Prediction of Aerothermal Environment and Heat Transfer for Hypersonic Vehicles with Different Aerodynamic Shapes Based on C++

This research paper discusses constructing a unified framework to develop a full-rate scheme for hypersonic heating calculations. The method uses a flow tracing technique with normal phase vector adjustment in a non-structured delineated grid combined with empirical formulations for convective heat transfer standing and non-standing heat flow engineering. This is done using dev-C++ programming in the C++ language environment. Comparisons of the aerodynamic thermal environment with wind tunnel experimental data for the Space Shuttle and Apollo return capsules and standing point heat transfer measurements for the Fire II return capsule was carried out in the hypersonic Mach number range of 6 - 35 Ma. The tests were carried out on an 11th Gen Intel(R) Core(TM) i5-1135G7 processor with a valuable test time of 45 mins. The agreement is good, but due to the complexity of the space shuttle tail, the measurements are still subject to large errors compared to wind tunnel experiments. A comparison of the measured Fire-II return capsule standing-point heat values with the theory for calculating standing-point heat fluxes simulated using Fay & Riddell and wind tunnel experiments is provided to verify the validity of this procedure for hypersonic vehicle heat transfer prediction. The heat fluxes assessed using this method for different aerodynamic profiles of hypersonic vehicles agree very well with the theoretical solution.

vehicles and contributes to the design and development of high-speed vehicles [1]. To this end, accurate prediction of heat transfer rates is a significant issue for researchers and developers working within current space programmes [2]. A low computational cost convective heat transfer technique based on the optimisation of convective heat transfer coefficients has been proposed by Avallone [3] et al. Recent work on the numerical study of convective and hypersonic flows includes the work of Ryzhkov and Kuzenov [4]. A modified non-equilibrium model for oxygen, vital for hypersonic cruise vehicles, has recently been proposed by Kim [5] et al. Reactive gas-surface interactions were investigated by Yang [6] et al. and Bouyahiaoui [7] [8] using an open-source solver for CO 2 flow, which provides a good model for the Martian atmosphere. Steffen [9] performed temperature-sensitive paint (TSP) tests to obtain the convective parameter ρck for measuring various objects in hydrodynamic and aerodynamic experiments Saiprakash et al. discussed the effect of angle of attack and obtuseness on the heating rate distribution of an obtuse cone model at hypersonic velocities [10]. Estruch-Sample [11] [12] discussed a more detailed description of the understanding of hypersonic heat flow and the proposal of an engineering method to predict the location and magnitude of the highest heat transfer rate. In 2020, Shen [13] presented the effect of angle of attack variations on a hypersonic vehicle's incoming heat transfer and thermal protection system (TPS) under offdesign conditions. Moreira numerically simulated the atmospheric re-entry vehicle SARA using the Navier-Stokes equations using the finite volume method [14]. Mohammed and Kim et al. used aerodynamic thermal load progenitors and considered local piston theory and the Eckert reference enthalpy temperature method to effectively predict the temperature variation of the entire mission trajectory of a hypersonic vehicle [15] [16].
Many researchers have proposed several solutions to the problem of aerodynamic heating of hypersonic vehicle surfaces. These include research work using numerical computational methods, indirect measurements of the heat flow distribution on the surface of an object using temperature-sensitive coatings, and discussions of the effects of different wind conditions on the heating rate distribution of the classical model. There has never been a systematic, efficient and low-cost solution. In this paper, a C++-based aerodynamic thermal calculation program is constructed to obtain the surface heat flow through the surface element method, radius of curvature calculation, and streamline tracking techniques for the Space Shuttle Orbiter, AS-202, and FIRE-II, respectively. The calculated results are in good agreement with the wind tunnel experimental results.

Definition of a Computational Model
In this paper, NASA's open source parametric geometric modelling software Open VSP (Open Vehicle Sketch Pad) was used for the parametric description and automatic generation of the 3D CAD models of the Apollo Command Module (AS-202 Flight Test) [17] and Space Shuttle Orbiter [18]. The open source

Surface Element Method and Surface Pressure Calculation
The essence of the solution by the surface element method is the assumption that the aerodynamic properties of each grid are only related to the parameters of the free incoming flow and the geometrical parameters of the current grid   ( ) C p is the local friction coefficient and R is the gas constant. According to the cold wall assumption, let the wall temperature be 300 K, can calculate the wall enthalpy H w . Adiabatic wall enthalpy calculation formula is The relevant factorless parameter is assumed to be constant, taking Pr = 0.71 [22].

Surface Pneumatic Thermal Environment and Heat Flow Calculations
Based on a comparative study of the accuracy of different standing heat flow formulas in the relevant literature [23], the Kemp-Riddell formula was selected for this paper to calculate.
where ρ 0 = 1.225 kg/m 3 , v c = 7900 m/s, R N is the radius of curvature of the standing point (m); q ws is the standing point heat flow density, and h s is the standing point hysteresis enthalpy.
In this paper, the Voronoi method of Meyer [24] is chosen to calculate the best-fitting surface using sufficient adjacent triangles in the least squares sense.
The principal curvature is then calculated directly from this cubic surface. The average value of the principal curvature is used to determine the local radius.
The curvature and radius of curvature are calculated as where the mixing area is the area of the red area in Figure 4.

Results and Analysis of Program Calculations
The next set of results is for the Space Shuttle Orbiter module. The re-entry conditions are listed in Table 1 Figure 5 shows the surface temperatures predicted using the methods in this paper. Details of the centreline pressure and temperature distributions are shown in Figure 6 and Figure 7. This paper does a good job of predicting centreline pressure and it also does a good job of predicting windward centreline temperature. On the leeward side of the vehicle, a trend towards increased heating on the vertical tail is captured, but the change in temperature and magnitude is not accurately predicted.         Figure 2. Figure 12 shows the surface pressure distribution along the Apollo centreline and Figure 5 compares the results of this paper's solution with those of CBAERO and DPLR along the vehicle centreline. In general, the pressure field is well predicted, as is the overall temperature on the heat shield. The method in this paper does capture the peak heating in the shoulder of the return capsule, but the distribution beyond the shoulder is not consistent with the DPLR results.
To validate the standing heat flow density method, this paper compares data from the FIRE-II flight experiment, shown in Figure 13. The FIRE-II project was a suborbital re-entry test conducted by NASA in 1965 using a scaled-down

Conclusions
This paper used a C++-based aerodynamic engineering calculation program to predict three re-entry vehicle shapes, including the return module and re-entry vehicle, flying at speeds from Mach 6 to Mach 35. In the Fire-II flight state of 1639s-1643s, the air is subjected to pyrolysis and chemical reactions that affect the prediction of heat flow at the stationary point, which the authors will consider in their subsequent work.
The ability of the method to predict the convective heating, and thermodynamic environment of the vehicle, based on the vehicle shape, and flight speed, is compared with high fidelity CFD and flight test data. As a tool for rapid engineering methods, comparison with flight test data was found to be "reasonable" for predicting complex flow fields for various re-entry vehicles. The short time required to predict a complete set of flight data using this method is an effective tool for predicting the complete aerothermodynamic environment early in the conceptual and preliminary design phase of a hypersonic vehicle.