A program for calculating the aerodynamic properties of hypersonic vehicles based on the surface element method was developed using the general-purpose programming language C++. The calculated values of lift coefficients, drag coefficients, and surface pressure coefficients are discussed with the results of wind tunnel experiments using the HL-20 lift body and the NASA hypersonic aircraft STS Columbia OV-102 as research subjects. Finally, the results of the experimental and wind tunnel studies of the aerodynamic characteristics of the HL-20 lift body at an altitude of 65 km and Mach numbers of 6 and 10 Ma are discussed. The maximum error in the aerodynamic characteristics at 6 Ma does not exceed 3%, consistent with the results. The maximum error at 10 Ma occurs in the 11° - 14° angle of attack and does not exceed 10%, which is still within the error tolerance. The STS results for NASA’s hypersonic aircraft were also tested using this procedure. Experimental aerodynamic data for the Colombian OV-102 aircraft. The results show that the program takes only 10 minutes to calculate the results, with no more than 2% error from the wind tunnel experimental results.
Hypersonic vehicles are receiving worldwide attention. Their design and development require an in-depth understanding of hypersonic flows. Accurate prediction of hypersonic flow around re-entry vehicles remains one of the most challenging problems in aerospace engineering. The aerodynamic properties of hypersonic vehicles are a prerequisite for determining their aerodynamic shape, flight trajectory, and flight performance. The pressure and surface sassafras distribution, closely related to aerodynamics, is critical for deciding hypersonic vehicles’ loading conditions and thermal environment. Irimpan, K. et al. addressed the problem of nose tip transition control of surface roughness of hypersonic spheres [
The hypersonic vehicle aerodynamic engineering calculation program developed in this paper consists of four parts: the open-source program NETGEN [
As in
surface element coordinate system. It is then possible to calculate the angle of impact of the free incoming flow with the vehicle’s surface. The velocity vector of the free incoming flow is input through the interaction window, and the normal vector of the surface element is calculated with the correction completed in the previous subsection by Equation (1) to calculate the magnitude of the impact angle.
θ = π 2 − cos − 1 N ⋅ V | N | | V | (1)
Taking values in the range [−π/2, π/2].
Different empirical formulas need to be used for the windward and leeward surfaces in the engineering calculations of aerodynamic engineering properties. For the classical Newtonian theory to calculate the vehicle’s aerodynamic properties, it is assumed that there is no collision between the fluid and the leeward surface, considering Cp = 0. The pressure coefficient of each surface element is directly related to the magnitude of the aerodynamic force on that surface element. The procedure designed in this paper chooses the Dahlem-Buck formula for calculating the windward surface based on the Newtonian method and the tangent cone method [
1) Dahlem-Buck formula
C p = C p D ⋅ C p c o n e ( M a ∞ ≤ 20 ) C p c o n e ( M a ∞ = 20 ) (2)
C p D = { [ 1 sin 3 / 4 ( 4 θ ) + 1 ] sin 2 θ , 0 ≤ θ ≤ 22.5 ˚ K sin 2 θ , θ ≥ 22.5 ˚ (3)
By fitting a large amount of experimental data, the values taken in the Dahlem-Barker formula can be calculated with different fitting formulas according to the vehicle’s various parts.
For the fuselage:
K = 2.38 + 0.03792 θ − 0.002521 θ 2 + 0.00004583 θ 3 + 2.917 × 10 − 7 θ 4 (4)
For the wings:
K = 3.24 − 0.08867 θ + 0.002775 θ 2 − 4.333 × 10 − 5 θ 3 + 2.5 × 10 − 7 θ 4 (5)
For operating the helm surface:
K = 1.15 + 0.004179 θ + 0.0009958 θ 2 − 4.166 × 10 − 6 θ 3 + 4.166 × 10 − 8 θ 4 (6)
2) ACM Experience formula
C p = max [ − ( θ 15 ) ( 1 M a 2 ) − ( 1 M a 2 ) ] (7)
The program uses the two methods mentioned above to calculate the surface pressure coefficient for each surface element and stores the calculation results in the.dat folder.
The coupling effects of the viscous-free aerodynamic properties under hypersonic conditions are minor. The axial force, normal force, lateral force, and moment coefficients on each surface element can be obtained. Summing these coefficients, the whole model’s total aerodynamic force and moment coefficients can be obtained. The modeled body coordinate system performs the calculation of the surface element aerodynamic forces and moments. In order to get the total aerodynamic forces and moment coefficients, they need to be converted to the body and velocity coordinate systems for processing.
C x = ∑ C p n x Δ A S r e f (8)
C y = ∑ C p n y Δ A S r e f (9)
C z = ∑ C p n z Δ A S r e f (10)
Thus, based on the impact angle and the incoming flow conditions, each aerodynamic parameter of the vehicle can be calculated.
Lift factor:
C L = − C x sin α + C z cos α (11)
Non-viscous drag coefficient:
C D = C x cos α sin β + C y sin β + C z sin α cos β (12)
Pitch moment coefficient:
C M = [ ∑ C p ( x − x C G ) n z Δ A − ∑ C p ( z − z C G ) n x Δ A ] ( S r e f b r e f ) (13)
Sref is the reference surface area of the vehicle, bref is Feature-length, and CG is the position of the center of gravity.
The measured flow field at the windward surface of the NASA Space Shuttle STS Columbia OV-102 is provided in Ref. 2. A program was used to calculate the surface pressure coefficients at the streamlines along the center streamline of the Shuttle orbiter, and the flow chart of the space shuttle is divided by tecplot, as shown in
Using Solidworks to model the spacecraft STS Columbia OV-102, the program calculations were imported into the post-processing Tecplot software. The surface flow lines were divided using stream traces, as shown in
The HL-20 space shuttle orbiter model can be exported through the open-source open-vsp software to export the geometric model file, as shown in
The model is imported into the pre-processing software proe5.0 for meshing, as shown in
In NASA wind tunnel experiments, a large amount of experimental data is provided in the experimental environment from negative to positive angles of attack (−5˚ to 35˚) at speeds from Mach 1.5 to Mach 10. In this paper, the aerodynamic characteristics data at different angles of attack are selected for arithmetic verification under the operating conditions of Ma = 6 and 10. The calculated results are compared with the wind tunnel experimental data for analysis.
As shown in Figures 6-8,
with the wind tunnel experimental values. At 10 Ma, with the increase of the angle of attack, the maximum error of the lift coefficient appears at the angle of attack of 20˚, the error is 16%, and the error of the drag coefficient is not more than 5%.
In this study, an STL surface mesh-based procedure is proposed for the aerodynamic prediction of hypersonic vehicles to calculate the aerodynamic properties of hypersonic velocities. Different Mach numbers, angles of attack, and models are used to calculate the surface pressure distribution. The surface pressure coefficients along the central axis of the STS Columbia OV-102 are calculated using the streamline tracking technique. The calculated results were verified with wind tunnel experimental data of the HL-20 high-lift body vehicle at Mach 6 and Mach 10, and the results were in good agreement. The variation of aerodynamic properties was obtained for the given conditions. An appropriate method of surface pressure calculation was chosen for this study. The results show that the method’s accuracy is good due to selecting an appropriate surface pressure calculation method in each region of the hypersonic vehicle surface. The number of HL-20 high-lift surface elements is 43,587. Compared to the usual CFD calculations, the aerodynamic calculation program in this paper runs on an 11th generation Intel(R) Core(TM) i5-1135G7 processor in only 210 seconds of physical time. A set of 20 iterations from negative to positive angles of attack (−5˚ to 30˚) can be run in 0.5 hours. Based on the low time consumption of this method, the accuracy is high. It will be more versatile and flexible in the early design phase of hypersonic vehicles, especially in optimizing hypersonic vehicle configurations and surface hypersonic heat flow transport calculations. In future work, the results of the aerodynamic characteristic coefficients calculated by the procedure in this paper can be used in the Kemp-Riddell heat flow formulation for heat transfer coefficient and heat flow density calculations [
The authors declare no conflicts of interest regarding the publication of this paper.
Huang, T.Q., He, G.Y. and Wang, Q. (2022) Calculation of Aerodynamic Characteristics of Hypersonic Vehicles Based on the Surface Element Method. Advances in Aerospace Science and Technology, 7, 112-122. https://doi.org/10.4236/aast.2022.72007