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Drag reduction for the combination of spike and counterflow jet on blunt body at high Mach number flow
Acta Astronautica 133 (2017) 103–110
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Research paper
Drag reduction for the combination of spike and counterflow jet on blunt body at high Mach number flow Z. Eghlima, K. Mansour
MARK
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Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Hypersonic Spike Counterflow jet Drag reduction
Drag reduction at high speed flows around blunt bodies is one of the major challenges in the field of aerodynamics. Using of spikes and counterflow jets each of them separately for reducing of drag force is well known. The present work is description of flow field around a hemispherical nose cylinder with a new combination of spike and counterflow jet at free stream of Mach number of 6.The air gas was injected through the nozzle at the nose of the hemispherical model at sonic speed. In this numerical analysis, axisymmetric Reynolds-averaged Navier-Stokes equations was solved by k-ω (SST) turbulence model. The results were validated with experimental results for spiked body without jet condition. Then the results presented for different lengths of spike and different pressures of counterflow jets. The results show a significant reduction in the drag coefficient about 86–90% compared to the spherical cylinder model without jet and spike for practical models (L/D=1.5 and 2). Furthermore also our results indicate that the drag reduction is increased even more with increasing of the length of the spike.
1. Introduction
1.1. Previous studies about counterflow jet
The drag reduction in aerodynamic applications by a spike or a jet spike on a blunt-nosed body at supersonic and hypersonic flows is well known and were studied years ago [1–6]. The wave drag reduction by using a spiked or opposing jet is derived from both the splitting of a single strong shock into multiple shock waves and effectively replacing the blunt body by a slender displacement. Even if the accumulative pressure rise across the multiple and sequential shock wave is identical to that of a single shock, the entropy jump across the multiple wave system is much less. This difference is because of proportionality of the cubic power of the pressure jump due to the entropy increment across each shock wave. The blunt body with injection will, thus, produce a lower wave drag. There are also disadvantages of these drag reduction devices in that they can induce unsteady motion with large-amplitude oscillations through free-shear-layer instability. Fig. 1 shows a typical jet issuing from a body against a supersonic airstream. The bow shock stands away from the body surface, and takes a form appropriate to a new body consisting of the original body with a protrusion due to the jet flow. The boundary of this protrusion is defined by the interface, the stream surface between the jet flow and the mainstream flow.
The opposing jet in supersonic flows has been considered a lot because of its wide applications on drag and heating reduction at supersonic and hypersonic flows. The experiments on a jet from a blunt body opposing supersonic flows mainly investigated the mean flow quantities, such as the pressure distribution on the body surface, the bow shock stand-off mean position and the shock structures complexity [1,7,8]. These studies revealed that the total pressure ratio of the jet to the free stream is a key parameter affecting the aerodynamic features. In addition, complex sustained motions of the flow field were observed experimentally in some jet conditions. Recently, with the development of the aeronautics and astronautics, the advantage of opposing jet is more appealing to the researcher. In this century, some scholars kept doing research on this method. Hayashi [8–10] did the numerical and experiment studies of thermal protection system by opposing jet and obtained some valuable conclusions. The high precise simulation of Navier-Stokes equations was used by Tian [11] to study the detailed influences of the free Mach number, jet Mach number, attack angle on the heat flux reduction and the mechanism was discussed.
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Corresponding author. E-mail address: [email protected] (K. Mansour).
http://dx.doi.org/10.1016/j.actaastro.2017.01.008 Received 16 November 2016; Accepted 6 January 2017 Available online 12 January 2017 0094-5765/ © 2017 IAA. Published by Elsevier Ltd. All rights reserved.
Acta Astronautica 133 (2017) 103–110
Z. Eghlima, K. Mansour
w Y γ εm θ μ ρ σ τ Ω ω
Nomenclature Cd CP dj D e k H h L M p q PR R S T u v
Drag coefficient Pressure coefficient Diameter of the jet section Diameter of the main sphere Total energy per unit mass Turbulent kinetic energy Total enthalpy Enthalpy Length of the spikes Mach number Pressure Heat flux Ratio of jet to free stream total pressures Radius of base of model Source term Temperature Velocity in x-dir Velocity in y-dir
Velocity in z-dir Dissipation term Specific heat ratio Turbulent kinetic energy inclination of the dividing streamline Dynamic viscosity Density Turbulent Prandtl number Stress tensor Mean vorticity Specific dissipation rate
Subscripts 0 j O w ∞
Due to base model (without any jet and spike) Jet Total or stagnation value Wall condition Free stream
number 6. In 2014, Mansour and Khorsandi [17] investigated numerically the surface pressure distribution and drag coefficient of a blunt nose cone with an aerospike in hypersonic free stream Mach number of 6. The geometric model they studied was the same model in ref.[16] and they used k-ε turbulence model.
1.2. Previous studies about aerospike Flow fields around a spiked body were experimentally investigated in the 1950s. For example, flow fields around a spiked blunt body at Mach number 6.8 were experimentally investigated by Crawford1 in 1959 [2]. Yamauchi et al. [12] in 1995 have numerically studied the flow field around a spiked blunt body at free stream Mach numbers of 2.01, 4.14 and 6.80 for different ratio of L/D (Length of spike to base diameter). Mehta in 2000 calculated the flow field around a forward facing spike attached to a hemisphere-cylinder nose tip at a free stream Mach number of 6.8 for different spike lengths [13]. Asif and Zahir in 2004 studied supersonic flow (M∞=1.8) and hypersonic flow (M∞=5, 6.8, 8) around a blunt nose body with the attachments of 4 forward facing spikes and estimated aerodynamic forces using CFD tool, PAK3D [14]. In this paper, four different geometries of spikes and two different lengths have been examined to study the forebody flow and its effects on static aerodynamics coefficients. In 2009, Mehta again studied numerically the effect of the various types of aerospike configurations on the reduction of aerodynamic drag and wall heat flux, this time at a length to diameter ratio of 0.5, at Mach 6 and at a zero angle of incidence [15]. In 2010, Kalimuthu and Mehta [16] experimentally studied the pressure variation on the blunt nose body and the aerodynamic coefficients such as drag, lift and pitching moment over the forward facing hemisphere aero spike at Mach
1.3. Previous studies about combination of the jet and spike The concept of combination of these two methods is new; counterflow jet and aerospike. Jiang at 2009 [18] conducted Experiments in a hypersonic wind tunnel at a nominal Mach number of 6. It is shown previously that the shock/shock interaction on the blunt body is avoided due to injection and consequently the peak pressure at the reattachment point is reduced by 70% under a 4° attack angle. Wei Huang et al. at 2015 [19] investigated the influences of length-todiameter ratio of aerospike and jet pressure ratio on the drag reduction by combinational opposing jet and aerospike concept at supersonic Mach number of 2.5. The rejecting gas was nitrogen. The maximum drag reduction coefficient is 65.02% compared to the without spike conditions (with jet), and it occurs when the jet pressure ratio is 0.4. The peak pressure location moves nearly from 40 to 55 deg, and it is nearly the same irrespective of the variation of the jet pressure ratio. Anyway, this method of combination has not been applied to the hypersonic flows previously. Present study has calculated flow field around a hemispherical nose cylinder model in the free stream of Mach number of 6 without and with a counterflow jet at sonic speed. The material injecting to the jet is air and it is injected from the top of the spike's nose. The results for without jet conditions are validated with experimental and numerical studies in the given refs. [16] and [17]. The results show a significant reduction in pressure distribution on the surface and drag coefficient. In this numerical analysis, axisymmetric Reynolds-averaged Navier-Stokes equations were solved by using of k-ω (SST) turbulence model. The results are presented for spiked blunt body without and with a counterflow jet with different length to base spike ratios and jet to free stream pressure ratios. The purpose of this study is to show how much drag reduction produces by counterflow jet adding to the spiked blunt body at free stream Mach number of 6. Actually in addition to drag reduction due to the spike attached with a blunt body, what is the effect of counterflow jet on the pressure coefficient over main sphere at different pressures of jet and lengths of spike?
Fig. 1. - Principal features of the counterflow jet around a schematic spherical nose cylinder.
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Splitting Method) flux splitting method [22] was applied to quicken the convergence speed. The solver used a time-marching procedure to calculate the flow. The steady mode employs local time stepping that leads to fast convergence to the flow field. The second-order flux limiter was used to avoid the false oscillations and to achieve a better spatial accuracy. These oscillations would occur with second order spatial discretization schemes to the cause of shocks and high gradient streams in the solution domain. The fully implicit scheme was used that is intrinsically stable for linear systems and it is good for compressible viscous flows. For modeling the turbulent terms, Turbulence model of SST (shearstress transport) k-ω was simulated. The SST k-ω turbulence model is a two-equation eddy-viscosity model which has developed by Menter in 1993 and it has become very popular [23]. The shear stress transport (SST) formulation combines the k-ε and k-ω turbulence models. Authors who use the SST k-ω model often merit it for its good capability in adverse pressure gradients and flow separation. The SST k-ω model does produce a bit too large turbulence levels in regions with large normal strain or strong acceleration, like stagnation regions. This tendency is much less pronounced than with a normal k-ε model though. So, we have decided to use SST k-ω model for modeling the flow because of its high pressure gradients such as shocks and separations. The most common approach to this problem is to define an eddy viscosity, ε m in the same form as the laminar viscosity. For modeling the turbulence flow:
2. Geometry definition A spherical nose cylinder was modeled. The diameter of the cylinder (D) is 40 mm and length of the parental body is 1.25D. Hemisphere nose cylinder aero spike configurations were used in this study with the same dimensions in ref. [16] and ref. [17]. The dimensions of the hemisphere spike body considered in present study (with and without jet) are shown in Fig. 2. The spike consists of a hemispherical nose and a cylindrical part of it. The diameter of the cylindrical spike is 0.1D (2 mm). The ratio L/D changes from 1.5 to 7.5 for different conditions. Spikes were attached to the nose of the parental body using a screw. 3. Computational grid and domain The first challenge for these numerical calculations was generating grid. As we have axisymmetric conditions, only 180 deg grid was need to calculations. The structured grids generated over the model without and with jet are illustrated in Fig. 3 and Fig. 4 at three views for each grid. Mesh refinement was used to study grid for insuring correct results of numerical work. The grids near the wall are refined for considering viscous effect and keeping the turbulence y-plus (y+) about 1. Total grids for all models and conditions have about 100000– 600000 cells. The grids have been adapted after initial run at the locations where the shocks and high gradient values happen. The meshes have been refined at near the two shocks due to free stream and jet flow. Grid adaptation generally is used for to obtain the correct and precise results in numerical approaches.
U = U + Ú , where U is mean and Ú is fluctuation part of velocity field. Thus, for a two-dimensional flow the term −ρÚi Új that appears in Navier-stokes equations was modeled as below:
4. Governing equations and numerical procedure In the present study, the axisymmetric Reynolds-averaged NavierStokes (RANS) equations are solved. For flows with high Mach numbers (M∞=6 in this case), we face to high Reynolds numbers and consequently turbulent flows. So we used RANS equations and a turbulence model to obtain the flow field over the blunt bodies. The time-dependent axisymmetric Reynolds-averaged Navier-Stokes equations for conservation laws in integral form can be written as:
∂/∂t
∫V WdV + ∮ [F − G]. dA = ∫V Sdv,
∂U −ρUí Uj́ = ρε m i , ∂y
where ε m=k/ω . The turbulence kinetic energy, k and the specific dissipation rate, ω, are obtained from the following transport equations:
μ ⎞ ∂k ⎤ ͠ ∂ ∂ ∂ ⎡⎛ ⎥ +G k +Yk +Sk ⎢ ⎜μ + t ⎟ (ρk)+ (ρkUi) = ∂xi ∂xj ⎣ ⎝ σk ⎠ ∂xj ⎦ ∂t
(1)
that the vectors W, F and G are defined as
⎧ ρ⎫ ⎪ ⎪ ⎪ ρu ⎪ W =⎨ ρv ⎬, ⎪ ρw ⎪ ⎪ ρe ⎪ ⎩ ⎭
⎧ ρv ⎫ ⎪ ⎪ ρvu +piˆ ⎪ ⎪ ⎪ ⎪ ˆ F =⎨ ρvv+pj ⎬, ⎪ ⎪ ⎪ ρvw+pkˆ ⎪ ⎪ ρve+pv ⎪ ⎩ ⎭
⎧ 0 ⎫ ⎪ τxi ⎪ ⎪ ⎪ G=⎨ τyi ⎬ ⎪ τzi ⎪ ⎪ τij vj +q ⎪ ⎩ ⎭
(5)
(6)
And
μ ⎞ ∂ε ⎤ ∂ ∂ ∂ ⎡⎛ ⎢ ⎜μ + t ⎟ ⎥ +Gω−Yω+Dω + (ρω)+ (ρωUi) = ∂t ∂xi ∂xj ⎣ ⎝ σω ⎠ ∂xj ⎦
Sω
(2)
Here the vector S includes body forces and energy sources that are known source terms and the ρ, (u, v, w), e and p are the density, velocity components in direction (i, j, k), total energy per unit mass, and pressure of the fluid respectively. τ is stress tensor, and q is the heat flux. Total energy, e is related to the total enthalpy, H by
e = H − p /ρ
(3)
Where
H = h + v 2 /2
(4)
The steady part of the above equations have been solved with a computational means used a density based coupled double precision solver. This solver used the second order of solution (upwind) for discretization. Method of modeling the equations have been verified previously in [20] and [21] . The computational code employed a finite volume discretization technique and the governing equations are discretized in space without any intermediate mapping starting from an integral formulation. For flux function, AUSM (Advection Upstream
Fig. 2. - Geometry of the model without jet (upper) and with jet (lower).
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(7)
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Fig. 4. Typical grid around the model with jet (distant and close-up view). Fig. 3. Typical grid around the model without jet (distant and close-up view). Table 1 Boundary conditions.
In these equations, σk and σω are the turbulent Prandtl numbers for k and ω respectively that both equal to 2.0. G͠ k represents the generation of turbulence kinetic energy due to mean velocity gradients.Gω represents the generation of ω, calculated. Yk and Yω represent the dissipation of k and ω due to turbulence. Dω represents the cross-diffusion term, calculated as described below. Sk and Sω are source terms.
G͠ k = min (G k,10ρβ*k ω)
Mach number Total pressure (Pa) Total temperature (K)
(8)
(9)
And
β* = 0. 09 Gω =
α Gk, υt
6 8.345×105 449
1 8.345×105×PR 449
Where Ω w is the mean vorticity at the wall. For more information about the turbulence model, see the reference [22]. The Courant number is about 0.5. The solution converged by roughly in order of 10−3 for most of the cases. To ensure the integrity of the results of the turbulence model, y-plus (y+) curves on the bodies were checked. The order of y-plus was about 1. This result shows that the grids near to the body are in sub-region turbulent boundary layer and the turbulence model have worked.
∂Uj ∂xi
Counterflow jet
ωw >100Ω w
That,
G k = −ρU′U′ i j
Free stream
(10) 5. Boundary conditions
That υ t is the kinematic eddy viscosity and α = 0. 52 . The equations for the turbulent energy k and its dissipation rate ω were solved with the first order of accuracy. In the derivation of the k–ω (SST) model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The specific turbulent energy k is equal to zero at the walls. The specific dissipation rate at the walls was specified a value which is larger than
It is considered a hypersonic flow with a free-stream Mach number 6 around a hemispherical nose with an aerospike perturbed by an opposing sonic jet placed on its nose. There are so many phenomena in real high speed flows which have been discussed very well in other refs. [24–27] but those effect were not 106
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Fig. 5. Validation and grid study for without jet conditions for (A) L/D=1.5 and (B) L/D=2 by illustrating pressure coefficient distribution along the surface of the main sphere.
⎛ T ⎞3/2 (Tref + C ) ⎟ μ = μref ⎜ T+C ⎝ Tref ⎠
Table 2 CD total for without jet condition. L/D
Method
Cd
CD/Cd0
Drag reduction
1.5 1.5 2 2
Experiment (Kalimuthu) Present study Experiment (Kalimuthu) Present study
0.26 0.27 0.20 0.22
0.29 0.3 0.23 0.24
71% 70% 77% 76%
(11)
Tref is a reference temperature that is equals to 273.15 K for air. μref is reference viscosity at reference temperature that was set to be 1.76×10−5 kg/m-s for air. C is Sutherland's constant that is 110.56 K for air. 6. Computational results and discussion The results of this study are illustrated by the curves of pressure coefficient distribution on the main sphere of the models and drag coefficients versus total pressure ratios of jet to free stream and spike's length to base diameter. Firstly, validation of the present study with experimental study of Kalimuthu [16] are shown for L/D=1.5 and 2 at without jet condition. Then, the results of new combination of spike and counter flow jet are shown for same L/D and total pressure ratios of 0.1, 0.4 and 0.8 to study the effect of pressure ratio on the flow. Finally in this section, the results are shown for different L/D of 1.5, 2, 3.5, 5 and 7.5 at PR=0.4 to investigate the effect of spike length on drag reduction.
applied in the present work, so an ideal gas was assumed for equations of state of the free stream and the jet flow. The boundary conditions for inlet boundaries of the models contains free upstream and counterflow jet are given as constant Mach and pressure and that for outlet boundaries of the models are given as constant gauge pressure and backflow total temperature. The grids near the wall are refined for considering viscous effect and keeping the turbulence y+ about 1. No-slip, adiabatic and stationary wall conditions was applied to the wall surfaces of the bodies. The free stream and counterflowing jet conditions are shown in Table 1. The static values of pressure and temperature was calculated from ideal gas equations for air. In this study, the material of the free stream flow and the injected gas is air. Free stream Mach number is 6. Density value of air was calculated from ideal gas law. The thermal conductivity of air was set to 0.0242 W/m-K. Due to face with high Mach numbers, the viscosity may vary significantly with temperature, so we have used known Sutherland law for explaining this dependency. The Sutherland law is written as:
6.1. Validation: the result of pressure coefficient distribution for the case without jet conditions In present study, validation of the code and CFD method was conducted by grid study and comparing the results with other experimental and numerical studies [15,16]. In some studies such as [28] that use an unsteady solver, the accumulated errors and reliability factors are calculated based on the time steps and physical simulation
Fig. 6. Grid study for the models with counterflow jet at PR=0.8 for (A) L/D=1.5 and (B) L/D=2 by illustrating the pressure coefficient distribution along the surface of the main sphere.
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Fig. 7. Presure coefficient distribution along the surface of the main sphere for (A) L/D=1.5 and (B) L/D=2.
Table 3 Total drag reduction percent by increasing PR. L/D
PR
Cd
Cd/Cd0
Drag reduction
1.5 1.5 1.5 1.5 2 2 2 2
0 0.1 0.4 0.8 0 0.1 0.4 0.8
0.27 0.13 0.10 0.09 0.22 0.10 0.10 0.11
0.30 0.14 0.12 0.10 0.24 0.11 0.11 0.13
70% 86% 88% 90% 76% 89% 89% 87%
time, but in present study that have employed an steady-state solver, the grid study and comparing with other studies are sufficient for verification of the applying method. Grid study was conducted by refining the mesh at places with high gradient values obtained from initial (Coarse) grid. The results of grid study must converge to constant values. Fig. 5 shows the grid studies for L/D=1.5 and 2 by drawing the pressure coefficient distributions on the main sphere. The results are compared with the experimental results of Kalimuthu [16] and the numerical results of Mansour [17] for L/D=1.5 and the result for L/ D=2 are compared with only experimental results that are available [16] . It is seen that the grids for numerical approach was converged and the result have a good agreement with the other works. Table 2 shows the drag coefficient and drag reductions compared to Cd0 for experiment and present numerical study. Cd0 that is the drag coefficient for the spherical nose cylinder (without jet and spike), is equal to 0.9 obtained by experimental studies of Kalimuthu [16]. Drag reduction for L/D=1.5 is about 70–71% and for L/D=2 is about 76–77% for all results shown in the tables.
Fig. 9. Drag coefficient versus L/D for PR=0.4. Table 4 Total drag reduction percent by increasing L/D. L/D
PR
Cd
CD/Cd0
Drag reduction
1.5 2 3.5 5 7.5
0.4 0.4 0.4 0.4 0.4
0.10 0.10 0.07 0.05 0.05
0.12 0.11 0.08 0.06 0.05
88% 89% 92% 94% 95%
6.2. The results of combination of spike and counter flow jet for studying the effect of PR Again the grid study was conducted for the models with jet at different PRs, but 2 typical curves are shown (Fig. 6). Fig. 6 shows grid
Fig. 8. Drag coefficient versus total pressure ratio for (A) L/D=1.5 and (B) L/D=2.
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Fig. 10. Mach contours captured for different conditions.
of the length of the spike to L/D=2, change in jet pressure does not cause much change in total drag coefficient. For proving this claim, we also calculated the drag coefficient for L/D=5 that were obtained values of 0.067, 0.052 and 0.056 for PR=0.1, 0.4 and 0.8. These results are in a small range and have almost the same value compare to base drag coefficient, Cd0.
study for the models with counterflow jet at PR=0.8 for (A) L/D=1.5 and (B) L/D=2 by illustrating the pressure coefficient distribution along the surface of the main sphere. It is seen that also the grids for numerical approach was converged for with jet conditions. Fig. 7 shows the total drag coefficients for the models with total pressure ratios of 0 (without jet), 0.1, 0.4 and 0.8. From Fig. 7, it seems that by increasing 109
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compared to the spherical cylinder model without jet and spike for practical models (L/D=1.5 and 2). Also increasing of the L/D leads to decreasing of drag to 88–95% compared to Cd0.
Also Table 3 shows the total drag and drag reduction percent which have been shown in Fig. 8. It is seen that increasing of the PR leads to a little decreasing of drag for L/D=1.5 and almost to be constant drag for L/D=2.
References 6.3. The results of combination of spike and counter flow jet for studying the effect of L/D
[1] P.J. Finley, The flow of a jet from a body opposing a supersonic free stream, J. Fluid Mech. 26 (1966) 337–368. [2] D.H. Crawford, Investigation of flow over a spiked nose hemisphere-cylinder at Mach number of 6.8 NASA-TN-D-118, 1959. [3] S.M. Bogdonoff, I.E. Vas, Preliminary investigations of spiked bodies at hypersonic speeds, J. Aerosp. Sci. 26 (1959) 65–74. [4] E.A. Barber Jr., An experimental investigation of stagnation-point injection, J. Spacecr. Rockets 2 (1965) 770–774. [5] J.S. Shang, W.L. Hankey, R.E. Smith, Flow oscillations of spike-tipped bodies, AIAA J. 20 (1982) (25, 26.). [6] W. Calarese, J.S. Shang, W.L. Hankey, Investigation of Self-Sustained Shock Oscillations on a Spike-Tipped Body at Mach 3, Proceedings of ASME Winter Annual Meeting, American Society of Mechanical Engineers, Fair. eld, NJ pp. 151– 156, 1981. [7] C.H.E. Warren, An experimental investigation of the effect of ejecting a coolant gas at the nose of a bluff body, J. Fluid Mech. 8 (1950) 400–417. [8] K. Karashima, K. Sato, An experimental study of an opposing jet, Bull. Inst. Space Aeronaut. Sci. Univ. Tokyo 11 (1975) 53–64. [9] K. Hayashi, S. Aso, Y. Tani, Experimental study on thermal protection system by opposing jet in supersonic flow, J. Spacecr. Rockets 43 (1) (2006) 233–235. [10] K. Hayashi, S. Aso, Y. Tani, Numerical study of thermal protection system by opposing jet, in: Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV188, 2005. [11] T. Tian, C. Yan, Numerical simulation on opposing jet in hypersonic flow, J. Beijing Univ. Aeronaut. Astronaut. 34 (1) (2008) 9–12. [12] M. Yamauchi, K. Fujii, F. Higashino, Numerical investigation of supersonic flows around a spiked blunt body, J. Spacecr. Rockets 32 (1) (1995) 32–42. [13] R.C. Mehta, Numerical heat transfer study over spiked blunt bodies at Mach 6.8, J. Spacecr. 37 (5) (2000) 700–703. [14] M. Asif, S. Zahir, Computational investigations aerodynamic forces at supersonic/ hypersonic flow past a blunt body with various forward facing spikes, AIAA 5189 (2004). [15] R.C. Mehta, Numerical heat transfer study around a spiked blunt-nose body at Mach 6, Heat Mass Transf. 49 (2013) 485–496. [16] R. Kalimuthu, R.C. Mehta, E. Rathakrishnan, Drag reduction for spike attached to blunt-nosed body at Mach 6, J. Spacecr. Rockets 47 (1) (2010). [17] K. Mansour, M. Khorsandi, The drag reduction in spherical spiked blunt body, Acta Astronaut. 99 (2014) 92–98. [18] Zonglin Jiang, Yunfeng Liu, Guilai Han, Wei Zhao, Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles, Acta Mech. Sin. 25 (2009) 417–419. [19] W. Huang, J. Liu, X. Zhi-xun, Drag reduction mechanism induced by a combinational opposing jet and spike concept in supersonic flows, Acta Astronaut. 115 (2015) 24–31. [20] Z. Eghlima, K. Mansour, Effect of nose shape on the shock standoff distance at nearsonic flows, J. Thermophys. Aeromech. 23 (4) (2016) 499–512. [21] K. Mansour, P. Meskinkhoda, Computational analysis of flow fields around flanged diffusers, J. Wind Eng. Ind. Aerodyn. 124 (2014) 109–120. [22] M.-S. Liou, C. Steffen, A new flux splitting scheme, J. Comput. Phys. 107 (1993) 23–39. [23] F.R. Menter, Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA Paper, 1993, pp. 93–2906. [24] N.N. Smirnov, V.F. Nikitin, Modeling and simulation of hydrogen combustion in engines, Int. J. Hydrog. Energy 39 (2) (2014) 1122–1136. [25] Yu.A. Dem’yanov, V.I. Lapygin, On investigation of recirculation flows in the zone of separation of turbulent boundary layer, J. Appl. Math. Mech. 24 (2) (1960) 237–239. [26] Yu.A. Dem’yanov, V.I. Lapygin, Solution of the problems of spacecraft aerothermodynamics, Fluid Dyn. 47 (4) (2012) 527–542. [27] N.N. Smirnov, V.F. Nikitin, S. Alyari Shurekhdeli, Investigation of self-sustaining waves in metastable systems: deflagrationto-detonation transition, J. Propul. Power 25 (3) (2009) 593–660. [28] N.N. Smirnov, V.B. Betelin, V.F. Nikitin, L.I. Stamov, D.I. Altoukhov, Accumulation of errors in numerical simulations of chemically reacting gas dynamics, Acta Astronaut. 117 (2015) 338–355.
For PR=0.4 that appears a good drag reduction for all models, we have studied the effect of L/D. Fig. 9 shows the drag coefficient values versus L/D for PR=0.4. Also Table 4 shows the total drag and drag reduction percent that have been shown in Fig. 9. It is seen that increasing of the L/D leads to decreasing of drag 88–95% of Cd0. Mach contours are shown for observing the differences between the flows around different conditions. Mach contours captured for with jet conditions at L/D=1.5, 2, 5, & 7.5 and PR=0, 0.4 & 0.8 are shown in Fig. 10. It is seen that by increasing the length of spikes (From L/D=1.5 to 7.5), the shocks near the nose of spikes takes away from the main sphere and the shock near the main sphere becomes weaker, that it can cause more drag reduction on the model. Furthermore, by increasing the PR from 0.4 to 0.8, there are not any significant changes in the Mach contours, as seen previously in the Fig. 8. 7. Conclusions This paper describes a computational study on the drag reduction for a spherical nose cylinder with combination of spike and counterflow jet as two known technic for drag reduction method. Steady Reynoldsaveraged Navier-Stokes equations were solved by employing the K-ω (SST) turbulence model. Study of combination of spike and counterflow jet was conducted firstly for two spherical nose cylinder spike with length to main sphere diameter ratios (L/D) of 1.5 and 2, and for free stream to jet total pressure ratios (PR) of 0.1, 0.4 and 0.8, Then the study was done for different L/D of 1.5, 2, 3.5, 5 and 7.5 at PR=0.4 to investigate the effect of spike length on the flow. The purpose of this study is to know how much drag reduction produces by counterflow jet adding to the spiked blunt body at free stream Mach number of 6. Actually in addition to drag reduction due to the spike attached with a blunt body, what is the effect of counterflow jet on pressure coefficient of main sphere and consequently drag coefficient at different pressures of jet and lengths of spike? Validation was done for spiked model L/D=1.5 and 2 without jet by comparing the results with experimental study of Kalimuthu et al. [16] and numerical study of Mansour et al. [17]. There is a good agreement between the present study and other works. For L/D=1.5, total drag coefficient is reduced slightly with increasing the pressure of the jet. But it seems that by increasing of the length of the spike to L/D=2, change in jet pressure does not cause much change in total drag coefficient. Also by increasing of the length of the spike from L/D=1.5 to L/D=2, 3.5, 5 and 7.5, total drag coefficient is reduced significantly. It should be noted that practically increasing of the L/D to large values is not appropriate for structure. Finally, it can be concluded that combination of spike and counter flow jet at the nose of spike have a double effect on drag reduction of blunt body at Mach number of 6 compared to the spherical cylinder without any spike and jet(Cd0). There is about 86–90% drag reduction
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Research paper
Drag reduction for the combination of spike and counterflow jet on blunt body at high Mach number flow Z. Eghlima, K. Mansour
MARK
⁎
Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran
A R T I C L E I N F O
A BS T RAC T
Keywords: Hypersonic Spike Counterflow jet Drag reduction
Drag reduction at high speed flows around blunt bodies is one of the major challenges in the field of aerodynamics. Using of spikes and counterflow jets each of them separately for reducing of drag force is well known. The present work is description of flow field around a hemispherical nose cylinder with a new combination of spike and counterflow jet at free stream of Mach number of 6.The air gas was injected through the nozzle at the nose of the hemispherical model at sonic speed. In this numerical analysis, axisymmetric Reynolds-averaged Navier-Stokes equations was solved by k-ω (SST) turbulence model. The results were validated with experimental results for spiked body without jet condition. Then the results presented for different lengths of spike and different pressures of counterflow jets. The results show a significant reduction in the drag coefficient about 86–90% compared to the spherical cylinder model without jet and spike for practical models (L/D=1.5 and 2). Furthermore also our results indicate that the drag reduction is increased even more with increasing of the length of the spike.
1. Introduction
1.1. Previous studies about counterflow jet
The drag reduction in aerodynamic applications by a spike or a jet spike on a blunt-nosed body at supersonic and hypersonic flows is well known and were studied years ago [1–6]. The wave drag reduction by using a spiked or opposing jet is derived from both the splitting of a single strong shock into multiple shock waves and effectively replacing the blunt body by a slender displacement. Even if the accumulative pressure rise across the multiple and sequential shock wave is identical to that of a single shock, the entropy jump across the multiple wave system is much less. This difference is because of proportionality of the cubic power of the pressure jump due to the entropy increment across each shock wave. The blunt body with injection will, thus, produce a lower wave drag. There are also disadvantages of these drag reduction devices in that they can induce unsteady motion with large-amplitude oscillations through free-shear-layer instability. Fig. 1 shows a typical jet issuing from a body against a supersonic airstream. The bow shock stands away from the body surface, and takes a form appropriate to a new body consisting of the original body with a protrusion due to the jet flow. The boundary of this protrusion is defined by the interface, the stream surface between the jet flow and the mainstream flow.
The opposing jet in supersonic flows has been considered a lot because of its wide applications on drag and heating reduction at supersonic and hypersonic flows. The experiments on a jet from a blunt body opposing supersonic flows mainly investigated the mean flow quantities, such as the pressure distribution on the body surface, the bow shock stand-off mean position and the shock structures complexity [1,7,8]. These studies revealed that the total pressure ratio of the jet to the free stream is a key parameter affecting the aerodynamic features. In addition, complex sustained motions of the flow field were observed experimentally in some jet conditions. Recently, with the development of the aeronautics and astronautics, the advantage of opposing jet is more appealing to the researcher. In this century, some scholars kept doing research on this method. Hayashi [8–10] did the numerical and experiment studies of thermal protection system by opposing jet and obtained some valuable conclusions. The high precise simulation of Navier-Stokes equations was used by Tian [11] to study the detailed influences of the free Mach number, jet Mach number, attack angle on the heat flux reduction and the mechanism was discussed.
⁎
Corresponding author. E-mail address: [email protected] (K. Mansour).
http://dx.doi.org/10.1016/j.actaastro.2017.01.008 Received 16 November 2016; Accepted 6 January 2017 Available online 12 January 2017 0094-5765/ © 2017 IAA. Published by Elsevier Ltd. All rights reserved.
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w Y γ εm θ μ ρ σ τ Ω ω
Nomenclature Cd CP dj D e k H h L M p q PR R S T u v
Drag coefficient Pressure coefficient Diameter of the jet section Diameter of the main sphere Total energy per unit mass Turbulent kinetic energy Total enthalpy Enthalpy Length of the spikes Mach number Pressure Heat flux Ratio of jet to free stream total pressures Radius of base of model Source term Temperature Velocity in x-dir Velocity in y-dir
Velocity in z-dir Dissipation term Specific heat ratio Turbulent kinetic energy inclination of the dividing streamline Dynamic viscosity Density Turbulent Prandtl number Stress tensor Mean vorticity Specific dissipation rate
Subscripts 0 j O w ∞
Due to base model (without any jet and spike) Jet Total or stagnation value Wall condition Free stream
number 6. In 2014, Mansour and Khorsandi [17] investigated numerically the surface pressure distribution and drag coefficient of a blunt nose cone with an aerospike in hypersonic free stream Mach number of 6. The geometric model they studied was the same model in ref.[16] and they used k-ε turbulence model.
1.2. Previous studies about aerospike Flow fields around a spiked body were experimentally investigated in the 1950s. For example, flow fields around a spiked blunt body at Mach number 6.8 were experimentally investigated by Crawford1 in 1959 [2]. Yamauchi et al. [12] in 1995 have numerically studied the flow field around a spiked blunt body at free stream Mach numbers of 2.01, 4.14 and 6.80 for different ratio of L/D (Length of spike to base diameter). Mehta in 2000 calculated the flow field around a forward facing spike attached to a hemisphere-cylinder nose tip at a free stream Mach number of 6.8 for different spike lengths [13]. Asif and Zahir in 2004 studied supersonic flow (M∞=1.8) and hypersonic flow (M∞=5, 6.8, 8) around a blunt nose body with the attachments of 4 forward facing spikes and estimated aerodynamic forces using CFD tool, PAK3D [14]. In this paper, four different geometries of spikes and two different lengths have been examined to study the forebody flow and its effects on static aerodynamics coefficients. In 2009, Mehta again studied numerically the effect of the various types of aerospike configurations on the reduction of aerodynamic drag and wall heat flux, this time at a length to diameter ratio of 0.5, at Mach 6 and at a zero angle of incidence [15]. In 2010, Kalimuthu and Mehta [16] experimentally studied the pressure variation on the blunt nose body and the aerodynamic coefficients such as drag, lift and pitching moment over the forward facing hemisphere aero spike at Mach
1.3. Previous studies about combination of the jet and spike The concept of combination of these two methods is new; counterflow jet and aerospike. Jiang at 2009 [18] conducted Experiments in a hypersonic wind tunnel at a nominal Mach number of 6. It is shown previously that the shock/shock interaction on the blunt body is avoided due to injection and consequently the peak pressure at the reattachment point is reduced by 70% under a 4° attack angle. Wei Huang et al. at 2015 [19] investigated the influences of length-todiameter ratio of aerospike and jet pressure ratio on the drag reduction by combinational opposing jet and aerospike concept at supersonic Mach number of 2.5. The rejecting gas was nitrogen. The maximum drag reduction coefficient is 65.02% compared to the without spike conditions (with jet), and it occurs when the jet pressure ratio is 0.4. The peak pressure location moves nearly from 40 to 55 deg, and it is nearly the same irrespective of the variation of the jet pressure ratio. Anyway, this method of combination has not been applied to the hypersonic flows previously. Present study has calculated flow field around a hemispherical nose cylinder model in the free stream of Mach number of 6 without and with a counterflow jet at sonic speed. The material injecting to the jet is air and it is injected from the top of the spike's nose. The results for without jet conditions are validated with experimental and numerical studies in the given refs. [16] and [17]. The results show a significant reduction in pressure distribution on the surface and drag coefficient. In this numerical analysis, axisymmetric Reynolds-averaged Navier-Stokes equations were solved by using of k-ω (SST) turbulence model. The results are presented for spiked blunt body without and with a counterflow jet with different length to base spike ratios and jet to free stream pressure ratios. The purpose of this study is to show how much drag reduction produces by counterflow jet adding to the spiked blunt body at free stream Mach number of 6. Actually in addition to drag reduction due to the spike attached with a blunt body, what is the effect of counterflow jet on the pressure coefficient over main sphere at different pressures of jet and lengths of spike?
Fig. 1. - Principal features of the counterflow jet around a schematic spherical nose cylinder.
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Splitting Method) flux splitting method [22] was applied to quicken the convergence speed. The solver used a time-marching procedure to calculate the flow. The steady mode employs local time stepping that leads to fast convergence to the flow field. The second-order flux limiter was used to avoid the false oscillations and to achieve a better spatial accuracy. These oscillations would occur with second order spatial discretization schemes to the cause of shocks and high gradient streams in the solution domain. The fully implicit scheme was used that is intrinsically stable for linear systems and it is good for compressible viscous flows. For modeling the turbulent terms, Turbulence model of SST (shearstress transport) k-ω was simulated. The SST k-ω turbulence model is a two-equation eddy-viscosity model which has developed by Menter in 1993 and it has become very popular [23]. The shear stress transport (SST) formulation combines the k-ε and k-ω turbulence models. Authors who use the SST k-ω model often merit it for its good capability in adverse pressure gradients and flow separation. The SST k-ω model does produce a bit too large turbulence levels in regions with large normal strain or strong acceleration, like stagnation regions. This tendency is much less pronounced than with a normal k-ε model though. So, we have decided to use SST k-ω model for modeling the flow because of its high pressure gradients such as shocks and separations. The most common approach to this problem is to define an eddy viscosity, ε m in the same form as the laminar viscosity. For modeling the turbulence flow:
2. Geometry definition A spherical nose cylinder was modeled. The diameter of the cylinder (D) is 40 mm and length of the parental body is 1.25D. Hemisphere nose cylinder aero spike configurations were used in this study with the same dimensions in ref. [16] and ref. [17]. The dimensions of the hemisphere spike body considered in present study (with and without jet) are shown in Fig. 2. The spike consists of a hemispherical nose and a cylindrical part of it. The diameter of the cylindrical spike is 0.1D (2 mm). The ratio L/D changes from 1.5 to 7.5 for different conditions. Spikes were attached to the nose of the parental body using a screw. 3. Computational grid and domain The first challenge for these numerical calculations was generating grid. As we have axisymmetric conditions, only 180 deg grid was need to calculations. The structured grids generated over the model without and with jet are illustrated in Fig. 3 and Fig. 4 at three views for each grid. Mesh refinement was used to study grid for insuring correct results of numerical work. The grids near the wall are refined for considering viscous effect and keeping the turbulence y-plus (y+) about 1. Total grids for all models and conditions have about 100000– 600000 cells. The grids have been adapted after initial run at the locations where the shocks and high gradient values happen. The meshes have been refined at near the two shocks due to free stream and jet flow. Grid adaptation generally is used for to obtain the correct and precise results in numerical approaches.
U = U + Ú , where U is mean and Ú is fluctuation part of velocity field. Thus, for a two-dimensional flow the term −ρÚi Új that appears in Navier-stokes equations was modeled as below:
4. Governing equations and numerical procedure In the present study, the axisymmetric Reynolds-averaged NavierStokes (RANS) equations are solved. For flows with high Mach numbers (M∞=6 in this case), we face to high Reynolds numbers and consequently turbulent flows. So we used RANS equations and a turbulence model to obtain the flow field over the blunt bodies. The time-dependent axisymmetric Reynolds-averaged Navier-Stokes equations for conservation laws in integral form can be written as:
∂/∂t
∫V WdV + ∮ [F − G]. dA = ∫V Sdv,
∂U −ρUí Uj́ = ρε m i , ∂y
where ε m=k/ω . The turbulence kinetic energy, k and the specific dissipation rate, ω, are obtained from the following transport equations:
μ ⎞ ∂k ⎤ ͠ ∂ ∂ ∂ ⎡⎛ ⎥ +G k +Yk +Sk ⎢ ⎜μ + t ⎟ (ρk)+ (ρkUi) = ∂xi ∂xj ⎣ ⎝ σk ⎠ ∂xj ⎦ ∂t
(1)
that the vectors W, F and G are defined as
⎧ ρ⎫ ⎪ ⎪ ⎪ ρu ⎪ W =⎨ ρv ⎬, ⎪ ρw ⎪ ⎪ ρe ⎪ ⎩ ⎭
⎧ ρv ⎫ ⎪ ⎪ ρvu +piˆ ⎪ ⎪ ⎪ ⎪ ˆ F =⎨ ρvv+pj ⎬, ⎪ ⎪ ⎪ ρvw+pkˆ ⎪ ⎪ ρve+pv ⎪ ⎩ ⎭
⎧ 0 ⎫ ⎪ τxi ⎪ ⎪ ⎪ G=⎨ τyi ⎬ ⎪ τzi ⎪ ⎪ τij vj +q ⎪ ⎩ ⎭
(5)
(6)
And
μ ⎞ ∂ε ⎤ ∂ ∂ ∂ ⎡⎛ ⎢ ⎜μ + t ⎟ ⎥ +Gω−Yω+Dω + (ρω)+ (ρωUi) = ∂t ∂xi ∂xj ⎣ ⎝ σω ⎠ ∂xj ⎦
Sω
(2)
Here the vector S includes body forces and energy sources that are known source terms and the ρ, (u, v, w), e and p are the density, velocity components in direction (i, j, k), total energy per unit mass, and pressure of the fluid respectively. τ is stress tensor, and q is the heat flux. Total energy, e is related to the total enthalpy, H by
e = H − p /ρ
(3)
Where
H = h + v 2 /2
(4)
The steady part of the above equations have been solved with a computational means used a density based coupled double precision solver. This solver used the second order of solution (upwind) for discretization. Method of modeling the equations have been verified previously in [20] and [21] . The computational code employed a finite volume discretization technique and the governing equations are discretized in space without any intermediate mapping starting from an integral formulation. For flux function, AUSM (Advection Upstream
Fig. 2. - Geometry of the model without jet (upper) and with jet (lower).
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(7)
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Fig. 4. Typical grid around the model with jet (distant and close-up view). Fig. 3. Typical grid around the model without jet (distant and close-up view). Table 1 Boundary conditions.
In these equations, σk and σω are the turbulent Prandtl numbers for k and ω respectively that both equal to 2.0. G͠ k represents the generation of turbulence kinetic energy due to mean velocity gradients.Gω represents the generation of ω, calculated. Yk and Yω represent the dissipation of k and ω due to turbulence. Dω represents the cross-diffusion term, calculated as described below. Sk and Sω are source terms.
G͠ k = min (G k,10ρβ*k ω)
Mach number Total pressure (Pa) Total temperature (K)
(8)
(9)
And
β* = 0. 09 Gω =
α Gk, υt
6 8.345×105 449
1 8.345×105×PR 449
Where Ω w is the mean vorticity at the wall. For more information about the turbulence model, see the reference [22]. The Courant number is about 0.5. The solution converged by roughly in order of 10−3 for most of the cases. To ensure the integrity of the results of the turbulence model, y-plus (y+) curves on the bodies were checked. The order of y-plus was about 1. This result shows that the grids near to the body are in sub-region turbulent boundary layer and the turbulence model have worked.
∂Uj ∂xi
Counterflow jet
ωw >100Ω w
That,
G k = −ρU′U′ i j
Free stream
(10) 5. Boundary conditions
That υ t is the kinematic eddy viscosity and α = 0. 52 . The equations for the turbulent energy k and its dissipation rate ω were solved with the first order of accuracy. In the derivation of the k–ω (SST) model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The specific turbulent energy k is equal to zero at the walls. The specific dissipation rate at the walls was specified a value which is larger than
It is considered a hypersonic flow with a free-stream Mach number 6 around a hemispherical nose with an aerospike perturbed by an opposing sonic jet placed on its nose. There are so many phenomena in real high speed flows which have been discussed very well in other refs. [24–27] but those effect were not 106
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Fig. 5. Validation and grid study for without jet conditions for (A) L/D=1.5 and (B) L/D=2 by illustrating pressure coefficient distribution along the surface of the main sphere.
⎛ T ⎞3/2 (Tref + C ) ⎟ μ = μref ⎜ T+C ⎝ Tref ⎠
Table 2 CD total for without jet condition. L/D
Method
Cd
CD/Cd0
Drag reduction
1.5 1.5 2 2
Experiment (Kalimuthu) Present study Experiment (Kalimuthu) Present study
0.26 0.27 0.20 0.22
0.29 0.3 0.23 0.24
71% 70% 77% 76%
(11)
Tref is a reference temperature that is equals to 273.15 K for air. μref is reference viscosity at reference temperature that was set to be 1.76×10−5 kg/m-s for air. C is Sutherland's constant that is 110.56 K for air. 6. Computational results and discussion The results of this study are illustrated by the curves of pressure coefficient distribution on the main sphere of the models and drag coefficients versus total pressure ratios of jet to free stream and spike's length to base diameter. Firstly, validation of the present study with experimental study of Kalimuthu [16] are shown for L/D=1.5 and 2 at without jet condition. Then, the results of new combination of spike and counter flow jet are shown for same L/D and total pressure ratios of 0.1, 0.4 and 0.8 to study the effect of pressure ratio on the flow. Finally in this section, the results are shown for different L/D of 1.5, 2, 3.5, 5 and 7.5 at PR=0.4 to investigate the effect of spike length on drag reduction.
applied in the present work, so an ideal gas was assumed for equations of state of the free stream and the jet flow. The boundary conditions for inlet boundaries of the models contains free upstream and counterflow jet are given as constant Mach and pressure and that for outlet boundaries of the models are given as constant gauge pressure and backflow total temperature. The grids near the wall are refined for considering viscous effect and keeping the turbulence y+ about 1. No-slip, adiabatic and stationary wall conditions was applied to the wall surfaces of the bodies. The free stream and counterflowing jet conditions are shown in Table 1. The static values of pressure and temperature was calculated from ideal gas equations for air. In this study, the material of the free stream flow and the injected gas is air. Free stream Mach number is 6. Density value of air was calculated from ideal gas law. The thermal conductivity of air was set to 0.0242 W/m-K. Due to face with high Mach numbers, the viscosity may vary significantly with temperature, so we have used known Sutherland law for explaining this dependency. The Sutherland law is written as:
6.1. Validation: the result of pressure coefficient distribution for the case without jet conditions In present study, validation of the code and CFD method was conducted by grid study and comparing the results with other experimental and numerical studies [15,16]. In some studies such as [28] that use an unsteady solver, the accumulated errors and reliability factors are calculated based on the time steps and physical simulation
Fig. 6. Grid study for the models with counterflow jet at PR=0.8 for (A) L/D=1.5 and (B) L/D=2 by illustrating the pressure coefficient distribution along the surface of the main sphere.
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Fig. 7. Presure coefficient distribution along the surface of the main sphere for (A) L/D=1.5 and (B) L/D=2.
Table 3 Total drag reduction percent by increasing PR. L/D
PR
Cd
Cd/Cd0
Drag reduction
1.5 1.5 1.5 1.5 2 2 2 2
0 0.1 0.4 0.8 0 0.1 0.4 0.8
0.27 0.13 0.10 0.09 0.22 0.10 0.10 0.11
0.30 0.14 0.12 0.10 0.24 0.11 0.11 0.13
70% 86% 88% 90% 76% 89% 89% 87%
time, but in present study that have employed an steady-state solver, the grid study and comparing with other studies are sufficient for verification of the applying method. Grid study was conducted by refining the mesh at places with high gradient values obtained from initial (Coarse) grid. The results of grid study must converge to constant values. Fig. 5 shows the grid studies for L/D=1.5 and 2 by drawing the pressure coefficient distributions on the main sphere. The results are compared with the experimental results of Kalimuthu [16] and the numerical results of Mansour [17] for L/D=1.5 and the result for L/ D=2 are compared with only experimental results that are available [16] . It is seen that the grids for numerical approach was converged and the result have a good agreement with the other works. Table 2 shows the drag coefficient and drag reductions compared to Cd0 for experiment and present numerical study. Cd0 that is the drag coefficient for the spherical nose cylinder (without jet and spike), is equal to 0.9 obtained by experimental studies of Kalimuthu [16]. Drag reduction for L/D=1.5 is about 70–71% and for L/D=2 is about 76–77% for all results shown in the tables.
Fig. 9. Drag coefficient versus L/D for PR=0.4. Table 4 Total drag reduction percent by increasing L/D. L/D
PR
Cd
CD/Cd0
Drag reduction
1.5 2 3.5 5 7.5
0.4 0.4 0.4 0.4 0.4
0.10 0.10 0.07 0.05 0.05
0.12 0.11 0.08 0.06 0.05
88% 89% 92% 94% 95%
6.2. The results of combination of spike and counter flow jet for studying the effect of PR Again the grid study was conducted for the models with jet at different PRs, but 2 typical curves are shown (Fig. 6). Fig. 6 shows grid
Fig. 8. Drag coefficient versus total pressure ratio for (A) L/D=1.5 and (B) L/D=2.
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Fig. 10. Mach contours captured for different conditions.
of the length of the spike to L/D=2, change in jet pressure does not cause much change in total drag coefficient. For proving this claim, we also calculated the drag coefficient for L/D=5 that were obtained values of 0.067, 0.052 and 0.056 for PR=0.1, 0.4 and 0.8. These results are in a small range and have almost the same value compare to base drag coefficient, Cd0.
study for the models with counterflow jet at PR=0.8 for (A) L/D=1.5 and (B) L/D=2 by illustrating the pressure coefficient distribution along the surface of the main sphere. It is seen that also the grids for numerical approach was converged for with jet conditions. Fig. 7 shows the total drag coefficients for the models with total pressure ratios of 0 (without jet), 0.1, 0.4 and 0.8. From Fig. 7, it seems that by increasing 109
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compared to the spherical cylinder model without jet and spike for practical models (L/D=1.5 and 2). Also increasing of the L/D leads to decreasing of drag to 88–95% compared to Cd0.
Also Table 3 shows the total drag and drag reduction percent which have been shown in Fig. 8. It is seen that increasing of the PR leads to a little decreasing of drag for L/D=1.5 and almost to be constant drag for L/D=2.
References 6.3. The results of combination of spike and counter flow jet for studying the effect of L/D
[1] P.J. Finley, The flow of a jet from a body opposing a supersonic free stream, J. Fluid Mech. 26 (1966) 337–368. [2] D.H. Crawford, Investigation of flow over a spiked nose hemisphere-cylinder at Mach number of 6.8 NASA-TN-D-118, 1959. [3] S.M. Bogdonoff, I.E. Vas, Preliminary investigations of spiked bodies at hypersonic speeds, J. Aerosp. Sci. 26 (1959) 65–74. [4] E.A. Barber Jr., An experimental investigation of stagnation-point injection, J. Spacecr. Rockets 2 (1965) 770–774. [5] J.S. Shang, W.L. Hankey, R.E. Smith, Flow oscillations of spike-tipped bodies, AIAA J. 20 (1982) (25, 26.). [6] W. Calarese, J.S. Shang, W.L. Hankey, Investigation of Self-Sustained Shock Oscillations on a Spike-Tipped Body at Mach 3, Proceedings of ASME Winter Annual Meeting, American Society of Mechanical Engineers, Fair. eld, NJ pp. 151– 156, 1981. [7] C.H.E. Warren, An experimental investigation of the effect of ejecting a coolant gas at the nose of a bluff body, J. Fluid Mech. 8 (1950) 400–417. [8] K. Karashima, K. Sato, An experimental study of an opposing jet, Bull. Inst. Space Aeronaut. Sci. Univ. Tokyo 11 (1975) 53–64. [9] K. Hayashi, S. Aso, Y. Tani, Experimental study on thermal protection system by opposing jet in supersonic flow, J. Spacecr. Rockets 43 (1) (2006) 233–235. [10] K. Hayashi, S. Aso, Y. Tani, Numerical study of thermal protection system by opposing jet, in: Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV188, 2005. [11] T. Tian, C. Yan, Numerical simulation on opposing jet in hypersonic flow, J. Beijing Univ. Aeronaut. Astronaut. 34 (1) (2008) 9–12. [12] M. Yamauchi, K. Fujii, F. Higashino, Numerical investigation of supersonic flows around a spiked blunt body, J. Spacecr. Rockets 32 (1) (1995) 32–42. [13] R.C. Mehta, Numerical heat transfer study over spiked blunt bodies at Mach 6.8, J. Spacecr. 37 (5) (2000) 700–703. [14] M. Asif, S. Zahir, Computational investigations aerodynamic forces at supersonic/ hypersonic flow past a blunt body with various forward facing spikes, AIAA 5189 (2004). [15] R.C. Mehta, Numerical heat transfer study around a spiked blunt-nose body at Mach 6, Heat Mass Transf. 49 (2013) 485–496. [16] R. Kalimuthu, R.C. Mehta, E. Rathakrishnan, Drag reduction for spike attached to blunt-nosed body at Mach 6, J. Spacecr. Rockets 47 (1) (2010). [17] K. Mansour, M. Khorsandi, The drag reduction in spherical spiked blunt body, Acta Astronaut. 99 (2014) 92–98. [18] Zonglin Jiang, Yunfeng Liu, Guilai Han, Wei Zhao, Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles, Acta Mech. Sin. 25 (2009) 417–419. [19] W. Huang, J. Liu, X. Zhi-xun, Drag reduction mechanism induced by a combinational opposing jet and spike concept in supersonic flows, Acta Astronaut. 115 (2015) 24–31. [20] Z. Eghlima, K. Mansour, Effect of nose shape on the shock standoff distance at nearsonic flows, J. Thermophys. Aeromech. 23 (4) (2016) 499–512. [21] K. Mansour, P. Meskinkhoda, Computational analysis of flow fields around flanged diffusers, J. Wind Eng. Ind. Aerodyn. 124 (2014) 109–120. [22] M.-S. Liou, C. Steffen, A new flux splitting scheme, J. Comput. Phys. 107 (1993) 23–39. [23] F.R. Menter, Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA Paper, 1993, pp. 93–2906. [24] N.N. Smirnov, V.F. Nikitin, Modeling and simulation of hydrogen combustion in engines, Int. J. Hydrog. Energy 39 (2) (2014) 1122–1136. [25] Yu.A. Dem’yanov, V.I. Lapygin, On investigation of recirculation flows in the zone of separation of turbulent boundary layer, J. Appl. Math. Mech. 24 (2) (1960) 237–239. [26] Yu.A. Dem’yanov, V.I. Lapygin, Solution of the problems of spacecraft aerothermodynamics, Fluid Dyn. 47 (4) (2012) 527–542. [27] N.N. Smirnov, V.F. Nikitin, S. Alyari Shurekhdeli, Investigation of self-sustaining waves in metastable systems: deflagrationto-detonation transition, J. Propul. Power 25 (3) (2009) 593–660. [28] N.N. Smirnov, V.B. Betelin, V.F. Nikitin, L.I. Stamov, D.I. Altoukhov, Accumulation of errors in numerical simulations of chemically reacting gas dynamics, Acta Astronaut. 117 (2015) 338–355.
For PR=0.4 that appears a good drag reduction for all models, we have studied the effect of L/D. Fig. 9 shows the drag coefficient values versus L/D for PR=0.4. Also Table 4 shows the total drag and drag reduction percent that have been shown in Fig. 9. It is seen that increasing of the L/D leads to decreasing of drag 88–95% of Cd0. Mach contours are shown for observing the differences between the flows around different conditions. Mach contours captured for with jet conditions at L/D=1.5, 2, 5, & 7.5 and PR=0, 0.4 & 0.8 are shown in Fig. 10. It is seen that by increasing the length of spikes (From L/D=1.5 to 7.5), the shocks near the nose of spikes takes away from the main sphere and the shock near the main sphere becomes weaker, that it can cause more drag reduction on the model. Furthermore, by increasing the PR from 0.4 to 0.8, there are not any significant changes in the Mach contours, as seen previously in the Fig. 8. 7. Conclusions This paper describes a computational study on the drag reduction for a spherical nose cylinder with combination of spike and counterflow jet as two known technic for drag reduction method. Steady Reynoldsaveraged Navier-Stokes equations were solved by employing the K-ω (SST) turbulence model. Study of combination of spike and counterflow jet was conducted firstly for two spherical nose cylinder spike with length to main sphere diameter ratios (L/D) of 1.5 and 2, and for free stream to jet total pressure ratios (PR) of 0.1, 0.4 and 0.8, Then the study was done for different L/D of 1.5, 2, 3.5, 5 and 7.5 at PR=0.4 to investigate the effect of spike length on the flow. The purpose of this study is to know how much drag reduction produces by counterflow jet adding to the spiked blunt body at free stream Mach number of 6. Actually in addition to drag reduction due to the spike attached with a blunt body, what is the effect of counterflow jet on pressure coefficient of main sphere and consequently drag coefficient at different pressures of jet and lengths of spike? Validation was done for spiked model L/D=1.5 and 2 without jet by comparing the results with experimental study of Kalimuthu et al. [16] and numerical study of Mansour et al. [17]. There is a good agreement between the present study and other works. For L/D=1.5, total drag coefficient is reduced slightly with increasing the pressure of the jet. But it seems that by increasing of the length of the spike to L/D=2, change in jet pressure does not cause much change in total drag coefficient. Also by increasing of the length of the spike from L/D=1.5 to L/D=2, 3.5, 5 and 7.5, total drag coefficient is reduced significantly. It should be noted that practically increasing of the L/D to large values is not appropriate for structure. Finally, it can be concluded that combination of spike and counter flow jet at the nose of spike have a double effect on drag reduction of blunt body at Mach number of 6 compared to the spherical cylinder without any spike and jet(Cd0). There is about 86–90% drag reduction
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