Inverse Determination of Smelter wall Erosion Shapes Using a Fourier Series Method
ABSTRACT An algorithm has been developed for the non-destructive determination of local thickness of the refractory material walls in smelter furnaces. This method uses measurements of temperature and heat flux at a number of points on the outer (fixed) surface of the furnace and assumes that the inner (guessed) surface of the furnace wall is isothermal. The temperature field is then predicted in the furnace wall subject to the measured temperature values on the external surface and the isothermal solidus temperature on the inner surface of the wall. The shape determination method then uses the difference between the measured and the computed heat fluxes on the outer surface of the furnace as a forcing function in an elastic membrane concept for the determination of the inner (melt refractory) surface shape. The initial guess of the wall inner shape can be significantly different from the final (unknown) wall shape. The entire wall shape determination procedure requires typically 5-15 temperature field analysis in the furnace wall material.
Recent development of aerodynamic design methodologies : inverse design and optimization
Multi Objective Aerodynamic Optimization - Inverse Optimization Method for Aerodynamic Shape Design - Subsonic Aerodynamic Design - Parametric Airfoils and Wings - Using Existing Low-Field Analysis for Inverse Design of Three-Dimensional Aerodynamic Shapes - Numerical Methods for Inverse Solution in Aerodynamic Design of Turbomachinery - Inverse Blade Design Based on Permeable Wall Concept - An Inverse Design Method for Wings Using Integral Equations and its Recent Progress - Application of Transonic Inverse Method to the Development of Aerospace Products - Aerodynamic Design of Wing-Engine Configuration under Effect of Jet Plume
Shock-Free Wing Design
A simple numerical method for generating wing shapes that will be shock free at a specified supercritical Mach number is described. The method involves using a fictitious gas law for the supersonic domain to make the governing equations elliptic. Requirements on this gas law are detailed and a method for computing the real flow in the supersonic domain, given initial data on the embedded sonic surface, is described. The failure of the method to yield a shock-free flow when a limit surface occurs in the supersonic flow, and the difficulties that arise because the initial-value problem for the supersonic domain is ill-posed, are delineated. Finally, a small perturbation algorithm is used to illustrate the procedure and results are given for a simple baseline wing. NCREASED fuel efficiency, and in the case of commercial aircraft, productivity, can be achieved by operating aircraft at supercritical Mach numbers, provided that shock waves can be avoided or made acceptably weak. Two-dimensional procedures for prescribing airfoil sections that are shock free have already provided improvements in aircraft efficiency by employing these airfoils on swept wings. Three-dimensional effects have compromised such designs to some extent, and extensive wind tunnel development tests have been required to recapture the benefits of these "supercritical airfoils." Sobieczky et al. l demonstrated a method of modifying baseline configurations so that they would be shock free at a prescribed Mach number and lift coefficient. This procedure provides a special opportunity for improving aircraft per- formance through a careful selection of the baseline con- figuration in order to provide wings and wing-body com- binations that are shock free at supercritical Mach numbers, and that have acceptable off-design performance. Yu2 and Yu and Rubbert3 have also documented that this procedure is possible and demonstrated its application. As was first described by Sobieczky,4 a numerical algorithm is used to solve a fictitious set of equations for the flow past the baseline configuration. These equations are identical to the correct equations for subsonic portions of the flow, but they are modified when the flow becomes super- sonic, so that even though the flow speed is larger than the local speed of sound the equations themselves remain elliptic. This procedure generates a numerical solution that satisfies the appropriate equations where the flow is subsonic, and the appropriate boundary conditions on the configuration outside of the supersonic zone. The results of this calculation provide the flowfield at the sonic surface. This surface and flowfield define an ill-posed initial value problem for the supersonic domain that is to be solved using the correct equations. Because this problem is ill-posed in three dimensions any numerical method must, in principle, be unstable. This in- stability, however, is of no consequence for moderate to high aspect ratios. However, if the detailed definition of the spanwise modifications required to make the wing shock free