Velocity distribution and shear velocity behaviour of decelerating flows over a gravel bed

1999 ◽  
Vol 26 (4) ◽  
pp. 468-475 ◽  
Author(s):  
Hossein Afzalimehr ◽  
François Anctil
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Outer Region ◽  
Shear Velocity ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Gravel Bed ◽  
Parabolic Law

The behaviour of the bed shear stress in the presence of a decelerating flow over a gravel bed has been examined. The collected observations revealed that the velocity distribution in the outer region of the boundary layer may be described by a parabolic law. The results obtained by parabolic law are comparable to the bed shear stress estimated via the St-Venant method. At a specific cross section, shear velocities estimated by the parabolic and the St-Venant methods divert considerably from the estimation by zero pressure gradient method. For constant bottom slope and relative roughness, the estimated bed shear stresses based on the parabolic and the St-Venant methods are proportional to the flow discharge, whereas this tendency is not accounted for by the zero pressure gradient model.Key words: velocity distribution, shear velocity, decelerating flows, gravel bed, boundary layer.

scholarly journals BED SHEAR STRESS IN UNSTEADY FLOW

2011 ◽  
Vol 1 (32) ◽  
pp. 8 ◽  
Author(s):  
Paul Andrew Guard ◽  
Peter Nielsen ◽  
Tom E Baldock
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Water Surface ◽  
Free Stream ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Horizontal Pressure Gradient ◽  
Friction Factors ◽  
Horizontal Pressure

Standard engineering methods of estimating bed shear stress using friction factors can fail spectacularly in unsteady hydrodynamic conditions. This paper demonstrates this fact using direct measurements of bed shear stresses under irregular waves using a shear plate apparatus. The measurements are explained in terms of the influence of the horizontal pressure gradient and the shear stresses acting on the surface of the plate. The horizontal fluid velocity at the edge of the boundary layer and the water surface elevation and slope were also measured. The paper demonstrates that the water surface measurements can be used to obtain accurate estimates of the forces on the bed, by employing Fourier analysis techniques or an innovative convolution integral method. The experimental results indicate that an offshore bed shear stress may be recorded while the free stream velocity remains onshore at all times. This demonstrates the failure of the standard engineering friction factor method in this scenario, since negative friction factors would be required. Important questions are raised regarding the appropriate definition for the bed shear stress when the vertical gradient of the shear stress is large. It is shown that it is problematic to define a single value for a “bed” shear stress in the presence of a strong horizontal pressure gradient. It is also argued that the natural driver for any model used to predict bed shear stress is the pressure gradient (or its proxy the free stream acceleration), rather than the velocity. This allows for accurate calculation of both acceleration effects (more rapid acceleration leads to a thinner boundary layer and higher shear stress) and also the direct action of the horizontal pressure gradient.

Reynolds-shear-stress measurements in a compressible boundary layer within a shock-wave-induced adverse pressure gradient

1974 ◽  
Vol 65 (1) ◽  
pp. 177-188 ◽  
Author(s):  
W. C. Rose ◽  
M. E. Childs
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Heat Transfer ◽  
Shear Stresses ◽  
Turbulent Heat ◽  
Wave Induced

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient

1951 ◽  
Vol 18 (1) ◽  
pp. 95-100
Author(s):  
Donald Ross ◽  
J. M. Robertson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Pressure Recovery ◽  
Stress Coefficient ◽  
Wall Shear

Abstract As an interim solution to the problem of the turbulent boundary layer in an adverse pressure gradient, a super-position method of analysis has been developed. In this method, the velocity profile is considered to be the result of two effects: the wall shear stress and the pressure recovery. These are superimposed, yielding an expression for the velocity profiles which approximate measured distributions. The theory also leads to a more reasonable expression for the wall shear-stress coefficient.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

scholarly journals Instability and Transition of a Boundary Layer over a Backward-Facing Step

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 35
Author(s):  
Ming Teng ◽  
Ugo Piomelli
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Adverse Pressure Gradient ◽  
Transition Process ◽  
Transition To Turbulence ◽  
Recirculation Region ◽  
Backward Facing Step ◽  
Freestream Velocity ◽  
Displacement Thickness

The development of secondary instabilities in a boundary layer over a backward-facing step is investigated numerically. Two step heights are considered, h/δo*=0.5 and 1.0 (where δo* is the displacement thickness at the step location), in addition to a reference flat-plate case. A case with a realistic freestream-velocity distribution is also examined. A controlled K-type transition is initiated using a narrow ribbon upstream of the step, which generates small and monochromatic perturbations by periodic blowing and suction. A well-resolved direct numerical simulation is performed. The step height and the imposed freestream-velocity distribution exert a significant influence on the transition process. The results for the h/δo*=1.0 case exhibit a rapid transition primarily due to the Kelvin–Helmholtz instability downstream of step; non-linear interactions already occur within the recirculation region, and the initial symmetry and periodicity of the flow are lost by the middle stage of transition. In contrast, case h/δo*=0.5 presents a transition road map in which transition occurs far downstream of the step, and the flow remains spatially symmetric and temporally periodic until the late stage of transition. A realistic freestream-velocity distribution (which induces an adverse pressure gradient) advances the onset of transition to turbulence, but does not fundamentally modify the flow features observed in the zero-pressure gradient case. Considering the budgets of the perturbation kinetic energy, both the step and the induced pressure-gradient increase, rather than modify, the energy transfer.

scholarly journals Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 932
Author(s):  
Rodrigo González ◽  
Aldo Tamburrino ◽  
Andrea Vacca ◽  
Michele Iervolino
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Momentum Equation ◽  
Parallel Plates ◽  
Analytical Computation ◽  
Pulsatile Pressure ◽  
Pulsatile Pressure Gradient

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

scholarly journals Effects of Free-Stream Turbulence Intensity on a Boundary Layer Recovering From Concave Curvature Effects

1993 ◽  
Author(s):  
Michael D. Kestoras ◽  
Terrence W. Simon
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Outer Region ◽  
Free Stream Turbulence ◽  
Flat Wall ◽  
Curvature Effects ◽  
Turbulent Eddies ◽  
Concave Wall

Experiments are conducted on a flat recovery wall downstream of sustained concave curvature in the presence of high free-stream turbulence (TI∼8%). This flow simulates some of the features of the flow on the latter parts of the pressure surface of a gas turbine airfoil. The combined effects of concave curvature and TI, both present in the flow over a turbine airfoil, have so far little been studied. Computation of such flows with standard turbulence closure models has not been particularly successful. This experiment attempts to characterize the turbulence characteristics of this flow. In the present study, a turbulent boundary layer grows from the leading edge of a concave wall then passes onto a downstream flat wall. Results show that turbulence intensities increase profoundly in the outer region of the boundary layer over the recovery wall. Near-wall turbulent eddies appear to lift off the recovery wall and a “stabilized” region forms near the wall. In contrast to a low-free-stream turbulence intensity flow, turbulent eddies penetrate the outer parts of the “stabilized” region where sharp velocity and temperature gradients exist. These eddies can more readily transfer momentum and heat. As a result, skin friction coefficients and Stanton numbers on the recovery wall are 20% and 10%, respectively, above their values in the low-free-stream turbulence intensity case. Stanton numbers do not undershoot flat-wall expectations at the same ReΔ2 values as seen in the low-TI case. Remarkably, the velocity distribution in the core of the flow over the recovery wall exhibits a negative gradient normal to the wall under high free-stream turbulence intensity conditions. This velocity distribution appears to be the result of two effects: 1) cross transport of kinetic energy by boundary work in the upstream curved flow and 2) readjustment of static pressure profiles in response to the removal of concave curvature.

scholarly journals The Effect of Habitat Structure Boulder Spacing on Near-Bed Shear Stress and Turbulent Events in a Gravel Bed Channel

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1423
Author(s):  
Amir Golpira ◽  
Fengbin Huang ◽  
Abul B.M. Baki
Keyword(s):  
Shear Stress ◽  
Habitat Structure ◽  
Open Channel ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quadrant Analysis ◽  
Bed Shear Stress ◽  
Gravel Bed ◽  
Restoration Practices ◽  
Ejections And Sweeps

This study experimentally investigated the effect of boulder spacing and boulder submergence ratio on the near-bed shear stress in a single array of boulders in a gravel bed open channel flume. An acoustic Doppler velocimeter (ADV) was used to measure the instantaneous three-dimensional velocity components. Four methods of estimating near-bed shear stress were compared. The results suggested a significant effect of boulder spacing and boulder submergence ratio on the near-bed shear stress estimations and their spatial distributions. It was found that at unsubmerged condition, the turbulent kinetic energy (TKE) and modified TKE methods can be used interchangeably to estimate the near-bed shear stress. At both submerged and unsubmerged conditions, the Reynolds method performed differently from the other point-methods. Moreover, a quadrant analysis was performed to examine the turbulent events and their contribution to the near-bed Reynolds shear stress with the effect of boulder spacing. Generally, the burst events (ejections and sweeps) were reduced in the presence of boulders. This study may improve the understanding of the effect of the boulder spacing and boulder submergence ratio on the near-bed shear stress estimations of stream restoration practices.

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