattaching shear layer at Mach 2.9. The flow was disturbed near separation by air injection normal to the plane of the shear layer. This perturbation was found to dramatically increase the intensity of pressure fluctuations in the vicinity of reattachment. A local increase in shear layer growth rate was also observed in the perturbed flow.
The results of two component velocity and turbulence measurements are presented which were obtained on a planar reacting shear layer burning hydrogen. Quantitative LDV and temperature measurements are presented with and without chemical reaction within the shear layer at a velocity ratio of 0.34 and a high speed Mach number of 0.7. The comparison showed that the reacting shear layer grew faster than that without reaction. Using a reduced width coordinate, the reacting and non-reacting profiles were very similar. The peak turbulence for both cases was 20 percent.
The structure of the attached turbulent flow in the vicinity of a NACA 4412 airfoil equipped with a single-slotted flap was studied. The airfoil/flap configuration was tested at a Mach number of 0.06 and a Reynolds number of 1.3 x 10 to the 6th in a 7- by 10-Foot Wind Tunnel. Surface-pressure measurements were made on the main airfoil and on the flap. Detailed measurements, obtained using a high-spatial-resolution laser Doppler anemometer, were made of the mean velocity flow field and of the second-order statistical quantities (Reynolds stresses) in the boundary layers, wakes, and merging shear layers. The experimental observations are compared with theoretical predictions of pressure, mean velocity, and Reynolds stress.