Rearward-facing Step Research Articles

Time-dependent behavior of a reattaching shear layer

Conditionally sampled velocities have been measured in a reattaching turbulent shear layer behind a rearward facing step in an effort to understand unsteady behaviour of reattaching flows. Laser-Doppler velocimeter measurements were conditionally sampled on the basis of instantaneous flow direction near reattachment. Conditions of abnormally short reattachment and abnormally long reattachment were considered. Ensemble-averages of measurements made during these conditions were used to obtain mean velocities and Reynolds stresses. In the mean flow, conditional streamlines show a global change in flow pattern which correlates with wall-flow direction. This motion can loosely be described as a flapping of the shear layer. Stresses shown also vary with the change in flow pattern. Yet, the global flapping motion does not appear to contribute much to the fluctuating energy in the flow. A second type of fluctuating motion (vortical) was observed. Spectral analysis of both wall static pressure and streamwise velocity show that the majority of energy in the flow resides in frequencies characteristic of roll-up and pairing of vortical structure seen in free shear layers (St = 0.2). Two-point velocity correlations also indicate a vortical behaviour of the flow. It is conjectured that the flapping is a disorder of the roll-up and pairing process occurring in the shear layer.

Vortex simulation of laminar recirculating flow

The accuracy of the random vortex method, a numerical scheme that combines the representation of the vorticity field by a number of Lagrangian vortex elements of finite cores with a stochastic simulation of diffusion using random walk, is investigated. The converged solutions for a 2-dimensional entry flow in a channel and a recirculating flow behind a rearward-facing step, both in the laminar range of Reynolds numbers, are compared with analytical results and experimental data, respectively. It is shown that the computed results converge as the strength of computational vortex elements is decreased, and that the method is accurate to within the experimental errors. The convergence properties are used to devise a scheme for optimizing the choice of the numerical parameters.

Advanced hybrid rocket motor experiments

Results of experiments performed with an advanced, automated measuring system and dealing with combusion of polymethylmethacrylate and polyethylene with oxygen and different mixtures of oxygen and nitrogen are reported. Factors affecting the regression rate of the fuel are the mass flux, the geometry, the pressure level and the presence of oscillations, the composition of the oxidizer and the burning time. The effect of pressure on the regression rate appears to be stronger at lower pressures. A newly developed technique allows the measurement of the local instantaneous regression rate. The dependence of this regression rate on the various above mentioned parameters varies from location to location in the motor. The characteristic velocity depends on the mixture ratio and on the residence time of the reacting gases. A rearward facing step increases the mean regression rate and changes the profile of the burned fuel grain. Such a step is necessary to obtain combustion with mixtures containing 20% oxygen and 80% nitrogen.

Pressure distributions behind a rearward facing segmented step

Effects of 3-D disturbances on a separating flow past a rearward facing step have been studied with emphasis on pressure distributions in the separation and reattachment regions. The results show that the 3-D disturbances to a separating shear layer diminish rapidly and the flow downstream of reattachment appears to have a 2-D global shearlayer structure.

A COUPLED MARCHING PROCEDURE FOR THE PARTIALLY PARABOLIZED NAVIER-STOKES EQUATIONS

A coupled finite-difference formulation is described for solving a reduced form of the compressible Navier-Stokes equations by a multiple space marching procedure. The properties of the equations are discussed and the solution algorithm presented. The scheme is used to compute incompressible flows by taking the incompressible limit (M about 0.1) of the compressible formulation. A separate Poisson equation is not required for the pressure. Results are compared with experimental data and other numerical predictions for low Reynolds number channel inlet flow, flow over a rearward-facing step in a channel, and flow near the trailing edge of a flat plate.

A Viscous-Inviscid Interaction Procedure—Part 2: Application to Turbulent Flow Over a Rearward-Facing Step

The viscous-inviscid interaction numerical procedure described in Part 1 is used to predict steady, two-dimensional turbulent flow over a rearward-facing step. The accuracy of predictions is observed to be quite sensitive to the specification of length scale in the turbulence modeling. The best results are observed when the length scale is specified algebraically downstream of the step using parameters characteristic of the step geometry. Predictions of mean flow quantities and reattachment length are shown to be in generally good agreement with measurements obtained over a range of channel expansion ratios.

A Viscous-Inviscid Interaction Procedure—Part 1: Method for Computing Two-Dimensional Incompressible Separated Channel Flows

A viscous-inviscid interaction scheme has been developed for computing steady incompressible laminar and turbulent flows in two-dimensional duct expansions. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is computed by numerically solving the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively along displacement surfaces. Details of the procedure are presented in the present paper (Part 1), along with example applications to separated flows. The results compare favorably with experimental data. Applications to turbulent flows over a rearward-facing step are described in a companion paper (Part 2).

A Coupled Marching Procedure for the Partially Parabolized Navier-Stokes Equations

A coupled finite-difference formulation is described for solving a reduced form of the compressible Navier-Stokes equations by a multiple space marching procedure. The properties of At equations are discussed and the solution algorithm presented. The scheme is used to compute incompressible flows by taking the incompressible limit(M ˜ 0.1) of the compressible formulation. A separate Poisson equation is not required for the pressure. Results are compared with experimental data and other numerical predictions for low Reynolds number channel inlet flow, flow over a rearward-facing step in a channel, and flow near the trailing edge of a flat plate.

Features of a reattaching turbulent shear layer in divergent channelflow

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Turbulent Heat Transfer Computations for Rearward-Facing Steps and Sudden Pipe Expansions

Results of numerical calculations for heat transfer in turbulent recirculating flow over two-dimensional, rearward-facing steps and sudden pipe expansions are presented. The turbulence models used in the calculation are the standard k – ε model and the low-Reynolds number version of this model. The k – ε models have been improved to account for the effects of streamline curvature and pressure-strain (scalar) interactions including wall damping. A sequence of two computational passes is performed to obtain optimal results over the entire flow field. The presented results consist of computed distributions of heat transfer coefficents for several Reynolds numbers, emphasizing the low-to-moderate Reynolds number regime. The heat transfer results also include correlations of Nusselt numnber for both side and bottom walls. The computed heat transfer results and typical computed fluid dynamic results are compared with available experimental data.

Numerical simulation of a turbulent flame stabilized behind a rearward-facing step

Flow of combustible mixtures in a plane channel past a smooth contraction followed by an abrupt expansion, in a typical dump combustor configuration, is modeled by a two-dimensional numerical technique based on the random vortex method. Both the inert and the reacting case are considered. In the latter, the flame is treated as an interface, self-advancing at a prescribed normal burning speed, while the dynamic effects of expansion due to the exothermicity of combustion are expressed by volumetric source lines delineated by its front. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and the reattachment length. The stochastic turbulent velocity components manifest interesting differences, especially near the walls where three-dimensional effects of turbulence are expected to be of importance.

Laser Velocimeter Measurements in Highly Turbulent Recirculating Flows

This paper presents the results of an extensive study of subsonic separated flows using a laser Doppler velocimeter. Both a rectangular rearward facing step and cylindrical (axisymmetric) sudden expansion geometry were studied. The basic objectives were to resolve the question of whether a velocity bias error does, in fact, occur in LDV measurements in highly turbulent flows of this type and, if so, how it may be eliminated; map the velocity field (mean velocity, turbulence intensity, Reynolds stress, etc.) including the entire recirculation zone; and compare experimental results with numerical predictions based on the k-ε turbulence model. Measurements were carried out using a one-dimensional LDV operating in forward scatter with signal processing by means of a commercial counter-type processor. Results obtained show that velocity bias does occur in turbulent flows and that it can be overcome by proper data acquisition procedures. The results also indicate that the important mean velocity and turbulence quantities can be obtained with reasonable accuracy using a one-dimensional LDV system. Although the k-ε turbulence model provides a good qualitative picture of the flow field, it does not yield a completely adequate quantitative description. Results obtained here illustrate the discrepancies to be expected and provide a basis for further model development.

Supersonic flow over a rearward facing step with transverse nonreacting hydrogen injection

This work involves an application of computational fluid dynamics to a problem associated with the flow in the combustor region of a supersonic combustion ramjet engine (Scramjet). In particular, a time-dependent, finite difference method is used to. solve the complete two-dimensional Reynolds averaged Navier-Stokes equations for the turbulent supersonic flow of air over a rearward-facing step, with transverse H2 injection downstream of the step. To delineate the purely fluid dynamic effects, the flow is treated as nonreacting; however, detailed binary diffusion of H2-air is included, along with a variable Lewis number. Results are obtained and compared for cases with and without H2 injection. The influence of the wall temperature boundary conditions (adiabatic vs constant temperature) is studied, and is shown to have little impact on the flow both near and far away from the wall. These numerical results are the first to be obtained for this flow geometry, expecially at,conditions germaine to a Scramjet. They demonstrate that such an application of computational fluid dynamics can be useful for the study of inlet-combustor interactions, and the flameholding potential of the rearward-facing step.

Combustion in a turbulent mixing layer formed at a rearward-facing step

A premixed propane/air flame was stabilized in a turbulent mixing layer formed at a rearward-facing step. The mean and rms averages of the turbulent velocity flowfield were determined by laser velocimetry for both reacting (phi = 0.57) and nonreacting flows (Re = 15,000-37,000 based on step height). The reacting-flow was visualized by high-speed schlieren photography. Large-scale structures dominate the reacting mixing layer. The growth of the large-scale structures was tied to the propagation of the flame. The linear growth rate of the reacting mixing layer defined by the mean velocity profiles was unchanged by combustion but the virtual origin moves downstream. The reacting mixing layer boundaries based on the mean velocity profiles were shifted toward the recirculation zone and reattachment lengths were shortened by 30 percent. The edge of the flame controlled by the large-scale structure development propagated faster into the incoming reactants than the boundary of the mixing layer given by the mean velocity flowfield. Thus, the region of high velocity gradient did not coincide with the region of high reaction and heat transfer.

Applicability of the independence principle to subsonic turbulent flow over a swept rearward-facing step

Prandtl (1946) has concluded that for yawed laminar incompressible flows the streamwise flow is independent of the spanwise flow. However, Ashkenas and Riddell (1955) have reported that for turbulent flow the 'independence principle' does not apply to yawed flat plates. On the other hand, it was also found that this principle may be applicable to many turbulent flows. As the sweep angle is increased, a sweep angle is reached which defines the interval over which the 'independence principle' is valid. The results obtained in the present investigation indicate the magnitude of the critical angle for subsonic turbulent flow over a swept rearward-facing step.

Shape and Dimensions of Stationary Dunes in Rivers

The shape and dimensions (length, height) of sand dunes in rivers are calculated by use of the measured bed shear stress distribution downstream a rearward-facing step. The transport of sediment is split up into bed load and suspended load, which makes it possible to explain the transition to plane bed. The model can predict flow-resistance curves in alluvial streams.

Pulsating flow over a step

An experimental study has been made of air flow over a rearward facing step where the free-stream velocity has been perturbed by a sinusoidal fluctuation of 1 Hz. Velocities have been measured using a laser Doppler anemometer employing a gated photon correlation signal detection system. This allows mean velocities and fluctuating components to be measured at different phase positions in the cycle. It is shown that the stability of the separated flow region behind the step is strongly perturbed by the free-stream oscillations and that the position of reattachment of the turbulent boundary layer is dependent on the phase of the free-stream velocity. Shedding of the vortex occurs when the retardation of the free-stream velocity is a maximum.

Effects of Adverse Pressure Gradient on the Incompressible Reattaching Flow over a Rearward-Facing Step

The turbulent, incompressible reattaching flow over a rearward-facing step has been studied by many researchers over the years. One of the principal quantities determined in these experiments has been the distance from the step to the point (or region) where the separated shear layer reattaches to the surface (x(r)). The values for x(r)/h, where h is the step height, have covered a wider range than can reasonably be attributed to experimental technique or inaccuracy. Often the reason for a largely different value of x(r)/h can be attributed to an incompletely developed turbulent layer, or a transitional or laminar boundary layer. However, for the majority of experiments where the boundary layer is believed to be fully developed and turbulent, x(r)/h still varies several step heights; generally, 5 1/2 approximately < x(r)/h approximately < 7 1/2. This observed variation has usually been attributed to such variables as l/h (step length to height, h/delta (step height to initial boundary-layer thickness), R(e)(theta)), or the experimental technique for determining reattachment location. However, there are so many different combinations of variables in the previous experiments that it was not possible to sort out the effects of particular conditions on the location of reattachment. In the present experiment velocity profiles have been measured in and around the region of separated flow. Results show a large influence of adverse pressure gradient on the reattaching flow over a rearward-facing step that has not been reported previously. Further, the many previous experiments for fully developed, turbulent flow in parallel-walled channels have shown a range of reattachment location that has not been explained by differences in initial flow conditions. Although these initial flow conditions might contribute to the observed variation of reattachment location, it appears that the pressure gradient effect can explain most of that variation.

Measurements of turbulent flow downstream of a rearward-facing step

Measurements have been made in a water channel of the flow in and around the separation region due to a rearward-facing step. Detailed profiles of mean velocities, turbulence intensities and Reynolds shear stress are presented. The turbulence measurements reveal the development of a new shear layer, which splits at reattachment with about one-sixth of the mass flow deflected upstream. The new shear layer is associated with a region of roughly constant values of both the non-dimensional mixing lengthl/xand the shear correlation coefficientK. The mixing-length ratio is larger than that found in plane mixing layers, whereas the shear coefficient is roughly the same. There is strong evidence that near the wall the length scales increase more rapidly with distance from the wall than in an attached boundary layer, and that a local maximum occurs.

Flow Immediately behind a Step in a Simulated Supersonic Combustor

Results are presented from a series of nonburning flow tests in which extensive instream and wall pressure and fluid sample measurements were made to characterize the flow immediately behind a rearward facing step in a simulated supersonic combustor. Pitot pressure data were used to determine simplified flowfield models for the cases of flow both with and without a simulated precombustion shock and simulated fuel injection. The effects of the shock on the flowfield and fuel-air distribution in the main stream and recirculation zone behind the step, as well as the implications for the placement of ignition devices and piloting, are discussed. N supersonic combustion ramjet (scramjets), certain combustor configurations employ in their design a rear- ward facing step downstream of the fuel injector. This sudden step increase in combustor area has been beneficial to com- bustor operation in several ways. Among these are: 1) the step helps to isolate or limit the interaction of the combustion process with the inlet flowfield of the engine; 2) the step limits the combustor pressure rise by spreading the pressure gradient from the combustion shock along the wall, limiting excessive local heat transfer due to shock impingement; and 3) the step serves as a flame-holding region. The purpose of the present work is to improve the understanding of the flow pat- terns and fuel distribution in the mainstream and in the recir- culation zone behind the step, so that fuel injectors and/or ignition aids can be located more effectively to improve the supersonic combustion of hydrocarbon fuels or fuel blends. Generally, in supersonic combustion, an oblique shock will be present at the combustor entrance. Waltrup and Billig developed a semi-empirical pseudo-one-dimensional analysis that defined the pressure field and attendant separation zone in the precombustion interaction region of constant area com- bustors.!3 Waltrup and Cameron presented wall shear and boundary-layer measurements that completed the depiction of the instream and wall flow structure for a shock-separate d flow of this type.4 These works also demonstrated the feasibility of producing the shock structure and shock/boun- dary-layer interactions analogous to those present at the com- bustor entrance in a simple nonreacting system, where throt- tling rather than combustion is the cause of compression. This technique permits detailed measurement of the flowfield to be made in a much less hostile environment where in- strumentation will not be destroyed by the high temperatures (~4000°R-5000°R) encountered in flows with combustion. Although exact duplication of local flow divergence caused by spatial and time variations in heat release cannot be achieved with throttling, extensive comparison of the throttle test data and combustor data showed that sufficient similarity of the two flows was obtained for studying the effects of the corn-