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Dehoux, F., Benhamadouche, S. and Manceau, R. An elliptic blending differential flux model for natural, mixed and forced convection 2017 Int. J. Heat Fluid Fl.
Vol. 63, pp. 190-204 
DOI PDF 
Abstract: Several modifications are introduced to the Elliptic Blending Differential Flux Model proposed by Shin et al. (2008) to account for the influence of wall blockage on the turbulent heat flux. These modifications are introduced in order to reproduce, in association with the most recent version of the EB-RSM, the full range of regimes, from forced to natural convection, without any case-specific modification. The interest of the new model is demonstrated using analytical arguments, a priori tests and computations in channel flows in the different convection regimes, as well as in a differentially heated cavity.
BibTeX:
@article{Dehoux2017,
  author = {Dehoux, F. and Benhamadouche, S. and Manceau, R.},
  title = {An elliptic blending differential flux model for natural, mixed and forced convection},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2017},
  volume = {63},
  pages = {190-204},
  doi = {http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.09.003}
}
de Laage de Meux, B., Audebert, B., Manceau, R. and Perrin, R. Anisotropic Linear Forcing for synthetic turbulence generation in LES and hybrid RANS/LES modeling 2015 Phys. Fluids
Vol. 27(035115) 
DOI PDF 
Abstract: A general forcing method for Large Eddy Simulation (LES) is proposed for the purpose of providing the flow with fluctuations that satisfy a desired statistical state. This method, the Anisotropic Linear Forcing (ALF) introduces an unsteady linear tensor function of the resolved velocity which acts as a restoring force in the mean velocity and resolved stress budgets. The ALF generalizes and extends several forcing previously proposed in the literature. In order to make it possible to impose the integral length scale of the turbulence generated by the forcing term, an alternative formulation of the ALF, using a differential spatial filter, is proposed and analyzed. The anisotropic forcing of the Reynolds stresses is particularly attractive, since unsteady turbulent fluctuations can be locally enhanced or damped, depending on the target stresses. As such, it is shown that the ALF is an effective method to promote turbulent fluctuations downstream of the LES inlet or at the interface between RANS and LES in zonal hybrid RANS/LES modeling. The detailed analysis of the influence of the ALF parameters in spatially developing channel flows and hybrid computations where the ALF target statistics are given by a RANS second-moment closure show that this original approach performs as well as the synthetic eddy method. However, since the ALF method is more flexible and significant computational savings are obtained, the method appears a promising all-in-one solution for general embedded LES simulations.
BibTeX:
@article{DeLaageDeMeux2015,
  author = {de Laage de Meux, B. and Audebert, B. and Manceau, R. and Perrin, R.},
  title = {Anisotropic Linear Forcing for synthetic turbulence generation in LES and hybrid RANS/LES modeling},
  journal = {Phys. Fluids},
  year = {2015},
  volume = {27},
  number = {035115},
  doi = {http://dx.doi.org/10.1063/1.4916019}
}
Friess, C., Manceau, R. and Gatski, T. Toward an equivalence criterion for hybrid RANS/LES methods 2015 Comput. Fluids
Vol. 122, pp. 233-246 
DOI PDF 
Abstract: A criterion is established to assess the equivalence between hybrid RANS/LES methods, called H-equivalence, based on the modeled energy of the unresolved scales, which leads to similar low-order statistics of the resolved motion. Different equilibrium conditions are considered, and perturbation analyses about the equilibrium states are performed. The procedure is applied to demonstrate the equivalence between two particular hybrid methods, and leads to relationships between hybrid method parameters that control the partitioning of energy between the resolved and unresolved scales of motion. This equivalence is validated by numerical results obtained for the cases of plane and periodically constricted channel flows. This concept of H-equivalence makes it possible to view different hybrid methods as models for the same system of equations: as a consequence, detached-eddy simulation (DES), which is shown to be H-equivalent to the temporal partially integrated transport model (T-PITM) in inhomogeneous, stationary situations, can be interpreted as a model for the subfilter stress involved in the temporally filtered Navier-Stokes equations.
BibTeX:
@article{Friess2015,
  author = {Friess, Ch. and Manceau, R. and Gatski, T.B.},
  title = {Toward an equivalence criterion for hybrid RANS/LES methods},
  journal = {Comput. Fluids},
  year = {2015},
  volume = {122},
  pages = {233-246},
  doi = {http://dx.doi.org/10.1016/j.compfluid.2015.08.010}
}
Manceau, R. Recent progress in the development of the Elliptic Blending Reynolds-stress model 2015 Int. J. Heat Fluid Fl.
Vol. 51, pp. 195-220 
DOI PDF 
Abstract: The Elliptic Blending Reynolds Stress Model (EB-RSM), originally proposed by Manceau and Hanjalic (2002) to extend standard, weakly inhomogeneous Reynolds stress models to the near-wall region, has been subject to various modifications by several authors during the last decade, mainly for numerical robustness reasons. The present work revisits all these modifications from the theoretical standpoint and investigates in detail their influence on the reproduction of the physical mechanisms at the origin of the influence of the wall on turbulence. The analysis exploits recent DNS databases for high-Reynolds number channel flows, spanwise rotating channel flows with strong rotation rates, up to complete laminarization, and the separated flow after a sudden expansion without and with system rotation. Theoretical arguments and comparison with DNS results lead to the selection of a recommended formulation for the EB-RSM model. This formulation shows satisfactory predictions for the configurations described above, in particular as regards the modification of the mean flow and turbulent anisotropy on the anticyclonic or pressure side.
BibTeX:
@article{Manceau2015,
  author = {Manceau, R.},
  title = {Recent progress in the development of the Elliptic Blending Reynolds-stress model},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2015},
  volume = {51},
  pages = {195-220},
  doi = {http://dx.doi.org/10.1016/j.ijheatfluidflow.2014.09.002}
}
Manceau, R., Perrin, R., Hadžiabdić, M. and Benhamadouche, S. Investigation of the interaction of a turbulent impinging jet and a heated, rotating disk 2014 Phys. Fluids
Vol. 26(3) 
DOI PDF 
Abstract: The case of a turbulent round jet impinging perpendicularly onto a rotating, heated disc is investigated, in order to understand the mechanisms at the origin of the influence of rotation on the radial wall jet and associated heat transfer. The present study is based on the complementary use of an analysis of the orders of magnitude of the terms of the mean momentum and Reynolds stress transport equations, available experiments and dedicated Reynolds-Averaged Navier-Stokes (RANS) computations with refined turbulence models. The Reynolds number Rej = 14,500, the orifice-to-plate distance H =5 D, where D is the jet-orifice diameter, and the four rotation rates were chosen to match the experiments of Minagawa and Obi [``Development of turbulent impinging jet on a rotating disk,'' Int. J. Heat Fluid Fl. 25, 759-766 (2004)] and comparisons are made with the Nusselt number distribution measured by Popiel and Boguslawski [``Local heat transfer from a rotating disk in an impinging round jet,'' J. Heat Transf. 108, 357-364 (1986)], at a higher Reynolds number. The overestimation of turbulent mixing in the free-jet before the impact on the disk is detrimental to the prediction of the impingement region, in particular of the Nusselt number close to the symmetry axis, but the self-similar wall jet developing along the disk is correctly reproduced by the models. The analysis, experiments and computations show that the rotational effect do not directly affect the outer layer, but only the inner layer of the wall jet. A noteworthy consequence is that entrainment at the outer edge of the wall jet is insensitive to rotation, which explains the dependence of the wall-jet thickness on the inverse of the non-dimensional rotation rate, observed in the experiments and the Reynolds stress model computations, but not reproduced by the eddy-viscosity models, due to the algebraic dependence to the mean flow. The analysis makes moreover possible the identification of a scenario for the appearance of rotational effects when the rotation rate is gradually increased. For weak rotation rates, the rotation-induced boundary layer appears but does not break the self-similar solution observed for the case without rotation. For intermediate rotation rates, the production of the azimuthal Reynolds stress becomes much stronger than other components, leading to a complete modification of the turbulence anisotropy which is reproduced only by Reynolds stress models. For strong rotation rates, centrifugal effects dominate, leading to an acceleration and thinning of the jet, and consequently an increase of turbulent production and heat transfer, reproduced by all the turbulence models.
BibTeX:
@article{Manceau2014,
  author = {Manceau, R. and Perrin, R. and Hadžiabdić, M. and Benhamadouche, S.},
  title = {Investigation of the interaction of a turbulent impinging jet and a heated, rotating disk},
  journal = {Phys. Fluids},
  year = {2014},
  volume = {26},
  number = {3},
  doi = {http://dx.doi.org/10.1063/1.4867380}
}
Dehoux, F., Lecocq, Y., Benhamadouche, S., Manceau, R. and Brizzi, L.-E. Algebraic modeling of the turbulent heat fluxes using the elliptic blending approach. Application to forced and mixed convection regimes 2012 Flow Turbul. Combust.
Vol. 88(1), pp. 77-100 
DOI PDF 
Abstract: The present paper focuses on the application of the elliptic blending approach to the modeling of turbulent heat fluxes, in order to account for the influence of solid boundaries. The analytical justification of the extension to the temperature-pressure gradient correlation term of this approach, originally applied to the velocity-pressure gradient, is given. The assumption of weak equilibrium enables the derivation of two new algebraic flux models valid down to the wall. It is shown, with both a priori tests and computations in forced and mixed convection regimes, that the predictions of the streamwise heat-flux and the temperature variance are significantly improved by the use of elliptic blending. A particular attention is devoted to the issue of the modeling of the correlation length scale involved in the elliptic blending for the heat fluxes, which is shown to have a significant influence on the predictions.
BibTeX:
@article{Dehoux2012,
  author = {Dehoux, F. and Lecocq, Y. and Benhamadouche, S. and Manceau, R. and Brizzi, L.-E.},
  title = {Algebraic modeling of the turbulent heat fluxes using the elliptic blending approach. Application to forced and mixed convection regimes},
  journal = {Flow Turbul. Combust.},
  year = {2012},
  volume = {88},
  number = {1},
  pages = {77-100},
  doi = {http://dx.doi.org/10.1007/s10494-011-9366-8}
}
Fadai-Ghotbi, A., Friess, C., Manceau, R. and Borée, J. A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending 2010 Phys. Fluids
Vol. 22(055104) 
DOI PDF 
Abstract: The aim of the present work is to develop a seamless hybrid Reynolds-averaged Navier-Stokes (RANS) large-eddy simulation (LES) model based on transport equations for the subgrid stresses, using the elliptic-blending method to account for the nonlocal kinematic blocking effect of the wall. It is shown that the elliptic relaxation strategy of Durbin is valid in a RANS (steady) as well as a LES context (unsteady). In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive zone of the turbulent energy spectrum, the model is based on transport equations for the subgrid-stress tensor. The partially integrated transport model (PITM) methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber kappac, and thus the transition from RANS to LES, by making the Ceps2 coefficient in the dissipation equation of a RANS model a function of kappac. The equivalence between the PITM and the Smagorinsky model is shown when kappac is in the inertial range of the energy spectrum. The extension of the underlying RANS model used in the present work, the elliptic-blending Reynolds-stress model, to the hybrid RANS-LES context, brings out some modeling issues. The different modeling possibilities are compared in a channel flow at Retau=395. Finally, a dynamic procedure is proposed in order to adjust during the computation the dissipation rate necessary to drive the model toward the expected amount of resolved energy. The final model gives very encouraging results in comparison to the direct numerical simulation data. In particular, the turbulence anisotropy in the near-wall region is satisfactorily reproduced. The contribution of the resolved and modeled fields to the Reynolds stresses behaves as expected: the modeled part is dominant in the near-wall zones (RANS mode) and decreases toward the center of the channel, where the relative contribution of the resolved part increases. Moreover, when the mesh is modified, the amount of resolved energy changes but the total Reynolds stresses remain nearly constant.
BibTeX:
@article{FadaiGhotbi2010,
  author = {Fadai-Ghotbi, A. and Friess, Ch. and Manceau, R. and Borée, J.},
  title = {A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending},
  journal = {Phys. Fluids},
  year = {2010},
  volume = {22},
  number = {055104},
  doi = {http://dx.doi.org/10.1063/1.3415254}
}
Fadai-Ghotbi, A., Friess, C., Manceau, R., Gatski, T. and Borée, J. Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence 2010 Int. J. Heat Fluid Fl.
Vol. 31(3), pp. 378-389 
DOI PDF 
Abstract: A consistent formalism is developed for seamless hybrid RANS-LES models in inhomogeneous, stationary flows, based on Eulerian temporal filtering. The issues of Galilean invariance of the filtering process and consistency with the Reynolds average are addressed. The similarity of the RANS and TLES equations suggests the use of the same form of model for the two limiting approaches. The inconsistency of the existing TLES models with the RANS limit leads to the choice of the opposite strategy: adapting a RANS model to the TLES limit. The method proposed to achieve this adaptation is the Temporal Partially Integrated Transport Model (TPITM), a temporal version of the spatial PITM. The applicability of the method is shown by performing channel flow simulations using transport equations for the subfilter stresses, derived from the Elliptic-Blending Reynolds-Stress RANS Model (EB-RSM). Finally, the fact that the temporal filter width can be implicitly defined by the associated spatial filter width suggests that most of the unsteady approaches used in everyday applications, such as DES, SAS, URANS, among others, can be regarded as temporally filtered approaches.
BibTeX:
@article{FadaiGhotbi2010b,
  author = {Fadai-Ghotbi, A. and Friess, Ch. and Manceau, R. and Gatski, T.B. and Borée, J.},
  title = {Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2010},
  volume = {31},
  number = {3},
  pages = {378-389},
  doi = {http://dx.doi.org/10.1016/j.ijheatfluidflow.2009.12.008}
}
Fadai-Ghotbi, A., Manceau, R. and Borée, J. Revisiting URANS computations of the backward-facing step flow using second moment closures. Influence of the numerics. 2008 Flow Turbul. Combust.
Vol. 81(3), pp. 395-414 
DOI PDF 
Abstract: Previous studies have shown that Unsteady Reynolds-Averaged Navier-Stokes (URANS) computations are able to reproduce the vortex shedding behind a backward-facing step. The aim of the present work is to investigate not only the quantitative predictions of the URANS methodology concerning the characteristic frequencies, but also the amplitude of the energy of the resolved eddies, by using the Elliptic Blending Reynolds Stress Model. This innovative low-Reynolds number second moment closure reproduces the non-viscous, non-local blocking effect of the wall on the Reynolds stresses, and it is compared to the standard k-epsilon and LRR models using wall-functions. Consistent with previous studies, in the 2D computations shown in the present article, the vortex shedding is captured with the correct Strouhal number, when second moment closures are used. To complete these previous analyses, we particularly focus here on the energy contained in the unsteady, resolved part and its dependency on the numerical method. This energy is less than 5% of the total energy and is strongly dependent on the mesh. Using a refined mesh, surprisingly, a steady solution is obtained. It is shown that this behaviour can be linked to the very small spatial oscillations at the step corner, produced by numerical dispersion, which act as perturbations that are sufficient to excite the natural mode of the shear layer, when the local Peclet number, comparing convection and diffusion effects, is high enough. This result suggests that URANS is not appropriate to quantitatively predict the amplitude of the large-scale structures developing in separated shear-layers, and that URANS results must be interpreted with care in terms of temporal variations of forces, temperatures, etc., in industrial applications using marginally fine meshes.
BibTeX:
@article{FadaiGhotbi2008,
  author = {Fadai-Ghotbi, A. and Manceau, R. and Borée, J.},
  title = {Revisiting URANS computations of the backward-facing step flow using second moment closures. Influence of the numerics.},
  journal = {Flow Turbul. Combust.},
  year = {2008},
  volume = {81},
  number = {3},
  pages = {395-414},
  doi = {http://dx.doi.org/10.1007/s10494-008-9140-8}
}
Perret, L., Delville, J., Manceau, R. and Bonnet, J.-P. Turbulent inflow conditions for large-eddy simulation based on low-order empirical model 2008 Phys. Fluids
Vol. 20(7), pp. 1-17 
DOI PDF 
Abstract: Generation of turbulent inflow boundary conditions is performed by interfacing an experimental database acquired by particle image velocimetry to a computational code. The proposed method ensures that the velocity fields introduced as inlet conditions in the computational code present correct one- and two-point spatial statistics and a realistic temporal dynamics. This approach is based on the use of the proper orthogonal decomposition (POD) to interpolate and extrapolate the experimental data onto the numerical mesh and to model both the temporal dynamics and the spatial organization of the flow in the inlet section. Realistic representation of the flow is achieved by extracting and modeling independently its coherent and incoherent parts. A low-order dynamical model is derived from the experimental database in order to provide the temporal evolution of the most energetic structures. The incoherent motion is modeled by employing time series of Gaussian random numbers to mimic the temporal evolution of higher order POD modes. Validation of the proposed method is provided by performing a large-eddy simulation of a turbulent plane mixing layer, which is compared to experimental results.
BibTeX:
@article{Perret2008,
  author = {Perret, L. and Delville, J. and Manceau, R. and Bonnet, J.-P.},
  title = {Turbulent inflow conditions for large-eddy simulation based on low-order empirical model },
  journal = {Phys. Fluids},
  year = {2008},
  volume = {20},
  number = {7},
  pages = {1-17},
  doi = {http://dx.doi.org/10.1063/1.2957019}
}
Gatski, T.B., Rumsey, C.L. and Manceau, R. Current Trends in Modeling Research for Turbulent Aerodynamic Flows 2007 Phil. Trans. R. Soc. A
Vol. 365(1859), pp. 2389-2418 
DOI PDF 
Abstract: The engineering tools of choice for the computation of practical engineering flows have begun to migrate from those based on the traditional Reynolds-averaged Navier-Stokes approach to methodologies capable, in theory if not in practice, of accurately predicting some instantaneous scales of motion in the flow. The migration has largely been driven by both the success of Reynolds-averaged methods over a wide variety of flows and the inherent limitations of the method itself. Practitioners, emboldened by their ability to predict a wide variety of statistically steady equilibrium turbulent flows, have now turned their attention to flow control and non-equilibrium flows, i.e. separation control. This review gives some current priorities in traditional Reynolds-averaged modelling research as well as some methodologies being applied to a new class of turbulent flow control problem.
BibTeX:
@article{Gatski2007,
  author = {Gatski, T. B. and Rumsey, C. L. and Manceau, R.},
  title = {Current Trends in Modeling Research for Turbulent Aerodynamic Flows},
  journal = {Phil. Trans. R. Soc. A},
  year = {2007},
  volume = {365},
  number = {1859},
  pages = {2389-2418},
  doi = {http://dx.doi.org/10.1098/rsta.2007.2015}
}
Carpy, S. and Manceau, R. Turbulence modelling of statistically periodic flows: synthetic jet into quiescent air 2006 Int. J. Heat Fluid Fl.
Vol. 27, pp. 756-767 
DOI PDF 
Abstract: Computations of a 2D synthetic jet are performed with usual RANS equations solved in time-accurate mode (URANS), with the standard k-epsilon model and the Rotta + IP second moment closure. The purpose of the present work is to investigate the ability of these standard turbulence models to close the phase-averaged Navier-Stokes equations. Results are compared with recent experiments by Yao et al. made available to the CFD Validation of Synthetic Jets and Turbulent Separation Control workshop held in Williamsburg in 2004. Comparisons of the performance of the models with experimental data show that the evolution of the vortex dipole generated by inviscid mechanisms is not correctly reproduced by the k-? model. The Reynolds-stress model gives much more realistic predictions. However, several characteristics are not well predicted, as for instance the convection velocity. A detailed analysis shows that the vortex dipole dynamics is essentially inviscid during the early blowing phase, when the flow is more transitional than fully turbulent. Turbulence develops and influences the dynamics of the vortices only at a later stage of the blowing phase. Consequently, it is of importance that the turbulence models do not predict erroneously high levels of turbulence. In particular, the present study shows that the correct prediction of the region of negative production that appears during the deceleration of the blowing velocity, due to the misalignment of the strain and anisotropy tensors, is crucial. Therefore, linear eddy-viscosity models must be discarded for this type of pulsed flows, in particular for flow control using synthetic jets.
BibTeX:
@article{Carpy2006,
  author = {Carpy, S. and Manceau, R.},
  title = {Turbulence modelling of statistically periodic flows: synthetic jet into quiescent air},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2006},
  volume = {27},
  pages = {756-767},
  doi = {http://dx.doi.org/10.1016/j.ijheatfluidflow.2006.04.002}
}
Perret, L., Delville, J., Manceau, R. and Bonnet, J.-P. Generation of turbulent inflow conditions for LES from Stereoscopic PIV measurements 2006 Int. J. Heat Fluid Fl.
Vol. 27(4), pp. 576-584 
DOI PDF 
Abstract: A novel method to generate inflow data for unsteady numerical simulations is proposed. This method consists in coupling an experimental database obtained by stereoscopic PIV measurements which are under-resolved in time to a numerical code. Based on the proper orthogonal decomposition of this database, the proposed approach enables the adaptation of the experimental mesh to the grid of the simulation and the modelling of the temporal dynamics of the flow field in the inlet section by Gaussian random time series that present the correct one- and two-point statistics. To test this method, a LES of a turbulent plane mixing layer configuration is performed.
BibTeX:
@article{Perret2006,
  author = {Perret, L. and Delville, J. and Manceau, R. and Bonnet, J.-P.},
  title = {Generation of turbulent inflow conditions for LES from Stereoscopic PIV measurements},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2006},
  volume = {27},
  number = {4},
  pages = {576-584},
  doi = {http://dx.doi.org/10.1016/j.ijheatfluidflow.2006.02.005}
}
Thielen, L., Hanjalić, K., Jonker, H. and Manceau, R. Predictions of flow and heat transfer in multiple impinging jets with an elliptic-blending second-moment closure 2005 Int. J. Heat Mass Tran.
Vol. 48(8), pp. 1583-1598 
DOI  
Abstract: We present numerical computations of flow and heat transfer in multiple jets impinging normally on a flat heated surface, obtained with a new second-moment turbulence closure combined with an elliptic blending model of non-viscous wall blocking effect. This model provides the mean velocity and turbulent stress fields in very good agreement with PIV measurements. The exploration of several simpler closures for the passive thermal field, conducted in parallel, confirmed that the major prerequisite for the accurate prediction of the temperature field and heat transfer is to compute accurately the velocity and stress fields. If this is achieved, the conventional anisotropic eddy-diffusivity model can suffice even in complex flows. We demonstrate this in multiple-impinging jets where such a model combination provided the distribution of Nusselt number over the solid plate in good agreement with experiments. Extension of the elliptic blending concept to full second-moment treatment of the heat flux and its truncation to a quasi-linear algebraic model is also briefly discussed. © 2004 Elsevier Ltd. All rights reserved.
BibTeX:
@article{Thielen2005,
  author = {Thielen, L. and Hanjalić, K. and Jonker, H. and Manceau, R.},
  title = {Predictions of flow and heat transfer in multiple impinging jets with an elliptic-blending second-moment closure},
  journal = {Int. J. Heat Mass Tran.},
  year = {2005},
  volume = {48},
  number = {8},
  pages = {1583-1598},
  doi = {http://dx.doi.org/10.1016/j.ijheatmasstransfer.2004.10.025}
}
Manceau, R. and Hanjalić, K. Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure 2002 Phys. Fluids
Vol. 14(2), pp. 744-754 
DOI PDF 
Abstract: A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure-strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function ?, for which an elliptic equation is solved. The approach preserves the main features of Durbin's Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called "the elliptic blending model," offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Re T=590, the model was applied in the computation of the channel flow at a "real-life" Reynolds number of 10 6, showing a good prediction of the logarithmic profile of the mean velocity.
BibTeX:
@article{Manceau2002,
  author = {Manceau, R. and Hanjalić, K.},
  title = {Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure},
  journal = {Phys. Fluids},
  year = {2002},
  volume = {14},
  number = {2},
  pages = {744-754},
  doi = {http://dx.doi.org/10.1063/1.1432693}
}
Manceau, R., Carlson, J.R. and Gatski, T.B. A rescaled elliptic relaxation approach: neutralizing the effect on the log layer 2002 Phys. Fluids
Vol. 14(11), pp. 3868-3879 
DOI PDF 
Abstract: An alternative scaling for the relaxation function describing the velocity pressure-gradient correlation used in the elliptic relaxation procedure for both eddy-viscosity and Reynolds stress models is presented. While other alternatives have been proposed to neutralize the adverse effect on log-layer dynamics, they have relied on altering the original differential formulation. A simpler alternative is presented here that involves a rescaling of the relaxation function with the isotropic dissipation rate as well as the turbulent kinetic energy. Various comparative tests are made and the new rescaled formulation is shown to provide improved and accurate predictions for both the eddy-viscosity and Reynolds stress models.
BibTeX:
@article{Manceau2002b,
  author = {Manceau, R. and Carlson, J. R. and Gatski, T. B.},
  title = {A rescaled elliptic relaxation approach: neutralizing the effect on the log layer},
  journal = {Phys. Fluids},
  year = {2002},
  volume = {14},
  number = {11},
  pages = {3868-3879},
  doi = {http://dx.doi.org/10.1063/1.1511547}
}
Manceau, R., Wang, M. and Laurence, D. Inhomogeneity and anisotropy effects on the redistribution term in Reynolds-averaged Navier-Stokes modelling 2001 J. Fluid Mech.
Vol. 438, pp. 307-338 
DOI PDF 
Abstract: A channel flow DNS database at Retau = 590 is used to assess the validity of modelling the redistribution term in the Reynolds stress transport equations by elliptic relaxation. The model assumptions are found to be globally consistent with the data. However, the correlation function between the fluctuating velocity and the Laplacian of the pressure gradient, which enters the integral equation of the redistribution term, is shown to be anisotropic. It is elongated in the streamwise direction and strongly asymmetric in the direction normal to the wall, in contrast to the isotropic, exponential model representation used in the original elliptic relaxation model. This discrepancy is the main cause of the slight amplification of the energy redistribution in the log layer as predicted by the elliptic relaxation equation. New formulations of the model are proposed in order to correct this spurious behaviour, by accounting for the rapid variations of the length scale and the asymmetrical shape of the correlation function. These formulations do not rely on the use of so-called 'wall echo' correction terms to damp the redistribution. The belief that the damping is due to the wall echo effect is called into question through the present DNS analysis.
BibTeX:
@article{Manceau2001,
  author = {Manceau, R. and Wang, M. and Laurence, D.},
  title = {Inhomogeneity and anisotropy effects on the redistribution term in Reynolds-averaged Navier-Stokes modelling},
  journal = {J. Fluid Mech.},
  year = {2001},
  volume = {438},
  pages = {307-338},
  doi = {http://dx.doi.org/10.1017/S0022112001004451}
}
Picart, D., Manceau, R. and Fauré, J.-P. A penetroviscosimeter for Newtonian and visco-plastic fluids 2001 Instrum. Sci. Technol.
Vol. 29(3), pp. 169-184 
DOI  
Abstract: The penetration test has been widely used by engineers to characterize the behavior of materials such as soils, fresh concrete, or concentrated suspensions. These approaches provide related measurements to rheological properties by means of empirical parameters. The present paper, based on Bikerman's works,(1) describes an analytical method for a penetration test, for Newtonian or Binghamian fluids. Characteristics of the flow between the bowl and the plunger are determined using an end effect correction method. In the case of Newtonian fluids, the theoretical developments are validated by experiments on a standard material. The material density is also determined using the same measurements. For the Bingham behavior, the total set of equations is presented. The limiting cases of low and infinite velocity are studied and applied to a very concentrated suspension. The viscosity and the yield stress are compared to the results of capillary and vane shear experiments. The same order of magnitude is found. However, we show here that these properties are only equivalent ones for this material, due to the slip motion observed at the penetrometer walls.
BibTeX:
@article{Picart2001,
  author = {Picart, D. and Manceau, R. and Fauré, J.-P.},
  title = {A penetroviscosimeter for Newtonian and visco-plastic fluids},
  journal = {Instrum. Sci. Technol.},
  year = {2001},
  volume = {29},
  number = {3},
  pages = {169-184},
  doi = {http://dx.doi.org/10.1081/CI-100103464}
}
Ukeiley, L., Cordier, L., Manceau, R., Delville, J., Glauser, M. and Bonnet, J.-P. Examination of the Large-Scale Structures in a Turbulent Mixing Layer. Part 2: Dynamical Systems Model 2001 J. Fluid Mech.
Vol. 441, pp. 67-108 
DOI PDF 
Abstract: The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier-Strokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/ spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.
BibTeX:
@article{Ukeiley2001,
  author = {Ukeiley, L. and Cordier, L. and Manceau, R. and Delville, J. and Glauser, M. and Bonnet, J.-P.},
  title = {Examination of the Large-Scale Structures in a Turbulent Mixing Layer. Part 2: Dynamical Systems Model},
  journal = {J. Fluid Mech.},
  year = {2001},
  volume = {441},
  pages = {67-108},
  doi = {http://dx.doi.org/10.1017/S0022112001004803}
}
Manceau, R. and Hanjalić, K. A new form of the elliptic relaxation equation to account for wall effects in RANS modelling 2000 Phys. Fluids
Vol. 12(9), pp. 2345-2351 
DOI PDF 
Abstract: Different methods for improving the behavior in the logarithmic layer of the elliptic relaxation equation, which enable the extension of Reynolds stress models or eddy viscosity models down to the wall, are tested in a channel flow at Retau=590 and compared with direct numerical simulation (DNS) data. First, a priori tests are performed in order to confirm the improvement predicted by the theory, either with the Rotta+IP (isotropization of production) model or the Speziale-Sarkar-Gatski (SSG) model as the source term of the elliptic relaxation equation. The best form of the model is then used for full simulations, in Durbin second moment closure or in the frame of the v2 - f model. It is shown that the results can be significantly improved, in particular by using a formulation based on the refinement of the modeling of the two-point correlations involved in the redistribution term.
BibTeX:
@article{Manceau2000,
  author = {Manceau, R. and Hanjalić, K.},
  title = {A new form of the elliptic relaxation equation to account for wall effects in RANS modelling},
  journal = {Phys. Fluids},
  year = {2000},
  volume = {12},
  number = {9},
  pages = {2345-2351},
  doi = {http://dx.doi.org/10.1063/1.1287517}
}
Manceau, R., Parneix, S. and Laurence, D. Turbulent heat transfer predictions using the vvf model on unstructured meshes 2000 Int. J. Heat Fluid Fl.
Vol. 21(3), pp. 320-328 
DOI PDF 
Abstract: Durbin's three transport equation model, the so-called v2-f model, has been implemented in an industrial finite element code, N3S, developed at the research and development department of Ele ctricite de France, enabling the use of unstructured meshes. Validations by comparison with other co des have been performed in the cases of the channel flow at Retau = 395, and the backward-facing ste p at Re = 5100. The test case of the 2D periodic ribbed-channel flow has then been computed, without heat transfer at Re(H) = 37,200, and with a constant heat flux imposed at the ribbed-wall at Re(H) = 12,600. The results obtained show the ability of the model to predict accurately the enhancement o f heat transfer due to the ribs, which is of primary interest for industrial applications
BibTeX:
@article{Manceau2000b,
  author = {Manceau, R. and Parneix, S. and Laurence, D.},
  title = {Turbulent heat transfer predictions using the vvf model on unstructured meshes},
  journal = {Int. J. Heat Fluid Fl.},
  year = {2000},
  volume = {21},
  number = {3},
  pages = {320-328},
  doi = {http://dx.doi.org/10.1016/S0142-727X(00)00016-3}
}
Picart, D., Manceau, R. and Fauré, J.-P. Characterization of paste extrudable explosives using a penetration test 1999 Propellants, explosives, pyrotechnics
Vol. 24, pp. 227-231 
 
Abstract: Penetration tests have been widely used to investigate the behavior of concentrated suspensions. Unfortunately, empirical parameters were introduced to relate measurements to material rheological parameters such as viscosity or yield stress. On the contrary, this paper describes an analytical method available for viscoplastic materials (Bingham constitutive law). A comparison is made, for an explosive paste, between this approach and some others rheological techniques. At last, the proposed method is used to analyse the influence of the paste components on the flow of high concentrated explosive suspensions.
BibTeX:
@article{Picart1999,
  author = {Picart, D. and Manceau, R. and Fauré, J.-P},
  title = {Characterization of paste extrudable explosives using a penetration test},
  journal = {Propellants, explosives, pyrotechnics},
  year = {1999},
  volume = {24},
  pages = {227-231}
}
Cordier, L., Manceau, R., Delville, J. and Bonnet, J.-P. Sur la relation entre la théorie de la stabilité linéaire et la décomposition orthogonale aux valeurs propres : cas de la couche de mélange plane turbulente 1997 C. R. Acad. Sci. Paris
Vol. 324(IIb), pp. 551-557 
DOI PDF 
Abstract: We develop a low-order dynamical system to model the dynamics of quasi two-dimensional coherent structures in the plane mixing layer. This system is obtained by a Galerkin projection of the Euler equations onto the first proper orthogonal decomposition (POD) mode. We point out that the first POD mode alone includes the main linear instability of the flow.
BibTeX:
@article{Cordier1997,
  author = {Cordier, L. and Manceau, R. and Delville, J. and Bonnet, J.-P.},
  title = {Sur la relation entre la théorie de la stabilité linéaire et la décomposition orthogonale aux valeurs propres : cas de la couche de mélange plane turbulente},
  journal = {C. R. Acad. Sci. Paris},
  year = {1997},
  volume = {324},
  number = {IIb},
  pages = {551-557},
  doi = {http://dx.doi.org/10.1016/S1251-8069(97)83188-0}
}