Simulation Modelling Approach

Computational Fluid Dynamics (CFD) is a tool used to simulate the flow of fluids over a range of geometrical and flow conditions. This is accomplished by splitting a given flow domain up into small control volumes or cells and solving the Navier-Stokes equations using an iterative approach and a set of boundary conditions. A large number of approaches to solving these equations exist, each with a computational cost associated with the nature and level of complexity of the flow and the methodology used to either model or solve the turbulent structures.

4.1.1 Solver Features

The numerical solver used for this project is Star-CCM+® developed by CD-adapco. Star CCM+ is more than just a CFD solver, it is an entire engineering process for solving problems including flow (of fluids or solids), heat transfer and stress. Star CCM+ is a more complete package than a typical CFD solver as it contains the functionality to define, mesh, solve and visualise solutions in a single package. It is a very powerful tool with physics modelling capabilities including;

• Solvers

o Segregated or coupled • Time

o Steady, implicit and explicit unsteady • Turbulence

o RANS, LES and DES • Compressibility

o Ideal or real gas • Heat Transfer

o Conjugate heat transfer and radiation

Star-CCM+ also contains an automated meshing tool. This tool can ‘shrink-wrap’ a high quality triangulated surface mesh onto the geometrical model, closing holes in the geometry and joining disconnected or overlapping surfaces to create a single, manifold surface which can be used to generate the computational mesh without user intervention. From this either a polyhedral or hexahedral mesh can be automatically created with user defined control volumes allowing increased mesh control. A high quality prism-layer mesh is automatically extruded from solid walls within the domain with conformal meshes created on interfaces between multiple physical domains.

In order to create a mesh, the domain geometry has to be defined. This is done using Siemens NX CAD software. Once the flow passage has been defined, the flow domain is tailored parametrically based on the diameter of the passage profile and a constant plate thickness which is taken from the test plate geometry. This solid model is exported from NX as a parasolid file, which is then imported into Star-CCM+ as a part and each face is assigned to a particular boundary.

A powerful analysis suite is also available within Star-CCM+, with scalars, vectors, streamlines and other data all updated live as the solution iterates. Data can also be exported for further analysis using other tools.

4.1.2 Turbulence Model

A RANS based turbulence approach is used for this study. Details of the Reynolds Averaging process as applied to the Navier-Stokes equations are covered in section 2.4.2.3. As the goal of

this study is to develop a tool allowing the quick assessment and down-selection of a large number of candidate designs in terms of their relative performance, the choice of this relatively simple approach to turbulence modelling is an attractive one. In this case the 𝑘𝑘-𝜀𝜀 model is chosen in the two-layer realizable formulation. Details of the realizable 𝑘𝑘-𝜀𝜀 turbulent model can be found in a paper by Shih et al (63). Described in detail by the authors, the two layer approach allows the 𝑘𝑘-𝜀𝜀 model to be applied in the viscous sublayer and divides the computation into two layers. In the layer next to the wall, the turbulent dissipation rate 𝜀𝜀 and the turbulent viscosity 𝜇𝜇𝑒𝑒 are specified as functions of wall distance while 𝑘𝑘 is solved in the entire flow. This two layer formulation blends this one-equation model with the two-equation 𝑘𝑘-𝜀𝜀 model smoothly. This explicit specification of 𝜀𝜀 and 𝜇𝜇𝑒𝑒 is arguably no less empirical than the traditional damping function approach and the results are often as good or better.

4.1.3 Flow, Energy and Species Models

The solver used in this study is the coupled model; this solves the conservation equations for mass, momentum and energy simultaneously using a pseudo-time marching approach, driving the unsteady form of the governing equations to a steady state. A pseudo-transient term replaces the physical time derivative and the solution advances in pseudo-time to drive this term to zero. The discretized equations are solved implicitly; this results in a wider stability margin permitting Courant numbers greater than unity. As a result the pseudo-time steps can be larger providing relatively fast convergence rates over an explicit spatial integration scheme but requiring more storage space. A 2nd order accurate upwind discretisation scheme is also employed here. 𝐶𝐶𝑃𝑃𝑇𝑇𝑃𝑃𝑎𝑎𝑜𝑜𝑡𝑡 𝑜𝑜𝑇𝑇𝑚𝑚𝑏𝑏𝑅𝑅𝑃𝑃 = ∆𝑡𝑡 �𝑇𝑇𝑒𝑒𝑖𝑖 ∆𝑥𝑥𝑒𝑒 𝑒𝑒 𝑒𝑒=1 Equation 82 The coupled species model introduces an extra transport equation which, along with global mass continuity, provides a means of updating the mass fraction field and defining the mixture composition of nitrogen and air where applicable. This is required to ensure the method used to calculate adiabatic effectiveness is consistent with the experiment in which the heat-mass transfer analogy is employed, drawing a parallel between gas concentration and temperature distribution and allowing the PSP technique to be employed.

The coupled flow model is chosen for this study since the solutions are generally more robust and accurate than the segregated model and whilst more memory is required for this model, the computational resources available are sufficient to run a coupled case (42).

4.1.4 Initial Conditions

The simulation is initialised using the ‘expert initialisation’ functionality built into StarCCM+. This procedure steps through a number of grid densities (typically 10) from very coarse to the full resolution defined by the meshing procedure and solves an inviscid calculation for each using the solution of the previous grid resolution as a starting point. This provides a good first approximation of the flow field, reducing the number of iterations required to reach a converged solution compared to initialising from uniform initial conditions.

The turbulence model is then applied with main stream flow turbulence intensity and length scale set to match the experimental conditions and the solution is run until convergence is reached.