A study of performance parameters on drag and heat flux reduction efficiency of combinational novel cavity and opposing jet concept in hypersonic flows

Acta Astronautica 131 (2017) 204–225

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A study of performance parameters on drag and heat flux reduction efficiency of combinational novel cavity and opposing jet concept in hypersonic flows

MARK

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Xi-wan Sun, Zhen-yun Guo, Wei Huang , Shi-bin Li, Li Yan Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China

A R T I C L E I N F O

A BS T RAC T

Keywords: Hypersonic flow Drag and heat reduction Forward-facing cavity Opposing jet Jet operating conditions Freestream angle of attack Physical dimensions

The drag reduction and thermal protection system applied to hypersonic re-entry vehicles have attracted an increasing attention, and several novel concepts have been proposed by researchers. In the current study, the influences of performance parameters on drag and heat reduction efficiency of combinational novel cavity and opposing jet concept has been investigated numerically. The Reynolds-average Navier-Stokes (RANS) equations coupled with the SST k-ω turbulence model have been employed to calculate its surrounding flowfields, and the first-order spatially accurate upwind scheme appears to be more suitable for three-dimensional flowfields after grid independent analysis. Different cases of performance parameters, namely jet operating conditions, freestream angle of attack and physical dimensions, are simulated based on the verification of numerical method, and the effects on shock stand-off distance, drag force coefficient, surface pressure and heat flux distributions have been analyzed. This is the basic study for drag reduction and thermal protection by multiobjective optimization of the combinational novel cavity and opposing jet concept in hypersonic flows in the future.

1. Introduction The drag reduction and thermal protection system applied to hypersonic vehicles have attracted an increasing attention because the high pressure and aerodynamic heating will cause the damage of the aircraft surface and electronic devices. It attaches profound importance to conduct a survey on drag and heat reduction schemes of hypersonic re-entry vehicle [1,2]. The research progress of experimental investigations have been reviewed in Ref. [3]. The combinational opposing jet and aerospike concept [4–9], the combinational opposing jet and forward-facing cavity concept [10–12] and the combinational forward-facing cavity and energy deposition concept [13] have made up for some defects such as the ablation of aerospike and the unsteady flows in forward-facing cavity, and improved the drag and heat reduction efficiency greatly. In our previous study [14], the research progress of combinational forward-facing cavity and opposing jet concept was investigated in detail, and a parabolic cavity configuration was proposed to substitute the conventional one, as shown in Fig. 1. After comparing the drag and heat reduction efficiency of the two configurations numerically, we

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Corresponding author. E-mail address: [email protected] (W. Huang).

http://dx.doi.org/10.1016/j.actaastro.2016.11.044 Received 19 October 2016; Accepted 28 November 2016 Available online 01 December 2016 0094-5765/ © 2016 IAA. Published by Elsevier Ltd. All rights reserved.

come to the conclusion that the multi-objective optimization [15,16] is an essential process since each scheme has both advantages and disadvantages. The parametric investigation on the performance should be conducted based on the numerical method as a preliminary research for optimization [17,18]. The jet operating conditions, freestream angle of attack (AoA) and physical dimensions may be worth selecting as the parametric variables to minimize both the drag force and heat transfer rate [19–22]. In the current study, the effects of these parameters on shock stand-off distance [23], drag force coefficient, surface pressure and heat flux distribution are investigated numerically by the commercial software FLUENT. However, the axisymmetric assumption employed in Ref. [14]. is abandoned, and three-dimensional flowfields [24] are simulated in this study. Research progress of relative topics will be reviewed in corresponding sections. In the following study, the drag and heat reduction mechanism induced by a combinational novel cavity and opposing jet concept will be investigated numerically. In Section 2, the three-dimensional physical model is described, as well as the boundary conditions. In Section 3, the numerical method is provided, as well as the selection of spatially accurate model and grid independence analysis. The effects of

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Fig. 1. Sketch of the geometrical models employed in the current study [14].

⎧ y 2 + 2bxy + cx 2 + 2dx + 2ey + f = 0 ⎨ ⎩ b2 = c

(1)

The coefficients are solved by the coordinate values of the points P and E, as well as the tangent slope. The vertical coordinate and the slope at the point P are denoted as m and q respectively. The coordinates of the point E are denoted as (n, p), and p equals the radius of the cavity exit, Ro. The equation is solved by the software MATLAB, and the solution of the straight line and invalid solution should be both abandoned. The coefficients in Eq. (1) are as follows

⎧ b = − mq − pq 2m − 2p + nq ⎪ ⎪ c = b2 ⎪ 2 2 2 2 2 3 2 2 ⎪ d = 2m pq − nm q − 4mp q + 3nmpq + 2p q − 2np q ⎪ 2 2 2 2 4 + 4 − 8 + − 4 + 4 m mnq mp n q npq p ⎨ ⎪ 2m3 + 2m 2nq − 2m 2p + mn 2q 2 − 2mp2 − 2np2 q + 2p3 ⎪e = − 4m 2 + 4mnq − 8mp + n 2q 2 − 4npq + 4p2 ⎪ ⎪ f = 4m3p + m2n2q 2 + 4m2npq − 8m2p2 − 4mnp2 q + 4mp3 ⎪ 4m 2 + 4mnq − 8mp + n 2q 2 − 4npq + 4p2 ⎩

Table 1 Boundary conditions. Contents Freestream Mach number Freestream total pressure Freestream total temperature Opposing jet Mach number Jet total pressure ratio Jet static pressure Opposing jet species Opposing jet total temperature Wall temperature

Unit Ma∞ P0∞ T0∞ Maopp PR – T0j Tw

– Pa K – – Pa – K K

7.96 1,939,211 1955 0.5, 1, 2 0.07, 0.14, 0.28 72,374, 144,749, 289,498 H2, CH4, N2, Air, CO2 300 300

(2)

It should be noted that a geometric constrain conditions should be satisfied, namely the tangent slope at the point P should be greater than the slope of the line segment PE.

p − Rt − Rf (1 − cosβ ) L − (R −

R 2 − p 2 ) − Rf sin β

< tan β (3)

Herein, the radius of the front ball is denoted as R.

jet operating conditions, freestream angles of attack and physical dimensions are studied in Sections 4, 5 and 6 respectively. In Section 7, some valuable conclusions are summarized.

2.2. Boundary conditions Similar to our previous study [14], the boundary conditions used in this study is shown in Table 1, and this is also referred to Saravanan et al.'s experiment [25] and Lu et al.'s study [26]. The outlet of the flow field is kept as a hypersonic one so that the outlet boundary condition is extrapolated [26]. The air is assumed to be calorically perfect gas. The jet exit orifice is set to be pressure inlet, and the jet pressure ratio (PR) is defined as follows [8,27]：

2. Physical model 2.1. Geometric model The geometric models employed have been introduced in Ref. [14], and the generation principle by graphing method has been sketched in Fig. 2. The graphing method has the merits of simpleness and perceptual intuition, but lacks of precision. Moreover, it would be inconvenient for batch production of geometric models when conducting optimization. In the current study, the analytical solution is presented by computing the undetermined coefficients of the parabolic curve PE equation in Fig. 2. A general parabolic equation can be expressed as

PR =

P0j P0∞

(4)

Herein, P0j and P0∞ are total pressures of the jet and freestream respectively. The jet PRs chosen in Table 1 can ensure steady-state flowfields around the hypersonic blunt body [28]. The stability of 205

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Fig. 3. Grid of symmetry planes and wall.

Fig. 4. Comparison of axisymmetric and three dimensional grids.

flowfield is essential for drag and heat reduction scheme, since the unsteady flows would result in vehicle oscillations and increase the difficulty in manipulation of the aircraft. Further, the peak heat flux and total heat transfer rate in the unsteady flow induced by the opposing jet when PR=0.2 [27] may exceed the baseline case, which implies the failure in heat reduction as well.

3. Numerical approach and grid independency analysis 3.1. Numerical approach The commercial software ICEM and FLUENT integrated in ANSYS 13.0 are used to obtain the grid systems and numerical results. Numerical method can be referred to Ref. [14], and the SST k-ω turbulent model should be employed [29]. However, from the Fig. 9 and Table 7 in Ref. [14], the axisymmetric assumption [30] may not be totally credible since the heat flux distributions showed much difference from the three-dimensional results. In order to obtain convictive conclusions, three-dimensional grid systems are employed in the current study, see Fig. 3. The three-dimensional Reynolds-average Navier-Stokes (RANS) equations are employed to simulate the flowfields, along with the density based (coupled) double precision solver of FLUENT. With suitable under-relaxation factors, the CourantFriedrichs-Levy (CFL) number is set as 0.5 at first and increases to 2

Table 2 Grid system information.

First cell height /mm Regrid Cell number Face number Node number

1-Coarse

2-Moderate

3-Refined

0.0005 7.36 820,787 2,477,064 805,400

0.00035 5.1 890,232 2,625,689 870,180

0.00025 3.68 979,011 2,952,664 994,800

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Fig. 5. Computational results of different grid scales when employing the first-order model (density unit: kg/m3).

it refers to three-dimensional RANS equations, the selection of spatially accurate model should be discussed. Many authors employ the second-order [4,11,12,31] spatially accurate upwind scheme for combinational cavity and opposing jet configuration. In Refs. [32,33], Huang et al. studied the cantilevered ramp injectors in supersonic flows by using the first-order spatially accurate upwind scheme, and the predicted results show reasonable agreement with the experimental data in the open literature. Since the quantitative experiment for combinational cavity and opposing jet configuration has never been presented in open literature [3], the single opposing jet scheme of multi-component gas mixture when PR=0.6 in Refs. [34,35] is studied to verify the numerical approach. From Lu et al.'s [26,28,36] study, the flowfields of the combinational configuration and the single opposing jet scheme share many similarities, such as Mach disk, reattachment shock wave and

Table 3 Validation metrics of St with the first-order model.

Validation metric

Coarse

Moderate

Refined

0.571

0.515

0.512

with the progress of convergence to ensure stability. The solutions can be considered as converged when all the residuals reach their minimum values after falling for more than four orders of magnitude, and the difference between the computed inflow and the outflow mass flux is required to drop below 0.001 kg/s. In Ref. [14], the second-order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting was employed to quicken the convergence speed. When

Table 4 GCIs of pressure and St distributions with the first-order model.

Pressure St

Theta (°)

10

20

30

40

50

60

70

80

90

GCI12 GCI23 GCI12 GCI23

0.112 0.019 0.903 0.295

0.322 0.089 0.932 0.233

0.178 0.045 0.420 0.111

0.132 0.022 0.152 0.063

0.078 0.007 0.094 0.019

0.020 0.010 0.011 0.067

0.023 0.057 0.054 0.085

0.143 0.014 0.067 0.071

0.345 0.091 0.252 0.068

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Fig. 6. Computational results of different grid scales when employing the second-order model (density unit: kg/m3).

(segment BC in Fig. 3) increases appropriately with the refinement of grid scales. However, the node number outside the shock wave (segment AB in Fig. 3) varies slightly, which leads to few differences of the grids in Table 2. An exponential stretching formula is used to create appropriate clustering near the wall surface at the rate of 1.1. When the first-order spatially accurate upwind scheme is employed, the pressure distributions of the surface generatrices in Planes y=0 and z=0 show stability and consistency in each grid scale, as well as the Stanton numbers (St) distribution. The definition of St can be referred to Eqs. (2) and (3) in Ref. [14].

triple point [1]. The grid system can never be axisymmetric, since O subdivision should be conducted in such configuration in ICEM, which causes that the grids in Plane y=0 have higher quality values than those in Plane y=z. Therefore, we only extract parameters or contours from Planes y=0 and z=0 when comparing the flowfields of different cases in the following study. The grid system of single opposing jet scheme is shown in Fig. 4, and the position where shock wave generates has been predicted by the schlieren figures [27] and refined for better capturing accuracy. The first cell heights of three grid scales are determined by Regrid defined in Ref. [14], and see Table 2. Surface y+ could be set near 1 correspondingly [14]. Node numbers of radial (segment AD in Fig. 3) and circumferential (segment EF in Fig. 3) directions are kept unchanged at 82 and 25 respectively. Since the surface heat flux is the main parameter taken into account, the first cell height is strictly refined, and the node number between the shock wave and wall

St =

Taw = T∞{1 +

First cell height /mm Regrid Cell number Face number Node number CD

2-Moderate

3-Refined

0.02 7.36 803,472 2,423,393 816,656 0.2348

0.015 5.1 827,602 2,496,543 835,596 0.2366

0.01 3.68 841,092 2,536,633 854,656 0.2374

3

Pr [(γ − 1)/2]M∞2}

(5) (6)

Herein, qw is the surface heat flux, Taw is the adiabatic wall temperature, and Tw is the wall temperature, ρ∞, u∞, T∞ and M∞ are the freestream density, velocity, temperature and Mach number, respectively. Pr is the Prandtl number, cp∞ is the specific heat and γ is the ratio of specific heats. The pressure and St distributions of different grid scales are sketched in Fig. 5(a) and (b) respectively, and the density contours are compared with the schlieren figure in Fig. 5(c)– (e). Here, we also employ the Validation metric (V) and Grid Convergence Index (GCI) in Ref. [14]. to respectively analyze the numerical accuracy and grid independency quantitatively, see Tables 3 and 4. The definition of the Validation metric is

Table 5 Grid system information and CD. 1-Coarse

qw (Taw − Tw )ρ∞cp∞u∞

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Fig. 7. Grid independency results of the first-order model and the sampling points on generatrix for GCIs. Table 6 Parabolic configuration GCIs of pressure and St distributions when employing the firstorder model.

Pressure St

V=1−

1 N

x (m)

0.002

0.005

0.010

0.020

0.030

0.040

GCI12 GCI23 GCI12 GCI23

0.1754 0.0004 0.0425 0.0430

0.1041 0.0972 0.0019 0.0055

0.0380 0.0051 0.0023 0.0011

0.0335 0.0060 0.0006 0.0001

0.0313 0.0014 0.0001 0.0002

0.0126 0.0124 0.0001 0.0006

N

y(xi ) − Y (xi ) Y (xi )

∑ Tanh i =1

Table 7 Parabolic configuration GCIs of pressure and St distributions when employing the second-order model.

Pressure St

ε=

ε rp − 1

(7)

(8)

f2 − f1 f1

0.002

0.005

0.010

0.020

0.030

0.040

GCI12 GCI23 GCI12 GCI23

0.0585 0.1645 0.1539 0.0639

0.0371 0.1255 0.0807 0.0397

0.0012 0.2272 0.0494 0.1918

0.0266 0.1717 0.0249 0.0117

0.0319 0.0592 0.0099 0.0084

0.0018 0.0295 0.0047 0.0067

the theoretical value p=1.97 for a theoretically second-order method [14]. f1 and f2 are the concerned results of the refined grid and a relatively coarser one respectively. The contours of different cases show consistency with the schlieren figure, but the shock stand-off distances are all a little greater. Even though the case with the coarse grid possesses the most similar Stanton number distributions with the experimental data, most GCI23s are smaller than GCI12s, which means the numerical results appear convergence with the refinement of grid scales. Therefore, the first-order spatially accurate upwind scheme is effective in the numerical simulation of the single opposing jet scheme. When the second-order spatially accurate upwind scheme is employed, see Fig. 6, the density contours of each case consist better with the schlieren figure, especially the shock stand-off distance. Pressure distributions also show a high degree of consistency (see

Here, Y(xi) is the experimental measurement corresponding to the dependent variable y at x=xi. The definition of the Grid Convergence Index is

GCI = Fs

x (m)

(9)

Herein, Fs is a factor of safety, and it is set to be 1.25 since there are three sets of grids for each configuration. r is the grid refinement ratio, and it is calculated to be 1.4. p is the convergence rate, and we choose

Fig. 8. Grid independency results when employing the second-order model.

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Fig. 9. Coarse grid case when employing the second-order model (temperature unit: K).

The results of grid independency analysis are shown in Fig. 7(a) and (b), and the drag force coefficients are listed in Table 6. The parameter GCI is also used here, see Table 6, and six sampling points of the typical locations on the generatrix has been designated in Fig. 7(c). It can be observed that the results of different cases possess similar values and tendency, and the results show convergence with the refinement of grid system since most GCI12s are greater than GCI23s. What's more, most GCIs of St approach 0, and this suggests that the numerical model is of great applicability. Further, the numerical results of conventional configuration show the same changing tendency on the surface wall [28]. After switch to the second-order model after converging, it takes a long time to obtain a basically steady result, see Fig. 8 and Table 7. Even though there exists no apparent difference among the values of the three cases, the results fail to show convergence with refinement since most GCI12s are lower than CGI23s. What's more, Figs. 9–11 sketch the flowfields at the Plane x=0.01 m of the three cases at different iterative steps when the residuals and pressure distributions keep almost constant. Distinct changes appear in the contours of the coarse and refined cases, and the Stanton numbers vary considerably when the pressure distributions and flowfield keeps unchanged in the moderate case. In conclusion, the first-order spatially accurate upwind scheme is more suitable for the following study in this article, which can save the computing resources as well.

Fig. 6(a)), but not for Stanton number distributions. In Fig. 6(b) and (c), the Stanton number distributions are extracted from a certain iterative step of the coarse and refined cases when flowfields have kept unchanged. Even though the values are closer to the experimental data, the results fail to show axial symmetry or stability during the whole computational process. In conclusion, the heat flux simulation is more complicated [37], and the second-order spatially accurate upwind scheme should not be employed under the current condition. However, it can be suggested that the flowfields may be more consistent with the experimental data if steady results can be obtained by using the second-order spatially accurate upwind scheme. 3.2. Grid independency analysis The grid independency analysis of the parabolic configuration will be conducted in this section. PR is set as 0.28, and the compression air is employed as the opposing jet. The grid system information has been shown in Table 5. Similarly, the first cell height is changed strictly while the node numbers of radial and circumferential directions are kept unchanged at 82 and 25 respectively. The nodes of axial direction increase accordingly with the refinement of grid scales. An exponential stretching formula is used to create appropriate clustering near the wall surface at the rate of 1.1. The first-order spatially accurate upwind scheme is employed at first. Each case could converge when the number of iteration step reaches about 15,000–20,000 after 4 hours. 210

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Fig. 10. Moderate grid case when employing the second-order model (temperature unit: K).

the peak values of pressure and Stanton number along the spherical wall decrease with the increase of the jet PR, and the locations move backward slightly. There is a change of heat flux and pressure tendency at about x=0.01 m, because the flow changes from a low-speed expansion one around the hemisphere into a direct one along the cone [31]. The drag reduction efficiency of parabolic configuration is better than the conventional one when PR=0.07, but the drag coefficient increases with a higher PR. This may result from the reactive force of the inner cavity surface when jet expands more intensively [14]. However, the parabolic configuration fail to bring about better heat flux reduction efficiency, even though the shock stand-off distance is larger and the pressure values are lower than the conventional one at the same PR. This implies that the effects of configuration on the surface pressure and Stanton number distributions are different. Fig. 14 depicts the static and total pressure distributions of the symmetry axes of the two configurations when jet PR is 0.28. As to the conventional configuration, it can be observed that there exists a strong shock wave inside the cavity, and the total pressure loss ratio is nearly 60% according to the line graph. Also, there is a relatively weaker shock wave at the cavity exit. In contrast, the jet total pressure inside the parabolic cavity only decreases slightly due to expansion, and the higher jet energy may impair the heat reduction effect. However, a stronger jet issuing from the cavity can generate larger vortex near the nose-tip, lengthening the shock stand-off distance and decreasing the

4. Influences of jet operating conditions In this section, the influence of jet operating conditions on drag and heat reduction efficiency of combinational novel cavity and opposing jet configuration has been investigated numerically. In Section 4.1, the jet total pressure ratio (PR) is set to be 0.07, 0.14 and 0.28 in order to compare the efficiencies of conventional and parabolic configurations. In Section 4.2, hydrogen, methane, nitrogen, air and carbon dioxide are chosen as the jet species. In Section 4.3, the Mach numbers of opposing jet (Maopp) vary from 0.5 (subsonic) to 2 (supersonic). 4.1. Influence of jet PR Lu et al. pointed out that a higher PR may result in a better drag reduction [38] and thermal protection [26,28,31,36] effect for combinational conventional cavity and opposing jet configuration. In our previous study [14], it was proposed that the parabolic configuration will face larger drag force but a lower heat flux distribution with a higher PR. Herein, both the configurations will be investigated under the current conditions. Sonic compression air issues from the jet orifice in this section. Fig. 12 plots the comparison of pressure and Stanton number distributions, as well as the drag coefficients. Fig. 13 presents the Mach number contours of different cases. From Fig. 13, the shock stand-off distance increases with the increase of the jet PR. Similar to Ref. [14], 211

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Fig. 11. Refined grid case when employing the second-order model (temperature unit: K).

objective optimization in the near future. The jet PR is set as 0.28. In the following sections, the shock stand-off distance Δ will be replaced by Δ/R, which is a nondimensional parameter divided by the sphere radius R. Drag force coefficients and shock stand-off distances of different cases with increasing relative molecular weights are compared in Fig. 16. In Fig. 17(a) and (b), Mach contours are depicted, and the mass fraction contour of carbon dioxide and streamlines in temperature contour are presented in Fig. 17(c). Fig. 18 plots the comparison of surface pressure and Stanton number distributions. It can be observed that most cooling jet molecule exists inside the shock wave, and the cases with relatively smaller molecular weights show better heat reduction efficiency. However, the drag force coefficients or shock stand-off distances fail to change monotonously. The rapid increase of pressure distribution on the surface back-end of the case issuing methane may be the reason of a higher drag force. In addition, it should be noticed that the maximum temperatures of flowfields with the species of hydrogen [45] and methane have exceeded their ignition points. But this has been neglected here since only the influence of molecular weights is considered and steady flowfields are simulated. The results of cases with nitrogen and air show consistency, and this implies the rationality of their substitution [34,42]. In order to investigate thoroughly whether cooling jet species with similar relative molecular weights can replace each other when employing ideal-gas

surface pressure. Therefore, multi-objective optimization [39] should be conducted to find a configuration to minimize both the drag force coefficient and heat transfer rate, which can obtain better efficiency than the conventional one with lower jet PR. Herein, the original sphere-cone is simulated under the same freestream condition as well, see Fig. 15, and the drag force coefficient is 0.5108. Moving from the leading stagnation points to the sphere shoulders, the peak values of pressure and Stanton number decrease one order of magnitude when adopting combinational scheme. Also, the high-temperature region is cooled and pushed away from the surface, see Fig. 15(b). The drag reduction can exceed 50% for most cases. Therefore, the parabolic configuration proposed is verified effective compared with the original sphere-cone.

4.2. Influence of jet species There exist disagreements about the influence of various jet species on the efficiency of schemes related to opposing jet, and the influence has been ascribed to the molecular weight [12,34,40]. Air is employed to substitute nitrogen since they have similar relative molecular weight in Ref. [34], and their difference was amended in Refs. [41,42]. However, the influence of jet species on combinational configuration has never been studied. In the current study, hydrogen, methane, nitrogen, air and carbon dioxide [43,44] are chosen as the jet species. Only the parabolic configuration is investigated here for its multi212

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Fig. 12. CD and pressure and St distributions at different PRs.

Fig. 13. Comparison of Mach contours at different PRs.

assumption in hypersonic flows, extra cases of ethane (C2H6) and ethylene (C2H4) are investigated, see Fig. 19. Further, the thermodynamic properties parameters of all the species used in this section are listed Table 8, which should be input to FLUENT before computing.

The pressure values vary slightly especially on the surface frontend, while the Stanton number distributions differ greatly. Gases with similar relative molecular weights may contribute to similar surface pressure reduction, but not thermal protection efficiency since they 213

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Fig. 14. Pressure distributions of the axes when PR=0.28.

Fig. 15. The flowfield information of original sphere-cone (temperature unit: K).

share distinct thermodynamic properties, such as specific heat and thermal conductivity for nitrogen and ethylene. This implies that nitrogen and air can replace each other in these configurations not only because of similar molecular weights, but also similar thermodynamic properties. 4.3. Influence of opposing jet Mach numbers With regard to the single opposing jet scheme, supersonic jets from the orifices are employed by some experiments [46–48]. Lu et al. [31,38] concluded that higher jet Mach numbers may result in better thermal protection efficiency for conventional configuration, but no supersonic jet has been used in their study. In the current section, only the parabolic configuration is investigated for its multi-objective optimization, and jet Mach number is set as 0.5, 1 and 2. PR is fixed at 0.28, and the opposing jet is compression air. Drag force coefficients and shock stand-off distances of different cases with increasing relative molecular weights are plotted in Fig. 20, and Fig. 21 draws the comparison of surface pressure and Stanton number distributions. In Fig. 22(a) and (b), Mach contours are depicted, and pressure distributions of the axes are compared in Fig. 22(c).

Fig. 16. Comparison of CD and shock stand-off distance for different species.

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Fig. 17. Comparison of Mach number contours of different species and mass fraction and temperature contours of jet being CO2 (temperature unit: K).

Fig. 18. Comparison of pressure and St distributions with different species.

Fig. 19. Comparison of pressure and St distributions of different species with similar relative molecular weights.

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Table 8 Thermodynamic properties excerpted from FLUENT database. Gas species

H2

CH4

C2H4

N2

Air

C2H6

CO2

Relative molecular weight Specific heat (J/kg K) Thermal conductivity (W/m K) Viscosity (kg/m s)

2 14,283 0.1672 8.41E−06

16 2222 0.0332 1.09E−05

28 2233 0.214 1.03E−5

28 1040.67 0.0242 1.66E−05

29 1006 0.0242 1.79E−05

30 1731 0.0207 9.29E−6

44 840.37 0.0145 1.37E−05

5. Influences of freestream angle of attack Drag reduction and thermal protection systems of hypersonic vehicle nose-tip are often designed under the condition of no angle of attack (AoA, denoted as α) or angle of sideslip (AoS, denoted as β only in this section). The vehicle flying with angle of attack is inevitable, which is commonly between ± 10° [50]. The efficiency of the thermal protection system with opposing jet would be impaired considerably at an AoA or AoS, and usually the drag force may increase accordingly. In Ref. [51], Lu et al. conducted a research of the angle of attack characteristics of a hemisphere nose-tip with an opposing jet thermal protection system in supersonic flow. They concluded that the heat flux on the windward generatrix is close to the maximum of the original sphere when the angle of attack reaches 10°, and this leads to the failure of protection. Therefore, self-aligning aerospike [52] or aerodisk [53–55] have been proposed to improve the performance at a high AoA. The influences of AoA and AoS on drag and heat reduction efficiency of the combinational cavity and opposing jet concept has never been investigated in the open literature, and the novel configuration will be studied in this section of AoA ranging from 2 to 10°.

Fig. 20. Comparison of CD and shock stand-off distance for different Maopp.

5.1. Equivalent angle of attack of axisymmetric configuration

Sonic jet from the orifice brings about the farthest shock stand-off distance and lowest Stanton number values, and accordingly the highest drag force coefficient. From Fig. 22(c), intensive normal shock wave appears at the cavity exit when subsonic or supersonic jet is employed, and their surface pressure and St distributions differ slightly. In this study, the nozzle wall contour is designed under the condition when the flow at the throat is sonic, and shock waves may generate if not under this working condition [49]. Therefore, the opposing jet Mach number should accord with the nozzle wall contour designed for parabolic configuration and avoids random setting in order for higher heat reduction efficiency.

The sketch of AoA (α) and AoS (β) is shown in Fig. 23. With respect to axisymmetric configuration, each plane containing the center line can be considered as the symmetry plane. Therefore, an equivalent angle of attack αe could be obtained according to the geometric relationship

cos αe = cos α cos β

(10)

When employing the assumption of small angle, it could be deduced by omitting the quantities of high order that

Fig. 21. Comparison of surface pressure and St distributions for different Maopp.

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Fig. 22. Comparison of Mach contours and pressure distributions of the axes.

and the transition relation from normal (N) and axial (A) forces to lift (L) and drag (D) is

L = N cos α − A sin α D = N sin α + A cos α

(13)

Taking the bottom area as the reference area, the lift coefficient CL and drag coefficient CD are plotted against AoA in Fig. 25. Herein, the relative incremental ratio of CD to the value under no AoA and the liftto-drag ratio is denoted as Eα and L/D respectively. Employing the theory of unary linear regression, the lift-curve slope CL, α could be calculated by regarding each set of α (rad) and CL as a pair of coordinate (xi, yi)

CL, α =

∑ (xi − x )(yi − y ) ∑ (xi − x )2

(14)

x and y in Eq. (14) are the average values. The lift-curve slope is only about 0.275 (rad−1), since the blunt nose-tip is not a lifting body configuration [56]. The aerodynamic forces show generally linear variation at a small AoA, and the drag force increases rapidly when AoA increases.

Fig. 23. Sketch of AoA and AoS.

5.3. Results of flowfield Taking the case at the AoA of 7° as an example, the Mach contours of the Planes z=0, y=0 and x=0.01 m, the temperature contour and streamline distribution are depicted in Fig. 26(a) and (b). The surface pressure and Stanton number distributions of both windward and leeward generatrices are plotted in Fig. 26(c). It could be observed that the pressure and aerodynamic heating is relieved greatly on the leeward side due to the larger vortex, and only the windward pressure and Stanton number values of each case are extracted to make a comparison in the following study. Surface pressure and Stanton number distributions at different AoAs are sketched in Fig. 27, and they share similar changing tendency. The peak values increase and move to the front-end at a higher AoA, since the vortex at the windward side is squeezed smaller with the increase of AoA, see Fig. 26(b). However, the drag force and peak St at the 10° AoA are still much lower than the original spherecone in Fig. 15, which validates the drag and heat reduction efficiency within the AoA range considered in this section.

Fig. 24. Sketch of aerodynamic force R and its components.

⎛ β2 ⎞ α2 + β 2 α 2 ⎞⎛ ⎟≈1− ⎟⎜1 − cos αe = cos α cos β ≈ ⎜1 − + O(α 2β 2 ) 2 ⎠⎝ 2⎠ 2 ⎝ (11)

⇒ αe =

α 2 + β 2 + O(αβ )

(12)

When the values of α and β are both 10°, the relative error equals 0.24%, and this implies the rationality under the condition of small angle. In the following sections, only the influence of AoA is investigated.

6. Influences of physical dimensions In this section, the effects of physical dimensions on drag and heat reduction efficiency of combinational novel cavity and opposing jet configuration has been investigated numerically. In Section 6.1, the cavity dimensions are changed in order to analyze the influences of length and exit diameter. In Section 6.2, the cavity lip is rounded to

5.2. Results of aerodynamic force It should be noticed that the forces monitored by default in FLUENT are actually normal and axial forces instead of lift and drag. The aerodynamic force R and its components are depicted in Fig. 24, 217

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Fig. 25. Comparison of aerodynamic force at different AoAs.

Fig. 26. Contours and pressure and St distributions when α=7° (pressure unit: Pa; temperature unit: K).

Fig. 27. Comparison of surface pressure and St distributions at different AoAs.

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the cases with 6 mm exit diameter vary slightly. These phenomena could be explained as follows. From Fig. 30(a), there exist shock waves on the axes of the cases with 6 mm diameter due to the restriction of cavity walls (the shock wave generates outside the cavity when L=6 mm). In contrast, no shock wave appears inside the cavities when D=12 mm, but the longer cavity will result a larger loss in jet energy. Therefore, the cavity with smaller diameter and shorter length would contribute to drag and heat reduction at the same time, but result in a greater surface pressure distribution. However, the cavity should not be abandoned as a speedup nozzle [1] since the single opposing jet scheme of the sphere-cone configuration investigated by Lu et al. [38] suggests that its efficiency would be impaired at a low PR without a cavity. Mach contours of different cases with the same h are compared in Fig. 31. It can be observed that the larger cavity under the same h may generate a greater shock stand-off distance, and the jet has a stronger trend to expand front against the freestream, which would reduce its effect in cooling the outside surface wall.

Table 9 Case setting for different L and D. No

L (mm)

D (mm)

h

1 2 3 4 5 6 7 8

6 9 12 18 12 18 24 36

6 6 6 6 12 12 12 12

1 1.5 2 3 1 1.5 2 3

compare with the sharp configuration. In Section 6.3, the initial expansion lines of the nozzle cavity are varied. Only the parabolic configuration is investigated here in order for its multi-objective optimization in the near future. The PR of each case is fixed at 0.28, and the sonic compression air issues from the orifice.

6.2. Influence of rounding lip radius 6.1. Influences of cavity length and exit diameter

As to the single forward-facing cavity scheme, Engblom et al. [64,65] rounded the lips in the experiments, and observed that the rounding lips could eliminate the recirculation region, and alleviate heating inside the cavity. The research of the influence on the combinational forward-facing cavity and opposing jet concept has never been investigated. In this section, the rounding lip radius sketched in Fig. 32 is set as 0 (sharp lip), 1 and 2 mm. Drag force coefficients and shock stand-off distances of different cases are plotted against lip radius in Fig. 33, and Fig. 34 draws the comparison of surface pressure and Stanton number distributions, as well as the Mach contours. It could be seen that the drag force increases at a higher lip radius and the shock stand-off distance decreases accordingly. The surface pressure values increase while the Stanton number does not change monotonously, and the heat reduction efficiency would be impaired greatly when the lip radius equals 2 mm. The influence of the rounding lips results from two conflicting effects as discussed in Section 6.1, namely the shorter cavity length but the larger exit radius. From Fig. 34(c) and (d), it could be noticed that due to the rounding lip, the jet issuing from the cavity has a stronger trend to flow toward the outside surface wall instead of expand the front against the freestream, which is implied by the squeezed Mach disk and the shorter shock stand-off distance. The heating inside the cavities with sharp or rounding lip have been alleviated due to the presence of opposing jet. However, the pressure distributions on the rounding lips are plotted in Fig. 35, and the dotted lines are the lip curves. Because some part of the lip curve faces towards the freestream, there exists a minimum point of pressure and the values increase rapidly near the inner surface, which contributes to higher drag force coefficients. In conclusion, there would be no apparent advantages of heat reduction when employing rounding lip for combinational novel cavity and opposing jet concept, but would result in a much more severe pressure distribution on the lip than the outside surface wall. Therefore, the rounding lip configuration should be avoided in the combinational concept within the range of conditions considered in the current study.

In most experimental [57–60] or numerical [61–63] investigations of the single forward-facing cavity scheme, the cavity dimensions, especially the length-to-diameter ratio, have a profound impact on thermal protection efficiency. Lu [38] conducted a research on the conventional combinational concept with different cavity dimensions. It was proposed that a greater cavity length has little influence on drag force but contributes to better heat reduction efficiency. Both of the drag force and heat flux fail to change monotonically with the cavity diameter, and there exists an optimal choice of the cavity diameter for aerodynamic heating reduction. In this section, the effects of the parabolic cavity length and exit diameter are investigated, see Table 9. The length to diameter ratio L/D is denoted as h to investigate its effects. Drag force coefficients and shock stand-off distances of different cases with increasing h of different exit diameters are plotted in Fig. 28, and Fig. 29 draws the comparison of surface pressure and Stanton number distributions. The drag force increases at a higher h, and the shock stand-off distance decreases. The surface pressure distributions when exit diameter is 12 mm are lower, but the drag and heat reduction efficiency are weaker. The Stanton number distributions of

6.3. Influences of initial expansion line It is sketched in Fig. 2 that the initial expansion lines should be charactered by the radius Rf and attachment angle β when designing a maximum thrust nozzle cavity, and these two parameters would influence the inside flowfield properties greatly [49,66]. In this section, Rf is set as 0.5, 1 and 1.5 mm, and β is set as 15°, 21°, 27°. However,

Fig. 28. Comparison of CD and shock stand-off distance for different cases.

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Fig. 29. Comparison of pressure and St distributions for different cases.

Fig. 30. Pressure distributions of the axes in cavities for different cases.

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Fig. 31. Comparison of mach contours for different h.

different nozzle contours of varied parameter combinations are shown in Fig. 36 (the vertical coordinates are enlarged for better comparison). It could be noticed that the initial expansion radius makes little difference when other parameters are fixed, and this implies that the flowfields would not vary apparently. Therefore, only the attachment angle β is changed in this section, and the expansion radius is fixed at 1 mm. Drag force coefficients and shock stand-off distances of different cases with increasing initial attachment angles are plotted in Fig. 37, and Fig. 38 draws the comparison of surface pressure and Stanton number distributions. It could be observed that the influence of attachment angle is non-significant, especially the similar Stanton

Fig. 32. Sketch of the parabolic configuration with rounding lip.

Fig. 33. Comparison of CD and shock stand-off distance for different lip radii.

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Fig. 34. Comparison of surface pressure and St distributions and Mach contour for different lip radii.

Fig. 35. Pressure distributions of the lip.

Fig. 36. Contours of different initial expansion lines.

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generate when the attachment angle equals 21°. Therefore, when applied to combinational drag and heat reduction scheme, the initial expansion radius and attachment angle make little difference but should be selected according to the physical dimensions and jet operating conditions in order for better performance. 7. Conclusion In this article, the influence of jet operating conditions, freestream angle of attack and physical dimensions on drag and heat flux reduction efficiency of combinational novel cavity and opposing jet concept in hypersonic flows has been investigated numerically, and the shock stand-off distance, drag force coefficient and the distributions of surface pressure and Stanton number are chosen to draw a comparison. Based on the parabolic configuration proposed, the analytical generation principle is presented. Different from our previous study [14], three-dimensional flowfield and the first-order spatially accurate upwind scheme are employed after grid independency analysis of both the single opposing jet scheme and the parabolic configuration. The design of thermal protection system (TPS) calls for multi-objective optimization approach to minimize both the drag force coefficient and heat transfer rate in the near future. We come to the following conclusions:

Fig. 37. Comparison of CD and shock stand-off distance for different initial attachment angles.

number distributions. However, the smaller attachment angle may be beneficial to surface pressure reduction. In Ref. [67], it is suggested that the maximum thrust and best expansion performance may

•

The first-order spatially accurate upwind scheme is more suitable for

Fig. 38. Comparison of surface pressure and St distributions and Mach contours.

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• • • • • • • •

both the single opposing jet scheme and the parabolic configuration to obtain the steady and axisymmetric results in three-dimensional flowfields. A longer shock stand-off distance would usually brings about better drag reduction, but surface pressure and Stanton number distributions fail to present obvious pattern. The parabolic configuration proposed is verified an effective drag and heat reduction method compared with the original sphere-cone, and the multi-objective optimization approach should be conducted to find a configuration, which can obtain better efficiency than the conventional one with lower jet PR. Jets with smaller molecular weights show better heat reduction efficiency, and gases with both similar molecular weights and similar thermodynamic properties can replace each other as the cooling jet. The opposing jet Mach number should accord with the nozzle wall contour designed for parabolic configuration and avoids random setting in order for higher heat reduction efficiency. The combinational novel configuration is validates effective on drag and heat reduction at an AoA of 10°. The length to diameter ratio L/D is a useful parameter, and the cavity with smaller diameter and shorter length would contribute to drag and heat reduction simultaneously, but would result in a greater surface pressure distribution. There would be no apparent advantages of heat reduction when employing rounding lip for combinational novel cavity and opposing jet concept, but would result in a much more severe pressure distribution on the lip than the outside surface wall. The initial expansion radius and attachment angle make little difference but should be selected according to the physical dimensions and jet operating conditions in order for the best performance.

[13] [14]

[15] [16]

[17]

[18]

[19] [20]

[21]

[22] [23] [24]

[25] [26]

[27] [28]

Acknowledgements

[29]

The authors would like to express their thanks for the support from the Science Foundation of National University of Defense Technology (No. JC14-01-01) and the National Natural Science Foundation of China (No. 11502291). Also, the authors thank the anonymous reviewers for some very critical and constructive recommendations on this paper.

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