Clive A. J. Fletcher

An Automatic Design Optimization Tool and its Application to Computational Fluid Dynamics

In this paper we describe the Nimrod/O design optimization tool, and its application in computational fluid dynamics. Nimrod/O facilitates the use of an arbitrary computational model to drive an automatic optimization process. This means that the user can parameterise an arbitrary problem, and then ask the tool to compute the parameter values that minimize or maximise a design objective function. The paper describes the Nimrod/O system, and then discusses a case study in the evaluation of an aerofoil problem. The problem involves computing the shape and angle of attack of the aerofoil that maximises the lift to drag ratio. The results show that our general approach is extremely flexible and delivers better results than a program that was developed specifically for the problem. Moreover, it only took us a few hours to set up the tool for the new problem and required no software development.

Gas particle industrial flow simulation using RANSTAD

A turbulent gas particle finite-volume flow simulation of a representative coal classifier is presented. Typical values of the loading ratio permit a one-way coupling analysis. As a case study, the computational fluid dynamics code,ranstad, and the modelling aspects are discussed in some detail. The simulation indicates that small (≈ 30 µm) coal particles pass through the classifier to the furnace but that large (≈ 300 µm) particles are captured and remilled. The computational simulation indicates that the classifier performance can be improved by internal geometric modification.

Incompressible Viscous Flow

In this chapter no assumption is made about the relative magnitude of the velocity components, consequently, reduced forms of the Navier-Stokes equations (Chap. 16) are not available. Instead the full Navier-Stokes equations must be considered; however, it will be assumed that the flow is incompressible.

Parallel CFD Simulations of Multiphase Systems: Jet into a Cylindrical Bath and Rotary Drum on a Rectangular Bath

Most of the developed commercial CFD (Computational Fluid Dynamics) packages do not attempt to document (or don’t want to publish !!) the detailed algorithm for parallelising the code; even the ordinary solution strategies are tedious to learn sometimes. However, industrial engineers are more concerned about quick and correct solutions of their problems. Key features of this paper are the use of the domain decomposition and encapsulated message passing to enable execution in parallel. A parallel version of a CFD code, FLUENT, has been applied to model some multiphase systems on a number of different platforms. The same models considered for all the platforms to compare the parallel efficiency of CFD in those machines. Two physical models: one is a liquid jet directed into a cylindrical bath to disperse buoyant particles suspended on the top of the bath (3D), and the second one is a rotary drum rotating on a free surface to drag down particles from the free surface. The free surface, high gradient of the velocity, particle-particle, particle-wall collisions make most industrial flow simulations computationally expensive. For many complex systems, like here, the computational resources required limit the detail modelling of CFD. The implementations of computational fluid dynamics codes on distributed memory architectures are discussed and analyzed for scalability. For commercial CFD packages, in many cases the solution algorithms are black boxes, even though parallel computing helps in many cases to overcome the limitations, as shown here. The performance of the code has been compared in terms of CPU, accuracy, speed etc. In short, this research is intended to establish a strategic procedure to optimize a parallel version of a CFD package, FLUENT. The parallelised CFD code shows the excellent efficiency and scalability on a large number of platforms.

Partial Differential Equations

As an example to show how the Laplace transform may be applied to the solution of partial differential equations, we consider the diffusion of heat in an isotropic solid body.

Boundary Layer Flow

Traditionally it has been useful to consider boundary layer flow as a separate category (Table 11.4 and Sect. 11.4). From a computational perspective it is convenient to classify boundary layer flow as a flow for which viscous diffusion is significant only in directions normal to the surface on which the boundary layer occurs (Fig. 15.1) and for which the normal momentum equation can be replaced with the condition that the pressure is constant. For such flows the governing equations are non-elliptic, if the pressure solution is given. This permits very efficient single-pass marching algorithms to be introduced (in the x direction in Fig. 15.1).

Flows Governed by Reduced Navier—Stokes Equations

In this chapter categories of viscous-inviscid flow equations, intermediate between the full Navier-Stokes equations and the boundary layer equations will be considered. These intermediate categories are called reduced Navier-Stokes (RNS) equations.

Preliminary Computational Techniques

In this chapter an examination will be made of some of the basic computational techniques that are required to solve flow problems. For a specific problem the governing equations (Chap. 11) and the appropriate boundary conditions (Chaps. 11 and 2) will be known. Computational techniques are used to obtain an approximate solution of the governing equations and boundary conditions.

Weighted Residual Methods

Applying the WRM methods described in Sect. 5.1 produces the following coefficients in the approximate solution, Coefficient a1 a1 Galerkin 2.912378 -1.690000 Subdomain 2.577660 -1.408464 Least-squares 2.558151 -1.412076 The corresponding solutions are x Galerkin Subdomain Least-squares Exact 0.2 0.50889 0.45384 0.44998 0.50000 0.4 0.84770 0.76288 0.75598 0.86603 0.6 0.98207 0.89500 0.88699 1.00000 0.8 0.87763 0.81808 0.81200 0.86603 1.0 0.50000 0.50000 0.50000 0.50000 error 0.01205 0.06595 0.07107 Clearly for this problem the Galerkin formulation is most accurate. However all three methods are reasonably accurate since only two coefficients are to be chosen.

Multidimensional Diffusion Equation

A broad conclusion from Chap. 7 is that implicit schemes are more effective than explicit schemes for problems with significant dissipation, as exemplified by the one-dimensional diffusion equation.