Numerical Calculations of the Hypersonic Viscid–Inviscid Flow Inside Simple Ducts of Circular Cross-Section

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Abstract
Summary: The method of characteristics and an implicit finite-difference scheme are used to investigate the interaction between the internal flow field and laminar boundary layer in ducts of circular cross-section under the conditions of high Mach number and low Reynolds number. The displacement thickness is added on to the body to form a new “effective body shape” which is used to re-calculate the inviscid flow. Iterations are performed and a solution is obtained when the surface pressures in two consecutive iterations converge to within a specified tolerance. The calculated surface pressures on a 10 degree conical duct placed in a hypersonic stream at M∞=8·34, Re∞=7·5 × 106 and M∞=10·4, Re∞=4·625 × 106 with γ=1·4 show good agreement with experiments. The results are computed for constant wall temperature, using a value of Tw/Tstag=0·23, and the Prandtl number is assumed to be constant and equal to 0·7 throughout the calculations. The type of shock-wave interaction near the axis of symmetry is determined and the computation terminates after the fluid properties behind the reflected shock have been calculated.

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