Turbulent combined oscillatory flow and current in a pipe

1998 ◽  
Vol 373 ◽  
pp. 313-348 ◽  
Author(s):  
C. R. LODAHL ◽  
B. M. SUMER ◽  
J. FREDSØE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Cross Section ◽  
Oscillatory Flow ◽  
Combined Flow ◽  
The Mean ◽  
Wall Shear ◽  
A Current

This work concerns the combined oscillatory flow and current in a circular, smooth pipe. The study comprises wall shear stress measurements, and laser-Doppler-anemometer velocity and turbulence measurements. Three kinds of pipes were used, with diameters D=19 cm, 9 cm, and 1.1 cm, enabling the influence of the parameter R/δ to be studied in the investigation (R/δ ranging from about 3 to 53), where R is the radius of the pipe, and δ is the Stokes layer thickness. The ranges of the two other parameters of the combined flow processes, namely the current Reynolds number, Rec, and the oscillatory-flow boundary-layer (i.e. the wave–boundary layer) Reynolds number, Rew, are: Rec=0−1.6×105, and Rew=0−7×106. The transition to turbulence in the combined flow case occurs at a current Reynolds number larger than the conventional value, ca. 2×103, depending on Rew, and R/δ. A turbulent current can be laminarized by superimposing an oscillatory flow. The overall average value of the wall shear stress (the mean wall shear stress) may retain its steady-current value, it may decrease, or it may increase, depending on the flow regime. The increase (which can be as much as a factor of 4) occurs when the combined flow is in the wave-dominated regime, while the oscillatory-flow component of the flow is in the turbulent regime. The component of the wall shear stress oscillating around the mean wall shear stress can also increase with respect to its oscillatory-flow-alone value. For this to occur, the originally laminar oscillatory boundary layer needs to become a fully developed turbulent boundary layer, when a turbulent current is superimposed. This increase can be as much as O(3–4). The velocity profiles across the cross-section of the pipe change near the wall when an oscillatory flow is superimposed on a current, in agreement with the results of the wall shear stress measurements. The period-averaged turbulence profiles across the cross-section of the pipe behave differently for different flow regimes. When the two components of the flow are equally significant, the turbulence profile appears to be different from those corresponding to the fundamental cases; the level of turbulence increases (only slightly) with respect to those experienced in the fundamental cases.

Supplementary Boundary-Layer Approximations for Turbulent Flow

1989 ◽  
Vol 111 (4) ◽  
pp. 420-427 ◽  
Author(s):  
L. C. Thomas ◽  
S. M. F. Hasani
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Wall Shear

Approximations for total stress τ and mean velocity u are developed in this paper for transpired turbulent boundary layer flows. These supplementary boundary-layer approximations are tested for a wide range of near equilibrium flows and are incorporated into an inner law method for evaluating the mean wall shear stress τ0. The testing of the proposed approximations for τ and u indicates good agreement with well-documented data for moderate rates of blowing and suction and pressure gradient. These evaluations also reveal limitations in the familiar logarithmic law that has traditionally been used in the determination of wall shear stress for non-transpired boundary-layer flows. The calculations for τ0 obtained by the inner law method developed in this paper are found to be consistent with results obtained by the modern Reynolds stress method for a broad range of near equilibrium conditions. However, the use of the proposed inner law method in evaluating the mean wall shear stress for early classic near equilibrium flow brings to question the reliability of the results for τ0 reported for adverse pressure gradient flows in the 1968 Stanford Conference Proceedings.

Near-Wall Measurements in Turbulent Boundary Layers Using Laser Doppler Anemometry

2002 ◽  
Author(s):  
T. Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
The Mean ◽  
Wall Shear ◽  
Near Wall

Near wall measurements have been performed in a zero pressure gradient turbulent boundary layer at low to moderate local Reynolds numbers using Laser-Doppler Anemometry in order to investigate how accurately the wall shear stress can be determined. Also, scaling problems are particularly difficult at low Reynolds numbers since they involve simultaneous influences of both inner and outer scales and this is most clearly observed in the near-wall region. In order to fully describe the zero pressure gradient turbulent boundary layer at low to moderate local Reynolds numbers it is necessary to accurately measure a number of quantities. These include the mean velocity and Reynolds stresses, and their spatial derivatives all the way down to the wall (y+∼1). Integral parameters that need to be measured are the wall shear stress and boundary layer thickness, particularly the momentum thickness. Problems with the measurement of field properties get worse close to a wall, and they get worse for increasing local Reynolds number. Three different approaches to measure the wall shear stress were examined. It was found that small measurement errors in the mean velocity close to the wall significantly reduced the accuracy in determining the wall shear stress by measuring the velocity gradient at the wall. The constant stress layer was found to be affected by the advection terms. However, it was found that taking the small pressure gradient into account and improving on the spatial resolution in the outer part of the boundary layer made the momentum integral method reliable.

Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to 13650

2014 ◽  
Vol 743 ◽  
pp. 202-248 ◽  
Author(s):  
Sébastien Deck ◽  
Nicolas Renard ◽  
Romain Laraufie ◽  
Pierre-Élie Weiss
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flat Plate ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Large Scale ◽  
Wall Shear ◽  
High Reynolds

AbstractA numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range $3060\leq Re_{\theta }\leq 13\, 650$. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately $5\delta $ to $6 \delta $ long which are meandering with a lateral amplitude of $0.3 \delta $ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted $C_{f,2}$, is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that $C_{f,2}$ is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength $\lambda _x >\delta $ contribute to more than $60\, \%$ of $C_{f,2}$, and that those larger than $\lambda _x >2\delta $ still represent approximately $45\, \%$ of $C_{f,2}$.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer

1998 ◽  
Vol 359 ◽  
pp. 329-356 ◽  
Author(s):  
H. H. FERNHOLZ ◽  
D. WARNACK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Reynolds Stresses ◽  
The Mean

The effects of a favourable pressure gradient (K[les ]4×10−6) and of the Reynolds number (862[les ]Reδ2[les ]5800) on the mean and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper and a companion paper (Part 2). The measurements consist of extensive hot-wire and skin-friction data. The former comprise mean and fluctuating velocities, their correlations and spectra, the latter wall-shear stress measurements obtained by four different techniques which allow testing of calibrations in both laminar-like and turbulent flows for the first time. The measurements provide complete data sets, obtained in an axisymmetric test section, which can serve as test cases as specified by the 1981 Stanford conference.Two different types of accelerated boundary layers were investigated and are described: in this paper (Part 1) the fully turbulent, accelerated boundary layer (sometimes denoted laminarescent) with approximately local equilibrium between the production and dissipation of the turbulent energy and with relaxation to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases the standard logarithmic law fails but there is no single parametric criterion which denotes the beginning or the end of this breakdown. However, it can be demonstrated that the departure of the mean-velocity profile is accompanied by characteristic changes of turbulent quantities, such as the maxima of the Reynolds stresses or the fluctuating value of the skin friction.The boundary layers described here are maintained in the laminarescent state just up to the beginning of relaminarization and then relaxed to the turbulent state in a zero pressure gradient. The relaxation of the turbulence structure occurs much faster than in an adverse pressure gradient. In the accelerating boundary layer absolute values of the Reynolds stresses remain more or less constant in the outer region of the boundary layer in accordance with the results of Blackwelder & Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising wall shear stress and in the centre region of the boundary layer with the increase of production.

scholarly journals Pulsatile flow in circular tubes of varying cross-section with suction/injection

1994 ◽  
Vol 35 (3) ◽  
pp. 366-381 ◽  
Author(s):  
Peeyush Chandra ◽  
J. S. V. R. Krishna Prasad
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Cross Section ◽  
Pulsatile Flow ◽  
Normal Velocity ◽  
Fluid Exchange ◽  
Circular Tubes ◽  
Permeable Walls ◽  
Wall Shear

AbstractWe consider here pulsatile flow in circular tubes of varying cross-section with permeable walls. The fluid exchange across the wall is accounted for by prescribing the normal velocity of the fluid at the wall. A perturbation analysis has been carried out for low Reynolds number flows and for small amplitudes of oscillation. It has been observed that the magnitude of the wall shear stress and the pressure drop decrease as the suction velocity increases. Further, as the Reynolds number is increased, the magnitude of wall shear stress increases in the convergent portion and decreases in the divergent portion of a constricted tube.

Wall shear stress in accelerating turbulent pipe flow

2011 ◽  
Vol 685 ◽  
pp. 440-460 ◽  
Author(s):  
S. He ◽  
C. Ariyaratne ◽  
A. E. Vardy
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Initial Period ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Acceleration Rate ◽  
The Mean ◽  
Wall Shear ◽  
Turbulent Wall

AbstractAn experimental study of wall shear stress in an accelerating flow of water in a pipe ramping between two steady turbulent flows has been undertaken in a large-scale experimental facility. Ensemble averaged mean and r.m.s. of the turbulent fluctuations of wall shear stresses have been derived from hot-film measurements from many repeated runs. The initial Reynolds number and the acceleration rate were varied systematically to give values of a non-dimensional acceleration parameter $k$ ranging from 0.16 to 14. The wall shear stress has been shown to follow a three-stage development. Stage 1 is associated with a period of minimal turbulence response; the measured turbulent wall shear stress remains largely unchanged except for a very slow increase which is readily associated with the stretching of existing turbulent eddies as a result of flow acceleration. In this condition of nearly ‘frozen’ turbulence, the unsteady wall shear stress is driven primarily by flow inertia, initially increasing rapidly and overshooting the pseudo-steady value, but then increasing more slowly and eventually falling below the pseudo-steady value. This variation is predicted by an analytical expression derived from a laminar flow formulation. The start of Stage 2 is marked by the generation of new turbulence causing both the mean and turbulent wall shear stress to increase rapidly, although there is a clear offset between the responses of these two quantities. The turbulent wall shear, reflecting local turbulent activities near the wall, responds first and the mean wall shear, reflecting conditions across the entire flow field, responds somewhat later. In Stage 3, the wall shear stress exhibits a quasi-steady variation. The duration of the initial period of nearly frozen turbulence response close to the wall increases with decreasing initial Reynolds number and with increasing acceleration. The latter is in contrast to the response of turbulence in the core of the flow, which previous measurements have shown to be independent of the rate of acceleration.

Flow and Thermal Fields in a Pendant Droplet Moving on Lyophobic Surface

2010 ◽  
Author(s):  
Basant Singh Sikarwar ◽  
K. Muralidhar ◽  
Sameer Khandekar
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Reynolds Number ◽  
Shear Stress ◽  
Heat Transfer Coefficient ◽  
Wall Shear Stress ◽  
Transfer Coefficient ◽  
Maximum Shear Stress ◽  
Computational Domain ◽  
Wall Shear

Clusters of liquid drops growing and moving on physically or chemically textured lyophobic surfaces are encountered in drop-wise mode of vapor condensation. As opposed to film-wise condensation, drops permit a large heat transfer coefficient and are hence attractive. However, the temporal sustainability of drop formation on a surface is a challenging task, primarily because the sliding drops eventually leach away the lyophobicity promoter layer. Assuming that there is no chemical reaction between the promoter and the condensing liquid, the wall shear stress (viscous resistance) is the prime parameter for controlling physical leaching. The dynamic shape of individual droplets, as they form and roll/slide on such surfaces, determines the effective shear interaction at the wall. Given a shear stress distribution of an individual droplet, the net effect of droplet ensemble can be determined using the time averaged population density during condensation. In this paper, we solve the Navier-Stokes and the energy equation in three-dimensions on an unstructured tetrahedral grid representing the computational domain corresponding to an isolated pendant droplet sliding on a lyophobic substrate. We correlate the droplet Reynolds number (Re = 10–500, based on droplet hydraulic diameter), contact angle and shape of droplet with wall shear stress and heat transfer coefficient. The simulations presented here are for Prandtl Number (Pr) = 5.8. We see that, both Poiseuille number (Po) and Nusselt number (Nu), increase with increasing the droplet Reynolds number. The maximum shear stress as well as heat transfer occurs at the droplet corners. For a given droplet volume, increasing contact angle decreases the transport coefficients.

On the Effects of a Flexible Structure on Boundary Layer Stability and Transition

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Ashraf Al Musleh ◽  
Abdelkader Frendi
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Young Modulus ◽  
Boundary Layer Transition ◽  
Beam Equation ◽  
Flexible Structure ◽  
Boundary Layer Stability ◽  
Wall Shear ◽  
Fluid Wall Shear Stress

Delaying the onset of boundary layer transition has become a major research area in the last few years. This delay can be achieved by either active or passive control techniques. In the present paper, the effects of flexible or compliant structures on boundary layer stability and transition is studied. The Orr-Sommerfeld equation coupled to a beam equation representing the flexible structure is solved for a Blasius type boundary layer. A parametric study consisting of the beam thickness and material properties is carried out. In addition, the effect of fluid wall shear stress on boundary layer stability is analyzed. It is found that high density and high Young modulus materials behave like rigid structures and therefore do not alter the stability characteristic of the boundary layer. Whereas low density and low Young modulus materials are found to stabilize the boundary layer. High values of fluid wall shear stress are found to destabilize the boundary layer. Our results are in good agreement with those published in the literature.

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