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R. Poletto¹, A. Revell, T. Craft, N. Jarrin Towards a DF-SEM University of Manchester 5 May 2010 Email: [email protected] R. Poletto – Towards a DF-SEM 1 RANS 1 – Method description 2 – DFSEM development 3 – Code_Saturne ➢ ` LES A – Introduction B – Method scheme C – Fluctuating velocities Inlet condition for the LES, to couple RANS and LES, requires the creation of a synthetic turbulent velocity field from a previous RANS solutions Define the area where it is necessary to use the LES ➢ Obtain a RANS solution at the inlet (velocity profile, k, ε, ω, …) ➢ Use this solution to activate any synthetic turbulence method and create the LES inlet - Periodic ChanFlow - Random numbers - Vortex method - Spectral method - Turb. fluctuations - SEM - DFSEM ... No inlet. We solve LES as long as we get a periodic profile Applies some random generated fluctuation Uses the vorticity to define the v-w inlet velocity components Fluctuations are generated using trigonometric functions It defines cosinusoidal fluctuations in each directions An eddies distribution creates the fluctuations As SEM, but the eddies create divergence free velocities ... R. Poletto – Towards a DF-SEM 2 1 – Method description 2 – DFSEM development 3 – Code_Saturne A – Introduction B – Method scheme C – Fluctuating velocities Create a random set of points (eddies centres) and calculate for each of them some characteristics (σ, Reynolds stresses) Calculate the fluctuating velocities using the generated eddies positions Convect the eddies positions R. Poletto – Towards a DF-SEM 3 1 – Method description 2 – DFSEM development 3 – Code_Saturne A – Introduction B – Method scheme C – Fluctuating velocities SEM the ck takes into account the Lund coefficients → complete reconstruction of the Reynolds stresses statistics fσ is a shape function → defines the velocity distribution around the eddy centres xk DFSEM the cross product makes the method divergence free qσ is a shape function and it must have the following characteristics: dependent only on rk R. Poletto – Towards a DF-SEM 4 1 – Method description 2 – DFSEM development 3 – Code_Saturne A – Introduction B – Method scheme C – Fluctuating velocities Vb = Eddy box volume N = Eddy number Stream function We need the stream function, whose Laplacian is the vorticity field and whose rotor is the velocity field σ = Eddy lengh scale α = Eddy intensity gσ = Eddy shape function Vorticity rotor We can eliminate the second term, since we want a divergence free velocity Green Function R. Poletto – Towards a DF-SEM In the DF-SEM we basically apply the SEM fluctuations to the vorticity field instead of the velocity field. Then, from the synthetic vorticity field we calculate a Divergence Free velocity field 5 1 – Method description 2 – DFSEM development 3 – Code_Saturne A – Introduction B – Method scheme C – Fluctuating velocities Vb = Eddy box volume N = Eddy number Stream function We need the stream function, whose Laplacian is the vorticity field and whose rotor is the velocity field σ = Eddy lengh scale α = Eddy intensity gσ = Eddy shape function Vorticity rotor We can eliminate the second term, since we want a divergence free velocity Green Function R. Poletto – Towards a DF-SEM Relation between eddies shape function in velocity field and the one in vorticity field 6 1 – Method description 2 – DFSEM development 3 – Code_Saturne A – Reynolds stresses B – Future development WHERE The output Reynolds stresses in the DFSEM depends on: distances of the eddies squared shape function We may split the inlet into several parts and introduce in each part a particular shape function, which better fits the local Reynolds tensor. R. Poletto – Towards a DF-SEM 7 1 – Method description 2 – DFSEM development 3 – Code_Saturne R. Poletto – Towards a DF-SEM A – Reynolds stresses B – Future development 8 1 – Method description 2 – DFSEM development 3 – Code_Saturne usini1.F A – Implementation B – Results activation of the synthetic turbulence subroutines caltri.F memsyn.F tridim.F memory management (usclim.F) ussynt.F user adjustable subroutine which sets the synthetic turbulence method (random numbers, SEM, DFSEM, …) and the inlet surfaces and it reads the previous RANS solution syntur.F it implements all the synthetic turbulence methods and applies them to the inlet surfaces R. Poletto – Towards a DF-SEM varsem.h main variables used by the new subroutines 9 1 – Method description 2 – DFSEM development 3 – Code_Saturne * Results by N. Jarrin R. Poletto – Towards a DF-SEM A – Implementation B – Results SEM compared with other synthetic turbulence methods shows a better fitting. Of course it still needs to be improved (and the DFSEM may give us a chance) in order to get a quicker convergence to the periodic LES result. 10