A harmonic gradient method for unsteady supersonic flow calculations

Abstract

An accurate and effective method for calculations of unsteady three-dimensional supersonic flow has been developed. The present method is capable of handling general cases of planar, coplanar, and nonplanar wing planforms in the complete frequency domain. A harmonic-gradient potential model is provided for elementary doublet panels to be made compatible with the wave number generated. Consequently the number of panel elements required is least affected by the given Mach number and reduced frequency. Thus, the required panel number can be optimized to as few as 30, a fraction of the number required by the existing methods. To assess the accuracy and effectiveness of the present method, comparison with various available data is given. AC P h i L m M (x,y,z) (X,Y,Z) a. CO Subscripts J T.E. Nomenclature = lifting pressure coefficient = structural mode shapes = reference chord length = slope of leading or trailing edge of the panel element = freestream Mach number = wing-fixed coordinates; (x,y,z) = (X/$L, Y/L, Z/L) (see Fig. 1) = control point location in (x,y,z) coordinates = true physical coordinates = position of leading or trailing edge of the panel element at 77 = 0 = moving coordinates (see Fig. 1) = oscillatory potential = modified velocity potential = ^e ikMX = doublet solution of modified potential = circular frequency of harmonic motion = index of the number of chordwise element in the yth strip = index of the number of strip -trailing edge of the wing -wake

Transonic-Aerodynamic-Influence-Coefficient Approach for Aeroelastic and MDO Applications

“…The modalbased matrix [A m ] contains intrinsically all of the necessary aerodynamic information as provided by the baseline pressure-mode relation Eq. (2). The present AIC procedure is not con ned to a particular set of CFD methods.…”

From Piston Theory to a Unified Hypersonic-Supersonic Lifting Surface Method

“…4 Nevertheless, supersonic lifting surface methods, such as the harmonic gradient method (HGM, or known as the ZONA51 code), 4 are con ned to planforms of very thin sections, whereby no thickness effect can be accounted for. On the other hand, it has been known for some time that the supersonic thickness effect could render a forward shift in the aerodynamic center, thereby reducing the utter speed.…”

Application of Navier–Stokes simulations for aeroelastic stability assessment in transonic regime

“…It is here speculated that it may be due to possible excessive numerical error introduced by a spurious entropy production behind the detached leading edge shock wave. To support this hypothesis we simply show the results obtained by using the harmonic gradient method [46] known as ZONA-51, a linearised supersonic potential method. In fact, the agreement with the experiment is good for it, both in terms of flutter velocity and frequency, better than any RANS simulation seen for the present test case.…”