Probabilistic Aspects of Scramjet Design

Abstract

Scramjet design is characterized by a multitude of design variables influencing a highly nonlinear and complex system. Methods such as mean line calculations, high fidelity computational fluid dynamics, and empirical studies are generally used to derive aircraft engine performance. Because of the high complexity and the incomplete knowledge of hypersonic flow regimes, the question of robust design arises in the given context and leads to the need of probabilistic methodology. In this paper a probabilistic approach to scramjet engine design assessing both inflow and model uncertainty is presented. The two different types of uncertainty are quantified with respect to their different nature by use of a two-step bootstrap methodology. A descriptive sampling Monte Carlo method is employed to propagate the quantified uncertainties through the engine model to exemplify the high sensitivity of net thrust vector to present uncertainties and to analyze the correlation between the parameters variations. Nomenclature A = area, m 2 E i = error vector of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) F net;x , F net;y = net thrust in x and y directions, N G i = vector of geometrical parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) h = duct height, m L = segment length, m Ma = Mach number _ m = mass flow, kg s 1 n = surface normal vector p = static pressure, Pa px, px j y = probability of x; probability of x assuming y Re x = Reynolds number S fuel = vector of fuel parameters (see Fig. 1) T = static temperature, K v = velocity, m s 1 X i = vector of deterministic flow parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) X i = vector of probabilistic flow parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) = ramp angle, deg = boundary-layer displacement thickness, m = mean value x = spline describing the geometry of the nozzle expansion ramp = flow density, kg m 3

Uncertainty Propagation in Integrated Airframe Propulsion System Analysis for Hypersonic Vehicles

“…To compensate for unmodeled physics and simplifications, an uncertainty propagation approach is used to quantify sensitivity, robustness and reliability of a given configuration with respect to identified uncertainties. 16,17 The simplifying assumptions, such as fixed geometry or the neglect of real gas effects introduce uncertainty which affects the reliability of the analysis. For this class of problems the uncertainty due to both unmodeled physics and the need to use approximate or reduced order models (ROM) for several components, must be propagated through the analysis.…”

“…7,16 Simplified models are computationally efficient and enable comprehensive analysis of a hypersonic vehicle in a controloriented or optimization-oriented framework. To compensate for unmodeled physics and simplifications, an uncertainty propagation approach is used to quantify sensitivity, robustness and reliability of a given configuration with respect to identified uncertainties.…”

“…19 In Ref. 16, the effect of uncertainty associated with the use of approximate models in the analysis of the propulsion system of a hypersonic vehicle is propagated to the net thrust as a function of fuel inflow rate for two fixed configurations using MCS. Error associated with the approximate models have a significant impact on the prediction of the thrust.…”

Uncertainty Propagation in Integrated Airframe–Propulsion System Analysis for Hypersonic Vehicles

“…Modeling the aerothermoelastic-propulsion interactions requires several simplifying assumptions in each component of the analysis [7,21]. Simplified models are computationally efficient and enable comprehensive analysis of a hypersonic vehicle in a control-oriented or optimization-oriented framework.…”

“…Simplified models are computationally efficient and enable comprehensive analysis of a hypersonic vehicle in a control-oriented or optimization-oriented framework. To compensate for unmodeled physics and simplifications, an uncertainty propagation approach has been used to quantify sensitivity, robustness, and reliability of a given configuration with respect to identified uncertainties [21][22][23][24]. The most effective approaches for propagating uncertainty in aeroelastic problems are direct Monte Carlo simulations (MCSs) [21] and response surface-based methods such as stochastic collocation (SC) or polynomial chaos expansion (PCE).…”