Bao Wen

Topological Geometry Interpretation of Supersonic Inlet Start/Unstart Based on Catastrophe Theory

U NSTART phenomenon is one of the most important issues of hypersonic inlets. If an inlet is not started, the mass capture will be greatly reduced, and the spillage drag will be excessive. For hypersonic air-breathing engines, inlet unstart will cause a large drop of both engine thrust and specific impulse, and it may cause catastrophic damage during hypersonic flight. Over the past decades, many investigations have been conducted to examine the mechanisms of inlet start and unstart. Mayer and Paynter [1,2] simulated an axisymmetric inlet unstart due to the variation of freestream variables such as temperature, velocity, and pressure. Neaves and McRae [3] simulated the 3-D inlet unstart caused by a combustor perturbation. Zha et al. [4,5] investigated unstart transient mechanism of a typical axisymmetric inlet at angle of attack. Cox et al. [6] presented several mechanisms of hypersonic inlet unstart, including backpressure unstart, overcontraction unstart, and angle of attack unstart. Van Wie and Kwok [7], Yuan and Liang [8], and others have observed the nonlinear catastrophe and hysteresis phenomena of inlet start/unstart. These studies have made contributions from different aspects. As from these studies, the start/unstart process is influenced by many factors, and the physical law is complex with strong nonlinearities such as catastrophe, hysteresis, etc. Because inlet unstart may cause catastrophic damage to the aircraft, it must be avoided and controlled during hypersonic flight. With this consideration, it is important to study the physical law of inlet start/unstart, for example, to study the catastrophe boundaries of inlet start/unstart at different operation conditions (different flight Mach number, angle of attack, flight height, and back pressure). The physical law of inlet start/unstart will be important for further application (i.e., avoid or control inlet unstart). As known, the transition between inlet start and unstart is mainly characterized by catastrophe, and such systems can be studied by catastrophe theory. With this consideration, this paper will try to use the topological geometry method in catastrophe theory to study the physical law of inlet start/unstart. In general, catastrophe theory permits the establishment of qualitative and general solutions of the catastrophe behaviors, and it can deal with complex systems with catastrophe properties. In this paper,first, the catastrophemechanism of inlet start/unstart is analyzed. Second, the nonlinear catastrophe, hysteresis, and bifurcation features of inlet start/unstart are simulated based on the topological geometrymethod in catastrophe theory, and the catastrophe boundaries of inlet start/unstart are obtained. Third, the physical laws inlet start/unstart are interpreted along typical control routes around the catastrophe boundaries.

Catastrophe Model for Supersonic Inlet Start/Unstart

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.

Distributed parameter control arithmetic for an axisymmetrical dual-mode scramjet

Dual-mode scramjet is one of the candidates for hypersonic flight propulsion system which will be used in wide range of flight Mach numbers from 4 to 12 or higher, wherein dual-mode scramjet should be well designed to be suitable for subsonic/supersonic combustion operation according to the flight conditions. Therefore this system is required to operate in a finite number of operational modes that necessitate robust, stable, and smooth transitions between them by which selective operability of supersonic/subsonic combustion modes and efficient combustor operation in these modes may be realised. A key issue in making mode transition efficient and stable is mode transition control. The major problem in mode transition control is the handling of the various flow and combustion coupling effects of dual-mode scramjet whose physical states are spatially coupled and whose governing equations are partial differential equations. Involving these distributed parameter issues, our basic idea is using the shape control theory to study the control problems of mode transition for dual-mode scramjet with the aim of achieving the desirable design properties and increasing control reliabilities. This specific approach is motivated by the promise of novel techniques in control theory developed in recent years. Concrete control arithmetic of this approach, such as shape control model, sensitivity analysis and gradient-based optimisation procedure, are given in this paper. Simulation results for an axisymmetric, wall-injection dual-mode scramjet show the feasibility and validity of the method.

Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model

Abstract The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.

An idea of distributed parameter control for scramjet engines

Scramjet engines are used under extreme temperatures and with wide range of Mach numbers from 3 to 8 or higher and have shown different control properties from other airbreathing engines. New control problems involving distributed parameter control have been found concerning investigations of the control of scramjet engines whose physical states are spatially interacted and whose governing equations are partial differential equations. The work of this paper is based on the application of distributed parameter control conception to study the control problems of scramjet engines with the aim of achieving the desirable design properties and increasing control reliability. A new control idea based on shape control theory is put forward to realise the distributed parameter control of scramjet engines with the preconditions of proper space dimension and frequency-domain simplification. Simulation results and theoretic analysis for an axisymmetric, wall-injection scramjet engine show the feasibility and validity of the control idea.

Distributed Parameter Control Method for Dual-Mode Scramjets

Because dual-mode scramjets are used under extreme temperatures and with wide range of Mach numbers, they show different control properties from other airbreathing engines. Comparatively, new control problems have been found concerning investigations of the control method for the dual-mode scramjets whose physical states are spatially interacted and whose governing equations are partial differential equations. Such control problems are called distributed parameter control problems which have been studied for several decades but implemented in few fields. The work of this paper is based on the application of distributed parameter control conception to study the control problems of the dual-mode scramjets with the aim of achieving the desirable design properties and increasing control reliability. A new design method based on shape control theory is put forward to realize the distributed parameter control of the dual-mode scramjets with the preconditions of proper space dimension and frequency-domain simplification, and simulation results for a classical dual-mode scramjet show the feasibility and validity of the method.

Observers Design for Shock Position of Supersonic Inlet Based on Equilibrium Manifold

A state observer based on equilibrium manifold is designed to estimate the normal shock position of supersonic inlet. By solving an eigenvalue assignment problem in real time, the gains of the observer are determined according to scheduling variable and desired dynamic performance. The design procedures for both single-input nonlinear systems are presented. Application of the observer to a supersonic inlet to demonstrate its construction and performance is also presented. Nomenclature P1 = pressure at 2

Integrated Thermal Management Method of Energy Based On Closed Brayton Cycle for Scramjet

= temperature at turbine inlet (the maximal temperature) of the cycle τ = temperature ratio of the cycle e = pressure ratio of the cycle ηt = turbine efficiency ηc = compressor efficiency ηth = thermal efficiency of the cycle ωt = power of turbine ωc = power of compressor ωe = power of electric generation Q1 = heat insertion Q2 = heat rejection hfc = hear sink Gf1 = fuel flow used as coolant at regenerative actively cooling Gf2 = fuel flow used as coolant at thermal protection pattern based on CBC Abstract Thermal protection of Hypersonic Vehicle/Scramjet is the critical technology for hypersonic technology,but as for the inner thermal environment of engine is very severe, there is still certain development bottleneck for existing thermal protection. Thermodynamic electric power generation system based on Closed Brayton Cycle discussed in the article, aiming at putting forward a new method and new concept to release the pressure of scramjet thermal protection, and providing enough electric power for hypersonic vehicle. The source of the thought and the constitution of the system are mainly systematically introduced, at last, some initial calculation results are given. Index Terms—scramjet, thermal protection, thermal environment, thermal management

A zero-phase-lag torsional filter for large turbine-generators based on the general observer

The large turbine-generator units have more potential of the torsional interaction with the decrease in the torsional mode frequencies of the shaft system and the increase in the bandwidth of the control systems. A zero-phase-lag torsional filter based on the general observer is developed as a generic countermeasure against the torsional interaction with the control systems in this paper. Different from the general torsional filter, the proposed filter can selectively minimize the torsional oscillation component while the rigid rotation speed is all-pass with zero phase lag, and furthermore, provide additional degrees of freedom which can be used to implement synthesis of some performance specifications for robustness requirements. The synthesis procedure of the zero-phase-lag torsional filter is formulated as a mixed sensitivity problem based on the loop shaping approach. A case study based on the IEEE first benchmark model is given to illustrate the design procedure and performance of the zero-phase-lag torsional filter.