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.

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 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.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

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.

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.

Characteristics of a turbulent boundary layer with an external turbulent uniform shear flow

1976 ◽  
Vol 77 (2) ◽  
pp. 369-396 ◽  
Author(s):  
Q. A. Ahmad ◽  
R. E. Luxton ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Shear Flow ◽  
Free Stream ◽  
Reynolds Shear Stress ◽  
Wall Layer ◽  
Turbulence Level ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean

Measurements are presented of both mean and fluctuating velocity components in a turbulent boundary layer subjected to a nearly homogeneous external turbulent shear flow. The Reynolds shear stress in the external shear flow is small compared with the wall shear stress. Its transverse mean velocity gradient λ (≃ 6 s−l) is also small compared with typical gradients based on outer variables (say Uw/δ, where Uwis the value of the linear velocity profile extrapolated to the wall and δ is the boundary-layer thickness), but is of the same order as Ut/δ (Ur is the friction velocity). The influence of both positive and negative transverse velocity gradients on the turbulent wall layer is investigated over a streamwise region where the normal Reynolds stresses in the external flow are approximately equal and constant in the streamwise direction. In this region, the integral length scale of the external flow is of the same order of magnitude as that of the wall layer. Measurements in the boundary layer are also given for an un-sheared external turbulent flow (λ = 0) with a turbulence level Tu of 1.5%, approximately the same as that for h = ± 6 s−1. (Tu, is defined as the ratio of the r.m.s. longitudinal velocity fluctuation to Uw.) The measurements are in good agreement with those available in the literature for a similar free-stream turbulence level and show that the external turbulence level and length scale exert a large influence on the turbulence structure in the boundary layer. The additional effect of the external shear on the mean velocity and turbulent energy budget distributions in the inner region of the boundary layer is found to be small. In the outer region, the ‘wake’ component of the mean velocity defect is lowered by the presence of free-stream turbulence and one extra effect due to the external shear is an increase in the Reynolds shear stress when h is positive and a decrease when h is negative. Another interesting effect due to the shear is the appearance near the edge of the layer of a small but distinct region where the local mean velocity is constant and the Reynolds shear stress is negligible.

Turbulent Boundary Layers on Surfaces Covered With Filamentous Algae

2000 ◽  
Vol 122 (2) ◽  
pp. 357-363 ◽  
Author(s):  
Michael P. Schultz
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulence Intensity ◽  
Reynolds Shear Stress ◽  
Skin Friction Coefficient ◽  
Laser Doppler Velocimeter ◽  
Mean Velocity ◽  
Rough Walls ◽  
The Mean ◽  
Stress Profiles

Turbulent boundary layer measurements have been made on surfaces covered with filamentous marine algae. These experiments were conducted in a closed return water tunnel using a two-component, laser Doppler velocimeter (LDV). The mean velocity profiles and parameters, as well as the axial and wall-normal turbulence intensities and Reynolds shear stress, are compared with flows over smooth and sandgrain rough walls. Significant increases in the skin friction coefficient for the algae-covered surfaces were measured. The boundary layer and integral thickness length scales were also increased. The results indicate that profiles of the turbulence quantities for the smooth and sandgrain rough walls collapse when friction velocity and boundary layer thickness are used as normalizing parameters. The algae-covered surfaces, however, exhibited a significant increase in the wall-normal turbulence intensity and the Reynolds shear stress, with only a modest increase in the axial turbulence intensity. The peak in the Reynolds shear stress profiles for the algae surfaces corresponded to the maximum extent of outward movement of the algae filaments. [S0098-2202(00)01902-7]

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