The numerical simulation of fluid flow and heat/mass-transfer phenomena requires the numerical solution of the Navier-Stokes and energy-conservation equations coupled with the continuity equation. Numerical or false diffusion is the phenomenon of inserting errors in the calculations that compromise the accuracy of the computational solution. The Taylor series analysis that reveals the truncation/discretization errors of the differential equations terms should not be termed as false diffusion. Numerical diffusion appears in multi-dimensional flows when the differencing scheme fails to account for the true direction of the flow. Numerical errors associated with false diffusion are investigated via two- and three-dimensional problems. A numerical scheme must satisfy necessary criteria for the successful solution of the convection-diffusion formulations. The common practice of approximating the diffusion terms via the central-difference approximation is satisfactory. Attention is directed to the convection terms since these approximations induce false diffusion. The equations of all the conservation equations in this study are discretized by the finite volume method.
Part of the book: Numerical Simulations in Engineering and Science
During the design of an aircraft, a significant parameter that is taken into consideration is aerodynamic heating. Aerodynamically induced heating affects both the structure of the aircraft and its vulnerability to heat-seeking missiles in modern warfare. As a result, the ability to calculate efficiently the heating produced as well as the pressure distribution in such flows is crucial. Therefore, in this present study, the PHOENICS CFD code as modified by DRA Farnborough in order to calculate heat transfer and pressure measurement on a 5-inch hemispherical concave nose at a Mach number of 2.0 is evaluated and customized in order to produce faster and more accurate results. Apart from numerical alterations, different turbulence models are being examined as well as different discretization schemes. Numerical solutions show improvement up to 6% in comparison with the original model, both in terms of convergence rate and in terms of agreement with the available experimental data. With the new modeling suggested in the present work, the significance of both the discretization scheme and the choice of the turbulence modeling is demonstrated for the flows under consideration. The use of a high-order discretization scheme is suggested for more acute areas of the body modeled in order to improve results further.
Part of the book: Computational Models in Engineering