[[CfdTm.ResearchSummary0009][]]  :  

Improved modelling of ﬁre  Mahmoud Assad:  September 2009 
In highly nonequilibrium flows the mean strain and turbulent stresses can be significantly misaligned. Simple eddy viscosity models cannot capture this, but more expensive stress transport models can. The Cas model approximates effects of this misalignment in a computationally cheap manner, retaining some of the accuracy of more expensive schemes. The highly unsteady flow behind an aerofoil at 20 degrees incidence shows promising results.
%BEGINLATEX% \begin{align} \tau^r_{ij}\frac{2}{3}\tau_{kk}\delta_{ij} =& \underbrace{2 f_b \nu_r ( \overline{S}_{ij}\langle \overline{S}_{ij} \rangle)}_{\mbox{\small{locally isotropic}}} \underbrace{ 2(1f_b)\nu_a \langle \overline{S}_{ij} \rangle}_{\mbox{\small{inhomogeneous}}} \label{eq:tauhyb} \end{align} %ENDLATEX%
Here, %$\overline{S}_{ij}$% is the instantaneous filtered strain and %$ \langle \overline{S}_{ij} \rangle$% is the averaged one. The "locally isotropic" part is due to the large scale eddies and is proportional to the fluctuating velocities. The "inhomogeneous" part corresponds to the anisotropy introduced by the mean shear. The fluctuating contribution is modelled using a Smagorinsky turbulent viscosity %$\nu_r$% and the contribution due to the averaged field is modelled using the elliptic relaxation model %$\varphi  f$% to account for the near wall effects in the definition of the turbulent viscosity %$\nu_a$%. The blending function %$f_b$% is introduced to avoid double counting of the stresses. It varies smoothly from zero at the wall to one far from it. The averaged velocity field is obtained via a running average of the instantaneous velocity and it is used to calculate all the production and convection terms on the RANS equations.
This model takes into account the fact that the structures are not isotropic when the solid boundaries are approached and therefore eases the grid refinement requirements of a standard Smagorinsky LES calculation.
See more information here
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%BEGINLATEX{label="eq:one"}% \begin{align} \label{eq:sembase} \mathcal{U}_i(x_j,t) = \sqrt{\frac{V_b}{N}} \sum_{k=1}^{N} \varepsilon^{k}_i f_L(x_1x^{k}_1) f_L(x_2x^{k}_2) f_L(x_3x^{k}_3) \end{align} %ENDLATEX% where %$V_b$% is the volume of the 'box of eddies' B over which eddies are going to be generated, %$N$% is the number of eddies, %$L$% is the turbulence lengthscale and %$f_L$% is a symmetric function that characterises the decay of the fluctuations generated by each eddy about its centre. In the simulation presented here, the function %$f_L$% is a tent function which reads %BEGINLATEX% \begin{align} f_L(r)&= \sqrt{ \frac{3}{2L} }(1r/L)\ \ \mbox{ if } r\le L\ &=\ 0 \qquad \qquad \quad \mbox{otherwise} \end{align} %ENDLATEX% The turbulence lengthscale %$L$% is computed from %BEGINLATEX% \begin{align} L=\max (k^{3/2}/\varepsilon,\Delta) \end{align} %ENDLATEX% where %$\Delta=\max(\Delta x, \Delta y, \Delta z)$% in order for the synthetic structures generated at the inlet to be discretised on the computational mesh. The intensity of the fluctuations %$\varepsilon^{(k)}_i$% are taken from independent normal distribution %$N(0,1)$%. The initial position of each eddy %$k$% is taken from a uniform distribution over a 'box of eddies' B defined by %BEGINLATEX% \begin{equation*} B=\{ (x_i)\in \mathbb{R}^3,\ \ \ x_{i,\min} < x_i < x_{i,\max} \}, \end{equation} %ENDLATEX% where %BEGINLATEX% \begin{equation*} x_{i,\min} = \min_{x\in P} (x_iL) \quad \mbox{and} \quad x_{i,\max} = \max_{x\in P} (x_i+L) \end{equation} %ENDLATEX% and %$P$% is the inlet plane where the velocity fluctuations are computed. In order for the synthetic signal to be correlated in time, the eddies are convected through the inlet plane with the bulk velocity %$U_b$% over the boundary layer %BEGINLATEX% \begin{align} x^{k}_1(t+dt)=x^{k}_1(t)+U_b\ dt. \end{align} %ENDLATEX% Once an eddy is convected outside of the box, it is regenerated upstream and its intensities %$\varepsilon^{(k)}_i$% are drawn again. The signal computed from equation (%REFLATEX{eq:one}%) has spatial and temporal correlations and satisfies %$\langle u_i\rangle =0$% and %$\langle u_iu_j\rangle =\delta_{ij}$%. It can be modified as follow %BEGINLATEX% \begin{align}\label{eq:reconstruction} u_i = \langle U_i\rangle + a_{ij}\mathcal{U}_j, \end{align} %ENDLATEX% where %$\langle U_j\rangle$% is a target mean velocity profile and %$a_{ij}$% is the Cholesky decomposition of a target Reynolds stress tensor %$R_{ij}$%.
The thesis of Sofiane Berrouk investigates turbulent particleladen Large eddy Simulation (LES). It adapts a Langevintype stochastic diffusion process that models inertial particle transport by the subfilter (subgrid scale) motion for hybrid EulerianLagrangian LES. This modelling is particularly crucial for dispersion and deposition of inertial particles with small relaxation times compared to the smallest LESresolved turbulence time scales. When generating stochastically subfilter turbulent fluctuations, particle inertia and cross trajectory effects should be taken into account to properly model the time increment of fluid velocity seen by inertial particles along their trajectories. The performance of LES using this stochastic model is compared to LES that uses only the filtered velocity field and to RANS using the same stochastic model.
Simulation findings of small inertial particle dispersion and deposition in lightlyloaded particleladen turbulent pipe and bend flows demonstrate the superiority of LES compared to RANS in predicting particle dispersion and deposition statistics. More importantly, the use of a stochastic approach to model the subfilter scale fluctuations has proven crucial for results concerning the smallStokesnumber particles. The performance of the model for highlyloaded particlefluid flows needs to be assessed and additional validations for nonequilibrium turbulent flows are required. .
Year  Title 

2011  I. Afgan, Y. Kahil, S. Benhamadouche and P. Sagaut: Large eddy simulation of the flow around single and two sidebyside cylinders at subcritical Reynolds numbers. Physics of Fluids ,2011 
2010  S. Rolfo , J. C. Uribe, D. Laurence: LES and Hybrid RANS/LES of turbulent flow in fuel rod bundle in a triangular array. Direct and LargeEddy Simulation VII ,2010 
2010  Billard, F. and Laurence, D. and Uribe, J.: An improved dissipation rate equation for the v2f model to account for turbulent transport mechanism in a boundary layer. ETMM8 ,2010 
2010  J. Uribe, N. Jarrin, R. Prosser, D. Laurence: Development of a Twovelocities Hybrid RANSLES Model and its Application to a Trailing Edge Flow. Journal of Flow Turbulence and Combustion (DOI: 10.1007/s1049401092636) ,2010 
2010  R. Poletto, A. Revell, T. Craft, N. Jarrin: Towards a DFSEM (abstract). TSFP ,2010 
2009  JP. Chabard, D. Laurence: Heat and fluid flow simulations for deciding tomorrow's energies. (THMT6)Turbulence, Heat and Mass Transfer 6, 1418 September 2009, Rome. ,2009 
2009  N. Jarrin , R. Prosser , J. Uribe , S. Benhamadouche, D. Laurence: Reconstruction of Turbulent Fluctuations for Hybrid RANSLES simulations using a synthetic Eddy Method. Int. Journal of Heat and Fluid Flow ,2009 
2009  C. Péniguel, I. Rupp, JP. Juhel, S. Rolfo, M. Guillaud, N. Gervais: Three Dimensional Conjugated Heat Transfer Analysis in Sodium Fast Reactor WireWrapped Fuel Assembly. Proceedings of ICAPP ‘09 Tokyo, Japan, May 1014, 2009 Paper 9311 ,2009 
2009  J. Uribe, A. Revell, C. Moulinec, V. Kitsios, A. Ooi, and J. Soria. : Computation of ﬂow around a naca 0015 aerofoil with znmf jet control: Potential savings of an unstructured mesh?. 6th International Symposium on Turbulence and Shear Flow Phenomena., Seoul, Korea, ,2009 
2009  Moulinec, C., Sunderland, A. G., Emerson, D., Gu, X., Fournier, Y., Uribe, J. C.: Developing a Petaflop Computational Fluid Dynamics Capability for Energy and Environment. International conference on parallel, distributed and grid computing for engineering ,2009 
2009  C. Turner and R. Prosser: The application of laminar kinetic energy to laminarturbulent transition prediction. 6th Turbulence, Heat and Mass Transfer conference, Rome, Italy ,2009 
2008  N. Jarrin, J. C. Uribe, R. Prosser and D. Laurence: Synthetic Inflow boundary conditions for wall bounded flows. Notes on Numerical fluid mechanics and multidisciplinary designAdvances in Hybrid RANSLES models (S.H. Peng and W. Haase eds.) ,2008 
2008  A. S. Berrouk, D. Laurence: Stochastic modelling of aerosol deposition for LES of 90° bend turbulent flow. International Journal of Heat and Fluid Flow ,2008 
2008  A. S. Berrouk, D. E. Stock, D. Laurence, J. J. Riley: Heavy particle dispersion from a point source in turbulent pipe flow. International Journal of Multiphase Flow ,2008 
2008  Billard, F. Uribe, J.C. and Laurence, D.: A new formulation of the %$\overline{v^2}f$% model using elliptic blending and its application to heat transfer prediction. Proc. of 7th Int. Symp. on Engineering Turbulence Modelling and Measurements ,2008 
2008  A.G. Sunderland, M. Ashworth, N. Li, C. Moulinec, Y. Fournier and J. Uribe: Towards Petascale Computing with Parallel CFD codes. _Parallel CFD 2008, May 1922, 2008, Lyon, France _ ,2008 
2007  Berrouk AS, Laurence D, Riley JJ, et al.: Stochastic modeling of fluid velocity seen by heavy particles for twophase LES of nonhomogeneous and anisotropic turbulent flows . _JOURNAL OF TURBULENCE _ ,2007 
2007  Berrouk AS, Laurence D, Riley JJ, et al.: Stochastic modeling of fluid velocity seen by heavy particles for twophase LES of nonhomogeneous and anisotropic turbulent flows . ERCOFTAC SERIES Euromech Colloquium 477: ParticleLaden Flow, JUN 2123, 2006 Univ Twente, Enschede, NETHERLANDS ,2007 
2007  Uribe, J. C., Jarrin, N., Prosser, R. and Laurence, D.: Two Velocities hybrid RANSLES of a trailing edge flow. _IUTAM Symposium "Unsteady Separated Flows and their Control"  Corfu Greece June 2007, _ ,2007 
2007  Uribe, J.C., Jarrin, N., Prosser, R. and Laurence, D.: Hybrid V2F RANS LES model and synthetic inlet turbulence applied to a trailing edge flow. Turbulence and Shear Flow Phenomena 5 ,2007 
2007  M. Aounallah, Y. Addad, S. Benhamadouche, O. Imine, L. Adjlout, D. Laurence : Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall. Int. J. Heat & Mass Transfer ,2007 
2007  Revell A, Duraisamy K, Iaccarino G: Advanced Turbulence modelling of wingtip vortices. Turbulence and Shear Flow Phenomena TSPF5, Munich. Germany. 27 August 2007 ,2007 
2007  Revell A, Craft T J, Laurence D R P.: Turbulence modelling of Strongly Detached Unsteady Flows: The Circular Cylinder. Second Symposium on Hybrid RANSLES Methods, Corfu, Greece.. 17 June 2007 ,2007 
2006  Revell, A.J., Benhamadouche, S., Craft, T.J., Laurence, D.R.: A stressstrain lag eddy viscosity model for unsteady mean flow. Int. J. Heat Fluid Flow ,2006 
2006  Jarrin, N., Benhamadouche, S., Laurence, D. and Prosser, R.: A syntheticeddy method for generating inflow conditions for LES. Int. J. Heat and Fluid Flow ,2006 
2006  S. Benhamadouche, N. Jarrin, Y. Addad, D. Laurence: Synthetic turbulent inflow conditions based on a vortex method for largeeddy simulation. PCFD, Int. Journal ,2006 
2006  Revell A, Craft T J, Laurence D R P: A stressstrain lag EVM for mean unsteady and nonequilibrium flows. Code_Saturne User Conference, Paris, France.. November 2006 ,2006 
2006  Uribe J, Utyuzhnikov S V, Revell A, Gerasimov A, Laurence D R P.: Methods used and highlighted results from UMIST. . "FLOMANIA — A European Initiative on Flow Physics Modelling". . Springer. ISBN 9783540287865. 2006 ,2006 
2005  Benhamadouche S., Laurence D., Jarrin N., Afgan I., Moulinec C.: Large Eddy Simulation of flow across inline tube bundles.. _NURETH11 (Nuclear Reactor ThermalHydraulics), Avignon FR, Oct. 2005 _ ,2005 
2005  Benhamadouche, S., Uribe, J., Jarrin, N., Laurence, D.: Large Eddy Simulation of a symmetric bump on structured and unstructured grids, comparisons with RANS and TRANS models.. Turbulence and Shear Flow Phenomena 4 ,2005 
2005  Revell A, Craft T J, Laurence D R P.: Development and implementation of the three equation stressstrain lag turbulence model. Code_Saturne User Conference, Paris, France. November 2005 ,2005 
2005  Revell A, Benhamadouche S, Craft T J, Laurence D R P, Yaqobi K.: A stressstrain lag eddy viscosity model for unsteady mean flow. Engineering Turbulence Modelling and Experiments 6: ERCOFTAC International Symposium on Engineering Turbulence and Measurements  ETMM6, Sardinia, Italy.. Editor W. Rodi, M. Mulas, eds.. 22 May 2005 ,2005 
2004  Laurence, D. Uribe, J. C. and Utyuzhnikov, S. V.: A robust formulation of the v2f model. Flow Turbulence and Combustion ,2004 
2004  Addad Y., Benhamadouche S., and Laurence D.: The negatively buoyant walljet: LES database. _Int. J. Heat fluid Flow _ ,2004 
2003  Addad Y., Benhamadouche S., and Laurence D.: The negatively buoyant walljet: LES database. 4th Int. Symposium on THMT, Turkey, 1217 October ,2003 
2003  Jarrin N., Benhamadouche S., Addad Y., Laurence D.: Synthetic turbulence inflow conditions for largeeddy simulation. 4th Int. Symposium on THMT, Turkey ,2003 
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