Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Inviscid stability of compressible flows past compliant surfaces

Mandeep Deka, Gaurav Tomar, Viswanathan Kumaran

Abstract

The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and analyze the inviscid equations to derive the theorems. We show that the generalised inflection point criteria of compressible rigid wall flows is modified for flows past dissipative compliant walls. Theorems on the bounds for the wave-speed for unstable modes in the inviscid limit are derived. These are similar to the ones for incompressible compliant wall flows, but are different from compressible rigid wall flows. A new criterion for existence of neutral modes with wave-speeds outside the range of minimum and maximum base velocities is derived for compressible flows past non-dissipative compliant walls. We show that in external compressible flows, neutral modes without a critical point can exist even with dissipative compliant walls, which is not the case in the incompressible limit.

Inviscid stability of compressible flows past compliant surfaces

Abstract

The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and analyze the inviscid equations to derive the theorems. We show that the generalised inflection point criteria of compressible rigid wall flows is modified for flows past dissipative compliant walls. Theorems on the bounds for the wave-speed for unstable modes in the inviscid limit are derived. These are similar to the ones for incompressible compliant wall flows, but are different from compressible rigid wall flows. A new criterion for existence of neutral modes with wave-speeds outside the range of minimum and maximum base velocities is derived for compressible flows past non-dissipative compliant walls. We show that in external compressible flows, neutral modes without a critical point can exist even with dissipative compliant walls, which is not the case in the incompressible limit.
Paper Structure (10 sections, 10 theorems, 66 equations, 1 figure)

This paper contains 10 sections, 10 theorems, 66 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Formulation
  3. Results
  4. Theorems for neutral ($c_I = 0$) modes.
  5. Theorems of stable/unstable ($c_I \neq 0$) modes.
  6. Theorems for purely span-wise perturbations ($k_x = 0$).
  7. Summary
  8. Normal mode equations
  9. Boundary conditions for the compressible Rayleigh equation
  10. Purely spanwise modes

Key Result

Proposition 1

A neutral mode for an internal flow or a subsonic neutral mode for an external flow, with $\hbox{Min}(\bar{u}) < c_R < \hbox{Max}(\bar{u})$, can exist in the inviscid limit, in a compressible flow past non-dissipative compliant surfaces ($D=0$) only if, at the location where $\bar{u} = c_R$.

Figures (1)

  • Figure 1: Schematic of a compressible flow past compliant walls.

Theorems & Definitions (10)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6
  • Proposition 7
  • Proposition 8
  • Proposition 9
  • Proposition 10