Verification and Validation of the IMPNS Flow Solver Using the X-15 Flight Experiment

Abstract

An extensive verification and validation study of Cranfield University's IMPNS flow solver has been performed for a complete hypersonic air-vehicle configuration. A hierarchical approach was adopted in which the vehicle aerodynamics were decomposed and related flow phenomenon studied. Using this hierarchy bench mark solutions and laboratory experiments were identified that provide the basis of the verification and validation exercises. Detailed comparisons of iterative and grid converged IMPNS computations with benchmark solutions and wind tunnel measurements are presented. Computations of the X15 wind tunnel and flight experiments are described and comparison is made with measured surface static pressures, off surface total pressure measurements and Schlieren flow visualization that demonstrate the reliability and capability of the IMPNS flow solver for complex configurations. I. Introduction he last decade has seen continuing development of high-performance computers and supporting infrastructure together with progress in the understanding of the application of computational fluid dynamics (CFD) to increasingly complex aerodynamic problems. This is leading to the deployment of CFD in support of the engineering design function at earlier points in the product design cycle creating a number of new challenges that have not been fully addressed by the research community. Chief amongst which is how to address analysis error and uncertainty in the design process. Computational Fluid Dynamics (CFD) is fundamentally a deterministic process, the continuum model equations have a unique solution and this solution can be approached asymptotically using numerical methods provided sufficient care is taken in the choice and application of the discretization scheme. However, errors inherent in the mathematical modeling are uncertain and depend upon the physical phenomena excited by the flow. A common practice in the engineering application of CFD is to assume a nominal value for the error and uncertainty. At the detailed design stage this poses no significant problems as the physical phenomena are unlikely to be significantly altered by the allowed design variations and consequently the level of modeling uncertainty can be considered uniform. Thus despite the presence of error and uncertainty no special treatment is required for credible design choices. Earlier in the process, at the concept stage the design choices may exhibit a wide variation of physical phenomena all of which have differing levels of modeling uncertainty and clearly the assumption of a uniform, nominal value is erroneous. Since almost 80% of lifecycle cost is determined during the initial stages of product development, accounting for error and uncertainty is the key to using high-fidelity analysis tools early in the design process where they can have maximum influence. It is in this light that a new approach is needed. Clearly when trying to establish whether a computational simulation is reliable or not we require some knowledge of the 'right answer'. Identifying what is meant by the 'right answer' is difficult, but raises a number of important and fundamental issues. The purpose of any computational simulation is to predict the behavior of a physical system and so at the most fundamental level the reliability of the simulation can be tested by comparing with the physical reality. However, real world experimental measurements are themselves subject to error and uncertainty and so may not provide a reliable basis for comparison. Instead we can consider comparison with laboratory experiments which offer a more controllable environment but may introduce new sources of error and are