# Developments at the University of Manchester:

Here is a list of some of the recent developments carried out at the University of Manchester. Click on the thumbnails to start a slideshow with larger images. Here is a list of the research topics related to Code_Saturne. For the complete list see here.
Title Author Start Date
CFD analysis of Fuel Rod Bundles using a FV Unstructured Code Stefano Rolfo: September 2006
The Effect of Plugged Tubes on Gas Mixing in AGR Boilers Alastair West: October 2008
A Study into the effect of underlining RANS model on a Delayed Detached-Eddy Simulation Neil Ashton: July 2008
Using the concept of laminar kinetic energy to predict transitional flow Clare Turner: January 2007

 : Mahmoud Assad: [[CfdTm.ResearchSummary0009][]] Improved modelling of ﬁre September 2009
Number of topics: 7

## RANS models

### Code Friendly v2-f model

Work on a code friendly version of the low Reynolds %$\overline{v^2}-f$% was carried out during the PhD by Juan Uribe ending in 2006. The elliptic relaxation model has been proven to be effective is modeling the near-wall effects but the numerical issues arising from the boundary conditions makes it difficult to use in segregated solvers such as Code_Saturne. A new version of the model was developed based on the ratio %$\varphi=\overline{v^2}/k$%. The new version was implemented in Code_Saturne and tested on different flow configurations including separation, reattachment and buoyancy. The model was able to capture the near wall effects yielding good predictions for mean flow variables.

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### Stress-Strain Lag model

This work involved the derivation, development and implementation of a three equation turbulence model using Code_Saturne. This was complete by Alistair Revell during his PhD degree, which was completed in 2006. The thesis is available here.

In highly non-equilibrium 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.

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## Hybrid models

A hybrid RANS-LES model has been derived based on the Schumann approach of splitting the contribution from the averaged velocity field and the fluctuating one into the subgrid tensor:

%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(1-f_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.

.

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## Synthetic Eddy Method

Since in LES or hybrid RANS/LES, the unsteady motions of energy-carrying turbulent structures are resolved, the velocity fluctuations imposed at the inflow of the computational domain must represent the contributions of these turbulent structures. Although providing accurate inflow boundary conditions, the simulation of the upstream boundary layers requires extra CPU and data storage resources. Synthetic turbulence generation methods, though less accurate, provide the main simulation with inlet boundary conditions for only a fraction of the CPU time needed in the computation of the upstream flow. The main idea of the Synthetic Eddy Method is to assume that the turbulent inflow is composed of a superposition of coherent structures with particular intensities, shapes and length-scales. Assumptions are made regarding the characteristics of the inflow structures using information provided by the RANS statistics. A random distribution of eddies with prescribed intensities, shapes and sizes is then generated. If %$x^k$% , %$y^k$% and %$z^{k}$% are the %$x$%, %$y$% and %$z$% coordinate of the centre of eddy %$k$%, the velocity signal generated by the SEM reads

%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_1-x^{k}_1) f_L(x_2-x^{k}_2) f_L(x_3-x^{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} }(1-|r/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} \}, %ENDLATEX% where %BEGINLATEX% \begin{equation*} x_{i,\min} = \min_{x\in P} (x_i-L) \quad \mbox{and} \quad x_{i,\max} = \max_{x\in P} (x_i+L) %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 %$R_{ij}$%.

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## Stochastic Lagrangian modelling for LES of dispersed turbulent Two-phase flows.

The thesis of Sofiane Berrouk investigates turbulent particle-laden Large eddy Simulation (LES). It adapts a Langevin-type stochastic diffusion process that models inertial particle transport by the sub-filter (sub-grid scale) motion for hybrid Eulerian-Lagrangian LES. This modelling is particularly crucial for dispersion and deposition of inertial particles with small relaxation times compared to the smallest LES-resolved turbulence time scales. When generating stochastically sub-filter 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 lightly-loaded particle-laden 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 sub-filter scale fluctuations has proven crucial for results concerning the small-Stokes-number particles. The performance of the model for highly-loaded particle-fluid flows needs to be assessed and additional validations for non-equilibrium turbulent flows are required. .

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## Turbulent flow across in-line tube bundles.

As part of the collaboration with University of Science and Technology of Oran (USTO), Dalila Ammour has studied the flow in tube bundles which is of great interest to the power generation industry. Safety studies require predictions of vibrations caused by fluid-structure interaction or large temperature fluctuations that eventually lead the thermal stripping. The cross flow in a 2D and 3D square in-line tube bundle has been computed for pitch ratio of P/D=T/D=1.44 and Reynolds number of 70000. The URANS models tested include the standard κ – ε, Menter's shear stress transport (MSST) and the Reynolds Stress Models (RSM). Other more recent models have been also used, the new SST-Cas model for 2D and 3D calculations and the DES approach for 3D simulation. This case was computed using Code_Saturne based on the finite volume method. Quantitative and qualitative results have been analyzed and then compared with LES and experimental data. The 2D simulations fail to capture the complete flow physics while the 3D calculations on the other hand seem to produce better results of pressure and velocity profiles and agree better with LES and experiments. Good predictions are obtained with the new SST-Cas model. The code Star-CD has been used for comparison. It produces similar results and confirms the asymmetry of the flow. Frequencies of oscillations have been studied. This was done by using Density Power Spectrum (DPS) and localizing the peak values (the most energetic frequency). By applying DPS to the velocity's and pressure's signals, one clear peak is obtained around the frequency 45Hz (St=0.84) similar than the LES. It means that a large recirculation coexists in the bottom of the tube where the shear stress is higher.
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## Research Projects

### Pipe Bends and Junctions

Advantica is an engineering consultancy company specialised in the sectors of gas, oil, water and electric industries. As part of a contract with the University of Manchester, a study of turbulence induced vibrations in pipe bends was carried out. Code_Saturne was used in part of these studies. The code was installed in the company's machines and training was provided for the specialist in CFD on how to use the code. CFD codes were used to examine the influence of several key factors in the flow, where the primary case of interest is the flow through a simple 90 degree bend at a Reynolds number of 17 million. A range of cutting edge turbulence modelling schemes were applied to this case and a robust methodology for the construction and examination of the testcase was validated. The numerical results were presented in the form of mean and instantaneous flow flield plots, point time-histories and corresponding frequency spectra.
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### CTR, Stanford Summer Program 2006

Alistair Revel took part in the summer program at the Center for Turbulence Research in Stanford. His work on trailing vortices was done using Code_Saturne. The numerical calculation of the trailing vortex shed from the wingtip of an aircraft has attracted significant attention in recent years. An accurate prediction of the flow over the wing is required to provide the correct initial conditions for the trailing vortex, while careful modeling is also necessary in order to account for the turbulence in the vortex core. As such, recent works have concluded that in order to achieve results of satisfactory accuracy, the use of complex turbulence modeling closures and numerical grids of considerable size is an absolute necessity. In Craft et al. (2006) it was proposed that a Reynolds stress-transport model (RSM) should be used, while Duraisamy & Iaccarino (2005) obtained optimal results with a version of the v2-f which was specifically sensitised to streamline curvature. The authors report grid requirements upward of 7 million grid points, highlighting the substantial numerical cost involved with predicting this flow. The computations were reported for the flow over a NACA0012 half-wing with rounded wingtip at an incidence angle of 10◦. The primary aim was to assess the performance of a new turbulence modeling scheme which accounts for the stress-strain misalignment effects in a turbulent flow. This three-equation model bridges the gap between popular two equation eddy-viscosity models (EVM) and the seven equations of a RSM. Relative to a RSM, this new approach inherits the stability advantages of an eddy-viscosity scheme, together with a lower computational expense, and it has already been validated for a range of unsteady mean flows.

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## HPC Facility Installations

Code_Saturne has been installed and tested in the different high performance parallel facilities to which the University of Manchester has access:

### HPCx

The HPCx platform at Daresbury is number 65 in the June 2007 Top 500 Supercomputer list. The HPCx system comprises 160 IBM POWER5 eServer nodes, i.e. 2560 processors, delivering 15.36 TeraFlop/s peak, or 12.9 TeraFlops/s sustained (as rated in the Top500 list). The system is equipped with 5.12 TByte of memory and 72 TByte of disk. http://www.hpcx.ac.ukl

### MACE

Main cluster at the school of MACE in the University of Manchester. Comprises 100 nodes each with two Intel(R) Xeon(TM) CPU 2.80GHz.

### NGS

National Grid Service. Four main cores at Manchester, Oxford and Leeds each comprises of 48 nodes with 2 dual-core Opteron 64-bit processors, 8GB RAM and 8 nodes with 4 dual-core Opteron 64-bit processors, 32GB RAM http://www.ngs.ac.uk

## Presence

### Dissemination

The work carried out by the group using Code_Saturne has been disseminated in several journals and conferences.
Year Title
2011 I. Afgan, Y. Kahil, S. Benhamadouche and P. Sagaut:
Large eddy simulation of the flow around single and two side-by-side 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 Large-Eddy 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 Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow. Journal of Flow Turbulence and Combustion (DOI: 10.1007/s10494-010-9263-6) ,2010
2010 R. Poletto, A. Revell, T. Craft, N. Jarrin:
Towards a DF-SEM (abstract). TSFP ,2010
2009 J-P. Chabard, D. Laurence:
Heat and fluid flow simulations for deciding tomorrow's energies. (THMT6)Turbulence, Heat and Mass Transfer 6, 14-18 September 2009, Rome. ,2009
2009 N. Jarrin , R. Prosser , J. Uribe , S. Benhamadouche, D. Laurence:
Reconstruction of Turbulent Fluctuations for Hybrid RANS-LES 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 Wire-Wrapped Fuel Assembly. Proceedings of ICAPP ‘09 Tokyo, Japan, May 10-14, 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 laminar-turbulent 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 RANS-LES 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 19-22, 2008, Lyon, France _ ,2008
2007 Berrouk AS, Laurence D, Riley JJ, et al.:
Stochastic modeling of fluid velocity seen by heavy particles for two-phase LES of non-homogeneous 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 two-phase LES of non-homogeneous and anisotropic turbulent flows . ERCOFTAC SERIES Euromech Colloquium- 477: Particle-Laden Flow, JUN 21-23, 2006 Univ Twente, Enschede, NETHERLANDS ,2007
2007 Uribe, J. C., Jarrin, N., Prosser, R. and Laurence, D.:
Two Velocities hybrid RANS-LES 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 RANS-LES Methods, Corfu, Greece.. 17 June 2007 ,2007
2006 Revell, A.J., Benhamadouche, S., Craft, T.J., Laurence, D.R.:
A stress-strain 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 synthetic-eddy method for generating inflow conditions for LES. Int. J. Heat and Fluid Flow ,2006
Synthetic turbulent inflow conditions based on a vortex method for large-eddy simulation. PCFD, Int. Journal ,2006
2006 Revell A, Craft T J, Laurence D R P:
A stress-strain lag EVM for mean unsteady and non-equilibrium 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 978-3-540-28786-5. 2006 ,2006
2005 Benhamadouche S., Laurence D., Jarrin N., Afgan I., Moulinec C.:
Large Eddy Simulation of flow across in-line tube bundles.. _NURETH-11 (Nuclear Reactor Thermal-Hydraulics), 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 T-RANS 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 stress-strain 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 stress-strain 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
The negatively buoyant wall-jet: LES database. _Int. J. Heat fluid Flow _ ,2004
The negatively buoyant wall-jet: LES database. 4th Int. Symposium on THMT, Turkey, 12-17 October ,2003
Synthetic turbulence inflow conditions for large-eddy simulation. 4th Int. Symposium on THMT, Turkey ,2003
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Number of topics: 38

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Topic revision: r18 - 2010-04-13 - 09:07:49 - JuanUribe
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