Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

2021 ◽  
Vol 33 (3) ◽  
pp. 035142
Author(s):  
Tie Wei ◽  
Daniel Livescu
Keyword(s):  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Transverse Flow ◽  
The Mean ◽  
Turbulent Plane ◽  
Plane Jet

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Turbulent Boundary Layers Subjected to Multiple Strains

1999 ◽  
Vol 121 (3) ◽  
pp. 526-532 ◽  
Author(s):  
Andreas C. Schwarz ◽  
Michael W. Plesniak ◽  
S. N. B. Murthy
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Laser Doppler Velocimeter ◽  
Strain Rates ◽  
The Mean ◽  
Convex Curvature ◽  
Multiple Strain Rates

Turbomachinery flows can be extremely difficult to predict, due to a multitude of effects, including interacting strain rates, compressibility, and rotation. The primary objective of this investigation was to study the influence of multiple strain rates (favorable streamwise pressure gradient combined with radial pressure gradient due to convex curvature) on the structure of the turbulent boundary layer. The emphasis was on the initial region of curvature, which is relevant to the leading edge of a stator vane, for example. In order to gain better insight into the dynamics of complex turbulent boundary layers, detailed velocity measurements were made in a low-speed water tunnel using a two-component laser Doppler velocimeter. The mean and fluctuating velocity profiles showed that the influence of the strong favorable pressure augmented the stabilizing effects of convex curvature. The trends exhibited by the primary Reynolds shear stress followed those of the mean turbulent bursting frequency, i.e., a decrease in the bursting frequency coincided with a reduction of the peak Reynolds shear stress. It was found that the effects of these two strain rates were not superposable, or additive in any simple manner. Thus, the dynamics of the large energy-containing eddies and their interaction with the turbulence production mechanisms must be considered for modeling turbulent flows with multiple strain rates.

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

scholarly journals High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

2016 ◽  
Vol 801 ◽  
pp. 670-703 ◽  
Author(s):  
Hangjian Ling ◽  
Siddarth Srinivasan ◽  
Kevin Golovin ◽  
Gareth H. McKinley ◽  
Anish Tuteja ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Profile ◽  
Drag Reduction ◽  
Slip Velocity ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Roughness Elements ◽  
The Mean

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

Turbulent Structure With Microbubbles Generated by Electrolysis in a Horizontal Channel Flow

2018 ◽  
Author(s):  
Takamichi Hiroi ◽  
Tatsuya Hamada ◽  
Masahiko Makino ◽  
Chiharu Kawakita
Keyword(s):  
Shear Stress ◽  
Channel Flow ◽  
Void Fraction ◽  
Reynolds Shear Stress ◽  
Water Channel ◽  
Turbulent Structure ◽  
Equivalent Diameter ◽  
Structure Of Flow ◽  
The Mean ◽  
Current Value

The turbulent structure of flow field with microbubbles which is generated by electrolysis in a horizontal water channel is investigated at Reynolds number Rem = 24000 (based on the channel height). Firstly, Shadow Image Technique (SIT) is applied to investigate the relation between the shape and the velocity of microbubbles. The experiments have been carried out at the current value 100mA, 200mA, 300mA. The amount of gas generated by electrolysis per unit time is estimated 1.89–5.67 mm3/s. The void fraction is 0.95 × 10−5 – 2.93 × 10−4 %. The mode of the equivalent diameter is 5–10 μm regardless of the condition of the current value. In contrast the mean of the equivalent diameter increases with the increasing of the current value. The mean streamwise velocity of microbubbles increases with the current value. Secondly, Particle Image Velocimetry (PIV) is applied to investigate the turbulent structure in a microbubble channel flow. The experiments have been carried out at the current value 250mA, 300mA. The streamwise mean velocity decreases with the increasing of the current value. The velocity normal from the wall increases by microbubbles. The turbulent intensity with microbubble is bigger than that without microbubble. The Reynolds shear stress with microbubble, however, is smaller than that without microbubble. The decreasing of contribution to the friction coefficient of the turbulent component is calculated about 6.4 % using FIK identify at a low void fraction 2.93 × 10−4 %. The increasing of the frequency of inner interaction and outer interaction causes the decreasing of Reynolds shear stress is clarified by quadrant analysis.

Errors Characterization of a RANS Simulation

2021 ◽  
Author(s):  
Hugo D. Pasinato ◽  
Ezequiel Arthur Krumrick
Keyword(s):  
Shear Stress ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Strain Tensor ◽  
Numerical Code ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Rans Simulation ◽  
Eddy Viscosity Model ◽  
The Mean

Abstract This research uses data from direct numerical simulation (DNS) to characterize the different errors associated with a Reynolds-averaged Navier-Stokes (RANS) simulation. The statistics from DNS (Reynolds stresses, kinetic energy of turbulence, $\kappa$, and dissipation of turbulence, $\epsilon$), are fed into a RANS simulation with the same Reynolds number, geometry, and numerical code used for DNS. Three integral metrics error based on the mean velocity, the moduli of the mean rate-of-strain tensor, and the wall shear stress are used to characterize the errors associated with the RANS technique, with the RANS model, and with the linear eddy viscosity model (LEVM). For developed and perturbed flow, it is found that the mean velocity of the RANS simulations with the DNS statistics is almost the same as the mean velocity from DNS data. This procedure enables the study of the relative importance of the different Reynolds stresses in a particular flow. It is shown that for the bounded perturbed turbulent flows studied here, almost all the necessary effects of turbulence are contained in the Reynolds shear stress.

A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Similarity Function ◽  
Mixing Length ◽  
Flow Properties ◽  
Normal Coordinate ◽  
Streamwise Location ◽  
The Mean

A novel two-equations model for computing the flow properties of a spatially-developing, incompressible, zero-pressure-gradient, turbulent boundary layer over a smooth, flat wall is developed. The mean streamwise velocity component inside the boundary layer is described by the Reynolds-averaged Navier–Stokes equation where the Reynolds shear stress is given by an extended mixing-length model. The nondimensional form of the mixing length is described by a polynomial function in terms of the nondimensional wall normal coordinate. Moreover, a stream function approach is applied with a leading-order term described by a similarity function. Two ordinary differential equations are derived for the solution of the similarity function along the wall normal coordinate and for its streamwise location. A numerical integration scheme of the model equations is developed and enables the solution of flow properties. The coefficients of the mixing-length polynomial function are modified at each streamwise location as part of solution iterations to satisfy the wall and far-field boundary conditions and adjust the local boundary layer thickness, δ99.4, to a location where streamwise speed is 99.4% of the far-field streamwise velocity. The elegance of the present approach is established through the successful solution of the various flow properties across the boundary layer (i.e., mean streamwise velocity, viscous stress, Reynolds shear stress, skin friction coefficient, and growth rate of boundary layer among others) from the laminar regime all the way to the fully turbulent regime. It is found that results agree with much available experimental data and direct numerical simulations for a wide range of Reθ based on the momentum thickness (Reθ) from 15 up to 106, except for the transition region from laminar to turbulent flow. Furthermore, results shed light on the von Kármán constant as a function of Reθ, the possible four-layer nature of the mean streamwise velocity profile, the universal profiles of the streamwise velocity and the Reynolds shear stress at high Reθ, and the scaling laws at the outer region.

scholarly journals Near-field flow structure of a confined wall jet on flat and concave rough walls

2008 ◽  
Vol 606 ◽  
pp. 27-49 ◽  
Author(s):  
I. ALBAYRAK ◽  
E. J. HOPFINGER ◽  
U. LEMMIN
Keyword(s):  
Shear Stress ◽  
Shear Layer ◽  
Outer Layer ◽  
Reynolds Shear Stress ◽  
Near Field ◽  
Wall Jet ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Free Jet ◽  
The Mean

Experimental results are presented of the mean flow and turbulence characteristics in the near field of a plane wall jet issuing from a nozzle onto flat and concave walls consisting of fixed sand beds. This is a flow configuration of interest for sediment erosion, also referred to as scouring. The measurements were made with an acoustic profiler that gives access to the three components of the instantaneous velocities. For the flat-wall flow, it is shown that the outer-layer spatial growth rate and the maxima of the Reynolds stresses approach the values accepted for the far field of a wall jet at a downstream distance x/b0 ≈ 8. These maxima are only about half the values of a plane free jet. This reduction in Reynolds stresses is also observed in the shear-layer region, x/b0 < 6, where the Reynolds shear stress is about half the value of a free shear layer. At distances x/b0 > 11, the maximum Reynolds shear stress approaches the value of a plane free jet. This change in Reynolds stresses is related to the mean vertical velocity that is negative for x/b0 < 8 and positive further downstream. The evolution of the inner region of the wall jet is found to be in good agreement with a previous model that explicitly includes the roughness length.On the concave wall, the mean flow and the Reynolds stresses are drastically changed by the adverse pressure gradient and especially by the development of Görtler vortices. On the downslope side of the scour hole, the flow is nearly separating with the wall shear stress tending to zero, whereas on the upslope side, the wall-friction coefficient is increased by a factor of about two by Görtler vortices. These vortices extend well into the outer layer and, just above the wall, cause a substantial increase in Reynolds shear stress.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

Turbulent Mixing in the Developing Region of Coaxial Jets

1973 ◽  
Vol 95 (3) ◽  
pp. 467-473 ◽  
Author(s):  
D. Dura˜o ◽  
J. H. Whitelaw
Keyword(s):  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Velocity Ratio ◽  
Jet Flows ◽  
Normal Stresses ◽  
Downstream Location ◽  
Mean Velocity ◽  
Coaxial Jets ◽  
Developing Region ◽  
The Mean

Measurements of mean velocity, the three normal stresses and Reynolds shear stress are reported in the developing region of coaxial jet flows. The measurements were obtained with three velocity ratios, i.e., values of the ratio of maximum initial pipe velocity to maximum initial annulus velocity of 0, 0.23, and 0.62 and at downstream distances up to 17 outer diameters. The results show that coaxial jets tend to reach a self-preserving state much more rapidly than axisymmetric single jets; that the mean velocity, normal stresses, and Reynolds shear stress attain this state at a similar downstream location; and that, for the particular geometry investigated, a velocity ratio of around 0.15 corresponds to the slowest rate of development. Relationships between mean velocity gradient, Reynolds shear stress, and turbulent kinetic energy are examined to assess their ability to characterize the present flow: the results indicate the need to take account of the normal stresses in any proposed mathematical model.

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