scholarly journals Direct numerical simulation of turbulent flow over a backward-facing step

1997 ◽  
Vol 330 ◽  
pp. 349-374 ◽  
Author(s):  
HUNG LE ◽  
PARVIZ MOIN ◽  
JOHN KIM
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Shear Layer ◽  
Stokes Equations ◽  
Recirculation Region ◽  
Wall Region ◽  
Free Shear Layer ◽  
Backward Facing Step ◽  
Temporal Behaviour ◽  
Log Law

Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

Computational Study of the Synthetic Jet on Separated Flow Over a Backward-Facing Step

2010 ◽  
Author(s):  
Koichi Okada ◽  
Kozo Fujii ◽  
Koji Miyaji ◽  
Akira Oyama ◽  
Taku Nonomura ◽  
...  
Keyword(s):  
Shear Layer ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Frequency Characteristics ◽  
Synthetic Jet ◽  
Recirculation Region ◽  
Backward Facing Step ◽  
Freestream Velocity ◽  
Jet Control

Frequency effects of the synthetic jet on the flow field over a backward facing step are investigated using numerical analysis. Three-dimensional Navier-Stokes equations are solved. Implicit large-eddy simulation using high-order compact difference scheme is conducted. The present analysis is addressed on the frequency characteristics of the synthetic jet for understanding frequency characteristics and flow filed. Three cases are analyzed; the case computing flow over backward facing step without control, the case computing flow with synthetic jet control at F+h = 0.2, and the case computing flow with synthetic jet control at F+h = 2.0, where non-dimensional frequency F+h is normalized with the height of backward-facing step and the freestream velocity. The present computation shows that separation length in the case of the flow controlled at F+h = 0.2 is 20 percent shorter than the case without control. Strong two-dimensional vortices generated from the synthetic jet interact with the shear layer, which results in the increase of the Reynolds stress in the shear layer region. These vortices are deformed into three-dimensional structures, which make Reynolds stress stronger in the recirculation region. Size of the separation length in the case of the flow controlled at F+h = 2.0 is almost the same as the case without control because the mixing between the synthetic jet and the shear layer is not enhanced. Weak and short periodic vortices induced from the synthetic jet do not interacts with the shear layer very much and diffuse in the recirculation region.

scholarly journals Effect of geometry and Reynolds number on the turbulent separated flow behind a bulge in a channel

2017 ◽  
Vol 823 ◽  
pp. 100-133 ◽  
Author(s):  
J.-P. Mollicone ◽  
F. Battista ◽  
P. Gualtieri ◽  
C. M. Casciola
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Shear Layer ◽  
Separation Bubble ◽  
Recirculation Region ◽  
Planar Channel ◽  
Energy Fluxes ◽  
Recirculation Bubble ◽  
Small Scales

Turbulent flow separation induced by a protuberance on one of the walls of an otherwise planar channel is investigated using direct numerical simulations. Different bulge geometries and Reynolds numbers – with the highest friction Reynolds number simulation reaching a peak of $Re_{\unicode[STIX]{x1D70F}}=900$ – are addressed to understand the effect of the wall curvature and of the Reynolds number on the dynamics of the recirculating bubble behind the bump. Global quantities reveal that most of the drag is due to the form contribution, whilst the friction contribution does not change appreciably with respect to an equivalent planar channel flow. The size and position of the separation bubble strongly depends on the bump shape and the Reynolds number. The most bluff geometry has a larger recirculation region, whilst the Reynolds number increase results in a smaller recirculation bubble and a shear layer more attached to the bump. The position of the reattachment point only depends on the Reynolds number, in agreement with experimental data available in the literature. Both the mean and the turbulent kinetic energy equations are addressed in such non-homogeneous conditions revealing a non-trivial behaviour of the energy fluxes. The energy introduced by the pressure drop follows two routes: part of it is transferred towards the walls to be dissipated and part feeds the turbulent production hence the velocity fluctuations in the separating shear layer. Spatial energy fluxes transfer the kinetic energy into the recirculation bubble and downstream near the wall where it is ultimately dissipated. Consistently, anisotropy concentrates at small scales near the walls irrespective of the value of the Reynolds number. In the bulk flow and in the recirculation bubble, isotropy is restored at small scales and the isotropy recovery rate is controlled by the Reynolds number. Anisotropy invariant maps are presented, showing the difficulty in developing suitable turbulence models to predict separated turbulent flow dynamics. Results shed light on the processes of production, transfer and dissipation of energy in this relatively complex turbulent flow where non-homogeneous effects overwhelm the classical picture of wall-bounded turbulent flows which typically exploits streamwise homogeneity.

Computational Studies of Turbulent Flow in an Isothermal Suddenly Enlarged Combustion Chamber

2004 ◽  
Author(s):  
D. P. Mishra ◽  
T. Vishak
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Combustion Chamber ◽  
Shear Layer ◽  
Turbulence Intensity ◽  
Stokes Equations ◽  
Isothermal Condition ◽  
Expansion Ratio ◽  
Computational Studies ◽  
Reattachment Length

The present work is concerned with computational studies of turbulent flow under isothermal condition in a suddenly enlarged combustion chamber using time averaged Navier-Stokes equations with an eddy-viscosity turbulence closure model. Results were compared well with that of experimental data available in open literature. The effect of inlet turbulence intensity is found to be the dominant parameter determining the flow field. However this effect is found to be decreasing with the increase in the expansion ratio. The increase of turbulence level decreases the reattachment length due to the energy supply to the separating shear layer, which is a major factor determining the reattachment length. It has been found out that for same expansion ratio, the reattachment length attains a minimum value for low turbulence Reynolds number, increases with increase in Reynolds number, and attains a maximum limit. Both the turbulent kinetic energy and the turbulent dissipation rate are found to be maximum in the shear layer and also keep increasing with the increase in turbulence intensity.

Large-scale motions in a plane wall jet

2019 ◽  
Vol 877 ◽  
pp. 239-281 ◽  
Author(s):  
Ebenezer P. Gnanamanickam ◽  
Shibani Bhatt ◽  
Sravan Artham ◽  
Zheng Zhang
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Large Scale ◽  
Plane Wall ◽  
Shear Stresses ◽  
Wall Jet ◽  
Wall Region ◽  
Free Shear Layer ◽  
Large Scale Structures ◽  
Scale Structures

The plane wall jet (PWJ) is a wall-bounded flow in which a wall shear layer develops in the presence of extremely energetic flow structures of the outer free-shear layer. The structure of a PWJ, developing in still air, was studied with the focus on the large scales in the flow. Wall-normal hot-wire anemometry (HWA) measurements along with double-frame particle image velocimetry (PIV) measurements (wall-normal–streamwise plane) were carried out at streamwise distances up to $162b$, where $b$ is the slot width of the PWJ exit. The nominal PWJ Reynolds number based on exit parameters was $Re_{j}\approx 5940$. Comparisons with a zero-pressure-gradient boundary layer (ZPGBL) at nominally matched friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ were also carried out as appropriate, to highlight key features of the PWJ structure. Consistent with previous work, the PWJ showed a dependence of the peak turbulent stresses on the jet exit Reynolds number. The turbulent production showed a peak corresponding to the near-wall cycle similar to the peak seen in the ZPGBL. However, another turbulent production peak was observed in the outer free-shear layer that was an order of magnitude larger than the inner one. Along with the change in sign of the viscous and Reynolds shear stresses, the PWJ was shown to have a region of very low turbulent production between these two peaks. The dissipation rate increased over the PWJ layer with a peak also in the outer region. Visualizations of the flow and two-point correlations reveal that the most energetic large-scale structures within a PWJ are vortical motions in the wall-normal–streamwise plane similar to those structures seen in free-shear layers. These structures are referred to as J (for jet) type structures. In addition two-point correlations reveal the existence of large-scale structures in the wall region which have a signature similar to those structures seen in canonical boundary layers. These structures are referred to as W (for wall) type structures. Instantaneous PIV realizations and flow visualizations reveal that these W type large-scale features are consistent with the paradigm of hairpin vortex packets in the wall region. The J type structures were seen to intrude well into the wall region while the W type structures were also seen to extend into the outer shear layer. Further, these large-scale structures were shown to modulate the amplitude of the finer scales of the flow.

Computational Study of Frequency and Amplitude Effects on Separation Flow Control With the Synthetic Jet

2009 ◽  
Author(s):  
Koichi Okada ◽  
Kozo Fujii ◽  
Koji Miyaji
Keyword(s):  
Shear Layer ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Frequency Characteristics ◽  
Synthetic Jet ◽  
Recirculation Region ◽  
Separation Flow ◽  
Control Case ◽  
Backward Facing Step

In order to investigate the frequency and amplitude effects of the synthetic jet on the flow field, numerical simulation is carried out. Even though the final objective of this study is to understand mechanism of separation control for various objects, streamline and bluff bodies, the configuration of backward-facing step is chosen as the first step because of the simplicity. Three-dimensional Navier-Stokes equations are solved. Implicit large eddy simulation using high-order compact difference scheme is applied. The present analysis is addressed on the frequency characteristics of the synthetic jet for understanding frequency characteristics and flow-filed. Three cases are selected, No-control, F+h = 0.2 and F+h = 2.0, where non-dimensional frequency F+h is normalized with the height of backward-facing step and the free stream velocity. The present computation shows that at F+h = 2.0, separation length is 20 percent shorter than the No-control case. Strong two-dimensional vortices generated from the synthetic jet interact with the shear layer, which results in the increase of the Reynolds stress in the shear layer region. These vortices are deformed into three-dimensional structures, which make Reynolds stress stronger in the recirculation region. At F+h = 2.0, size of the separation length is almost same as the No-control case because the mixing between the synthetic jet and the shear layer is not enhanced. Weak and short periodic vortices induced from the synthetic jet do not interacts with the shear layer very much and diffuse in the recirculation region.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

Experimental Investigation of the Flow Through Axisymmetric Expansions

1989 ◽  
Vol 111 (4) ◽  
pp. 464-471 ◽  
Author(s):  
M. Stieglmeier ◽  
C. Tropea ◽  
N. Weiser ◽  
W. Nitsche
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Shear Layer ◽  
Test Facility ◽  
Recirculation Region ◽  
Velocity Measurements ◽  
Forward Scatter ◽  
Separated Shear Layer ◽  
Flow Through ◽  
Diffusion Rates

This study examines the flow field in three axisymmetric expansions having diffuser half-angles of 14, 18, and 90 deg, respectively. Velocity measurements were performed at a Reynolds number of Re = 1.56 × 104 using a single component LDA operated in forward scatter. The test facility was refractive index matched, allowing measurement of the velocities U, V, W, u2, v2, w2, uv and uw upstream of, and throughout the entire recirculation region. The results indicate that the diffuser geometry influences the separated shear layer appreciably over the entire length of the diffuser section. The production of turbulence immediately after separation is much higher in the case of the 14 and 18 deg diffuser compared to the 90 deg expansion, leading to higher diffusion rates in the separated shear layer, and hence earlier reattachment of the shear layer.

Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number

2012 ◽  
Vol 693 ◽  
pp. 319-344 ◽  
Author(s):  
Xueming Shao ◽  
Tenghu Wu ◽  
Zhaosheng Yu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Large Scale ◽  
Horizontal Channel ◽  
Small Scale ◽  
Channel Height ◽  
Wall Region ◽  
Sediment Layer ◽  
Particle Settling ◽  
Volume Fractions

AbstractA fictitious domain method is used to perform fully resolved numerical simulations of particle-laden turbulent flow in a horizontal channel. The effects of large particles of diameter 0.05 and 0.1 times the channel height on the turbulence statistics and structures are investigated for different settling coefficients and volume fractions (0.79 %–7.08 %) for the channel Reynolds number being 5000. The results indicate the following. (a) When the particle sedimentation effect is negligible (i.e. neutrally buoyant), the presence of particles decreases the maximum r.m.s. of streamwise velocity fluctuation near the wall by weakening the intensity of the large-scale streamwise vortices, while increasing the r.m.s. of the streamwise fluctuating velocity in the region very close to the wall and in the centre region. On the other hand, the particles increase the r.m.s. of transverse and spanwise fluctuating velocities in the near-wall region by inducing the small-scale vortices. (b) When the particle settling effect is so substantial that most particles settle onto the bottom wall and form a particle sediment layer (SL), the SL plays the role of a rough wall and parts of the vortex structures shedding from the SL ascend into the core region and substantially increase the turbulence intensity there. (c) When the particle settling effect is moderate, the effects of particles on the turbulence are a combination of the former two situations, and the Shields number is a good parameter for measuring the particle settling effects (i.e. the particle concentration distribution in the transverse direction). The average velocities of the particle are smaller in the lower half-channel and larger in the upper half-channel compared to the local fluid velocities in the presence of gravity effects. The effects of the smaller particles on the turbulence are found to be stronger at the same particle volume fractions.

An experiment on the stability of small disturbances in a stratified free shear layer

1972 ◽  
Vol 52 (3) ◽  
pp. 499-528 ◽  
Author(s):  
R. S. Scotti ◽  
G. M. Corcos
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Test Section ◽  
Richardson Number ◽  
Molecular Diffusion ◽  
Free Shear Layer ◽  
Horizontal Beam ◽  
Theoretical Predictions ◽  
Critical Richardson Number ◽  
The Stability

A statically stable stratified free shear layer was formed within the test section of a wind tunnel by merging two uniform streams of air after uniformly heating the top stream. The two streams were accelerated side by side in a contraction section. The resulting sheared thermocline thickened gradually as a result of molecular diffusion and was characterized by nearly self-similar temperature (odd), velocity (odd) and Richardson number (even) profiles. The minimum Richardson numberJ0could be adjusted over the range 0·07 ≥J0≥ 0·76; the Reynolds number Re varied between 30 and 70. Small periodic disturbances were introduced upstream of the test section by a fine wire oscillating in the thermocline. The wire generated a narrow horizontal beam of internal waves, which propagated downstream and remained confined within the thermocline. The growth or decay of these waves was observed in the test section. The results confirm the existence of a critical Richardson number the value of which is in plausible agreement with theoretical predictions (J0≅ 0·22 for the Reynolds number of the experiment). The growth rate is a function of the wavenumber and is somewhat different from that computed for the same Reynolds and Richardson numbers, but the calculation assumed velocity and density profiles which were also somewhat different.

Influence of Viscoelasticity on Turbulent Flow Over a Backward-Facing Step

2015 ◽  
Author(s):  
Akito Ikegami ◽  
Takahiro Tsukahara ◽  
Yasuo Kawaguchi
Keyword(s):  
Fluid Flow ◽  
Turbulent Flow ◽  
Newtonian Fluid ◽  
Expansion Ratio ◽  
Weissenberg Number ◽  
Recirculation Region ◽  
Viscoelastic Flows ◽  
Backward Facing Step ◽  
Mean Velocity ◽  
Significant Difference

We studied viscoelastic turbulent flow over a backward-facing step of the expansion ratio ER = 1.5 using DNS (direct numerical simulation) at a friction Reynolds number Reτ0 of 100. We chose the Giesekus model as a viscoelastic constitutive equation, and the Weissenberg number is Wiτ0 = 10 and 20. Visualized instantaneous vortices revealing that a few vortices occur only above the recirculation regions in the viscoelastic fluid flow compared to those in the Newtonian flow. This phenomenon might be caused by the fluid viscoelasticity that would suppress the Kelvin-Helmholz vortex emanating from the step edge. The reattachment length from the step is 6.80h for the Newtonian fluid, 7.82h for Wiτ0 = 10, and 8.82h for Wiτ0 = 20, where h is the step height. In the mean velocity distributions normalized by maximum inlet velocity, we have observed no significant difference among the three fluids, except for region near the upper or bottom wall, i.e., the recirculation and recovery regions at the front and behind the reattachment point. The streamwise turbulent intensity u’rms is weaken in the recirculation region of the viscoelastic flows. In terms of v’rms, its magnitude in the recirculation region becomes largest in the case of Wiτ0 = 10, not for the Newtonian fluid flow or more viscoelastic case of Wiτ0 = 20.

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