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Reduction of wave drag on parameterized blunt bodies using spikes with varied tip geometries
Acta Astronautica 160 (2019) 25–35
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Reduction of wave drag on parameterized blunt bodies using spikes with varied tip geometries
T
Suhaas Mohandas, R. Krishna Siddharth, Bibin John∗ School of Mechanical Engineering, Vellore Institute of Technology (VIT), Vellore, Tamil Nadu, India-632 014
A R T I C LE I N FO
A B S T R A C T
Keywords: Blunt body Aero-spike Wave drag reduction Recirculation region
Aeospike based wave drag reduction is investigated using two-equation turbulence model applied to Faver averaged Navier Stokes solver. Three different blunt bodies are considered in a low supersonic stream of Mach number 2. The considered blunt bodies differ in their degree of bluntness defined in terms of half cone angle, area of flattened front side and radius of bluntness. The zero angle of attack flowfield around these three bodies are computationally analyzed with and without the presence of aft spikes to evaluate the wave drag resulting from the formation of front shock structure. The influence of spike configuration on the wave drag is also investigated. The various considered spike tip geometries include aero-disk, sharp and blunt with the length of all the spikes being equal to the base diameter of the blunt bodies (L/D = 1). It has been found that the 3221 blunt body when coupled with a blunt tipped spike yielded the lowest drag coefficient of 0.3, despite the 3221 having the highest standalone drag coefficient of 0.86, among the blunt bodies when simulated individually without spikes. The physics behind the wave drag reduction associated with each combination of blunt body and spike configuration is presented with clarity. This study portrays the importance of taking bluntness factor, semicone angle, fineness ratio and blunt body shape factor into consideration while proposing the generalized optimum spike configuration for minimum drag attainment.
1. Introduction
facilitating a larger payload volume. This however presents a hindering factor when drag reduction is also necessary. On the other hand, a blunt body design intended to decrease drag by using a sharper fore front, results in the formation of an attached shock wave leading to an increase in heat flux. In light of the necessity to reduce both heat flux and drag, many methods have been introduced and investigated over the years using computational methods and through rigorous experimentation. A couple of examples include, the incorporation of spikes, energy deposition, stagnation point injection of gases or liquids, etc. Mechanically, the simplest of them would be the case of spike based drag reduction which divides the incoming flow, diverting a major portion of it away from the blunt body in contrast to the full ram which the blunt body will otherwise face. The magnitude and angle of flow deflection will depend on the size and shape of the spike and will play a vital role in reducing the pressure and temperature experienced by a significant portion of the blunt body due to the presence of a recirculation zone. Depending on the aforementioned factors, spike length to blunt body base diameter ratio (L/D) and the blunt body geometry, the position of the separation shock will vary and accordingly the re-attachment shock as well. The more delayed the re-attachment shock, the lesser will be the pressure accumulation which
. Re-entry vehicle aerodynamics has been a major part of research for aerodynamicists ever since the dawn of space flight. Space Shuttles, capsules and ICBMs upon re-entry from space to earth are subjected to extreme temperatures and atmospheric drag forces due to high velocities and the thickening of the atmosphere as the density rises with a decrease in altitude. The same scenario can be observed during launch of these vehicles to space as well, however the density variation is reversed. In case of space shuttles and ICBMs the reduction of heat flux is critical to its design as they have to withstand such high temperatures upon re-entry. Whereas the minimization of drag is a subject which has to be dealt with in situations where the there is a necessity to reduce overall fuel consumption and subsequently the material and space required to accommodate the fuel, like in the case of missiles and light weight and low thrust rockets during launch where the drag force is significant in comparison to the thrust. This is due to high air densities at low altitudes combined with large speeds. . Lower heat fluxes on the fore-bodies of aerospace vehicles are generally achieved by adopting a blunt shape which leads to the formation of a detached shock wave with an added advantage of
∗
Corresponding author. E-mail address: [email protected] (B. John).
https://doi.org/10.1016/j.actaastro.2019.04.017 Received 8 August 2018; Received in revised form 4 March 2019; Accepted 8 April 2019 Available online 11 April 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Illustration of flow field around blunt bodies without and with different spikes. Courtesy - Sahoo et al [11].
eventually pertains to a lower drag and heat flux. The aero-disk, sharp and blunt tipped spikes are well known and have been studied in the past. Each of them deflect the incoming flow uniquely as shown in Fig. 1, giving widely varying results from which it is possible to choose the best design. The spike-blunt system is also easier to simulate given the simplicity of the flow field and its mostly non transient nature. This approach eventually has been found to cater to the need of reducing both drag and heat flux. Crawford [1] in 1959, through series of experiments first recorded the reduction of drag and heat flux at Mach 6.8 when using sharp spikes of varying lengths. This study is still being used as the validation case in many of the latest research works in this field. Followed by Crawford's work many recent studies have been reported in this field. Drag reduction on a spiked conical body with spherical leading edge has been investigated by dHumieres and Stollery [2]. Almost 77% reduction in drag has been reported while attaching spike to the blunt model kept in the laminar hypersonic flow. An important numerical study focusing on the spike based drag reduction can be seen in the works of Gauer and Paull [3] in which drag reduction on a blunted cone model has been investigated at three different hypersonic Mach numbers. The parametric effect of spike length has also been studied in this work. Such studies have also been conducted with different spikes at hypersonic speeds by many other researchers in the recent past [4–10]. However, it is to be noted that in most of the literature which investigated the use of spikes, the blunt bodies used are hemispherical in shape. Similarly, the blunt body-spike systems seem to be researched extensively mostly at hypersonic speeds. Sahoo et al. [11] is an exception where the flow speed was supersonic (M = 2), but again the blunt body was hemispherical in shape. The mechanism of drag reduction has been explained adopting dividing streamline approach, which pushes away the separation point. Mostly experimental results are found for such a study except in Sahoo et al. [11] where various models including the k − ω turbulence model has been adopted. The flow field on a main hemispherical body with spike could abruptly change in shock structure is observed. It is considered to be a violent mode of unsteadiness and has been reported to be occurring for spikes having the smaller length to body diameter. Driving mechanism of pulsation has been described based on various hypotheses. Sahoo et al. [11] have used three variants of spikes namely the aerospike, sharp spike and blunt nose spike with a hemispherical blunt body for Mach 2 flow inside a wind tunnel at a pressure of 40897.45Pa. They have also performed numerical simulations using the k − ω model. The exact same conditions, spike parameters and turbulence model for the simulations have been used, which helped in validating the simulation methodology and model selection presented in this work. For the purpose of blunt body parameterization, the specifications and design codes given by Brooks and Trescot [12] are used. Tahani et al. [7]and Gerdroodbary et al. [6] have also conducted similar studies while the former has two types of aerodisks which are flat faced aero disk also called an aerospike by Sahoo et al. [11] and blunt nosed aero disk with the third one being a sharp spike. But all the blunt bodies in the aforementioned references were ideal cases and not really the designs incorporated in missiles and space shuttles nose cones. Most literature and research articles found till now have either
performed inviscid simulations or have used simplistic turbulence models like the k − ε , Spalart Allmaras (a one equation model) which are not ideal for spiked blunt body simulations as there are adverse pressure gradients and flow separations. Models like the k − ω model and SST model usually perform better for such flows. Since the SST model is computationally expensive and time consuming, the k − ω model is used. It has been used only in a few studies as the literature suggest, one among them being Sahoo et al. [11]. It was understood from the literature that the performance of k − ω turbulence model was better than the k − ε model by comparing the simulation results with experimental results. Another important point to be noted is that in most of the literature available pertaining to this field of research, hemispherical blunt bodies or roughly parameterized blunt bodies are used. But these designs are seldom implemented in actual missiles and spacecraft noses. In this paper however, we make use of the design standards, codes and parameters laid out by Brooks and Trescot [12] which is a NASA report and represents a realistic design of the blunt bodies used in the space vehicles. Moreover, to the date nobody has investigated the effect of aerospike geometries on wave drag reduction by attaching to blunt bodies of different geometric features. Therefore, the objectives of present study are twofold. First objective is to identify the variation of drag penalty with change in bluntness of the body. Second objective is to test whether optimum spike configurations proposed in the literature are really optimum when employed with diverse blunt bodies of identical base diameter. 2. Methodology Supersonic flow over the blunt body has been simulated by solving 2D-axisymmetric, Faver averaged Navier stokes equations in a two dimensional computational domain using finite volume method. Additionally, equations of turbulent kinetic energy (k) and specific rate of dissipation (ω) were solved to obtain the turbulent characteristics of the flow. Vector form of the k and ω equations are;
∂ ∂ ∂ ⎛ ∂k ⎞ (ρk ) + (ρkvi ) = ⎜Γk ⎟ + Gk − yk + Sk ∂t ∂x i ∂x j ⎝ ∂x j ⎠
(1)
∂ ∂ ∂ ⎛ ∂ω ⎞ (ρω) + (ρωvi ) = ⎜Γω ⎟ + Gω − yω + Sω ∂t ∂x i ∂x j ⎝ ∂x j ⎠
(2)
The effective diffusitivites are defined as;
Γk = μ +
μt ; σk
Γw = μ +
μt σω
(3)
where σk and σω stand to represent turbulent Prandtl numbers for k and ω respectively. The turbulent viscosity μt can be calculated as a function of density (ρ), k and ω. Suitable damping coefficient may also be considered while calculating the μt to account for the low Reynolds number effect. The term Gk in the k-equation represents the production of turbulent kinetic energy. Fluent calculates this term from the equation for the transport of k as; 26
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Gk = −ρui′ u′j
∂uj ∂x i
(4)
The production of ω is evaluated from the relation;
ω Gw = −α Gk k
(5)
Additionally Yk and Yω in the above governing equations represent the dissipation of k and ω respectively. The detailed definitions for these terms can be seen in the reporting of Wilcox [13,14]. The suitable values of model constants are also mentioned in those papers. Further, to account for the compressibility effect, Fluent considers a compressibility function in the calculation of dissipation terms. The compressibility correction term is given by
0 Mt ≤ Mt 0 F (Mt ) = ⎧ 2 2 M − M M ⎨ t > Mt 0 t t 0 ⎩
(6)
Where
Mt2 =
2k a2
Fig. 2. Blunt body schematic indicating all design parameters. Courtesy Brooks and Trescot [12].
Mt0 = 0.25
a=
γRT
Table 1 First digit denotes nose-bluntness factor K.
Since the flow is at zero angle of attack and the blunt body of interest is symmetric about the axis of rotation, the strategy of following 2D-axisymmetric simulation instead of complete three dimensional solution was found to be accurate enough for the resolution of flowfield in this case. Moreover, it also offers a great advantage in terms of reduced computational time. In the past, Gerdroodbary and Hosseinalipour [6] have also reported about the ample nature 2D-axisymmetric simulations in accurately predicting flowfield and surface properties in an identical flow scenario. Out of the different twoequation turbulent models available in the solver, the k − ω model is specifically opted for the present study upon considering its accuracy in resolving the flow separation and shear layer correctly. This superiority of k − ω model has also been reported by other researchers [11,15], for diverse high speed flow studies. . The blunt body and spike configurations used in the present study are adapted from the literature. The design codes for the spikes were taken from Sahoo et al. [11] and the blunt body specifications were adapted from Brooks and Trescot [12] who had taken into consideration the nose cone angle, the fineness ratio, nose bluntness and base shape and their effects on the static aerodynamic characteristics of short, blunt cones at angles of attack from 00 to 1800 in the transonic regime. In the reporting of latter, blunt body-parameters were tabulated and formulated in detail to choose from, along with the variation of coefficients of drag and lift for various angles of attack and Mach numbers from 0.8 to 1.2. It is from those graphs that the blunt body designs for the present study are selected. The ones with lowest, highest and medium drag were selected for the investigation with the addition of three different spike geometries namely, the sharp, blunt nose, and the aero-disk. All the design parameters of the blunt body are indicated in the schematic shown in Fig. 2. The body design, follows a four-digit numbering system where every digit pertains to some dimensional aspect as given in Tables 1–4 In Table 2, K = b/ a and in Table 3, λ = l/ d ; where a, b, l and d are represented in the blunt body schematics. As per this numbering system, three specific blunt models are selected for the present study. It was found that the blunt body with the lowest amount of coefficient of drag was coded 1221, the highest being 3221 and the medium drag blunt body being 2221. Thus opted blunt models are to be analyzed with the addition of the spikes to understand the effectiveness of different spike configurations in the context of aerodynamic drag reduction of each models. The spikes used in the present study are sized according to Sahoo et al. [11] and are represented schematically in Fig. 3. This is done, as the latter had already established these
First digit
K
1 2 3
0 (Spherical) 0.50 0.75
Table 2 Second digit denotes fineness ratio(λ). second digit
λ
1 2 3
0.5 0.75 1.0
Table 3 Third digit denotes cone semi angle θ Third digit
θ, deg
1 2 3
10 15 20
Table 4 Fourth digit denotes base shape. Fourth digit
Shape
1 2 3
Flat Convex Concave
dimensions as optimal for the present analysis. Taking into consideration the aforementioned design parameters, a series of blunt body-spike combinations were designed and subjected to numerical investigations. . As discussed earlier, the computational domain is constructed as a 2D domain, upon considering the axisymmetric nature of the flowfield. A sample computational domain (without spike) meshed with quadrilateral elements is presented in Fig. 4. The numerical boundary conditions imposed at the physical boundaries of the domain are also mentioned. At the inlet of the computational domain, freestream variables corresponding to test section conditions of the experimental study 27
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Fig. 3. Spike types and geometry. (D is the base Diameter of Blunt Body) Courtesy - Sahoo et al. [11].
unconditional stability, the complexity involved in the present flowfield forced the authors to limit the Courant-Friedrichs-Lewy number to 0.5 in most of the runs. More accurate Flux difference splitting upwind scheme ROE is used for the calculation of convective fluxes. The upwind schemes are well known for their shock capturing capability [17]. Therefore, no additional shock fitting techniques were considered in the present study. The viscous flux terms are computed using the gradients of flow and turbulent variables obtained at the cell centroids. Least square cell based approach is employed to calculate gradients at the cell centroids while the solver settings are made to ensure second order spatial accuracy of the solution. The working fluid has been taken as air and modelled as ideal gas. Sutherland's viscosity law has been employed to calculate fluid viscosity at each cell centroid based on the local static temperature. The solver took specific heat at constant pressure (CP ) of air as 1005 J / kgK when modelled as ideal gas. Additionally, the pre-set value of constant Prandtl number has been employed to evaluate thermal conductivity with the help of computed viscosity and specified CP . Inlet freestream conditions were used to initialize the domain as it was the best possible pre-known initial guess for supersonic flowfield. The solution convergence is monitored mainly based on density residue and is considered as steady state once the absolute residue of density falls below 10−6 . Additionally, the equality of inlet and exit mass flow rate is also analyzed to ensure the steady state nature of the flowfield in each case.
Fig. 4. Computational domain considered for the validation study.
conducted by Sahoo et al. [11] are imposed. The Mach number at the inlet is set to 2.0, whereas freestream static pressure and temperature are taken as 0.408 bar and 243.9 K respectively. These static conditions are derived from the reported test section Reynolds number of 3.5 × 105 (based on the base diameter of model) and stagnation pressure of 3.2 bar. Since the outflow is predominantly supersonic, pressure outlet boundary condition is assigned to the exit boundary of the domain. At this boundary, flow variables are extrapolated from the immediate left cells of boundary faces. The surfaces representing the blunt body and spike are modelled as no-slip, isothermal walls and are assigned with a constant temperature of 300K . The symmetry plane represents the axis of the blunt body-spike configuration. The grid sample provided is not the final grid on which simulations are done, rather it is given just to explain the meshing and computational strategy followed in the present study. Exhaustive grid independence study has been performed for each domain before finalizing the grid to be used for the accurate resolution of flowfield and surface parameters. Such grid refinement ensured enough number of grid points at the probable locations higher gradients resulting from the shock formation a flow separation. A boundary layer meshing strategy has been adapted near the wall regions to accurately capture the boundary layer. Further the wall y+ values were adjusted by keeping very small first layer height, so as to satisfy the y+ requirement of k − ω model. . Commercial CFD package ANSYS Fluent v15.0 [16] is employed to solve flow governing equations at the cell centroids of the computational domain. The numerical algorithm of this solver enables its user to choose either explicit or implicit time integration strategy depending on the requirement of the flow problem. In the present study, steady flow simulations are targeted, hence implicit time integration is opted. Although, implicit schemes are well known for their nature of
3. Validation of solution methodology A set of initial validation simulations were performed to confirm the correctness and accuracy of solver settings considered for the present study. First to understand the flow structure at the nose region of a blunt body, the freestream and model parameters of White [18] were considered. The primary focus of this study was the replication of White's experimentally obtained results through current computational frame work. The identification of appropriate mesh structure required for accurately resolving the flow features was also aimed through this study. An inlet pressure of 22729.3 Pa and temperature of 300 K with the freestream Mach number of 2.23 at zero angle of attack were used as mentioned by White [18]. The computational domain for the blunt body without spike was initially meshed with 25000 non-overlapping quadrilateral cells as shown in Fig. 4. Then, it was refined to 65000 cells and in the third phase, number of cells increased to 90000. For the study of flow over the blunt body attached with spike of flat face, the computational domain was meshed with more number of cells. For the spiked domain, the number of cells in the domain are 60000, 100000, 200000 for coarse, medium and fine mesh respectively. Simulations were performed on all three grid levels until the flowfield reached to steady state. As mentioned earlier, convergence has been monitored mainly through density residue. It has been observed that convergence in continuity happen after the convergence of momentum and energy. Hence, authors are on the opinion that convergence of density residue ensures steady state nature of the solution. A sample convergence plot 28
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4. Results and discussion The validated numerical set up has been further employed to investigate drag reduction when different combinations of blunt body and spike are considered. However, it is important to understand the aerodynamics of flow over blunt bodies without a spike as it is very essential to assess the performance of different spike designs when attached to different blunt bodies. The parameterized blunt bodies chosen for this study are the 1221, 2221 and 3221 whose nomenclature is based on a 4-digit numbering system provided by Brooks and Trescot [12], where each number corresponds to a certain geometric feature as mentioned in the previous sections. It can be noted that all the digits except the first one, are the same for each blunt body, meaning that the fineness ratio, cone semi-angle and base shape remain unchanged. The difference between the three bodies is the nose-bluntness factor with the 3221 having the highest bluntness and 1221 having the lowest. All the blunt bodies are subjected to the same free-stream velocity, air density and have the same base area. Based on the grid refinement information gained during the validation and verification study, similar kind of meshing strategy has been followed in this phase as well. The refined meshes used for the simulations had more than 90000 cells. The cell counts were slightly different for different bodies as their shapes were not the same. . The Mach contours obtained for different blunt shapes are compared in Fig. 8. The bow shock created by the presence of blunt nose section is evidenced in all three images. Irrespective of the shape, the stagnation region of each blunt body has a subsonic field, which is supported by the low values of Mach number in that region. It is obvious that, the shock created ahead of any axisymmetric blunt body placed in a supersonic field at zero angle of attack has 900 shock angle at the stagnation line. Hence the shock strength of the shock wave at the stagnation line is the same in all three cases. Therefore the stagnation point pressure values are found to be the same in all three blunt body cases. However the shock shapes are not identical at locations which are away from the stagnation streamline. From Fig. 8, it can be seen that the frontal sections of 3221 and 2221 have larger subsonic pockets than that of 1221. This means for the former the dynamics pressure loss is higher which translates into a high static pressure on a larger portion of the body surface area when compared to the latter. This can be seen in Fig. 9 Which shows the static pressure distribution along the blunt bodies without spikes. It can be observed that the maximum static pressure in the stagnation region is the same for all. However, the length along which a high static pressure persists is different. For the 3221 a high static pressure persists for a slightly larger length along the body than for 2221. The plot for 1221 is close to that of 2221. The minimum Cp values in the distributions are corresponding to pressure behind the expansion fans forming at the shoulder of the blunt body. This dip region pressure coefficient is lowest in case of 3221, but in
Fig. 5. Convergence history of residuals.
obtained on a medium level grid is shown in Fig. 5. Thus obtained steady state surface pressure distributions are then compared with experimental result in Fig. 6. It is very clear from these images that the numerical results obtained on coarse grid is deviating considerably from the experimental values for almost all locations of the blunt body. However the surface pressure distributions obtained with medium and fine grids of base model and fine grid of spiked model match perfectly with experimental data. Further refinement of the grid was observed to be needless as it was not changing the solution results but increasing the computational time. This study proves the correctness of solver settings adapted in this research. Further to show that the current numerical frame work is independent of freestream and geometry conditions, we consider another supersonic blunt body flow experimented by Sahoo et al. [11]. The boundary conditions were similar to the previous setup with only freestream conditions being different. The freestream pressure was set as 40800 Pa and the Mach number was 2. The freestream temperature was computed to be 243.95 K. The corresponding freestream Reynolds number is 3.5 × 105 . The same kind of grid refinement was followed in this case as well. The solution results obtained on the final refined grid are compared with experimental measurements in Fig. 7 and shows excellent agreement of present computational and reported experimental results both in case of base model and blunt body with spike. Here the blunt body and spike dimensions are different from the White's study. The spike section of Sahoo's study had a sharp nose section opposed to flat face of spike” used in the experiments of White [18]. Hence the numerical study applied to Sahoo's [11] experimental freestream and geometric conditions further ensures that the adapted numerical setup is both geometry and freestream independent. Therefore, these validation studies provide complete confidence to apply the same numerical frame work for other parametric investigations.
Fig. 6. Pressure distribution along the non-dimensionalized length (s/d) of the blunt body for first part of the validation. The reference here is White [18]. 29
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Fig. 7. Pressure coefficient distribution along the non-dimensionalized length (S/D) of the blunt body for second part of the validation. There reference here is Sahoo et al. [11] (a) Only Blunt Body (b) Sharp spike with blunt body.
Table 5 the drag value obtained for this blunt body is the highest. Hence it can be inferred that the effect of this low pressure region on the total drag is nullified due to the lower inclination of the surface where it occurs. The below given, conventionally used equation for the calculation of pressure drag on an elemental area substantiates the previous inference.
dFD = −p . dA. cosθ Here “p” is the static pressure on the elemental area (dA ), “θ” is the angle between the outward normal area vector and the free stream velocity vector. As a result of low bluntness factor, the “θ” is such that “− cosθ ” is small for a large portion of the 1221 blunt body, whereas 3221 and 2221 have a straight vertical face and subsequently “− cosθ ” is at its maximum (− cosθ =1 for θ = 1800 ), for a large portion of area. This combined with the previously mentioned pressure distribution factor leads to the lowest drag coefficient in case of 1221 blunt body. The drag coefficient (CD ) values of three reference bodies are tabulated in Table 5. The product of freestream dynamic pressure and base area of the blunt body has been considered to non-dimensionalize drag force in the form of drag coefficient. from the It is evident that the 3221 body has the highest drag as a result of the largest vertical/blunt area or nose-bluntness ratio among the three. The 2221 body's blunt portion is significantly smaller in area than that of 3221 but higher than the 1221. Due to this, it has an intermediate drag, although it is closer to 1221 than to 3221. It should also be noted that the shear stress acting on the surface of the blunt body has share on the total drag of the body. However, the subdivisions of total drag coefficients presented in Table 5 clearly evidence that pressure drag has major contribution to the total drag. The frictional drag mainly depends on the total wetted area of the blunt body.
Fig. 9. Comparison of surface pressure coefficient distributions obtained for the reference blunt bodies. Table 5 values obtained for three reference bodies. Blunt body
Pressure drag coeff.
Viscous drag coeff.
Total drag coeff.
(CDpre )
(CDvisc )
(CD )
1221 2221 3221
0.54 0.60 0.852
0.0081 0.0079 0.0078
0.55 0.61 0.86
Fig. 8. Comparison of Mach contours of reference blunt bodies (a) 1221, (b) 2221, (c) 3221. 30
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inclination of separation shock and flow structure downstream of the reattachment are observed to be largely depending on the configuration of blunt body. For instance, the separation location of 1221 body is 33.8 mm ahead of its stagnation point, whereas, the same for 2221, 3221 are 38.8 mm and 45.8 mm respectively. The location of separation is also seen to be affecting the orientation of separation shock. Moreover as the separation location moves upstream the separation shock starts interacting with the spike lip shock. Such interactions are very prominent in the cases of 2221 and 3221. Additionally, the larger bluntness of blunt body makes the separation shock more steeper, hence enhancing the property jump across it. Strongest separation shock can be observed in the case of 3221. Although the structure and intensity of flowfield differ when attaching the sharp spike to bodies of different bluntness factor, the sharp spike makes considerable reduction of overall drag on the blunt body. This fact is very evident from the surface pressure distribution comparisons given in Fig. 12. The stagnation point pressure values are considerably lowered upon employing the sharp spike. The stagnation point CP reduced from 1.665 of base model to 0.667 in case of sharp spikes. The peak surface pressure location is shifted from stagnation point to the point of reattachment. However, the location and magnitude of peak pressure is not the same for all three blunt bodies. These observations point towards the fact that the reattachment locations are different for different blunt bodies even if the spike configuration is same. Here in the present study, the most forward reattachment location can be observed for 2221 body, the next is 1221 and for 3221 the reattachment of flow happens far downstream as compared to that of other two bodies. Hence the largest size of separation can be assumed in case of 3221 body, which is also well supported by the qualitative representation of separation bubble in the schlieren images in Fig. 11(a). The occurrence of a larger flow separation zone ahead of the blunt body will certainly reduce the overall drag on the blunt body. The overall drag reduction resulting from the recasting of stagnation point flow structure due to the sharp spike can be assessed by referring Tables 6 and 7 and is found to be more for the body of large bluntness (3221). It has maximum a drag penalty when considered without spike. However, upon attaching the sharp spike, the formation of a large front separation zone creates a significant drop in the surface pressure, thus reducing the overall drag considerably in this case. The reduction of overall drag coefficient of 3221 from 0.86 to 0.334 is very surprising as it has maximum post reattachment pressure as depicted in Fig. 12. It has to be attributed to the fact that this peak pressure location is not at the frontal face of the blunt body, rather it happens at the shoulder of the body which is oblique to the oncoming ow due to which this peak pressure effect on the drag is mitigated. For the other two bodies, although sharp spike creates low pressure recirculation zone ahead of them, the reattachments happen at the surfaces which are nearly normal to the flow. Therefore, the drag reductions of those bodies are not as high as that of 3221. The use of blunt spike is found to yield a performance identical to that observed with the sharp spike. Here, the additional effect that the blunt spike brought into the ow is a detached spike lip shock, as opposed to an attached one in case of the sharp spike. The formed detached shock has a crucial role in the downstream flow alteration. Since the flow approaching the stagnation point of blunt body is crossing the strong bow shock, the boundary layer developing on the spike surface will be covered by a variable entropy layer. If the entropy layer height is larger than the boundary layer height at a given location, then the boundary layer will have higher stability against separation [19]. On the other hand, if the entropy layer is completely swallowed by the boundary layer, the flow will easily get separated due to decrease in density within the boundary layer. Here the comparison of numerical schlieren images made in Fig. 11 clearly shows the upstream shift of separation point on the blunt spike in comparison with that of the sharp spike. This observation is true for all three blunt body cases. The largest separated recirculation zone can be again observed in case of 3221 body. Another important feature to be noted is that in none of the cases,
5. Analysis of blunt bodies with spikes To properly understand the effect of using the spikes, it is imperative to observe the angle of the spike leading edge shock (lip shock) measured from the horizontal (which is responsible for the most upstream flow deflection), the position of formation and extent of the shear layer which encompasses a re-circulation/separated zone and the position of the re-attachment/body shock, all of which are depicted in Fig. 1. The function of the spike is to deflect a sizable amount of flow from the blunt bodies which otherwise have to endure the full ram of the flow field. The angle of flow deflection or the obliquity of the spike shock depends on the shape of the spike tip. This along with the diameter and length of the spike determines the portion of the flow deflected. However when it comes to the size of the re-circulation region, the shear layer onset and re-attachment zone, it is not just the parameters of the spike, but also the geometry of the blunt body which plays a major role. Eventually the total drag on the blunt body-spike system is a function of the aforementioned flow characteristics which are in turn dependent on the geometries of the blunt body and spike and the incoming Mach and Reynolds number. To understand these aspects; simulations have been carried out on different blunt bodies of present consideration by attaching them with diverse spike configurations mentioned in the previous section. The computational domain, meshing strategy followed and boundary conditions used for these studies are represented in Fig. 10. Entire domain has been meshed using structured quadrilateral cells. The key regions of interest, including near wall area of blunt body and spike surfaces were refined very accurately to ensure correct predictions of flow features at those sections. The Schlieren images of three different blunt bodies when attached with sharp spike, blunt spike and aero-spike are compared in Fig. 11. Beginning with the 1221 blunt body, the use of sharp spike causes a shock of significant strength attached to the tip of the sharp spike. The flow get turned little away from the stagnation line of the blunt body across this lip shock. However, the immediate next expansion reverts the flow back to the axis direction of the blunt body. The flow continues as attached along the spike surface for some more distance and eventually gets separated on the spike surface ahead of the stagnation region of the blunt body. An additional separation shock can be seen ahead of the separation zone in Fig. 11(a). Such flow separation on the spike is seen to be creating a large low pressure recirculation zone ahead of the blunt body. The separated flow later reattaches on the blunt body at a location downstream of the stagnation point of the blunt body. The point of separation and reattachment, size of separation zone,
Fig. 10. A sample meshed computational domain used for the spike based drag reduction study. 31
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Fig. 11. Schlieren images of flowfield around the blunt bodies attached with spike configurations.
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Table 6 CD values of different blunt body-spike configurations. Model
No spike
Sharp spike
Blunt spike
Aero-spike
1221 2221 3221
0.55 0.61 0.86
0.432 0.395 0.334
0.387 0.367 0.300
0.420 0.321 0.319
Table 7 Percentage reduction of CD obtained with different spike configurations. Model
Sharp spike
Blunt spike
Aero-spike
1221 2221 3221
21.4% 35.24% 61.12%
29.63% 39.83% 65.12%
23.63% 47.37% 62.29%
models, though their intensities are different. The drag reductions observed with blunt spike and various base model configurations are tabulated in Tables 6 and 7 It is evident from this table that the drag reductions are more prominent when using blunt spike in place sharp spike. The percentage reduction of drag enhanced from 21.4% to 29.63% while using blunt spike instead of sharp on the 1221. Similar drag reduction trends can also be observed for the other two models as well. In line with the observations of sharp spike studies, the highest drag reduction with blunt spike can be noted in case of 3221, while the least is observed on the 1221. However, the decrease in drag coefficient obtained by switching from sharp to blunt spike is more in the case of the 1221. These drag variations are to be discussed under the light of surface pressure information. The surface pressure coefficient comparisons made in Fig. 12 show the considerably lowered values of CP everywhere in the frontal sections of all three blunt bodies. When compared with the observations of the sharp spike, there is a slight shift of reattachment locations for 1221 and 2221 cases which can be noted by analyzing the peak pressure locations on the pressure graphs. For the 3221 body, the peak pressure location of blunt spike case is almost the same as that of sharp spike case. So, mainly the upstream extension of recirculation zone on the spike surface, along with a slight change in reattachment points can be taken as the reason for comparative improvement in drag reduction observed with blunt spike. In the case of 1221, the downstream shift of reattachment location creates a peak pressure at a more slated portion of the blunt body, thus offering higher relative drag reduction in comparison with sharp spike case. The curved nature of spike leading edge shock also leads to higher deflection of oncoming flow away from the stagnation region of blunt body thereby reducing the amount of incoming fluid ramming on to the blunt body. This is another reason for having lower values of CD while using blunt spike instead of sharp spike. But this effect has a strong coupling with the recirculation zone enhancement effect discussed earlier. As a whole the blunt spike is identified to be a better option than the sharp spike as far as only drag reduction is of interest. The aero-disk spike has highest impact on blunt body aerodynamics in drag reduction point of view. It is very interesting to see that the flat frontal section of aero-disk could lead to the flow separation point falling exactly on the shoulder of the disk itself. The strong bow shock induced by the vertical face of the aero-disk which deflects the major portion of supersonic flow away from the stagnation point of the blunt body. Therefore the expansion fan created at the shoulder of the aerodisk could not turn the flow back to the surface of the spike body, hence creating a large separated zone behind the aero-disk. The resulting low pressure recirculation zone covers a major portion of the frontal area of the blunt body. This is the reason, drag coefficients are considerably reduced when attaching an aero-disk spike to the blunt bodies. However, the use of aero-disk is not offering better drag reduction than the blunt spike in two of the present blunt body cases. For 1221 and 3221 blunt bodies, the overall drag coefficients obtained with aero-disk
Fig. 12. Comparison of surface pressure coefficient distributions obtained with different blunt body-spike configurations.
the spike leading edge shock interacts with the separation or reattachment shocks. Therefore the shock-shock interaction patterns downstream of the separation location are the same for all three
33
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spike are higher than that obtained with the blunt spike. This attributes to the fact that the drag contribution of spike to the total drag of the blunt body-spike geometry increases with increase in frontal area of the spike. The schlieren images given in Fig. 11(c) and the pressure coefficient comparisons made in Fig. 12 support this argument. In case of aero-disk spike, the surface pressure values can be noticed to be diminished everywhere on the blunt body surface in contrast to that of other two spike cases, although the drag reduction doesn't have the same order of drop This is because of added drag penalty resulting from the spike configuration. In the case of 2221 body, the surface pressures are low enough to compensate the drag enhancement resulting from the flat tip of aero-spike, hence better drag reduction than blunt and sharpspike is recorded in this case. However this is not the same for the other two blunt bodies. 6. Effect of spikes on surface heatflux . Although analysis of surface heatflux is not the primary focus of the present work, it is worthy to have a short elucidation on the variation of surface heatflux under different spike and blunt body conditions. It is to be noted here that all the simulations were carried out with isothermal wall condition of Tw = 300K . Maintaining such an isothermal condition for the space vehicle surfaces is practically difficult. In reality the surface temperature may vary with time and space. However, the current assumption of isothermal wall can help in the approximate estimation of heatflux over the model surface. Thus obtained surface heatflux predictions on different bodies when attached with different spikes are presented in Fig. 13. Here the Stanton number, the non-dimensional representation of surface heatflux, is calculated as (St =q˙ / ρ∞ U∞ CP (T0 − Tw ) ). Where, q˙ is the local surface heatflux, ρ∞, U∞ are freestream density and velocity respectively. The Stanton number comparisons presented in Fig. 13 clearly evidence that the stagnation point heatflux has significant drop in the presence of spikes. Again, this observation has to be attributed to the existence separation zone ahead of the blunt bodies when attached with spikes. Moreover, in the presence of spikes; the highest surface heatflux recorded at the post reattachment location. Surprisingly, the peak post reattachment heatflux was observed with sharp spike. The blunt spike and Aero-spike cases have better performance in terms of lowered surface heat loads. The lowest heatflux values are noted with aero-disk spike cases. The aerodisk spike cases had largest front separation regions in all three blunt body cases. Moreover in those cases, the flow reattachment has happened at the slanted surfaces of the blunt bodies. That is the reason for significantly reduced surface heatflux values observed with aero-disk spikes. The moderate Stanton number values observed with blunt spike cases can also be reasoned out in the same line. But it is to be stated here that the aero-disk spike will have shorter life as compared to blunt and sharp spikes. The tips of the spikes are actually exposed to high heatflux and this magnitude will be maximum in case of aero-disk spike. Hence the attainment of surface heatflux reduction noted with aero-disk spike will be in the expense of frequent replacement of aerodisk spike. 7. Conclusion Computational investigation of solid spike based drag reduction on three different blunt bodies has been carried out. The present numerical drag predictions on customized blunt body showed an increase in drag with increase in bluntness factor. Three different spike configurations were considered, viz. sharp, blunt and aero-disk spike to investigate the effectiveness of spike based drag reduction for the customized blunt body. It has been observed that the blunt spike outperforms the sharp one in terms of reduction in aero-dynamic drag. The use of aero-disk spike was noted to be the best option for moderately blunted body (2221). For other two bodies, one with least bluntness (1221) and the other with maximum bluntness (3221), the use of blunt spike was
Fig. 13. Comparison of Stanton number distribution over the blunt bodies.
identified as the best drag reduction option out of the tested cases. This study also reveals that the effectiveness of drag reduction resulting from the spike improves with an improvement in bluntness factor. The percentage of drag reduction was noted to be the highest for body of large 34
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bluntness (3221). Irrespective of the configuration of spike, the formation of low pressure recirculation region ahead of the blunt body is identified as the mechanism responsible for the drag reduction in each case. Although aero-disk spike created flow separation well ahead of that observed with blunt or sharp spike, the overall drag prediction of this set up was higher than that of blunt spike in case of 1221 and 3221 bodies. This contradicting observation was due to increased drag contribution of the flat aero-disk. Base diameter of the blunt body is noted as an insufficient scaling parameter when defining optimum spike geometry for parameterized blunt body. On the light of present research outcomes, it is recommended to additionally include the bluntness factor (K), fineness ratio (λ), semi cone angle (θ) and shape factor into scaling law of optimum spike geometry that gives minimum drag. It is also proved that the spikes are capable of reducing stagnation region heatflux. However, the post reattachment heatflux values are of same or higher magnitude in comparison with stagnation point heatflux of reference bodies. Aero-disk spike shown to be significantly reducing the surface heatflux over the blunt body in the expense of elevated heatflux at the aero-disk front.
without a forward facing spike, Comput. Fluids 26 (7) (1997) 741–754. [5] R. Kalimuthu, R.C. Mehta, E. Rathakrishnan, Drag reduction for spike attached to blunt-nosed body at mach 6, J. Spacecr. Rocket. 47 (1) (2010) 219. [6] M.B. Gerdroodbary, S. Hosseinalipour, Numerical simulation of hypersonic flow over highly blunted cones with spike, Acta Astronaut. 67 (1) (2010) 180–193. [7] M. Tahani, M. Karimi, A.M. Motlagh, S. Mirmahdian, Numerical investigation of drag and heat reduction in hypersonic spiked blunt bodies, Heat Mass Transf. 49 (10) (2013) 1369–1384. [8] M. Ahmed, N. Qin, Recent advances in the aerothermodynamics of spiked hypersonic vehicles, Prog. Aero. Sci. 47 (6) (2011) 425–449. [9] R. Mehta, Numerical simulation of the flow field over conical, disc and flat spiked body at mach 6, Aeronaut. J. 114 (1154) (2010) 225–236. [10] V. Menezes, S. Saravanan, K. Reddy, Shock tunnel study of spiked aerodynamic bodies flying at hypersonic mach numbers, Shock Waves 12 (3) (2002) 197–204. [11] D. Sahoo, S. Das, P. Kumar, J. Prasad, Effect of spike on steady and unsteady flow over a blunt body at supersonic speed, Acta Astronaut. 128 (2016) 521–533. [12] C.W. Brooks, C.D. Trescot, Transonic Investigation of the Effects of Nose Bluntness, Fineness Ratio, Cone Angle, and Base Shape on the Static Aerodynamic Characteristics of Short, Blunt Cones at Angles of Attack to, National Aeronautics and Space Administration, 1963. [13] D.C. Wilcox, et al., Turbulence Modeling for CFD vol. 2, DCW industries La Canada, CA, 1993. [14] D.C. Wilcox, Formulation of the kw turbulence model revisited, AIAA J. 46 (11) (2008) 2823–2838. [15] M.B. Gerdroodbary, S. Bishehsari, S. Hosseinalipour, K. Sedighi, Transient analysis of counter flowing jet over highly blunt cone in hypersonic flow, Acta Astronaut. 73 (2012) 38–48. [16] ANSYS® Fluent, Release 15.0. [17] B. John, G. Sarath, V. Kulkarni, G. Natarajan, Performance comparison of flux schemes for numerical simulation of high-speed inviscid flows, Progress Comput. Fluid. Dynamics, Int. J 14 (2) (2014) 83–96. [18] J. White, Alaa 93-0968 Application of Navier-Stokes Flowfield Analysis to the Aerothermodynamic Design of an Aerospike-Configured Missile, (1993). [19] B. John, V. Kulkarni, Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed, Comput. Fluids 96 (2014) 177–190 https://doi.org/10.1016/j.compfluid.2014.03.004.
References [1] D.H. Crawford, Investigation of the Flow over a Spiked-Nose Hemisphere-Cylinder at a Mach Number of 6.8, National Aeronautics and Space Administration, Washington, 1959. [2] G. dHumières, J. Stollery, Drag reduction on a spiked body at hypersonic speed, Aeronaut. J. 114 (1152) (2010) 113–119. [3] M. Gauer, A. Paull, Numerical investigation of a spiked blunt nose cone at hypersonic speeds, J. Spacecr. Rocket. 45 (3) (2008) 459–471. [4] R. Mehta, T. Jayachandran, Navier-Stokes solution for a heat shield with and
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Reduction of wave drag on parameterized blunt bodies using spikes with varied tip geometries
T
Suhaas Mohandas, R. Krishna Siddharth, Bibin John∗ School of Mechanical Engineering, Vellore Institute of Technology (VIT), Vellore, Tamil Nadu, India-632 014
A R T I C LE I N FO
A B S T R A C T
Keywords: Blunt body Aero-spike Wave drag reduction Recirculation region
Aeospike based wave drag reduction is investigated using two-equation turbulence model applied to Faver averaged Navier Stokes solver. Three different blunt bodies are considered in a low supersonic stream of Mach number 2. The considered blunt bodies differ in their degree of bluntness defined in terms of half cone angle, area of flattened front side and radius of bluntness. The zero angle of attack flowfield around these three bodies are computationally analyzed with and without the presence of aft spikes to evaluate the wave drag resulting from the formation of front shock structure. The influence of spike configuration on the wave drag is also investigated. The various considered spike tip geometries include aero-disk, sharp and blunt with the length of all the spikes being equal to the base diameter of the blunt bodies (L/D = 1). It has been found that the 3221 blunt body when coupled with a blunt tipped spike yielded the lowest drag coefficient of 0.3, despite the 3221 having the highest standalone drag coefficient of 0.86, among the blunt bodies when simulated individually without spikes. The physics behind the wave drag reduction associated with each combination of blunt body and spike configuration is presented with clarity. This study portrays the importance of taking bluntness factor, semicone angle, fineness ratio and blunt body shape factor into consideration while proposing the generalized optimum spike configuration for minimum drag attainment.
1. Introduction
facilitating a larger payload volume. This however presents a hindering factor when drag reduction is also necessary. On the other hand, a blunt body design intended to decrease drag by using a sharper fore front, results in the formation of an attached shock wave leading to an increase in heat flux. In light of the necessity to reduce both heat flux and drag, many methods have been introduced and investigated over the years using computational methods and through rigorous experimentation. A couple of examples include, the incorporation of spikes, energy deposition, stagnation point injection of gases or liquids, etc. Mechanically, the simplest of them would be the case of spike based drag reduction which divides the incoming flow, diverting a major portion of it away from the blunt body in contrast to the full ram which the blunt body will otherwise face. The magnitude and angle of flow deflection will depend on the size and shape of the spike and will play a vital role in reducing the pressure and temperature experienced by a significant portion of the blunt body due to the presence of a recirculation zone. Depending on the aforementioned factors, spike length to blunt body base diameter ratio (L/D) and the blunt body geometry, the position of the separation shock will vary and accordingly the re-attachment shock as well. The more delayed the re-attachment shock, the lesser will be the pressure accumulation which
. Re-entry vehicle aerodynamics has been a major part of research for aerodynamicists ever since the dawn of space flight. Space Shuttles, capsules and ICBMs upon re-entry from space to earth are subjected to extreme temperatures and atmospheric drag forces due to high velocities and the thickening of the atmosphere as the density rises with a decrease in altitude. The same scenario can be observed during launch of these vehicles to space as well, however the density variation is reversed. In case of space shuttles and ICBMs the reduction of heat flux is critical to its design as they have to withstand such high temperatures upon re-entry. Whereas the minimization of drag is a subject which has to be dealt with in situations where the there is a necessity to reduce overall fuel consumption and subsequently the material and space required to accommodate the fuel, like in the case of missiles and light weight and low thrust rockets during launch where the drag force is significant in comparison to the thrust. This is due to high air densities at low altitudes combined with large speeds. . Lower heat fluxes on the fore-bodies of aerospace vehicles are generally achieved by adopting a blunt shape which leads to the formation of a detached shock wave with an added advantage of
∗
Corresponding author. E-mail address: [email protected] (B. John).
https://doi.org/10.1016/j.actaastro.2019.04.017 Received 8 August 2018; Received in revised form 4 March 2019; Accepted 8 April 2019 Available online 11 April 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Illustration of flow field around blunt bodies without and with different spikes. Courtesy - Sahoo et al [11].
eventually pertains to a lower drag and heat flux. The aero-disk, sharp and blunt tipped spikes are well known and have been studied in the past. Each of them deflect the incoming flow uniquely as shown in Fig. 1, giving widely varying results from which it is possible to choose the best design. The spike-blunt system is also easier to simulate given the simplicity of the flow field and its mostly non transient nature. This approach eventually has been found to cater to the need of reducing both drag and heat flux. Crawford [1] in 1959, through series of experiments first recorded the reduction of drag and heat flux at Mach 6.8 when using sharp spikes of varying lengths. This study is still being used as the validation case in many of the latest research works in this field. Followed by Crawford's work many recent studies have been reported in this field. Drag reduction on a spiked conical body with spherical leading edge has been investigated by dHumieres and Stollery [2]. Almost 77% reduction in drag has been reported while attaching spike to the blunt model kept in the laminar hypersonic flow. An important numerical study focusing on the spike based drag reduction can be seen in the works of Gauer and Paull [3] in which drag reduction on a blunted cone model has been investigated at three different hypersonic Mach numbers. The parametric effect of spike length has also been studied in this work. Such studies have also been conducted with different spikes at hypersonic speeds by many other researchers in the recent past [4–10]. However, it is to be noted that in most of the literature which investigated the use of spikes, the blunt bodies used are hemispherical in shape. Similarly, the blunt body-spike systems seem to be researched extensively mostly at hypersonic speeds. Sahoo et al. [11] is an exception where the flow speed was supersonic (M = 2), but again the blunt body was hemispherical in shape. The mechanism of drag reduction has been explained adopting dividing streamline approach, which pushes away the separation point. Mostly experimental results are found for such a study except in Sahoo et al. [11] where various models including the k − ω turbulence model has been adopted. The flow field on a main hemispherical body with spike could abruptly change in shock structure is observed. It is considered to be a violent mode of unsteadiness and has been reported to be occurring for spikes having the smaller length to body diameter. Driving mechanism of pulsation has been described based on various hypotheses. Sahoo et al. [11] have used three variants of spikes namely the aerospike, sharp spike and blunt nose spike with a hemispherical blunt body for Mach 2 flow inside a wind tunnel at a pressure of 40897.45Pa. They have also performed numerical simulations using the k − ω model. The exact same conditions, spike parameters and turbulence model for the simulations have been used, which helped in validating the simulation methodology and model selection presented in this work. For the purpose of blunt body parameterization, the specifications and design codes given by Brooks and Trescot [12] are used. Tahani et al. [7]and Gerdroodbary et al. [6] have also conducted similar studies while the former has two types of aerodisks which are flat faced aero disk also called an aerospike by Sahoo et al. [11] and blunt nosed aero disk with the third one being a sharp spike. But all the blunt bodies in the aforementioned references were ideal cases and not really the designs incorporated in missiles and space shuttles nose cones. Most literature and research articles found till now have either
performed inviscid simulations or have used simplistic turbulence models like the k − ε , Spalart Allmaras (a one equation model) which are not ideal for spiked blunt body simulations as there are adverse pressure gradients and flow separations. Models like the k − ω model and SST model usually perform better for such flows. Since the SST model is computationally expensive and time consuming, the k − ω model is used. It has been used only in a few studies as the literature suggest, one among them being Sahoo et al. [11]. It was understood from the literature that the performance of k − ω turbulence model was better than the k − ε model by comparing the simulation results with experimental results. Another important point to be noted is that in most of the literature available pertaining to this field of research, hemispherical blunt bodies or roughly parameterized blunt bodies are used. But these designs are seldom implemented in actual missiles and spacecraft noses. In this paper however, we make use of the design standards, codes and parameters laid out by Brooks and Trescot [12] which is a NASA report and represents a realistic design of the blunt bodies used in the space vehicles. Moreover, to the date nobody has investigated the effect of aerospike geometries on wave drag reduction by attaching to blunt bodies of different geometric features. Therefore, the objectives of present study are twofold. First objective is to identify the variation of drag penalty with change in bluntness of the body. Second objective is to test whether optimum spike configurations proposed in the literature are really optimum when employed with diverse blunt bodies of identical base diameter. 2. Methodology Supersonic flow over the blunt body has been simulated by solving 2D-axisymmetric, Faver averaged Navier stokes equations in a two dimensional computational domain using finite volume method. Additionally, equations of turbulent kinetic energy (k) and specific rate of dissipation (ω) were solved to obtain the turbulent characteristics of the flow. Vector form of the k and ω equations are;
∂ ∂ ∂ ⎛ ∂k ⎞ (ρk ) + (ρkvi ) = ⎜Γk ⎟ + Gk − yk + Sk ∂t ∂x i ∂x j ⎝ ∂x j ⎠
(1)
∂ ∂ ∂ ⎛ ∂ω ⎞ (ρω) + (ρωvi ) = ⎜Γω ⎟ + Gω − yω + Sω ∂t ∂x i ∂x j ⎝ ∂x j ⎠
(2)
The effective diffusitivites are defined as;
Γk = μ +
μt ; σk
Γw = μ +
μt σω
(3)
where σk and σω stand to represent turbulent Prandtl numbers for k and ω respectively. The turbulent viscosity μt can be calculated as a function of density (ρ), k and ω. Suitable damping coefficient may also be considered while calculating the μt to account for the low Reynolds number effect. The term Gk in the k-equation represents the production of turbulent kinetic energy. Fluent calculates this term from the equation for the transport of k as; 26
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Gk = −ρui′ u′j
∂uj ∂x i
(4)
The production of ω is evaluated from the relation;
ω Gw = −α Gk k
(5)
Additionally Yk and Yω in the above governing equations represent the dissipation of k and ω respectively. The detailed definitions for these terms can be seen in the reporting of Wilcox [13,14]. The suitable values of model constants are also mentioned in those papers. Further, to account for the compressibility effect, Fluent considers a compressibility function in the calculation of dissipation terms. The compressibility correction term is given by
0 Mt ≤ Mt 0 F (Mt ) = ⎧ 2 2 M − M M ⎨ t > Mt 0 t t 0 ⎩
(6)
Where
Mt2 =
2k a2
Fig. 2. Blunt body schematic indicating all design parameters. Courtesy Brooks and Trescot [12].
Mt0 = 0.25
a=
γRT
Table 1 First digit denotes nose-bluntness factor K.
Since the flow is at zero angle of attack and the blunt body of interest is symmetric about the axis of rotation, the strategy of following 2D-axisymmetric simulation instead of complete three dimensional solution was found to be accurate enough for the resolution of flowfield in this case. Moreover, it also offers a great advantage in terms of reduced computational time. In the past, Gerdroodbary and Hosseinalipour [6] have also reported about the ample nature 2D-axisymmetric simulations in accurately predicting flowfield and surface properties in an identical flow scenario. Out of the different twoequation turbulent models available in the solver, the k − ω model is specifically opted for the present study upon considering its accuracy in resolving the flow separation and shear layer correctly. This superiority of k − ω model has also been reported by other researchers [11,15], for diverse high speed flow studies. . The blunt body and spike configurations used in the present study are adapted from the literature. The design codes for the spikes were taken from Sahoo et al. [11] and the blunt body specifications were adapted from Brooks and Trescot [12] who had taken into consideration the nose cone angle, the fineness ratio, nose bluntness and base shape and their effects on the static aerodynamic characteristics of short, blunt cones at angles of attack from 00 to 1800 in the transonic regime. In the reporting of latter, blunt body-parameters were tabulated and formulated in detail to choose from, along with the variation of coefficients of drag and lift for various angles of attack and Mach numbers from 0.8 to 1.2. It is from those graphs that the blunt body designs for the present study are selected. The ones with lowest, highest and medium drag were selected for the investigation with the addition of three different spike geometries namely, the sharp, blunt nose, and the aero-disk. All the design parameters of the blunt body are indicated in the schematic shown in Fig. 2. The body design, follows a four-digit numbering system where every digit pertains to some dimensional aspect as given in Tables 1–4 In Table 2, K = b/ a and in Table 3, λ = l/ d ; where a, b, l and d are represented in the blunt body schematics. As per this numbering system, three specific blunt models are selected for the present study. It was found that the blunt body with the lowest amount of coefficient of drag was coded 1221, the highest being 3221 and the medium drag blunt body being 2221. Thus opted blunt models are to be analyzed with the addition of the spikes to understand the effectiveness of different spike configurations in the context of aerodynamic drag reduction of each models. The spikes used in the present study are sized according to Sahoo et al. [11] and are represented schematically in Fig. 3. This is done, as the latter had already established these
First digit
K
1 2 3
0 (Spherical) 0.50 0.75
Table 2 Second digit denotes fineness ratio(λ). second digit
λ
1 2 3
0.5 0.75 1.0
Table 3 Third digit denotes cone semi angle θ Third digit
θ, deg
1 2 3
10 15 20
Table 4 Fourth digit denotes base shape. Fourth digit
Shape
1 2 3
Flat Convex Concave
dimensions as optimal for the present analysis. Taking into consideration the aforementioned design parameters, a series of blunt body-spike combinations were designed and subjected to numerical investigations. . As discussed earlier, the computational domain is constructed as a 2D domain, upon considering the axisymmetric nature of the flowfield. A sample computational domain (without spike) meshed with quadrilateral elements is presented in Fig. 4. The numerical boundary conditions imposed at the physical boundaries of the domain are also mentioned. At the inlet of the computational domain, freestream variables corresponding to test section conditions of the experimental study 27
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Fig. 3. Spike types and geometry. (D is the base Diameter of Blunt Body) Courtesy - Sahoo et al. [11].
unconditional stability, the complexity involved in the present flowfield forced the authors to limit the Courant-Friedrichs-Lewy number to 0.5 in most of the runs. More accurate Flux difference splitting upwind scheme ROE is used for the calculation of convective fluxes. The upwind schemes are well known for their shock capturing capability [17]. Therefore, no additional shock fitting techniques were considered in the present study. The viscous flux terms are computed using the gradients of flow and turbulent variables obtained at the cell centroids. Least square cell based approach is employed to calculate gradients at the cell centroids while the solver settings are made to ensure second order spatial accuracy of the solution. The working fluid has been taken as air and modelled as ideal gas. Sutherland's viscosity law has been employed to calculate fluid viscosity at each cell centroid based on the local static temperature. The solver took specific heat at constant pressure (CP ) of air as 1005 J / kgK when modelled as ideal gas. Additionally, the pre-set value of constant Prandtl number has been employed to evaluate thermal conductivity with the help of computed viscosity and specified CP . Inlet freestream conditions were used to initialize the domain as it was the best possible pre-known initial guess for supersonic flowfield. The solution convergence is monitored mainly based on density residue and is considered as steady state once the absolute residue of density falls below 10−6 . Additionally, the equality of inlet and exit mass flow rate is also analyzed to ensure the steady state nature of the flowfield in each case.
Fig. 4. Computational domain considered for the validation study.
conducted by Sahoo et al. [11] are imposed. The Mach number at the inlet is set to 2.0, whereas freestream static pressure and temperature are taken as 0.408 bar and 243.9 K respectively. These static conditions are derived from the reported test section Reynolds number of 3.5 × 105 (based on the base diameter of model) and stagnation pressure of 3.2 bar. Since the outflow is predominantly supersonic, pressure outlet boundary condition is assigned to the exit boundary of the domain. At this boundary, flow variables are extrapolated from the immediate left cells of boundary faces. The surfaces representing the blunt body and spike are modelled as no-slip, isothermal walls and are assigned with a constant temperature of 300K . The symmetry plane represents the axis of the blunt body-spike configuration. The grid sample provided is not the final grid on which simulations are done, rather it is given just to explain the meshing and computational strategy followed in the present study. Exhaustive grid independence study has been performed for each domain before finalizing the grid to be used for the accurate resolution of flowfield and surface parameters. Such grid refinement ensured enough number of grid points at the probable locations higher gradients resulting from the shock formation a flow separation. A boundary layer meshing strategy has been adapted near the wall regions to accurately capture the boundary layer. Further the wall y+ values were adjusted by keeping very small first layer height, so as to satisfy the y+ requirement of k − ω model. . Commercial CFD package ANSYS Fluent v15.0 [16] is employed to solve flow governing equations at the cell centroids of the computational domain. The numerical algorithm of this solver enables its user to choose either explicit or implicit time integration strategy depending on the requirement of the flow problem. In the present study, steady flow simulations are targeted, hence implicit time integration is opted. Although, implicit schemes are well known for their nature of
3. Validation of solution methodology A set of initial validation simulations were performed to confirm the correctness and accuracy of solver settings considered for the present study. First to understand the flow structure at the nose region of a blunt body, the freestream and model parameters of White [18] were considered. The primary focus of this study was the replication of White's experimentally obtained results through current computational frame work. The identification of appropriate mesh structure required for accurately resolving the flow features was also aimed through this study. An inlet pressure of 22729.3 Pa and temperature of 300 K with the freestream Mach number of 2.23 at zero angle of attack were used as mentioned by White [18]. The computational domain for the blunt body without spike was initially meshed with 25000 non-overlapping quadrilateral cells as shown in Fig. 4. Then, it was refined to 65000 cells and in the third phase, number of cells increased to 90000. For the study of flow over the blunt body attached with spike of flat face, the computational domain was meshed with more number of cells. For the spiked domain, the number of cells in the domain are 60000, 100000, 200000 for coarse, medium and fine mesh respectively. Simulations were performed on all three grid levels until the flowfield reached to steady state. As mentioned earlier, convergence has been monitored mainly through density residue. It has been observed that convergence in continuity happen after the convergence of momentum and energy. Hence, authors are on the opinion that convergence of density residue ensures steady state nature of the solution. A sample convergence plot 28
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4. Results and discussion The validated numerical set up has been further employed to investigate drag reduction when different combinations of blunt body and spike are considered. However, it is important to understand the aerodynamics of flow over blunt bodies without a spike as it is very essential to assess the performance of different spike designs when attached to different blunt bodies. The parameterized blunt bodies chosen for this study are the 1221, 2221 and 3221 whose nomenclature is based on a 4-digit numbering system provided by Brooks and Trescot [12], where each number corresponds to a certain geometric feature as mentioned in the previous sections. It can be noted that all the digits except the first one, are the same for each blunt body, meaning that the fineness ratio, cone semi-angle and base shape remain unchanged. The difference between the three bodies is the nose-bluntness factor with the 3221 having the highest bluntness and 1221 having the lowest. All the blunt bodies are subjected to the same free-stream velocity, air density and have the same base area. Based on the grid refinement information gained during the validation and verification study, similar kind of meshing strategy has been followed in this phase as well. The refined meshes used for the simulations had more than 90000 cells. The cell counts were slightly different for different bodies as their shapes were not the same. . The Mach contours obtained for different blunt shapes are compared in Fig. 8. The bow shock created by the presence of blunt nose section is evidenced in all three images. Irrespective of the shape, the stagnation region of each blunt body has a subsonic field, which is supported by the low values of Mach number in that region. It is obvious that, the shock created ahead of any axisymmetric blunt body placed in a supersonic field at zero angle of attack has 900 shock angle at the stagnation line. Hence the shock strength of the shock wave at the stagnation line is the same in all three cases. Therefore the stagnation point pressure values are found to be the same in all three blunt body cases. However the shock shapes are not identical at locations which are away from the stagnation streamline. From Fig. 8, it can be seen that the frontal sections of 3221 and 2221 have larger subsonic pockets than that of 1221. This means for the former the dynamics pressure loss is higher which translates into a high static pressure on a larger portion of the body surface area when compared to the latter. This can be seen in Fig. 9 Which shows the static pressure distribution along the blunt bodies without spikes. It can be observed that the maximum static pressure in the stagnation region is the same for all. However, the length along which a high static pressure persists is different. For the 3221 a high static pressure persists for a slightly larger length along the body than for 2221. The plot for 1221 is close to that of 2221. The minimum Cp values in the distributions are corresponding to pressure behind the expansion fans forming at the shoulder of the blunt body. This dip region pressure coefficient is lowest in case of 3221, but in
Fig. 5. Convergence history of residuals.
obtained on a medium level grid is shown in Fig. 5. Thus obtained steady state surface pressure distributions are then compared with experimental result in Fig. 6. It is very clear from these images that the numerical results obtained on coarse grid is deviating considerably from the experimental values for almost all locations of the blunt body. However the surface pressure distributions obtained with medium and fine grids of base model and fine grid of spiked model match perfectly with experimental data. Further refinement of the grid was observed to be needless as it was not changing the solution results but increasing the computational time. This study proves the correctness of solver settings adapted in this research. Further to show that the current numerical frame work is independent of freestream and geometry conditions, we consider another supersonic blunt body flow experimented by Sahoo et al. [11]. The boundary conditions were similar to the previous setup with only freestream conditions being different. The freestream pressure was set as 40800 Pa and the Mach number was 2. The freestream temperature was computed to be 243.95 K. The corresponding freestream Reynolds number is 3.5 × 105 . The same kind of grid refinement was followed in this case as well. The solution results obtained on the final refined grid are compared with experimental measurements in Fig. 7 and shows excellent agreement of present computational and reported experimental results both in case of base model and blunt body with spike. Here the blunt body and spike dimensions are different from the White's study. The spike section of Sahoo's study had a sharp nose section opposed to flat face of spike” used in the experiments of White [18]. Hence the numerical study applied to Sahoo's [11] experimental freestream and geometric conditions further ensures that the adapted numerical setup is both geometry and freestream independent. Therefore, these validation studies provide complete confidence to apply the same numerical frame work for other parametric investigations.
Fig. 6. Pressure distribution along the non-dimensionalized length (s/d) of the blunt body for first part of the validation. The reference here is White [18]. 29
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Fig. 7. Pressure coefficient distribution along the non-dimensionalized length (S/D) of the blunt body for second part of the validation. There reference here is Sahoo et al. [11] (a) Only Blunt Body (b) Sharp spike with blunt body.
Table 5 the drag value obtained for this blunt body is the highest. Hence it can be inferred that the effect of this low pressure region on the total drag is nullified due to the lower inclination of the surface where it occurs. The below given, conventionally used equation for the calculation of pressure drag on an elemental area substantiates the previous inference.
dFD = −p . dA. cosθ Here “p” is the static pressure on the elemental area (dA ), “θ” is the angle between the outward normal area vector and the free stream velocity vector. As a result of low bluntness factor, the “θ” is such that “− cosθ ” is small for a large portion of the 1221 blunt body, whereas 3221 and 2221 have a straight vertical face and subsequently “− cosθ ” is at its maximum (− cosθ =1 for θ = 1800 ), for a large portion of area. This combined with the previously mentioned pressure distribution factor leads to the lowest drag coefficient in case of 1221 blunt body. The drag coefficient (CD ) values of three reference bodies are tabulated in Table 5. The product of freestream dynamic pressure and base area of the blunt body has been considered to non-dimensionalize drag force in the form of drag coefficient. from the It is evident that the 3221 body has the highest drag as a result of the largest vertical/blunt area or nose-bluntness ratio among the three. The 2221 body's blunt portion is significantly smaller in area than that of 3221 but higher than the 1221. Due to this, it has an intermediate drag, although it is closer to 1221 than to 3221. It should also be noted that the shear stress acting on the surface of the blunt body has share on the total drag of the body. However, the subdivisions of total drag coefficients presented in Table 5 clearly evidence that pressure drag has major contribution to the total drag. The frictional drag mainly depends on the total wetted area of the blunt body.
Fig. 9. Comparison of surface pressure coefficient distributions obtained for the reference blunt bodies. Table 5 values obtained for three reference bodies. Blunt body
Pressure drag coeff.
Viscous drag coeff.
Total drag coeff.
(CDpre )
(CDvisc )
(CD )
1221 2221 3221
0.54 0.60 0.852
0.0081 0.0079 0.0078
0.55 0.61 0.86
Fig. 8. Comparison of Mach contours of reference blunt bodies (a) 1221, (b) 2221, (c) 3221. 30
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inclination of separation shock and flow structure downstream of the reattachment are observed to be largely depending on the configuration of blunt body. For instance, the separation location of 1221 body is 33.8 mm ahead of its stagnation point, whereas, the same for 2221, 3221 are 38.8 mm and 45.8 mm respectively. The location of separation is also seen to be affecting the orientation of separation shock. Moreover as the separation location moves upstream the separation shock starts interacting with the spike lip shock. Such interactions are very prominent in the cases of 2221 and 3221. Additionally, the larger bluntness of blunt body makes the separation shock more steeper, hence enhancing the property jump across it. Strongest separation shock can be observed in the case of 3221. Although the structure and intensity of flowfield differ when attaching the sharp spike to bodies of different bluntness factor, the sharp spike makes considerable reduction of overall drag on the blunt body. This fact is very evident from the surface pressure distribution comparisons given in Fig. 12. The stagnation point pressure values are considerably lowered upon employing the sharp spike. The stagnation point CP reduced from 1.665 of base model to 0.667 in case of sharp spikes. The peak surface pressure location is shifted from stagnation point to the point of reattachment. However, the location and magnitude of peak pressure is not the same for all three blunt bodies. These observations point towards the fact that the reattachment locations are different for different blunt bodies even if the spike configuration is same. Here in the present study, the most forward reattachment location can be observed for 2221 body, the next is 1221 and for 3221 the reattachment of flow happens far downstream as compared to that of other two bodies. Hence the largest size of separation can be assumed in case of 3221 body, which is also well supported by the qualitative representation of separation bubble in the schlieren images in Fig. 11(a). The occurrence of a larger flow separation zone ahead of the blunt body will certainly reduce the overall drag on the blunt body. The overall drag reduction resulting from the recasting of stagnation point flow structure due to the sharp spike can be assessed by referring Tables 6 and 7 and is found to be more for the body of large bluntness (3221). It has maximum a drag penalty when considered without spike. However, upon attaching the sharp spike, the formation of a large front separation zone creates a significant drop in the surface pressure, thus reducing the overall drag considerably in this case. The reduction of overall drag coefficient of 3221 from 0.86 to 0.334 is very surprising as it has maximum post reattachment pressure as depicted in Fig. 12. It has to be attributed to the fact that this peak pressure location is not at the frontal face of the blunt body, rather it happens at the shoulder of the body which is oblique to the oncoming ow due to which this peak pressure effect on the drag is mitigated. For the other two bodies, although sharp spike creates low pressure recirculation zone ahead of them, the reattachments happen at the surfaces which are nearly normal to the flow. Therefore, the drag reductions of those bodies are not as high as that of 3221. The use of blunt spike is found to yield a performance identical to that observed with the sharp spike. Here, the additional effect that the blunt spike brought into the ow is a detached spike lip shock, as opposed to an attached one in case of the sharp spike. The formed detached shock has a crucial role in the downstream flow alteration. Since the flow approaching the stagnation point of blunt body is crossing the strong bow shock, the boundary layer developing on the spike surface will be covered by a variable entropy layer. If the entropy layer height is larger than the boundary layer height at a given location, then the boundary layer will have higher stability against separation [19]. On the other hand, if the entropy layer is completely swallowed by the boundary layer, the flow will easily get separated due to decrease in density within the boundary layer. Here the comparison of numerical schlieren images made in Fig. 11 clearly shows the upstream shift of separation point on the blunt spike in comparison with that of the sharp spike. This observation is true for all three blunt body cases. The largest separated recirculation zone can be again observed in case of 3221 body. Another important feature to be noted is that in none of the cases,
5. Analysis of blunt bodies with spikes To properly understand the effect of using the spikes, it is imperative to observe the angle of the spike leading edge shock (lip shock) measured from the horizontal (which is responsible for the most upstream flow deflection), the position of formation and extent of the shear layer which encompasses a re-circulation/separated zone and the position of the re-attachment/body shock, all of which are depicted in Fig. 1. The function of the spike is to deflect a sizable amount of flow from the blunt bodies which otherwise have to endure the full ram of the flow field. The angle of flow deflection or the obliquity of the spike shock depends on the shape of the spike tip. This along with the diameter and length of the spike determines the portion of the flow deflected. However when it comes to the size of the re-circulation region, the shear layer onset and re-attachment zone, it is not just the parameters of the spike, but also the geometry of the blunt body which plays a major role. Eventually the total drag on the blunt body-spike system is a function of the aforementioned flow characteristics which are in turn dependent on the geometries of the blunt body and spike and the incoming Mach and Reynolds number. To understand these aspects; simulations have been carried out on different blunt bodies of present consideration by attaching them with diverse spike configurations mentioned in the previous section. The computational domain, meshing strategy followed and boundary conditions used for these studies are represented in Fig. 10. Entire domain has been meshed using structured quadrilateral cells. The key regions of interest, including near wall area of blunt body and spike surfaces were refined very accurately to ensure correct predictions of flow features at those sections. The Schlieren images of three different blunt bodies when attached with sharp spike, blunt spike and aero-spike are compared in Fig. 11. Beginning with the 1221 blunt body, the use of sharp spike causes a shock of significant strength attached to the tip of the sharp spike. The flow get turned little away from the stagnation line of the blunt body across this lip shock. However, the immediate next expansion reverts the flow back to the axis direction of the blunt body. The flow continues as attached along the spike surface for some more distance and eventually gets separated on the spike surface ahead of the stagnation region of the blunt body. An additional separation shock can be seen ahead of the separation zone in Fig. 11(a). Such flow separation on the spike is seen to be creating a large low pressure recirculation zone ahead of the blunt body. The separated flow later reattaches on the blunt body at a location downstream of the stagnation point of the blunt body. The point of separation and reattachment, size of separation zone,
Fig. 10. A sample meshed computational domain used for the spike based drag reduction study. 31
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Fig. 11. Schlieren images of flowfield around the blunt bodies attached with spike configurations.
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Table 6 CD values of different blunt body-spike configurations. Model
No spike
Sharp spike
Blunt spike
Aero-spike
1221 2221 3221
0.55 0.61 0.86
0.432 0.395 0.334
0.387 0.367 0.300
0.420 0.321 0.319
Table 7 Percentage reduction of CD obtained with different spike configurations. Model
Sharp spike
Blunt spike
Aero-spike
1221 2221 3221
21.4% 35.24% 61.12%
29.63% 39.83% 65.12%
23.63% 47.37% 62.29%
models, though their intensities are different. The drag reductions observed with blunt spike and various base model configurations are tabulated in Tables 6 and 7 It is evident from this table that the drag reductions are more prominent when using blunt spike in place sharp spike. The percentage reduction of drag enhanced from 21.4% to 29.63% while using blunt spike instead of sharp on the 1221. Similar drag reduction trends can also be observed for the other two models as well. In line with the observations of sharp spike studies, the highest drag reduction with blunt spike can be noted in case of 3221, while the least is observed on the 1221. However, the decrease in drag coefficient obtained by switching from sharp to blunt spike is more in the case of the 1221. These drag variations are to be discussed under the light of surface pressure information. The surface pressure coefficient comparisons made in Fig. 12 show the considerably lowered values of CP everywhere in the frontal sections of all three blunt bodies. When compared with the observations of the sharp spike, there is a slight shift of reattachment locations for 1221 and 2221 cases which can be noted by analyzing the peak pressure locations on the pressure graphs. For the 3221 body, the peak pressure location of blunt spike case is almost the same as that of sharp spike case. So, mainly the upstream extension of recirculation zone on the spike surface, along with a slight change in reattachment points can be taken as the reason for comparative improvement in drag reduction observed with blunt spike. In the case of 1221, the downstream shift of reattachment location creates a peak pressure at a more slated portion of the blunt body, thus offering higher relative drag reduction in comparison with sharp spike case. The curved nature of spike leading edge shock also leads to higher deflection of oncoming flow away from the stagnation region of blunt body thereby reducing the amount of incoming fluid ramming on to the blunt body. This is another reason for having lower values of CD while using blunt spike instead of sharp spike. But this effect has a strong coupling with the recirculation zone enhancement effect discussed earlier. As a whole the blunt spike is identified to be a better option than the sharp spike as far as only drag reduction is of interest. The aero-disk spike has highest impact on blunt body aerodynamics in drag reduction point of view. It is very interesting to see that the flat frontal section of aero-disk could lead to the flow separation point falling exactly on the shoulder of the disk itself. The strong bow shock induced by the vertical face of the aero-disk which deflects the major portion of supersonic flow away from the stagnation point of the blunt body. Therefore the expansion fan created at the shoulder of the aerodisk could not turn the flow back to the surface of the spike body, hence creating a large separated zone behind the aero-disk. The resulting low pressure recirculation zone covers a major portion of the frontal area of the blunt body. This is the reason, drag coefficients are considerably reduced when attaching an aero-disk spike to the blunt bodies. However, the use of aero-disk is not offering better drag reduction than the blunt spike in two of the present blunt body cases. For 1221 and 3221 blunt bodies, the overall drag coefficients obtained with aero-disk
Fig. 12. Comparison of surface pressure coefficient distributions obtained with different blunt body-spike configurations.
the spike leading edge shock interacts with the separation or reattachment shocks. Therefore the shock-shock interaction patterns downstream of the separation location are the same for all three
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spike are higher than that obtained with the blunt spike. This attributes to the fact that the drag contribution of spike to the total drag of the blunt body-spike geometry increases with increase in frontal area of the spike. The schlieren images given in Fig. 11(c) and the pressure coefficient comparisons made in Fig. 12 support this argument. In case of aero-disk spike, the surface pressure values can be noticed to be diminished everywhere on the blunt body surface in contrast to that of other two spike cases, although the drag reduction doesn't have the same order of drop This is because of added drag penalty resulting from the spike configuration. In the case of 2221 body, the surface pressures are low enough to compensate the drag enhancement resulting from the flat tip of aero-spike, hence better drag reduction than blunt and sharpspike is recorded in this case. However this is not the same for the other two blunt bodies. 6. Effect of spikes on surface heatflux . Although analysis of surface heatflux is not the primary focus of the present work, it is worthy to have a short elucidation on the variation of surface heatflux under different spike and blunt body conditions. It is to be noted here that all the simulations were carried out with isothermal wall condition of Tw = 300K . Maintaining such an isothermal condition for the space vehicle surfaces is practically difficult. In reality the surface temperature may vary with time and space. However, the current assumption of isothermal wall can help in the approximate estimation of heatflux over the model surface. Thus obtained surface heatflux predictions on different bodies when attached with different spikes are presented in Fig. 13. Here the Stanton number, the non-dimensional representation of surface heatflux, is calculated as (St =q˙ / ρ∞ U∞ CP (T0 − Tw ) ). Where, q˙ is the local surface heatflux, ρ∞, U∞ are freestream density and velocity respectively. The Stanton number comparisons presented in Fig. 13 clearly evidence that the stagnation point heatflux has significant drop in the presence of spikes. Again, this observation has to be attributed to the existence separation zone ahead of the blunt bodies when attached with spikes. Moreover, in the presence of spikes; the highest surface heatflux recorded at the post reattachment location. Surprisingly, the peak post reattachment heatflux was observed with sharp spike. The blunt spike and Aero-spike cases have better performance in terms of lowered surface heat loads. The lowest heatflux values are noted with aero-disk spike cases. The aerodisk spike cases had largest front separation regions in all three blunt body cases. Moreover in those cases, the flow reattachment has happened at the slanted surfaces of the blunt bodies. That is the reason for significantly reduced surface heatflux values observed with aero-disk spikes. The moderate Stanton number values observed with blunt spike cases can also be reasoned out in the same line. But it is to be stated here that the aero-disk spike will have shorter life as compared to blunt and sharp spikes. The tips of the spikes are actually exposed to high heatflux and this magnitude will be maximum in case of aero-disk spike. Hence the attainment of surface heatflux reduction noted with aero-disk spike will be in the expense of frequent replacement of aerodisk spike. 7. Conclusion Computational investigation of solid spike based drag reduction on three different blunt bodies has been carried out. The present numerical drag predictions on customized blunt body showed an increase in drag with increase in bluntness factor. Three different spike configurations were considered, viz. sharp, blunt and aero-disk spike to investigate the effectiveness of spike based drag reduction for the customized blunt body. It has been observed that the blunt spike outperforms the sharp one in terms of reduction in aero-dynamic drag. The use of aero-disk spike was noted to be the best option for moderately blunted body (2221). For other two bodies, one with least bluntness (1221) and the other with maximum bluntness (3221), the use of blunt spike was
Fig. 13. Comparison of Stanton number distribution over the blunt bodies.
identified as the best drag reduction option out of the tested cases. This study also reveals that the effectiveness of drag reduction resulting from the spike improves with an improvement in bluntness factor. The percentage of drag reduction was noted to be the highest for body of large 34
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bluntness (3221). Irrespective of the configuration of spike, the formation of low pressure recirculation region ahead of the blunt body is identified as the mechanism responsible for the drag reduction in each case. Although aero-disk spike created flow separation well ahead of that observed with blunt or sharp spike, the overall drag prediction of this set up was higher than that of blunt spike in case of 1221 and 3221 bodies. This contradicting observation was due to increased drag contribution of the flat aero-disk. Base diameter of the blunt body is noted as an insufficient scaling parameter when defining optimum spike geometry for parameterized blunt body. On the light of present research outcomes, it is recommended to additionally include the bluntness factor (K), fineness ratio (λ), semi cone angle (θ) and shape factor into scaling law of optimum spike geometry that gives minimum drag. It is also proved that the spikes are capable of reducing stagnation region heatflux. However, the post reattachment heatflux values are of same or higher magnitude in comparison with stagnation point heatflux of reference bodies. Aero-disk spike shown to be significantly reducing the surface heatflux over the blunt body in the expense of elevated heatflux at the aero-disk front.
without a forward facing spike, Comput. Fluids 26 (7) (1997) 741–754. [5] R. Kalimuthu, R.C. Mehta, E. Rathakrishnan, Drag reduction for spike attached to blunt-nosed body at mach 6, J. Spacecr. Rocket. 47 (1) (2010) 219. [6] M.B. Gerdroodbary, S. Hosseinalipour, Numerical simulation of hypersonic flow over highly blunted cones with spike, Acta Astronaut. 67 (1) (2010) 180–193. [7] M. Tahani, M. Karimi, A.M. Motlagh, S. Mirmahdian, Numerical investigation of drag and heat reduction in hypersonic spiked blunt bodies, Heat Mass Transf. 49 (10) (2013) 1369–1384. [8] M. Ahmed, N. Qin, Recent advances in the aerothermodynamics of spiked hypersonic vehicles, Prog. Aero. Sci. 47 (6) (2011) 425–449. [9] R. Mehta, Numerical simulation of the flow field over conical, disc and flat spiked body at mach 6, Aeronaut. J. 114 (1154) (2010) 225–236. [10] V. Menezes, S. Saravanan, K. Reddy, Shock tunnel study of spiked aerodynamic bodies flying at hypersonic mach numbers, Shock Waves 12 (3) (2002) 197–204. [11] D. Sahoo, S. Das, P. Kumar, J. Prasad, Effect of spike on steady and unsteady flow over a blunt body at supersonic speed, Acta Astronaut. 128 (2016) 521–533. [12] C.W. Brooks, C.D. Trescot, Transonic Investigation of the Effects of Nose Bluntness, Fineness Ratio, Cone Angle, and Base Shape on the Static Aerodynamic Characteristics of Short, Blunt Cones at Angles of Attack to, National Aeronautics and Space Administration, 1963. [13] D.C. Wilcox, et al., Turbulence Modeling for CFD vol. 2, DCW industries La Canada, CA, 1993. [14] D.C. Wilcox, Formulation of the kw turbulence model revisited, AIAA J. 46 (11) (2008) 2823–2838. [15] M.B. Gerdroodbary, S. Bishehsari, S. Hosseinalipour, K. Sedighi, Transient analysis of counter flowing jet over highly blunt cone in hypersonic flow, Acta Astronaut. 73 (2012) 38–48. [16] ANSYS® Fluent, Release 15.0. [17] B. John, G. Sarath, V. Kulkarni, G. Natarajan, Performance comparison of flux schemes for numerical simulation of high-speed inviscid flows, Progress Comput. Fluid. Dynamics, Int. J 14 (2) (2014) 83–96. [18] J. White, Alaa 93-0968 Application of Navier-Stokes Flowfield Analysis to the Aerothermodynamic Design of an Aerospike-Configured Missile, (1993). [19] B. John, V. Kulkarni, Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed, Comput. Fluids 96 (2014) 177–190 https://doi.org/10.1016/j.compfluid.2014.03.004.
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