Aerothermal Loads Research Articles

ED-ResNet: Euler Equation Embedding Double-Series Residual Neural Network for Aerothermal Modeling

The data-driven aerothermal modeling method provides strong support for the hypersonic aircraft design. To reduce the training samples and improve the global geometric generalization ability, the Euler equation embedding double-series residual neural network (ED-ResNet) is presented. Firstly, the wall inviscid solution is approximated to the information of the boundary layer outer edge by solving the Euler equation. Then, based on the principle of feature construction, the physical features of the boundary layer outer edge can be constructed. Finally, the double-series residual neural network (D-ResNet) is employed to establish the aerothermal model by using physical features of the boundary layer outer edge as input data. The physical features of the boundary layer outer edge are the bridge between the Euler equation and D-ResNet; it has a prior ability to distinguish the quality of generalization. The performance of the proposed ED-ResNet is validated using hypersonic double-ellipsoid, hypersonic ellipsoid, and blunt cone. The results indicate that with only four training samples, ED-ResNet can obtain high-precision aerothermal extrapolation prediction results with an error of less than 7% relative to Reynolds-averaged Navier–Stokes calculation results. Meanwhile, the ED-ResNet can successfully predict aerothermal loads for unknown geometric shapes, with a global geometric generalization error less than 13%.

Aerothermal characterization of the CALLISTO vehicle during descent

AbstractAerothermal loads are a design driving factor during launcher development as the thermal loads directly influence thermal protection system (TPS) design and successively the possible flight trajectory and mission profiles. Recent developments in reusable launch vehicles (RLV) (e.g. SpaceX, Blue Origin) have added the dimension of refurbishment to the challenges the thermal design must consider. With the current European launcher roadmap moving towards a reusable first stage aerothermal loads may significantly change. The CALLISTO vehicle is a flight demonstrator for future reusable launcher stages and their technologies developed by a tri-national consortium and planned to fly in 2025. For this vehicle the highest heat fluxes are mainly due to heating from hot exhaust gases and heated air in the proximity of the aft bay and on the exposed structures like legs and fins. In the presented study we conducted computational fluid dynamics (CFD) studies to determine the aerothermal loads on the vehicle during descent through the landing approach corridor for both phase B and phase C aeroshapes. A defining difference to previous aerothermal databases (ATD) is that the CALLISTO demonstrator is planned to execute a series of test flights with different energy levels, as well as a final demo flight. This leads to an large parameter space the final aerothermal database needs to cover. The database development is described in detail and analysed for integral and local loads, as well as interpolation uncertainties. The final phase C database allows interpolation of interface heatfluxes for the entire flight domain (Mach number, density $$\rho )$$ ρ ) at varying angle of attack (AoA). Further the sensitivity of the plume-vehicle interaction to angle of attack, chemistry, thrust vector control (TVC) and engine throttling are investigated for a critical Mach number indicating further areas of improvement for future databases.

Simulation of Hypersonic Shock-Boundary Layer Interaction Using Shock-Strength Dependent Turbulence Model

Shock-induced flow separation is important in hypersonic intake unstart and for unsteady aero-thermal loads. This work presents a computational study of shock-boundary layer interaction (SBLI) at hypersonic Mach numbers. The objective is to accurately predict the separation bubble size for oblique shock impingement on a turbulent boundary layer and for two-dimensional axisymmetric cone-flare SBLI cases. We use the Reynolds-averaged Navier Stokes method with an advanced shock-strength-dependent turbulence model. A recently developed transport equation-based shock sensor is employed to identify the location and strength of shock waves. The computational results are found to match experimental measurements of surface pressure and skin-friction coefficient for a series of test cases, highlighting the effects of Mach number, shock generator angle, and wall cooling on the size of the separation bubble. Results are also found to conform to the scaling of SBLI separation size found in the literature. This is one of the few such corroborations for hypersonic axisymmetric SBLI.

Aerothermal Loads on a Representative Porous Mesostructure at Flight Conditions Using Direct Simulation Monte Carlo

Spacecraft require thermal protection systems (TPS) in order to survive the extreme conditions present during atmospheric entry missions. Porous ablators are a class of TPS materials that have been used successfully on several entry missions, although they can be difficult to model because of their complex nature at the micro- and mesoscales. Specifically, the processes that lead to mechanical erosion (spallation) of these materials are poorly understood. In order to gain insight into the spallation process, the current work computes aerothermal loads on a mesostructure representative of FiberForm (the substrate of phenolic impregnated carbon ablator) by leveraging a simulation framework involving loosely coupled Computational Fluid Dynamics-Direct Simulation Monte Carlo (CFD-DSMC) simulations of hypersonic boundary layers. CFD boundary layers are extracted from two altitudes, 68.9 and 81 km, along the Stardust entry trajectory and are imposed as boundary conditions on a DSMC simulation over an artificially generated mesostructure, which is representative of the charred layer of the TPS material. In order to produce high-quality results, the DSMC boundary conditions require careful consideration; specifically, Chapman–Enskog distributions are needed to account for large velocity and temperature gradients. Visualizations of the DSMC flowfield indicate excellent agreement with the original CFD data, and the aerothermal loads (heat flux and traction force) on the surface were examined using probability density functions. Additionally, the effects of pyrolysis blowing through the mesostructure on the surface properties are also determined.

Modelling and Parametric Study for Panel Flutter Problem using Functionally Graded Materials

Abstract In this paper we will demonstrate the possibility of weight optimization of panels under aero-thermal loading in hypersonic flow using functionally graded materials (FGM). The in-plane volume fraction of two constituents (Aluminium and Nickel) is modelled using polynomial distributions. Different material grading layouts are investigated, including cases with Nickel concentrated at corners, sides, midpoints and center. The solution of the problem utilized a higher order element with C1 continuity. The study covers the linear boundaries of the panel flutter problem as well as the non-linear post-buckling deflections. The results indicated Nickel placement strategies are shown to enhance dynamic pressure and vibration performance for a given mass reduction through optimal center and edge localization. Overall, the integrated modelling approach demonstrates the potential to systematically optimize stability, weight and integrity in hypersonic flow to optimize the weight of panels subject to aero-thermal loads.

Transient Plasma Wind Tunnel Testing Under Thermomechanical Loads for Reentry Break-Up Analysis

This paper introduces a novel approach for transient plasma wind tunnel testing in an arcjet facility, enabling the experimental simulation of the aerothermal loads along reentry trajectory segments. Such experiments newly allow for the investigation of the causes of break-up events. The trajectory segment is simulated by duplicating the time-resolved profiles of the characteristic flow parameters, namely, heat flux and stagnation pressure as well as the mechanical load, which represents the aerodynamic forces. In arcjet facilities, the parameters that govern the plasma condition are split into variable and constant parameters, which define the available altitude range that can be replicated. The variable conditions arc current and ambient pressure were determined with steady-state trajectory points and traces determined between these conditions resulting in a full trajectory segment. The test time then relates directly to an altitude on the trajectory segment, which allows for an experimental determination of the main break-up altitude. The methodology is applied to a trajectory segment of the transport vehicle CYGNUS OA6, covering an altitude range from 85 to 70 km. A transient break-up experiment on an aluminum bar yielded a failure at an altitude corresponding to 77.6 km, showing a thermomechanical characteristic. These results align well with the observed break-up altitude of CYGNUS OA6, showing the potential of the proposed method.

Modeling the Interaction of Proximal Fragments for Destructive Atmospheric Entry Analysis

The destructive atmospheric entry process is distinguished by the formation of several fragments due to the severe aerothermal loads encountered during the descent. The proximity of debris leads to shock wave interactions and collisions between bodies, influencing the overall dynamics of the fragments and affecting the prediction of demise and ground impact location. To account for these effects, the use of computational fluid dynamics is introduced to resolve the shock interaction patterns by employing a quasi-steady approach, and the use of a simple rigid-body collision model is introduced to represent the dynamics of fragments in the cloud of debris. The quasi-steady approach is assessed and validated by comparative analysis with a few studies in the literature. One of these examples is the rebuilding of the VKI’s experiment of a free-flying ring crossing a shock wave generated by the presence of a stationary cylinder. The impact of explicitly modeling collision dynamics in the trajectory of fragments and ground spread distance is validated by considering a set of relevant test cases from the literature and tested them for destructive atmospheric reentry of the Attitude Vernier Upper Module, the launcher VEGA upper stage.

Nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) beams subjected to aero-thermal loads

This paper studies the nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) cantilever beams subjected to aero-thermal loads. The nonlinear partial differential equations governing the problem are determined based on the Euler-Bernoulli beam theory using the von Kármán-type geometrical nonlinearities. The Galerkin method is then applied to discretize the differential equations and to transform them into a nonlinear ordinary differential equation. The coupled ordinary differential equations are solved analytically using the method of multiple time scales (MTS) to study the nonlinear forced vibration time response of the selected FG-FRCL structures, where a large parametric study checks for the effect of power-index, uniform temperature rise, velocity of the free stream air and Mach number on their axial and lateral response, with interesting insights from a scientific and design purposes.

Thermo-Structural Response Prediction of UHTCC Control Surface for Hypersonic Cruise Vehicle

One of the most complex issues that govern the design of a hypersonic vehicle is aerodynamic heating which is much more severe for an air-breathing vehicle as it operates within the atmosphere for longer durations. Due to the detrimental impact of aerodynamic heating on the vehicle structure, it is imperative to develop a robust thermal protection system that can protect the vehicle from high temperatures. However, the development of sophisticated TPS for slender components is impractical and, therefore, requires a hot structure system that can operate at substantial aerothermal loads. The aim of this study is to predict the impact of aero-heating on a UHTCC-based hot structure system of a hypersonic cruise vehicle through uncoupled thermo-structural analysis of the control surface. Validation of numerical methods implemented is done through literature comparison and grid independency tests.

Aero-Thermal Analysis of the Critical Factors in a Winged Reusable Launch Vehicle for Safer Re-Entry

This paper presents a brief review of the critical factors and phenomena involved in the aero-thermal analysis of a winged reusable launch vehicle. The heat flux evaluation for the re-entry phase is assessed based on the suitability of the available simulation techniques under diverse conditions. This is followed by a short description of the physics involved in each of the factors, their corresponding effects on the main objective and the usual and possible future strategies to deal with them. Finally, the ultimate thermal management of the vehicle surface is discussed based on the literature reviews and a comparative study is depicted showing the benefits over previous ideas. This work can be of use for further research on low wing loading effect to validate the reduction in heat flux and hence the aero-thermal loads thereby ensuring a safer and an affordable atmospheric re-entry for future space explorers.

Linearly combined transition model based on empirical spot growth correlations

The transition from laminar to turbulent flow in a hypersonic boundary layer is modeled using an intermittency-based linear combination approach. A simplified transition model like this enables a quick assessment of aero-thermal loads and the overall flight efficiency of high-speed vehicles during the initial design phase by weighting purely laminar and turbulent flow results on the basis of an empirically calculated intermittency. The transition model presented within this work includes an empirical model to account for Mach number, Reynolds number, wall temperature and pressure gradient effects on turbulent spot growth based on available turbulent spot studies in the literature. A validation of the transition model is carried out for a number of different test cases and a methodology to extend the model to generic geometries is presented to enable a more general application.

Investigation of flow control methods for reducing heat flux on a V-shaped blunt leading edge under real gas effects

Complex shock interactions and severe aerothermal loads are often encountered on the lips of three-dimensional inward-turning inlets, which presents significant challenges to the performance and safety of hypersonic flight vehicles. However, there have been few investigations on reducing the heat flux of the lips, especially when considering real gas effects. It is, therefore, necessary to investigate flow control methods that are suitable for the lips under real gas effects. Three flow control methods are implemented in this work—a passive method with the shock control bump and stagnation bulge, an active method with counterflow jet, and a combined method. The lip is simplified as a V-shaped blunt leading edge to eliminate the influence of other structures. Numerical simulations are performed at freestream Mach numbers ranging from 6.0 to 12.0. The principles and abilities of different flow control methods for reducing heat flux are compared and analyzed. Although the passive and active methods can reduce the heat flux by more than 40% at low Mach numbers, they have an apparent deficiency under strong real gas effects at high Mach numbers. Moreover, the active method causes new heat flux peaks near the nozzle and at the reattachment position of the flow separation zone. Therefore, a combined method is proposed for further reducing the heat flux. By coupling the passive and active methods, the combined method can reduce the heat flux by nearly 60%. In general, the flow control methods investigated in this work can achieve satisfactory heat flux reduction abilities.

BAYESIAN IDENTIFICATION OF PYROLYSIS MODEL PARAMETERS FOR THERMAL PROTECTION MATERIALS USING AN ADAPTIVE GRADIENT-INFORMED SAMPLING ALGORITHM WITH APPLICATION TO A MARS ATMOSPHERIC ENTRY

For space missions involving atmospheric entry, a thermal protection system is essential to shield the spacecraft and its payload from the severe aerothermal loads. Carbon/phenolic composite materials have gained renewed interest to serve as ablative thermal protection materials (TPMs). New experimental data relevant to the pyrolytic decomposition of the phenolic resin used in such carbon/phenolic composite TPMs have recently been published in the literature. In this paper, we infer from these new experimental data an uncertainty-quantified pyrolysis model. We adopt a Bayesian probabilistic approach to account for uncertainties in the model identification. We use an approximate likelihood function involving a weighted distance between the model predictions and the time-dependent experimental data. To sample from the posterior, we use a gradient-informed Markov chain Monte Carlo method, namely, a method based on an Ito stochastic differential equation, with an adaptive selection of the numerical parameters. To select the decomposition mechanisms to be represented in the pyrolysis model, we proceed by progressively increasing the complexity of the pyrolysis model until a satisfactory fit to the data is ultimately obtained. The pyrolysis model thus obtained involves six reactions and has 48 parameters. We demonstrate the use of the identified pyrolysis model in a numerical simulation of heat-shield surface recession in a Martian entry.

Physics-Infused Reduced-Order Modeling of Aerothermal Loads for Hypersonic Aerothermoelastic Analysis

This paper presents a novel physics-infused reduced-order modeling (PIROM) methodology for efficient and accurate modeling of nonlinear dynamical systems. The PIROM consists of a physics-based analytical component that represents the known physical processes and a data-driven dynamical component that represents the unknown physical processes. The PIROM is applied to the aerothermal load modeling for hypersonic aerothermoelastic (ATE) analysis and is found to accelerate the ATE simulations by two to three orders of magnitude while maintaining an accuracy comparable to high-fidelity solutions based on computational fluid dynamics. Moreover, the PIROM-based solver is benchmarked against the conventional proper-orthogonal decomposition/kriging surrogate model and is found to significantly outperform the accuracy, generalizability, and sampling efficiency of the latter in a wide range of operating conditions and in the presence of complex structural boundary conditions. Finally, the PIROM-based ATE solver is demonstrated by a parametric study on the effects of boundary conditions and rib supports on the ATE response of a compliant and heat-conducting panel structure. The results not only reveal the dramatic snapthrough behavior with respect to spring constraints of boundary conditions but also demonstrate the potential of the PIROM to facilitate the rapid and accurate design and optimization of multidisciplinary systems such as hypersonic structures.

Aerodisk Effect on Hypersonic Boundary Layer Transition and Heat Transfer of HIFiRE-5 Vehicle

The substantial aerodynamic drag and severe aerothermal loads, which are closely related to boundary layer transition, challenge the design of hypersonic vehicles and could be relieved by active methods aimed at drag and heat flux reduction, such as aerodisk. However, the research of aerodisk effects on transitional flows is still not abundant. Based on the improved k-ω-γ transition model, this study investigates the influence of the aerodisk with various lengths on hypersonic boundary layer transition and surface heat flux distribution over HIFiRE-5 configuration under various angles of attack. Certain meaningful analysis and results are obtained: (i) The existence of aerodisk is found to directly trigger separation-induced transition, moving the transition onset near the centerline upstream and widening the transition region; (ii) The maximum wall heat flux could be effectively reduced by aerodisk up to 52.1% and the maximum surface pressure can even be reduced up to 80.4%. The transition shapes are identical, while the variety of growth rates of intermittency are non-monotonous with the increase in aerodisk length. The dilation of region with high heat flux boundary layer is regarded as an inevitable compromise to reducing maximum heat flux and maximum surface pressure. (iii) With the angle of attack rising, first, the transition is postponed and subsequently advanced on the windward surface, which is in contrast to the continuously extending transition region on the leeward surface. This numerical study aims to explore the effects of aerodisk on hypersonic boundary layer transition, enrich the study of hypersonic flow field characteristics and active thermal protection system considering realistic boundary layer transition, and provide references for the excogitation and utilization of hypersonic vehicle aerodisk.

New insights into the nonlinear stability of nanocomposite cylindrical panels under aero-thermal loads

In the present study, thermal-aerodynamic postbuckling and thermal flutter behaviors of functionally graded (FG) graphene nanoplatelets (GPLs) reinforced composite (GPLRC) cylindrical panels are theoretically investigated. Homogenization techniques such as the modified Halpin-Tsai model and Voigt’s rule are applied to calculate resultant material properties. The derived model of the cylindrical panel is based on assumptions of the first-order shear deformation theory (FSDT) and von Kármán geometrical nonlinearity. The aerodynamic load induced by the supersonic airflow is determined by the first-order piston theory, whilst the thermal load is based on the quasi-steady thermal stress theory. The element-free improved moving least-square Ritz (IMLS-Ritz) method is applied to develop the nonlinear equations solved with the aid of the Newton-Raphson method. The accuracy and effectiveness of the established numerical model are verified by comparisons with the results from the literature. Effects of key parameters such as aerodynamic pressure, temperature rise, GPL distributions and weight fraction, and geometric properties of cylindrical panels are carried out to comprehensively examine their aerothermoelastic responses. Finally, new insights into the stability of graphene platelet reinforced panels under aerodynamic and thermal loadings are presented and deeply discussed.

Gas–surface interactions in a large-scale inductively coupled plasma wind tunnel investigated by emission/absorption spectroscopy

Precise prediction of aerothermal loads is significantly limited by the unclear interactions between the thermal protection system surface and the surrounding high-enthalpy gas. To address this, we propose an optical diagnostic method based on optical emission spectroscopy and laser absorption spectroscopy to investigate the gas–surface interactions within the boundary layer. Experiments are conducted in an air plasma flow produced by the 1.2 MW inductively coupled plasma wind tunnel at the China Academy of Aerospace Aerodynamics with an enthalpy of 20 MJ/kg and a heating time of 100 s. The cylindrical samples made of pure silicon carbide are tested, and quartz samples with the same exposed geometry are tested in parallel as a reference material. The optical emission spectroscopy system has four spectrometers to cover the wide wavelength range of 200–1100 nm, providing qualitative, spatially, and spectrally resolved measurements of the multi-species radiative emission adjacent to the sample surface. Laser absorption spectroscopy is deployed at different axial locations to quantify the number density and translational temperature of OI (3s5S) with a 500 Hz scanning rate and 200 kHz acquisition rate. Additionally, the surface temperature of each sample is detected by an infrared pyrometer. Scanning electron microscopy and energy dispersive spectrometry are performed before and after the plasma heating. Our measurement results provide valuable information on surface reaction pathways and catalytic recombination effects on atomic oxygen number density distributions. Finally, these self-consistent results show that the proposed method is reliable to deeply investigate gas–surface interactions within boundary layer in harsh aerothermal environment.

Coupled Simulation of Hypersonic Fluid–Structure Interaction with Plastic Deformation

Supersonic and hypersonic vehicles experience significant aerothermal loads from the exterior flowfield and/or their propulsion system. Thus, reliable prediction of aerothermal heating is important for the design of such vehicles. However, even modest temperature changes can lead to buckling of mechanically constraint lightweight structures. This deformation changes the flowfield, which can lead to locally amplified heating, which in turn increases deformation and temperature even further. Thus, fluid–structure coupled modeling of such problems is crucial for the reliable prediction of the resulting temperatures. To investigate these phenomena numerically, we conducted a three-dimensional thermomechanical simulation of fluid–structure interaction (FSI) for thermal buckling. It is necessary to use a thermomechanically coupled model because the temperature and deformation distributions across the panel are highly nonlinear and dependent on both the flowfield and the state of the structure. Due to the high temperatures () in the metallic panel and the constrains, which allow no uniform expansion, the stresses exceed the yield stress, and plasticity occurs. A strong two-way coupled FSI simulation was set up and split into a thermal solid, a mechanical solid, and a fluid computation. The simulated temperature and displacement distribution were compared to experiments conducted in the arc-heated wind tunnel L3K at the German Aerospace Center (DLR). We obtained good agreement between the simulation and experimental results. The observed deformation of the structure was found to locally increase the wall heat flux by up to 40%.

Impact of Anisotropic Mesh Adaptation on the Aerothermodynamics of Atmospheric Reentry

The presence of complex geometries and/or multiple bodies during atmospheric reentry may lead to complex and directional flow features, such as shock waves and shear layers, that need to be correctly predicted to ensure accurate calculation of the aerothermal loads during reentry. Central in ensuring reliable numerical prediction of loads is the adoption of meshes that ensure grid independence and minimize the misalignment between the directional flow features and the grid cell interfaces, a situation that is known to give rise to nonphysical behaviors and spurious oscillations. The use of anisotropic unstructured grid adaptation is here presented as a means to ensure appropriate grid resolution and alignment with directional flow features for cases where the use of structured grids is not always possible or practical. Results highlight the effectiveness and reliability of anisotropic mesh adaptation in successfully predicting the location of shock discontinuities as well as surface aerothermodynamic quantities, while providing results comparable with established approaches relying on structured meshes. Results are presented for single- and multiple-body cases through comparison with experimental data and reference numerical solutions.

Development and Verification of Nonequilibrium Reacting Airflow Modeling in ANSYS Fluent

High-speed flow problems of practical interest require a solution of nonequilibrium aerothermochemistry to accurately predict important flow phenomena, including surface heat transfer and stresses. The complex coupling of nonequilibrium effects on the aerothermal load remains a challenging aspect of hypersonic flow modeling. As a majority of these flow problems are in the continuum regime, computational fluid dynamics (CFD) is a useful tool for modeling nonequilibrium flows. However, there are a limited number of CFD solvers with nonequilibrium flow modeling capabilities that are highly scalable on parallel architectures and can handle complex geometries. This work demonstrates that a commercial general purpose CFD solver can be effectively modified to include high-fidelity nonequilibrium aerothermochemistry and transport models. The paper presents modifications of a general purpose CFD solver, ANSYS Fluent, using the user defined functions to model salient aspects of nonequilibrium flow in air with a five-species reacting mixture: , , NO, N, and O. The modifications to the solver include Gupta–Yos high temperature mixing laws and Park’s two-temperature nonequilibrium chemistry models. The developed solver was verified for several benchmark nonequilibrium flow problems and compared with the available experimental data and other nonequilibrium flow simulations. The work establishes future possibilities for coupled aerothermal and electromagnetic simulations in thermochemical nonequilibrium.