Taking CFD for a spin

Dave Wilson gets his teeth into two new Computational Fluid Dynamics packages from the UK and USA

Two new software packages for Computational Fluid Dynamics promise to make that software a lot easier for design engineers to use. The first is CFX 5 from UK-based AEA Technology, software that combines CAD input and automatic meshing. The second is a more radical CFD package from US-based Exa (see page 24).

With the announcement of its CFX 5 fluid analysis tool, AEA claims to have solved some of the problems traditionally associated with using Computational Fluid Dynamics software. Not only does the new package offer designers automatic meshing, but it eliminates some of the problems associated with the earlier Navier Stokes approach.

Because the system is based on MSC/Patran, it allows complex geometries to be created and accessed from CADD 5, Catia, Euclid 3, Pro/Engineer and Unigraphics systems.

Meshing is virtually automatic. Having created or imported the geometry, the user has only to indicate the mesh resolution before the software builds the complete tetrahedral mesh automatically. The solver uses an unstructured tetrahedral mesh for which the user only needs to specify the geometry, surface mesh and boundary conditions and the solver automatically performs the meshing. Specific modelling options, boundary conditions and fluid properties are all defined through a system of menus and forms.

This speeds up pre-processing time and produces high quality meshes resulting in fast convergence. The tetrahedral meshes also enable the user to have accurate representations of the most complex geometries.

But the real difference lies in a new algorithm that has been developed to reduce CPU time to a fraction of that previously required.

Traditional CFD systems have used Navier-Stokes equations, a set of partial differential equations that describe fluid flow. But the complexity of these equations is such that analytical solutions can only be found for the simplest of flows. What is more, these equations must solve for velocities and pressure together, and the system is non-linear in the momentum equations.

With CFD, the area of interest is subdivided into a large number of cells. In each of them, the partial differential equations (that express the conservation of mass, momentum and heat) can be rewritten as algebraic equations that relate the velocity, temperature, and mass fraction in that cell to those in all its immediate neighbours.

Once the equations have been discretised in this way, a solution procedure still needs to be specified to solve them. This is especially difficult as the equations for the conservation of momentum are non-linear.

Traditional methods use what is known as a Simple segregated algorithm. This first calculates the velocity field by solving the momentum conservation equations with a guessed pressure field. However, in the linearisation process, the coefficients of the equations are themselves functions of the guessed velocities, and the achieved solution is therefore called semi-implicit.

These new velocities are then used to calculate the pressure field by solving a pressure-correction equation that is derived from the mass conservation equation. This generates a new pressure field that is different from that used previously in the momentum equations and therefore the velocities no longer satisfy conservation of momentum.

An iterative procedure is therefore needed between the momentum and mass equations to solve the complete flow field. It is only when the iterations have converged that the new values of both velocity and pressure satisfy the conservation of both mass and momentum.

CFX 5’s new coupled solver offers a radically different approach in which all the hydrodynamic equations are solved as a single system. Therefore, after one iteration, the velocity field and pressure `almost’ satisfy both momentum and mass conservation. `Almost’, because the equations are nonlinear and there is still some error. Iterations are still needed to achieve the correct solution.

However, as after each iteration both momentum and mass continuity are satisfied, far fewer iterations are necessary than for the Simple algorithm to achieve a converged solution. For the iteration procedure, CFX 5 uses a pseudo-time step method in which the solution procedure behaves as a transient and evolves smoothly to the accurate field flow.

Typically, CFX 5 requires only one or two dozen iterations to converge, where a segregated solver would need hundreds or thousands of iterations. Naturally, this makes it a lot faster. Models presently available in CFX 5 are: transient and steady-state flow, laminar and turbulent flow, heat transfer, buoyancy and transport of passive scalars.

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