Theoretical investigation of some thermal effects in turbulence modeling

Fluid compressibility effects arising from thermal rather than dynamical aspects are theoretically investigated in the framework of turbulent flows. The Mach number is considered low and not to induce significant compressibility effects which here occur due to a very high thermal gradient within the flowfield. With the use of the Two-Scale Direct Interaction Approximation approach, essential turbulent correlations are derived in a one-point one-time framework. In the low velocity gradient limit, they are shown to directly depend on the temperature gradient, assumed large. The impact of thermal effects onto the transport equations of the turbulent kinetic energy and dissipation rate is also investigated, together with the transport equation for both the density and the internal energy variance.      

Computational and experimental study of annular photo-reactor hydrodynamics

The performance of ultraviolet (UV) reactors used for water treatment is greatly influenced by the reactor hydrodynamics due to the non-homogeneity of the radiation field. Reliable modeling of the reactor flow structures is therefore crucial for the design process. In this study, the turbulent flow through two characteristic annular UV-reactor configurations, with inlets concentric (L-shape) and normal (U-shape) to the reactor axis, was investigated through computational fluid dynamic (CFD). The modeling results were evaluated with the velocity profiles from particle image velocimetry (PIV) experiments. The influence of mesh structure and density, as well as three turbulence models: Standard κ–, Realizable κ–, and Reynolds stress model (RSM), on the simulation results were evaluated. Mesh-independent solutions were achieved at mean cell volumes of 5 × 10⁻⁹ m³. The Realizable κ– displayed the best overall match to the experimental PIV measurements. In general, the CFD models showed a close agreement with the experimental data for the majority of the reactor domain and captured the influences of reactor configuration and internal reactor structures on the flow distribution. The validated CFD hydrodynamic models could be integrated with kinetic and radiation distribution models for UV-reactor performance simulation.     

Numerical and analytical study of transverse supersonic flow over a flat cone

Quasisteady supersonic flow over a flat cone on a plane surface is studied. A formula is derived for the angle through which the flow lines turn at the cone. The results are used to justify the use of two-dimensional simulations of the flow. Peak pressures and total impulses are obtained numerically for various cone angles.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Formation of vortex breakdown in conical–cylindrical cavities

Numerical simulations in confined rotating flows were performed in this work, in order to verify and characterize the formation of the vortex breakdown phenomenon. Cylindrical and conical–cylindrical geometries, both closed, were used in the simulations. The rotating flow is induced by the bottom wall, which rotates at constant angular velocity. Firstly the numerical results were compared to experimental results available in references, with the purpose to verify the capacity of the computational code to predict the vortex breakdown phenomenon. Further, several simulations varying the parameters which govern the characteristics of the flows analyzed in this work, i.e., the Reynolds number and the aspect ratio, were performed. In these simulations, the limits for the transitional regime and the vortex breakdown formation were verified. Steady and transient cases, with and without turbulence modeling, were simulated. In general, some aspects of the process of vortex breakdown in conical–cylindrical geometries were observed to be different from that in cylinders.     

Experimental analysis of unsteady separated flows in a supersonic planar nozzle

The unsteady aspects of shock-induced-separation patterns have been investigated inside a Mach 2 planar nozzle. The mean location of the shock can vary by changing, relatively to the nozzle throat, the height of the second throat which is positioned downstream of the square test section. This study focuses on the wall pressure fluctuations spectra and the unsteady behaviour of the shock. Symmetric shock configurations appear both for the largest openings of the second throat, and for the smallest openings. For an intermediate opening the shock system exhibits asymmetrical configurations. A coating with roughnesses sticked on the throat part of the nozzle in order to modify the state of the incoming boundary layers (from smooth to rought turbulent statement) is a driver for the asymmetry. The fluctuating displacements of the shock patterns were analysed by using an ultra fast shadowgraph visualization technique. A spectral analysis of the unsteady wall pressure measurements has revealed low frequency phenomena governed by large structure dynamics in the separated flows. Communicated by K. Takayama PACS 02.60.Cb; 05.10.Ln; 47.11.+j; 47.15.Cb; 47.40.Nm     

Modal decomposition‐based global stability analysis for reduced order modeling of 2D and 3D wake flows

The method for computation of stability modes for two‐ and three‐dimensional flows is presented. The method is based on the dynamic mode decomposition of the data resulting from DNS of the flow in the regime close to stable flow (fixed‐point dynamics, small perturbations about steady flow). The proposed approach is demonstrated on the wake flows past a 2D, circular cylinder, and a sphere. The resulting modes resemble the eigenmodes computed conventionally from global stability analysis and are used in model order reduction of the flow. The designed low‐dimensional Galerkin model uses continuous mode interpolation between dynamic mode decomposition mode bases and reproduces the dynamics of Navier–Stokes equations. Copyright © 2015 John Wiley & Sons, Ltd.     

Measurement of recombination rate parameters in nonequilibrium supersonic expansions of ionized argon and neon

Two wavelength interferometry techniques and a two dimensional Fourier transform analysis are used to produce contour maps of the heavy particle densities and ionization fractions for supersonic corner expansions of ionized argon and neon. A new phase unwrapping algorithm is employed to minimize noise problems previously encountered because of phase discontinuities associated with shock waves and flow luminosity. Determination of recombination rate coefficients is achieved through the measurement of gradients in the ionization fraction.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Anisotropy Invariant Reynolds Stress Model of Turbulence (AIRSM) and its Application to Attached and Separated Wall-Bounded Flows

Numerical predictions with a differential Reynolds stress closure, which in its original formulation explicitly takes into account possible states of turbulence on the anisotropy-invariant map, are presented. Thus the influence of anisotropy of turbulence on the modeled terms in the governing equations for the Reynolds stresses is accounted for directly. The anisotropy invariant Reynolds stress model (AIRSM) is implemented and validated in different finite-volume codes. The standard wall-function approach is employed as initial step in order to predict simple and complex wall-bounded flows undergoing large separation. Despite the use of simple wall functions, the model performed satisfactory in predicting these flows. The predictions of the AIRSM were also compared with existing Reynolds stress models and it was found that the present model results in improved convergence compared with other models. Numerical issues involved in the implementation and application of the model are also addressed.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.     

Correlation of laminar-turbulent transition data over flat plates in supersonic/hypersonic flow including leading edge bluntness effects

The paper discusses flat plate boundary layer transition in supersonic/hypersonic flow conditions. Examination of experimental infrared thermography data illustrates the importance of the leading edge thickness and (non-) uniformity to the transition process. Such observations have triggered the collection of a wide range of experimental data on supersonic/hypersonic flat plate boundary layer transition, and a number of attempts to correlate this data with characteristic parameters including leading edge thickness. Results indicate a strong dependence of the relevant transition parameters on the pressure field in the transition region, as this is determined by the combined effects of leading edge thickness and boundary layer growth/viscous interaction, and particularly on the relative importance of the two effects. In fact, two distinct correlation zones are established, depending on whether the pressure distribution at the onset of transition is dominated by leading edge bluntness effects or by boundary layer growth and viscous interaction, thus limiting the observed data scatter to reasonable levels.Received: 13 August 2002, Accepted: 7 February 2003, Published online: 28 April 2003     

3D phase field modeling of electrohydrodynamic multiphase flows

A 3D phase field model is developed to investigate the electrohydrodynamic (EHD) two phase flows. The explicit finite difference method, enhanced by parallel computing, is employed to solve the coupled nonlinear governing equations for the electric field, the fluid flow field and free surface deformation. Numerical tests indicate that an appropriate interpolation of densities within the interface is critical in ensuring numerical stability for highly stratified flows. The 3D phase field model compares well with the Taylor theory for the deformation of a single dielectric droplet in an electric field. Computed results show that the deformation of a leaky dielectric droplet in an electric field undergoes various stages before it reaches the final oblate shape. This is caused by the free charge relaxation near the fluid–fluid interface. The coalescence of four droplets in an electric field illustrates a truly 3D deformation behavior and a complex evolving fluid flow field associated with the participating droplets. The coalescence is a result of combined actions produced by the global electric force, the circulatory flows generated by the local electrohydrodynamic stress and the electrically-induced deformation. The 3D phase field model is also applied in modeling of an electrohydrodynamic patterning process for manufacturing nanoscaled structures, in which complex 3D flow structures develop as the electrically-induced deformation evolves.     

Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow

Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results.     

Numerical analysis of a 3D hydrodynamic contact

We study here the numerical analysis of a hydrodynamic contact in a particular configuration: the 3D incompressible viscous flow of a fluid dragged by a smooth plate over a rough surface. The mathematical model takes into account and discretizes the local topography of the rough profile. The simulation outcome will be the 3D velocity and pressure fields of the fluid film within the contact borders. This work is limited to the study of numerical resolution methods working solely in finite differences. The algorithms will be tested by analysing and comparing their results with analytically known flows. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system

We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of [Elena and Schiestel, 1996] and [Schiestel and Elena, 1997] widely validated in various rotor-stator cavities with throughflow ( [Poncet, 2005], [Poncet et al., 2005] and [Haddadi and Poncet, 2008]) and heat transfer (Poncet and Schiestel, 2007). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson (1995) in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-ε model of Naser (1997). Then, the second order model is applied for a large range of rotational Reynolds (3744 ? Re_i ? 37,443) and Prandtl numbers (0.01 ? Pr ? 12), flow rate coefficient (0 ? C_w ? 30,000) in a very narrow cavity of radius ratio s = R_i/R_o = 0.961 and aspect ratio L = (R_o − R_i)/h = 0.013, where R_i and R_o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Re_i, C_w, and Pr.     

Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls

The effects of wall roughness on turbulence structure modifications were explored by numerical experiments, carried out using Large Eddy Simulation techniques. The wall geometry was made using an archetypal artificial method, thus to achieve irregular two- and three-dimensional shapes. The proposed roughness shapes are highly irregular and are characterised by high and small peaks, thus it can be considered a practical realistic roughness. Their effects are analysed comparing the turbulence quantities over smooth, 2D and 3D rough walls of fully developed channel flow at relatively low friction Reynolds number ${\mathit{Re}}_{\tau }=395$. Both transitional and fully rough regimes have been investigated. The two rough surfaces were built in such a way that the same mean roughness height and averaged mean deviation is obtained. Despite of this, very different quantitative and qualitative results are generated. The analysis of the mean quantitative statistics and turbulence fluctuations shows that deviations are mainly concentrated in the inner layer. These results support the Townsend’s similarity hypothesis. Among the geometrical parameters, which characterise the wall geometries, roughness slope correlates well with the roughness function $\mathrm{\Delta }{U}^{+}$. Specifically, a logarithmic law is proposed to predict the downward shift of the velocity profile for the transitional regime. Instantaneous view of turbulent organised structures display differences in small-scale structures. The flow field over rough surfaces is populated with coherent structures shorter than those observed over flat planes. The comparative analysis of both streaks and wall-normal vortical structures shows that 2D and 3D irregularities have quite different effects. The results highlight that 3D rough wall are representative of a more realistic surface compared to idealised 2D roughness.     

Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

On the use of a two-layer model for large-eddy simulations of supersonic boundary layers with separation

The two-layer modeling approach has become one of the most promising and successful methodology for simulating turbulent boundary layers in the past ten years. In the present study, a mixed wall model for large-eddy simulations (LES) of high-speed flows is proposed which combine two approaches; the thin-Boundary Layer Equations (TBLE) model of Kawai and Larsson (1994) and the analytical wall-layer model of Duprat et al. (2011) for streamwise pressure gradients. The new hybrid model has been efficiently implemented into a three-dimensional compressible LES solver and validated against DNS of a spatially-evolving supersonic boundary layer (BL) under moderate and strong pressure gradients, before being employed for the prediction of nozzle flow separations at different flow conditions, ranging from weakly to highly over-expanded regimes. A good agreement is obtained in terms of mean and fluctuating quantities compared to the DNS results. Particularly, the current wall-modeled LES results are found to perfectly match the DNS data of supersonic BL with/out pressure gradient. It is also shown that the model can account for the effect of the large-scale turbulent motions of the outer layer, indicating a good interaction between the inner and the outer part of the wall layer. In terms of simulations costs and improvements of computing power, the obtained results highlight the capability of the current wall-modeling LES strategy in saving a considerable amount of computational time compared to the wall-resolved LES counterpart, allowing to push further the simulations limits. Furthermore, the application of these computationally low-costly LES simulations to nozzle flow separation allows to clearly identify the origin of the shock unsteadiness, and the existence of broadband and energetically-significant low-frequency oscillations (LFO) in the vicinity of the separation region.     

Particles-induced turbulence: A critical review of physical concepts,numerical modelings and experimental investigations

The presence of solid particles or water droplets in continuous fluid flow can either induce turbulence attenuation or amplification. The modification of the state of the turbulence depends on the characteristics of the particles, such as volume fraction, mean diameter, mass density, or carrier phase flow properties. In this brief review, the main physical concepts related to the most important physical aspects of turbulence modulation are summarized. Different criteria used to distinguish the enhancement or the attenuation effects of the particles on the carrier phase flows are recalled. For the interest of large-scale industrial applications, several theoretical,experimental and empirical approaches are discussed, which provides an interesting framework for the study of the effect of particles on turbulence behavior modification.