LDV Measurements of Spatially Periodic Flows Over a Detached Solid-Rib Array

1997 ◽  
Vol 119 (2) ◽  
pp. 383-389 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chih-Ping Yang ◽  
Hsin-Li Lee
Keyword(s):  
Fluid Dynamic ◽  
Turbulent Shear ◽  
Parameter Distribution ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Height Ratio ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Periodic Flows ◽  
Spatially Periodic

Measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for spatially periodic flows in a duct of width-to-height ratio 2 with a detached solid-rib array. The Reynolds number based on the duct hydraulic diameter and cross-sectional bulk mean velocity (Ub), the pitch to rib-height ratio, and the rib-height to duct-height ratio were 2 × 104, 10, and 0.133, respectively. The rib-detached-distance to rib-height ratio was varied from 0 to 3.25 (duct axis) to study its effect on wake length and asymmetry, convective velocity and turbulent kinetic energy immediately behind the rib, maximum turbulent shear stress, and turbulence anisotropy. The results showed that the dominant fluid dynamic factors responsible for the reported peak values of local Nusselt number around the detached rib could be identified. Moreover, the turbulence structure parameter distribution and anisotropy were analyzed to examine the basic assumptions embedded in the turbulence models. Furthermore, the secondary-flow mean velocities were found to be one to two order of magnitude smaller than Ub.

scholarly journals Computational and Experimental Study of Turbulent Flow Past an Array of Bluff Bodies Aligned Along the Channel Axis

1997 ◽  
Author(s):  
Tong-Miin Liou ◽  
Shih-Hui Chen
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Channel Height ◽  
Bluff Bodies ◽  
Reynolds Stresses ◽  
Height Ratio ◽  
Channel Axis ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Phase Cycle

Computations and measurements of time mean velocities, total fluctuation intensities, and Reynolds stresses are presented for spatially periodic flows past an array of bluff bodies aligned along the channel axis. The Reynolds number based on the channel hydraulic diameter and cross-sectional bulk mean velocity, the pitch to rib-height ratio, and the rib-height to channel-height ratio were 2 × 104, 10, and 0.133, respectively. The unsteady phase-averaged Navier-Stokes equations were solved using a Reynolds stress model with wall function and wall-related pressure strain treatment to reveal the feature of examined unsteady vortex shedding flow. Laser Doppler velocimetry measurements were performed to measure the velocity filed. Code verifications were performed through comparisons with others’ measured developing single-rib flow and our measured fully developed rib-array flow. The computed results and measured data are found in reasonable agreement, which justifies the turbulence model adopted. The calculated phase-averaged flow field clearly displays the vortex shedding behind the rib and is characterized in terms of shedding Strouhal number, vortex trajectory, vortex celerity, and vortex travelling distance in a phase cycle. Furthermore, the difference between the computed developing single-rib flow and fully developed rib-array flow is addressed.

Flowfield Investigation of the Effect of Rib Open Area Ratio in a Rectangular Duct

1998 ◽  
Vol 120 (3) ◽  
pp. 504-512 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chih-Wen Kao ◽  
Shih-Hui Chen
Keyword(s):  
Computational Models ◽  
Fluid Dynamic ◽  
Fluid Flows ◽  
Area Ratio ◽  
Open Area ◽  
Height Ratio ◽  
Mean Velocity ◽  
Dynamic Factors ◽  
Nusselt Number Distribution ◽  
Spatially Periodic

The spatially periodic turbulent fluid flows and friction in a rectangular passage of width-to-height ratio of 4:1 with perforated rectangular ribs mounted on one wall have been studied using laser Doppler velocimetry and pressure probing. The parameters fixed were rib height to duct hydraulic diameter ratio of 0.106, rib width-to-height ratio of 0.76, rib pitch-to-height ratio of 10, and Reynolds number of 2 × 104, while the main parameter investigated was the rib open-area ratio (β) with values of 0%, 10%, 22%, 38%, and 44%. Two critical ranges of β and three characteristic flow regimes were identified, which provides useful references of practical tests of computational models. The results also showed that the dominant fluid dynamic factors responsible for the reported peak values of local Nusselt number distribution could be recognized. Moreover, the secondary-flow mean velocity components were found to be one to two orders of magnitude smaller than the bulk mean velocity.

Turbulent Flow Past an Array of Bluff Bodies Aligned Along the Channel Axis

1998 ◽  
Vol 120 (3) ◽  
pp. 520-530 ◽  
Author(s):  
Tong-Miin Liou ◽  
Shih-Hui Chen
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Channel Height ◽  
Bluff Bodies ◽  
Reynolds Stresses ◽  
Height Ratio ◽  
Channel Axis ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Phase Cycle

Computations and measurements of time mean velocities, total fluctuation intensities, and Reynolds stresses are presented for spatially periodic flows past an array of bluff bodies aligned along the channel axis. The Reynolds number based on the channel hydraulic diameter and cross-sectional bulk mean velocity, the pitch to rib-height ratio, and the rib-height to channel-height ratio were 2 × 104, 10, and 0.13, respectively. The unsteady phase-averaged Navier-Stokes equations were solved using a Reynolds stress model with wall function and wall-related pressure strain treatment to reveal the feature of examined unsteady vortex shedding flow. Laser Doppler velocimetry measurements were performed to measure the velocity field. Code verifications were performed through comparisons with others’ measured developing single-rib flow and our measured fully developed rib-array flow. The possible causes for the differences between the experiments and computations are discussed. The calculated phase-averaged flow field clearly displays the vortex shedding behind the rib and is characterized in terms of shedding Strouhal number, vortex trajectory, vortex celerity, and vortex travelling distance in a phase cycle. Furthermore, the difference between the computed developing single-rib flow and fully developed rib-array flow is addressed.

The law of the wall in turbulent flow

1995 ◽  
Vol 451 (1941) ◽  
pp. 165-188 ◽  
Keyword(s):  
Turbulence Models ◽  
Turbulence Theory ◽  
Turbulent Shear ◽  
Wall Region ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Logarithmic Law ◽  
The Law ◽  
Simple Flows

The ‘law of the wall’ for the inner part of a turbulent shear flow over a solid surface is one of the cornerstones of fluid dynamics, and one of the very few pieces of turbulence theory whose results include a simple analytic function for the mean velocity distribution, the logarithmic law. Various aspects of the law have recently been questioned, and this paper is a summary of the present position. Although the law of the wall for velocity has apparently been confirmed by experiment well outside its original range, the law of the wall for temperature seems to apply only to very simple flows. Since the two laws are derived by closely analogous arguments this throws suspicion on the law of the wall for velocity. Analysis of simulation data, for all the Reynolds stresses including the shear stress, shows that law-of-the-wall scaling fails spectacularly in the viscous wall region, even when the logarithmic law is relatively well behaved. Virtually all turbulence models are calibrated to reproduce the law of the wall in simple flows, and we discuss whether, in practice or in principle, their range of validity is larger than that of the law of the wall itself: the present answer is that it is not; so that when the law of the wall (or the mixing-length formula) fails, current Reynolds-averaged turbulence models are likely to fail too.

LDV Measurements of Periodic Fully Developed Main and Secondary Flows in a Channel With Rib-Disturbed Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 109-114 ◽  
Author(s):  
T.-M. Liou ◽  
Y.-Y. Wu ◽  
Y. Chang
Keyword(s):  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Secondary Flows ◽  
Laser Doppler Velocimeter ◽  
Parameter Distribution ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Production Term ◽  
Basic Assumptions

Laser-Doppler velocimeter measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for periodic fully developed flows in a channel with square rib-disturbed walls on two opposite sides. Quantities such as the vorticity thickness and turbulent kinetic energy are used to characterize the flow. The investigated flow was periodic in space. The Reynolds number based on the channel hydraulic diameter was 3.3×104. The ratios of pitch to rib-height and rib-height to chamber-height were 10 and 0.133, respectively. Regions where maximum and minimum Reynolds stress and turbulent kinetic energy occurred were identified from the results. The growth rate of the shear layers of the present study was compared with that of a backward-facing step. The measured turbulence anisotropy and structure parameter distribution were used to examine the basic assumptions embedded in the k–ε and k–ε–A models. For a given axial station, the peak axial mean-velocity was found not to occur at the center point. The secondary flow was determined to be Prandtl’s secondary flow of the second kind according to the measured streamwise mean vorticity and its production term.

Full-coverage film cooling. Part 1. Three-dimensional measurements of turbulence structure

1980 ◽  
Vol 101 (1) ◽  
pp. 129-158 ◽  
Author(s):  
S. Yavuzkurt ◽  
R. J. Moffat ◽  
W. M. Kays
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Film Cooling ◽  
Outer Boundary ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Test Plate ◽  
Apparent Paradox ◽  
Full Coverage

Hydrodynamic measurements were made with a triaxial hot wire in the full-coverage region and the recovery region following an array of injection holes inclined downstream, at 30° to the surface. The data were taken under isothermal conditions at ambient temperature and pressure for two blowing ratios: M = 0·9 and M = 0·4. (The ratio M = ρjetUjet/ρ∞U∞, where U is the mean velocity and ρ is the density. Subscripts jet and ∞ stand for injectant and free stream, respectively.) Profiles of the three mean-velocity components and the six Reynolds stresses were obtained at several spanwise positions at each of five locations down the test plate.In the full-coverage region, high levels of turbulence kinetic energy (TKE) were found for low blowing and low TKE levels for high blowing. This observation is especially significant when coupled with the fact that the heat transfer coefficient is high for high blowing, and low for low blowing. This apparent paradox can be resolved by the hypothesis that entrainment of the mainstream fluid must be more important than turbulent mixing in determining the heat transfer behaviour at high blowing ratios (close to unity).In the recovery region, the flow can be described in terms of a two-layer model: an outer boundary layer and a two-dimensional inner boundary layer. The inner layer governs the heat transfer.

scholarly journals A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis

1995 ◽  
Vol 298 ◽  
pp. 361-388 ◽  
Author(s):  
A. E. Perry ◽  
Ivan Marušić
Keyword(s):  
Boundary Layers ◽  
Momentum Equation ◽  
Wall Structure ◽  
Turbulence Structure ◽  
Quasi Equilibrium ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Convolution Integrals ◽  
Using Data

The attached eddy hypothesis developed for zero pressure gradient boundary layers and for pipe flow is extended here to boundary layers with arbitrary streamwise pressure gradients, both favourable and adverse. It is found that in order to obtain the correct quantitative results for all components of the Reynolds stresses, two basic types of eddy structure geometries are required. The first type, called type-A, is interpreted to give a ‘wall structure’ and the second, referred to as type-B, gives a ‘wake structure’. This is in analogy with the conventional mean velocity formulation of Coles where the velocity is decomposed into a law of the wall and a law of the wake.If the above mean velocity formulation is accepted, then in principle, once the eddy geometries are fixed for the two eddy types, all Reynolds stresses and associated spectra contributed from the attached eddies can be computed without any further empirical constants. This is done by using the momentum equation and certain convolution integrals developed here based on the attached eddy hypothesis. The theory is developed using data from equilibrium and quasi-equilibrium flows. In Part 2 the authors’ non-equilibrium data are used.

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.

Developing turbulent boundary layers with system rotation

1985 ◽  
Vol 157 ◽  
pp. 405-448 ◽  
Author(s):  
J. H. Watmuff ◽  
H. T. Witt ◽  
P. N. Joubert
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Secondary Circulations ◽  
Spatially Periodic

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

Experimental investigation of turbulent shear flow with quadratic mean-velocity profiles

1976 ◽  
Vol 73 (1) ◽  
pp. 165-188 ◽  
Author(s):  
H. K. Richards ◽  
J. B. Morton
Keyword(s):  
Flow Direction ◽  
Correlation Coefficients ◽  
Velocity Profiles ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Quadratic Mean ◽  
The Mean

Three turbulent shear flows with quadratic mean-velocity profiles are generated by using an appropriately designed honeycomb and parallel-rod grids with adjustable rod spacing. The details of two of the flow fields, with quadratic mean-velocity profiles with constant positive mean-shear gradients ($\partial^2\overline{U}_1/\partial X^2_2 >0$), are obtained, and include, in the mean flow direction, the development and distribution of mean velocities, fluctuating velocities, Reynolds stresses, microscales, integral scales, energy spectra, shear correlation coefficients and two-point spatial velocity correlation coefficients. A third flow field is generated with a quadratic mean velocity profile with constant negative mean-shear gradient ($\partial^2\overline{U}_1/\partial X^2_2 < 0$), to investigate in the mean flow direction the effect of the change in sign on the resulting field. An open-return wind tunnel with a 2 × 2 × 20 ft test-section is used.

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