Downstream-facing Step Research Articles

Analysis of Unsteady Confined Viscous Flows With Variable Inflow Velocity and Oscillating Walls

The inflow velocities in various components of many engineering systems often display variations in time (fluctuations) during the operation cycle, which may substantially affect the flow-induced vibrations and instabilities of these systems. For this reason, the aeroelasticity study of these systems should include the effect of the inflow velocity variations, which until now has not been taken into account. This paper presents a fluid-dynamic analysis of the unsteady confined viscous flows generated by the variations in time of the inflow velocities and by oscillating walls, which is required for the study of flow-induced vibration and instability of various engineering systems. The time-accurate solutions of the Navier–Stokes equations for these unsteady flows are obtained with a finite-difference method using artificial compressibility on a stretched staggered grid, which is a second-order method in space and time. A special decoupling procedure, based on the utilization of the continuity equation, is used in conjunction with a factored alternate direction scheme to substantially enhance the computational efficiency of the method by reducing the problem to the solution of scalar tridiagonal systems of equations. This method is applied to obtain solutions for the benchmark unsteady confined flow past a downstream-facing step, generated by harmonic variations in time of the inflow velocity and by an oscillating wall, which display multiple flow separation regions on the upper and lower walls. The influence of the Reynolds number and of the oscillation frequency and the amplitudes of the inflow velocity and oscillating wall on the formation of the flow separation regions are thoroughly analyzed in this paper. It was found that for certain values of the Reynolds number and oscillation frequency and amplitudes, the flow separation at the upper wall is present only during a portion of the oscillatory cycle and disappears for the rest of the cycle, and that for other values of these parameters secondary flow separations may also be formed.

UNSTEADY CONFINED VISCOUS FLOWS WITH OSCILLATING WALLS AND MULTIPLE SEPARATION REGIONS OVER A DOWNSTREAM-FACING STEP

This paper presents computational solutions for unsteady viscous flows in channels with a downstream-facing step, followed by an oscillating floor. These solutions of the unsteady Navier–Stokes equations are obtained with a time-integration method using artificial compressibility in a fixed computational domain, which is obtained via a time-dependent coordinate transformation from the fluid domain with moving boundaries. The computational method is first validated for steady viscous flows past a downstream-facing step by comparison with previous numerical solutions and experimental results. This method is then used to obtain solutions for unsteady viscous flows with multiple separation regions over a downstream-facing step with oscillating walls, for which there are no previously known solutions. Thus, the present results may be used as benchmark solutions for the unsteady viscous flows with multiple separation regions between fixed and oscillating walls.

Effects of Internal Nozzle Geometry on Compression-Ramp Mixing in Supersonic Flow

An experimental study based onow visualization has been conducted in a constant-area duct ® tted with a swept-ramp fuel injector to explore mixing enhancement techniques for supersonic combustion ramjet (scramjet) engines.ThemainowwasairatMach2,andthehydrogenfuelwassimulatedbyhelium injectedatMach 1.70 and by air injected at Mach 1.63. Mie scattering from ethanol-seeded helium or air was used to visualize the simulated fuelow injected into the main airstream. Six injector nozzle inserts for preconditioning the simulated fuel jet were tested to explore its interaction with the vorticalow produced by the ramp. The six nozzle inserts were as follows: circular nozzle (baseline), nozzle with three downstream facing steps in the divergent section, nozzle with four vortex generators, elliptical nozzle, tapered-throat nozzle, and trapezoidal nozzle. Mixing characteristics of the different inserts were inferred from image analysis. The results indicate that the mixing process is dominated by the ramp-generated vorticity, the injectors' inner geometry having a secondary effect. It also was found that the simulated fuel± air mixing in the far ® eld is nearly independent of the injector geometry, molecular weight of the injected gas, and the initial convective Mach number.

Effects of internal nozzle geometry on compression-ramp mixing in supersonic flow

An experimental study based on flow visualization has been conducted in a constant-area duct fitted with a swept-ramp fuel injector to explore mixing enhancement techniques for supersonic combustion ramjet (scramjet) engines. The main flow was air at Mach 2, and the hydrogen fuel was simulated by helium injected at Mach 1.70 and by air injected at Mach 1.63. Mie scattering from ethanol-seeded helium or air was used to visualize the simulated fuel flow injected into the main airstream. Six injector nozzle inserts for preconditioning the simulated fuel jet were tested to explore its interaction with the vortical flow produced by the ramp. The six nozzle inserts were as follows: circular nozzle (baseline), nozzle with three downstream facing steps in the divergent section, nozzle with four vortex generators, elliptical nozzle, tapered-throat nozzle, and trapezoidal nozzle. Mixing characteristics of the different inserts were inferred from image analysis.

FLOW ABOUND TWO-DIMENSIONAL ROUGHNESS ELEMENTS

Flow around two-dimensional roughness elements in the form of rectangular blocks has been analyzed for reynolds number 0 ≤Re≤40 and blocks of aspect ratio 0.01 ≤W/h≤∞. A very good agreement exists between numerical and experimental results. The size of the upstream separation zone weakly depends on the length of the block but decreases rapidly with an increase of the Reynolds number. In contrast, the length of the downstream separation zone increases almost linearly as Re increases. While this length depends weakly on the aspect ratio of the block, the velocity magnitude inside the separation zone considerably increases with a decrease of the length of the block. The coupling between the upstream and downstream separation zones rapidly disappears when W/h increases and both zones can be considered independent and identical to those at the upstream and downstream facing steps with W/h≥6.

Enhancement of fine-scale turbulence for improving fuel-rich plume combustion

A passive method to enhance fine-scale mixing was developed and studied in cold flows. Its effect on the combustion intensity and flame stability was then studied in reacting flows. Hot-wire anemometry was used to map the mean and turbulent flowfields of the nonreacting flows. Reacting flows were studied in a free flame and ducted gas-generator fuel-rich plume using planar laser-induced fluorescence imaging, a rake of thermocouples , and high-speed photography. A modified circular nozzle having several downstream-facing steps upstream of its exit was used to introduce numerous inflection points in the initial mean velocity profiles, thus producing multiple corresponding sources of fine-scale turbulence generators and reducing the strain rates in the initial region. Cold flow tests showed turbulence increases of up to six times the initial turbulence level relative to a circular nozzle and a substantial decrease of the mean velocity gradient. The flame of this nozzle was more intense with a homogeneous heat release in the free-flame experiments and ducted-plume combustion experiments, even when the gas-generator exhaust velocity was supersonic. Secondary plume ignition was obtained under conditions that prevented sustained afterburning using the circular nozzle.

Steady laminar flow over a downstream-facing step as a critical test case for the upwind Petrov-Galerkin finite element method

Galerkin finite element methods based on symmetric weighting functions give oscillations in the solution of steady Navier-Stokes equations when the Reynolds number is large. To overcome this difficulty Galerkin methods with asymmetric weighting functions can be used. In the present paper a critical test case is calculated with this so-called Petrov-Galerkin method. Comparison between calculations and experiments proofs that the accuracy of the method is good, even for a Reynolds number based on mesh size as high as two hundred.

A finite element analysis of flow over a backward facing step

The finite element method is used to solve both laminar and turbulent flow over a downstream facing step with a one equation model used for the turblent flow analysis. The effect of using upwind elements is investigated and the results are compared with published experimental and numerical data.

Inception of Cavitation From a Backward Facing Step

Cavitation inception measurements are reported for flow past a downstream facing step with the height of the step varying from about 0.4 to 5 percent of the forebody diameter. The forebody was a 49 mm hemispherical nose and σi values were found to be very strong function of the height of the step. In addition, σi values were found to depend on whether the boundary layer approaching the step was laminar or turbulent. Generally σi values for turbulent case were lower.

Laminar Separation, Reattachment, and Transition of the Flow Over a Downstream-Facing Step

Results of an experimental investigation of the laminar flow of air over a downstream-facing step are presented. The experiments include visual observations of smoke filaments (in the viscous layer), qualitative velocity fluctuation measurements, and mean velocity profiles. Results are reported over a range of 0.36 – 1.02 cm in step height, 0.61 – 2.44 m/sec in free stream velocity at the step, and 0.16 – 0.51 cm in boundary layer displacement thickness at the step. Laminar flow to reattachment of a free shear layer is observed for subsonic flow and two criteria for which transition to turbulence at reattachment exists are presented. The laminar reattachment length is not a constant number of step heights as for turbulent flow, but varies with Reynolds number and boundary layer thickness at the step. The shape of the velocity profile at reattachment is found to be similar to the shape of a laminar boundary layer profile at separation and the boundary layer profiles downstream of reattachment are similar to those in a laminar boundary layer developing toward separation except that they are traversed in the reverse sense.

Closure to “Discussion of ‘Laminar Separation, Reattachment, and Transition of the Flow Over a Downstream-Facing Step’” (1970, ASME J. Basic Eng., 92, pp. 739–741)

Closure to “Discussion of ‘Laminar Separation, Reattachment, and Transition of the Flow Over a Downstream-Facing Step’” (1970, ASME J. Basic Eng., 92, pp. 739–741)

Effect of a shoulder modification on turbulent supersonic base flow.

It has been observed experimentally by Hama and discussed theoretically by Weinbaum that effects of the fast expansion and consequent lip shock at the shoulder of a supersonic base or downstream-facing step can be quite appreciable at high Mach number. Hama found that the lip shock can be much stronger than has been assumed. He also drew attention to characteristic humps or peaks in the pressure distribution on the reattachment surface; these, he showed, could be attributed to secondary waves directed toward the surface from the point of interaction of the lip shock with the main recompression shock. Scherberg and Smith have also drawn attention to the possible strong effects connected with a lip shock. In this note, we report some further observations of the occurrence of this phenomenon, and its elimination by a small modification at the shoulder to alleviate the fast expansion there.

Errata: "Observations of Turbulent Reattachment behind an Axisymmetric Downstream-Facing Step in Supersonic Flow"

Errata: "Observations of Turbulent Reattachment behind an Axisymmetric Downstream-Facing Step in Supersonic Flow"

Observations of turbulent reattachment behind an axisymmetric downstream-facing step in supersonic flow.

Supersonic flow over a downstream-facing step on the circumference of a large, ducted, axisymmetric body was used to study flow reattachment. Step heights h were 0.25, 1.00, and 1.68 in., compared to a body radius of 6 in. Freestream Mach numbers were in the range 2 to 4.5. Theturbulent boundary-layer thickness just ahead of the step varied from 0.14 to 0.19 in. (momentum thicknesses of about 0.01 in.). Surface pressure distributions throughout the region of separation and reattachment were measured, and points of reattachment were determined. Comparison of the shapes of the pressure distributions for various step heights shows that the initial (steepest) parts of the reattachment pressure rise, up to the point of reattachment, tend to become superimposed when plotted against x/h. Downstream reattachment the curves branch out, exhibiting a dependence on geometry and probably on initial shear layer profile. In the region of the initial pressure rise (near the end of the dead air region) dynamic pressures are low; the pressure rise there apparently is balanced by turbulent shear stress.

Remarks on Snow Cornice Theory and Related Experiments With Sink Flows

A review is made of Ringleb’s theory on snow cornice-like flows and of the published, unsuccessful attempts at experimental verification. Arguments are presented which render the theory an unlikely representation of real fluid flows. The flow over a downstream-facing step in a channel, with either of two types of sinks located immediately downstream of the step, was investigated experimentally. A vortex and associated smooth expansion of the exterior flow behind the step were established for sufficiently high sink rates. A model of the step-sink flow is suggested and found consistent with results presented here and elsewhere.