Wall region of a relaxing three-dimensional incompressible turbulent boundary layer

1978 ◽  
Vol 85 (1) ◽  
pp. 33-56 ◽  
Author(s):  
K. S. Hebbar ◽  
W. L. Melnik
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Velocity Ratio ◽  
Three Dimensional ◽  
Cross Flow ◽  
Wall Region ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Angle ◽  
The Mean

An experimental investigation was conducted at selected locations in the wall region of a three-dimensional turbulent boundary layer relaxing in a nominally zero external pressure gradient behind a transverse hump (in the form of a 30° swept, 5 ft chord, wing-type model) faired into the side wall of a low-speed wind tunnel. The boundary layer (approximately 3·5 in. thick near the first survey station, where the length Reynolds number was 5·5 × 106) had a maximum cross-flow velocity ratio of 0·145 and a maximum cross-flow angle of 21·9° close to the wall. The hot-wire data indicated that the apparent dimensionless velocity profiles in the viscous sublayer are universal and that the wall influence on the hot wire is negligible beyond y+= 5. The existence of wall similarity in the relaxing flow field was confirmed in the form of a log law based on the resultant mean velocity and resultant friction velocity (obtained from the measured skin friction).The smallest collateral region extended from the point nearest to the wall (y+≈ 1) up to y+= 9·7, corresponding to a resultant mean velocity ratio (local to free-stream) of 0·187. The unusual feature of these profiles was the presence of a narrow region of slightly decreasing cross-flow angle (1° or less) that extended from the point of maximum cross-flow angle down to the outer limit of the collateral region. A sublayer analysis of the flow field using the measured local transverse pressure gradient slightly overestimated the decrease in cross-flow angle. It is concluded that, in the absence of these gradients, the skewing of the flow could have been much more pronounced practically down to the wall (limited only by the resolution of the sensor), implying a near-wallnon-collateralflow field consistent with the equations of motion in the neighbourhood of the wall.The streamwise relaxation of the mean flow field based on the decay of the cross-flow angle was much faster in the inner layer than in the outer layer. Over the stream-wise distance covered, the mean flow in the inner layer and the wall shear-stress vector relaxed to a two-dimensional state in approximately 10 boundary-layer thicknesses whereas the relaxation of the turbulence was slower and was not complete over the same distance.

Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer

1982 ◽  
Vol 119 ◽  
pp. 121-153 ◽  
Author(s):  
Udo R. Müller
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Field ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Acceleration ◽  
The Mean

An experimental study of a steady, incompressible, three-dimensional turbulent boundary layer approaching separation is reported. The flow field external to the boundary layer was deflected laterally by turning vanes so that streamwise flow deceleration occurred simultaneous with cross-flow acceleration. At 21 stations profiles of the mean-velocity components and of the six Reynolds stresses were measured with single- and X-hot-wire probes, which were rotatable around their longitudinal axes. The calibration of the hot wires with respect to magnitude and direction of the velocity vector as well as the method of evaluating the Reynolds stresses from the measured data are described in a separate paper (Müller 1982, hereinafter referred to as II). At each measuring station the wall shear stress was inferred from a Preston-tube measurement as well as from a Clauser chart. With the measured profiles of the mean velocities and of the Reynolds stresses several assumptions used for turbulence modelling were checked for their validity in this flow. For example, eddy viscosities for both tangential directions and the corresponding mixing lengths as well as the ratio of resultant turbulent shear stress to turbulent kinetic energy were derived from the data.

The Mean Flow Structure Around and Within a Turbulent Junction or Horseshoe Vortex—Part I: The Upstream and Surrounding Three-Dimensional Boundary Layer

1988 ◽  
Vol 110 (4) ◽  
pp. 406-414 ◽  
Author(s):  
J. D. Menna ◽  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Flow Structure ◽  
Vortex Flow ◽  
Three Dimensional ◽  
Horseshoe Vortex ◽  
Mean Flow ◽  
Complex Flow ◽  
Mean Velocity ◽  
Standard Case ◽  
The Mean

The mean flow structure upstream, around, and in a turbulent junction or horseshoe vortex is reported for an incompressible, subsonic flow. This fully documented, unified, comprehensive, and self-consistent data base is offered as a benchmark or standard case for assessing the predictive capabilities of computational codes developed to predict this kind of complex flow. Part I of these papers defines the total flow being documented. The upstream and surrounding three-dimensional turbulent boundary layer-like flow away from separation has been documented with mean velocity field and turbulent kinetic energy field measurements made with hot film anemometry, and local wall shear stress measurements. Data are provided for an initial condition plane well upstream of the junction vortex flow to initiate a boundary layer calculation, and freestream or edge velocity, as well as floor static pressure, are reported to proceed with the solution. Part II of these papers covers the flow through separation and within the junction vortex flow.

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.

Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow

2019 ◽  
Vol 865 ◽  
pp. 928-962 ◽  
Author(s):  
Haohua Zong ◽  
Marios Kotsonis
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Velocity Ratio ◽  
Vortex Pair ◽  
Synthetic Jets ◽  
Low Energy ◽  
Vortex Rings ◽  
Wall Region ◽  
Mean Velocity ◽  
Counter Rotating Vortex Pair

Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$  kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.

Turbulent Wake of a Stack and the Influence of Velocity Ratio

2006 ◽  
Author(s):  
M. S. Adaramola ◽  
D. Sumner ◽  
D. J. Bergstrom
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Shear Stress ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Turbulent Wake ◽  
Mean Velocity ◽  
Distinct Structure ◽  
Flow Reynolds Number ◽  
Cross Flow Velocity

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake of a cylindrical stack of AR = 9 was investigated with two-component thermal anemometry. The cross-flow Reynolds number was ReD = 2.3×104, the jet Reynolds number ranged from Red = 7×103 to 4.6×104, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-height ratio of δ/H = 0.5 at the location of the stack. The flow around the stack was broadly classified into three flow regimes depending on the value of R, which were the downwash (R &lt; 0.5), cross-wind dominated (0.5 &lt; R &lt; 1.5), and jet-dominated (R &gt; 1.5) regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields.

A three-dimensional turbulent boundary layer

1965 ◽  
Vol 22 (2) ◽  
pp. 285-304 ◽  
Author(s):  
A. E. Perry ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Outer Part ◽  
Outer Region ◽  
Experimental Results ◽  
Mean Velocity ◽  
Polar Plot ◽  
Law Of The Wall ◽  
The Mean

The purpose of this paper is to provide some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing. For the cases considered the yawing is caused by an obstruction attached to the wall upon which the boundary layer is developing. Only incompressible flow is considered.§1 of the paper is concerned with the outer region of the boundary layer and deals with a phenomenon observed by Johnston (1960) who described it with his triangular model for the polar plot of the velocity distribution. This was also observed by Hornung & Joubert (1963). It is shown here by a first-approximation analysis that such a behaviour is mainly a consequence of the geometry of the apparatus used. The analysis also indicates that, for these geometries, the outer part of the boundary-layer profile can be described by a single vector-similarity defect law rather than the vector ‘wall-wake’ model proposed by Coles (1956). The former model agrees well with the experimental results of Hornung & Joubert.In §2, the flow close to the wall is considered. Treating this region as an equilibrium layer and using similarity arguments, a three-dimensional version of the ‘law of the wall’ is derived. This relates the mean-velocity-vector distribution with the pressure-gradient vector and wall-shear-stress vector and explains how the profile skews near the wall. The theory is compared with Hornung & Joubert's experimental results. However at this stage the results are inconclusive because of the lack of a sufficient number of measured quantities.

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.

A model for inhomogeneous turbulent flow

1970 ◽  
Vol 317 (1530) ◽  
pp. 417-433 ◽  
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
The Self ◽  
Diffusion Equations ◽  
Mean Flow ◽  
Mean Velocity ◽  
Closed Set ◽  
Law Of The Wall ◽  
The Mean ◽  
Model Equations

A set of model equations is given to describe the gross features of a statistically steady or 'slowly varying’ inhomogeneous field of turbulence and the mean velocity distribution. The equations are based on the idea that turbulence can be characterized by ‘densities’ which obey nonlinear diffusion equations. The diffusion equations contain terms to describe the convection by the mean flow, the amplification due to interaction with a mean velocity gradient, the dissipation due to the interaction of the turbulence with itself, and the dif­fusion also due to the self interaction. The equations are similar to a set proposed by Kolmo­gorov (1942). It is assumed that both an ‘energy density’ and a ‘vorticity density’ satisfy diffusion equations, and that the self diffusion is described by an eddy viscosity which is a function of the energy and vorticity densities; the eddy viscosity is also assumed to describe the diffu­sion of mean momentum by the turbulent fluctuations. It is shown that with simple and plausible assumptions about the nature of the interaction terms, the equations form a closed set. The appropriate boundary conditions at a solid wall and a turbulent interface, with and without entrainment, are discussed. It is shown that the dimensionless constants which appear in the equations can all be estimated by general arguments. The equations are then found to predict the von Kármán constant in the law of the wall with reasonable accuracy. An analytical solution is given for Couette flow, and the result of a numerical study of plane Poiseuille flow is described. The equations are also applied to free turbulent flows. It is shown that the model equations completely determine the structure of the similarity solutions, with the rate of spread, for instance, determined by the solution of a nonlinear eigenvalue problem. Numerical solutions have been obtained for the two-dimensional wake and jet. The agreement with experiment is good. The solutions have a sharp interface between turbulent and non-turbulent regions and the mean velocity in the turbulent part varies linearly with distance from the interface. The equations are applied qualitatively to the accelerating boundary layer in flow towards a line sink, and the decelerating boundary layer with zero skin friction. In the latter case, the equations predict that the mean velocity should vary near the wall like the 5/3 power of the distance. It is shown that viscosity can be incorporated formally into the model equations and that a structure can be given to the interface between turbulent and non-turbulent parts of the flow.

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