Boundary layers in micropolar liquids

1970 ◽  
Vol 67 (2) ◽  
pp. 469-476 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Steady Flow ◽  
Boundary Layers ◽  
Standard Length ◽  
Vital Role ◽  
Rigid Boundary ◽  
Important Significance ◽  
Micropolar Liquid

AbstractConsideration is given to the steady flow of a micropolar liquid near a rigid boundary. It is shown that while micro-inertia itself is not important, nevertheless, some properties of the microstructure do play a vital rôle in determining the structure of the boundary layer. The Kármán—Polhausen method is used to provide an estimate of the shear stress at the boundary, and detailed calculations are given for flow near stagnation. The important significance of the standard length of the micropolar liquid is demonstrated for this flow, as for other flows in this medium.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

High Freestream Turbulence Effects on Turbulent Boundary Layers

1996 ◽  
Vol 118 (2) ◽  
pp. 276-284 ◽  
Author(s):  
K. A. Thole ◽  
D. G. Bogard
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Outer Region ◽  
Power Spectra ◽  
Turbulent Boundary Layers ◽  
Freestream Turbulence ◽  
Length Scales ◽  
Turbulent Eddies ◽  
Viscous Shear

High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.

scholarly journals Wall shear stress from jetting cavitation bubbles

2018 ◽  
Vol 846 ◽  
pp. 341-355 ◽  
Author(s):  
Qingyun Zeng ◽  
Silvestre Roberto Gonzalez-Avila ◽  
Rory Dijkink ◽  
Phoevos Koukouvinis ◽  
Manolis Gavaises ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
High Speed ◽  
Temporal Distribution ◽  
Surface Cleaning ◽  
Shear Stresses ◽  
Rigid Boundary ◽  
Equivalent Radius ◽  
Wall Shear

The collapse of a cavitation bubble near a rigid boundary induces a high-speed transient jet accelerating liquid onto the boundary. The shear flow produced by this event has many applications, examples of which are surface cleaning, cell membrane poration and enhanced cooling. Yet the magnitude and spatio-temporal distribution of the wall shear stress are not well understood, neither experimentally nor by simulations. Here we solve the flow in the boundary layer using an axisymmetric compressible volume-of-fluid solver from the OpenFOAM framework and discuss the resulting wall shear stress generated for a non-dimensional distance, $\unicode[STIX]{x1D6FE}=1.0$ ($\unicode[STIX]{x1D6FE}=h/R_{max}$, where $h$ is the distance of the initial bubble centre to the boundary, and $R_{max}$ is the maximum spherical equivalent radius of the bubble). The calculation of the wall shear stress is found to be reliable once the flow region with constant shear rate in the boundary layer is determined. Very high wall shear stresses of 100 kPa are found during the early spreading of the jet, followed by complex flows composed of annular stagnation rings and secondary vortices. Although the simulated bubble dynamics agrees very well with experiments, we obtain only qualitative agreement with experiments due to inherent experimental challenges.

Response of a turbulent boundary layer to sinusoidal free-stream unsteadiness

1990 ◽  
Vol 221 ◽  
pp. 131-159 ◽  
Author(s):  
G. J. Brereton ◽  
W. C. Reynolds ◽  
R. Jayaraman
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Steady Flow ◽  
Boundary Layers ◽  
Free Stream ◽  
Constant Pressure ◽  
External Conditions ◽  
Mean Structure ◽  
The Mean ◽  
Turbulence Production

In this paper, selected findings of a detailed experimental investigation are reported concerning the effects of forced free-stream unsteadiness on a turbulent boundary layer. The forced unsteadiness was sinusoidal and was superimposed locally on an otherwise-steady mainstream, beyond a turbulent boundary layer which had developed under constant-pressure conditions. Within the region over which free-stream unsteadiness was induced, the sinusoidal variation in pressure gradient was between extremes of zero and a positive value, with a positive average level. The local response of the boundary layer to these free-stream effects was studied through simultaneous measurements of the u- and v-components of the velocity fieldAlthough extensive studies of unsteady, turbulent, fully-developed pipe and channel flow have been carried out, the problem of a developing turbulent boundary layer and its response to forced free-stream unsteadiness has received comparatively little attention. The present study is intended to redress this imbalance and, when contrasted with other studies of unsteady turbulent boundary layers, is unique in that: (i) it features an appreciable amplitude of mainstream modulation at a large number of frequencies of forced unsteadiness, (ii) its measurements are both detailed and of high spatial resolution, so that the near-wall behaviour of the flow can be discerned, and (iii) it allows local modulation of the mainstream beyond a turbulent boundary layer which has developed under the well-known conditions of steady, two-dimensional, constant-pressure flowResults are reported which allow comparison of the behaviour of boundary layers under the same mean external conditions, but with different time dependence in their free-stream velocities. These time dependences correspond to: (i) steady flow, (ii) quasi-steadily varying flow, and (iii) unsteady flow at different frequencies of mainstream unsteadiness. Experimental results focus upon the time-averaged nature of the flow; they indicate that the mean structure of the turbulent boundary layer is sufficiently robust that the imposition of free-stream unsteadiness results only in minor differences relative to the mean character of the steady flow, even at frequencies for which the momentary condition of the flow departs substantially from its quasi-steady state. Mean levels of turbulence production are likewise unaffected by free-stream unsteadiness and temporal production of turbulence appears to result only from modulation of the motions which contribute to turbulence production as a time-averaged measure.

Vortex decay above a stationary boundary

1967 ◽  
Vol 27 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Albert I. Barcilon
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Swirling Flows ◽  
Rigid Boundary ◽  
Free Vortex ◽  
Stationary Boundary ◽  
Small Viscosity

An attempt is made to understand the decay of a free vortex normal to a stationary, infinite boundary. For rapidly swirling flows in fluids of small viscosity, thin boundary layers develop along the rigid boundary and along the axis, the axial boundary layer being strongly influenced by the behaviour of the plate boundary. An over-all picture of the flow is sought, with only moderate success in the region far from the origin. Near the origin, the eruption of the plate boundary layer into the axial boundary layer is studied.

An Approximate Method for the Calculation of Turbulent Boundary Layers in Diffusers

1957 ◽  
Vol 8 (1) ◽  
pp. 58-77 ◽  
Author(s):  
J. F. Norbury
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Approximate Method ◽  
Boundary Layers ◽  
Stress Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Form Parameter ◽  
Parameter Equation

SummaryAn approximate method is described for the calculation of turbulent boundary layers in which the turbulence is developed before the commencement of the adverse pressure gradient, as in most diffuser layers. It is based on a method due to Spence which has been modified and also extended to the calculation of three-dimensional diverging layers such as occur in ducts whose breadth is increasing. The velocity profiles occurring in a diverging layer are examined and it is shown that the inner part obeys the universal logarithmic law, as in two-dimensional layers. This result is used to obtain an equation for the form parameter in diverging layers, by substitution in the equation of motion and incorporation of the equations of momentum and continuity for diverging flow. The form parameter equation contains a term involving the gradient of shear stress at y = θ and values of this term are obtained by the analysis of experimental data and the substitution of known values for all the other terms in the form parameter equation. Values of the term involving shear stress gradient are then correlated in terms of known boundary layer quantities, and the resulting correlation allows the formulation of a step-by-step method for the solution of the form parameter equation. This may be used in conjunction with the momentum equation to predict the boundary layer growth. It was not found possible to effect a satisfactory correlation for boundary layers on lifting aerofoils, in which the turbulence develops within the adverse pressure gradient, and the method cannot be used for the prediction of such layers. The results of a number of calculations are given.

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.

Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

2012 ◽  
Vol 710 ◽  
pp. 5-34 ◽  
Author(s):  
Philipp Schlatter ◽  
Ramis Örlü
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Normal Velocity ◽  
Low Reynolds ◽  
Inflow Conditions

AbstractA recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

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