Heat Transfer In Hypersonic Flow Research Articles

Accurately predicting hypersonic transitional flow on cone via a symmetry approach

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics (SED) theory of wall turbulence, for accurately predicting the hypersonic flow heat transfer on cone. The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length (SL) function, and hence is named as SED-SL. This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers (TrBL) around straight cone at zero incidence, to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors (Mach number, temperature ratio, cone half angle, nose Reynolds number and noise level). The results demonstrate the universality of the postulated multi-regime similarity structure, in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone, but also the dependence of the transition onset location on the five influential factors. The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach. It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy, and then points out to an optimistic alternative way to construct hypersonic transition model.

Quantification of parametric uncertainty in k–ω–γ transition model for hypersonic flow heat transfer

The uncertain empirical values of closure coefficients in k–ω–γ transition model flaws the predictive capability. The current work aims to examine the uncertainty of k–ω–γ transition model due to uncertain closure coefficients for hypersonic flow over a flat plate and a straight cone, with introducing the stochastic expansions based on the point-collocation non-intrusive polynomial chaos method into computational fluid dynamics simulations for efficient and accurate uncertainty propagation. Specifically, five model coefficients are regarded as epistemic uncertain probabilistic variables on intervals. The output quantities of interests include the surface heat flux, skin friction coefficient, transition onsets and transition lengths. To better identify the key uncertainty contributor, Sobol indices are utilized as a variable-based global sensitivity analysis approach. Results show that the performance of the k–ω–γ transition model is highly susceptible to its closure coefficients evidenced by that small changes (10%) of model coefficients could yield more than 30% uncertainty in the transition onsets and roughly 17% uncertainty in the transition lengths. The largest uncertainty source contributing to the uncertainty in heat flux, Cf and transition onsets is C3 for hypersonic transitional flows. Besides, C4 dominates the uncertainty in transition lengths. In the future model improvement, attention should be paid to improve apprehension of rational values or constitutions of C2, C3 and C4.

A loosely-coupled gas-kinetic BGK scheme for conjugate heat transfer in hypersonic flows

The gas-kinetic BGK scheme has shown to be a promising method in hypersonic flow simulation from many previous studies. In this paper, a loosely-coupled BGK scheme is developed for solving conjugate heat transfer (CHT) problems in hypersonic flows. For more accurate evaluation of heat flux and better numerical stability, some modifications to the original BGK scheme are suggested, including using an improved way to calculate slopes of distribution functions and applying a non-simplified Prandtl number fix. Different from most CHT solvers that adopt different methods in fluid and solid domains, the BGK scheme can also be extended to simulate the heat transfer in structures, as long as an appropriate BGK model for the heat conduction equation is constructed. The dual-time steeping approach and a recently-developed implicit JFNK–BGK method are used to obtain the time-accurate solutions in individual domains. To achieve the fluid-thermal coupling, two loosely-coupled algorithms are employed, which are based on quasi-steady and unsteady flow computations, respectively. For comprehensive validation of the developed method, several cases of standalone hypersonic flows, standalone structural heat transfers and a typical CHT problem are investigated, and its performances are shown by comparisons with other numerical and experimental results.

Uncertainty and sensitivity analysis of SST turbulence model on hypersonic flow heat transfer

Due to the lacking of knowledge and incomplete information about the closure coefficients in Menter Shear Stress Transport (SST) turbulence model, numerical predictions of hypersonic flow heat transfer possess some uncertainties. The objective of this work is to investigate the uncertainty and identify the key parameters contributing most to the uncertainty in hypersonic aeroheating predictions. In the current study, the nine closure coefficients in SST turbulence model are treated as uncertainty variables represented with intervals, meanwhile stochastic expansion based on non-intrusive polynomial chaos (NIPC) expansion is utilized to represent and propagate the uncertainties, afterwards the Sobol indices evaluated by the polynomial chaos expansion coefficients are used to rank the relative contribution of each closure coefficient. Totally, 110 CFD evaluations are adopted to quantify the uncertainty and sensitivity in hypersonic flow heat transfer. Specifically, uncertainty and sensitivity analysis are performed for hypersonic flow over the double-ellipsoid model and the X-33 flight vehicle. The numerical results show that heat flux is more sensitive to uncertainty of closure coefficients compared to pressure. For the SST model, the coefficients which contribute most to uncertainty in hypersonic flow heat are σω1, κ and a1. While a1 is one of the dominant source of heat flux and pressure in the shock region near the wall.

Thermal protection characteristics for a combinational opposing jet and platelet transpiration cooling nose-tip

A combinational opposing jet and platelet transpiration cooling nose-tip is analyzed. Platelet transpiration is introduced to the opposing jet thermal protection system (TPS) in hypersonic vehicles to enhance the cooling efficiency in the reattachment region without increasing the overall cooling intensity, thereby saving the total coolant consumption. In this study, the combinational cooling nose-tip is simplified with a limited number of enlarged transpiration orifices instead of micro-pores. The two-equation shear stress transport k-w turbulence model is utilized to study the flow field and surface heat transfer in hypersonic flow, and the numerical method is validated against experimental data available in the literature. The peak heat flux reduces more than 6.6% of the combinational cooling nose-tip than that of the opposing jet TPS with the same total coolant consumption. Thus, platelet transpiration can help save the coolant consumption to reach a similar cooling efficiency. The transpiration gas can cover the surface to insulate heating. Results show that the cooling efficiency increases with increasing transpiration intensity. Finally, the peak heat flux of the four-orifice model reduces more than 3.7% than that of the two-orifice model. The cooling efficiency is improved as the number of orifices is increased. This result indicates that the cooling efficiency of the simplified model is underestimated than that of real structures with a large number of transpiration micro-pores.

Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows

This study is concerned with predicting surface heat transfer in viscous hypersonic flows using high-order discontinuous Galerkin (DG) methods. Currently, finite-volume (FV) schemes are most commonly employed for computing flows in which surface heat transfer is a target quantity; however, these schemes suffer from large sensitivities to a variety of factors, such as the inviscid flux function and the computational mesh. High-order DG methods offer advantages that can mitigate these sensitivities. As such, a simple and robust shock capturing method is developed for DG schemes. The method combines intraelement variations for shock detection with smooth artificial viscosity (AV) for shock stabilization. A parametric study is performed to evaluate the effects of AV on the solution. The shock capturing method is employed to accurately compute double Mach reflection and viscous hypersonic flows over a circular half-cylinder and a double cone, the latter of which involves a complex flow topology with multiple shock interactions and flow separation. Results show this methodology to be significantly less sensitive than FV schemes to mesh topology and inviscid flux function. Furthermore, quantitative comparisons with state-of-the-art FV calculations from an error vs. cost perspective are provided.

Assessment of chemical kinetic models on hypersonic flow heat transfer

The objective of this study is to assess the performance of chemical kinetic model for heat transfer acting on the hypersonic vehicle. Four different chemical kinetic models, including Dunn Kang model, Gupta model, Park 87 model and Park 91 model, are implemented and assessed. The differences among these models are obvious, consisting of the elementary reactions, the method of evaluating backward rate coefficients and chemical kinetic rates. In order to further investigate the performance of these models for hypersonic aeroheating prediction, three typical test cases are employed: (1) the heat transfer acting on ELECTRE vehicle at Mach number 13, (2) the heat transfer acting on Apollo command module at Mach number 20.5 and (3) the heat transfer acting on Space Shuttle Orbiter at Mach number 20.985. Firstly, the behaviors of these models are demonstrated by comparing the numerical results with the flight data or experimental data in detail. Secondly, the reasons for the discrepancies of heat fluxes computed with these models are discussed. The results reveal that the heat fluxes acting on ELECTRE vehicle and the head of Space Shuttle Orbiter predicted by these chemical kinetic models are in good consistency and agree well with the flight or experimental data. With the increasing of complexity of the vehicle’s geometry, the differences of heat flux, especially the peak heat flux, become more and more obvious, and the maximum difference among them may exceed 25%. The numerical results also indicate that the numerical prediction of heat transfer acting on complicated geometry exhibits a relatively strong sensitivity to the choice of chemical kinetic models. The difference of chemical kinetic rates and the complicated flow structure in the flowfield may be the primary reasons for the heat flux discrepancies.

A laminar kinetic energy transition model appropriate for hypersonic flow heat transfer

A laminar kinetic energy transition model appropriate for hypersonic flow heat transfer is proposed in this paper. Based on the laminar kinetic energy transition model at low speed, three rectifications are made to make it possess the ability to predict hypersonic flow transition. Firstly, turbulence length scale is revised to consider boundary layer information directly and reflect the kinematic wall effect correctly at hypersonic speed. Secondly, large-scale eddy viscosity is reconstructed to take hypersonic unstable modes into account to describe the procedure of flow instability. Additionally, for the sake of a better results of the full-turbulence simulation and to be compatible with the revised transition model, the eddy viscosity in sheer stress transport model is adopted to substitute for small-scale eddy viscosity. The model has been applied to a number of relevant test cases, including flat plate boundary layers and boundary layer transition over a blunt cone at different Reynolds numbers. The test cases demonstrate the capacity of the model to reproduce transition flow behavior with a reasonable degree of accuracy and reflect the effect of Reynolds number successfully. While it still needs further investigation to capture the overshoot of heat transfer and take more factors showing significant influence on transition into consideration.

Uncertainty Quantification of Hypersonic Reentry Flows with Sparse Sampling and Stochastic Expansions

The objective of this study was to introduce a combined sparse sampling and stochastic expansion approach for efficient and accurate uncertainty quantification. The new techniques are applied to high-fidelity, hypersonic reentry flow simulations, which may contain large numbers of aleatory and epistemic uncertainties. Stochastic expansion coefficients were obtained using the point-collocation nonintrusive polynomial chaos technique with a number of samples less than the minimum number required for a total-order expansion. This study introduced two methods of measuring the accuracy of the expansion coefficients, as well as their convergence with iteratively increasing sample size. The newly developed approaches were demonstrated on two model problems. The first was a model for stagnation point, convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results showed that accurate expansion coefficients could be obtained with half of the minimum number of samples required for a total-order expansion. The second problem was a high-fidelity, computational fluid dynamics model for radiative heat flux prediction on a hypersonic inflatable aerodynamic decelerator during Mars entry. The model consisted of 93 uncertain parameters, coming from both flowfield and radiation modeling. Results indicated that an accurate surrogate model could be obtained with only about 15% of the number of samples required for a total-order expansion when compared with previous work.

Multistep Uncertainty Quantification Approach Applied to Hypersonic Reentry Flows

The objective of this study was to introduce and demonstrate a computationally efficient, multistep uncertainty quantification approach for high-fidelity, hypersonic reentry flow simulations, which may include large numbers of aleatory and epistemic uncertainties. The multistep uncertainty quantification approach included several key components, including a sensitivity-based dimension reduction process that used a local sensitivity analysis at selected sample locations to approximate global sensitivities. Other components included a method to update existing deterministic samples after dimension reduction and a modified point-collocation nonintrusive polynomial chaos method that incorporates existing local sensitivity information. The multistep uncertainty quantification approach was demonstrated on two model problems. The first was a model for stagnation point convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results in reduced dimensions compared well with Monte Carlo simulations. The second problem was a high-fidelity, computational fluid dynamics model for stagnation point radiative heat flux on a Hypersonic Inflatable Aerodynamic Decelerator during a Mars entry. The model consisted of 93 uncertain parameters, coming from both flowfield and radiation modeling. The model was reduced to ten and five uncertain variables, accounting for 95 and 90% of the total output variance, respectively. Pure aleatory, epistemic, and mixed uncertainty quantification analyses were in agreement with previous work, proving the potential and applicability of the multistep uncertainty quantification process for complex hypersonic reentry flow models.

A132 極超音速流中での物体表面温度の測定法

A new type of measurement for surface temperature and heat transfer in hypersonic flow with use of temperature-sensitive paint by the fluorescent phosphor, which is excited by ultraviolet rays, is presented.At first, the relation between temperature and fluorescent intensity is calibrated in static condition.Then, the calibration experiment is applied to a wedge and a cone model in hypersonic flow of Mach 7, and accuracy of this measurement system is evaluated. Simultaneously, surface temperature is visualized by the fluorescence pattern.Solving an unsteady, one-dimensional heat conduction equation, the distribution of heat flux is obtained from the surface temperature distribution, and the boundary layer transition in hypersonic flow is detected and visualized using the cone model with tripping wire.

Evaluation of total body heat transfer in hypersonic flow

Evaluation of total body heat transfer in hypersonic flow

Radiative and convective heat transfer in hypersonic flow around a blunt body

The heat transfer in the vicinity of the critical point is investigated for hypersonic air flow around a blunt body. The gas-dynamical conservation equations are solved simultaneously with the radiative transport equation in integral form. Allowance is made for the viscosity, heat conduction, and the actual radiation parameters of air, including spectral line emission. Profiles are obtained for the thermodynamic variables along the critical line. The dependence of the radiative and convective components of the aerodynamic heating on the velocity and pressure ahead of the shock front as well as the radius of curvature of the blunt nose section is discussed. Approximate relations having the form of similarity laws are derived for the heat fluxes in the vicinity of the critical point. The limits of applicability of the thermodynamic equilibrium approximation in the shock-compressed layer are discussed. The influence of absorption of radiation from the compressed layer by the cold freestream on the aerodynamic heating is considered. Attention is given in this case to the dependence of the spectral absorption coefficient for the cold air on the intensity of the radiation incident upon it.