Near-wall damping in model predictions of separated flows

Different near-wall scalings are reviewed by the use of data from direct numerical simulations (DNS) of attached and separated adverse pressure gradient turbulent boundary layers. The turbulent boundary layer equation is analysed in order to extend the validity of existing wall damping functions to turbulent boundary layers under severe adverse pressure gradients. A proposed near-wall scaling is based on local quantities and the wall distance, which makes it applicable for general computational fluid dynamics (CFD) methods. It was found to have a similar behaviour as the pressure-gradient corrected analytical y^* scaling and avoids the inconsistencies present in the y⁺ scaling. The performance of the model is illustrated by model computations using explicit algebraic Reynolds stress models with near-wall damping based on different scalings.     

The influence of normal stress anisotropy in predicting scalar dispersion with the v–f model

A numerical study of scalar dispersion is presented to investigate the effectiveness of pairing the v²–f turbulence model with algebraic models for the scalar flux. This approach is contrasted with utilizing a full Second Moment Closure (SMC) as the flow field input to the scalar model. Predictions of scalar transport in a turbulent channel and over a wavy wall are compared to available DNS databases. The latter case includes a scalar release from a point source and therefore detailed comparisons of the three-component turbulent scalar flux are reported. It is found that the transported variable v², representing the near wall turbulent velocity fluctuation scale, can be used to increase the level of normal stress anisotropy provided to algebraic scalar models and thereby improve mean scalar prediction over that of the Standard Gradient Diffusion Hypothesis (SGDH). Improvement is most significant in the near wall region. Three specifications of the normal stresses, derived from v², are considered to provide the link from the v²–f model to the algebraic flux models used to close the scalar transport equation. Barycentric maps are used to examine the state of turbulence anisotropy in each case. As the anisotropy in the normal stress specification becomes more accurate, improvements are realized in the prediction of the spanwise flux as well as the mean concentration.     

Numerical Modeling of Combustion of Fuel-Droplet-Vapour Releases in the Atmosphere

The paper is concerned with a numerical simulation of fuel cloud behaviour which follows releases of a liquid fuel. The main aim of the work is to develop further a mathematical model to simulate such releases into the atmosphere. The model is validated by a comparison with experimental results. The influence of boundary conditions for turbulent kinetic energy k and its dissipation rate ε on the solution is investigated. It is concluded that the solution depends mainly on the combination of k and ε in the form k ^3/2/ε rather than each of these values separately. A way to define the boundary conditions for k and ε is suggested. The KIVA-II code has been used as the base of the code used. The original code has been modified to simulate low Mach number atmospheric flows, radiation, soot formation and turbulent combustion. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Two-Time-Scale Model for Turbulent Mixing Flows Induced by Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

A two-time-scale closure model for compressible flows previously developed is extended to turbulent Rayleigh-Taylor and Richtmyer-Meshkov driven flows where mixing coexists with mean pressure gradients. Two model coefficients are calibrated with the help of Canuto-Goldman's model. For several Rayleigh-Taylor configurations, it is shown that the characteristic lengths scale as t ² while the kinetic energies and spectral transfers behave as t ² and t, respectively. The computed phenomenological coefficients of Youngs' scaling law are compared with experimental data ones. Comparisons with Youngs' three-dimensional numerical simulation (The Physics of Fluids A 3 (1991) 1312) are also performed. Finally three shock tube experiments, where the Richtmyer-Meshkov instability initiates the mixing, are simulated. The mixing thickness evolution is well reproduced while the turbulence levels seem to be overestimated with such first order models. The capability of the two-time-sale model to recover available data for different turbulent flows allows us to conclude to a more universal behavior in comparison with single-time-scale models. This revised version was published online in July 2006 with corrections to the Cover Date.     

Near-wall flow in a three-dimensional boundary layer on the endwall of a 30° bend

 Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y ⁺≈2 for the mean flow and y ⁺≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality. The ratio of these two quantities, the a ₁ structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y ⁺<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer, however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall. Received: 16 July 1996/Accepted: 14 July 1997     

Suitability of the k–ω turbulence model for scramjet flowfield simulations

The suitability of Wilcox's 2006 k– ω turbulence model for scramjet flowfield simulations is demonstrated by validation against five test cases that have flowfields representative of those to be expected in scramjets. The five test cases include a 2D flat plate, an axisymmetric cylinder, a backward‐facing step, the mixing of a pair of coaxial jets and the interaction between a shock wave and turbulent boundary layer. A generally good agreement between the numerical and experimental results is obtained for all test cases. These tests reveal that despite the turbulence model's sensitivity to freestream turbulence properties, the numerically predicted skin friction agrees with experimental data and theoretical correlations to their degree of uncertainty. The tests also confirm the importance of using a y⁺ value of less than 1 in getting accurate surface heat transfer distributions. In the coaxial jets case, the importance of matching the turbulence intensities at the inflow plane in improving the predictions of the turbulent mixing phenomena is also shown. A review of guidelines with regard to the setting up of grids and specification of freestream turbulence properties for turbulent Reynolds‐averaged Navier–Stokes CFD simulations is also included in this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

We conducted a large eddy simulation (LES) of a locally applied electromagnetic control of turbulent thermal convection of an electrically conductive fluid (electrolyte solution) inside of a slender enclosure. Generic configurations, consisting of two or three magnets of opposite polarities located below the lower wall, and two oppositely charged electrodes along the side walls, are considered. The neutral situation (pure thermal convection) is selected to be in turbulent regime at Ra = 10⁷, Pr = 7. A magnetically extended Smagorinsky type model for the subgrid turbulent stresses and a simple-gradient diffusion model for the subgrid turbulent heat fluxes are used. Different intensities of applied DC current through electrodes are imposed. The effects of the resulting Lorentz force on flow, turbulence reorganisation and wall-heat transfer are analysed. It is demonstrated that significant flow and turbulence structure reorganisation takes place in the proximity of the lower horizontal wall and in the central parts of the enclosure—even for weak DC current of I = 1 A. Significant turbulence increase, generated by the elevated electromagnetic mixing, produced significant enhancements of the wall-heat transfer—up to 70% for the 2-magnet configuration.     

Thermal and dynamic optimization of the convective flow in Trombe Wall shaped channels by numerical investigation

Two-dimensional, laminar, transitional and turbulent simulations were obtained by solving the fully-elliptic governing equations of the motion established by natural convection in channels, with Trombe Wall configuration, for different geometrical parameters and symmetrical heating. In transitional and turbulent cases, the low-Re k−ω turbulence model has been employed. To validate the numerical results, some comparisons with experimental results taken from literature have been carried out. Numerical results for the average Nusselt number and the non-dimensional induced mass-flow rate have been obtained for a wide and not yet covered range of the Rayleigh number varying from 10⁵ to 10¹². Correlations for the thermal and the mass-flow optimum wall-to-wall spacing have been presented. Finally, additional configurations including discrete heat sources have been studied, in order to obtain thermal and dynamic improvements. These intermediate devices were tested as turbulence generators, in the transitional range of Rayleigh numbers.     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

Large Eddy Simulation of Turbulent Convective Cavity Flow

The large eddy simulation model with Smagorinsky subgrid-scale model was applied to two-dimensional turbulent convective cavity flow. The Reynolds number is lying from 1×10⁴ to 4×10⁵ and Archimedes number from 0 to 0.4. The simulation results were compared with the k?? model results and experimental results wherever possible. Flow results were in good agreement with experimental data across the mid-planes. Effects of Smagorinsky constant and grid resolution were investigated.     

Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures

Two-dimensional numerical studies of flow and temperature fields for turbulent natural convection and surface radiation in inclined differentially heated enclosures are performed. Investigations are carried out over a wide range of Rayleigh numbers from 10⁸ to 10¹², with the angle of inclination varying between 0° and 90°. Turbulence is modeled with a novel variant of the k–ε closure model. The predicted results are validated against experimental and numerical results reported in literature. The effect of the inclination of the enclosure on pure turbulent natural convection and the latter’s interaction with surface radiation are brought out. Profiles of turbulent kinetic energy and effective viscosity are studied to observe the net effect on the intensity of turbulence caused by the interaction of natural convection and surface radiation. The variations of local Nusselt number and average Nusselt number are presented for various inclination angles. Marked change in the convective Nusselt number is found with the orientation of enclosure. Also analyzed is the influence of change in emissivity on the flow and heat transfer. A correlation relevant to practical applications in the form of average Nusselt number, as a function of Rayleigh number, Ra, radiation convection parameter, N _RC and inclination angle of the enclosure, φ is proposed.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Influence of the variable thermophysical properties on the turbulent buoyancy-driven airflow inside open square cavities

The effects of the air variable properties (density, viscosity and thermal conductivity) on the buoyancy-driven flows established in open square cavities are investigated, as well as the influence of the stated boundary conditions at open edges and the employed differencing scheme. Two-dimensional, laminar, transitional and turbulent simulations are obtained, considering both uniform wall temperature and uniform heat flux heating conditions. In transitional and turbulent cases, the low-Reynolds k − ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate have been obtained for a wide and not yet covered range of the Rayleigh number varying from 10³ to 10¹⁶. The results obtained taking into account variable properties effects are compared with those calculated assuming constant properties and the Boussinesq approximation. For uniform heat flux heating, a correlation for the critical heating parameter above which the burnout phenomenon can be obtained is presented, not reported in previous works. The effects of variable properties on the flow patterns are analyzed.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000     

Prediction of developing turbulent flow in 90°‐curved ducts using linear and non‐linear low‐Re k–ε models

This paper reports the outcome of applying two different low‐Reynolds‐number eddy‐viscosity models to resolve the complex three‐dimensional motion that arises in turbulent flows in ducts with 90^° bends. For the modelling of turbulence, the Launder and Sharma low‐Re k–ε model and a recently produced variant of the cubic non‐linear low‐Re k–ε model have been employed. In this paper, developing turbulent flow through two different 90^° bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross‐section the curvature induces a strong secondary flow, while for the rectangular cross‐section the secondary motion is confined to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross‐section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross‐section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean flow field, the non‐linear k–ε model returns superior predictions of the turbulence field and also of the pressure and friction coefficients. Copyright © 2006 John Wiley & Sons, Ltd.     

Turbulent kinetic energy balance in the wake of a self-propelled body

An experimental study of the turbulent wake of a self-propelled body in a wind tunnel is reported. A significant difference is formed between the turbulent kinetic energy balance in a wake with drag and in the wake of a self-propelled body: the production term is very small in comparison with the other terms of the turbulent kinetic energy balance, and this result seems to be typical of self-propulsion. The axial evolution of the wake radius and turbulent kinetic energy profiles are described. Sufficiently far downstream from the body, a self-similar profile is found. Particular attention is devoted to the turbulent kinetic energy balance; all the terms in the energy balance are evaluated experimentally.List of Symbols D diameter of the body - L axial length scale - l radial length scale - R radius of the body - r radial coordinate - r ^* radius of the wake - U mean axial velocity scale - Û defect velocity - U _e freestream velocity - u fluctuating velocity scale - x axial coordinate - dissipation rate - = r/r ^* radial relative direction - azimuthal coordinate - kinematic viscosity - density     

A METHOD OF DISCRETE DISPLACEMENTS FOR MODELLING THE CONTRIBUTION OF FINITE-SIZE ORGANIZED FLUID STRUCTURES TO TRANSPORT PROCESSES IN TURBULENT PIPE FLOW

A method of modelling the contribution of finite-size organized streams and fluid structures to the processes of turbulent transport is presented for the example of developed turbulent pipe flow. The method is applied to construct the turbulent length (L) and eddy viscosity coefficient (ν_t) employed to compute the average characteristics of the flow. The average effects of action of these organized fluid structures and streams are modelled as the final results of discrete displacements of certain model turbulent signals between nodes associated in pairs as well as the results of effective discrete displacements of these pairs. The displacement of information about the organization of two nodes into a pair identifies the displacement of the pair. These nodes constitute a network whose parameters have been established a priori analytically by considering a sequence of model turbulent lengths scaled with their distance to the wall. The model turbulent signals are evaluated at respective discrete nodes with the help of a certain finite difference turbulence model closed by L and ν_t and realized on an appropriate numerical grid. The non-uniform grid spacing has been related unambiguously in a rational way to the sequence of model turbulent lengths. Results elucidating specific features of this discrete modelling, particularly its differences from the continuous approach, are presented. Good agreement of the results with available experimental data is demonstrated. The average characteristics of the flow structure predicted for a wide range of Reynolds number (Re) are unique or bifurcated for particular Re intervals. The latter case suggests the occurrence of switching from one type of flow structure organization to another with the ambient conditions unchanged.     

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder¹ and followers^2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.