Haut PDF An implicit method for turbulent boundary layers simulation

An implicit method for turbulent boundary layers simulation

An implicit method for turbulent boundary layers simulation

Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY Unite´ de recherche INRIA Rennes, Ir[r]

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Drag modulation in turbulent boundary layers subject to different bubble injection strategies

Drag modulation in turbulent boundary layers subject to different bubble injection strategies

Drag reduction a b s t r a c t The aim of this study is to investigate numerically the interaction between a dispersed phase composed of micro-bubbles and a turbulent boundary layer flow. We use the Euler–Lagrange approach based on Direct Numerical Simulation of the continuous phase flow equations and a Lagrangian tracking for the dispersed phase. The Synthetic Eddy Method (SEM) is used to generate the inlet boundary condition for the simulation of the turbulent boundary layer. Each bubble trajectory is calculated by integrating the force balance equation accounting for buoyancy, drag, added-mass, pressure gradient, and the lift forces. The numerical method accounts for the feedback effect of the dispersed bubbles on the carrying flow. Our approach is based on local volume average of the two-phase Navier–Stokes equations. Local and temporal variations of the bubble concentration and momentum source terms are accounted for in mass and momentum balance equations. To study the mechanisms implied in the modulation of the turbulent wall structures by the dispersed phase, we first consider simulations of the minimal flow unit laden with bubbles. We observe that the bubble effect in both mass and momentum equations plays a leading role in the modification of the flow structures in the near wall layer, which in return generates a significant increase of bubble volume fraction near the wall. Based on these findings, we discussed the influence of bubble injection methods on the modulation of the wall shear stress of a turbulent boundary layer on a flat plate. Even for a relatively small bubble volume fraction injected in the near wall region, we observed a modulation in the flow dynamics as well as a reduction of the skin friction.
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A characteristic inlet boundary condition for compressible, turbulent, multispecies turbomachinery flows

A characteristic inlet boundary condition for compressible, turbulent, multispecies turbomachinery flows

1. Introduction Specifying inlet and outlet boundary conditions for compress- ible simulation still remains a key issue (Colonius [8] ) especially for unsteady flows where wave reflections must be controlled. In this field, characteristic boundary conditions have progressively become standard. Initially introduced by Thompson [48] , Euler Characteristic Boundary Conditions (ECBC) was then extended by Poinsot and Lele [34] to viscous flows by proposing the Navier– Stokes Characteristic Boundary Conditions (NSCBC) approach. This method specifies a given number of quantities –for example static pressure for an outlet, velocity and temperature for an inlet– on the boundary condition, and allowing the outgoing waves, com- puted by the numerical scheme, to leave the domain with min- imum reflection. The NSCBC strategy has been later extended to multi-species reacting flows and to aeroacoustics (Baum et al. [3] , Okong’o and Bellan [31] , Moureau et al. [29] , Poinsot and Veynante
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Assessment of time implicit discretizations for the computation of turbulent compressible flows

Assessment of time implicit discretizations for the computation of turbulent compressible flows

Restrictions on the maximum allowable time step of explicit time integration methods can be very severe for direct and large eddy simulations of compressible turbulent flows at high Reynolds numbers, for which extremely small space steps have to be used close to solid walls in order to capture tiny and elongated boundary layer structures. A way of increasing stability limits is to use implicit time integration schemes. However, the price to pay is a higher computational cost per time step, higher discretization errors and lower parallel scalability. A successful implicit time scheme should provide the best possible compromise between these opposite requirements. In this paper, several implicit schemes assessed against two explicit time integration techniques, namely a standard four-stage and a six-stage optimized Runge–Kutta methods, in terms of computational cost required to achieve a threshold accuracy level for the simulation of compressible turbulent flows. Pre- cisely, a second-order backward scheme solved by means of matrix-free quasi-exact Newton subiterations is compared to time-accurate Runge–Kutta implicit residual smoothing (IRS) schemes. A new IRS scheme of fourth-order accuracy, based on a bilaplacian operator, is developed to improve the accuracy of the classical second-order approach. Numerical re- sults show that the proposed IRS scheme leads to reductions in computational time by about a factor 5 for an accuracy comparable to that of the corresponding explicit Runge- Kutta scheme.
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On the generation of the mean velocity profile for turbulent boundary layers with pressure gradient under equilibrium conditions

On the generation of the mean velocity profile for turbulent boundary layers with pressure gradient under equilibrium conditions

and to the mixing length model by Spalding (18) reported in Galbraith and Head (19) . The analytical and numerical approaches are then applied to model a boundary layer with and without an adverse streamwise pressure gradient. The remainder of the paper is structured in five sections. Section 2 presents the benchmark velocity profiles that are used in Sections 4 and 5 for the validation of the analytical and numerical predictions. Section 3.1 details the analytical method used to generate the composite velocity profile in a turbulent boundary layer. Section 3.2 details the numerical method based on the interactive boundary layer model. Section 4 validates both methods using zero pressure gradient velocity data over the Reynolds number range 422 ≤ Re θ ≤ 31,000 and presents a comparison of the new mixing length model with other mixing length schemes and experiment. Section 5 extends the validation to adverse pressure gradient boundary layers and summarises the limitations of the numerical methods. Concluding remarks are given in Section 6.
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Large Eddy Simulation of Highly Compressible Jets with Tripped Boundary Layers

Large Eddy Simulation of Highly Compressible Jets with Tripped Boundary Layers

In this study, a boundary-layer tripping method permitting to obtain an initially turbulent supersonic jet is studied. The influence of the tripped jet boundary layers on the flow and acoustic fields of the jet is analyzed. The impact of nozzle-exit turbulence levels on the noise radiation and notably on the acoustic components specific to supersonic jets (screech noise, broadband shock-associated noise, mixing noise and Mach wave radiation) is discussed.

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An implicit time marching Galerkin method for the simulation of icing phenomena with a triple layer model

An implicit time marching Galerkin method for the simulation of icing phenomena with a triple layer model

transfer in the normal direction including phase change as well as source terms (previously described Galerkin method). It is worth noting that the dimension of U n+1 k depends on k, md and n since layers may appear or disappear during a time step. There are two main difficulties in the construction of the implicit method. First, as all the cells of the mesh are coupled with their left and right neighbouring cells through the running liquid film, it is complicated to devise a global implicitation of the method (i.e. a method which would simultaneously yield U n+1 k in every cell). To overcome this problem, a fixed point algorithm is used. The general idea is to perform a local implicitation and iterate over the cells until convergence so as to construct a sequence
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Optimal perturbations in swept leading edge boundary layers.

Optimal perturbations in swept leading edge boundary layers.

For an assessment of the current status of laminar flow control technology in an aeronautical context, the reader is referred to the comprehensive review of Joslin (1998) and the book of Gad-el Hak (2000). At a more fundamental level, applica- tions of control theory (Abergel and T´emam (1990)) to the delay of boundary layer transition have recently led to very encouraging results. For general accounts and reviews of the applications of control theory to transitional or turbulent flows, the reader is referred to Gunzburger (1997), Lumley and Blossey (1998) and Bewley (2001) among others. We restrict here the discussion to studies that are directly relevant to this investigation, namely optimal control methodologies involving ad- joint formulations in a continuous setting and applied to boundary layer transition. More specifically, the optimal control problem for perturbations within the flow is viewed as the minimization of an objective functional involving a measure of the perturbation energy, under the constraint that disturbances satisfy for instance the linear Navier-Stokes equations (Gunzburger 1997, Joslin et al. (1997)). For that purpose, an iterative method based on the calculation of the gradient of the ob- jective functional with respect to the control variables, e.g. wall blowing/suction, is implemented in order to reach a local minimum in function space. The gradi- ent vector of the objective functional may conveniently be expressed in terms of an adjoint state which is solution of an adjoint system of equations and boundary conditions. Such a formulation is carried out in the context of continuous linear in- stability partial differential equations. Discretization is only performed a posteriori in order to effectively solve numerically the direct and adjoint systems. Other for- mulations, which are not considered here, involve instead an a priori discretization before resorting to an optimization scheme. Such approaches are appropriate when the evaluation of the gradient of th objective functional in terms of the adjoint is numerically delicate.
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A characteristic inlet boundary condition for compressible, turbulent, multispecies turbomachinery flows

A characteristic inlet boundary condition for compressible, turbulent, multispecies turbomachinery flows

1. Introduction Specifying inlet and outlet boundary conditions for compress- ible simulation still remains a key issue (Colonius [8] ) especially for unsteady flows where wave reflections must be controlled. In this field, characteristic boundary conditions have progressively become standard. Initially introduced by Thompson [48] , Euler Characteristic Boundary Conditions (ECBC) was then extended by Poinsot and Lele [34] to viscous flows by proposing the Navier– Stokes Characteristic Boundary Conditions (NSCBC) approach. This method specifies a given number of quantities –for example static pressure for an outlet, velocity and temperature for an inlet– on the boundary condition, and allowing the outgoing waves, com- puted by the numerical scheme, to leave the domain with min- imum reflection. The NSCBC strategy has been later extended to multi-species reacting flows and to aeroacoustics (Baum et al. [3] , Okong’o and Bellan [31] , Moureau et al. [29] , Poinsot and Veynante
En savoir plus

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Drag modulation in turbulent boundary layers subject to different bubble injection strategies

Drag modulation in turbulent boundary layers subject to different bubble injection strategies

Drag reduction a b s t r a c t The aim of this study is to investigate numerically the interaction between a dispersed phase composed of micro-bubbles and a turbulent boundary layer flow. We use the Euler–Lagrange approach based on Direct Numerical Simulation of the continuous phase flow equations and a Lagrangian tracking for the dispersed phase. The Synthetic Eddy Method (SEM) is used to generate the inlet boundary condition for the simulation of the turbulent boundary layer. Each bubble trajectory is calculated by integrating the force balance equation accounting for buoyancy, drag, added-mass, pressure gradient, and the lift forces. The numerical method accounts for the feedback effect of the dispersed bubbles on the carrying flow. Our approach is based on local volume average of the two-phase Navier–Stokes equations. Local and temporal variations of the bubble concentration and momentum source terms are accounted for in mass and momentum balance equations. To study the mechanisms implied in the modulation of the turbulent wall structures by the dispersed phase, we first consider simulations of the minimal flow unit laden with bubbles. We observe that the bubble effect in both mass and momentum equations plays a leading role in the modification of the flow structures in the near wall layer, which in return generates a significant increase of bubble volume fraction near the wall. Based on these findings, we discussed the influence of bubble injection methods on the modulation of the wall shear stress of a turbulent boundary layer on a flat plate. Even for a relatively small bubble volume fraction injected in the near wall region, we observed a modulation in the flow dynamics as well as a reduction of the skin friction.
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An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows

An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows

In this work we present an a posteriori high-order nite volume scheme for the computation of compressible turbulent ows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the ow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical ux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of
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Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems

Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems

of Γ A (x; y) as an m × m matrix. 3) Assume 1 + n = 2. The first construction for complex coefficients is in [ AMcT ] for scalar operators (m = 1). An analogous estimate was obtained in [ DoK ], Theo- rem 2.21, for systems but was only carried out explicitly assuming strong ellipticity. See also [ CDoK ]. [ B , Chapter 4] used the construction in [ AMcT ] and showed uniqueness and also that it is possible to choose the constant of integration in such a way the symmetry relation holds. This construction extends mutatis mutandi to systems and does give the above estimates, with possible exception of uniqueness as the argument relies on properties of harmonic functions.
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DNS and modeling of the turbulent boundary layer over an evaporating liquid film

DNS and modeling of the turbulent boundary layer over an evaporating liquid film

In this paper, the above methodology (DNS combined with the- ory) is used to study the interaction between an evaporating liquid film and the turbulent boundary layer created in the vicinity of a wall in the generic configuration of the periodic turbulent channel flow. The liquid film flow is not solved but only its impact on the gaseous boundary layer is studied, through the boundary condition that reflects the film surface properties. The objective is to give a detailed understanding and build a model of the boundary layer structure above the film surface. In this two-way interaction, the liquid film evaporation is influenced by the near-wall gradients of species and the wall temperature, while the mass flux due to evaporation blows the boundary layer away from the wall, thereby changing the flow profiles and deviating significantly from the classical wall functions. It has been shown in previous studies that the boundary layer structure and more specifically the distance be- tween the wall and the laminar-turbulent transition depend on the
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Locally implicit discontinuous Galerkin method for time domain electromagnetics

Locally implicit discontinuous Galerkin method for time domain electromagnetics

Figure 10: S attering of a plane wave by an air raft. Time evolution of the E z omponent at a sele ted point. 7.2 Exposure of head tissues to a lo alized sour e radiation We now onsider a more realisti problem whi h onsists in the simulation of the exposure of a geometri al model of head tissues to an ele tromagneti wave emitted by a lo alized sour e. Starting from MR images of the Visible Human proje t [RHGJ03℄, head tissues are segmented and the interfa es of a sele ted number of tissues (namely , the skin, the skull and the brain) are triangulated. Dierent strategies an be used in order to obtain a smooth and a urate segmentation of head tissues and asso iated interfa e triangulations. A rst strategy onsists in using a mar hing ube algorithm [LC87℄ whi h leads to huge triangulations of interfa es between segmented subdomains. These triangulations an then be regularized, rened and de imated in order to obtain reasonable surfa e meshes, for example using the YAMS [Fre03℄ re-meshing tool. Another strategy onsists in using a variant of Chew's algorithm [Che93℄, based on Delaunay triangulation restri ted to the interfa e, whi h allows to ontrol the size and aspe t ratio of interfa e triangles [BO05℄. Surfa e meshes of the skin, skull and brain resulting from su h a pro edure are presented on Fig. 11. Then, these triangulated surfa es are used as inputs for the generation of volume meshes. In this study, the GHS3D tetrahedral mesh generator [GHS91℄ is used to mesh volume domains between the various interfa es. Note that the exterior of the head must also be meshed, up to a ertain distan e from the skin. The omputational domain is here arti ially bounded by a sphere on whi h the Silver-Müller ondition is imposed. Moreover, a simplied mobile phone model is in luded and pla ed in verti al position lose to the right ear (see Fig. 12).
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Control in fluid mechanics and boundary layers

Control in fluid mechanics and boundary layers

The other approach goes the other way around. Indeed, in finite dimension, it is known that if ˙ y = F (y) + Bu where F is quadratic is controllable, then ˙ y = F (y) + Ay + Bu is controllable too (see [57 , Theorem 3.8]). Likewise, for fluid systems, trying to get a small time controllability result implies to work at high Reynolds number (ie. with big fluid velocities, or low viscosity) inside the domain. Therefore, inertial forces prevail and the fluid system behaves like its null viscosity hyperbolic limit system. In our case, we expect to deduce results for Navier-Stokes from the Euler sytem. For Euler, global controllability has been shown in [ 51 ] by Coron for the 2D case (see also [ 53 ]) and by Glass for the 3D case in [ 94 ]. Their proofs rely on the return method introduced by Coron in [ 50 ] (see also [ 55 , Chapter 6]). For Navier-Stokes, things get harder. In [ 59 ], Coron and Fursikov show a global controllability result in the case of a 2D manifold without boundary. In [ 86 ], Fursikov and Imanuvilov show a global exact controllability result for 3D Navier-Stokes with a control acting on the whole boundary (ie. Γ = ∂Ω).
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Numerical simulation of resin transfer molding using linear boundary element method

Numerical simulation of resin transfer molding using linear boundary element method

Numerical simulation of resin transfer molding using linear boundary element methodF. Fabrice Schmidt, P Lafleur, Florentin Berthet, Pierre Devos.[r]

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Split energy cascade in turbulent thin fluid layers

Split energy cascade in turbulent thin fluid layers

6 that rotation causes a suppression of the enstrophy pro- duction similar to the effects of confinement, favoring the two-dimensionalization of the flow and the development of the inverse energy cascade. Nonetheless, this effect is not accompanied by the presence of a range of scales in which the enstrophy is conserved by the large-scale dy- namics. This is likely to affect the interactions between 2D and 3D modes. In the case of stably stratified fluid layers, it has been shown that the conversion of kinetic energy into potential energy, which is promptly trans- ferred toward the small diffusive scales, provides a fast dissipative mechanism which suppresses the large scale energy transfer [45]. Investigating the interactions be- tween 2D vortical modes and 3D potential modes will improve the understanding of this process.
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Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers

Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers

We are interested in this work with a precise asymptotic description of the solution y ε when ε is small. As a first motivation, we mention that system (1) can be seen as a simple example of complex models where the diffusion coefficient is small compared to the others. Actually, as discussed in [5], the model problem (1) is an embedded system of the Navier-Stokes system with non-characteristic boundary condition and viscosity coefficient equals to ε. A second motivation comes from the numerical approximation of (1) that may be not straightforward for small values of ε (we refer to [8], [23]). A third motivation comes from the asymptotic controllability property of (1) studied in [7] and which exhibits surprising behaviors, leaving many open questions.
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Simulation of an avalanche in a fluid with a soft-sphere / immersed boundary method including a lubrication force

Simulation of an avalanche in a fluid with a soft-sphere / immersed boundary method including a lubrication force

The simulation presented in figures 6 and 7 were first repeated for two specific density ratios r p / r = 8 and 16 (St and Re varying in the abovementioned range) and one specific Reynolds number Re = 1, without any lubrication model (19). We plot in figure 8 the restitution coefficient e /e n = –V R /V T (see figure 7 for definitions) as a function of Stokes number (23). For comparison, we included available experiment data of the rebound of a spherical inclusion with a wall or another particle. While the numerical results are in good agreement with experimental data for St 200, the restitution coefficient is clearly overestimated at lower St. This can be attributed to the low resolution of the flow field when the gap between the particle and the wall is of the order of the grid size. As a consequence, the film pressure stemming from the drainage of the liquid in the gap is underestimated so the particle rebound is artificially enhanced. This issue is overcome when one adds a lubrication force (19) in (3). Figure 9 shows the results obtained with the coupled IBM- DEM method with the lubrication model (19) for the case r p / r = 8. The numerical results fall in the range of the experimental data.
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Compressible turbulent channel flow with impedance
boundary conditions

Compressible turbulent channel flow with impedance boundary conditions

The interaction between a boundary layer and wall-impedance is a classic problem in aeroacoustics. Numerous theoretical investigations by Rienstra and co-workers 2,8–10 , to- gether with some companion experimental efforts 11 , have looked at the stability properties of boundary layers over homogeneous IBCs. In particular, the presence of hydro-acoustic in- stabilities was predicted under specific conditions, which were deemed to be rarely found in aeronautical practice. Such instability occurs when wall-normal acoustic wave propagation (controlled by the IBCs) becomes hydrodynamically significant. This type of instability has been reproduced in the present work, in a fully developed compressible turbulent flow, by tuning the characteristic resonant frequency of a mass-spring-damper model for the IBCs (a damped Helmholtz oscillator) to the characteristic hydrodynamic time scale of the flow. While the present results are purely numerical, experimental proof of concept of the pro- posed flow control strategy has already been successful obtained in the context of laminar flow separation control over an airfoil by Yang and Spedding 12 .
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