scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Large-scale features in turbulent pipe and channel flows

2007 ◽  
Vol 589 ◽  
pp. 147-156 ◽  
Author(s):  
J. P. MONTY ◽  
J. A. STEWART ◽  
R. C. WILLIAMS ◽  
M. S. CHONG
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Large Scale ◽  
Significant Progress ◽  
Mean Velocity ◽  
Characteristic Structure ◽  
Custom Made ◽  
Logarithmic Region ◽  
The Mean

In recent years there has been significant progress made towards understanding the large-scale structure of wall-bounded shear flows. Most of this work has been conducted with turbulent boundary layers, leaving scope for further work in pipes and channels. In this article the structure of fully developed turbulent pipe and channel flow has been studied using custom-made arrays of hot-wire probes. Results reveal long meandering structures of length up to 25 pipe radii or channel half-heights. These appear to be qualitatively similar to those reported in the log region of a turbulent boundary layer. However, for the channel case, large-scale coherence persists further from the wall than in boundary layers. This is expected since these large-scale features are a property of the logarithmic region of the mean velocity profile in boundary layers and it is well-known that the mean velocity in a channel remains very close to the log law much further from the wall. Further comparison of the three turbulent flows shows that the characteristic structure width in the logarithmic region of a boundary layer is at least 1.6 times smaller than that in a pipe or channel.

High-strain-rate free-surface boundary-layer flows

1983 ◽  
Vol 126 ◽  
pp. 443-461 ◽  
Author(s):  
J. R. Bertschy ◽  
R. W. Chin ◽  
F. H. Abernathy
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Water Table ◽  
High Strain ◽  
Laser Doppler Anemometry ◽  
Streamwise Velocity ◽  
Surface Boundary ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Law Of The Wall

Two-dimensional boundary-layer flows of water down an inclined table were investigated in both the laminar and turbulent regimes. Mean, r.m.s. and skewness and velocity spectra were determined from streamwise velocity measurements. Two laser-Doppler anemometry methods were developed (for studying polymer-solution flows using this same water table) and compared with measurements obtained using hot-film anemometry. All three techniques obtained consistent results.An analysis based on a von Mises transformation is presented which accurately predicts the mean-velocity profile and flow development in the laminar regime. High strain rates are achieved which can be varied independently of Reynolds number, and turbulent flows are easily generated by inserting a disturbance. These turbulent flows are surprisingly similar to more commonly investigated turbulent boundarylayer flows of much greater y+ extent. Turbulent water-table flows typically extend only to y+ = 100, yet mean velocity essentially follows the law of the wall, and intensity and skewness measurements are similar to those obtained in flows much less limited in y+.

The mean velocity profile in three-dimensional turbulent oundary layers

1963 ◽  
Vol 15 (3) ◽  
pp. 368-384 ◽  
Author(s):  
H. G. Hornung ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Leading Edge ◽  
Viscous Sublayer ◽  
Scale Model ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value ofyuτ/vwhich occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted againsty/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range ofy.

Turbulent boundary-layer interaction with a shock wave at a compression corner

1984 ◽  
Vol 143 ◽  
pp. 23-46 ◽  
Author(s):  
S. Agrawal ◽  
A. F. Messiter
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Momentum Equation ◽  
Wall Layer ◽  
Oblique Shock Wave ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Compression Corner ◽  
Boundary Layer Interaction

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

The Effects of Localized Blade Endwall Suction on Secondary Flows and Heat Transfer

2010 ◽  
Author(s):  
Rebecca Hollis ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
High Surface ◽  
Surface Heat ◽  
Secondary Flows ◽  
Surface Shear Stress ◽  
Mean Velocity ◽  
Surface Shear ◽  
Surface Heat Transfer ◽  
High Heat Transfer

Two methods of flow control were designed to mitigate the effects of the horseshoe vortex structure (HV) at an airfoil/endwall junction. An experimental study was conducted to quantify the effects of localized boundary layer removal on surface heat transfer in a low-speed wind tunnel. A transient infrared technique was used to measure the convective heat transfer values along the surface surrounding the juncture. Particle image velocimetry was used to collect the time-mean velocity vectors of the flow field across three planes of interest. Boundary layer suction was applied through a thin slot cut into the leading edge of the airfoil at two locations. The first, referred to as Method 1, was directly along the endwall, the second, Method 2, was located at a height ∼1/3 of the approaching boundary layer height. Five suction rates were tested; 0%, 6.5%, 11%, 15% and 20% of the approaching boundary layer mass flow was removed at a constant rate. Both methods reduced the effects of the HV with increasing suction on the symmetry, 0.5-D and 1-D planes. Method 2 yielded a greater reduction in surface heat transfer but Method 1 outperformed Method 2 aerodynamically by completely removing the HV structure when 11% suction was applied. This method however produced other adverse effects such as high surface shear stress and localized areas of high heat transfer near the slot edges at high suction rates.

Effect of Surface Wave on Development of Turbulent Boundary Layer Over a Train of Rib Roughness

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Santosh Kumar Singh ◽  
Pankaj Kumar Raushan ◽  
Koustuv Debnath ◽  
B. S. Mazumder
Keyword(s):  
Boundary Layer ◽  
Surface Wave ◽  
Turbulent Boundary Layer ◽  
Mean Flow ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Law Of The Wall ◽  
Wave Channel ◽  
Surface Data ◽  
Large Roughness

In this paper, detailed experimental results are reported to study the effect of the surface wave of different frequencies on unidirectional current over the bed-mounted train of rib roughness. The model roughness used in this study is transverse square ribs that lengthened across the entire width of the recirculating wave channel. The center-to-center rib pitch (P) was constant during the experiments, thus generating a broad range of near-bed flow patterns for each of the three different surface wave frequencies studied here. The relative submergence associated with the roughness height (k) was 8, which fall in the category of large roughness. Velocity measurements were conducted using acoustic Doppler velocimeter (ADV), and a surface wave of different frequencies was generated using the plunger-type wavemaker. The measured velocity data were analyzed to determine the relative importance of mean flow over the train of rib roughness. Mean velocity profiles illustrate the well-known downward shift from the flat surface data of the semi-logarithmic portion of the law of the wall. The width of the turbulent boundary layer increases with the superposition of surface wave compared to that of the current-only flow. The results also show that the mean reattachment length decreases due to the superposition of surface wave on unidirectional current.

Experimental Investigation of a Turbulent Boundary Layer Subjected to an Adverse Pressure Gradient

2011 ◽  
Author(s):  
Takanori Nakamura ◽  
Takatsugu Kameda ◽  
Shinsuke Mochizuki
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Adverse Pressure Gradient ◽  
Turbulent Intensity ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Scale ◽  
The Mean ◽  
The Law

Experiments were performed to investigate the effect of an adverse pressure gradient on the mean velocity and turbulent intensity profiles for an equilibrium boundary layer. The equilibrium boundary layer, which makes self-similar profiles, was constructed using a power law distribution of free stream velocity. The exponent of the law was adjusted to −0.188. The wall shear stress was measured with a drag balance by a floating element. The investigation of the law of the wall and the similarity of the streamwise turbulent intensity profile was made using both a friction velocity and new proposed velocity scale. The velocity scale is derived from the boundary layer equation. The mean velocity gradient profile normalized with the height and the new velocity scale exists the region where the value is almost constant. The turbulent intensity profiles normalized with the friction velocity strongly depend on the nondimensional pressure gradient near the wall. However, by mean of the local velocity scale, the profiles might be achieved to be similar with that of a zero pressure gradient.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

scholarly journals Wind Turbulence Statistics of the Atmospheric Inertial Sublayer under Near-Neutral Conditions

Atmosphere ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 1087
Author(s):  
Eslam Reda Lotfy ◽  
Zambri Harun
Keyword(s):  
Boundary Layer ◽  
Atmospheric Stability ◽  
Turbulent Velocity ◽  
Stability Conditions ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Turbulent Statistics ◽  
The Mean ◽  
The Law ◽  
Velocity Variances

The inertial sublayer comprises a considerable and critical portion of the turbulent atmospheric boundary layer. The mean windward velocity profile is described comprehensively by the Monin–Obukhov similarity theory, which is equivalent to the logarithmic law of the wall in the wind tunnel boundary layer. Similar logarithmic relations have been recently proposed to correlate turbulent velocity variances with height based on Townsend’s attached-eddy theory. The theory is particularly valid for high Reynolds-number flows, for example, atmospheric flow. However, the correlations have not been thoroughly examined, and a well-established model cannot be reached for all turbulent variances similar to the law of the wall of the mean-velocity. Moreover, the effect of atmospheric thermal condition on Townsend’s model has not been determined. In this research, we examined a dataset of free wind flow under a near-neutral range of atmospheric stability conditions. The results of the mean velocity reproduce the law of the wall with a slope of 2.45 and intercept of −13.5. The turbulent velocity variances were fitted by logarithmic profiles consistent with those in the literature. The windward and crosswind velocity variances obtained the average slopes of −1.3 and −1.7, respectively. The slopes and intercepts generally increased away from the neutral state. Meanwhile, the vertical velocity and temperature variances reached the ground-level values of 1.6 and 7.8, respectively, under the neutral condition. The authors expect this article to be a groundwork for a general model on the vertical profiles of turbulent statistics under all atmospheric stability conditions.

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.

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