Turbulent diffusion near a free surface

2000 ◽  
Vol 407 ◽  
pp. 145-166 ◽  
Author(s):  
LIAN SHEN ◽  
GEORGE S. TRIANTAFYLLOU ◽  
DICK K. P. YUE
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Turbulent Diffusion ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Numerical Study ◽  
Turbulent Shear ◽  
Surface Boundary ◽  
Mean Flow ◽  
The Mean

We study numerically and analytically the turbulent diffusion characteristics in a low-Froude-number turbulent shear flow beneath a free surface. In the numerical study, the Navier–Stokes equations are solved directly subject to viscous boundary conditions at the free surface. From an ensemble of such simulations, we find that a boundary layer develops at the free surface characterized by a fast reduction in the value of the eddy viscosity. As the free surface is approached, the magnitude of the mean shear initially increases over the boundary (outer) layer, reaches a maximum and then drops to zero inside a much thinner inner layer. To understand and model this behaviour, we derive an analytical similarity solution for the mean flow. This solution predicts well the shape and the time-scaling behaviour of the mean flow obtained in the direct simulations. The theoretical solution is then used to derive scaling relations for the thickness of the inner and outer layers. Based on this similarity solution, we propose a free-surface function model for large-eddy simulations of free-surface turbulence. This new model correctly accounts for the variations of the Smagorinsky coefficient over the free-surface boundary layer and is validated in both a priori and a posteriori tests.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

scholarly journals Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity

2018 ◽  
Vol 848 ◽  
pp. 631-647 ◽  
Author(s):  
Eunok Yim ◽  
J.-M. Chomaz ◽  
D. Martinand ◽  
E. Serre
Keyword(s):  
Boundary Layer ◽  
Similarity Solution ◽  
Rotating Disk ◽  
Transition To Turbulence ◽  
Mean Flow ◽  
Self Similarity ◽  
Mean Velocity ◽  
Global Mode ◽  
Spatial Growth ◽  
The Mean

The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor–stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counter-clockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers $m$, in the range $m\in [32,78]$. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.

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.

Endwall Loss and Mixing Analysis of a High Lift Low Pressure Turbine Cascade

2012 ◽  
Author(s):  
M. Eric Lyall ◽  
Paul I. King ◽  
Rolf Sondergaard
Keyword(s):  
Low Energy ◽  
Turbulent Shear ◽  
Surface Boundary ◽  
Test Bed ◽  
Mean Flow ◽  
Suction Surface ◽  
High Lift ◽  
Vortical Structures ◽  
Surface Separation ◽  
The Mean

A high lift LPT profile designated L2A is used as a test bed for studying the origin of endwall mixing loss and the role of vortical structures in loss development. It is shown analytically and experimentally that the mixing forces within the endwall wake can be decoupled into either mean flow or turbulent forces, and can be further classified as either reversible or irreversible. Among the irreversible forces, mean flow shear is negligible compared to turbulent shear, suggesting that turbulence dissipation is the dominant cause of loss generation. As a result, the mean flow components of the vortical structures do not generate significant mixing losses. Rather than mixing effects, the mean flow of the vortices cause the suction surface boundary layer to separate inside the passage, thereby generating the large low energy regions typical of endwall flows. Losses are generated as the low energy regions mix out. This vortex separation effect is demonstrated with an experiment using a profile fence and pressure surface modification near the endwall. The findings in this paper suggest that profile modifications near the endwall that suppress suction surface separation may provide loss reductions additive to those that weaken vortical structures, such as endwall contouring.

scholarly journals Numerical Study of Violent Impact Flow Using a CIP-Based Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qiao-ling Ji ◽  
Xi-zeng Zhao ◽  
Sheng Dong
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Large Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Small Scale ◽  
Surface Boundary ◽  
Two Phase ◽  
Constrained Interpolation

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

Endwall Loss and Mixing Analysis of a High Lift Low Pressure Turbine Cascade

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
M. Eric Lyall ◽  
Paul I. King ◽  
Rolf Sondergaard
Keyword(s):  
Low Pressure ◽  
Low Energy ◽  
Turbulent Shear ◽  
Surface Boundary ◽  
Test Bed ◽  
Mean Flow ◽  
High Lift ◽  
Vortical Structures ◽  
Low Pressure Turbine ◽  
The Mean

A high lift low pressure turbine (LPT) profile designated L2A is used as a test bed for studying the origin of endwall mixing loss and the role of vortical structures in loss development. It is shown analytically and experimentally that the mixing forces within the endwall wake can be decoupled into either mean flow or turbulent forces and can be further classified as either reversible or irreversible. Among the irreversible forces, mean flow shear is negligible compared to turbulent shear, suggesting that turbulence dissipation is the dominant cause of loss generation. As a result, the mean flow components of the vortical structures do not generate significant mixing losses. Rather than mixing effects, the mean flow of the vortices causes the suction surface boundary layer to separate inside the passage, thereby generating the large low energy regions typical of endwall flows. Losses are generated as the low energy regions mix out. This vortex separation effect is demonstrated with an experiment using a profile fence and pressure surface modification near the endwall. The findings in this paper suggest that profile modifications near the endwall that suppress flow separation may provide loss reductions additive to modifications aimed at weakening vortical structures, such as endwall contouring.

Free-surface turbulent wake behind towed ship models: experimental measurements, stability analyses and direct numerical simulations

2002 ◽  
Vol 469 ◽  
pp. 89-120 ◽  
Author(s):  
LIAN SHEN ◽  
CHIONG ZHANG ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Growth Rates ◽  
Stokes Equations ◽  
Turbulent Wake ◽  
Wake Flow ◽  
Experimental Measurements ◽  
Surface Boundary ◽  
Mean Flow ◽  
Transition Mechanism ◽  
Surface Normal

We combine experimental, theoretical and numerical efforts to investigate the turbulent wake far behind a surface ship at model scales. Experimental measurements using digital particle image velocimetry (DPIV) are performed for the wakes of three towed hulls with beam-to-draught ratios b/d = 1, 2, 6. Based on model speed and beam, the Reynolds and Froude numbers are O(103) and O(10−2) respectively. Distinct surface features associated with persistent surface-normal vorticity have been identified, which are characterized by large-scale meandering structures. Both lateral and longitudinal scales of the meandering are quantified, with the former found to increase as b/d decreases and the latter independent of b/d. Based on measurements at multiple horizontal and vertical planes, profiles of the mean flow and fluctuation intensity for each velocity component are obtained. To understand the turbulence transition mechanism, an Orr–Sommerfeld stability analysis (OS) is formulated for the wake flow with free-surface boundary conditions, and solved by using a fourth-order finite-difference scheme. Unstable modes antisymmetric to the wake centre-plane are identified. Consistent with the experimental results, the growth rates of unstable modes increase substantially as b/d decreases, while the dependence of meandering wavelengths on b/d is found to be weak. Finally, we perform direct numerical simulation (DNS) of Navier–Stokes equations for the wake flow. The growth rates of unstable modes agree well with the predictions by OS analysis. Compared with experiments, DNS accurately captures the surface-normal vorticity signatures, the meandering features, as well as statistics of turbulence intensity. We also obtain from DNS a detailed description of enstrophy, turbulence length scales, and vortex structures for the wake flow.

Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity

2013 ◽  
Vol 733 ◽  
pp. 558-587 ◽  
Author(s):  
Xin Guo ◽  
Lian Shen
Keyword(s):  
Surface Wave ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Direction ◽  
Stokes Drift ◽  
Mechanistic Study ◽  
Velocity Spectrum ◽  
Surface Boundary ◽  
Mean Flow ◽  
Random Forcing

AbstractDirect numerical simulation is performed to study the effect of progressive gravity waves on turbulence underneath. The Navier–Stokes equations subject to fully nonlinear kinematic and dynamic free-surface boundary conditions are simulated on a surface-following mapped grid using a fractional-step scheme with a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. To facilitate a mechanistic study that focuses on the fundamental physics of wave–turbulence interaction, the wave and turbulence fields are set up precisely in the simulation: a pressure-forcing method is used to generate and maintain the progressive wave being investigated and to suppress other wave components, and a random forcing method is used to produce statistically steady, homogeneous turbulence in the bulk flow beneath the surface wave. Cases with various moderate-to-large turbulence-to-wave time ratios and wave steepnesses are considered. Study of the turbulence velocity spectrum shows that the turbulence is dynamically forced by the surface wave. Mean flow and turbulence vorticity are studied in both the Eulerian and Lagrangian frames of the wave. In the Eulerian frame, statistics of the underlying turbulence field indicates that the magnitude of turbulence vorticity and the inclination angle of vortices are dependent on the wave phase. In the Lagrangian frame, wave properties and the accumulative effect on turbulence vorticity are studied. It is shown that vertical vortices are tilted in the wave propagation direction due to the cumulative effects of both the Stokes drift velocity and the correlation between turbulence fluctuations and wave strain rate, whereas for streamwise vortices, these two factors offset each other and result in a negligible tilting effect.

scholarly journals Characteristics of the flow around conventional and supercritical airfoils

1985 ◽  
Vol 160 ◽  
pp. 155-179 ◽  
Author(s):  
A. Nakayama
Keyword(s):  
Boundary Layer ◽  
Normal Pressure ◽  
Lower Surface ◽  
Surface Boundary ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Trailing Edge ◽  
Surface Boundary Layer ◽  
Supercritical Airfoil ◽  
The Mean

Measurements of the mean and fluctuating velocities have been obtained with pressure and hot-wire probes in the attached boundary layers and wakes of two airfoil models at a low Mach number. The first model is a conventional airfoil at zero incidence and the second an advanced supercritical airfoil at an angle of attack of 4°. The mean-flow and Reynolds-stress data and related quantities are presented with emphasis on the trailing-edge region. The results indicate that the flow around the conventional airfoil is a minor perturbation of a symmetric flat-plate flow with small wake curvature and weak viscous–inviscid interaction. The flow around the supercritical airfoil is in considerable contrast with strong streamwise pressure gradients, non-negligible normal pressure gradients, and large surface and streamline curvatures of the trailing-edge flow. The near wake is strongly curved and intense mixing occurs between the retarded upper-surface boundary layer and strongly accelerated lower-surface boundary layer.

scholarly journals Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

2021 ◽  
Author(s):  
Alexander Vakhrushev ◽  
Abdellah Kharicha ◽  
Ebrahim Karimi-Sibaki ◽  
Menghuai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Applied Magnetic Field ◽  
Numerical Study ◽  
Flow Direction ◽  
Experimental Studies ◽  
Submerged Entry Nozzle ◽  
Mean Flow ◽  
Slab Caster ◽  
The Mean

AbstractA numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

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