Thermostructural concepts for hypervelocity vehicles

Shih, Peter K.; Prunty, Jack; Mueller, Richard

doi:10.2514/6.1988-2295

Cited by 7 publications

(6 citation statements)

References 2 publications

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“…While any values of θ k and p k would result in a kriging model that interpolates the sample points exactly, the "best" kriging model is that which utilizes those values of θ k and p k which minimize the function given in Eq. (27).…”

Section: Viia Overview Of Kriging Theorymentioning

confidence: 95%

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Enhanced Modal Solutions for Structural Dynamics in Aerothermoelastic Analysis

Falkiewicz

Cesnik

2011

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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Hypersonic vehicle design and simulation require models that are of low order. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics in the hypersonic regime. This work focuses on the development of efficient modal solutions for structural dynamics of hypersonic vehicle structures under transient thermal loads. The problem is outlined and aerothermoelastic coupling mechanisms are described. A previously developed reducedorder, time-domain aerothermoelastic simulation framework is used as the starting point for this study. This paper focuses on three main modeling areas: 1) The effect of aerodynamic heating on the evolution of free vibration modes shapes and frequencies is examined, 2) A surrogate modeling technique is employed for directly updating the generalized stiffness matrix and thermal loads based on the transient temperature distribution and 3) Basis augmentation techniques are employed in order to obtain more accurate solutions for the structural dynamic response. The techniques to be studied are described and applied to a representative hypersonic vehicle elevator structure. Nomenclature= vector of inputs to function C(b, X) = kriging correlation matrix C = correlation matrix c = vector of POD modal coordinates c = vector of POD modal coordinates for transformed system c p = specific heat at constant pressure d = structural modal coordinates, kriging sample point E = modulus of elasticity F T = thermal load vector of full system in physical space F S = structural load vector of full system in physical space Full = solution vector of full-order model f T = generalized thermal load vector of reduced system in modal space f S = generalized structural load vector of reduced system in modal space G(X (i) , X (j) ) = Gaussian correlation function for kriging model H i = coefficient matrices in numerical integration for structural response h = altitude h i = thickness of i-th layer of thermal protection system K T = thermal conductivity matrix of full system in physical space K G = geometric stiffness matrix K S = structural stiffness matrix * Ph.D. Candidate, K * S = modified structural stiffness matrix k * S = generalized stiffness matrix of reduced system in modal space k T = generalized thermal conductivity matrix of reduced system in modal space L = lower triangular factor in decomposition of K * S L ∞ = L ∞ error l = number of augmented mode shapes lb i = lower bound for i-th POD modal coordinate M = Mach number M T = thermal capacitance matrix of full system in physical space M S = structural mass matrix of full system in physical space m T = generalized thermal capacitance matrix of reduced system in modal space m S = generalized mass matrix of reduced system in modal space MAC i,j = modal assurance criterion value corresponding to modes i and j max i = maximum value of i-th POD modal coordinate min i = minimum value of i-th POD modal coordinate MS = margin of safety with respect to POD bounds NRMSE =...

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Section: Viia Overview Of Kriging Theorymentioning

confidence: 95%

“…[27][28][29][30] This study considers a thermal protection system consisting of an outer heat shield and middle insulation layer on top of the skin as shown in Fig. 7.…”

Section: Shear Layermentioning

confidence: 99%

Enhanced Modal Solutions for Structural Dynamics in Aerothermoelastic Analysis

Falkiewicz

Cesnik

2011

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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“…These challenges require innovative solutions: new high temperature materials, thermal protection system (TPS), and possibly coated leading edges with active cooling. The maximum operating temperature of titanium-based alloys varies between 800 to 1300 K. 29,30 Those materials were studied for potential application in the NASP program. In Ref.…”

Section: Structural Modelmentioning

confidence: 99%

Uncertainty Propagation in Integrated Airframe Propulsion System Analysis for Hypersonic Vehicles

Lamorte

Friedmann

Dalle

et al. 2011

17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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“…The equilibrium surface temperature is the peak temperature that the thermal-structure can achieve, since heat conducted into the structure is zero when the surface fluxes are balanced [18][19][20] . In the absence of active cooling, the incoming aerodynamic heat flux is balanced entirely by thermal radiation from the surface under equilibrium conditions.…”

Section: Introductionmentioning

confidence: 99%

Coupled Analysis of Aerodynamic Heating, Radiative Heat Transfer and Heat Conduction for Hypersonic Vehicles

Chen¹,

Liu²,

Yue³

2015

20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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The aerodynamic heating results in the rapid rise of the surface temperature of hypersonic vehicles. As a key factor that influences the selection and design of thermal structures, equilibrium surface temperatures occur when the aerodynamic heat flux imposed on the surface is balance by thermal radiation from the surface, which are typically utilized in the conceptual and preliminary designs of hypersonic vehicles. Obviously the equilibrium surface temperature is the peak temperature that thermal-structure can achieve, since heat conducted into the structure is not calculated when the surface fluxed are balanced. In order to accurately obtain the temperature environment over specified trajectories, an integrated coupled approach in which the aerodynamic heating, radiative heat transfer and structure heat conduction are all taken into account is proposed. This study aims to develop a coupled analysis methodology for the temperature environment prediction under combined aerodynamic heating, radiative transfer and structure heat conduction. The integrated coupled approach is used to obtain the temperature environment of the typical control surface for a representative hypersonic trajectory. Results illustrate that the temperature environment obtained by integrated coupled approach is obviously lower than that by equilibrium, which regularly leads to 25% maximum percent error on the leading edge, 48% maximum percent error on the other regions. Furthermore, the estimation temperature is associated with the trajectory, which indicates that during climbing phase, the difference of surface temperature obtained by equilibrium and coupled approach is much larger than that during gliding phase. Nomenclatureaero q = aerodynamic heating flux rad q = radiative heating flux cond q = heat conduction flux h  = heat transfer coefficient r h = recover enthalpy w h = wall enthalpy St = Stanton number e  = local air density e u = local air velocity f c = local skin friction coefficient r p = Prandtl number Re = Reynolds number x = distance from the top to the point of interest along the surface  = air viscosity coefficient *  = air density coefficient based on reference enthalpy  = air viscosity coefficient based on reference enthalpy N R = radius of curvature at the leading edge   = air density u  = air velocity c u = velocity at the sea level sl  = density at the sea level * h = reference enthalpy  = Boltzmann constant, 23 1.3806505 10 / J K      = emissivity of surface w T = surface temperature k = thermal conduction coefficient R T = equilibrium temperature trans t  = time step of heat conduction aero t  = time step of aerodynamic heating

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Thermostructural concepts for hypervelocity vehicles

Cited by 7 publications

References 2 publications

Enhanced Modal Solutions for Structural Dynamics in Aerothermoelastic Analysis

Enhanced Modal Solutions for Structural Dynamics in Aerothermoelastic Analysis

Uncertainty Propagation in Integrated Airframe Propulsion System Analysis for Hypersonic Vehicles

Coupled Analysis of Aerodynamic Heating, Radiative Heat Transfer and Heat Conduction for Hypersonic Vehicles

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