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Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration
Accepted Manuscript Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration Jie Huang, Wei-Xing Yao, Xian-Yang Shan PII:
S0094-5765(18)31697-7
DOI:
https://doi.org/10.1016/j.actaastro.2018.11.039
Reference:
AA 7206
To appear in:
Acta Astronautica
Received Date: 18 October 2018 Revised Date:
20 November 2018
Accepted Date: 25 November 2018
Please cite this article as: J. Huang, W.-X. Yao, X.-Y. Shan, Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration, Acta Astronautica (2018), doi: https://doi.org/10.1016/j.actaastro.2018.11.039. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration
a
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Jie Huanga, Wei-Xing Yaoa,b,∗, Xian-Yang Shanc
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle,
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b
Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China c
System Design Institute of Hubei Aerospace Technology Academy, Wuhan 430040, China
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Abstract: In order to reduce the hypersonic aerodynamic drag and heating, a combined spike and rear opposing jet configuration is proposed in this paper, and the CFD method is adopted to analyze the drag and heat reduction efficiency. The results show that the spike pushes the bow shock wave away from the blunt body, which translates the normal shock wave into the oblique shock wave and reduces the shock wave intensity. In addition, the low temperature jet gas is injected into the flow field, which reduces the temperature of the flow field after the shock
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wave. So the combined configuration reduces the aerodynamic drag and heating of the blunt body by the reconstruction of flow field, and the drag and heat reduction efficiency is better than the other configurations that already exist. The influences of the length of spike, total pressure of the opposing jet and jet gas on the drag and heat
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reduction efficiency are studied. The results show that increasing the length of the spike and the total pressure of the opposing jet can effectively improve the drag and heat reduction efficiency, and the decreasing rates of the
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aerodynamic drag and heating slow down gradually with the increase of above two parameters. In addition, the nitrogen has the best drag reduction efficiency and the carbon dioxide has the best heat reduction efficiency. The investigations in this paper verify the advantages and application in engineering of the combined configuration proposed in this paper.
Keywords: Hypersonic; Drag and heat reduction; Combined configuration; Spike; Opposing jet.
∗
Corresponding author. E-mail address: [email protected] (W.X. Yao).
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diameter of blunt body
d1, d2
diameter of spike and opposing jet
e
total energy per unit mass of air
Fc
non-viscous flux vector
Fv
viscous flux vector
∆h
height of the first layer wall grid
k
turbulent kinetic energy
L
length of spike
Ma∞
Mach number of free stream
Ma0
Mach number of opposing jet
m
mass of jet gas
n
normal unit vector
Pw
wall pressure
P0
total pressure of opposing jet
P∞
static pressure of free stream
Qw
wall heat flux
Qt
total heat flux of blunt body
Qmax
maximum wall heat flux of blunt body
Re
Reynolds number
T∞ Tw
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S
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D
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drag coefficient
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Cd
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Nomenclature
reference area
static temperature of free stream wall temperature
T0
total temperature of opposing jet
u, v, w
velocity components in the rectangular coordinates
V∞
speed of free stream
Vi
volume of the control volume
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conservative vector
y+
dimensionless parameter of turbulent model angle of attack α
α
angle of attack
γ
ratio of specific heat
ε
turbulent dissipation rate
λ
heat conductivity coefficient of gas
µ
dynamic viscosity of air
µT
eddy viscosity
ρ
density of gas
τij
viscous stress components
ω
specific dissipation rate
Introduction
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1.
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The hypersonic vehicles, such as the space vehicle and high-speed missile, are subjected to the huge shock wave drag during the flight [1–2], which will seriously affect the aerodynamic performance of the hypersonic vehicle. In
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addition, the hypersonic vehicle is also subjected to the huge aerodynamic heating during the flight [3–5]. And some thermal protection measures must be taken to ensure the internal structure of the vehicle within the sustainable temperature range. Therefore, the investigations on the drag and heat reduction technology of the hypersonic vehicle
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are very importance to the performance and safety of the vehicle and has important engineering significance. The spike is a slender rod installed on the nose cone of the hypersonic vehicle, which is used to reduce
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aerodynamic drag and aerodynamic heating. Since the 1950s, experiments and numerical studies related to drag and heat reduction of the spike have been carried out. And the spike has been applied successfully in the engineering, such as the American UGM-133 Trident-Ⅱballistic missile and Russian 51T6 long-range interceptor missile. The spike can push the bow shock wave in front of the nose cone away from the wall. The core technology is to transform the strong shock wave into oblique shock wave, thus reducing the shock wave intensity, aerodynamic drag, and aerodynamic heating of the hypersonic vehicle [6–10]. Besides, the flow separation caused by the spike will form a recirculation zone in front of the nose cone of the hypersonic vehicle. Dem'yanov et al. [11–18] studied the drag and heat reduction efficiency of the blunt body with spike and aerodisk by the CFD numerical method. The
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results show that increasing the length and diameter of the spike can improve the drag and heat reduction efficiency of the system. In addition, increasing the size of the aerodisk can also improve the heat reduction efficiency, but the drag reduction efficiency increases first and then decreases with the increase of size of the aerodisk.
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In addition to spike configuration, some scholars began to study the application of the opposing jet technology in reducing aerodynamic drag and aerodynamic heating of the hypersonic vehicle in the 1960s[19–21]. Hayashi et al. [22–24] studied the effects of the opposing jet on aerodynamic drag and aerodynamic heating of the hypersonic nose cone by the experimental and CFD numerical methods. The results show that there is a recirculation zone in front of
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the nose cone. The opposing jet pushes the bow shock wave away from the nose cone and transforms it into the oblique shock wave, which reduces the shock wave intensity, aerodynamic drag and aerodynamic heating. In
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addition, the low temperature opposing jet is injected into the flow field, and can separate the high temperature gas after the shock wave from the wall of the nose cone, thus effectively reducing the aerodynamic heating of the nose cone. Huang et al. [25–28] studied the effects of total pressure of the opposing jet on aerodynamic drag and aerodynamic heating of the hypersonic blunt body. The results show that increasing total pressure of the opposing jet can reduce the aerodynamic drag and aerodynamic heating of the hypersonic blunt body and improve the drag and heat reduction efficiency of the system.
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In order to further improve the drag and heat reduction efficiency, some combined configurations have been proposed in recent years. Huang et al. [29] studied the drag and heat reduction efficiency of the combined configuration with the forward-facing cavity and opposing jet. The results show that the combined configuration has
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an excellent drag and heat reduction efficiency, which is better than the single forward-facing cavity configuration and single opposing jet configuration. This combined configuration can work in stages. In the case of the low Mach
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number, the opposing jet is turned off, only the forward-facing cavity works. The opposing jet will be turned on in the high Mach number flow to improve the drag and heat reduction efficiency. Huang et al. [30, 31] studied the drag and heat reduction efficiency of the combined configuration with the spike and opposing jet, and the opposing jet is installed at the front of the spike. The results show that the drag and heat reduction efficiency of the combined configuration is better than the single spike configuration and single opposing jet configuration, and the spike has non-ablative property. Therefore, the combined configurations with the higher drag and heat reduction efficiency are the future research trend.
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In this paper, on the basis of the previous investigations, a new combined configuration with the spike and opposing jet is proposed, the opposing jet is in the root of the spike (in the front of the blunt body). However, the combined configuration proposed by Huang et al. [30, 31] has the opposing jet in the front of the spike. Section 2
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introduces the governing equations, numerical discretization algorithms and turbulent model in the aerodynamic analysis. Section 3 analyzes the drag and heat reduction efficiency of the combined configuration proposed in this paper and the previous configurations, and verifies the advantage of the combined configuration proposed in this paper. Section 4 studies the influences of the length of spike, total pressure of opposing jet and jet gas on the drag
Governing equations and numerical method
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2.
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and heat reduction efficiency. Finally, some conclusions are drawn in Section 5.
2.1. Governing equations and discretization method
The Navier-Stokes equations are adopted in the numerical analysis of the hypersonic aerodynamic analysis, and the integral form without considering the volume force and internal heat source is given by:
∫ WdV + ∫∫ V
∂V
( Fc − Fv )dS = 0
(1)
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∂ ∂t
where W is the conservative vector, Fc is the non-viscous flux vector, Fv is the viscous flux vector, ∂V is the boundary surface of the control volume V and n is the normal unit vector of the boundary surface. The detailed
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expressions of the above vectors are as follows:
W = (ρ
ρu ρv ρ w ρe)
T
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0 ρ ui + ρ vj + ρ wk τ i +τ j +τ k 2 ( ρ u + p )i + ρ uvj + ρ uwk xy xz xx Fv = τ yx i + τ yy j + τ yz k Fc = ρ uvi + ( ρ v 2 + p ) j + ρ vwk ρ uwi + ρ vwj + ( ρ w2 + p )k τ zx i + τ zy j + τ zz k ∏ x i + ∏ y j + ∏ z k ( ρ ue + up )i + ( ρ ve + vp ) j + ( ρ we + wp )k
(2)
(3)
∏ x = uτ xx + vτ xy + wτ xz − q x ∏ y = uτ yx + vτ yy + wτ yz − q y ∏ z = uτ zx + vτ zy + wτ zz − qz
(4)
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where ρ is the density, p is the pressure, u, v and w are the velocity components in the rectangular coordinates, qx, qy and qz are the heat flux components in the rectangular coordinates, γ is the ratio of specific heat, e is the total energy
2 3 2 τ yy = 2 µ v y − µ (u x + v y + wz ) 3 2 τ zz = 2 µ wz − µ (u x + v y + wz ) 3 τ xy = τ yx = µ (u y + vx )
τ xz = τ zx = µ (u z + wx ) τ yz = τ zy = µ (vz + wy )
(5)
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τ xx = 2 µ u x − µ (u x + v y + wz )
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per unit mass of air, which is denoted by p/((γ-1)ρ)+(u2+v2+w2)/2. The viscous stress components are as follows:
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The relationship between heat flux and temperature gradient follows Fourier’s law:
∂T ∂x ∂T q y = −λ ∂y ∂T qz = −λ ∂z q x = −λ
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(6)
In order to close governing equations, the equations of state are needed. As the functions of the pressure and temperature, the dynamic viscosity and thermal conductivity of air are important for the calculation accuracy of the aerodynamic analysis. In this paper, Sutherland formula is adopted to calculate the dynamic viscosity and thermal
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conductivity of air. The CFD method is adopted for the aerodynamic analysis. According to the finite volume
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method (FVM), the semi-discretized equations can be written as:
NF d WiVi = −∑ ( Fc − Fv ) N n∆S N dt N =1
(7)
where Wi and Vi are the conservative vector and the volume of the control volume i respectively, ∆SN is the area of the boundary surface and NF is the number of the boundary surface. The spatial discretization is conducted by the AUSM+ [31] scheme, which has the less numerical dissipation, higher shock wave wave resolution and stronger robustness. AUSM+ scheme divides the non-viscous flux vector into convection term Fe and pressure term P. At the interface of element, the expression is as follows:
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(9)
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Fe = Mai+1/2, j ,k
ρc 0 ρ cu n p x ρ cv P = ny p ρ cw nx p ρ cH 0 L/ R i +1/2, j , k
(8)
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Fi +1/ 2, j , k
ρV ρ uV + n p x = ρ vV + n y p = Fe + P ρ wV + nz p ρ HV i +1/ 2, j , k
AUSM+ scheme judges the upstream and downstream of the flow field through the Mach number at the interface
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of element:
(•) L (•) L / R = (•) R
Mai +1/2, j , k ≥ 0 Mai +1/ 2, j , k < 0
(10)
where Mai+1/2,j,k is the Mach number at the interface of element. The pressure term at the interface of element can be decomposed into:
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Pi +1/ 2, j , k = ψ + PL +ψ − PR
(11)
In order to obtain the monotone solution, the discretization of the non-viscous flux vector in Equation (8) is conducted by the completely upwind second-order MUSCL [33] scheme. In addition, the viscous flux vector Fv is
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discretized by the central difference scheme, the Menter's SST k-ω turbulent model [34] is adopted for the turbulent simulation and the LU-SGS [35] scheme is adopted in the time marching. Because the analysis in this paper does not
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consider the high temperature chemical non-equilibrium phenomena, the above governing equations and numerical algorithms do not involve real-gas effects in the hypersonic flow.
2.2. Turbulent model
In this paper, the Reynolds average Navier-Stokes (RANS) equations are calculated to obtain the aerodynamic force and aerodynamic heating. The turbulence model adopts Menter’s SST k-ω two equation model, which is a combination of k-ε [36] and k-ω [37] models. The dimensionless form Menter's SST k-ω turbulent model is as follow:
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µT ∂k M ∞ µ + σ k ∂x j Re M M µT ∂ω M ∞ ∂ ( ρω ) ∂ω ∂ ρ ∂k ∂ω M ∞ + ρu j = Pω ∞ − βρω 2 ∞ + + 2(1 − F1 ) µ + Re Re ∂x j ∂t ∂x j σ k ∂x j Re σ ω 2ω ∂x j ∂x j Re
M M ∂( ρ k ) ∂k ∂ + ρu j = Pk ∞ − β ′ρ kω ∞ + ∂t ∂x j Re Re ∂x j
ρ k a1 ρ k Re , ω SF2 M ∞
µT = min
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The expression of the eddy viscosity is as follow:
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where
1 ∂ui ∂u j + 2 ∂x j ∂xi
(12)
(13)
(14)
1 ∂u k 2 δ ij − ρ kδ ij 3 ∂xk 3
(15)
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S = 2 Sij Sij , Sij =
The expression of the Reynolds stress is as follow:
τ ij = 2 µT Sij −
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The approximate expression of generating term of turbulent kinetic energy and specific dissipation rate is as follow:
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Pk = τ ij
∂ui = µT S 2 ∂x j
γρ Pk Pω = µT
(16)
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For the more detailed information on the Menter's SST k-ω turbulent model equation, please refer to the references [38] and [39].
3.
Physical and numerical models
3.1. Physical model
In order to reduce the aerodynamic drag and aerodynamic heating of the hypersonic vehicle, a new combined configuration with the spike and opposing jet is proposed in this paper, and the physical model is shown in Fig. 1. The aerodynamic drag is for the whole model. However, the aerodynamic heating is for the blunt body, as the blunt
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body is the object of the thermal protection. The spike and opposing jet are installed on the nose cone of the blunt body, and the front end of the spike is the hemispheric shape. The shape of the blunt body is a hemisphere, the diameter D is 40mm, and the center of the hemisphere is the origin of the coordinates. The length L and diameter d1
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of the spike are 60mm and 3mm respectively, and the size of the opposing jet d2 is 1mm. The spike can push the bow shock wave away from the blunt body and translate the original bow shock wave into the oblique shock wave, which reduces the shock wave intensity and aerodynamic drag and heating of the blunt body. The opposing jet can also push the bow shock wave away from the blunt body. Besides, the low temperature jet gas is injected into the
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flow field to reduce the temperature of the flow field, and separates the high temperature gas after the shock wave from the blunt body. So a barrier is formed between the shock wave and blunt body, which can effectively reduce
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the aerodynamic heating of the blunt body.
3.2. Numerical model
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Fig. 1. Sketch of geometrical model in current study.
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This paper adopts ANSYS ICEM CFD software to establish the two-dimensional axisymmetric fluid calculation grid, as is shown in Fig. 2. The grid type is structured grid with 5 topology blocks. The boundary conditions of hypersonic aerodynamic analysis in this paper include the far field condition, non-slip isothermal wall, pressure inlet and axis. The Mach number Ma∞ is 5, the flight height H is 60 km, the static pressure P∞ is 21.96 Pa, the static temperature T∞ is 247.021K, the angle of attack α is 0° and the wall temperature of the blunt body and spike Tw is 300K. The opposing jet is the pressure inlet boundary condition, and the corresponding total pressure P0 is 3485.44Pa, the total temperature T0 is 450K and the jet Mach number Ma0 is 1.5.
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In this paper, the aerodynamic force and aerodynamic heating are calculated by solving the Reynolds Average Navier-Stokes (RANS) equations. The Menter’s SST k-ω two-equation model is adopted for the turbulent simulation. In order to meet the requirement of the Menter’s SST k-ω turbulent model and the analysis precision of
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the hypersonic aerodynamic analysis, the height of the first layer wall grid ∆h is set to 1×10-5m to ensure the dimensionless parameter y+ <1. In addition, the spatial discretization of the non-viscous flux vector adopts the AUSM+ scheme with the second-order precision, and the Courant-Friedrichs-Lewy (CFL) constant is set to 0.5. Because the convergence rate of the wall heat flux is far less than the convergence rate of the wall pressure in the
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hypersonic aerodynamic analysis, in this paper, the wall heat flux is monitored in the solving process, and the
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convergence of the wall heat flux is taken as the convergence standard of the whole flow field.
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Fig. 2. Grid system of model.
3.3. Grid independence analysis
For the hypersonic aerodynamic problems, the grid convergence must be considered. In order to eliminate the influence of the grid number on the calculation results, the grid independence analysis of the configuration without the opposing jet is conducted in this paper. Three CFD models with the different grid numbers are established, and the grid numbers of the coarse, medium and fine grids are 264252, 292658 and 323751 respectively. Fig. 3 presents the wall pressure and wall heat flux distributions along the central axis under the different grid numbers. The results show that the grid number mainly affects the wall pressure and wall heat flux in the front and middle of the blunt
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body. In addition, the calculation results obtained by the medium grid have little difference from that obtained by the fine grid, which indicates that the grid independence analysis results have been obtained. Considering the analysis
a) Wall presure
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precision and calculation amount, this paper adopts the medium grid as the grid system of the subsequent analysis.
b) Wall heat flux
Fig. 3. Wall pressure and wall heat flux distributions of spiked blunt body.
4.
Results and discussion
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4.1. Flow characteristics
In this paper, the aerodynamic drag and wall heat flux of the four different configurations are analyzed by the CFD method. Configuration 1 is the single blunt body, configuration 2 is the blunt body with the spike, configuration 3 is the blunt body with the spike and front jet, and configuration 4 is the blunt body with the spike
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and rear jet (combined configuration proposed in this paper). Fig. 4 presents the Mach cloud charts and the flow characteristics of the different configurations.
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According to Fig. 4(a), a strong bow shock wave is formed in front of the blunt body. The flow field near the stagnation point has the high pressure and high temperature, which will cause the serious aerodynamic drag and aerodynamic heating, and affect the performance and safety of the hypersonic vehicle. According to Fig. 4(b), the spike pushes the original bow shock wave away from the blunt body and translates it into the oblique shock wave, which can reduce the shock wave intensity. Therefore, configuration 2 can reduce aerodynamic drag and aerodynamic heating of the hypersonic vehicle. Besides according to the reattachment shock wave in front of the blunt body, it can be predicted that the maximum pressure and maximum heat flux of the blunt body will appear in the middle. According to Fig. 4(c), the front opposing jet pushes the bow shock wave in front of the spike further
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away from the wall and forms the Mach disk in front of the nozzle. Besides, the low temperature jet gas flows downstream, directly cools the spike and blunt body and has the effect of the thermal protection. According to Fig. 4(d), the rear opposing jet directly pushes the reattachment shock wave near the blunt body away from the wall, and
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reduces the reattachment shock wave intensity, wall pressure and wall heat flux of the blunt body. Besides, the low temperature jet gas is injected into the flow field, and separates the high temperature gas after the shock wave from the blunt body, which can effectively reduce the aerodynamic heating of the blunt body. Because the rear opposing jet of the configuration 4 is closer to the blunt body than the front opposing jet of the configuration 3, the rear
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opposing jet directly cools the wall of the blunt body and has better thermal protection efficiency than the front opposing jet. In addition, the reattachment shock wave in the configuration 4 is farther from the blunt body than that
beneficial for the drag and heat reduction.
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in the configuration 3, so the compressibility of the reattachment shock in the configuration 4 is weaker, and is
There is a single bow shock wave in the flow field of the configuration 1. However, besides the bow shock wave in front of the spike, there are the recirculation zone, shear layer, and reattachment shock wave in the flow field of the configurations 2~4. Especially in the flow field of the configuration 3, there is also a Mach disk in front of the nozzle. Fig. 5 presents the comparison of the streamlines in the flow field of configurations 2~4. The results show
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that configurations 2~4 form the recirculation zone in front of the blunt body. Because the front opposing jet of the configuration 3 is at the front of the spike. The front opposing jet has little influence on the recirculation zone, and the configurations 2 and 3 have the similar recirculation zone. In addition, because the recirculation zone formed by
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the rear opposing jet in configuration 4 squeezes and interferes with the recirculation zone formed by the spike, generating another recirculation zone in the middle. The recirculation zone in the configuration 4 is greater than that
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in the configurations 2 and 3.
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b) Configuration 2
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a) Configuration 1
c) Configuration 3
d) Configuration 4
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Fig. 4. Mach cloud charts of different analysis models.
Configuration 2
Configuration 4
a) Configurations 2 and 3
b) Configurations 2 and 4
Fig. 5. Comparison of fluid streamlines. 4.2. Comparison of drag and heat reduction efficiency
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Fig. 6 presents the wall pressure and wall heat flux of the blunt body for different analysis models. The results show that the configurations 2~4 can reduce the wall pressure and wall heat flux of the blunt body, and the configuration 4 has the best drag and heat reduction efficiency. Table 1 lists the total drag coefficient Cd of the
Cd =
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model and the maximum wall heat flux of the blunt body Qmax. The drag coefficient is defined as follows:
Fd 1 ρ ∞V∞2 S 2
(17)
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where Fd is the total aerodynamic drag of the analysis model, ρ∞ is the density of the free stream, V∞ is the speed of the free stream, S is the reference area which is denoted by πD2/4. The results in Table 1 show that the drag coefficients Cd of the configurations 2, 3 and 4 are 12.90%, 45.59% and 63.63% lower than that of configuration 1
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respectively, and the maximum wall heat fluxes Qmax of the configurations 2, 3 and 4 are 9.07%, 45.92% and 69.95% lower than that of the configuration 1 respectively. Therefore, the combined configuration proposed in this paper has the better drag and heat reduction efficiency than the other configurations.
Table 2 lists the contributions of the spike and blunt body to aerodynamic drag and total heat flux of the model. The results show that the aerodynamic drag and total wall heat flux of configuration 1 are all derived from itself. In
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the configurations 2~4, the contributions of the two parts to aerodynamic drag have little difference, and more than 96% of the aerodynamic drag is derived from the blunt body. However, in the configuration 4, the contribution of the blunt body to total heat flux is 80.2%, which is lower than contribution of the configurations 2 and 3. So the
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configuration 4 has the best thermal protection efficiency.
a) Wall presure
b) Wall heat flux
Fig. 6. Wall pressure and wall heat flux distributions of different analysis models.
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Table1
Model Configuration 1 Configuration 2 Configuration 3 Configuration 4
Cd 1.031 0.898 0.561 0.375
Table2
Qmax (kW/m2) 87.427 79.496 47.277 26.271
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Comparisons of drag coefficient and maximum heat flux of blunt body.
Contributions of different parts to drag coefficient and total heat flux.
4.3. Effect of total pressure of opposing jet
Drag Blunt body 100% 96.99% 98.04% 96.44%
Total heat flux Spike Blunt body 0 100% 10.58% 89.42% 7.56% 92.44% 19.80% 80.20%
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Configuration 1 Configuration 2 Configuration 3 Configuration 4
Spike 0 3.01% 1.96% 3.56%
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Model
In order to study the influence of total pressure of the opposing jet P0 on the combined configuration proposed in this paper, the different numerical analysis models are established. The influence of total pressure of the opposing jet is described by the pressure ratio PR which is denoted by the ratio of P0 to total pressure of free stream P0∞, and the
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influence of length of the spike is described by the length-diameter ratio L/D of length L to the diameter of the blunt body D. In this paper, the pressure ratio PR is set to 0, 0.1, 0.2, 0.3, 0.4 and 0.5, and the length-diameter ratio L/D is set to 1, 1.5, 2, 2.5 and 3. Figs. 7~11 show the wall pressure and wall heat flux distributions of the blunt body under the different pressure ratios PR and length-diameter ratios L/D. The results show that the wall pressure and wall heat
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flux decrease with the increase of pressure ratio PR. Besides, with the increase of pressure ratio PR, the decreasing rate of the wall pressure and wall heat flux decrease gradually. Therefore, when the pressure ratio increases to a
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certain value, increasing the pressure ratio can not reduce the wall pressure and wall heat flux of the blunt body anymore.
Tables 3 and 4 list the drag coefficient Cd, total heat flux of the blunt body Qt and the corresponding percentage decreases ∆Cd and ∆Qt under the different pressure ratios PR and length-diameter ratios L/D. The percentage decreases are defined as follows:
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∆ Cd = ∆Qt =
Cd , PR = 0 − Cd Cd , PR = 0 Qt , PR = 0 − Qt Qt , PR = 0
× 100% (18)
× 100%
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where Cd,PR=0 and Qt,PR=0 are the drag coefficient and total heat flux of the blunt body under pressure ratio PR=0. The results show that the drag coefficient and total heat flux of the blunt body decrease with the increase of the pressure ratio PR. For example, when L/D is 1.5, the drag coefficient and total heat flux of the blunt body are decreased by 67.93% and 66.92% respectively with the increase of pressure ratio PR from 0 to 0.5. So increasing the total
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pressure of the opposing jet can significantly reduce the aerodynamic drag of the hypersonic vehicle and improve the thermal protection efficiency of the system, which is beneficial to the performance and safety of the hypersonic
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vehicle. Fig. 12 presents the influence of the pressure ratio PR on the drag coefficient and total heat flux of the blunt body in the form of graphs. The results show that the slopes of all curves gradually decrease with the increase of the pressure ratio PR. So, the decreasing rates of the drag coefficient and total heat flux of the blunt body gradually decrease with the increase of pressure ratio PR.
Because the length of spike has no influence on the mass flow rate of jet, the pressure ratio is the only influence
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factor of mass flow rate of jet gas in this paper. Table 5 presents the mass flow rate of jet gas under each pressure ratio. The results show that the mass flow rate of jet gas varies linearly with pressure ratio. In addition, the mass flow rate of free stream on the cross-section of blunt body is 6.13×10-4Kg. As the pressure ratios are 0.1 and 0.5, the
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body.
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mass flow rates of jet gas are 3.87% and 19.36% of the mass flow rate of free stream on the cross-section of blunt
a) Wall presure
b) Wall heat flux
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Fig. 7. Comparisons of wall pressure and wall heat flux distributions, L/D=1.
a) Wall presure
b) Wall heat flux
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Fig. 8. Comparisons of wall pressure and wall heat flux distributions, L/D=1.5.
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a) Wall presure
b) Wall heat flux
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Fig. 9. Comparisons of wall pressure and wall heat flux distributions, L/D=2.
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a) Wall presure
b) Wall heat flux
b) Wall heat flux
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a) Wall presure
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Fig. 10. Comparisons of wall pressure and wall heat flux distributions, L/D=2.5.
Fig. 11. Comparisons of wall pressure and wall heat flux distributions, L/D=3. Table3
Comparison of drag coefficient for different analysis cases. Cd 0.979 0.638 0.524 0.436 0.379 0.336 0.898 0.550 0.450 0.375 0.325 0.288 0.839 0.499 0.408
∆Cd/% 0 34.831 46.476 55.465 61.287 65.679 0 38.753 49.889 58.241 63.808 67.929 0 40.524 51.371
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Parameter L/D=1.0, PR=0 L/D=1.0, PR=0.1 L/D=1.0, PR=0.2 L/D=1.0, PR=0.3 L/D=1.0, PR=0.4 L/D=1.0, PR=0.5 L/D=1.5, PR=0 L/D=1.5, PR=0.1 L/D=1.5, PR=0.2 L/D=1.5, PR=0.3 L/D=1.5, PR=0.4 L/D=1.5, PR=0.5 L/D=2.0, PR=0 L/D=2.0, PR=0.1 L/D=2.0, PR=0.2
Cd 0.340 0.296 0.263 0.794 0.463 0.379 0.316 0.275 0.245 0.761 0.440 0.360 0.301 0.262 0.233
∆Cd/% 59.476 64.720 68.653 0 41.688 52.267 60.202 65.365 69.144 0 42.181 52.694 60.447 65.572 69.382
Qt (W) 41.28 34.75 29.98 87.55 61.58 47.82 38.69 32.58 28.21
∆Qt/% 54.82 61.96 67.18 0 29.66 45.38 55.81 62.79 67.78
Parameter L/D=2.0, PR=0.3 L/D=2.0, PR=0.3 L/D=2.0, PR=0.5 L/D=2.5, PR=0 L/D=2.5, PR=0.1 L/D=2.5, PR=0.2 L/D=2.5, PR=0.3 L/D=2.5, PR=0.4 L/D=2.5, PR=0.5 L/D=3.0, PR=0 L/D=3.0, PR=0.1 L/D=3.0, PR=0.2 L/D=3.0, PR=0.3 L/D=3.0, PR=0.4 L/D=3.0, PR=0.5
Table4
Comparison of total heat flux of blunt body for different analysis cases. Parameter L/D=1.0, PR=0 L/D=1.0, PR=0.1 L/D=1.0, PR=0.2 L/D=1.0, PR=0.3 L/D=1.0, PR=0.4 L/D=1.0, PR=0.5 L/D=1.5, PR=0 L/D=1.5, PR=0.1 L/D=1.5, PR=0.2
Qt (W) 100.54 77.15 60.32 48.18 39.63 33.37 95.77 70.52 54.94
∆Qt/% 0 23.26 40.01 52.08 60.58 66.81 0 26.37 42.63
Parameter L/D=2.0, PR=0.3 L/D=2.0, PR=0.3 L/D=2.0, PR=0.5 L/D=2.5, PR=0 L/D=2.5, PR=0.1 L/D=2.5, PR=0.2 L/D=2.5, PR=0.3 L/D=2.5, PR=0.4 L/D=2.5, PR=0.5
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44.37 37.05 31.68 91.36 65.63 51.05
53.67 61.31 66.92 0 28.16 44.12
L/D=3.0, PR=0 L/D=3.0, PR=0.1 L/D=3.0, PR=0.2 L/D=3.0, PR=0.3 L/D=3.0, PR=0.4 L/D=3.0, PR=0.5
84.41 58.57 45.41 36.75 31.01 26.91
0 30.61 46.20 56.46 63.26 68.12
a) Cd
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L/D=1.5, PR=0.3 L/D=1.5, PR=0.4 L/D=1.5, PR=0.5 L/D=2.0, PR=0 L/D=2.0, PR=0.1 L/D=2.0, PR=0.2
b) Qt
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Fig. 12. Drag coefficient and total heat flux of blunt body varying with pressure ratio PR.
a) Cd
b) Qt
Fig. 13. Drag coefficient and total heat flux of blunt body varying with length-diameter ratio L/D. Table5 Mass flow rate of jet gas under each pressure ratio. PR m (10-5Kg)
4.4. Effect of length of spike
0.1 2.37
0.2 4.75
0.3 7.11
0.4 9.49
0.5 11.87
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Figs. 7~11 can also reflect the influence of length-diameter ratio L/D on the wall pressure and wall heat flux of the blunt body. The results show that the wall pressure and wall heat flux decrease with the increase of lengthdiameter ratio L/D. Besides, with the increase of length-diameter ratio L/D, the decreasing rate of the wall pressure
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and wall heat flux decrease gradually. Therefore, when the length-diameter ratio L/D increases to a certain value, the decreasing rates of aerodynamic drag and aerodynamic heating will be close to zero, and the aerodynamic drag and aerodynamic heating will remain constant. In fact, the length of spike should also consider requirements of the stiffness and strength, and proper length can be selected based on the aerodynamic and structural requirements.
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According to Table3 and 4, the drag coefficient and total heat flux of the blunt body decrease with the increase of the length-diameter ratio L/D. For example, when PR is 3, the drag coefficient and total heat flux of the blunt
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body are decreased by 30.96% and 23.72% respectively with the increase of length-diameter ratio L/D from 1 to 3. So increasing the length of spike can significantly reduce the aerodynamic drag of the hypersonic vehicle and improve the thermal protection efficiency of the system, which is beneficial to the performance and safety of the hypersonic vehicle. In addition, according to Fig. 13, the slopes of all curves gradually decrease with the increase of length-diameter ratio L/D, and the decreasing rates of the drag coefficient and total heat flux of the blunt body gradually decrease with the increase of length-diameter ratio L/D. Therefore, the length of spike can not be increased
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indefinitely. The drag and heat reduction, increase of the mass and structural stiffness and strength reduction caused
spike.
4.5. Effect of jet gas
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by the increase of the length of spike should be evaluated comprehensively, and select the appropriate the length of
In the above analysis, the jet gas is air. In order to study the influence of jet gas on the drag reduction and heat
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reduction efficiency of the combined configuration proposed in this paper, the jet gases nitrogen N2 and carbon dioxide CO2 are also considered in this paper. Fig. 14 presents the mass fractions of the jet gases N2 and CO2 in the flow field. Fig. 15 presents comparison of the streamlines in the flow field under the jet gases N2 and CO2. According to the above analysis results, in the flow fields, the mass distributions of the jet gases N2 and CO2 are the same, and the flow fields under the jet gases N2 and CO2 have the same streamlines as that under the jet gas air, which indicates that jet gases N2 and CO2 have no influence on the flow characteristics. Fig. 16 presents the wall pressure and wall heat flux distributions of the blunt body under the different gas jet gases. Table 6 lists the drag coefficient and total heat flux of the blunt body under the different gas jet gases.
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According to Fig. 16(a) and Table 6, the wall pressure distributions of the blunt body under the jet gases N2 and CO2 have little difference and are obviously lower than the wall pressure distribution under the jet gas air. And the drag coefficients under the jet gases N2 and CO2 are 15.47% and 14.67% lower than that under the jet gas air respectively.
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So the N2 has the best drag reduction efficiency. In addition, according to Fig. 16(b) and Table 6, the wall heat flux of the blunt body under the jet gases N2 and CO2 is slightly less than that under the jet gas air, and the corresponding total heat fluxes of the blunt body are 0.36% and 2.29% lower than that under the jet gas air respectively. So the jet
b) CO2
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a) N2
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gas CO2 has the best thermal protection efficiency, but the advantage is not obvious compared with air and N2.
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Fig. 14. Mass distributions of nitrogen and carbon dioxide.
Fig. 15. Comparison of fluid streamlines.
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b) Wall heat flux
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a) Wall pressure
Fig. 16. Comparisons of wall pressure and heat flux distributions under different jet gases, L/D=1.5, PR=0.3.
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Table6
Drag coefficient and total heat flux of blunt body under different jet gases. Jet gas Air N2 CO2
5.
Conclusion
Cd 0.375 0.317 0.320
Qt (W) 44.372 44.211 43.358
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In order to reduce the hypersonic aerodynamic drag and heating of the hypersonic vehicle, a new combined configuration with the spike and opposing jet is proposed in this paper, and the drag and heat reduction efficiency is studied by the CFD method. The following conclusions were obtained: The combined configuration effectively reduces the aerodynamic drag and aerodynamic heating of the
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1)
blunt body through reconstruction of the flow field. The spike pushes the bow shock wave away from the
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blunt body and translates it into an oblique shock wave, which reduces the shock wave intensity. Besides, the low temperature jet gas is injected into the flow field to separate the high temperature gas after the shock wave from the blunt body.
2)
The drag and heat reduction efficiency of the combined configuration is better than the other configurations,
which shows the advantage of the combined configuration proposed in this paper in engineering application.
3)
The aerodynamic drag and aerodynamic heating of the blunt body decreases with the increase of the length of spike and the total pressure of opposing jet, and the corresponding decreasing rates decrease gradually with the increase of the above two parameters. Therefore, when the length of spike and the total pressure of
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opposing jet increase to the certain values, the decreasing rates of aerodynamic drag and aerodynamic heating will be close to zero, and the aerodynamic drag and aerodynamic heating will remain constant. In fact, the length of spike should also consider requirements of the stiffness and strength, and proper length
4)
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can be selected based on the aerodynamic and structural requirements. The jet gases (air, nitrogen and carbon dioxide) have no influence on the flow characteristics, and the nitrogen has the best drag reduction efficiency and carbon dioxide has the best thermal protection efficiency.
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Acknowledgments
Education Institutions.
Conflict of interest statement
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This research in this paper was supported by the Priority Academic Program Development of Jiangsu Higher
There are no conflicts of interest in relation to this manuscript.
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References
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ACCEPTED MANUSCRIPT 1) A combined spike and rear opposing jet configuration is proposed. 2) CFD method is adopted to analyze drag and heat reduction efficiency. 3) New configuration reduces drag and heating by reconstruction of flow field.
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3) Drag and heat reduction efficiency is better than the other configurations.
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4) Effects of the length of spike, total pressure of jet and jet gas are studied.
S0094-5765(18)31697-7
DOI:
https://doi.org/10.1016/j.actaastro.2018.11.039
Reference:
AA 7206
To appear in:
Acta Astronautica
Received Date: 18 October 2018 Revised Date:
20 November 2018
Accepted Date: 25 November 2018
Please cite this article as: J. Huang, W.-X. Yao, X.-Y. Shan, Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration, Acta Astronautica (2018), doi: https://doi.org/10.1016/j.actaastro.2018.11.039. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Numerical investigation on drag and heat reduction mechanism of combined spike and rear opposing jet configuration
a
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Jie Huanga, Wei-Xing Yaoa,b,∗, Xian-Yang Shanc
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle,
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b
Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China c
System Design Institute of Hubei Aerospace Technology Academy, Wuhan 430040, China
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Abstract: In order to reduce the hypersonic aerodynamic drag and heating, a combined spike and rear opposing jet configuration is proposed in this paper, and the CFD method is adopted to analyze the drag and heat reduction efficiency. The results show that the spike pushes the bow shock wave away from the blunt body, which translates the normal shock wave into the oblique shock wave and reduces the shock wave intensity. In addition, the low temperature jet gas is injected into the flow field, which reduces the temperature of the flow field after the shock
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wave. So the combined configuration reduces the aerodynamic drag and heating of the blunt body by the reconstruction of flow field, and the drag and heat reduction efficiency is better than the other configurations that already exist. The influences of the length of spike, total pressure of the opposing jet and jet gas on the drag and heat
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reduction efficiency are studied. The results show that increasing the length of the spike and the total pressure of the opposing jet can effectively improve the drag and heat reduction efficiency, and the decreasing rates of the
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aerodynamic drag and heating slow down gradually with the increase of above two parameters. In addition, the nitrogen has the best drag reduction efficiency and the carbon dioxide has the best heat reduction efficiency. The investigations in this paper verify the advantages and application in engineering of the combined configuration proposed in this paper.
Keywords: Hypersonic; Drag and heat reduction; Combined configuration; Spike; Opposing jet.
∗
Corresponding author. E-mail address: [email protected] (W.X. Yao).
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diameter of blunt body
d1, d2
diameter of spike and opposing jet
e
total energy per unit mass of air
Fc
non-viscous flux vector
Fv
viscous flux vector
∆h
height of the first layer wall grid
k
turbulent kinetic energy
L
length of spike
Ma∞
Mach number of free stream
Ma0
Mach number of opposing jet
m
mass of jet gas
n
normal unit vector
Pw
wall pressure
P0
total pressure of opposing jet
P∞
static pressure of free stream
Qw
wall heat flux
Qt
total heat flux of blunt body
Qmax
maximum wall heat flux of blunt body
Re
Reynolds number
T∞ Tw
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S
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D
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drag coefficient
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Cd
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Nomenclature
reference area
static temperature of free stream wall temperature
T0
total temperature of opposing jet
u, v, w
velocity components in the rectangular coordinates
V∞
speed of free stream
Vi
volume of the control volume
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conservative vector
y+
dimensionless parameter of turbulent model angle of attack α
α
angle of attack
γ
ratio of specific heat
ε
turbulent dissipation rate
λ
heat conductivity coefficient of gas
µ
dynamic viscosity of air
µT
eddy viscosity
ρ
density of gas
τij
viscous stress components
ω
specific dissipation rate
Introduction
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1.
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The hypersonic vehicles, such as the space vehicle and high-speed missile, are subjected to the huge shock wave drag during the flight [1–2], which will seriously affect the aerodynamic performance of the hypersonic vehicle. In
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addition, the hypersonic vehicle is also subjected to the huge aerodynamic heating during the flight [3–5]. And some thermal protection measures must be taken to ensure the internal structure of the vehicle within the sustainable temperature range. Therefore, the investigations on the drag and heat reduction technology of the hypersonic vehicle
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are very importance to the performance and safety of the vehicle and has important engineering significance. The spike is a slender rod installed on the nose cone of the hypersonic vehicle, which is used to reduce
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aerodynamic drag and aerodynamic heating. Since the 1950s, experiments and numerical studies related to drag and heat reduction of the spike have been carried out. And the spike has been applied successfully in the engineering, such as the American UGM-133 Trident-Ⅱballistic missile and Russian 51T6 long-range interceptor missile. The spike can push the bow shock wave in front of the nose cone away from the wall. The core technology is to transform the strong shock wave into oblique shock wave, thus reducing the shock wave intensity, aerodynamic drag, and aerodynamic heating of the hypersonic vehicle [6–10]. Besides, the flow separation caused by the spike will form a recirculation zone in front of the nose cone of the hypersonic vehicle. Dem'yanov et al. [11–18] studied the drag and heat reduction efficiency of the blunt body with spike and aerodisk by the CFD numerical method. The
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results show that increasing the length and diameter of the spike can improve the drag and heat reduction efficiency of the system. In addition, increasing the size of the aerodisk can also improve the heat reduction efficiency, but the drag reduction efficiency increases first and then decreases with the increase of size of the aerodisk.
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In addition to spike configuration, some scholars began to study the application of the opposing jet technology in reducing aerodynamic drag and aerodynamic heating of the hypersonic vehicle in the 1960s[19–21]. Hayashi et al. [22–24] studied the effects of the opposing jet on aerodynamic drag and aerodynamic heating of the hypersonic nose cone by the experimental and CFD numerical methods. The results show that there is a recirculation zone in front of
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the nose cone. The opposing jet pushes the bow shock wave away from the nose cone and transforms it into the oblique shock wave, which reduces the shock wave intensity, aerodynamic drag and aerodynamic heating. In
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addition, the low temperature opposing jet is injected into the flow field, and can separate the high temperature gas after the shock wave from the wall of the nose cone, thus effectively reducing the aerodynamic heating of the nose cone. Huang et al. [25–28] studied the effects of total pressure of the opposing jet on aerodynamic drag and aerodynamic heating of the hypersonic blunt body. The results show that increasing total pressure of the opposing jet can reduce the aerodynamic drag and aerodynamic heating of the hypersonic blunt body and improve the drag and heat reduction efficiency of the system.
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In order to further improve the drag and heat reduction efficiency, some combined configurations have been proposed in recent years. Huang et al. [29] studied the drag and heat reduction efficiency of the combined configuration with the forward-facing cavity and opposing jet. The results show that the combined configuration has
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an excellent drag and heat reduction efficiency, which is better than the single forward-facing cavity configuration and single opposing jet configuration. This combined configuration can work in stages. In the case of the low Mach
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number, the opposing jet is turned off, only the forward-facing cavity works. The opposing jet will be turned on in the high Mach number flow to improve the drag and heat reduction efficiency. Huang et al. [30, 31] studied the drag and heat reduction efficiency of the combined configuration with the spike and opposing jet, and the opposing jet is installed at the front of the spike. The results show that the drag and heat reduction efficiency of the combined configuration is better than the single spike configuration and single opposing jet configuration, and the spike has non-ablative property. Therefore, the combined configurations with the higher drag and heat reduction efficiency are the future research trend.
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In this paper, on the basis of the previous investigations, a new combined configuration with the spike and opposing jet is proposed, the opposing jet is in the root of the spike (in the front of the blunt body). However, the combined configuration proposed by Huang et al. [30, 31] has the opposing jet in the front of the spike. Section 2
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introduces the governing equations, numerical discretization algorithms and turbulent model in the aerodynamic analysis. Section 3 analyzes the drag and heat reduction efficiency of the combined configuration proposed in this paper and the previous configurations, and verifies the advantage of the combined configuration proposed in this paper. Section 4 studies the influences of the length of spike, total pressure of opposing jet and jet gas on the drag
Governing equations and numerical method
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2.
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and heat reduction efficiency. Finally, some conclusions are drawn in Section 5.
2.1. Governing equations and discretization method
The Navier-Stokes equations are adopted in the numerical analysis of the hypersonic aerodynamic analysis, and the integral form without considering the volume force and internal heat source is given by:
∫ WdV + ∫∫ V
∂V
( Fc − Fv )dS = 0
(1)
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∂ ∂t
where W is the conservative vector, Fc is the non-viscous flux vector, Fv is the viscous flux vector, ∂V is the boundary surface of the control volume V and n is the normal unit vector of the boundary surface. The detailed
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expressions of the above vectors are as follows:
W = (ρ
ρu ρv ρ w ρe)
T
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0 ρ ui + ρ vj + ρ wk τ i +τ j +τ k 2 ( ρ u + p )i + ρ uvj + ρ uwk xy xz xx Fv = τ yx i + τ yy j + τ yz k Fc = ρ uvi + ( ρ v 2 + p ) j + ρ vwk ρ uwi + ρ vwj + ( ρ w2 + p )k τ zx i + τ zy j + τ zz k ∏ x i + ∏ y j + ∏ z k ( ρ ue + up )i + ( ρ ve + vp ) j + ( ρ we + wp )k
(2)
(3)
∏ x = uτ xx + vτ xy + wτ xz − q x ∏ y = uτ yx + vτ yy + wτ yz − q y ∏ z = uτ zx + vτ zy + wτ zz − qz
(4)
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where ρ is the density, p is the pressure, u, v and w are the velocity components in the rectangular coordinates, qx, qy and qz are the heat flux components in the rectangular coordinates, γ is the ratio of specific heat, e is the total energy
2 3 2 τ yy = 2 µ v y − µ (u x + v y + wz ) 3 2 τ zz = 2 µ wz − µ (u x + v y + wz ) 3 τ xy = τ yx = µ (u y + vx )
τ xz = τ zx = µ (u z + wx ) τ yz = τ zy = µ (vz + wy )
(5)
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τ xx = 2 µ u x − µ (u x + v y + wz )
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per unit mass of air, which is denoted by p/((γ-1)ρ)+(u2+v2+w2)/2. The viscous stress components are as follows:
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The relationship between heat flux and temperature gradient follows Fourier’s law:
∂T ∂x ∂T q y = −λ ∂y ∂T qz = −λ ∂z q x = −λ
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(6)
In order to close governing equations, the equations of state are needed. As the functions of the pressure and temperature, the dynamic viscosity and thermal conductivity of air are important for the calculation accuracy of the aerodynamic analysis. In this paper, Sutherland formula is adopted to calculate the dynamic viscosity and thermal
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conductivity of air. The CFD method is adopted for the aerodynamic analysis. According to the finite volume
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method (FVM), the semi-discretized equations can be written as:
NF d WiVi = −∑ ( Fc − Fv ) N n∆S N dt N =1
(7)
where Wi and Vi are the conservative vector and the volume of the control volume i respectively, ∆SN is the area of the boundary surface and NF is the number of the boundary surface. The spatial discretization is conducted by the AUSM+ [31] scheme, which has the less numerical dissipation, higher shock wave wave resolution and stronger robustness. AUSM+ scheme divides the non-viscous flux vector into convection term Fe and pressure term P. At the interface of element, the expression is as follows:
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(9)
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Fe = Mai+1/2, j ,k
ρc 0 ρ cu n p x ρ cv P = ny p ρ cw nx p ρ cH 0 L/ R i +1/2, j , k
(8)
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Fi +1/ 2, j , k
ρV ρ uV + n p x = ρ vV + n y p = Fe + P ρ wV + nz p ρ HV i +1/ 2, j , k
AUSM+ scheme judges the upstream and downstream of the flow field through the Mach number at the interface
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of element:
(•) L (•) L / R = (•) R
Mai +1/2, j , k ≥ 0 Mai +1/ 2, j , k < 0
(10)
where Mai+1/2,j,k is the Mach number at the interface of element. The pressure term at the interface of element can be decomposed into:
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Pi +1/ 2, j , k = ψ + PL +ψ − PR
(11)
In order to obtain the monotone solution, the discretization of the non-viscous flux vector in Equation (8) is conducted by the completely upwind second-order MUSCL [33] scheme. In addition, the viscous flux vector Fv is
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discretized by the central difference scheme, the Menter's SST k-ω turbulent model [34] is adopted for the turbulent simulation and the LU-SGS [35] scheme is adopted in the time marching. Because the analysis in this paper does not
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consider the high temperature chemical non-equilibrium phenomena, the above governing equations and numerical algorithms do not involve real-gas effects in the hypersonic flow.
2.2. Turbulent model
In this paper, the Reynolds average Navier-Stokes (RANS) equations are calculated to obtain the aerodynamic force and aerodynamic heating. The turbulence model adopts Menter’s SST k-ω two equation model, which is a combination of k-ε [36] and k-ω [37] models. The dimensionless form Menter's SST k-ω turbulent model is as follow:
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µT ∂k M ∞ µ + σ k ∂x j Re M M µT ∂ω M ∞ ∂ ( ρω ) ∂ω ∂ ρ ∂k ∂ω M ∞ + ρu j = Pω ∞ − βρω 2 ∞ + + 2(1 − F1 ) µ + Re Re ∂x j ∂t ∂x j σ k ∂x j Re σ ω 2ω ∂x j ∂x j Re
M M ∂( ρ k ) ∂k ∂ + ρu j = Pk ∞ − β ′ρ kω ∞ + ∂t ∂x j Re Re ∂x j
ρ k a1 ρ k Re , ω SF2 M ∞
µT = min
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The expression of the eddy viscosity is as follow:
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where
1 ∂ui ∂u j + 2 ∂x j ∂xi
(12)
(13)
(14)
1 ∂u k 2 δ ij − ρ kδ ij 3 ∂xk 3
(15)
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S = 2 Sij Sij , Sij =
The expression of the Reynolds stress is as follow:
τ ij = 2 µT Sij −
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The approximate expression of generating term of turbulent kinetic energy and specific dissipation rate is as follow:
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Pk = τ ij
∂ui = µT S 2 ∂x j
γρ Pk Pω = µT
(16)
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For the more detailed information on the Menter's SST k-ω turbulent model equation, please refer to the references [38] and [39].
3.
Physical and numerical models
3.1. Physical model
In order to reduce the aerodynamic drag and aerodynamic heating of the hypersonic vehicle, a new combined configuration with the spike and opposing jet is proposed in this paper, and the physical model is shown in Fig. 1. The aerodynamic drag is for the whole model. However, the aerodynamic heating is for the blunt body, as the blunt
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body is the object of the thermal protection. The spike and opposing jet are installed on the nose cone of the blunt body, and the front end of the spike is the hemispheric shape. The shape of the blunt body is a hemisphere, the diameter D is 40mm, and the center of the hemisphere is the origin of the coordinates. The length L and diameter d1
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of the spike are 60mm and 3mm respectively, and the size of the opposing jet d2 is 1mm. The spike can push the bow shock wave away from the blunt body and translate the original bow shock wave into the oblique shock wave, which reduces the shock wave intensity and aerodynamic drag and heating of the blunt body. The opposing jet can also push the bow shock wave away from the blunt body. Besides, the low temperature jet gas is injected into the
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flow field to reduce the temperature of the flow field, and separates the high temperature gas after the shock wave from the blunt body. So a barrier is formed between the shock wave and blunt body, which can effectively reduce
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the aerodynamic heating of the blunt body.
3.2. Numerical model
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Fig. 1. Sketch of geometrical model in current study.
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This paper adopts ANSYS ICEM CFD software to establish the two-dimensional axisymmetric fluid calculation grid, as is shown in Fig. 2. The grid type is structured grid with 5 topology blocks. The boundary conditions of hypersonic aerodynamic analysis in this paper include the far field condition, non-slip isothermal wall, pressure inlet and axis. The Mach number Ma∞ is 5, the flight height H is 60 km, the static pressure P∞ is 21.96 Pa, the static temperature T∞ is 247.021K, the angle of attack α is 0° and the wall temperature of the blunt body and spike Tw is 300K. The opposing jet is the pressure inlet boundary condition, and the corresponding total pressure P0 is 3485.44Pa, the total temperature T0 is 450K and the jet Mach number Ma0 is 1.5.
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In this paper, the aerodynamic force and aerodynamic heating are calculated by solving the Reynolds Average Navier-Stokes (RANS) equations. The Menter’s SST k-ω two-equation model is adopted for the turbulent simulation. In order to meet the requirement of the Menter’s SST k-ω turbulent model and the analysis precision of
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the hypersonic aerodynamic analysis, the height of the first layer wall grid ∆h is set to 1×10-5m to ensure the dimensionless parameter y+ <1. In addition, the spatial discretization of the non-viscous flux vector adopts the AUSM+ scheme with the second-order precision, and the Courant-Friedrichs-Lewy (CFL) constant is set to 0.5. Because the convergence rate of the wall heat flux is far less than the convergence rate of the wall pressure in the
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hypersonic aerodynamic analysis, in this paper, the wall heat flux is monitored in the solving process, and the
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convergence of the wall heat flux is taken as the convergence standard of the whole flow field.
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Fig. 2. Grid system of model.
3.3. Grid independence analysis
For the hypersonic aerodynamic problems, the grid convergence must be considered. In order to eliminate the influence of the grid number on the calculation results, the grid independence analysis of the configuration without the opposing jet is conducted in this paper. Three CFD models with the different grid numbers are established, and the grid numbers of the coarse, medium and fine grids are 264252, 292658 and 323751 respectively. Fig. 3 presents the wall pressure and wall heat flux distributions along the central axis under the different grid numbers. The results show that the grid number mainly affects the wall pressure and wall heat flux in the front and middle of the blunt
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body. In addition, the calculation results obtained by the medium grid have little difference from that obtained by the fine grid, which indicates that the grid independence analysis results have been obtained. Considering the analysis
a) Wall presure
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precision and calculation amount, this paper adopts the medium grid as the grid system of the subsequent analysis.
b) Wall heat flux
Fig. 3. Wall pressure and wall heat flux distributions of spiked blunt body.
4.
Results and discussion
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4.1. Flow characteristics
In this paper, the aerodynamic drag and wall heat flux of the four different configurations are analyzed by the CFD method. Configuration 1 is the single blunt body, configuration 2 is the blunt body with the spike, configuration 3 is the blunt body with the spike and front jet, and configuration 4 is the blunt body with the spike
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and rear jet (combined configuration proposed in this paper). Fig. 4 presents the Mach cloud charts and the flow characteristics of the different configurations.
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According to Fig. 4(a), a strong bow shock wave is formed in front of the blunt body. The flow field near the stagnation point has the high pressure and high temperature, which will cause the serious aerodynamic drag and aerodynamic heating, and affect the performance and safety of the hypersonic vehicle. According to Fig. 4(b), the spike pushes the original bow shock wave away from the blunt body and translates it into the oblique shock wave, which can reduce the shock wave intensity. Therefore, configuration 2 can reduce aerodynamic drag and aerodynamic heating of the hypersonic vehicle. Besides according to the reattachment shock wave in front of the blunt body, it can be predicted that the maximum pressure and maximum heat flux of the blunt body will appear in the middle. According to Fig. 4(c), the front opposing jet pushes the bow shock wave in front of the spike further
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away from the wall and forms the Mach disk in front of the nozzle. Besides, the low temperature jet gas flows downstream, directly cools the spike and blunt body and has the effect of the thermal protection. According to Fig. 4(d), the rear opposing jet directly pushes the reattachment shock wave near the blunt body away from the wall, and
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reduces the reattachment shock wave intensity, wall pressure and wall heat flux of the blunt body. Besides, the low temperature jet gas is injected into the flow field, and separates the high temperature gas after the shock wave from the blunt body, which can effectively reduce the aerodynamic heating of the blunt body. Because the rear opposing jet of the configuration 4 is closer to the blunt body than the front opposing jet of the configuration 3, the rear
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opposing jet directly cools the wall of the blunt body and has better thermal protection efficiency than the front opposing jet. In addition, the reattachment shock wave in the configuration 4 is farther from the blunt body than that
beneficial for the drag and heat reduction.
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in the configuration 3, so the compressibility of the reattachment shock in the configuration 4 is weaker, and is
There is a single bow shock wave in the flow field of the configuration 1. However, besides the bow shock wave in front of the spike, there are the recirculation zone, shear layer, and reattachment shock wave in the flow field of the configurations 2~4. Especially in the flow field of the configuration 3, there is also a Mach disk in front of the nozzle. Fig. 5 presents the comparison of the streamlines in the flow field of configurations 2~4. The results show
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that configurations 2~4 form the recirculation zone in front of the blunt body. Because the front opposing jet of the configuration 3 is at the front of the spike. The front opposing jet has little influence on the recirculation zone, and the configurations 2 and 3 have the similar recirculation zone. In addition, because the recirculation zone formed by
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the rear opposing jet in configuration 4 squeezes and interferes with the recirculation zone formed by the spike, generating another recirculation zone in the middle. The recirculation zone in the configuration 4 is greater than that
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in the configurations 2 and 3.
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b) Configuration 2
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a) Configuration 1
c) Configuration 3
d) Configuration 4
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Fig. 4. Mach cloud charts of different analysis models.
Configuration 2
Configuration 4
a) Configurations 2 and 3
b) Configurations 2 and 4
Fig. 5. Comparison of fluid streamlines. 4.2. Comparison of drag and heat reduction efficiency
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Fig. 6 presents the wall pressure and wall heat flux of the blunt body for different analysis models. The results show that the configurations 2~4 can reduce the wall pressure and wall heat flux of the blunt body, and the configuration 4 has the best drag and heat reduction efficiency. Table 1 lists the total drag coefficient Cd of the
Cd =
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model and the maximum wall heat flux of the blunt body Qmax. The drag coefficient is defined as follows:
Fd 1 ρ ∞V∞2 S 2
(17)
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where Fd is the total aerodynamic drag of the analysis model, ρ∞ is the density of the free stream, V∞ is the speed of the free stream, S is the reference area which is denoted by πD2/4. The results in Table 1 show that the drag coefficients Cd of the configurations 2, 3 and 4 are 12.90%, 45.59% and 63.63% lower than that of configuration 1
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respectively, and the maximum wall heat fluxes Qmax of the configurations 2, 3 and 4 are 9.07%, 45.92% and 69.95% lower than that of the configuration 1 respectively. Therefore, the combined configuration proposed in this paper has the better drag and heat reduction efficiency than the other configurations.
Table 2 lists the contributions of the spike and blunt body to aerodynamic drag and total heat flux of the model. The results show that the aerodynamic drag and total wall heat flux of configuration 1 are all derived from itself. In
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the configurations 2~4, the contributions of the two parts to aerodynamic drag have little difference, and more than 96% of the aerodynamic drag is derived from the blunt body. However, in the configuration 4, the contribution of the blunt body to total heat flux is 80.2%, which is lower than contribution of the configurations 2 and 3. So the
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configuration 4 has the best thermal protection efficiency.
a) Wall presure
b) Wall heat flux
Fig. 6. Wall pressure and wall heat flux distributions of different analysis models.
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Table1
Model Configuration 1 Configuration 2 Configuration 3 Configuration 4
Cd 1.031 0.898 0.561 0.375
Table2
Qmax (kW/m2) 87.427 79.496 47.277 26.271
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Comparisons of drag coefficient and maximum heat flux of blunt body.
Contributions of different parts to drag coefficient and total heat flux.
4.3. Effect of total pressure of opposing jet
Drag Blunt body 100% 96.99% 98.04% 96.44%
Total heat flux Spike Blunt body 0 100% 10.58% 89.42% 7.56% 92.44% 19.80% 80.20%
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Configuration 1 Configuration 2 Configuration 3 Configuration 4
Spike 0 3.01% 1.96% 3.56%
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Model
In order to study the influence of total pressure of the opposing jet P0 on the combined configuration proposed in this paper, the different numerical analysis models are established. The influence of total pressure of the opposing jet is described by the pressure ratio PR which is denoted by the ratio of P0 to total pressure of free stream P0∞, and the
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influence of length of the spike is described by the length-diameter ratio L/D of length L to the diameter of the blunt body D. In this paper, the pressure ratio PR is set to 0, 0.1, 0.2, 0.3, 0.4 and 0.5, and the length-diameter ratio L/D is set to 1, 1.5, 2, 2.5 and 3. Figs. 7~11 show the wall pressure and wall heat flux distributions of the blunt body under the different pressure ratios PR and length-diameter ratios L/D. The results show that the wall pressure and wall heat
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flux decrease with the increase of pressure ratio PR. Besides, with the increase of pressure ratio PR, the decreasing rate of the wall pressure and wall heat flux decrease gradually. Therefore, when the pressure ratio increases to a
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certain value, increasing the pressure ratio can not reduce the wall pressure and wall heat flux of the blunt body anymore.
Tables 3 and 4 list the drag coefficient Cd, total heat flux of the blunt body Qt and the corresponding percentage decreases ∆Cd and ∆Qt under the different pressure ratios PR and length-diameter ratios L/D. The percentage decreases are defined as follows:
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∆ Cd = ∆Qt =
Cd , PR = 0 − Cd Cd , PR = 0 Qt , PR = 0 − Qt Qt , PR = 0
× 100% (18)
× 100%
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where Cd,PR=0 and Qt,PR=0 are the drag coefficient and total heat flux of the blunt body under pressure ratio PR=0. The results show that the drag coefficient and total heat flux of the blunt body decrease with the increase of the pressure ratio PR. For example, when L/D is 1.5, the drag coefficient and total heat flux of the blunt body are decreased by 67.93% and 66.92% respectively with the increase of pressure ratio PR from 0 to 0.5. So increasing the total
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pressure of the opposing jet can significantly reduce the aerodynamic drag of the hypersonic vehicle and improve the thermal protection efficiency of the system, which is beneficial to the performance and safety of the hypersonic
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vehicle. Fig. 12 presents the influence of the pressure ratio PR on the drag coefficient and total heat flux of the blunt body in the form of graphs. The results show that the slopes of all curves gradually decrease with the increase of the pressure ratio PR. So, the decreasing rates of the drag coefficient and total heat flux of the blunt body gradually decrease with the increase of pressure ratio PR.
Because the length of spike has no influence on the mass flow rate of jet, the pressure ratio is the only influence
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factor of mass flow rate of jet gas in this paper. Table 5 presents the mass flow rate of jet gas under each pressure ratio. The results show that the mass flow rate of jet gas varies linearly with pressure ratio. In addition, the mass flow rate of free stream on the cross-section of blunt body is 6.13×10-4Kg. As the pressure ratios are 0.1 and 0.5, the
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body.
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mass flow rates of jet gas are 3.87% and 19.36% of the mass flow rate of free stream on the cross-section of blunt
a) Wall presure
b) Wall heat flux
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Fig. 7. Comparisons of wall pressure and wall heat flux distributions, L/D=1.
a) Wall presure
b) Wall heat flux
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Fig. 8. Comparisons of wall pressure and wall heat flux distributions, L/D=1.5.
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a) Wall presure
b) Wall heat flux
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Fig. 9. Comparisons of wall pressure and wall heat flux distributions, L/D=2.
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a) Wall presure
b) Wall heat flux
b) Wall heat flux
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a) Wall presure
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Fig. 10. Comparisons of wall pressure and wall heat flux distributions, L/D=2.5.
Fig. 11. Comparisons of wall pressure and wall heat flux distributions, L/D=3. Table3
Comparison of drag coefficient for different analysis cases. Cd 0.979 0.638 0.524 0.436 0.379 0.336 0.898 0.550 0.450 0.375 0.325 0.288 0.839 0.499 0.408
∆Cd/% 0 34.831 46.476 55.465 61.287 65.679 0 38.753 49.889 58.241 63.808 67.929 0 40.524 51.371
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Parameter L/D=1.0, PR=0 L/D=1.0, PR=0.1 L/D=1.0, PR=0.2 L/D=1.0, PR=0.3 L/D=1.0, PR=0.4 L/D=1.0, PR=0.5 L/D=1.5, PR=0 L/D=1.5, PR=0.1 L/D=1.5, PR=0.2 L/D=1.5, PR=0.3 L/D=1.5, PR=0.4 L/D=1.5, PR=0.5 L/D=2.0, PR=0 L/D=2.0, PR=0.1 L/D=2.0, PR=0.2
Cd 0.340 0.296 0.263 0.794 0.463 0.379 0.316 0.275 0.245 0.761 0.440 0.360 0.301 0.262 0.233
∆Cd/% 59.476 64.720 68.653 0 41.688 52.267 60.202 65.365 69.144 0 42.181 52.694 60.447 65.572 69.382
Qt (W) 41.28 34.75 29.98 87.55 61.58 47.82 38.69 32.58 28.21
∆Qt/% 54.82 61.96 67.18 0 29.66 45.38 55.81 62.79 67.78
Parameter L/D=2.0, PR=0.3 L/D=2.0, PR=0.3 L/D=2.0, PR=0.5 L/D=2.5, PR=0 L/D=2.5, PR=0.1 L/D=2.5, PR=0.2 L/D=2.5, PR=0.3 L/D=2.5, PR=0.4 L/D=2.5, PR=0.5 L/D=3.0, PR=0 L/D=3.0, PR=0.1 L/D=3.0, PR=0.2 L/D=3.0, PR=0.3 L/D=3.0, PR=0.4 L/D=3.0, PR=0.5
Table4
Comparison of total heat flux of blunt body for different analysis cases. Parameter L/D=1.0, PR=0 L/D=1.0, PR=0.1 L/D=1.0, PR=0.2 L/D=1.0, PR=0.3 L/D=1.0, PR=0.4 L/D=1.0, PR=0.5 L/D=1.5, PR=0 L/D=1.5, PR=0.1 L/D=1.5, PR=0.2
Qt (W) 100.54 77.15 60.32 48.18 39.63 33.37 95.77 70.52 54.94
∆Qt/% 0 23.26 40.01 52.08 60.58 66.81 0 26.37 42.63
Parameter L/D=2.0, PR=0.3 L/D=2.0, PR=0.3 L/D=2.0, PR=0.5 L/D=2.5, PR=0 L/D=2.5, PR=0.1 L/D=2.5, PR=0.2 L/D=2.5, PR=0.3 L/D=2.5, PR=0.4 L/D=2.5, PR=0.5
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44.37 37.05 31.68 91.36 65.63 51.05
53.67 61.31 66.92 0 28.16 44.12
L/D=3.0, PR=0 L/D=3.0, PR=0.1 L/D=3.0, PR=0.2 L/D=3.0, PR=0.3 L/D=3.0, PR=0.4 L/D=3.0, PR=0.5
84.41 58.57 45.41 36.75 31.01 26.91
0 30.61 46.20 56.46 63.26 68.12
a) Cd
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L/D=1.5, PR=0.3 L/D=1.5, PR=0.4 L/D=1.5, PR=0.5 L/D=2.0, PR=0 L/D=2.0, PR=0.1 L/D=2.0, PR=0.2
b) Qt
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Fig. 12. Drag coefficient and total heat flux of blunt body varying with pressure ratio PR.
a) Cd
b) Qt
Fig. 13. Drag coefficient and total heat flux of blunt body varying with length-diameter ratio L/D. Table5 Mass flow rate of jet gas under each pressure ratio. PR m (10-5Kg)
4.4. Effect of length of spike
0.1 2.37
0.2 4.75
0.3 7.11
0.4 9.49
0.5 11.87
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Figs. 7~11 can also reflect the influence of length-diameter ratio L/D on the wall pressure and wall heat flux of the blunt body. The results show that the wall pressure and wall heat flux decrease with the increase of lengthdiameter ratio L/D. Besides, with the increase of length-diameter ratio L/D, the decreasing rate of the wall pressure
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and wall heat flux decrease gradually. Therefore, when the length-diameter ratio L/D increases to a certain value, the decreasing rates of aerodynamic drag and aerodynamic heating will be close to zero, and the aerodynamic drag and aerodynamic heating will remain constant. In fact, the length of spike should also consider requirements of the stiffness and strength, and proper length can be selected based on the aerodynamic and structural requirements.
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According to Table3 and 4, the drag coefficient and total heat flux of the blunt body decrease with the increase of the length-diameter ratio L/D. For example, when PR is 3, the drag coefficient and total heat flux of the blunt
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body are decreased by 30.96% and 23.72% respectively with the increase of length-diameter ratio L/D from 1 to 3. So increasing the length of spike can significantly reduce the aerodynamic drag of the hypersonic vehicle and improve the thermal protection efficiency of the system, which is beneficial to the performance and safety of the hypersonic vehicle. In addition, according to Fig. 13, the slopes of all curves gradually decrease with the increase of length-diameter ratio L/D, and the decreasing rates of the drag coefficient and total heat flux of the blunt body gradually decrease with the increase of length-diameter ratio L/D. Therefore, the length of spike can not be increased
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indefinitely. The drag and heat reduction, increase of the mass and structural stiffness and strength reduction caused
spike.
4.5. Effect of jet gas
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by the increase of the length of spike should be evaluated comprehensively, and select the appropriate the length of
In the above analysis, the jet gas is air. In order to study the influence of jet gas on the drag reduction and heat
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reduction efficiency of the combined configuration proposed in this paper, the jet gases nitrogen N2 and carbon dioxide CO2 are also considered in this paper. Fig. 14 presents the mass fractions of the jet gases N2 and CO2 in the flow field. Fig. 15 presents comparison of the streamlines in the flow field under the jet gases N2 and CO2. According to the above analysis results, in the flow fields, the mass distributions of the jet gases N2 and CO2 are the same, and the flow fields under the jet gases N2 and CO2 have the same streamlines as that under the jet gas air, which indicates that jet gases N2 and CO2 have no influence on the flow characteristics. Fig. 16 presents the wall pressure and wall heat flux distributions of the blunt body under the different gas jet gases. Table 6 lists the drag coefficient and total heat flux of the blunt body under the different gas jet gases.
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According to Fig. 16(a) and Table 6, the wall pressure distributions of the blunt body under the jet gases N2 and CO2 have little difference and are obviously lower than the wall pressure distribution under the jet gas air. And the drag coefficients under the jet gases N2 and CO2 are 15.47% and 14.67% lower than that under the jet gas air respectively.
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So the N2 has the best drag reduction efficiency. In addition, according to Fig. 16(b) and Table 6, the wall heat flux of the blunt body under the jet gases N2 and CO2 is slightly less than that under the jet gas air, and the corresponding total heat fluxes of the blunt body are 0.36% and 2.29% lower than that under the jet gas air respectively. So the jet
b) CO2
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a) N2
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gas CO2 has the best thermal protection efficiency, but the advantage is not obvious compared with air and N2.
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Fig. 14. Mass distributions of nitrogen and carbon dioxide.
Fig. 15. Comparison of fluid streamlines.
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b) Wall heat flux
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a) Wall pressure
Fig. 16. Comparisons of wall pressure and heat flux distributions under different jet gases, L/D=1.5, PR=0.3.
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Table6
Drag coefficient and total heat flux of blunt body under different jet gases. Jet gas Air N2 CO2
5.
Conclusion
Cd 0.375 0.317 0.320
Qt (W) 44.372 44.211 43.358
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In order to reduce the hypersonic aerodynamic drag and heating of the hypersonic vehicle, a new combined configuration with the spike and opposing jet is proposed in this paper, and the drag and heat reduction efficiency is studied by the CFD method. The following conclusions were obtained: The combined configuration effectively reduces the aerodynamic drag and aerodynamic heating of the
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1)
blunt body through reconstruction of the flow field. The spike pushes the bow shock wave away from the
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blunt body and translates it into an oblique shock wave, which reduces the shock wave intensity. Besides, the low temperature jet gas is injected into the flow field to separate the high temperature gas after the shock wave from the blunt body.
2)
The drag and heat reduction efficiency of the combined configuration is better than the other configurations,
which shows the advantage of the combined configuration proposed in this paper in engineering application.
3)
The aerodynamic drag and aerodynamic heating of the blunt body decreases with the increase of the length of spike and the total pressure of opposing jet, and the corresponding decreasing rates decrease gradually with the increase of the above two parameters. Therefore, when the length of spike and the total pressure of
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opposing jet increase to the certain values, the decreasing rates of aerodynamic drag and aerodynamic heating will be close to zero, and the aerodynamic drag and aerodynamic heating will remain constant. In fact, the length of spike should also consider requirements of the stiffness and strength, and proper length
4)
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can be selected based on the aerodynamic and structural requirements. The jet gases (air, nitrogen and carbon dioxide) have no influence on the flow characteristics, and the nitrogen has the best drag reduction efficiency and carbon dioxide has the best thermal protection efficiency.
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Acknowledgments
Education Institutions.
Conflict of interest statement
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This research in this paper was supported by the Priority Academic Program Development of Jiangsu Higher
There are no conflicts of interest in relation to this manuscript.
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References
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ACCEPTED MANUSCRIPT 1) A combined spike and rear opposing jet configuration is proposed. 2) CFD method is adopted to analyze drag and heat reduction efficiency. 3) New configuration reduces drag and heating by reconstruction of flow field.
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3) Drag and heat reduction efficiency is better than the other configurations.
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4) Effects of the length of spike, total pressure of jet and jet gas are studied.