Catastrophe Model for Supersonic Inlet Start/Unstart

Abstract

Mathematical models may be very valuable for studying the flow laws of supersonic inlet start/unstart. From a viewpoint of structure stability, this paper makes a link between the catastrophe points of inlet start/unstart and the singular points in Whitney's singularity theory, from which we take notice of the conception of singularity classification, which may be helpful for modeling the catastrophe points of inlet start/unstart. By further research, Thom's catastrophe theory is found to be the right mathematical tool to classify general singularities by topological method. This paper makes an effort to model the catastrophe points of inlet start/unstart by the elementary catastrophe model in catastrophe theory and puts forward a new method to fit data to the catastrophe model. The method is based on nonlinear topological transformation, which has provided an improvement over the existing Cobb's method. Simulation results have shown that the present model is in good agreement with the data. Nomenclature M = Mach number u = independent variable V = potential function x = dependent variable = angle of attack = weight coefficient = weight coefficient = the location parameter = scale parameter = mass-flow-rate coefficient Subscripts 0 = incoming flow

Multistability and Complex Routes of Supersonic Inlet Start/Unstart

“…2. In [16], Tao et al further proposed a topological approach to model the hysteresis and bistability behaviors of inlet start/unstart using computational fluid dynamics data. The model's merit was that it could provide a model structure for studying the bistability behaviors of inlet start/unstart, and it could describe quantitatively the stability boundaries of inlet start/unstart, which was critical to the designs of inlet control system.…”

“…Recently, Bo and Kun-yuan [17] built an empirical equation for the self-starting limit of supersonic inlets, which presents the approximate relationship of maximum self-starting internal contraction ratio and average Mach number of cowl-lip section. Essentially, its model structure is the same as that in [16]. In this paper, we will further build a mechanistic model to describe the hysteresis and bifurcation behaviors of inlet start/unstart.…”