James P. Johnston

A Review of Research on Subsonic Turbulent Flow Reattachment

Introduction T reattachment of a turbulent shear layer is an important process in a large number of practical engineering configurations, including diffusers, airfoils with separation bubbles, buildings, and combustors. In order to predict these complicated flows, we must understand and be able to predict the behavior of reattaching shear layers. However, our current understanding of the reattachment process is poor, a fact demonstrated by our inability to predict simple reattaching flows over a wide range of parameters. In fact, a complete list of the parameters that affect reattachment has yet to be formulated. Among two-dimensional flows, the backward-facing step is the simplest reattaching flow. The separation line is straight and fixed at the edge of the step, and there is only one separated zone instead of two, as seen in the flow over a fence or obstacle. In addition, the streamlines are nearly parallel to the wall at the separation point, so significant upstream influence occurs only downstream of separation. Although they are not always stated explicitly, these are the reasons why most of the research on reattachment has been done in backward-facing step flows. The backward-facing step is also used as a building block flow for workers developing turbulence models. Therefore, it is important to supply data which can be used to test codes and information that may aid the development of future codes. Bradshaw and Wong reviewed the experimental data for reattaching flows in 1972. Since that time there has been a proliferation of new research in the area, particularly since the advent of the laser anemometer and the pulsed-wire anemometer. This research has been conducted by a number of independent groups, and therefore the net result is somewhat disorganized. Very little systematic study has been done on the effect of the governing parameters on reattachment. In addition, most of the experiments, when viewed separately, have failed to cast any new light on the underlying physics of the reattachment process. The purpose of this paper is twofold. The primary purpose is to review the available data for turbulent flows over backward-facing steps, including some new data of our own and other previously unpublished data. Second, we suggest several areas of research that we feel could lead to improvements in our ability to predict flows with separation bubbles. Several physical mechanisms will be proposed to explain some of the phenomena that have been observed. It is our hope that these suggestions will provoke further thought, comment, and research. The review covers subsonic flows over backward-facing steps in which the Reynolds number is high enough to insure that the separated shear layer is fully turbulent. Important work on laminar and transitional reattaching shear layers has been performed by Goldstein et al. and Armaly et al. but will not be referred to here. Primary emphasis is on planar flows, but some data from axisymmetric flows will be utilized. Double-sided, sudden expansion flows in which the flow is asymmetric are not considered here, because these flows are even more complicated than flows with a single separation bubble. A companion paper examines the uncertainty of the available data in more detail. It also assesses the usefulness of the various data sets as test cases for computational procedures.

Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow.

Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (i) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (ii) the total suppression of transition to turbulence in a stabilized layer; (iii) the development of large-scale roll cells on the de-stabilized side of the channel by growth of a Taylor-Gortler vortex instability. An appropriate local stability parameter is the Richardson number formulated by Bradshaw (1969) for this case and the analogous cases of flow over curved walls and of shear-layer flow with density stratification. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.

Roll-cell instabilities in rotating laminar and trubulent channel flows

The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of R ec = 88.53 and rotation number R o = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 o o = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.

Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

Although the number of data sets which show the effects of convex curvature on turbulence has increased in the last 10 years, the development of really good calculational models is being held back by a lack of reliable data. The pesent investigation is concerned with a set of experiments which provide a litle more information regarding the response of a boundary-layer flow to convex curvature. Careful measurements were conducted to show the response of the boudnary layer to a sudden change from flat wall to curvature, and from curvature to flat wall. It was found that curvature effects were clearly apparent one or two boundary-layer thicknesses downstream of the start of curvature, while the disappearance of the curvature effects on a flat wall was an extremely slow process.

On vortex generating jets

Vortex generating jets (VGJs) are jets that pass through a wall and into a crossflow to create a dominant streamwise vortex that remains embedded in the boundary layer over the wall. The VGJ is characterized by its pitch and skew angles (Φ and Θ) and the velocity ratio (VR) between the jet and the crossflow. For VR=1.0, the VGJ configuration of Φ=30°,Θ=60° has been identified as that which produces the vortex with the highest peak mean vorticity. Three-component laser Doppler velocimetry (LDV) data for this particular configuration demonstrate many interesting features of the flow. Mean velocity data show a deficit of streamwise momentum in the core of the vortex, thinning of the boundary layer on the downwash side of the vortex, and thickening of the boundary layer on the upwash side. Plots of the turbulent kinetic energy and the turbulent shear stress 〈uv〉 show that the turbulent structure of the boundary layer is grossly disturbed by the presence of the vortex. The turbulent transport of the turbulent kinetic energy shows the possibility for a gradient diffusion model in most regions, but not the vortex core.

Microscale Radial-Flow Compressor Impeller Made of Silicon Nitride: Manufacturing and Performance

A microscale, high-speed compressor impeller (12 mm diameter, 800,000 rpm) was tested for feasibility in regard to aerodynamic performance. The compressor was designed for application in a first-sized gas turbine generator. To survive high stresses at such high temperatures, the rotor was manufactured as a single turbine/compressor/shaft unit in silicon nitride, by the Mold SDM process. Performance testing was conducted in a cold-flow rig at reduced speed of 420,000 rpm. Results from a CFD code compared favorably to measured data at this speed. Extrapolation from test conditions to full design speed was accomplished by application of CFD applied at both speeds.

A New Probe for Measurement of Velocity and Wall Shear Stress in Unsteady, Reversing Flow

Separated turbulent flows exhibit instantaneous reversals of flow direction which make measurement of the velocity field extremely difficult. A three-wire heat-tracer technique has been employed to measure streamwise velocity of a low-speed air flow very near a smooth, solid wall; the wall shear stress is calculated using a similarity hypothesis. Initial results presented show the evolution of average wall shear stress and rms fluctuation intensity of wall shear stress in a reattaching 2-D flow downstream of a backward-facing step.

The relaxation of a turbulent boundary layer in an adverse pressure gradient

Reattached turbulent boundary layer relaxation downstream of a wall fence is investigated. An adverse pressure gradient is imposed upon it which is adjusted to bring the boundary layer into equilibrium. The pressure gradient is adjusted so as to bring the Clauser parameter G down to a value of about 11.4 and then maintain it constant. In the region from the reattachment point to 2 or 3 reattachment lengths downstream, the boundary layer recovers from the initial major effects of reattachment. Farther downstream, where G is constant, the pressure-gradient parameter changes very slowly and profiles of non-dimensionalized eddy viscosity appear self-similar. However, pressure gradient and eddy viscosity are both roughly twice as large as expected on the basis of previous equilibrium turbulent boundary layer studies.

Low Frequency Unsteadyness of a Reattaching Turbulent Shear Layer

Low-frequency unsteadiness of a reattaching shear layer was studied in the flow behind a backward-facing step. Spectral data from a hot-wire probe showed that a substantial fraction of the measured turbulence intensity occurs at frequencies significantly lower than the large eddy passing frequency. Several thermal tuft probes were used simultaneously to identify the source of the low-frequency disturbances. It was concluded that the reattaching free shear layer undergoes a non-periodic, roughly two-dimensional, vertical motion. The motion causes the impingement point of the reattaching shear layer to drift slowly up- and downstream over a range of approximately two step heights. The likely cause of the low-frequency motion is an instantaneous imbalance between the entrain-ment rate from the recirculation zone and the reinjection rate near reattachment.

A Wall-Flow-Direction Probe for Use in Separating and Reattaching Flows.

Abstract : The measurement of the exceedingly unsteady behavior of nominally two-dimensional, turbulent flows in regions of separation and reattachment is facilitated by the development of a new instrument; the wall-flow-direction probe which determines the instantaneous flow direction (upstream or downstream) in a thin layer of fluid very close to the wall. The probe was tested in low-speed, unsteady, separating and reattaching air flows. It appears to offer considerably more accuracy than other methods for the determination of the time mean separation and reattachment points. In addition, the probe and its control circuits are relatively inexpensive and easy to construct. (Author)