Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies

The unsteady turbulent flow around bodies at high Reynolds number is predicted by an anisotropic eddy-viscosity model in the context of the Organised Eddy Simulation (OES). A tensorial eddy-viscosity concept is developed to reinforce turbulent stress anisotropy, that is a crucial characteristic of non-equilibrium turbulence in the near-region. The theoretical aspects of the modelling are investigated by means of a phase-averaged PIV in the flow around a circular cylinder at Reynolds number 1.4×10⁵. A pronounced stress–strain misalignment is quantified in the near-wake region of the detached flow, that is well captured by a tensorial eddy-viscosity concept. This is achieved by modelling the turbulence stress anisotropy tensor by its projection onto the principal matrices of the strain-rate tensor. Additional transport equations for the projection coefficients are derived from a second-order moment closure scheme. The modification of the turbulence length scale yielded by OES is used in the Detached Eddy Simulation hybrid approach. The detached turbulent flows around a NACA0012 airfoil (2-D) and a circular cylinder (3-D) are studied at Reynolds numbers 10⁵ and 1.4×10⁵, respectively. The results compared to experimental ones emphasise the predictive capabilities of the OES approach concerning the flow physics capture for turbulent unsteady flows around bodies at high Reynolds numbers.     

LDA measurements in the turbulent round jet

In the present paper, LDA was used to measure the velocity field of turbulent round air jet flows. Two cases were investigated; a jet issuing vertically upward and freely in the laboratory surrounding environment, and a jet issuing vertically upward but out of wall section setting flush horizontally at the nozzle exit. Data were collected for three exit Reynolds numbers of 1.32 × 10⁴, 2.64 × 10⁴ and 3.96 × 10⁴, which correspond to exit velocities of 10 m/s, 20 m/s and 30 m/s respectively. For each Reynolds number, profile measurements of the mean velocity, turbulence intensity, skewness and flatness factors were made at 8 downstream stations up to 30 nozzle-exit diameter. The relative influence of using a wall at the jet exit plane on the jet behavior and characteristics is the objective of the present study. The experimental results indicate that the wall, placed at the exit plane, limits the interaction of the jet flow with the surroundings, and consequently results in a reduction in the velocity spread rate, kinematic momentum flux, and kinematic mass flux. Further, the flatness and skewness factors distributions across the jet flow registered relatively higher values in the outer region of the jet when the wall was used. This indicates a more intermittent behavior of the jet flow in that region due to the existence of the wall.     

TURBULENT ELLIPTIC WAKES

This paper describes results of an experimental study on turbulent wake of an elliptic disk set normal to the main flow, whose major diameter is 2·0 or 3·0 minor diameters, Reynolds number being 2·0×10⁴on the basis of the minor diameter D. Two periodic components of velocity fluctuations were found in the wake. One is centred around the minor plane, being due to the alternate shedding of rolled-up, hairpin-like vortices. The other is centred around the major plane, which is likely to be due to a meandering motion of the wake. The axis switching, which is a cross-over of half-widths in the major and minor planes plotted against the streamwise distance, occurred at approximately 4·0 D downstream of the disk. The mechanism of the axis switching is different from that in elliptic jets, and it is proposed that it is due to a difference in the growth rate of the fundamental Fourier modes in the minor and major planes. The structure of the wake is studied by flow visualization and a survey of the time-mean velocity, turbulence intensities and Reynolds shear stresses. Wavelet analysis of the velocity fluctuations disclosed a low-frequency unsteadiness in the wake. This unsteadiness has different representative frequencies in the major and minor planes, being approximately one-fifth of the frequency of the corresponding periodic component in both planes.     

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 10⁷–10⁸). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.     

Large eddy simulation of a confined square cavity with natural convection based on compressible flow equations

Large eddy simulation of natural convection in a confined square cavity is described. The use of a complex compressible code with an artificial acoustic stiffness correction method, allows the use of higher time steps for a faster time and statistical convergence. We consider a broadly studied experimental case, consisting of a natural convective flow in a confined square cavity, with vertical walls heated at different rates (active walls), set at Ra = 1.58 × 10⁹. Turbulent boundary layers developing on the active walls and a vertical stable stratification characterize the mean flow. It is shown here that the results of this study match the experimental results reported in literature; for instance, mean velocity results. Although results for rms velocity fluctuations are barely over-predicted, the peak region is properly represented, while the greatest disagreements are found in the turbulent heat flow rate (velocity–temperature correlations). Turbulent structures were identified using different visualization methods and statistical studies. The authors found that the boundary layers on the active walls almost reach the fully turbulent regime, tending toward the laminar regime along the horizontal walls.     

Large-eddy simulation in a mixing tee junction: High-order turbulent statistics analysis

This study analyses the mixing and thermal fluctuations induced in a mixing tee junction with circular cross-sections when cold water flowing in a pipe is joined by hot water from a branch pipe. This configuration is representative of industrial piping systems in which temperature fluctuations in the fluid may cause thermal fatigue damage on the walls. Implicit large-eddy simulations (LES) are performed for equal inflow rates corresponding to a bulk Reynolds number Re = 39,080. Two different thermal boundary conditions are studied for the pipe walls; an insulating adiabatic boundary and a conducting steel wall boundary. The predicted flow structures show a satisfactory agreement with the literature. The velocity and thermal fields (including high-order statistics) are not affected by the heat transfer with the steel walls. However, predicted thermal fluctuations at the boundary are not the same between the flow and the solid, showing that solid thermal fluctuations cannot be predicted by the knowledge of the fluid thermal fluctuations alone. The analysis of high-order turbulent statistics provides a better understanding of the turbulence features. In particular, the budgets of the turbulent kinetic energy and temperature variance allows a comparative analysis of dissipation, production and transport terms. It is found that the turbulent transport term is an important term that acts to balance the production. We therefore use a priori tests to evaluate three different models for the triple correlation.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Numerical characterization of micro heat exchangers using experimentally tested porous aluminum layers

A microporous heat exchanger device is being developed for cooling high-power electronics. The device uses a mechanically compressed aluminum porous layer to improve the heat transfer at the coolant/solid interface and to provide more uniform cooling of the electronics. The hydraulic characteristics (porosity, permeability, and Forchheimer coefficient) of nine distinct compressed layers are obtained experimentally. These layers have porosity from 0.3 to 0.7 and permeability from 1.8 × 10⁻¹⁰ m2 to 1.2 × 10⁻⁹ m2. The inertia coefficient varies from 0.3 to 0.9. These hydraulic characteristics are used in the numerical simulations of a real microporous heat exchanger for cooling phased-array radars in development. Thermal and hydraulic performances are illustrated in terms of total pressure drop across the heat exchanger, maximum temperature difference in the direction transverse to the electronic modules, and maximum temperature within the coolant passage. Results indicate that the proposed design is capable of achieving a maximum transverse temperature difference of 2°C using polyalphaolephin as coolant.     

Measurements of turbulence characteristics in an open-channel flow over a transitionally-rough bed using particle image velocimetry

The particle image velocimetry technique was used to measure characteristics of a turbulent flow over a transitionally-rough fixed bed in an open-channel flow. These conditions are typical of flows encountered in sediment transport problems. Measurements obtained with this technique were used to investigate the distributions of velocities, turbulence intensities, Reynolds stress, and third- and fourth-order moments in a region above y ⁺ = 10. The present results are in good agreement to those previously obtained on smooth walls and provide further evidence that PIV can be applied successfully to investigate turbulence in open-channel flows over a rough bed.     

Conjugate turbulent heat transfer in a square cavity with a solar control coating deposited to a vertical semitransparent wall

This paper presents a numerical study of the conjugate heat transfer (natural convection, surface thermal radiation and conduction) in a square cavity with turbulent flow. The cavity has one vertical isothermal wall, two horizontal adiabatic walls and one vertical semitransparent wall with a selective coating applied to the inner side to control the solar radiation transmission. Later on the semitransparent wall is replaced with another one without the selective coating. The mathematical model for the turbulent flow in the cavity was solved using the finite volume method. The system had the following conditions: the uniform temperature in the isothermal wall was 21 °C, the external ambient temperature was fixed at 35 °C and on the semitransparent wall the direct normal solar irradiation of 750 W/m² was considered constant. The Rayleigh number was varied in the range of 10⁹ ? Ra ? 10¹² by changing the lengths of the cavity from 0.70 m to 6.98 m, respectively. The results show that, even though the air temperature of the cavity with the solar control film coating semitransparent wall (case A) is higher compared with the one without solar film coating (case B), the total amount of heat going through the cavity is lower compared to the one going through the cavity without solar control film. The total amount of energy transferred to the air in cavity for the case A was 41.98% less than for the case B. A set of correlations for the Nusselt number was obtained for both cases considering the conjugate heat transfer.     

Flow and coupled heat transfer in the cavity between the rotor and stator

The turbulent flow and coupled heat transfer in the cavity between the rotor and stator is numerically simulated. Reynolds-averaged Navier-Stokes equations closed with equations of the k-ɛ turbulence model are used to calculate the viscous compressible gas flow characteristics and heat transfer; the unsteady heat conduction equation is used to calculate the temperature field in the metal. The influence of the mass flow rate of the coolant on the flow structure and efficiency of cooling of the rotor and stator walls is studied. The calculated results are compared with experimental data.     

Natural convection in partially cooled tilted cavities

Two-dimensional numerical simulations of laminar natural convection in a partially cooled, differentially heated inclined cavities are performed. One of the cavity walls is entirely heated to a uniformly high temperature (heat source) while the opposite wall is partially cooled to a lower temperature (heat sink). The remaining walls are adiabatic. The tilt angle of the cavity is varied from 0° (heated from left) to −90° (heated from top). The fast false implicit transient scheme (FITS) algorithm, developed earlier by the same authors, is modified to solve the derived variables vorticity-streamfunction formulation. The effects of aspect ratio (AR), sink–source ratio and tilt angle on the average Nusselt number are examined through a parametric study; solutions are obtained for two Grashof numbers, 10⁵ and 10⁷. Flow patterns and isotherms are used to investigate the heat transfer and fluid flow mechanisms inside the cavity. © 1998 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.     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

A stochastic Langevin model of turbulent particle dispersion in the presence of thermophoresis

Direct numerical simulation (DNS) and experimental data have shown that inertial particles exhibit concentration peaks in isothermal turbulent boundary layers, whereas tracer-like particles remain well mixed in the domain. It is therefore expected that the interactions between turbulence and thermophoresis will be strong in particle-laden flows where walls and carrier fluid are at significantly different temperatures. To capture turbulent particle dispersion with active thermophoresis, a coupled CFD-Lagrangian continuous random walk (CRW) model is developed. The model uses 3D mean flow velocities obtained from the Fluent 6.3 CFD code, to which are added turbulent fluid velocities derived from the normalized Langevin equation which accounts for turbulence inhomogeneities. The mean thermophoretic force is included as a body force on the particle following the Talbot formulation. Validation of the model is performed against recent integral thermophoretic deposition data in long pipes as well as the TUBA TT28 test with its detailed local deposition measurements. In all cases, the agreement with the data is very good. In separate parametric studies in a hypothetical cooled channel flow, it is found that turbulence strongly enhances thermophoretic deposition of particles with dimensionless relaxation times τ⁺ of order 1 or more. On the other hand, the thermophoretic deposition of very small inertia particles (τ⁺ < 0.2) in the asymptotic region far from the injection point tends to that which characterizes stagnant flow conditions, in agreement with the DNS results of Thakurta et al.     

Effects of two-dimensional V-shaped grooves on turbulent channel flow

Detailed Laser Doppler velocimeter (LDV) measurements have been carried out in a turbulent rectangular channel flow with one rough wall. The roughness elements of two-dimensional spanwise 120° V-shaped grooves are periodically arranged with different depths and pitches. The Reynolds number based on the centerline velocity, and the channel half height ranges from 2,740 to 20,000. The comparisons of turbulence statistics over smooth and rough walls indicate that the present roughness leads to a significant change in the turbulence both in the inner and in the outer flow. Particularly, the distribution density of the grooves is a key parameter to evaluate the effect of roughness. The low-Reynolds-number dependence of turbulence statistics is also observed. The rough walls with the same pitch-to-depth ratio exhibit the equivalent roughness function under the corresponding Reynolds numbers. The disagreement of velocity defect profiles between smooth and rough walls challenges the defect universal law. The variations of the turbulence stresses and Reynolds shear stress decomposition in the outer layer suggest that the turbulent motions may be modified by the present grooves. The importance of sweep events for the present groove-roughened walls is reflected by the differences in relative contribution to Reynolds shear stress from each quadrant and the higher-order moments over smooth and rough walls.     

Suppression of Low-frequency Variations in Vortex Shedding by a Splitter Plate Behind a Bluff Body

Measurements of instantaneous pressure fluctuations on a trapezoidal cross-section cylinder indicate that the low-frequency variations embedded in the vortex-shedding process can be successfully suppressed by insertion of a splitter plate whose length is twice the maximum width of the trapezoidal cylinder. The experiments were performed at Reynolds numbers in a range of 5 × 10³ to 4·5 × 10⁴. Spanwise correlation of the pressure fluctuations measured on the cylinder further indicates that the suppression of low-frequency variations improves the degree of two-dimensionality of vortex shedding. These findings are attributed to the presence of the splitter plate having an effect on stabilizing the vortex formation length which is comparable to the length of the splitter plate, thus eliminating the low-frequency variations embedded in the base pressure.     

Control of a submerged jet in a thin rectangular cavity

An innovative method is presented for control of an oscillatory turbulent jet in a thin rectangular cavity with a thickness to width ratio of 0.16. Jet flow control is achieved by mass injection of a secondary jet into the region above the submerged primary jet nozzle exit and perpendicular to the primary nozzle axis. An experimental model, a 2-D and a 3-D computational fluid dynamics (CFD) model are used to investigate the flow characteristics under various secondary injection mass flow rates and injection positions. Two-dimensional laser Doppler anemometry (LDA) measurements are compared with results from the CFD models, which incorporate a standard k–ε turbulence model or a 2-D and 3-D realisable k–ε model. Experimental results show deflection angles up to 23.3° for 24.6% of relative secondary mass flow are possible. The key to high jet control sensitivity is found to be lateral jet momentum with the optimum injection position at 12% of cavity width (31.6% of the primary nozzle length) above the primary nozzle exit. CFD results also show that a standard k–ε turbulence closure with nonequilibrium wall functions provides the best predictions of the flow.     

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.