scholarly journals Simulations of rib-roughened rough-to-smooth turbulent channel flows

2018 ◽  
Vol 843 ◽  
pp. 419-449 ◽  
Author(s):  
Umair Ismail ◽  
Tamer A. Zaki ◽  
Paul A. Durbin
Keyword(s):  
Large Scale ◽  
Wall Layer ◽  
Shear Stresses ◽  
Thin Wall ◽  
Computational Domain ◽  
Reynolds Stresses ◽  
Smooth Wall ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

High-fidelity simulations of turbulent flow through a channel with a rough wall, followed by a smooth wall, demonstrate a high degree of non-equilibrium within the recovery region. In fact, the recovery of all the flow statistics studied is incomplete by the streamwise exit of the computational domain. Above a thin wall layer, turbulence intensities significantly higher than fully developed, smooth-wall levels persist in the developing region. Within the thin wall layer, the profile shapes for turbulence stresses recover very quickly and wall-normal locations of characteristic peaks are established. However, even in this thin layer, complete recovery of magnitudes of turbulence stresses is exceptionally slow. A similar initially swift but eventually incomplete and slow relaxation behaviour is also shown by the skin friction. Between the turbulence shear and streamwise stresses, the turbulence shear stress shows a comparatively quick rate of recovery above a thin wall layer. Over the developing smooth wall, the balance is not merely between fluxes due to pressure and shear stresses. Strong momentum fluxes, which are directly influenced by the upstream roughness size, contribute significantly to this balance. Approximate curve fits estimate the streamwise distance required by the outer peaks of Reynolds stresses to attain near-fully-developed levels at approximately $20\unicode[STIX]{x1D6FF}{-}25\unicode[STIX]{x1D6FF}$, with $\unicode[STIX]{x1D6FF}$ being the channel half height. An even longer distance, of more than $50\unicode[STIX]{x1D6FF}$, might be needed by the mean velocity to approach near-fully-developed magnitudes. Visualizations and correlations show that large-scale eddies that are created above the roughness persist downstream, and sporadically perturb the elongated streaks. These streaks of alternating high and low momentum appear almost instantly after the roughness is removed. The mean flow does not re-establish an equilibrium log layer within the computational domain, and the velocity deficit created by the roughness continues throughout the domain. On the step change in roughness, near the wall, profiles for turbulence kinetic energy dissipation rate, $\unicode[STIX]{x1D716}$, and energy spectra indicate a sharp reduction in energy at small scales. Despite this, reversion towards equilibrium smooth-wall levels is slow, and ultimately incomplete, due to a rather slow adjustment of the turbulence cascade. The non-dimensional roughness height, $k^{+}$ ranges from 42 to 254 and the friction velocity Reynolds number at the smooth wall, $Re_{\unicode[STIX]{x1D70F}S}$, ranges from 284 to 1160 in the various simulations.

The formation of shear and density layers in stably stratified turbulent flows: linear processes

2002 ◽  
Vol 455 ◽  
pp. 243-262 ◽  
Author(s):  
M. GALMICHE ◽  
J. C. R. HUNT
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Shear Stresses ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
Linear Processes ◽  
Buoyancy Forces ◽  
Uniform Background ◽  
The Mean

The initial evolution of the momentum and buoyancy fluxes in a freely decaying, stably stratified homogeneous turbulent flow with r.m.s. velocity u′0 and integral lengthscale l0 is calculated using a weakly inhomogeneous and unsteady form of the rapid distortion theory (RDT) in order to study the growth of small temporal and spatial perturbations in the large-scale mean stratification N(z, t) and mean velocity profile ū(z, t) (here N is the local Brunt–Väisälä frequency and ū is the local velocity of the horizontal mean flow) when the ratio of buoyancy forces to inertial forces is large, i.e. Nl0/u′0[Gt ]1. The lengthscale L of the perturbations in the mean profiles of stratification and shear is assumed to be large compared to l0 and the presence of a uniform background mean shear can be taken into account in the model provided that the inertial shear forces are still weaker than the buoyancy forces, i.e. when the Richardson number Ri = (N/∂zū)2[Gt ]1 at each height.When a mean shear perturbation is introduced initially with no uniform background mean shear and uniform stratification, the analysis shows that the perturbations in the mean flow profile grow on a timescale of order N-1. When the mean density profile is perturbed initially in the absence of a background mean shear, layers with significant density gradient fluctuations grow on a timescale of order N−10 (where N0 is the order of magnitude of the initial Brunt–Väisälä frequency) without any associated mean velocity gradients in the layers. These results are in good agreement with the direct numerical simulations performed by Galmiche et al. (2002) and are consistent with the earlier physically based conjectures made by Phillips (1972) and Posmentier (1977). The model also shows that when there is a background mean shear in combination with perturbations in the mean stratification, negative shear stresses develop which cause the mean velocity gradient to grow in the density layers. The linear analysis for short times indicates that the scale on which the mean perturbations grow fastest is of order u′0/N0, which is consistent with the experiments of Park et al. (1994).We conclude that linear mechanisms are widely involved in the formation of shear and density layers in stratified flows as is observed in some laboratory experiments and geophysical flows, but note that the layers are also significantly influenced by nonlinear and dissipative processes at large times.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

scholarly journals A Framework for Parameterizing Eddy Potential Vorticity Fluxes

2012 ◽  
Vol 42 (4) ◽  
pp. 539-557 ◽  
Author(s):  
David P. Marshall ◽  
James R. Maddison ◽  
Pavel S. Berloff
Keyword(s):  
Stress Tensor ◽  
Potential Vorticity ◽  
Large Scale ◽  
Eddy Diffusivity ◽  
Linear Instability ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Conservation Of Energy ◽  
The Mean ◽  
Energy And Momentum

Abstract A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.

Hot-Wire Measurements Inside a Centrifugal Fan Impeller

1989 ◽  
Vol 111 (4) ◽  
pp. 363-368 ◽  
Author(s):  
A. Kjo¨rk ◽  
L. Lo¨fdahl
Keyword(s):  
Suction Side ◽  
Design Flow ◽  
Shear Stresses ◽  
Centrifugal Fan ◽  
Reynolds Stresses ◽  
Low Velocity ◽  
Mean Velocity ◽  
Attached Flow ◽  
The Mean ◽  
Velocity Region

Measurements of the three mean velocity components and five of the Reynolds stresses have been carried out in the blade passage of a centrifugal fan impeller. The impeller was of ordinary design, with nine backward curved blades, and all measurements were carried out at the design flow rate. The mean velocity measurements show that the flow can be characterized as an attached flow with almost linearly distributed velocity profiles. However, in a region near the suction side close to the shroud a low velocity region is created. From the turbulence measurements it can be concluded that relatively low values of the turbulent stresses are predominating in the center region of the channel. Closer to the walls higher values of the normal as well as shear stresses are noted.

scholarly journals A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow

2015 ◽  
Vol 774 ◽  
pp. 143-169 ◽  
Author(s):  
J.-H. Xie ◽  
J. Vanneste
Keyword(s):  
Large Scale ◽  
Interaction Mechanism ◽  
Coupled Model ◽  
Inertial Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Time Scale Separation ◽  
The Mean ◽  
Balanced Flow ◽  
Mesoscale Motion

Wind forcing of the ocean generates a spectrum of inertia–gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the non-dissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the ‘glm’ variant of Soward & Roberts, J. Fluid Mech., vol. 661, 2010, pp. 45–72), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon’s (J. Fluid Mech., vol. 719, 2013, pp. 165–182) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul’s (J. Mar. Res., vol. 55, 1997, pp. 735–766) equation for NIWs with a modified quasi-geostrophic (QG) equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potential-vorticity (PV) inversion – the relation between advected PV and advecting mean velocity – through a quadratic wave term, consistent with the GLM results of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 301–343). The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean. Idealised two-dimensional models are derived and simulated numerically to gain insight into NIW–mean-flow interaction processes. A simulation of a one-dimensional barotropic jet demonstrates how NIWs forced by wind slow down the jet as they propagate into the ocean interior. A simulation assuming plane travelling NIWs in the vertical shows how a vortex dipole is deflected by NIWs, illustrating the irreversible nature of the interactions. In both simulations energy is transferred from the mean flow to the NIWs.

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

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 Mean turbulence statistics in boundary layers over high-porosity foams

2018 ◽  
Vol 841 ◽  
pp. 351-379 ◽  
Author(s):  
Christoph Efstathiou ◽  
Mitul Luhar
Keyword(s):  
Boundary Layer ◽  
Pore Size ◽  
Slip Velocity ◽  
Large Scale ◽  
Smooth Wall ◽  
Mean Velocity ◽  
Velocity Deficit ◽  
Large Scale Structures ◽  
The Mean ◽  
Scale Structures

This paper reports turbulent boundary layer measurements made over open-cell reticulated foams with varying pore size and thickness, but constant porosity ($\unicode[STIX]{x1D716}\approx 0.97$). The foams were flush-mounted into a cutout on a flat plate. A laser Doppler velocimeter (LDV) was used to measure mean streamwise velocity and turbulence intensity immediately upstream of the porous section, and at multiple measurement stations along the porous substrate. The friction Reynolds number upstream of the porous section was $Re_{\unicode[STIX]{x1D70F}}\approx 1690$. For all but the thickest foam tested, the internal boundary layer was fully developed by ${<}10\unicode[STIX]{x1D6FF}$ downstream from the porous transition, where $\unicode[STIX]{x1D6FF}$ is the boundary layer thickness. Fully developed mean velocity profiles showed the presence of a substantial slip velocity at the porous interface (${>}30\,\%$ of the free-stream velocity) and a mean velocity deficit relative to the canonical smooth-wall profile further from the wall. While the magnitude of the mean velocity deficit increased with average pore size, the slip velocity remained approximately constant. Fits to the mean velocity profile suggest that the logarithmic region is shifted relative to a smooth wall, and that this shift increases with pore size until it becomes comparable to substrate thickness $h$. For all foams, the turbulence intensity was found to be elevated further into the boundary layer to $y/\unicode[STIX]{x1D6FF}\approx 0.2$. An outer peak in intensity was also evident for the largest pore sizes. Velocity spectra indicate that this outer peak is associated with large-scale structures resembling Kelvin–Helmholtz vortices that have streamwise length scale $2\unicode[STIX]{x1D6FF}{-}4\unicode[STIX]{x1D6FF}$. Skewness profiles suggest that these large-scale structures may have an amplitude-modulating effect on the interfacial turbulence.

Developing turbulent boundary layers with system rotation

1985 ◽  
Vol 157 ◽  
pp. 405-448 ◽  
Author(s):  
J. H. Watmuff ◽  
H. T. Witt ◽  
P. N. Joubert
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Secondary Circulations ◽  
Spatially Periodic

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

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