Reattachment Zone Research Articles

Turbulence statistics of periodically perturbed separated flow over backward-facing step

The turbulence statistics of an unsteady separated flow was experimentally investigated. A backward-facing step flow at Re=3700 was chosen as the test case, where periodic perturbation was introduced from its step edge. A two-dimensional particle imaging velocimeter (PIV) was used in the flow-field measurement. The measured results showed that the reattachment length was reduced by the applied periodic perturbation. There existed an optimum frequency for the promotion of the reattachment. When perturbed at the optimum frequency, St=0.19, the reattachment length was reduced by 30%. The Reynolds stress components were increased by the perturbation, and their distribution varied with the perturbation frequency. When perturbation at the optimum frequency was applied, Reynolds stress markedly increased near the reattachment zone. This increase in Reynolds stress enhanced the momentum transfer across the shear layer, enabling the promotion of the reattachment. On the other hand, the region where the perturbation at higher frequency than the optimum frequency increases Reynolds stress was limited immediately behind the step. The perturbation at lower frequency than the optimum frequency increased Reynolds stress in the region downstream of the reattachment zone. Therefore, both low- and high-frequency perturbations have less effect on the promotion of the reattachment than optimum-frequency perturbation.

Two friendly rules for the turbulent heat transfer enhancement

The effect of roughness elements on heat transfer in fluids is different from their effect in gases because of the different thermal resistance of the viscous sublayer. The distinctive feature of the process was examined in every detail and generalised by two rules deduced, one for fluids with Pr > 5 and another for gases. For fluids, small equally dispersed roughness elements can disturb the viscous sublayer sufficiently. For gases, the enhancement is reached by creation of many reattachment zones after obstacles. Two- to three-fold heat transfer enhancement within the limits of Reynolds analogy 2 St/ c f is attainable.

A numerical study of turbulent flow over a two-dimensional hill

Calculations of mean velocities and Reynolds stresses are reported for the recirculating flow established in the wake of two-dimensional polynomial-shaped obstacles that are symmetrical about a vertical axis and mounted in the water channel downstream of a fully developed channel flow for Re=6×104. The study involves calculations of mean and fluctuating flow properties in the streamwise and spanwise directions and include comparisons with experimental data [Almeida GP, Durão DFG, Heitor MV. Wake flows behind two-dimensional model hills. Experimental Thermal and Fluid Science 1993; 7: 87–101] for flow around a single obstacle with data resulting from the interaction of consecutive obstacles, using two versions of the low-Reynolds number differential second-moment (DSM) closure model. The results include analysis of the turbulent stresses in local flow co-ordinates and reveal flow structure qualitatively similar to that found in other turbulent flows with a reattachment zone. It is found that the standard isotropization of production model (IPM), based on that proposed by Gibson and Launder [Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 1978; 86(3): 191–511], with the incorporation of the wall reflection model of Craft and Launder [New wall-reflection model applied to the turbulent impinging jet. AIAA Journal 1992; 32(12): 2970–2972] predicts the mean velocities quite well, but underestimates the size of the recirculation region and turbulent quantities in the shear layer. These inadequacies are circumvented by adopting a new cubic Reynolds stress closure scheme based on that more recently developed by Craft and Launder [A Reynolds stress closure designed for complex geometries. International Journal of Heat and Fluid Flow 1996; 17: 245–254] which satisfies the two component limit (TCL) of turbulence. In this model the geometry-specific quantities, such as the wall-normal vector or wall distance, are replaced by invariant dimensionless gradient indicators. Also, the model captures the diverse behaviour of the different components of the stress dissipation, εij, near the wall and uses a novel decomposition for the fluctuating pressure terms. Copyright © 2001 John Wiley & Sons, Ltd.

Analysis Of Temperature Fluctuations In ATurbulent Flow Over A Backward-facing Step

A large-eddy simulation (LES) of the flow over a backward-facing step was conducted to investigate the heat transfer phenomena in the reattachment zone. The Navier-Stokes equations for an incompressible fluid with the temperature field considered as a passive scalar, are solved using a second-order accurate scheme in space and time. In order to have a fully turbulent flow in the domain, an auxiliary simulation is carried out to provide unsteady velocity and temperature fields at the entrance to the backward-facing step. The Mixed Scale Subgrid Model is used for the momentum equations while a scalar subgrid diffusivity model is employed for the temperature equation. The Reynolds number based on the bulk velocity (Ub) at the entrance and the step height (h) is 66 100. The mean reattachment point was predicted at x=5.4h which is close to the value calculated by Moss et al. [5] for the same expansion ratio and for a turbulent flow. Mean velocity field shows clearly that the shear layer issued from the step impacts the wall defining a recirculation zone in which the reversed flow spreads into the original shear layer. Just behind the step, a second recirculation region acts like an obstacle for the first reversal flow. The examination of the mean temperature field proves that the mixing behind the step is weak. From the shear layer to the reattachment zone, a large region exists containing warm fluid, but the fluid just behind the step remains cold. Apart from the fact that the temperature fluctuations are important in the shear layer, another region of high fluctuations was found to issue from the reattachment point and stretch toward the region of reversed flow.

Experimental and Numerical Investigation of Forced Convective Characteristics of Arrays of Channel Mounted Obstacles

An experimental investigation of the forced convective heat transfer of individual and arrays of multiple two-dimensional obstacles is reported. The airflow rate was varied from 800 ≤ ReDh ≤ 13000. The effects upon the Nusselt numbers and obstacle temperature differences of parametric changes in the Reynolds number, channel height, array configuration, and input heat flux are established. The input heat fluxes to the obstacles ranged from 950 ≤ q″ ≤ 20200 W/m2, which significantly extends beyond that seen in the open literature for forced convective air cooling of simulated electronic components. Comparisons of the obstacle mean Nusselt numbers are made with a two-dimensional laminar numerical model employing the Navier-Stokes equations. A set of correlations characterizing the heat transfer from the protruding heat sources within the channel is obtained. It was found that the obstacle temperature, the critical measure for electronic device failure, must be shown along with the corresponding Nusselt number to fully characterize the thermal state of the heated obstacle as the ratio definition of the Nusselt number can obscure large temperature increases. The results find that the proper placement of geometrically dissimilar obstacles, such as a taller obstacle, can be used to passively enhance the heat transfer in its vicinity. This effect would be dependent upon the flow rate and geometries in order to control the reattachment zones and their subsequent convective augmentation. The experimental results are found to be in good agreement with the results from the numerical simulation. Finally, a set of pertinent correlations for the arrays of channel mounted obstacles is given.

Transfert de chaleur au voisinage du point de recollement en aval d'une marche descendante

It has been noticed, although not yet explained, that in recirculating flows the heat transfer coefficient, which is maximum in the reattachment zone, does not correspond in position with the mean reattachment point. We propose an explanation based on impact (main component of velocity V < 0) and sweeping (main component of velocity U > 0) phenomena which are both induced by the vortical structures interacting with the heated wall. This approach uses information given by a numerical code based on the finite volume technique, as well as an analysis of the time evolution of the reattachment point X r and the point of maximum heat transfer X max . This analysis is supported by the time series and the profiles of the correlations relative to the velocities and temperature variables.

INFLUENCE OF SEPARATION ON SOUND GENERATED BY VORTEX-STEP INTERACTION

An analysis of the sound produced when a line vortex interacts at low Mach number with forward or backward facing steps is made. The radiation is dominated by an aeroacoustic dipole whose strength is equal to the unsteady drag on the step. The drag is determined by the vorticity distribution, and a correct estimate of the sound must therefore include contributions from vorticity in the separated flow induced by the vortex. The separation is modelled by assuming that the shed vorticity rolls up into a concentrated core, fed by a connecting sheet from the edge of the step of negligible circulation. The motion everywhere is irrotational except at the impinging vortex and the separation core, and the trajectory of the core is governed by an emended Brown & Michael equation. For large steps it is found that estimates of the generated sound that neglect separation are typically an order of magnitude too large. The sound levels predicted for small steps with and without separation are of comparable magnitudes, although the respectivephasesare different.Turbulentflow over a step frequently involves separation and large surface pressure fluctuations at reattachment zones. The results of this paper suggest that numerical schemes for determining the noise generated by turbulent flow over a step must take proper account of “forcing” of the separation region by the impinging turbulence and of vorticity production via the no-slip condition.

Instantaneous Three-Dimensional Vorticity Measurements in Vortical Flow over a Delta Wing

An attempt is made to explore the structures in the vortical flow over a delta wing by spatio-temporal measurements of velocity vectors and subsequent evaluation of vorticity vectors. A novel probe, with good spatial resolution, to measure the multipoint velocity vector has been designed and constructed. Tests results of the statistical properties from the measurements of instantaneous velocity and vorticity vectors in the turbulent boundary layers gave confidence to investigate the vortices over a 45-deg-swept-back delta wing and to explore their complex structure with this probe. The present measurements indicated the existence of discrete stationary vortices in the feeding shear layer region as well as a primary vortex where mean vorticity is at maximum and where the mean velocity excess is about 1.3U o . Large vorticity fluctuations, of the order of three to six times the mean vorticity, were measured between the low speed side of the shear layer and the surface of the delta wing. Such fluctuating vorticity statistics are presented for the first time. The shear layer reattachment zone and the region of secondary separation are associated with intense turbulence activities.

Heat Transfer Characteristics of a Radial Jet Reattachment Flame

A Radial Jet Reattachment Combustion (RJRC) nozzle forces primary combustion air to exit radially from the combustion nozzle and to mix with gaseous fuel in a highly turbulent recirculation region generated between the combustion nozzle and impingement surface. High convective heat transfer properties and improved fuel/ air mixing characterize this external mixing combustor for use in impingement flame heating processes. To understand the heat transfer characteristics of this new innovative practical RJRC nozzle, statistical design and analysis of experiments was utilized. A regression model was developed which allowed for determination of the total heat transfer to the impingement surface as well as the NOx emission index over a wide variety of operating conditions. In addition, spatially resolved flame temperatures and impingement surface temperature and heat flux profiles enabled determination of the extent of the combustion process with regards to the impingement surface. Specifically, the relative sizes of the reaction envelope, high temperature reaction zone, and low temperature recirculation zone were all determined. At the impingement surface in the reattachment zone very high local heat flux values were measured. This study provides the first detailed local heat transfer characteristics for the RJRC nozzle.

Unsteady Measurements near Leading Edge of Separated Flow.

A separation and reattaching flow formed by the boundary layer separation at the edge of a blunt circular cylinder at Reynolds number of 1.0×105 based on the main flow velocity U∞ and the diameter of the cylinder D is studied. The time-mean and root-mean-square values of fluctuating surface pressure on the front surface and along the side face are presented. The reattachment length is 1.73D and is constant along the circumference. From the mean pressure distribution on the front surface, the thickness of the laminar boundary layer at separation is estimated to be 1.86×10-4D. The low-frequency motion nLr/U=0.011 at the leading edge, which is regarded as the flapping of the separated shear layer, was also found in the initial boundary layer upstream of separation. This pressure fluctuation inside the initial boundary layer, which is clearly identified without other disturbance generated by the shear layer rolling up, recirculating or feedback motion from the reattachment zone, is caused by upstream propagation of the fluctuating motion of the separated shear layer. In addition to this low-frequency flapping motion, the high-frequency velocity fluctuations of the shear layer next to separation, which demonstrate the Kelvin-Helmoltz instability and the evolution of the shear layer, are important for understanding and control of separation.

Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct

The incompressible turbulent flow over a backward-facing step in a rectangular duct was investigated experimentally. The side wall effects on the core flow were determined by varying the aspect ratio (defined as the step span-to-height ratio) from 1 to 28. The Reynolds number, based on the step height and the oncoming free-stream velocity, was 26,500. Detailed velocity measurements were made, including the turbulent stresses, in a region which extended past the flow reattachment zone. Wall static pressure was also measured on both the step and flat walls. In addition, surface visualizations were obtained on all four walls surrounding the separated flow to supplement near-wall velocity measurements. The results show that the aspect ratio has an influence on both the velocity and wall pressure even for relatively large aspect ratios. For example, in the redevelopment region downstream of reattachment, the recovery pressure decreases with smaller aspect ratios. The three-dimensional side wall effects tend to slow down the relaxation downstream of reattachment for smaller aspect ratios as evidenced by the evolution of the velocity field. For the two smallest aspect ratios investigated, higher centerplane streamwise and transverse velocities were obtained which indicate a three-dimensional mean flow structure along the full span of the duct.

Rotor wake interaction with separated flow

Aerodynamic interactions represent one of the toughest challenges to computational methods for the prediction of rotorcraft performance, loads, and noise. Efforts over the past ten years using a simple hemisphere/cylinder airframe under a teetering two-bladed rotor have shown that most of the dominant effects can be predicted using potential-flow concepts, in the absence of massive flow separation and strong vortex-surface collision. Here, the prospects for modeling the separated flow interaction are studied. The rotor wake interacts with the separated flow over a pressure-instrumented boom, downstream of a backstep cut into the original cylinder. The undisturbed backstep flow is characterized using spectral analysis of the velocity and surface pressure fields. The interaction between the tip vortex and the backstep free shear layer is visualized using laser sheet videography, and measured in detail using laser velocimetry and pressure sensing. The tip vortex dominates the interaction, causing periodic destruction and reconstruction of the shear layer, and large-amplitude longitudinal motion of the reattachment zone. However, the characteristics of the undisturbed shear layer are still detected in the surface pressure spectra. The tip vortex and its collision with the boom surface appear to be unaffected by the shear layer interaction. It is argued that this experiment is a conservative representation of the interaction, so that occurrences on real rotorcraft should be less complex. Thus, while the separated flow interaction appears to be extremely complex at first sight, the dominant effects are surprisingly simple, and may be easily modeled.

Vorticity dynamics and scalar transport in separated and reattached flow on a blunt plate

Two‐dimensional calculations are performed for a Reynolds number of 1000 and an effective Prandtl number of unity to study the dynamics of large‐scale spanwise vortices with a passive scalar field in a separation and reattaching flow over a blunt plate. A triple decomposition technique is used to isolate the quasiperiodic fluctuations related to the large‐scale vortices shed from the separated shear layer. Three vortex shedding modes are identified in the reattachment zone, two of which involve partial pairings. The coherent vortices shed from the reattachment zone have a dominating effect on scalar transport, and act as ‘‘large‐scale mixers’’ by entraining wall scalar around their upstream periphery and free‐stream scalar on their lower downstream edge. There is a definite relationship between the phase‐averaged perturbations (due to the presence of coherent vortices) in the wall friction factor and wall scalar transport with their respective time mean maximums. On the other hand, although there does exist an explicit spatial relationship between the instantaneous stagnation point and instantaneous location of maximum wall scalar transport, there is no such relationship in the mean between the two locations, except that both are dependent on the vorticity dynamics in the reattachment region.

Wake flows behind two-dimensional model hills

Laser-Doppler measurements of velocity characteristics are reported for the recirculating flow established in the wake of two-dimensional, polynomial-shaped obstacles that are axisymmetrical about a vertical axis and mounted in a water channel downstream of a fully developed channel flow for Re = 6 × 10 4. The study involves measurements of the mean and fluctuating flow properties in the streamwise and spanwise directions and includes comparison of the flow around a single obstacle with that resulting from the interaction of consecutive obstacles. The results include analysis of the turbulent stresses in local flow coordinates and reveal flow structure qualitatively similar to that found in other turbulent flows with a reattachment zone and, for the case of multiple hills, resembling the flow over wavy surfaces of large amplitude. The implications of the results for the calculation of turbulent flows over curved boundaries using turbulence models are discussed.

Turbulence Measurements in Open‐Channel Flows over Artificial Bed Forms

Measurements of mean and turbulence characteristics in uniform open‐channel flows of constant mean depth over artificial fixed one‐dimensional periodic bed features were obtained using two‐component laser‐Doppler velocimetry. Two types of bed forms, based on triangular elements of the same height (≈20% of the flow depth) and wavelength (≈12.5 times the height) but of different shape, were studied: (1) 45° triangle ridges separated by a flat region; and (2) triangular elements approximating dunes with a mildly sloping upstream face instead of a flat region. The role of the total shear velocity, based on the mean energy slope and the mean flow depth, as a possible velocity scale is studied. Velocity defect and the Reynolds shear stress profiles were generally well approximated by the flat‐bed profiles for regions of flow far from the bed. Sufficiently far from the recirculation and reattachment zones, turbulence characteristics collapsed fairly well when scaled with the total shear velocity over most of the depth, but do not follow the flat‐bed behavior in the lower part of the flow. Possible implications of the clear‐water measurements for the description of suspended sediment concentration profiles and total suspended load computations are explored.

Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3-D disturbances is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Effects of pressure gradient on reattaching flow downstream of a rearward-facing step

Reattachment problems of separated flow on a solid surface such as an airfoil, diffuser, cavity wall, etc. are of interest because a rapid rise of pressure and heat transfer takes place at the reattachment zone. Among the solid surface models for the study of the separated flow reattachment, the rearward-facing step is one of the simplest since the separation point is readily known. A number of investigations for the rearward-facing step is one of the simplest since the separation point is readily known. A number of investigations for the rearward-facing step flow showed that the reattachment length is strongly affected by the pressure gradient. This paper presents the experimental results of reattachment length and wall static pressure distribution affected by the constant streamwise pressure gradients.

Analysing turbulent backward-facing step flow with the lowpass-filtered navier-stokes equations

High Reynolds number turbulent backward-facing step flow is studied using the large-eddy simulation technique proposed by Schumann. Central differencing on an equidistant cartesian grid and explicit time integration are chosen to predict the complicated flow structure. The comparison with experimental data indicates good agreement for the statistical quantities. Part of the disagreement is certainly due to scatter in the experimental data. Nevertheless, the results of the simulation may be further improved using globally or locally refined grids. Valuable information on the instantaneous flow behaviour in the free-shear layer and the reattachment zone is obtained from the simulation.

Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress

Measurements of reattachment length of a separated flow behind a backward-facing step for a range of Reynolds numbers (8000 < ReH < 40,000) and initial boundary-layer thickness (0 < δ/H < 2) were performed with the purpose of explaining the scatter in existing (high quality) data sets and to understand the effect of the initial shear-layer structure on the reattachment zone. The reattachment length for the case of laminar boundary layers upstream of the step were 30% smaller than when the boundary layer upstream of the step was turbulent. Measured values of the mean wall shear stress in the reattachment zone were also measurably affected by the upstream boundary-layer state. The (rms) levels of fluctuating wall stress were not sensitive to boundary-layer state, but rather to δ/H, as was the case for the pressure profiles in part 1 (Adams and Johnston 1988).

Effects of the separating shear layer on the reattachment flow structure Part 1: Pressure and turbulence quantities

The effect of the separating shear-layer thickness and shape on the structure of the flow in the reattachment region of a backward-facing step is examined using wall static-pressure profiles and turbulence data for a range of Reynolds number (800 < ReH< 40,000) and upstream boundary-layer thickness (0 < δ/H < 2). The reattachment pressure and the peak pressure in the reattachment zone decrease in a continuous manner as the upstream boundary layer thickens. The thinnest boundary layers follow the correlation of Roshko and Lau. Using the pressure data, correlations are developed which can be used to predict the level of turbulent shear stress in the near-wall region at reattachment, a location in which experimental data are extremely difficult to obtain.