Numerical investigation of the turbulent boundary layer over a bump

1998 ◽  
Vol 362 ◽  
pp. 229-271 ◽  
Author(s):  
XIAOHUA WU ◽  
KYLE D. SQUIRES
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Eddy Viscosity ◽  
Subgrid Scale ◽  
Internal Layers ◽  
Mean Flow ◽  
Eddy Viscosity Model ◽  
The Mean ◽  
Shear Production

Large-eddy simulation (LES) has been used to calculate the flow of a statistically two-dimensional turbulent boundary layer over a bump. Subgrid-scale stresses in the filtered Navier–Stokes equations were closed using the dynamic eddy viscosity model. LES predictions for a range of grid resolutions were compared to the experimental measurements of Webster et al. (1996). Predictions of the mean flow and turbulence intensities are in good agreement with measurements. The resolved turbulent shear stress is in reasonable agreement with data, though the peak is over-predicted near the trailing edge of the bump. Analysis of the flow confirms the existence of internal layers over the bump surface upstream of the summit and along the downstream trailing at plate, and demonstrates that the quasi-step increases in skin friction due to perturbations in pressure gradient and surface curvature selectively enhance near-wall shear production of turbulent stresses and are responsible for the formation of the internal layers. Though the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall is not followed by mean-flow separation. Certain turbulence characteristics in this region are similar to those previously reported in instantaneously separating boundary layers. The present investigation also explains the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements of Webster et al. (1996), i.e. the simultaneous uninterrupted development of an inner energy-equilibrium region and the monotonic decay of elevated turbulence shear production away from the wall. LES results were also used to examine response of the dynamic eddy viscosity model. While subgrid-scale dissipation decreases/increases as the turbulence is attenuated/enhanced, the ratio of the (averaged) forward to reverse energy transfers predicted by the model is roughly constant over a significant part of the layer. Model predictions of backscatter, calculated as the percentage of points where the model coefficient is negative, show a rapid recovery downstream similar to the mean-flow and turbulence quantities.

Near-wall measurements in a three-dimensional turbulent boundary layer

1997 ◽  
Vol 350 ◽  
pp. 189-208 ◽  
Author(s):  
DEBORA A. COMPTON ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Three Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

An experiment was performed to measure near-wall velocity and Reynolds stress profiles in a pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensional boundary layer (Reθ≈4000) was exposed to a strong spanwise pressure gradient. At the furthest downstream measurement locations there was also a fairly strong favourable streamwise pressure gradient.Measurements were made using a specially designed near-wall laser-Doppler anemometer (LDA), in addition to conventional methods. The LDA used short focal length optics, a mirror probe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μm in diameter and approximately 65 μm long.The data presented include mean velocity measurements and Reynolds stresses, all extending well below y+=10, at several profile locations. Terms of the turbulent kinetic energy transport equation are presented at two profile locations. The mean flow is nearly collateral (i.e. W is proportional to U) at the wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and the shear stress components are strongly affected by three-dimensionality. As a result, the ratio of shear stress to turbulent kinetic energy is suppressed throughout most of the boundary layer. The angles of stress and strain are misaligned, except very near the wall (around y+=10) where the angles nearly coincide with the mean flow angle. Three-dimensionality appears to mildly reduce the production of turbulent kinetic energy.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Turbulent Wall-Pressure Fluctuations: A New Model for Off-Axis Cross-Spectral Density

1997 ◽  
Vol 119 (2) ◽  
pp. 277-280 ◽  
Author(s):  
B. A. Singer
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Spectral Density ◽  
Flow Direction ◽  
Wall Pressure ◽  
Mean Flow ◽  
New Approach ◽  
Cross Spectral Density ◽  
The Mean ◽  
The Cross

Models for the distribution of the wall-pressure under a turbulent boundary layer often estimate the coherence of the cross-spectral density in terms of a product of two coherence functions. One such function describes the coherence as a function of separation distance in the mean-flow direction, the other function describes the coherence in the cross-stream direction. Analysis of data from a large-eddy simulation of a turbulent boundary layer reveals that this approximation dramatically underpredicts the coherence for separation directions that are neither aligned with nor perpendicular to the mean-flow direction. These models fail even when the coherence functions in the directions parallel and perpendicular to the mean flow are known exactly. A new approach for combining the parallel and perpendicular coherence functions is presented. The new approach results in vastly improved approximations for the coherence.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Subsonic Turbulent Flow Past a Planar Fence

1979 ◽  
Vol 101 (3) ◽  
pp. 373-375
Author(s):  
M. L. Agarwal ◽  
P. K. Pande ◽  
Rajendra Prakash
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flow Field ◽  
Boundary Conditions ◽  
Mean Flow ◽  
Governing Equations ◽  
Flow Past ◽  
Entire Flow ◽  
The Mean ◽  
Shape And Size

The mean flow past a fence submerged in a turbulent boundary layer is numerically simulated. The governing equations have been simplified by neglecting the convective effects of turbulence and solved numerically using experimental boundary conditions. The information obtained includes the shape and size of the upstream and downstream separation bubbles and the streamline pattern in the entire flow field. General agreement between the simulated and the experimental flow field was found.

519 Mean Flow Quantities of Turbulent Boundary Layer with the Adverse Pressure Gradient

2001 ◽  
Vol 2001.39 (0) ◽  
pp. 197-198
Author(s):  
Kentaro MURAMOTO ◽  
Takatsugu KAMEDA ◽  
Shinsuke MOCHIDUKI ◽  
Hideo OSAKA
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Mean Flow
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