Supersonic Engine Inlet

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Description: Active Control of a Supersonic Engine Inlet

Figure 1: Steady-state Mach contours inside diffuser. Freestream Mach number is 2.2.

This example considers unsteady flow through a supersonic diffuser as shown in xx--CrossReference--dft--fig1--xx. The diffuser operates at a nominal Mach number of 2.2, however it is subject to perturbations in the incoming flow, which may be due (for example) to atmospheric variations. In nominal operation, there is a strong shock downstream of the diffuser throat, as can be seen from the Mach contours plotted in Figure xx--CrossReference--dft--fig1--xx. Incoming disturbances can cause the shock to move forward towards the throat. When the shock sits at the throat, the inlet is unstable, since any disturbance that moves the shock slightly upstream will cause it to move forward rapidly, leading to unstart of the inlet. This is extremely undesirable, since unstart results in a large loss of thrust. In order to prevent unstart from occurring, one option is to actively control the position of the shock. This control may be effected through flow bleeding upstream of the diffuser throat.

A complete description of the benchmark can be downloaded as PDF file here.

Active Flow Control Setup

Figure 2: Supersonic diffuser active flow control problem setup.

xx--CrossReference--dft--fig2--xx presents the schematic of the actuation mechanism. Incoming flow with possible disturbances enters the inlet and is sensed using pressure sensors. The controller then adjusts the bleed upstream of the throat in order to control the position of the shock and to prevent it from moving upstream. In simulations, it is difficult to automatically determine the shock location. The average Mach number at the diffuser throat provides an appropriate surrogate that can be easily computed. There are several transfer functions of interest in this problem. The shock position will be controlled by monitoring the average Mach number at the diffuser throat. The reduced-order model must capture the dynamics of this output in response to two inputs: the incoming flow disturbance and the bleed actuation. In addition, total pressure measurements at the diffuser wall are used for sensing.

CFD Formulation

The unsteady, two-dimensional flow of an inviscid, compressible fluid is governed by the Euler equations. The usual statements of mass, momentum, and energy can be written in integral form as

$\begin{align} \frac{\partial}{\partial t}\iint\rho\mathrm{d}V + \oint\rho Q\cdot\mathrm{d}A & = 0 \end{align}$

Origin

This benchmark is part of the Oberwolfach Benchmark Collection; No. 38866, see also .

Data

The matrices are in Matrix Market format inlet.tar.gz. The size of the file is 5.4 MB. The matrix name is used as an extension of the matrix file.

Dimensions

System structure:

$\begin{align} E \dot{x}(t) &= Ax(t) + Bu(t) \\ y(t) &= Cx(t) \end{align}$

System dimensions:

$E \in \mathbb{R}^{11730 \times 11730}$, $A \in \mathbb{R}^{11730 \times 11730}$, $B \in \mathbb{R}^{11730 \times 2}$, $C \in \mathbb{R}^{1 \times 11730}$