Effect of thermochemical non-equilibrium on the aerodynamics of an ...

Acta Astronautica 139 (2017) 288–295

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Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro

Effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider under different angles of attack Zhen Liu, Jun Liu *, Feng Ding, Kai Li, Zhixun Xia College of Aerospace Science and Engineering, NUDT, Changsha 410073, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Osculating-cone waverider Thermochemical non-equilibrium flow Perfect gas Angle of attack

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.

1. Introduction During reentry and gliding, hypersonic vehicles carry out complex chemical reactions in the surrounding air, leading to different degrees of dissociation and ionization of oxygen and nitrogen. Moreover, the internal energy modes of molecules and atoms have different degrees of excitation. These phenomena are the high-temperature real gas effects, including chemical equilibrium/non-equilibrium and thermal equilibrium/non-equilibrium effects [1]. Because of the low density effect at high altitude, the thermochemical non-equilibrium effect occupies the main position in the reentry process [2,3]. So far, investigations of non-equilibrium flow around simple configurations such as wedges, sharp corners and blunt bodies have been reported by Spurk [4] and Rakich [5]. In recent years, researchers have performed many studies on the aerodynamic force, aerodynamic heating and pneumatic physics problems under thermochemical non-equilibrium flow conditions for axisymmetric spacecraft and blunt aircraft [6–14]. Furthermore, investigations of the high-temperature effect towards the waveriders have been underway since the early 1990s, but much attention has been paid to the equilibrium effect. Han et al. [15] studied the equilibrium gas effect on the hypersonic gliding waverider, and the results showed that real gas effects lead to a down-ward force moment. Zeng et al. [16] analyzed the equilibrium gas effect on the aerodynamic characteristics of a conical waverider. Results indicated that the equilibrium effect moves the pressure center backward for the conical

* Corresponding author. E-mail addresses: [email protected] (Z. Liu), [email protected] (J. Liu). http://dx.doi.org/10.1016/j.actaastro.2017.07.013 Received 1 March 2017; Received in revised form 19 May 2017; Accepted 9 July 2017 Available online 12 July 2017 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.

waverider, and this phenomenon is opposite to that of the space shuttle orbiters. Recent years, investigation of the non-equilibrium effect towards the waveriders has been underway. Liu et al. [17] investigated the non-equilibrium effect on the aerodynamic characteristics of a conical waverider, and the results showed that the non-equilibrium influence moves the pressure center forward by approximately 0.57% of the whole craft's length at an altitude of 60 km. However, there has been little research on the influence of the nonequilibrium effect towards the osculating-cone waverider, which is the crucial configuration for the integral design of air breathing hypersonic vehicles. Our previous work [18] studied the non-equilibrium effect on an osculating-cone waverider at the cruise angle of attack, and the results showed that the non-equilibrium influence moves the pressure center forward by approximately 1.33% of the whole craft's length at an altitude of 55 km and cruise attack angle of 6 . On the basis of our previous work, the study of the thermochemical non-equilibrium effect on the osculating-cone waverider under different angles of attack will be conducted using the non-equilibrium numerical simulation program TCNEQ3DP [19] developed by our team, which has been validated by numerous cases in hypersonic flow simulation [17]. 2. Osculating-cone waverider configuration and mesh In order to reflect the continuity of work, we chose the same configuration as that of Ref. [18]. Fig. 1 shows the definition of the

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volumetric efficiency. Equations (1) and (2) show the functions of shock wave on the base plane and trailing edge of the freestream surface, respectively.

y¼ y¼

Table 1 Design parameters of the osculating-cone waverider. Value

Ma β (deg) L (mm) Lw (mm) Ls (mm) Lu (mm) m n k

15 10 6000 4000 100 100 4 4 0.8

(1)

H; z 2 ½0; Lu H þ bðz Lu Þm ; z 2 ðLu ; Lw Þ

(2)

Herein, β is the angle of the shock wave, L and Lw are the length and width, respectively, of the osculating-cone waverider; Lu is half the length of the straight section on the trailing edge of the freestream surface; Ls is half the length of the straight section in shock wave on the base plane. The waverider analyzed in this study was designed on the basis of the parameters shown in Table 1. Fig. 2 shows the geometry of the osculating-cone waverider, whereas Fig. 3 shows its size. The commercial software ICEM-CFD was employed to generate the multi-block structured mesh. Because of its symmetry, and disregarding the sideslip angle, only half of the flow field was simulated. From our previous work [17,18], when the magnitude of the non-dimensional grid height of the first layer on the wall (Δn ) can reach a level of 105, the mesh is accurate enough for our analysis. In this study, Δn is 4 105. And the mesh has 3.57 106 nodes. Fig. 4 shows the grid at the symmetric plane and base plane.

Fig. 1. Definition of design parameters of the osculating-cone waverider.

Design parameter

0; z 2 ½0; Ls n aðz Ls Þ ; z 2 ðLs ; Lw Þ

3. Calculation conditions The degree of chemical reaction as well as the gas temperature in the boundary layer varies with the flight conditions. Therefore, a typical altitude of 55 km was chosen, and three Mach numbers, namely 15, 20, and 25, were also chosen to analyze different extents of the nonequilibrium effects. The sideslip angle for all cases was 0 , and the angles of attack were 0 , 6 , and 10 . The physical parameters of the incoming flow are obtained from the American standard atmosphere table. Table 2 shows the computational conditions for this study. The AUSMPW second order upwind scheme with MUSCL reconstruction was used for the inviscid fluxes, and the center difference scheme was used for the viscous fluxes. For time discretization, an approximately factored LU-SGS scheme was used. The total implicit time preconditioning method was employed to eliminate the rigid problem. The no-slip isothermal wall with a temperature of 300 K was set to be the wall boundary condition; this mainly influences the viscous force in the boundary layer, which has been improved in Ref. [18]. Gupta's eleven species model was utilized to describe the non-equilibrium gas mixture as well as a series of models, such as Park's two-temperature model [20] for vibration-dissociation coupling, the Landau-Teller model with Millikan and White's rates plus Park's modifying formula [21] for energy relaxation, Gupta's fit formula [22] for single species' transportation coefficients and Wilke's half experiential formula for the mixture's. Furthermore, the commercial software ANSYS Fluent [23] is used to calculate the viscous perfect gas flow field. And the CFD analyses are in laminar flow conditions.

Fig. 2. Isometric view of the osculating-cone waverider.

4. Results and analysis 4.1. Flow structure comparisons on the symmetric plane

Fig. 3. Orthographic view of the osculating-cone waverider (unit: mm).

The pressure and Mach number contours on the symmetric plane at the condition of Mach number 25 and 10 angle of attack are shown in Figs. 5 and 6. It can be seen that the slopes of the oblique shock wave for the non-equilibrium flow model and perfect gas model are different. That is to say, the thermochemical non-equilibrium changes the shape of the

design parameters of the osculating-cone waverider in current study. The middle region of the shock wave on the base plane is designed to be a straight line so as to obtain a uniform flow field at the entrance of the air inlet. The exterior margin of the shock wave on the base plane is designed to be a curve, and its function is exponential in order to improve 289

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Fig. 4. Structured grid employed in the osculating-cone waverider.

Table 2 Computational conditions. case case1 case2 case3 case4 case5 case6 case7 case8 case9

M∞ 15 15 15 20 20 20 25 25 25

H (km) 55 55 55 55 55 55 55 55 55

α ( ) 0 6 10 0 6 10 0 6 10

T∞ (K)

P∞ (Pa)

260.771 260.771 260.771 260.771 260.771 260.771 260.771 260.771 260.771

42.525 42.525 42.525 42.525 42.525 42.525 42.525 42.525 42.525

V∞ (km/s) 4.86 4.86 4.86 6.47 6.47 6.47 8.09 8.09 8.09

ρ∞ (kg/m2) 5.68 5.68 5.68 5.68 5.68 5.68 5.68 5.68 5.68

Fig. 5. Mach number contours in the symmetric plane under the condition of Ma 25 and 10 angle of attack.

Fig. 6. Pressure contours in the symmetric plane under the condition of Ma 25 and angle of 10 attack.

Fig. 7. Vibration temperature contours in the symmetric plane under the condition of 0 angle of attack.

290

4

10 104 104 104 104 104 104 104 104

μ∞ (N*s/m2) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

105 105 105 105 105 105 105 105 105

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Fig. 8. Vibration temperature contours in the symmetric plane under the condition of Ma 25.

vibration degree is significant exists mainly near the windward boundary layer at the tail of the waverider and the wake flow after it. Therefore, the high-temperature effect is stronger in the windward boundary layer at the tail of the osculating-cone waverider. Unlike the traditional blunt configuration, whose high-temperature gas effect mainly comes from the compression of the bow shock wave, the same effect for the osculatingcone waverider mainly appears at the tail where the viscous interactions dominate. For the configuration as the waverider, the leading attached shock wave is weak, and the compressed air is not strong enough to cause a chemical reaction at the head of the waverider.

Fig. 9. Illustration of X-constant slices.

oblique shock wave, and it is mainly reflected in the slope of the shock wave. When considering the high temperature gas effects, the flow past the shock will conduct a series of complex reactions, such as dissociation, and the chemistry reactions may decrease the temperature causing the boundary layer to be thinner. The phenomena would weaken the compression of flow, resulting in reduced distance between the shock wave and the waverider body. Fig. 7 shows the vibration temperature Tv contours under the condition of 0 angle of attack and Mach numbers 15, and 25. Fig. 8 shows the vibration temperature Tv contours under the condition of Mach number 25 and 6 and 10 angles of attack. It can be seen from Figs. 7 and 8 that the region where the molecular

4.2. Flow structure comparisons on the X-constant slices In order to compare the differences in the flow field between the two different gas models, three X-constant slices were selected, with nondimensional X/L coordinates of 0.1, 0.5 and 1.0; the positions of the planes are shown in Fig. 9. Herein, L stands for the length of the osculating-cone waverider. Fig. 10 shows the pressure contours on the Xconstant slices under the condition of angle of attack equals to 0 . And Fig. 11 shows the pressure contours on the X-constant slices under the

Fig. 10. Pressure contour comparison of perfect gas and non-equilibrium flow (α ¼ 0 ). 291

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Fig. 11. Pressure contour comparisons of perfect gas and non-equilibrium flow under the condition of Ma 25.

Fig. 12. Longitudinal distributions of wall pressure coefficient along the symmetric plane (α ¼ 0 ).

osculating-cone waverider body under the condition of angle of attack equals to 0 , it is shown that the distance between the shock wave and waverider body of the perfect gas model is smaller than the nonequilibrium flow results. Under the condition of zero angle of attack,

condition of Mach number equals to 25 and angle of attack equals to 6 and 10 . For each figure, the perfect gas results are on the right side, and the non-equilibrium flow results are on the left side. By comparing the distance between the shock wave and the

Fig. 13. Longitudinal distributions of wall pressure coefficient along the symmetric plane (α ¼ 6 ). 292

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Fig. 14. Longitudinal distributions of wall pressure coefficient along the symmetric plane (α ¼ 10 ).

Table 3 Aerodynamic force parameters and pressure center. M

15 15 15 20 20 20 25 25 25

H (km)

55 55 55 55 55 55 55 55 55

α ( )

0 6 10 0 6 10 0 6 10

CA

CN

Cmz

ΔXcp

Xcp(m)

Perfect

Neq

Perfect

Neq

Perfect

Neq

Perfect

Neq

0.0838 0.1675 0.3205 0.0789 0.1593 0.2624 0.0762 0.1600 0.2608

0.0718 0.1496 0.2225 0.0637 0.1412 0.2092 0.0601 0.1407 0.2044

0.3124 0.9072 1.4158 0.2975 0.8812 1.3841 0.2885 0.8657 1.3704

0.3056 0.8992 1.4087 0.2886 0.8638 1.3858 0.2782 0.8371 1.3298

0.1829 0.5180 0.8027 0.1747 0.5036 0.7876 0.1695 0.4952 0.7804

0.1745 0.5023 0.7813 0.1651 0.4822 0.7724 0.1592 0.4674 0.7419

3.512 3.426 3.402 3.523 3.429 3.414 3.526 3.432 3.417

3.426 3.351 3.328 3.432 3.349 3.344 3.434 3.351 3.348

1.43% 1.25% 1.23% 1.52% 1.33% 1.17% 1.53% 1.35% 1.15%

perfect gas results and the solid dots stand for the non-equilibrium ones. It can be seen from Figs. 12–14 that the pressure coefficient along the leeward side are much smaller than the windward side for both perfect gas results and non-equilibrium ones. The pressure distribution lines for the perfect gas model indicate that the pressure coefficient along the leeward side decreased slightly with increasing angle of attack, and the pressure coefficient along the windward side increased significantly with increasing angle of attack. When considering the thermochemical nonequilibrium effects, the changing rules of distributions of pressure coefficient are the same along the windward and leeward meridian lines on the symmetric plane with angle of attack. For the leeward side, the pressure coefficient of the non-equilibrium flow is larger than the perfect gas results. However, the pressure coefficient of the non-equilibrium flow is smaller than the perfect gas results in most regions of the windward side meridian line, and the difference becomes larger with the increase of Mach number for all three angles of attack.

the chemical reactions are weak, therefore, the shock layer has little difference. Under the conditions of angle of attack equals to 6 and 10 , the flow structures are overall the same for the two gas models on the slice of X/ L ¼ 0.1, which indicates that the high-temperature gas effects are not obvious in the front region of the osculating-cone waverider. For the slices of X/L ¼ 0.5 and X/L ¼ 1.0, the distance between the shock wave and waverider body of the perfect gas model is larger than the nonequilibrium flow results, which is opposite to the condition of 0 angle of attack. Figs. 12–14 show the wall longitudinal distributions of the pressure coefficient along the windward and leeward meridian lines on the symmetric plane for different angles of attack, in which the lines stand for the

4.3. High-temperature effect on aerodynamic forces Table 3 shows the calculation results of the osculating-cone waverider in both non-equilibrium flow and perfect gas, including the axial force parameters CA, normal force parameters CN, pitching moment parameters Cmz and absolute position of pressure center Xcp, as well as the percentage of pressure center forward distance ΔXcp; for all the parameters, the reference length and area are 6.0 m and 2.4343 m2, respectively. Moreover, the reference point for the pitching moment coefficient shown in Table 3 is the vertex of the osculating-cone waverider. In this study, the pitching moment coefficient is defined negative when the pitching moment raises the head of the vehicle. The percentage of pressure center forward distance ΔXcp is defined as equation (3).

ΔXcp ¼ Xcp

perfect

Xcp

neq

L

(3)

The changes in the regular patterns for aerodynamic coefficients with Mach number and angle of attack are similar for both the nonequilibrium flow and perfect gas. The normal force coefficient and

Fig. 15. Normal force coefficient with variation of attack angle at H ¼ 55 km. 293

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Fig. 18. Pitching moment coefficient with variation of Mach number at H ¼ 55 km.

Fig. 16. Normal force coefficient with variation of Mach number at H ¼ 55 km.

Fig. 19. X-coordinate of pressure center with variation of attack angle at H ¼ 55 km.

Fig. 17. Pitching moment coefficient with variation of attack angle at H ¼ 55 km.

gas results, the non-equilibrium pressure distribution brings an additional positive moment that raises the head of the waverider and moves the pressure center forward. As clearly shown in Figs. 19 and 20 and Table 3, the non-equilibrium effect moves the pressure center forward compared with perfect gas results. Furthermore, the percentage of pressure center forward distances ΔXcp decreases with increasing angle of attack, whereas it increases with increasing Mach number. Among them, the maximum forward distance is 1.53% of the whole craft's length under the condition of Mach number equals to 25 and angle of attack equals to 0 at the altitude of 55 km.

pitching moment coefficient increase with increasing angle of attack, whereas they decrease slightly with increasing Mach number. Furthermore, the X-coordinate of the pressure center moves forward with increasing angle of attack, and it moves backward with increasing Mach number. In order to compare the results more directly, Figs. 15–20 show the curves of the parameters in Table 3 varying with Mach number and angle of attack. Comparing the results for the non-equilibrium flow and perfect gas reveals that the normal force and pitching moment coefficients for the non-equilibrium model are slightly smaller than the perfect gas results for all cases, and the difference between the two gas models stays nearly the same as the Mach number varies. The reason is that the pressure coefficient of the non-equilibrium flow is smaller than the perfect gas results in most regions of the windward side, whereas for the leeward side, the pressure coefficient of the non-equilibrium flow is larger than the perfect gas results, as can be seen from Figs. 12–14. Compared with the perfect

5. Conclusions In this study, a comparison between thermochemical non-equilibrium flow and perfect gas past an osculating-cone waverider was performed. Numerical methods were employed to analyze the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone

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[2] [3] [4] [5] [6]

[7]

[8]

[9]

[10]

[11] [12] Fig. 20. X-coordinate of pressure center with variation of Mach number at H ¼ 55 km. [13]

waverider under different angles of attack. Some conclusions have been drawn. First, the thermochemical non-equilibrium effect changes the shape of the oblique shock wave for the osculating-cone waverider, which is mainly reflected in the slope of the shock wave, and the difference in the slope of the shock wave becomes more obvious with increasing angle of attack. Second, the thermochemical non-equilibrium effects make the shock layer thinner, resulting in temperature decrease in the shock layer. Third, the high temperature gas effect makes the pressure center move forward, and the forward distance decreases with increasing angle of attack and increases with increasing Mach number; furthermore, the maximum forward distance is 1.53% of the length of the whole craft under the conditions of Ma ¼ 15–25, α ¼ 0–10 .

[14]

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