On the relative impact of subgrid‐scale modelling and conjugate heat transfer in LES of hot jets in cross‐flow over cold plates

This work describes numerical simulations of a hot jet in cross‐flow with applications to anti‐ice systems of aircraft engine nacelles. Numerical results are compared with experimental measurements obtained at ONERA to evaluate the performances of LES in this industrial context. The combination of complex geometries requiring unstructured meshes and high Reynolds number does not allow the resolution of boundary layers so that wall models must be employed. In this framework, the relative influence of subgrid‐scale modelling and conjugate heat transfer in LESs of aerothermal flows is evaluated. After a general overview of the transverse jet simulation results, a LES coupled with a heat transfer solver in the walls is used to show that thermal boundary conditions at the wall have more influence on the results than subgrid scale models. Coupling fluid flow and heat transfer in solids simulations is the only method to specify their respective thermal boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Investigation of Two-Fluid Methods for Large Eddy Simulation of Spray Combustion in Gas Turbines

An extension of the large eddy simulation (LES) technique to two-phase reacting flows, required to capture and predict the behavior of industrial burners, is presented. While most efforts reported in the literature to construct LES solvers for two-phase flow focus on Euler–Lagrange formulation, the present work explores a different solution (‘two-fluid’ approach) where an Eulerian formulation is used for the liquid phase and coupled with the LES solver of the gas phase. The equations used for each phase and the coupling terms are presented before describing validation in two simple cases which gather some of the specificities of real combustion chamber: (1) a one-dimensional laminar JP10/air flame and (2) a non-reacting swirled flow where solid particles disperse (Sommerfeld and Qiu, Int. J. Multiphase Flow 19(6):1093–1127, 1993). After these validations, the LES tool is applied to a realistic aircraft combustion chamber to study both a steady flame regime and an ignition sequence by a spark. Results bring new insights into the physics of these complex flames and demonstrate the capabilities of two-fluid LES.     

A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes

We present a parallel fully implicit algorithm for the large eddy simulation (LES) of incompressible turbulent flows on unstructured meshes in three dimensions. The LES governing equations are discretized by a stabilized Galerkin finite element method in space and an implicit second-order backward differentiation scheme in time. To efficiently solve the resulting large nonlinear systems, we present a highly parallel Newton-Krylov-Schwarz algorithm based on domain decomposition techniques. Analytic Jacobian is applied in order to obtain the best achievable performance. Two benchmark problems of lid-driven cavity and flow passing a square cylinder are employed to validate the proposed algorithm. We then apply the algorithm to the LES of turbulent flows passing a full-size high-speed train with realistic geometry and operating conditions. The numerical results show that the algorithm is both accurate and efficient and exhibits a good scalability and parallel efficiency with tens of millions of degrees of freedom on a computer with up to 4096 processors. To understand the numerical behavior of the proposed fully implicit scheme, we study several important issues, including the choices of linear solvers, the overlapping size of the subdomains, and, especially, the accuracy of the Jacobian matrix. The results show that an exact Jacobian is necessary for the efficiency and the robustness of the proposed LES solver.     

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid-structure interaction

Fluid-structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one-dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two-dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.     

Closely coupled fluid-solid interface method with moving-average for LES based conjugate heat transfer solution

Fluid–solid coupled Conjugate Heat Transfer (CHT) simulations are relevant to many practical problems. Most existing interfacing methods have been developed for Reynolds averaged Navier-Stokes solvers. For high fidelity turbulence scale-resolved flow solvers however, the CHT interface methods face significant challenges arisen from a wide frequency spectrum of unsteady disturbances to be dealt with, compounded by the huge time scale disparity between fluid and solid domains.In this paper, a closely coupled non-partitioned (monolithic) CHT method is presented. The main issues of interest are the prohibitive time costs of direct time domain CHT methods and an extra mesh dependency in the solid domain when resolving high frequency turbulence disturbances. Based on a temporal Fourier spectral framework, the present CHT interface method entails a moving-average for the time-mean flow and a discrete Fourier transform on-the-fly at each time step. Taking advantage of a semi-analytical transfer function and harmonic balancing for the CHT interface, we can achieve solving the solid domain completely in its own time step (3–5 orders of magnitude larger than that of the fluid domain). The present interface method can effectively circumvent aliasing errors and extra solid domain mesh-dependence encountered by other time-domain coupling methods when applied to turbulence scale-resolved CHT solutions. Illustrative stability analyses also show that the numerical stability of the present CHT interface should require no more stringent conditions than that in either fluid or solid domain. The computational results and analyses highlight the advantages of the present methodology in terms of both the computational efficiency and accuracy, in comparison with a conventional directly coupled interface method. Furthermore, a case study aided by a simple interface response analysis highlights much augmented wall temperature fluctuations and higher sensitivity to the interface treatment when a low conductivity protection layer (Thermal Barrier Coating, TBC) is added. The present study underlines the relevance of accounting for fluid disturbances over a range of frequencies in an effective and accurate CHT interface treatment.     

Mesh adaptation for large‐eddy simulations in complex geometries

Large‐eddy simulation (LES) consists in explicitly simulating the large scales of the fluid motion and in modeling the influence of the smallest scales. Thanks to the steady growth of computational resources, LES can now be used to simulate realistic systems with complex geometries. However, when LES is used in such complex geometries, an adequate mesh has to be determined to perform valid LES. In this work, a strategy is proposed to assess the quality of a given mesh and to adapt it locally. Two different criteria are used as mesh adaptation criteria. The first criterion is defined to ensure a correct discretization of the mean field, whereas the second criterion is defined to ensure enough explicit resolution of turbulent scales motions. The use of both criteria is shown in canonical flow cases. As a second part of this work, a numerical strategy for mesh adaptation in high‐performance computing context is proposed by coupling the flow solver, YALES2, and the remeshing library, MMG3D, for massively parallel computations. This coupling enables an efficient and parallel remeshing of grids alleviating any memory or performance issues encountered in sequential tools. This strategy is finally applied to the simulation of the isothermal flow in a complex meso‐combustor to demonstrate the applicability of the adaptation methodology to complex turbulent flows. Copyright © 2015 John Wiley & Sons, Ltd.     

Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.     

Vortex mechanism of heat transfer enhancement in a channel with spherical and oval dimples

Vortex mechanism of heat transfer enhancement in a narrow channel with dimples has been investigated numerically using LES and URANS methods. The flow separation results in a formation of vortex structures which significantly enhance heat transfer on dimpled surfaces leading to a small increase in pressure loss. The heat transfer can be significantly increased by rounding the dimple edge and use of oval dimples. To get a deep insight into flow physics LES is performed for single phase flow in a channel with a spherical dimple. The instantaneous vortex formation and separation are investigated in and around the dimple area. Considered are Reynolds numbers (based on dimple print diameter) Re_D = 20,000 and Re_D = 40,000 the depth to print diameter ratio of Δ = 0.26. Frequency analysis of LES data revealed the presence of dominating frequencies in unsteady flow oscillations. Direct analysis of the flow field revealed the presence of coherent vortex structure inclined to the mean flow. The structure changes its orientation in time causing the long period oscillations with opposite-of-phase motion. Three dimensional proper orthogonal decomposition (POD) analysis is carried out on LES pressure and velocity fields to identify spatio-temporal structures hidden in the random fluctuations. Tornado-like spatial POD structures have been determined inside dimples.     

A quasi‐dynamic procedure for coupled thermal simulations

This paper outlines the development and adaptation of a coupling strategy for transient temperature analysis in a solid via a conjugate heat transfer method. This study proposes a quasi‐dynamic coupling procedure to bridge the temporal disparities between the fluid and the solid. In this approach, dynamic thermal modeling in the solid is coupled with a sequence of steady states in the fluid. This quasi‐dynamic algorithm has been applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate using the severe thermal conditions of a solid propellant rocket. Two different coupled thermal computations have been performed. In the first one—referred to as the reference computation—the coupling period is equal to the smallest solid time constant. In the second one, a very large coupling period is used. The results show that the procedure can predict accurate transient temperature fields at a reasonable computational cost. The simulation CPU time is approximately reduced by up to 90%, while maintaining a very good accuracy. All the details of the numerical test case are given in the paper. This application illustrates the capabilities and the overall efficiency of this coupled approach in a solid transient problem using long term simulations of time dependent flows. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparative Study of DNS,LES and Hybrid LES/RANS of Turbulent Boundary Layer with Heat Transfer Over 2d Hill

This paper first presents the turbulent heat transfer phenomenon of the boundary layer over a 2-dimensional hill using the direct numerical simulation (DNS). DNS results reveal turbulent heat transfer phenomena in the boundary layer over a 2-dimensional hill affected by the flow acceleration and the concave wall at the foreface of a hill, the convex wall at the top of the hill, and the flow deceleration, separation, and reattachment and the concave wall at the back of the hill. The prediction of turbulent heat transfer, the turbulence models of LES and HLR should be assessed in such heat transfer because these models have seldom been evaluated in the complex turbulent heat transfer. Therefore, this paper also presents evaluations of predictions of LES and HLR in the complicated turbulent heat transfer which is the boundary layer with heat transfer over a 2-dimensional hill. Consequently, this paper obviously shows the detailed turbulent heat transfer phenomena of a boundary layer over a 2-dimensional hill via DNS, and the evaluation results of prediction accuracy of LES and HLR for the heat transfer. LES and HLR give good prediction in comparison with DNS results, but the predicted reattachment and separation points are slightly different from DNS.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Multiphysics Simulation Combining Large-Eddy Simulation,Wall Heat Conduction and Radiative Energy Transfer to Predict Wall Temperature Induced by a Confined Premixed Swirling Flame

A multi-physics simulation combining large-eddy simulation, conjugate heat transfer and radiative heat transfer is used to predict the wall temperature field of a confined premixed swirling flame operating under atmospheric pressure. The combustion model accounts for the effect of enthalpy defect on the flame structure whose stabilization is here sensitive to the wall heat losses. The conjugate heat transfer is accounted for by solving the heat conduction within the combustor walls and with the Hybrid-Cell Neumann-Dirichlet coupling method, enabling to dynamically adapt the coupling period. The latter coupling procedure is enhanced to determine statistics (mean, RMS, \(\ldots \)) in a permanent regime accurately and efficiently thanks to an acceleration technique which is derived and validated. The exact radiative heat transfer equation is solved with an advanced Monte Carlo method with a local control of the statistical error. The coupled simulation is carried out with or without accounting for radiation. Excellent results for the wall temperature are achieved by the fully coupled simulation which are then further analyzed in terms of radiative effects, global energy budget and fluctuations of wall heat flux and temperature.     

Influence of Axisymmetric Assumptions on Large Eddy Simulations of a Confined Jet and a Swirl Flow

Axisymmetric geometries can be found in many practical flow applications. In the attempt to predict these flows numerically, RANS flow solvers can decrease the computational efforts dramatically by taking this axisymmetry into account and by computing only a pie-segment of the flow. However, the extension of the concept of axisymmetric flows to LES computations is not straightforward, since the boundary conditions on the axis of symmetry are altering the instantaneous flow field. In this study, the influence of the introduction of an axis of symmetry to LES computations is assessed by computations of a flow with and without swirl over an axisymmetric expansion. The LES computations are performed on a full three-dimensional and a 90° segment of the geometry. The results are compared and the influence of the axis put into relation with the gain in computational costs.     

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.     

MHD graphene-polydimethylsiloxane Maxwell nanofluid flow in a squeezing channel with thermal radiation effects

The magnetohydrodynamic (MHD) graphene-polydimethylsiloxane (PDMS) nanofluid flow between two squeezing parallel plates in the presence of thermal radiation effects is investigated. The energy efficiency of the system via the Bejan number is studied extensively. The governing partial differential equations are converted by using the similarity transformations into a set of coupled ordinary differential equations. The set of these converted equations is solved by using the differential transform method (DTM).The entropy generation in terms of the Bejan number, the coefficient of skin-friction, and the heat transfer rate is furthermore investigated under the effects of various physical parameters of interest. The present study shows that the Bejan number, the velocity and thermal profiles, and the rate of heat transfer decrease with a rise in the Deborah number De while the skin-friction coefficient increases. It is also observed that the entropy generation due to frictional forces is higher than that due to thermal effects. Thus, the study bears the potential application in powder technology as well as in biomedical engineering.     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

Computation of fluid flow with a parallel multigrid solver

A finite volume numerical method for the prediction of fluid flow and heat transfer in simple geometries was parallelized using a domain decomposition approach. The method is implicit, uses a colocated arrangement of variables and is based on the SIMPLE algorithm for pressure-velocity coupling. Discretization is based on second-order central difference approximations. The algebraic equation systems are solved by the ILU method of Stone.¹ To accelerate the convergence, a multigrid technique was used. The efficiency was examined on three different parallel computers for laminar flow in a pipe with an orifice and natural convection in a closed cavity. It is shown that the total efficiency is made up of three major factors: numerical efficiency, parallel efficiency and load-balancing efficiency. The first two factors were thoroughly investigated, and a model for predicting the parallel efficiency on various computers is presented. Test calculations indicate reasonable total efficiency and favourable dependence on grid size and the number of processors.     

Non-zonal detached eddy simulation coupled with a steady RANS solver in the wall region

Xiao and Jenny (2012) proposed an interesting hybrid LES/RANS method in which they use two solvers and solve the RANS and LES equations in the entire computational domain. In the present work this method is simplified and used as a hybrid RANS-LES method, a wall-modeled LES. The two solvers are employed in the entire domain. Near the walls, the flow is governed by the steady RANS solver; drift terms are added to the DES equations to ensure that the time-averaged DES fields agree with the steady RANS field. Away from the walls, the flow is governed by the DES solver; in this region, the RANS field is set to the time-averaged LES field. The disadvantage of traditional DES models is that the RANS models in the near-wall region – which originally were developed and tuned for steady RANS – are used as URANS models where a large part of the turbulence is resolved. In the present method – where steady RANS is used in the near-wall region – the RANS turbulence models are used in a context for which they were developed. In standard DES methods, the near-wall accuracy can be degraded by the unsteady agitation coming from the LES region. It may in the present method be worth while to use an accurate, advanced RANS model. The EARSM model is used in the steady RANS solver. The new method is called NZ S-DES . It is found to substantially improve the predicting capability of the standard DES. A great advantage of the new model is that it is insensitive to the location of the RANS-LES interface.