Dynamics and Control of Shock Motion in a Near-Isentropic Inlet

MacMartin, Douglas G.

doi:10.2514/6.2002-2943

Cited by 11 publications

(12 citation statements)

References 6 publications

(12 reference statements)

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“…The effect of divergence has been studied here computationally using a simple one-dimensional Euler scheme and the results for a selection of duct divergence angles, all with a steady shock strength of Mach 1.4 and the same downstream pressure perturbation amplitude, are presented in figure 9(a). This technique of perturbing the Euler equations was used by MacMartin (2004) to study the dynamics of a transonic shock in an engine intake and enabled him to develop a simple feedback-control system for shock instability based on the detection of shock position. The results in figure 9(a) show that at low frequency, the amplitudes of shock motion tend to limit values, which correspond to the difference in the steady shock positions at the extremes of the duct exit pressures.…”

Section: Analytical and Computational Studymentioning

confidence: 99%

Unsteady shock wave dynamics

2008

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An experimental study of an oscillating normal shock wave subject to unsteady periodic forcing in a parallel-walled duct has been conducted. Measurements of the pressure rise across the shock have been taken and the dynamics of unsteady shock motion have been analysed from high-speed schlieren video (available with the online version of the paper). A simple analytical and computational study has also been completed. It was found that the shock motion caused by variations in back pressure can be predicted with a simple theoretical model. A non-dimensional relationship between the amplitude and frequency of shock motion in a diverging duct is outlined, based on the concept of a critical frequency relating the relative importance of geometry and disturbance frequency for shock dynamics. The effects of viscosity on the dynamics of unsteady shock motion were found to be small in the present study, but it is anticipated that the model will be less applicable in geometries where boundary layer separation is more severe. A movie is available with the online version of the paper. IntroductionThe dynamic response of shock waves to unsteady perturbations in flow properties is a complex phenomenon. Current understanding has not yet reached the level where unsteady shock motion can be predicted reliably. The phenomenon is especially relevant to the behaviour of transonic shocks, which are sensitive to both upstream and downstream flow conditions. Changes in the flow properties ahead or downstream of a transonic shock can lead to shock motion. The exact nature of this motion is thought to depend on a combination of inviscid and viscous factors including the amplitude and frequency of the disturbance and the presence of boundary layers or regions of flow separation. The mechanism by which disturbances propagate through the flow to reach and influence the shock is also of interest for understanding the physics of unsteady shock motion.The large changes in local flow properties across shock waves mean that unsteady shock motion can lead to large undesirable local fluctuations in properties such as shear stress, pressure and the rate of heat transfer. For this reason, large-amplitude unsteady motion is of most concern in aerodynamic applications. Examples include buffet on transonic aerofoils and engine unstart in supersonic engine intakes, both of which can be caused by periodic pressure perturbations generated downstream of the shock. In a study of transonic buffet, Lee (2001) concluded that pressure perturbations originating in an aerofoil's wake play a key role in shock unsteadiness, while Seddon & Goldsmith (1999) state that engine unstart can be caused by disturbances generated at the face of a downstream compressor. In contrast, studies exploring the relationship between shock unsteadiness and upstream disturbances in the incoming flow have

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Section: Analytical and Computational Studymentioning

confidence: 99%

Unsteady shock wave dynamics

2008

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“…Early attempts at reduced-fidelity modeling of unsteady inlets employ the normal shock relations and model acoustic waves which perturb the flow and simulate shock motion. 13 Another popular approach is to use linearized Euler/Navier-Stokes equations. 14, 15 Linearized models however, apply only to one design point; for the purpose of this research, a nonlinear model capable of simulating the inlet over a range of conditions is desired.…”

Section: Projection-based Reduced-order Modelingmentioning

confidence: 99%

Reduced Order Modeling of Compressible Flows with Unsteady Normal Shock Motion

Marley

Duraisamy²,

Driscoll³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

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Projection-based reduced-order modeling has been used successfully to develop efficient models of fluid flows. However, a majority of the applications are limited to small perturbations about a nominal flow condition and do not typically address strong nonlinearities. In the present work, we assess the viability of reduced-order modeling to the problem of unstart in high-speed engine inlets. A complicating factor in this application is the presence of strong shock waves. Models based on a linearized flow assumption fail to capture the large shock motions associated with unstart. Projection-based, Proper Orthogonal Decomposition (POD) models can -in theory -account for such nonlinearities, but at a very high cost. Advances have been made recently in developing techniques to further accelerate projection-based models. One such method, the Discrete Empirical Interpolation Method (DEIM), is applied in this study to two nozzle flow cases: a fully-expanded nozzle and a nozzle with a normal shock present. In both examples, the model is based on a quasi-one-dimensional inviscid flow assumption. This study highlights the lack of robustness of the DEIM and proposes an alternative acceleration method based on L2-norm minimization. For both test cases, instances are found where DEIM is unstable but L2-norm minimization is not, motivating further work in nonlinear acceleration techniques employing optimization, including L2-norm minimization and compressed sensing.

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“…The T 05 dynamics (3) consists of 45 and T 05 ss terms. These terms are obtained using the relationship given by (10), where the input terms of (10) areṁ 4 , T 04 and P 5 . Also, the input termsṁ 4 and T 04 are computed by the following relationship…”

Section: Stability Analysis Of the Engine's Internal Dynamicsmentioning

confidence: 99%

“…Reference [6] has reported to control the shock-position by the variable nozzle against disturbances using the proportional integral (PI) control technique, where the rig-testing has been carried out to acquire the technique for detection of the shock-position with pressure transducers. In [9][10][11], the shock position control and the active control of the inlet using the proportional and proportional integral control techniques are discussed. In [12], the application of linear stochastic optimal control theory for the supersonic air-breathing inlet shock position control has been reported, in the presence of random airflow disturbances.…”

Section: Introductionmentioning

confidence: 99%

Robust control design of an air‐breathing engine for a supersonic vehicle using backstepping and UKF

Maity

Padhi

2017

Asian Journal of Control

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This paper presents an efficient robust control design approach for an air‐breathing engine for a supersonic vehicle using the Lyapunov stability theory based nonlinear backstepping control, augmented with unscented Kalman filter (UKF). The primary objective of the control design is to ensure that the thrust produced by the engine tracks the commanded thrust by regulating the fuel flow to the combustion chamber. Moreover, as the engine operates in a supersonic range, an important secondary objective is to manage the shock wave location in the intake for maximum pressure recovery with adequate safety margin by varying the throat area of the nozzle simultaneously. To estimate the states and parameters as well as to filter out the process and sensor noises, a UKF has been incorporated for robust output feedback control computation. Furthermore, independent control designs for the actuators have been carried out to assure satisfactory performance of the engine. Additionally, a guidance loop is designed to generate a typical flight trajectory of the representative vehicle using a nonlinear suboptimal input constrained model predictive static programming formulation for testing the performance of the engine. Simulation results clearly indicate quite successful robust performance of the engine during both climb and cruise phases.

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Dynamics and Control of Shock Motion in a Near-Isentropic Inlet

Cited by 11 publications

References 6 publications

Unsteady shock wave dynamics

Unsteady shock wave dynamics

Reduced Order Modeling of Compressible Flows with Unsteady Normal Shock Motion

Robust control design of an air‐breathing engine for a supersonic vehicle using backstepping and UKF

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