Implicit numerical computation of viscous high supersonic aerodynamics for a blunt-nosed “cruiser” configuration with shock fitting using the “sublime” code

The modern thrust in proposed commercial supersonic airliners is increasingly embracing “blunt-nosed” body design. Since a key drag component in aerodynamics is skin friction (viscous drag), the nose design with reduced area will reduce the skin friction. Blunt nosed bodies can achieve this drag reduction. Although pointed nose designs, (popular in previous aircraft e. g. Concorde), can achieve enhanced wave drag (i.e. drag generated by localized high speed airflow at near sonic speed) control and at supersonic speeds a pointed nose also keeps the shock wave stable and clear of the aircraft, however, the key design load in high supersonic/hypersonic cruisers (e.g. Boeing Mach 6 cruiser) is heat. H. Julian Allen of NASA established in the 1950s that in hypersonic flow (Mach > 5) a blunt nose is superior since the aircraft structural materials place an upper limit on aerodynamic heating. A pointed tip will produce an attached shock which will heat the tip to something close to the stagnation temperature of the flow. A blunt nose, however, will cause a separated shock. This creates more drag and higher heat loads overall but allows a controlled spread of the heat over a larger area and therefore produces lower peak loads. Motivated by recent developments in blunt nose design, in the present work, a numerical solution is presented for the steady viscous high supersonic/hypersonic axisymmetric flow field over a blunt cone with the Thin Layer Navier Stokes (TLNS) equations, a shock-fitting method and an implicit fourth order central difference alternating direction implicit (ADI) algorithm. Owing to high order terms of the Taylor series in the discretization of derivatives, this method has high accuracy and low numerical error (dispersion error) compared with lower order methods. The boundary-closure scheme has an important role in the numerical stability of this method. By using a coarse grid in this method, the results of numerical solution are found to be very close to those obtained with a fine grid employing the implicit second order (Beam-Warming) method. Higher accuracy of this method is identified relative to the second order method when the grid is being refined. The convergence rate of this method is also higher than the second order method. Furthermore, the convergence of the method can be adjusted to accommodate the computational hardware capabilities. The excellent potential of implicit fourth order methods in modern PC-based viscous supersonic computational fluid mechanics for supersonic commercial airliners is highlighted. Furthermore, comparison with ANSYS FLUENT (version 19.1) finite volume software is also included for Mach number of 6 and superior bow shock Mach contour computation is achieved with the ADI code