دانلود رایگان مقاله پیش بینی سریع جریان های مافوق صوت بدنه بلانت

Abstract

The present work discusses the practical advantages and disadvantages of using simplified numerical methods and computational fluid dynamics in parametric design studies of hypersonic blunt bodies. Similarly, the advantages of using problem-specific simplifications to the governing equations to reduce computational cost are discussed. The uncertainty associated with using various methods to analyze hypersonic blunt body flows has been quantified through comparison to numerical solutions of the compressible Navier–Stokes equations. In particular, selected methods that are well defined in the literature, such as the modified Newtonian method, transformed finite difference grids, and the method of characteristics in the supersonic region, have been utilized to solve two cases of interest. An improvement to the prediction methods has been achieved through the inclusion of an iterative interaction between the boundary layer displacement thickness and the external inviscid free-stream. Results were collected for accuracy and computing time for each method including under-resolved compressible Navier–Stokes simulations. The collective information was used as a case-study to discuss the balance an engineer must find between simulation fidelity, resolution, accuracy, simulation time, and development time.

6. Conclusion Simple analytical and numerical methods were used to analyze two hypersonic blunt body flow problems. A simple method for accounting for the weak viscous-inviscid interaction between the boundary layer and the external free-stream was given. The results were compared to those obtained from the numerical simulation of the compressible Navier–Stokes equations. The analysis was performed in the context of evaluating each methods merits to be used for the rapid design and analysis of hypersonic blunt bodies. The results showed that a specific surface inclination method (the modified Newtonian method, Section 2.2.1) has limited applicability because of its poor accuracy away from the forward stagnation point. A solution to the Euler equations using a shock-fitted fi- nite difference grid (Section 2.2.2) combined with the method of characteristics (Section 2.2.3) showed close agreement but reduced in accuracy at lower Reynolds numbers. A good approximation of the convective heat flux distribution was achieved using a simple integral calculation (Section 2.3.1). The integral boundary layer method (Section 2.3.2) utilizing a single parameter family of pro- files was found to under predict the shear stress around the body. The numerical solution to the compressible boundary layer equations (Section 2.3.3) showed close agreement to the CFD results for both shear stress and convective heat flux. The results from the simple viscous-inviscid interaction solution (Section 3) showed improved accuracy from the calculations where the interaction was ignored, particularly at low Reynolds numbers. The relative accuracy and computing time of each method was compared to a series of CFD simulations with reduced grid refinements. It was shown that an under-resolved CFD simulation can result in significantly reduced accuracy and still take several orders of magnitude longer to compute than lower order models.