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Particle-in-cell (PIC) simulations of a microwave oven free-running 2.45 GHz “cooker” ten-vane magnetron operating with a “cold” explosive-emission cathode in a uniform axial magnetic field are performed with two computer codes, improved concurrent electromagnetic PIC (ICEPIC), and CST Particle Studio (CST-PS). PIC simulations are done to compare results obtained by these two codes to each other and, in such a way, identify all possible advantages and disadvantages of each code performance as a reliable tool allowing to predict all important characteristics of the magnetron operation. Results of the PIC simulations show that the range of applied voltages within which the magnetron is able to operate in the $\pi $ -mode at an external uniform axial magnetic field 0.19 T is much broader as it is predicted by the CST-PS code, from 4.00 to 4.70 kV, than as it predicted by the ICEPIC code, from 3.90 to 4.10 kV. It is also shown that while the magnetron startup time gradually decreases, as it is predicted by the ICEPIC code, from about 700 ns (3.90 kV) to about 100 ns (4.20 kV) with the applied voltage increase, it initially chaotically varies, as it is predicted by the CST-PS code, between about 1000 ns (4.03 kV) and about 300 ns (4.01 kV) and only then gradually decreases down to 10–20 ns (4.40–4.60 kV) with the applied voltage increase. Additional PIC simulation with MAGIC or VORPAL codes would be interesting to perform as well to compare the obtained with these codes simulation results with results described in this article.

Computations were performed to understand propulsion tradeoffs that occur when a hypersonic vehicle travels along an ascent trajectory. Operability limits are plotted that define allowable flight c...

A generic waverider-type hypersonic aircraft that undergoes an ascent trajectory has been modeled using a first-principles reduced-order model. Two types of operability limits are added that represent boundaries on the aircraft trajectory map (of vehicle altitude versus Mach number). These boundaries are associated with engine unstart and ram–scram transition. The predicted unstart boundary is to be avoided; the ram–scram transition is a condition through which the aircraft must fly, but it is useful for the control system to know when this transition is approached to account for possible sudden changes in thrust and moments. The model shows that unstart occurs if the aircraft flies too high, too slow, or at too great of an acceleration. The unstart limit can be avoided by selecting a trajectory having sufficiently large dynamic pressure or a low vehicle acceleration. Optimizing these factors avoids an excessive value of the fuel–air ratio that is required for trim. The model also identifies an engine inl...

Air-breathing hypersonic vehicles are based on an airframe-integrated scramjet engine. The elongated forebody that serves as the inlet of the engine is subject to harsh aerothermodynamic loading, which causes it to deform. Unpredicted deformations may produce unstart, combustor chocking, or structural failure due to increased loads. An uncertainty quantification framework is used to propagate the effects of aerothermoelastic deformations on the performance of the scramjet engine. A loosely coupled airframe-integrated scramjet engine is considered. The aerothermoelastic deformations calculated for an assumed trajectory and angle of attack are transferred to a scramjet engine analysis. Uncertainty associated with deformation prediction is propagated through the engine performance analysis. The effects of aerodynamic heating and aerothermoelastic deformations at the cowl of the inlet are the most significant. The cowl deformation is the main contributor to the sensitivity of the propulsion system performance...

A general strategy is identified to compute the minimum fuel required for the ascent of a generic hypersonic vehicle that is propelled by a dual-mode ramjet–scramjet engine with hydrogen fuel. The study addresses the ascent of an accelerator vehicle rather than a high-speed cruiser. Two general types of ascent trajectories are considered: acceleration within scramjet mode, and acceleration across the ramjet–scramjet transition boundary maximum acceleration and maximum dynamic pressure (lowest allowed altitude) were shown to be near optimum for scramjet-mode trajectories, but optimized trajectories were found to be more complex when both modes are considered. The first-principles model used in this paper computes the combustion efficiency using finite-rate chemistry and a fuel–air mixing model. It also computes the inlet efficiency with a shock wave interaction code, and thus avoids empirical formulas for efficiency that were used in previous models.

An improved method has been developed to compute the thrust of a dual-mode scramjet, which is an engine with a combustor that operates both subsonically and supersonically. This strategy applies to any internal flow that can be modeled one-dimensionally. To handle the mathematical singularity at the location of thermal choking, the simple Shapiro method is expanded to create a new method that includes finite-rate chemistry and high-temperature gas properties. A forward shooting method is employed to find appropriate initial conditions for integration of the governing equations, which results in a unique transonic (choked) condition capable of reaching a supersonic state at the end of the domain. Solutions of the governing equations are computed using the propulsion code MASIV, which has been integrated into a hypersonic vehicle flight dynamics code. Computations for both ram-mode and scram-mode operations are compared to experimental results. Predictions are made for flight conditions of a hypersonic vehi...

interaction between operating condition and plume shape complicates the analysis of such nozzles compared to traditional bell nozzles. A method that is based on Riemann interactions is proposed for the analysis of two such nozzle geometries. The method assumes two-dimensional geometries and supersonic flow. Unlike the method of characteristics, this method accounts explicitly for the presence of oblique shocks and curved shear layers. Comparisons to both experiment and computational fluid dynamics are shown. The solution method requires no grid generation and typically runs in less than a minute on a single desktop computer, which is ideal for conceptual design, control design, or control evaluation studies. It includes high-temperature gas modeling and finite-rate chemistry. Nomenclature A = area c = specific heat Ex = momentum conservation error H = height or length scale M = Mach number nexp = number of discrete waves in expansion nsp = number of species p = pressure r = length of characteristic R = normalized gas constant T = temperature u = magnitude of flow velocity W = molecular weight x, y = spatial coordinates Y = mass fraction = angle between wave and upstream flow = ratio of specific heats = deflection angle across a wave = angle of deflection caused by boundary layer = flowpath angle = momentum thickness " = ratio of static pressures = Mach angle = Prandtl-Meyer angle = streamwise coordinate = density = angle between wave and x-axis ˙ ! = molar rate of production

DOI: 10.2514/1.50272 A new engine model has been developed for applications requiring run times shorter than a few seconds, such as design optimization or control evaluation. A reduced-order model for mixing and combustion has been developed that is based on nondimensional scaling of turbulent jets in crossflow and tabulated presumed probability distribution function flamelet chemistry. The three-dimensional information from these models is then integrated across cross-sectional planes so that a one-dimensional profile of the reaction rate of each species can be established. Finally, the one-dimensional conservation equations are integrated along the downstream axial direction and the longitudinal evolution of the flow can be computed. The reduced-order model accurately simulates real-gas effects such as dissociation, recombination, and finite rate chemistry for geometries for which the main flow is nearly onedimensional. Thus, this approach may be applied to any flowpath in which this is the case; ramjets, scramjets, and rockets are good candidates. Comparisons to computational fluid dynamics solutions and experimental data were conducted to determine the validity of this approach. I. Introduction T HIS work addresses the need for an improved control-oriented model of a dual-mode ramjet/scramjet propulsion system. Improvements are needed to include more realistic estimates of the losses of the propulsion efficiency due to shock wave interactions in the inlet, as well as due to gas dissociation and incomplete combustion in the combustor section. One problem is that previous lowerorder propulsion models [1–3] do not include the losses due to multiple shock interactions, gas dissociation, and incomplete combustioncausedby finiteratechemistry.Thisisaseriousproblem, because the main advantage of ascramjet engine over a ramjet isthat the scramjet reduces losses due to internal shock waves and gas dissociation [4]. That is, the scramjet eliminates the need for strong internalshockwavestodeceleratethegastosubsonicconditionsand maintains lower static temperatures than a ramjet, which reduces the dissociation losses. The present effort addresses previous shortcomings by including both of these types of losses into a code called MASIV. MASIV consists of several reduced-order models (ROMs). One is an inlet ROM that computes losses due to multiple shock/ expansion wave interactions; this ROM is described elsewhere [5]. The other is a fuel/air mixing/combustion ROM that is the focus of the present paper. MASIV has been incorporated into a larger hypersonic vehicle (HSV) code, which is available without charge and without International Traffic in Arms Regulations restrictions. Sincecomputational fluiddynamics(CFD)codestakemanyhours to reach solutions for reacting flows, they are difficult to apply to problems in which a large number of solutions are required. A tool that can solve these configurations in a short time to acceptable accuracyishighlydesirableforcontrolanddesignapplications,such

Scramjet vehicles, especially those used as part of an orbital launch system, must operate over a wide range of flight conditions. One component that has difficulty accommodating a range of Mach numbers is the inlet. In this article, only two-dimensional-type scramjet inlets are considered. Such an inlet with fixed geometry can be designed for a single Mach number (using approximately the shock-on-lip configuration) or a range of Mach numbers. However, the performance of the inlet tends to degrade as the size of the Mach number range increases. One method to improve this performance is to use a variable-geometry cowl. Three cowl motions are considered in this paper: moving the whole cowl up and down, moving the whole cowl forward and backward, and rotating the cowl lip. A low-order model designed for control-oriented applications is used to simulate wave interactions. The model is used to evaluate the benefits of each type of variable geometry, and an inlet designed for a wide range of Mach numbers is presented.

Turning flight of an X-43-like air-breathing hypersonic vehicle is discussed. Equations of motion for turning flight of an air-breathing hypersonic vehicle are derived, and several constant-altitude turning flight configurations are analyzed. In addition to calculating an operating map for a combination of altitudes and Mach numbers, a linearization is performed for the case of a 2g turn, and stability properties are discussed. The stability properties are compared to those of a non-turning flight condition at the same altitude and Mach number. A low-order vehicle model, which includes effects due to wave interactions, fuel mixing, and other factors, is used for the calculation.

Steady, level flight for an air-breathing hypersonic vehicles requires balancing intricate couplings among the engine, lifting surfaces, and control effectors. A newly developed fundamental model is used to determine the range of flight Mach numbers and altitudes at which this balance can be obtained. The hypersonic vehicle was developed specifically for flight dynamics evaluations, and the model can calculate the net forces and moments on a three-dimensional vehicle in less than ten seconds using a single 2.6 GHz processor. The propulsive model includes complex physics such as wave interactions, fuel mixing, and finite-rate chemistry. This type of model requires less computational resources than a model based on computational fluid dynamics and provides a more accurate characterization of the flight envelope than simplified models could.

Air-breathing hypersonic vehicles are based on an airframe-integrated scramjet engine. The elongated forebody that serves as the inlet of the engine is subject to harsh aerothermodynamic loading, which causes it to deform. Unpredicted deformations may produce unstart, combustor chocking, or structural failure due to increased loads. An uncertainty quantification framework is used to propagate the effects of aerothermoelastic deformations on the performance of the scramjet engine. A loosely coupled airframe-integrated scramjet engine is considered. The aerothermoelastic deformations calculated for an assumed trajectory and angle of attack are transferred to a scramjet engine analysis. Uncertainty associated with deformation prediction is propagated through the engine performance analysis. The effects of aerodynamic heating and aerothermoelastic deformations at the cowl of the inlet are the most significant. The cowl deformation is the main contributor to the sensitivity of the propulsion system performance...

Hypersonic vehicle flow path design must be approached as an entire system because of the interactions between overall thrust and moment on vehicle performance and stability. It is therefore difficult to design hypersonic vehicles using conventional design techniques such as component optimization. This study examines the design problem with a more unified approach, considering tradeoffs throughout the design space in order to consider what causes a vehicle to have acceptable performance throughout. Several combustor designs from the open literature are examined using a reduced-order model (ROM). Some design principles are proposed for placement of injectors and location of wall divergences and their angles. An automatic design framework suitable for multidisciplinary optimization (MDO) is presented. Previous models did not include a model for switching between ram-mode and scram-mode operation; the derivation of such a model also is presented.

Control evaluation and multidisciplinary optimization are two types of computation that require extremely fast computation of vehicle or component performance. These computations require relatively accurate prediction of performance and performance trends, but they do not need to retain full-fidelity information about every part of the vehicle. This paper presents some results of a computer code that predicts the performance of scramjet and ramjet powered vehicles. The code (including some rudimentary design capability) runs in less than 2 seconds. Run times for batch analysis can be faster because redesign is not required at each iteration. Thermodynamic performance traces are presented along the flow path length. Combustor performance and design are analyzed with respect to performance and stability over a range of operating conditions. Sensitivity plots of thrust with respect to Mach number and altitude are shown. Operating maps are presented for comparison between different proposed designs.

Control-oriented models of hypersonic vehicle propulsion systems require a reduced-order model of the scramjet nozzle that is accurate to within 10% but requires less than a few seconds of computational time. To achieve this goal, a reduced-order model is presented, which predicts the solution of a steady two-dimensional supersonic flow through a nozzle or around any other two-dimensional geometry. Expansion fans are modeled as a sequence of discrete waves instead of a continuous pressure change. Of critical importance to the model is the ability to predict the results of multiple wave interactions rapidly. A reduced mechanism is used to account for finite-rate chemistry, which is needed to accurately account for recombination in the nozzle. To assess the accuracy of the proposed method, some comparisons to CFD solutions of nozzle flows are presented.

This paper provides details of the combustion and inlet submodels used in the MichiganAir Force Scramjet In Vehicle (MASIV) model. The model solves conservation equations in 1-D, using several modeling techniques to retain some of the fidelity of higher-order simulations. Inlet wave interactions, fuel mixing and finite-rate chemistry are considered. The order of the problem is reduced by physics-based, experimentally-verified algebraic scaling laws, which retains the required physics but reduces the computation time of the problem to seconds, instead of the several days required by computational fluid dynamics (CFD). Scaling coecients and assumptions are given. The model is used to compute the performance of an experimental configuration for which real data are available.

A new scramjet engine model, called MASIV, has been developed for control-oriented applications. To reduce computational time, each component models the pertinent physical mechanisms while reducing the spatial dimensionality of the problem. New aspects of MASIV include real-gas dissociation, finite-rate chemistry, a new fuel-air mixing model, an assumed-PDF turbulent combustion model, and interactions of shocks and expansion waves. Strategies for designing 2D scramjet inlets are discussed. One approach is optimize an inlet for a single flight condition. When an inlet designed in this way is at the design condition, all shocks intersect at the cowl leading edge. This optimizes performance at the design condition, but for o-design operation losses are highly sensitive to changes in Mach number and angle of attack. An improved inlet design is described that operates eciently over a range of conditions. In addition, the scramjet combustor also is analyzed to show the eect of pressure distribution on thrust performance for five fuel injection locations. Results suggest general design guidelines, one of which is that injectors should be placed as far upstream as is practical, so that most of the combustion is completed upstream of the nozzle.

A new control-oriented scramjet engine model has been developed, named the MichiganAFRL Scramjet In Vehicle model (MASIV); it is used to compute thrust sensitivity to variation in flight conditions. The model solves conservation equations in 1-D, using several modeling techniques to retain some of the fidelity of higher-order simulations. A number complex physical processes are modeled (including jet mixing and finite rate chemistry) by a combination of ordinary dierential equations and algebraic scaling laws. The axial evolutions of the various flow quantities are computed in a short time, relative to computational fluid dynamics solutions. Although there is some loss of accuracy when using Reduced Order Models (ROMs), MASIV computes the overall performance of the flow path with respect to vehicle dynamics (thrust and drag) at an acceptable level for preliminary design and for use as a submodel for control design and evaluation. The model is exercised to predict the sensitivity of the thrust to variations in Mach number and angle of attack, and to compute the operating envelope of the engine.

To model the performance and operability limits of a dual-mode scramjet engine, the heat release distribution must be accurately predicted. This distribution controls the thermal choking point, and thus the proflles of pressure, Mach number, and heat transfer in the engine. The current research efiort consists of two parts: measurement of heat release distributions from OH* and CH* in a dual-mode combustor, and development of a 1-D scramjet engine performance model. A dual-mode combustor with transverse wall fuel injection and a cavity ∞ameholder is investigated experimentally for air stagnation temperatures of 1270-1520K. The upstream region of the heat release distribution depends on the ∞ame stabilization and spreading. The ∞ame length and downstream region of heat release distribution appear to be mixing limited for all cases. This result is used to develop a combustion model for a quasi-1-D scramjet combustor code.

A new scramjet engine model has been developed to support hypersonic vehicle design studies and flight dynamics and control system analysis. This paper explains the methodology and the governing equations for the new propulsion system model that is suitable for use with a control oriented dynamic model of a hypersonic vehicle. Previous propulsion models used for this purpose were based on simple Rayleigh flow for the combustion process, but despite this, captured the propulsion system interactions with the vehicle aerodynamics and structural dynamics. A new, higher fidelity propulsion system model is constructed that simulates numerous phenomena that were neglected in the Rayleigh flow approach. The new model is of higher fidelity, and therefore it is not designed to calculate the flow physics on a timescale that is suitable for dynamics and control simulations. Instead it will be used as a truth model and the starting point for the derivation of a reduced-order model. Specific phenomena that are included in the new model are: a pre-combustion shock train within the isolator and its interactions with the combustor, the loss of stagnation pressure due to gas dissociation and recombination, wall heat transfer and skin friction, a fuel-air mixing submodel, and a finite-rate chemistry and autoignition reaction mechanism. It is shown that the new propulsion system model expands the operability envelope as compared to the previous model by accommodating ramjet combustion, which occurs at high supersonic/low hypersonic flight Mach numbers.

This research effort is focused on developing a control-oriented model of a generic hypersonic vehicle that includes the interactions between several integrated components. The present paper addresses the interactions between the propulsion system and the flight dynamics of the vehicle model for two different propulsion system models. The first model is a low-fidelity propulsion model that assumes the combustion process is Rayleigh flow, and the combustor is coupled with an isentropic diffuser and internal nozzle, thus ignoring the effects of internal shock waves, area variations, and real gas effects. A second, higherfidelity propulsion system model that includes several new phenomena then analyzed. This model includes a pre-combustion shock train within the isolator and its interactions with the combustor, the loss of stagnation pressure due to gas dissociation and recombination, wall heat transfer and skin friction, a fuel-air mixing submodel, and a finite-rate chemistry description of autoignition. When the new propulsion model is added, it is observed that the poles and zeros undergo a shift, with the short-period poles moving closer to the imaginary axis. The unstable transmission zeros associated with the flight path angle are also observed to move towards the imaginary axis, and take a much more pronounced shift as compared to the short-period poles. This is attributed to a reduced lift curve slope and pitch stiffness for the high fidelity propulsion system model that stems from an change in the thrust sensitivity to angle-of-attack.