Discrete adjoint for coupled conjugate heat transfer

The typical method to solve multi-physics problems such as Conjugate Heat Transfer (CHT) is the partitioned approach which couples separate solvers through boundary conditions. Effective gradient-based optimisation of partitioned CHT problems requires the adjoint of the coupling to maintain the efficiency of the original multi-physics coupling, which is a significant challenge. The use of automatic differentiation (AD) has the potential to ease this burden and leads to generic gradient computation methods. In this paper, we present how to automate the generation of adjoint fluid and solid solvers for a CHT adjoint using Automatic Differentiation (AD). The derivation of the adjoint of the loose coupling algorithms is shown for three fixed-point coupling algorithms. Application of the coupled adjoint algorithm is shown to two CHT optimisation benchmark cases for inverse design and shape optimisation. The results demonstrate that Robin-based coupling algorithms have faster runtimes and are an attractive option for CHT optimisation problems

A coupled finite-volume CFD solver for two-dimensional elasto-hydrodynamic lubrication problems with particular application to rolling element bearings

This paper describes a new computational fluid dynamics methodology for modelling elastohydrodynamic contacts. A finite-volume technique is implemented in the ‘OpenFOAM’ package to solve the Navier-Stokes equations and resolve all gradients in a lubricated rolling-sliding contact. The method fully accounts for fluid-solid interactions and is stable over a wide range of contact conditions, including pressures representative of practical rolling bearing and gear applications. The elastic deformation of the solid, fluid cavitation and compressibility, as well as thermal effects are accounted for. Results are presented for rolling-sliding line contacts of an elastic cylinder on a rigid flat to validate the model predictions, illustrate its capabilities, and identify some example conditions under which the traditional Reynolds-based predictions deviate from the full CFD solution

Higher order time integration schemes for thermal coupling of flows and structures

The application of higher order implicit time integration schemes to conjugate heat transfer problems is analyzed with Dirichlet-Neumann as the decomposition method. In the literature, only up to second order implicit time integration schemes have been reported while there is a potential for gaining computational efficiency using higher orders. For loose coupling of the domains, the IMEX scheme consisting of the ESDIRK scheme for integrating the governing equations within the subdomains and an ERK scheme for explicit integration of the explicit coupling terms is utilized. The IMEX scheme is analyzed for two cases. In one, the material properties of the coupled domains are the same and in the other they are different. While for both cases, the IMEX scheme preserves the design order of the time integration scheme, different stability and accuracy properties are observed for the two. Finally, the computational efficiency of the higher order IMEX schemes relative to the second order scheme is demonstrated using a test case in 2-D involving coupled conduction problem of three domains

Numerical coupling procedure in steady conjugate heat transfer problems

This paper analyses the numerical stability of a coupling procedure between a CFD code and a conduction solver in a partitioned approach. A finite volume method is used in the fluid partition and a finite element method in the solid partition. Since our goal is to get a global fluid-solid solution, the analysis of the transient in the solid is not of particular interest. Consequently, the numerical method is based on the coupling of a steady state in the solid with a time-dependent solution in the fluid. At the shared interface, Dirichlet (on the fluid side) and Robin (on the solid side) conditions are applied. An interface stability study is performed according to the normal-mode analysis of the theory of Godunov-Ryabenkii. The existence of an optimal coupling parameter is highlighted

Numerical Analysis of Transient Teflon Ablation with a Domain Decomposition Finite Volume Implicit Method on Unstructured Grids

This work investigates numerically the process of Teflon ablation using a finite-volume discretization, implicit time integration and a domain decomposition method in three-dimensions. The interest in Teflon stems from its use in Pulsed Plasma Thrusters and in thermal protection systems for reentry vehicles. The ablation of Teflon is a complex process that involves phase transition, a receding external boundary where the heat flux is applied, an interface between a crystalline and amorphous (gel) phase and a depolymerization reaction which happens on and beneath the ablating surface. The mathematical model used in this work is based on a two-phase model that accounts for the amorphous and crystalline phases as well as the depolymerization of Teflon in the form of an Arrhenius reaction equation. The model accounts also for temperature-dependent material properties, for unsteady heat inputs and boundary conditions in 3D. The model is implemented in 3D domains of arbitrary geometry with a finite volume discretization on unstructured grids. The numerical solution of the transient reaction-diffusion equation coupled with the Arrhenius-based ablation model advances in time using implicit Crank-Nicolson scheme. For each time step the implicit time advancing is decomposed into multiple sub-problems by a domain decomposition method. Each of the sub-problems is solved in parallel by Newton-Krylov non-linear solver. After each implicit time-advancing step, the rate of ablation and the fraction of depolymerized material are updated explicitly with the Arrhenius-based ablation model. After the computation, the surface of ablation front and the melting surface are recovered from the scalar field of fraction of depolymerized material and the fraction of melted material by post-processing. The code is verified against analytical solutions for the heat diffusion problem and the Stefan problem. The code is validated against experimental data of Teflon ablation. The verification and validation demonstrates the ability of the numerical method in simulating three dimensional ablation of Teflon

Development of an object-oriented finite element program: application to metal-forming and impact simulations

During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations