Verification, Validation & Uncertainties in CFD applied to Reactor Thermal-Hydraulics

This is draft Engineering Doctorateexternal project for Sept 2009

There is today a world-wide and general interest for quantifying uncertainties in CFD studies, in industrial design obviously, across industry sectors but particularly safety applications where demand for “error bars” around CFD results is now pressing. A new series of workshops “ Benchmarking of CFD Codes for Applications to Nuclear Reactor Safety (CFD4NRS )” started only 2 years ago is well attended [1]. However, the Thermo-fluids group at Manchester essentially focused on turbulence modelling, has also actively and continuously contributed to benchmarking and best practice guidelines over many years and via collaborations with British Energy Ltd, ERCOFTAC and EDF [2]. The CFD group will provide expert training for the PhD candidate in thermal-hydraulics, but modelling issues aside and as a new development, the student will focus his/her research on “Verification and Validation”, initially quantifying discretisation and convergence errors which can be more easily checked from comparison to analytical solutions and grid refinement studies , extending beyond the classical “Richardson extrapolation” [3, 4], then on several means of quantifying sources of uncertainty.


The moment method proposed by Jasak & Gosman [6] is one of very few methods applicable to fully unstructured mesh CFD codes (www.code-saturne.org for EDF, www.cd-adapco.com/applications /power.html at AREVA). It consists in solving transport equations for a scalar and its square, which analytically leads to an identity, i.e. redundant information , but numerical solutions will show differences in poorly meshed areas, and this can provide a measure of numerical accuracy on a single mesh and whatever the complexity of the mesh . The novelty herein will be on identifying most meaningful physical quantities, for instance the turbulent kinetic energy k and it’s square root simultaneously then comparing k and .


Uncertainty in inlet conditions or other “input parameters” can now be studied via a large number of CFD simulations, using Monte Carlo or better, Design of Experiments and Morris’s method, together with the availability of free grid computing (e.g. unused overnight clusters of PCs) which are now sufficient for 3D RANS simulations. In [5] a clever procedure for defining error bars stemming from actual uncertainties in physical input parameters such as surface roughness or LES eddy viscosity is proposed.
Test cases will be selected for their relevance to the industrial safety sector, with a preference for problems involving buoyancy (turbulent mixed or natural convection, stratifications) which are particularly challenging [7, 8] and provide an opportunity to link with recent developments from the turbulence modelling group. The present programme may seem overly ambitious, but this is very much about coordinating efforts within a fairly large team of CFD experts and students, each one a with particular interest in one or two modeling approaches and test cases, while the candidate’s own focus should be on uncertainty and quality assessment over a number of test cases, many of which are well documented and ready to run from a Wikipedia type of collaborative website currently developed by the group in collaboration with EDF and other stakeholders [9].

  • [1] CFD4NRS workshops www.neq.fr/html/nsd/reports/2007nea6298/
  • [2] cfd.mace.manchester.ac.uk/ercoftac, www.ercoftac.org (Cf. Best Practice Guidelines and Qnet Knowledge Base),
  • [3] P. J. Roache, Code Verification by the Method of Manufactured Solutions, J. Fluids Eng, 124, 1 (2002) 4-10.
  • [4] J. Cadafalch, C. D. Pérez-Segarra, et al. Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer. J. Fluids Eng, 124, 1 (2002) 11-21.
  • [5] D. Xiu, G. E. Karniadakis, Modeling uncertainty in Fow simulations via generalized polynomial chaos, J. Computational Physics 187 (2003) 137–167.
  • [6] H. Jasak, AD Gosman, Automatic Resolution Control for the FV method, Numerical Heat Transfer, B-Fudamentals, 38-3 Oct 2000.
  • [7] K. Hanjalic, One point closure models for buoyancy driven flows, Annual reviews in Fluid Dynamics 2002.
  • [8] P. Joubert , P. Le Quéré et al. A numerical exercise for turbulent natural convection and pollutant diffusion in a two-dimensional partially partitioned cavity, I. J. of Thermal Sciences 44 (2005) 311–322
  • [9] cfd.mace.manchester.ac.uk/Saturne/TestCases

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Topic revision: r3 - 2009-02-16 - 18:01:46 - DominiqueLaurence
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