Abstract: A novel three-dimensional problem formulation is introduced for the simulation of turbulent interfacial multi-fluid flows. The strategy is built around the large eddy simulation (LES) concept, and can be employed for interfacial heat and mass transfer problems in which use can be made of either scalar transfer correlations, or exact mass/energy jump conditions. This multi-physics treatment capability at arbitrarily deformable interfaces translates into two main features: (i) a reconstructed distance function (RDF) is introduced to define a level-set interface-normal length scale, and (ii) an interfacial shear velocity is defined on the distance function support for further use in near-interface transport models. The solution algorithm uses VOF with piecewise planar interface reconstructions on a twice-as-fine mesh, and infers the convective mass fluxes from the interface solution to promote momentum conservation. The interfacial shear velocity defined on the distance function support is introduced to accommodate the asymptotic behaviour of turbulence approaching the interface in a proximity-dependent manner. Provided with highly accurate distance function data, the scheme generates near-interface damping functions that are second-order accurate and independent of interface orientation. The damping was found to be affected by errors introduced into shear velocity estimates by the high-frequency errors in the RDF scheme near the interface. The methodology has been applied for the simulation of a wave breaking scenario featuring multiple modes and interfacial length scales. (c) 2006 Elsevier Inc. All rights reserved.

Abstract: An extensive study of the most important hydrodynamic characteristics of fairly large-scale bubble plumes was conducted using several measurement techniques and a variety of tools to analyze the data. Particle image velocimetry (PIV), double-tip optical probes (OP) and photographic techniques were extensively applied to measure bubble and liquid velocities, void-fraction and bubble sizes. PIV measurements in a vertical plane crossing the centre of the injector provided the instantaneous velocity fields for both phases, as well as hydrodynamic parameters, such as the movement of the axis of the plume and its instantaneous shape. Statistical studies were performed using image processing to determine the distribution of the apparent instantaneous plume diameter and centreline position. An important finding was that there is little instantaneous spreading of the bubble plume core; the spreading of the time-averaged plume width (as measured from the time-averaged void-fraction and time-averaged liquid velocity fields) is largely due to plume meandering and oscillations. The liquid-phase stress tensor distributions obtained from the instantaneous velocity data indicate that, for the continuous phase, these stresses scale linearly with the local void-fraction in the range of 0.5% < alpha < 2.5%. The bubbles were found to be ellipsoidal, with shape factor e approximate to 0.5. (c) 2006 Elsevier Ltd. All rights reserved.

Abstract: A novel large-eddy simulation (LES) approach for computation of incompressible multi-fluid flows is presented and applied to a turbulent bubbling process driven by the downward injection of air into a water pool at Re-pipe approximate to 17,000. Turbulence is found to assume its highest intensity in the bulk of the gas flow, and to decay as the interface of the growing bubble is approached. Shear flow prevails in the area of jetting front the pipe, buoyancy-driven flow prevails away from the jetting region, and a third region of vigorous bubble break-up lay O(10(0))-O(10(1)) pipe diameters above the tip. Cascading of turbulent kinetic energy is accompanied by an instability-induced linear cascading of interface length scales (i.e. azimuthal modes), transferring energy from the most unstable mode to the smallest interface deformation scales. The LES shows the out-scatter of energy front the large-scale gas-side vortices down to interface wrinkling scales, and statistics prove the existence of a strong correlation between turbulence and interface deformations. Surface curvature was found to constitute a source of small-scale vorticity, and therefore of dissipation of turbulent kinetic energy. (c) 2006 Elsevier Inc. All rights reserved.

Abstract: Simulations of two-dimensional, two-way coupled particle-laden mixing layers were performed for particles with various Stokes numbers, at mass loadings between 0.1 and 0.5. This component complements Part I of the study, where particle and fluid transport was analyzed under one-way coupling. Under two-way coupling, the accumulation of particles in the periphery of the Kelvin-Helmholtz vortices results in the formation of intricate undulating patterns, and rupture and break-up of the vortices. At higher mass loadings the vortex structure is completely destroyed. The overall accumulation at the edges of the mixing layer is significantly reduced due to two-way coupling. The rate of evacuation of the vortex core was found to be much slower compared to one-way coupling. In a global sense, particles delay the development of the mixing layer in terms of saturation of the fundamental and the subharmonic modes. Significant generation of small-scale vorticity and higher energy in the small scales is observed at higher mass loadings. Particles are shown to increase the modal kinetic energy dissipation rate. The mean fluid kinetic energy balance shows that most of the kinetic energy exchange between the particle and fluid phases takes place at the edges of the mixing layer. As the mixing layer evolves, the kinetic energy exchange with the particle phase was shown to decrease in importance compared to the other terms in the mean kinetic energy balance; namely, the energy exchange between the mean and the modal fields and the modal transport term. (c) 2006 American Institute of Physics.

Abstract: Simulations of two-dimensional, particle-laden mixing layers were performed for particles with Stokes numbers of 0.3, 0.6, 1, and 2 under the assumption of one-way coupling using the Eulerian-Lagrangian method; two-way coupling is addressed in Part II. Analysis of interphase momentum transfer was performed in the Eulerian frame of reference by looking at the balance of fluid-phase mean momentum, mean kinetic energy, modal kinetic energy, and particle-phase mean momentum. The differences in the dominant mechanisms of vertical transport of streamwise momentum between the fluid and particle phases is clearly brought out. In the fluid phase, growth of the mixing layer is due to energy transfer from the mean flow to the unstable Kelvin-Helmholtz modes, and transport of mean momentum by these modes. In contrast, in the particle phase, the primary mechanism of vertical transport of streamwise momentum is convection due to the mean vertical velocity induced by the centrifuging of particles by the spanwise Kelvin-Helmholtz vortices. Although the drag force and the particle-phase modal stress play an important role in the early stages of the evolution of the mixing layer, their role is shown to decrease during the pairing process. After pairing, the particle-phase mean streamwise momentum balance is accounted for by the convection and drag force term. The particle-phase modal stress term is shown to be strongly connected to the fluid phase modal stress with a Stokes-number-dependent time lag in its evolution. (c) 2006 American Institute of Physics.

Abstract: A new volume tracking method is introduced for tracking interfaces in three-dimensional (3D) geometries partitioned with orthogonal hexahedra. The method approximates interface geometries as piecewise planar, and advects volumes in a single unsplit step using fully multidimensional fluxes that have their definition based in backward-trajectory remapping. By using multidimensional unsplit advection, the expense of high-order interface reconstruction is incurred only once per timestep. Simple departures from strict backward-trajectory remapping remove any need for consideration of volume computations involving shapes consisting of non-planar ruled surfaces. Second-order accuracy of the method is demonstrated even for vigorous 3D deformations. (c) 2005 Elsevier Ltd. All rights reserved.

Abstract: Large-eddy simulations (LES) of a turbulent interfacial gas-liquid flows are described in this paper. The variational multiscale approach (VMS) introduced by Hughes for single-phase flows is systematically assessed against direct numerical simulation (DNS) data obtained at a shear Reynolds number Re-star=171, and compared to LES results obtained with the Smagorinsky model, modified by a near-interface turbulence decay treatment. The models are incorporated in the same pseudospectral DNS solver built within the boundary fitting method used by Fulgosi for air-water flow. The LES are performed for physical conditions allowing low interface deformations that fall in the range of capillary waves of wave slope ak=0.01. The LES results show that both the modified Smagorinsky model and the VMS are capable to predict the boundary layer structure in the gas side, including the decay process, and to cope with the anisotropy of turbulence in the liquid blockage layer underneath the interface. Higher-order turbulence statistics, including the transfer of energy between the normal stresses is also well predicted by both approaches, but qualitatively the VMS results remain overall better than the modified Smagorinsky model. The study has demonstrated that the key to the prediction of the energy transfer mechanism is in the proper prediction of the fluctuating pressure field, which has been found out of reach of any of the LES methodologies. The superiority of the VMS is demonstrated through the analysis of the subgrid transport and exchange terms in the resolved kinetic energy, where it is indeed shown to be self-adaptive with regard to the eddy viscosity. Although VMS is shown to be sensitive to filter scale partition and model constant, the optimal setting can be easily translated in the interface tracking/finite-volume context, which makes it very useful for practical purposes. An important point is that the VMS approach yields very satisfactory results without the need for prescribing an ad-hoc damping function and the required distance to the interface. (c) 2006 American Institute of Physics.

Abstract: The modification of deposition mechanisms of small particles in wall turbulence due to enhanced near-wall fluctuations is presented. The direct numerical simulation database of turbulent air flow over a water surface populated by gravity-capillary waves of small wave slope was used to mimic the enhancement in fluctuation intensity. Lagrangian tracking of particles is performed under the assumption of one-way coupling between the particles and the flow. Two sets of particles have been considered with inertial response times of 5 and 15, respectively, normalized using the friction velocity at the air-water interface and the kinematic viscosity of air. Compared to wall-bounded flow, the particle deposition rates on the interface were found to be considerably higher; specifically for the low-inertia particles, an eightfold increase was observed. The deposition rate for particles of higher inertia increased by only 60%. The correlation characterizing particle deposition rates for wall-bounded flows, where the deposition rate is proportional to the square of the particle response time, was found to be invalid for the flow with enhanced near-wall turbulence. Comparison with experimental results on particle deposition onto rough walls showed better correlation. Depositing particles were divided into free-flight and diffusional deposition populations. Since the primary effect of the interfacial waves is to increase the turbulence intensity in the near-interface region with high particle concentration, a remarkable increase in diffusional deposition is observed. As in wall-bounded flows, diffusional deposition is seen to be the dominant mechanism of deposition. The free-flight mechanism, where particles acquire velocities high enough to travel directly to the interface, remains unaffected by enhanced near-wall velocity fluctuations. (c) 2005 Elsevier Ltd. All rights reserved.

Abstract: New needs and opportunities drive the development of novel computational methods for the design and safety analysis of light water reactors (LWRs). Some new methods are likely to be three dimensional. Coupling is expected between system codes, computational fluid dynamics (CFD) modules, and cascades of computations at scales ranging from the macro- or system scale to the micro- or turbulence scales, with the various levels continuously exchanging information back and forth. The ISP-42/PANDA and the international SETH project provide opportunities for testing applications of single-phase CFD methods to LWR safety problems. Although industrial single-phase CFD applications are commonplace, computational multifluid dynamics is still under development. However, first applications are appearing; the state of the art and its potential uses are discussed. The case study of condensation of steam/air mixtures injected from a downward-facing vent into a pool of water is a perfect illustration of a simulation cascade: At the top of the hierarchy of scales, system behavior can be modeled with a system code; at the central level, the volume-of-fluid method can be applied to predict large-scale bubbling behavior; at the bottom of the cascade, direct-contact condensation can be treated with direct numerical simulation, in which turbulent flow (in both the gas and the liquid), interfacial dynamics, and heat/ mass transfer are directly simulated without resorting to models.

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Abstract: Surface divergence models for prediction of scalar exchange at fluid-fluid interfaces are investigated. The models, based on the Hunt-Graham blocking theory, are shown to predict experimental data at unsheared interfaces, and new results of direct numerical simulation for deformable, nonbreaking sheared interfaces. The parameterization is in terms of the turbulent Reynolds number defined by the integral velocity and length scales in the bulk flow, which makes it useful for practical purposes. (C) 2004 Elsevier Ltd. All rights reserved.

Abstract: Particle dispersion and deposition in the region near the wall of a turbulent open channel is studied using direct numerical simulation of the flow, combined with Lagrangian particle tracking under conditions of one-way coupling. Particles with response times of 5 and 15, normalized using the wall friction velocity and the fluid kinematic viscosity, are considered. The simulations were performed until the particle phase reached a statistically stationary state before calculating relevant statistics. For both response times, particles are seen to accumulate strongly very close to the wall in the form of streamwise oriented streaks. Deposited particles were divided into two distinct populations; those with large wall-normal deposition velocities and small near-wall residence times referred to as the free-flight population, and particles depositing with negligible wall-normal velocities and large near-wall residence times (more than 1000 wall time units), referred to as the diffusional deposition population. Diffusional deposition (deposition induced by the small residual turbulent fluctuations near the wall) is found to be the dominant mechanism of deposition for both particle response times. The free-flight mechanism is shown to gain in importance only for tau(p)(+)=15 particles. For tau(p)(+)=5 particles only 10% deposit because of free flight, whereas the fraction is around 40% for tau(p)(+)=15 particles. This result runs counter to the widely held opinion that free flight is the dominant mechanism of deposition in wall-bounded flows and clearly quantifies the relative importance of the two mechanisms. A simple relationship between the particle wall-normal velocity on deposition and the residence time for free-flight particles is presented. Particle deposition locations over the period of the entire simulation reveal that, while diffusional deposition occurs mostly along streamwise oriented lines below the near-wall particle accumulation patterns, free-flight particles deposit more evenly over the wall. (C) 2003 American Institute of Physics.

Abstract: Direct numerical simulation has been performed to explore the turbulence near a freely deformable interface in a countercurrent air-water flow, at a shear Reynolds number Re-* = 171. The deformations of the interface fall in the range of capillary waves of waveslope ak = 0.01, and very small phase speed-to-friction velocity ratio, c/u(*). The results for the gas side are compared to open-channel flow data at the same shear Reynolds number, placing emphasis upon the influence of the waves in the interfacial viscosity-affected region, and away from it in the outer core flow. Comparison shows a similarity in the distribution of the turbulence intensities near the interface, confirming that for the range of flow conditions considered, the lighter phase perceives the interface like a flexible solid surface, at least in the limit of non-breaking waves. Overall, in a time-averaged sense, the interfacial motion affects the turbulence in the near-interface region; the most pertinent effect is a general dampening of the turbulent fluctuating field which, in turn, leads to a reduction in the interfacial dissipation. Furthermore, the turbulence is found to be less anisotropic at the interface than at the wall. This is confirmed by the analysis of the pressure-rate-of-strain tensor, where the effect of interfacial motion is shown to decrease the pressure strain correlation in the direction normal to the interface and in the spanwise direction. The analysis of the turbulent kinetic energy and Reynolds stress budgets reveals that the interface deformations mainly affect the so-called boundary term involving the redistribution of energy, i.e. by the action of pressure, turbulent fluctuations and molecular viscosity, and the dissipation terms, leaving the production terms almost unchanged. The non-zero value of the turbulent kinetic energy at the interface, together with the reduced dissipation, implies that the turbulent activity persists near the interface and contributes to accelerating the turbulent transfer mechanisms. Away from the interface, the decomposition of the fluctuating velocity gradient tensor demonstrates that the fluctuating rate-of-strain and rate-of-rotation at the interface influence the flow throughout the boundary layer more vigorously. The study also reveals the streaky structure over the deformable interface to be less organized than over a rigid wall. However, the elongation of the streaks does not seem to be much affected by the interfacial motion. A simple qualitative analysis of the quasi-streamwise vortices using different eduction techniques shows that the interfacial turbulent structures do not change with a change of boundary conditions.

Abstract: The impact of interfacial dynamics on turbulent heat transfer at a deformable, sheared gas-liquid interface is studied using Direct Numerical Simulation (DNS). The flow system comprises a gas and a liquid phase flowing in opposite directions. The governing equations for the two fluids are alternately solved in separate domains and then coupled at the interface by imposing continuity of velocity and stress. The deformations of the interface fall in the range of capillary waves of waveslope ak=0.01 (wave amplitude a times wavenumber k), and very small phase speed-to-friction velocity ratio, c/u(*). The influence of low-to-moderate molecular Prandtl numbers (Pr) on the transport in the immediate vicinity of the interface is examined for the gas phase, and results are compared to existing wall-bounded flow data. The shear-based Reynolds number Re-* is 171 and Prandtl numbers of 1, 5, and 10 were studied. The effects induced by changes in Pr in both wall-bounded flow and over a gas-liquid interface were analyzed by comparing the relevant statistical flow properties, including the budgets for the temperature variance and the turbulent heat fluxes. Overall, Pr was found to affect the results in very much the same way as in most of the available wall flow data. The intensity of the averaged normal heat flux at high Prandtl numbers is found to be slightly greater near the interface than at the wall. Similar to what is observed in wall flows, for Pr = I the turbulent viscosity and diffusivity are found to asymptote with z(+3), where z(+) is the distance to the interface, and with z(+n), where n>3 for Pr=5 and 10. This implies that the gas phase perceives deformable interfaces as impermeable walls for small amplitude waves with wavelengths much larger than the diffusive sublayers. Moreover, high-frequency fluctuating fields are shown to play a minor role in transferring heat across the interface, with a marked filtering effect of Pr. A new scaling law for the normalized heat transfer coefficient, K+ has been derived with the help of the DNS data. This law, which could be used in the range of Pr=1 to 10 for similar flow conditions, suggests an approximate Pr-3/5 relationship, lying between the Pr-1/2 dependence for free surfaces and the Pr-2/3 law for immobile interfaces and much higher Prandtl numbers. A close inspection of the transfer rates reveals a strong and consistent relationship between K+, the frequency of sweeps impacting the interface, the interfacial velocity streaks, and the interfacial shear stress.

Abstract: Numerical analysis of the standard continuum description of a dilute dispersed phase as applied to a laminar, particle-laden, mixing layer during its initial evolution has been performed. The flow has been previously analyzed under the framework of linear stability analysis where both the continuous and the dispersed phases are considered as continua. Earlier studies had neglected the closure terms resulting from the averaging of the nonlinear transport term involved in the derivation of the dispersed-phase momentum equations. In this work, Lagrangian particle tracking was coupled to an incompressible Navier-Stokes solver to directly estimate the closure terms (referred to as the averaging-stress terms) and compare them to the other terms balancing the dispersed-phase continuum equations. Calculations were performed for particle Stokes numbers of 1, 10, and 50, and for a mass loading of one. Dispersed-phase flow quantities such as the number density and velocity were determined by averaging the data in the spanwise direction. A parametric study of the influence of the number of particles, for Stokes number of one, showed that an improved approximation to a continuum can be obtained by increasing the number of particles. Examining the momentum balance in detail revealed that the main contributors were the time-derivative, convective, and the interfacial force terms. The averaging stress was at least two orders of magnitude smaller for all the Stokes numbers studied. However, the averaging stress, though negligible in magnitude, showed a deterministic variation in the center of the mixing layer. The results lend support to the currently used continuum equations for analyzing the stability of laminar, particle-laden mixing layers, and possibly other free-shear flows such as jet and wake flows. (C) 2003 Elsevier Science Ltd. All rights reserved.

Abstract: The paper examines a selection of well-established prediction methods employed for the modelling of multiphase turbulent flows presented in typical environmental and hydrodynamic applications. The main objective is to provide a basic understanding of the subject with a deliberate intention to simplifying the presentation. Turbulence is approached on the basis of the conventional one-point closure context. The experience gathered by the author and by others with various predictive strategies all based on the Eulerian-Eulerian (field description) and the Eulerian-Lagrangian methods are discussed and summarized: the goals, limitations. and required developments are described. Typical applications of each calculation method are presented, in which the interaction between the transported dispersed-phase and the field turbulence is treated on the basis of both one-way and two-way coupling. The case studies in question include aerosol production and transport over the oceans, pollutant dispersion in the atmospheric surface layer, hydrometeor impact on urban canopies, sedimentation of active sludge in secondary water clarifiers. and mixing and circulation within confined bubble plumes. Analysis of the various models reveals that for most of the reported applications the Reynolds averaged Navier-Stokes approach is inherently ill-posed and should be transcended by the promising large-eddy simulation concept. (C) 2002 Elsevier Science Ltd. All rights reserved.

Abstract: This paper reports on recent advances in the application of the large-eddy simulation (LES) approach to turbulent, vertical mixing layers containing bubbles at low void fraction. The method is based on the filtered multi-fluid equations derived from the application of a single component-weighted volume-averaging process. The subgrid-scale (SGS) modelling is based on the Smagorinsky kernel in both its original form and the dynamic procedure of Germano. Parameter studies have been undertaken to determine the effects of the ratio of the cut-off filter to the typical length scale characterizing the dispersed phase, the influence of the lift coefficient, the performance of the SGS models and the importance of inlet turbulence levels. A new model is proposed for possible bubble-induced turbulence modulation, in which the mixing length of the dispersed phase at the SGS is inferred dynamically from the resolved flow field. By averaging over times longer than the dynamic time scales of the turbulent fluctuations, mean quantities, including phase velocities and void fractions, are derived, which are then compared against experimental data. A critical discussion of the usefulness of LES approaches in this context is given. Overall, the LES approach shows considerable promise in regard to predicting mean quantities including phase velocities and void fractions.

Abstract: The paper presents recent trends in the development of prediction methods for the direct numerical simulation of multiphase flows based on the one-fluid formalism coupled with various interface tracking algorithms. The methods are based on solving a single set of transport equations for the whole computational domain and treating the different phases as a single fluid with variable material properties. Changes in these properties are accounted for by advecting a phase indicator function. Interfacial exchange terms are incorporated by adding the appropriate sources as delta functions or smoothed gradients of the composition field at or across the interface. The strategies are first discussed within the isothermal phase context and then for situations featuring interphase heat and mass transfer. Various aspects such as the treatment of capillary forces are discussed, supported by selected examples demonstrating recent progress drawn from the current work of the authors. (C) 2002 Published by Elsevier Science Inc.

Abstract: The paper presents recent trends in modeling jets in crossflow with relevance to film cooling of turbine blades. The aim is to compare two classes of turbulence models with respect to their predictive performance in reproducing near-wall flow physics and heat transfer. The study focuses on anisotropic models eddy-viscosity/diffusivity models and explicit algebraic stress models, up to cubic fragments of strain and vorticity tensors. The first class of models are direct numerical simulation (DNS) based two-layer approaches transcending the conventional k-epsilon model by means of a nonisotropic representation of the turbulent transport coefficients; this is employed in Connection with a near-wall one-equation model resolving the semi-viscous sublayer. The aspects of this new strategy are based on known channel-flow and boundary layer DNS statistics. The other class of models are quadratic and cubic explicit algebraic stress formulations rigorously derived from second-moment closures. The stress-strain relations are solved in the context of a two-layer strategy resolving the near-wall region by means of a nonlinear one-equation model; the outer core flow is treated by rise of the two-equation model. The models are tested for the film cooling of a flat plate by a row of streamwise injected jets. Comparison of the calculated and measured wall-temperature distributions shows that only the anisotropic eddy-viscosity/diffusivity model can correctly predict the spanwise spreading of the temperature field and reduce the strength of the secondary vortices. The wall-cooling effectiveness vias found to essentially depend on these two particular flow features. The non-linear algebraic stress models were of a mixed quality in film-cooling calculations.

Abstract: This paper presents salient features of the temporal stability of particle-laden mixing layers under uniform particle loadings. Results show the strong stabilizing influence of particles with Stokes numbers of the order of unity. The particles also significantly change the most unstable wavenumber which dominates the initial evolution of the mixing layer. Results from the linear stability analysis were used to evaluate the Eulerian-Lagrangian (particle tracking) methodology and excellent agreement was observed for the instability growth rates. Two methods of implementing the fluid-particle coupling, both based on projecting the coupling force onto the fluid nodes, were compared and found to give almost identical results; indicating little practical difference between the two in the present case. Analyzing the accuracy requirements for the velocity interpolation found second-order interpolation to be inadequate. Converged results were obtained with fourth- and sixth-order accurate interpolation schemes. (C) 2002 Elsevier Science B.V. All rights reserved.

Abstract: Temporal stability analysis of particle-laden mixing layers with uniform and nonuniform particle loadings is presented. New analytical results have been derived in the limit of small and large Stokes numbers using small-parameter expansions. A dichotomy in the behavior of the fluid-particle system, based on whether the particle diameter or density is increased to achieve large Stokes numbers, is clarified. Good agreement between the limiting analytical expressions and numerical results is obtained. Additional unstable modes are observed for nonuniform particle loadings for large Stokes numbers and high mass loadings conditions. The effect of the steepness of the nonuniformity is presented for the first time. The primary effect of nonuniformity, is an increase in the range of unstable wave numbers for small to intermediate Stokes numbers, and a change in the nature of the dominant Kelvin-Helmholtz instability from stationary to dispersive. The value of the most unstable wave number is shown to remain unaffected by the nonuniformity. (C) 2002 American Institute of Physics.

Abstract: Abstract: The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al, developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re k-epsilon with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary, layer flows, The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-a-vis that of momentum further leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.

Abstract: The efficiency of various modelling strategies based on the non-linear representation of Reynolds stress in terms of strain and vorticity rates, is addressed for vortex-shedding flows past a bluff body. Two of these models were successfully modified to cope with highly-strained flows. Further, a novel modelling methodology is proposed, based on zonal coupling of a second-order closure for turbulence, solving the outer core flow region, with a one-equation non-linear model for near-wall flow regions. The merits of each approach are evaluated through comparison of the results with the available experimental data for vortex-shedding flow past a square cylinder at Re = 22,000. All the models were found to reproduce fairly well the shedding dynamics, with a common predictive trend; that is, the total fluctuating energy is in good accord with the measurements whereas the turbulent kinetic energy is significantly underestimated. The stress-strain relationships were found to be more dominant with incorporating the cubic stress-strain products forming the anisotropic stress tensor. The novel zonal second-order closure was found to be superior to all other methods. The method was also capable to predict the periodic doubling phenomenon, in accord with direct numerical simulation (DNS) and experiments in which the flow was deliberately forced to two-dimensionality. (C) 2000 Elsevier Science Ltd. All rights reserved.

Abstract: Film cooling of a symmetrical turbine-blade model by lateral and non-lateral injection from one row of holes placed on each side near the leading edge is calculated with a 3D finite-volume method on multi-block grids. For various blowing rates, the flow and temperature fields are predicted, and in particular the contours of him-cooling effectiveness on the blade surface, which are compared with measurements. Various versions of the k-epsilon turbulence model are employed: the standard model with wall functions (WF), a two-layer version resolving the viscous sublayer with a one-equation model and an anisotropy correction due to Bergeles et al. [Num. Heat Transfer 1 (1978) 217-242] which acts to promote the lateral turbulent exchange. The original Bergeles proposal is modified for application in the viscous sublayer. With the standard model, the lateral spreading of the temperature field is underpredicted, leading to averaged film-cooling effectiveness values that are too low. The situation is improved by using the Bergeles correction, especially when the modified correction is applied with the two-layer model (TLK). This yields effectiveness contours in reasonably good agreement with the measurements, but the laterally averaged effectiveness is not predicted in all cases with good accurary. However, the trend of the various influence parameters is reproduced correctly. (C) 2001 Elsevier Science Inc. All rights reserved.

Abstract:

Abstract: Injection of coolant air from a showerhead injection system at the leading edge of a high pressure turbine blade is investigated using a fully implicit three-dimensional finite-volume method on multi-block grids. For various blowing rates, the calculation results for the velocity and pressure fields and turbulence intensity are compared with available experimental data. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. The standard k-epsilon turbulence model with wall functions is already capable of capturing the major details of the flow field including the injection-induced secondary-flow vortices, particularly so on the suction side. On the pressure side, however, the lateral jet spreading is underpredicted somewhat together with an exaggeration of the near-wall sink-flow vortices. On this side with convex walls, where turbulence anisotropy is appreciable according to the experiments, overall better predictions were obtained with the anisotropy correction of Bergeles et al. [23] promoting the Reynolds stress in the lateral direction. The correction has no beneficial effect on the suction side with concave walls where the turbulence anisotropy was observed to be much smaller.

Abstract: The paper addresses the predictive capability of a computational modelling method for turbulent flows over rough-walled circular cylinders. The near-wall treatment procedure, based on a straight extension of the wall functions, is included in a Reynolds-averaged Navier-Stokes equation solver using the k-epsilon model. The surface roughness effect is taken into account through the inclusion of a sink term in the momentum equations and a source term in the turbulent kinetic energy equation. Test investigations were performed for turbulent flows around two-and three-dimensional circular cylinders. Comparison with experimental data shows that the method performs fairly well in simulating the flow over a range of surface-roughness densities extending up to transitional roughness. The predicted results are found to agree well with the experimental data, including pressure and drag coefficient distributions. From a physical point of view, the computational results support the thesis which states that surface roughness helps to shift the flow regime without acting on the Reynolds number. (C) 1999 Elsevier Science Ltd. All rights reserved.

Abstract: Recent developments in computing turbulent and buoyant flow in sedimentation tanks are introduced. The test case is a circular, center-feed secondary clarifier with inclined bottom and central sludge withdrawal. Axisymmetry is assumed, and the flow and settling processes are modeled in a radial section by using the k-epsilon turbulence model on a two-dimensional, nonorthogonal grid. The computation domain includes the sludge blanket where the viscosity is affected by the rheological behavior of the sludge. The aim of the present study is to evaluate the sensitivity of the how and concentration fields to parameters that characterize (1) the rheological properties of highly concentrated regions; (2) the settling of sludge; and (3) the effect of stratification on the turbulent diffusion. The overall appearance of the fields proves to be similar, whereas the regions of high velocities and high gradients are strongly affected by using different parameters or approaches on rheology, settling, and diffusive transport, resulting in different sludge blanket heights.

Abstract: Film cooling effectiveness of a flat plate by a row of laterally injected jets is investigated using a Navier-Srokes equation solver which employs a finite-volume method with a multi-block technique. The paper compares measured and calculated temperature and velocity fields obtained with the standard k-epsilon and the k-epsilon based two-layer turbulence model for various blowing rates. The resolution of the viscosity-affected near-wall region with a one-equation turbulence model yielded a noticeable improvement in the prediction of film-cooling effectiveness compared to results obtained with wall functions. Furthermore, results of additional calculations using the ad hoc correction proposed by Bergeles et al. (1978), which attempts to promote the lateral diffusivity, combined with the two-layer model indicate that this anisotropy correction enhances indeed the spanwise spreading, but its application very close to the wall needs additional calibration. (C) 1998 Elsevier Science Inc. AU rights reserved.

Abstract: Predictions of three-dimensional airflows over a building-like model with complex boundaries by solving the Reynolds averaged Navier-Strokes equations are presented. The obstacle is placed in boundary layers characterized by different roughness, and which have a main stream velocity component at different angles to the object. The pressure distributions are compared to wind-tunnel measurements. The effect of turbulent characteristics of the oncoming flow on pressure distribution is shown out-lined through the simulation of various roughness sublayers. The different results suggest that only the base pressure distribution is seriously affected by turbulence intensity and surface roughness. These two parameters are found to be of major importance in reproducing accurately a natural boundary layer. Additionally, the calculations have shown that the flow field is very sensitive to the specification of inflow conditions for the rate of dissipation of turbulent kinetic energy. (C) 1998 Elsevier Science B.V. All rights reserved.

Abstract: Some wind tunnel investigations of gas dispersion around a rectangular building placed in a simulated atmospheric boundary layer have been conducted. Numerical simulations of these experiments have been performed by solving the Reynolds-averaged Navier-Stokes equations, combined with a Reynolds-stress turbulence model, and two variants of the two-layer model due to Rodi. It appears that only the second moment closure correctly predict the recirculating zones on the faces. In this case, calculated values of gas concentrations on the building model faces agree generally well with measurements.

Abstract: In 3-D steady calculations of the flow around a cube placed in developed-channel flow, various versions of the k-epsilon model were tested. For the near-wall treatment, standard wall functions were employed, as well as the two-layer approach in which the viscous sublayer is resolved with a one-equation model. Two versions of the one-equation model were tested. In addition, calculations were carried out with the Kato-Launder (1993) modification of the k-epsilon model which eliminates excessive turbulence production in stagnation regions. The various predictions are compared with the measurements of Martinuzzi and Tropea (1993).

Abstract: An investigation of the ability of numerical codes to predict wind loads on buildings and structures, using kappa-epsilon closure model for turbulence, has been undertaken at CSTB. We present in this paper four cases for which wind-tunnel measurements are available: Pressure coefficients around a cube model and a house model in a simulated atmospheric boundary layer, drag and lift forces on a hoarding model and a bridge section model, located in the CSTB climatic wind tunnel.

Abstract: An integrated approach is presented for numerical simulation of the wind-driven rain impacts on building surfaces. The numerical code combines Eulerian simulations of the turbulent flows, Lagrangian random-flight simulations of heavy particle trajectories, and impacting water rate computations. The flow is modelled using a version of CHENSI, a code based on the two-equation k-epsilon model developed to simulate flows in urban canopies and dispersion within streets and around buildings. Particle trajectories are computed by means of a Markov chain modified to model the effects of turbulence, gravity and inertia. Three different models are derived from the work of Edson and Fairall (1994, J. geophys. Res. 99, 25,296-25,311) and Mostafa and Mongia (1987, Int. J. Heat Mass Transfer 12, 2585-2593), and tested for application to raindrops that range in diameter from 0.2 to 2 mm. The distribution of impacting drops on the various boundaries of the calculation domain is used in combination with a rain distribution model to compute the amount of water that is absorbed by the street and building surfaces. A resulting set of simulations is compared to experimental data and semi-empirical formulations. The extension of the method to assess the impact of other atmospheric hydrometeors, e.g. snowflakes or fog drops, is discussed.