Novel design methodology of integrated waverider with drip-like intake based on planform leading-edge definition method

Journal Pre-proof Novel design methodology of integrated waverider with drip-like intake based on planform leading-edge definition method Shao-Hua Chen, Jun Liu, Feng Ding, Wei Huang PII:

S0094-5765(19)31384-0

DOI:

https://doi.org/10.1016/j.actaastro.2019.11.007

Reference:

AA 7752

To appear in:

Acta Astronautica

Received Date: 12 July 2019 Revised Date:

1 November 2019

Accepted Date: 4 November 2019

Please cite this article as: S.-H. Chen, J. Liu, F. Ding, W. Huang, Novel design methodology of integrated waverider with drip-like intake based on planform leading-edge definition method, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.11.007. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 IAA. Published by Elsevier Ltd. All rights reserved.

Novel design methodology of integrated waverider with drip-like intake based on planform leading-edge definition method Shao-Hua Chen1, 2*, Jun Liu1, 2, Feng Ding1, 2, Wei Huang1, 2 1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China 2. Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China Abstract: Based on the planform leading-edge definition method, a novel methodology for designing an inlet-airframe integrated waverider vehicle, has been proposed and the resulting intake owns the superiority of the drip-like shape. In this study, the design of the vehicle contour relies on the axisymmetric basic flowfield and leading-edge planform curves, namely the former is presently generated by a shock wave curve, and the latter produces a drip-like intake, on account of the 3D cowl lip curve. Importantly, defining the leading edge on the horizontal projection plane facilitates to adjust the planform shape of the integrated waverider and the sweep angle of the wing. At last, the new design methodology is proved to be effective to design an integrated hypersonic waverider vehicle. This study provides more options for designing novel inlet-airframe integrated hypersonic vehicles. Keywords: Integrated hypersonic waverider vehicle; drip-like intake; planform leading-edge definition; forebody-inlet and airframe axisymmetric basic flow model

*

Professor, corresponding author, E-mail: [email protected], Phone: +86 731 84576452, Fax: +86 731 84576447 1

Nomenclature MOC

Method of characteristics

Μ0

Free-stream Mach number

P0

Free-stream pressure, Pa

T0

Free-stream temperature, K

θ DC ,2 ( x )

Distribution of flow angle θ just downstream of the cowl shock wave DC, °

δ CG ( x )

The x-coordinate tilt angle δ along CG, °

M CG ( x )

The x-coordinate Mach number M along CG

xCF

x-direction coordinate distance between points C and F, m

δA

Tilt angle of curve AR at point A, °

δE

Tilt angle of streamline DE at point E, °

α

Angle of attack, °

1.

Introduction A hypersonic vehicle has broad development prospects [1]-[5]. It is notable that an air-breathing hypersonic

vehicle has shown significant improvement [6]-[9] on practical application. Lewis [10] pointed out that the propulsion system and airframe of an air-breathing hypersonic vehicle are difficult to distinguish from each other. Hence, an inlet-airframe integrated design concept is required. According to previous studies, the development of an integrated methodology relies on the advanced component design methods [11]-[13] and efficient integrated concepts [2], [14]-[16].

2

As an effective aerodynamic shape design methodology, the waverider [17] has a high lift-to-drag ratio [13] and effective air capture and compression abilities [18]. However, the integration between the engine and waverider intended for the design of air-breathing hypersonic vehicles may result in a decrease of the lift-to-drag ratio against the waverider configuration [19]. According to the waverider design methodology, the compression surface[3] is lofted by a number of streamlines starting at the leading-edge curve located on the shock wave surface of the basic flowfield [20]. The downstream streamline tracing technique [21] is applied in most situations. To achieve this, the coordinates of the leading-edge points along the leading-edge curves should be given before solving the streamlines. Kontogiannis et al. [22] listed two common approaches to obtain a leading-edge curve, namely an upper surface profile definition (USPD) and a planform leading edge definition (PLED). Therefore, the basic flowfield design method and the leading-edge definition are also of significance in the integrated methodology. The leading-edge angle based on PLED is an important parameter for a hypersonic vehicle design. To improve the lateral stability of crew re-entry vehicles based on the waverider design method, the wingtip fins are integrated into the CRV design by specifying a sweep angle [23]. In addition, Rana et al. [24] determined that typical leading-edge angles for hypersonic vehicles are 70°–78° according to several application projects on a lifting-body re-entry hypersonic vehicle. Moreover, the planform geometrical parameters require a free adjustment during the practical design procedure. Thus, the PLED is extremely useful and will be adopted in this study. Ding et al. [2] summarized two classes of a waverider design concept in an airframe/inlet integrated methodology for an air-breathing hypersonic vehicle. In the second class, namely, the airframe/inlet integration design methodology, by utilising the waverider’s high lift-to-drag ratio and the precompression ability of the engine, the waverider is applied to the entire vehicle design, including the wings and cowl. For example, an

3

integrated methodology put forward by Ding et al. [16] was used to generate an air-breathing hypersonic waverider vehicle, whose leading-edges of the entire body are attached to the bow shock wave of a basic flowfield. Considering the excellent features of the integrated concept, this paper advances the methodology and introduces some improvements for practicality. In Ref. [16], a basic inlet-airframe integrated axisymmetric flowfield model was introduced to the waverider airframe/inlet hypersonic vehicle design. In addition, all compression surface streamlines are solved in this basic flowfield. First, a basic axisymmetric flowfield is generated through an axisymmetric body using the method of characteristics (MOC) [25]. The cowl lip plane is the intersection of a bow shock wave and the left-running Mach line (originating from a point in an axisymmetric body contour). Therefore, the cowl lip plane cannot be pre-designed. In addition, the x-coordinate of the cowl lip plane is constant in all meridian planes. Thus, the cowl lip contour is only a circular arc, and this imposes a restriction on its future practical application. Based on the inlet-airframe integrated concept, an improved scheme is put forward in this study. First, a new basic flowfield model is generated through the airframe shock wave and the compression surface instead of the axisymmetric body. Second, the leading-edge curve is defined based on the planform leading-edge curve. In addition, the x-coordinate of the cowl lip curve will be adjustable in the width direction. Hence, the cowl lip turns into a three-dimensional curve free from the restriction of the in-plane arc. For this, a novel methodology of an inlet-airframe integrated waverider with a drip-like intake is developed in this study.

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2.

Design methodology of integrated waverider vehicle with a drip-like intake Fig. 1 shows a schematic representation of an integrated waverider vehicle with a drip-like intake and basic

flowfield (isentropic view). To be clear, the new design methodology inherits the design principle in Ref. [16]. Two modifications are adopted in this research. First, the axisymmetric generating shock wave of the basic flowfield is directly designable, as illustrated in Fig. 1. Second, the planform leading-edge definition method is applied. To do so, the cowl lip is expanded into a 3D curve. As shown in Fig. 1, the leading edge of the 3D cowl lip curve and the forebody form a drip-like intake. 2.1. Design methodology of the basic integrated axisymmetric flowfield The basic flowfield applied in Ref. [16] can be divided into two types. One, termed a basic airframe flowfield (external flow), is used to generate the lower surface of the wings and the exterior of the cowl. The other, called the basic forebody-inlet flowfield (internal-external integrated flow), serves the generation of the forebody-inlet surface. Detailed descriptions of the basic flowfield used in this study are provided below. A. Basic airframe flowfield design methodology Fig. 2 shows a schematic illustration of the basic airframe flowfield, ABR, defined in a two-dimensional cylindrical coordinate system, which is identical in any meridian plane. All crucial details are shown in Fig. 2. Region ABR has two different parts: AC1R and C1BR. Here, AC1R is a so-called shock-dependent region. The remaining region, C1BR, is the compression region. In addition, they are solved in order by the MOC. First, the AC1R region dependent on the given shock wave AR and free-stream condition (M0, P0, and T0) can be easily

solved. The shock wave curve function of AR is a third-order equation, as expressed in Eq. (1). The body contour AC1 is a streamline originating from point A, which is obtained using the streamline tracing technique when

solving the AC1R region. Meanwhile, the left-running Mach line C1R as the boundary between the AC1R and C1BR regions is another solution product. In addition, C1R intersects the shock AR at point R. The start and base plane of 5

the basic flowfield is the cross-section passing through point A and point R, respectively. Second, the C1BR region can be defined based on the body contour C1B and the solved boundary condition C1R. Here, C1B joins smoothly with the streamline AC1 at point C1, which is expressed by a cubic polynomial

equation (i.e., Eq. (1)) in the same cylindrical coordinate system[36] used in Fig. 2. According to Ref. [36], C1B can also be used to adjust the pressure distribution of the basic flow field ,which is helpful to optimize the shape and aerodynamic performance of the hypersonic waverider vehicle. r = a + bx + cx 2 + dx3

(1)

B. Basic forebody-inlet flowfield design methodology The basic flowfield ACGFED presented in Fig. 3 is used to generate a streamlined forebody-inlet surface. The ACGFED region is segmented by the cowl shock wave DC on the external and internal flows. The forebody shock AD part of the shock AR, the cowl shock wave DC, and the body contour AC build up the basic forebody flowfield ACD. The basic inlet flowfield is constituted by the cowl shock wave DC, cowl interior DEF, and centre body CG. It is notable that, along with the variation of the cowl lip plane, the basic forebody-inlet flowfield ACGFED changes accordingly.

In addition, the basic forebody flowfield (ACD region) shown in Fig. 3 is part of the basic airframe flowfield (ABR region) in Fig. 2. Therefore, the ACD region requires no repetitive calculations. However, region DCGFE, namely the basic inlet flowfield shown in Fig. 3, should be designed and solved by referring to Ref. [16]. A brief description of the solution steps and necessary input conditions are discussed below. Step 1: the solution of the cowl shock wave DC, as shown in Fig. 4. Ding et al. [16] adopts the flow angle after the cowl shock wave shown in Eq. (2) to control the locations and flow properties of the cowl shock wave which are solved by the predictor-corrector method.

6

θ DC ,2 = θ DC ,2 ( x ), x ∈ [ xD , xC ]

(2)

Step 2: the solution to the cowl shock-wave dependent region DCE and wall DE, as indicated in Fig. 5. Step 3: the solution to the cowl exterior EF and the CGFE region, as presented in Fig. 6. The cowl exterior and corresponding flow region are also solved by the MOC based on the distribution of Mach number and flow angle along the wall CG, as expressed by Eqs. (3) and (4). According to Ref. [16], the downstream boundary of the region CGFE is the Mach line GF the positions are of which are determined by xCF, that is to say the x-coordinate of point F.

δ CG = δ CG ( x ), x ∈ [ xC , xG ]

(3)

M CG = M CG ( x ), x ∈ [ xC , xG ]

(4)

2.2. Design methodology of integrated waverider vehicle with a drip-like intake based on the planform leading-edge definition method Fig. 7 demonstrates the integrated waverider vehicle with a drip-like intake based on the PLED method [22]. The leading-edge curves are solved by vertically projecting the planform leading-edge curves on the axisymmetric shock wave. Considering the symmetry of the vehicle, only the right half of the vehicle is presented. The dashed curve in Fig. 7 is not only the planform profile of the basic flowfield, but also the boundary of the basic flowfield. The thick solid curves are the leading edges of different components, as defined in Fig. 7. According to the design principle of the waverider, the above leading-edge curves are attached to the given axisymmetric shock wave, as shown in Fig. 1. Thus, the positions of the planform leading-edge curves cannot exceed the boundary of the basic flowfield between the start and base planes. Free from the restriction in Ref. [16], the planform profile curve of the cowl lip (curve 3-4 in Fig. 7) is designable. As indicated in Fig. 1, the cowl lip may be designed as a three-dimensional curve on the shock wave.

7

From the perspective of the basic flowfield used for to solve the streamlines constituting the surface, the integrated waverider vehicle is divided into two parts, namely an airframe and a forebody-inlet. According to Ref. [16], the airframe has two different components, namely the exterior cowl and the wings, which are intended to produce a high lift for the vehicle; the forebody-inlet used for air compression is composed of the forebody-inlet and cowl interior. The detailed design processes are discussed below. A. Design methodology of the airframe Fig. 8 shows the streamline DH used for the constitution of the cowl exterior. The cross point of the shock curve AR and a cowl lip curve 3-4 on the shock wave is the cowl lip point D. Point D is the start of the streamline of the cowl exterior DH, which is solved in the basic flowfield ABR of the airframe, as shown in Fig. 9. In addition, the position of point D along the corresponding meridian is determined based on the cowl lip plane, as indicated in Fig. 8 and Fig. 9. As depicted in Fig. 10, MN is the streamline of the down surface of the wing. Point M as the start of the streamline MN is the intersection point of the shock curve AR and leading-edge curve of wing 3-1. In addition to the streamline DH shown in Fig. 9, the streamline MN is also solved in the ABR region, as depicted in Fig. 11. B. Design methodology of the forebody and inlet The streamline DF presented in Fig. 12 is used to loft the cowl interior, and it is obtained during the process of solving the basic forebody-inlet flowfield shown in Fig. 6. It should be noted that the basic flowfield in Fig. 6 is not identical along the different meridian planes owing to the x-axis direction shift of the cowl lip plane, as depicted in Fig. 3. From the above descriptions, the basic flowfield used to solve the streamlines of the forebody and inlet depends on the cowl lip plane. For example, all streamlines of the forebody-inlet can be solved along a similar

8

meridian plane, as demonstrated in Fig. 13. The coordinate of start point P should be determined before the streamline tracing process as well. As displayed in Fig. 13, point P is the intersection of the leading-edge curve of forebody and the shock wave curve AD. Thus, the streamline PQ streamline traced in the ACGFED region, as shown in Fig. 14.

3.

Calculation example generation and numerical method 3.1. Example generation As shown in Fig. 15, a test case used for verification of the integrated waverider vehicle with a drip-like

intake, is generated. The geometrical parameters of the vehicle and its shape are presented in Fig. 16. In addition, all dimensions mentioned above are in millimetres. The design parameters of two types of basic flowfield are listed in Table 1 and Table 2. The parameters in Table 1 are used to determine the basic flowfield of Fig. 2. The two-dimensional cylindrical coordinates of points A and R, together with the shock wave angles at these two points, are used to solve the equation of the shock curve AR as expressed in Eq. (1). Similarly, the equation of the body contour curve C1B depends on points C1 and B. In

addition, the coordinate and slope of curve C1B at C1 can be defined by the curve AC1 when solving the region AC1R, as shown in Fig. 2. The coordinate of B is expressed in Eq. (5). As listed in Table 2, the input parameters

are applied for the design of the DCGFE region in Fig. 3. According to Ref. [16], the Mach number at point C is applied for the flow along the wall CG, as shown in Eq. (6) . rB = rc1 + ( xR − xc1 ) tan(δ c1 )

(5)

MCG(x) = MC

(6)

According to the design method illustrated in Fig. 7, the leading edges of different components including forebody-inlet and wings are defined by their planar contours. As shown in Eqs. (7) and (8) planar contours of the cowl lip and forebody have a parabolic equation, defined by two endpoints and the power, in terms of controlling 9

the slope at point 2 and point 4 as 90°. As illustrated in Fig. 17 (a), the position of point 2/3/4 are defined by the input paraments namely L1, L2, L and Wcowl. The coefficients, a1, b1, a2, b2 in Eq. (7) can be determined by Eqs. (9) to (12). The input parameters are depicted in Fig. 16. For simplicity, the power of the parabolic equation is set as 0.4. The mathematical forms of planform leading-edge curves of cowl lip and forebody are shown in Eqs. (15) and (16). z = a1 × ( x + b1 ) 1

(7)

z = a2 × ( − x + b2 )

(8)

n

a1 =

n2

Wcowl 2 L1n1

(9)

b1 = − xB + L a2 =

1 xB − L + L1  xB 1  1 0 0 1

(10)

Wcowl 2 Ln22

(11)

b2 = xB − L + L1 + L2

(12)

z = a3 + b3 x + c3 x 2 + d3 x3

(13)

( xB − L + L1 ) x

2

2 B

2 ( xB − L + L1 ) 2 xB

( xB − L + L1 )

  3 xB  2 3 ( xB − L + L1 )   3xB2 3

-1

0.5Wcowl   a3   0.5W   b   = 3   tan δW 1   c3       tan δW 2   d3 

(14)

In addition, the planform leading-edge curve of the wing is a third-order equation as shown in Eq. (13). As shown in Fig. 17 (b), given the slope at point 1/3 as well as the two points’ coordinate, the coefficients of Eq. (13) will be obtained by Eq. (14). Hence, the adjustment of the slope at two end-points can indirectly control the sweep angle along the leading-edge of the wing. And the width of the vehicle can be easily controlled through point 1. As the geometric parameters displayed in Fig. 16, the mathematical form of planform leading-edge curve of wing is shown in Eq. (17)

z =0.462974 × ( - x +2.8 ) 10

0.4

(15)

z =0.50 × ( x + 5.0) 0.4

(16)

z =0.001101x 3 + -0.007481x 2 + 0.183333x + -0.186093

(17)

As observed in Fig. 15, the design purpose of a drip-like intake formed in an integrated waverider vehicle is achieved. To validate the design methodology in this study, the detailed verifications of the flow structure of the basic integrated axisymmetric flowfield, as well as the vehicle traveling under the design conditions, are described in the next section. 3.2. Numerical approaches As mentioned above, the basic flowfield used for solving streamlines is a two-dimensional isentropic supersonic flow which can be quickly solved by MOC [25]. Thus, validations of the integrated waverider vehicle and the basic flowfield [16] is described through the inviscid flow fields employing Euler equations applying a density-based implicit solver provided by ANSYS Fluent [26].In addition, the second-order accurate AUSM method as a spatially upwind scheme is used to solve the flux vector. The least-squares cell-based gradients evaluation is applied in this study. To reduce the possibility of divergence, the CFL number is set below 0.5 [16] during the computation process.

The implicit coupled RANS equations and the k-ω SST as a turbulence model [16][27], are applied for the simulation of viscous flow fields as well as viscous aerodynamic performances, of the test case by ANSYS Fluent [26]. Particularly, the AUSM as a common numerical discretization method, namely the second order spatially accurate upwind scheme [28], is applied to solve the flux vector. The gradients are computed by the Green-Gauss cell-based gradient method [29]. The enhanced wall treatment [26] is used to deal with the flow in the near-wall region, and the walls use the adiabatic and no-slip boundary condition [12][30]. The air adopts the thermally and calorically perfect gas model [16][31]. The fluid viscosity is defined as the function of temperature and the

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function type namely the Sutherland Law [32] is expressed by Eq. (18).

T 1.5 µ =1.458 × 10 T + 110.4 -6

(18)

According to Ref. [16], the converge conditions mainly depend on the concerned values and the computed mass flux of the inflow and outflow. First, the relative difference of two concerned value between different steps is less than four orders of magnitude. Second, the mass flow rate through the boundaries of the computation region is smaller than 0.1% of that of the inflow or outflow. According to the previous descriptions, two types of basic flowfield need to be validated. However, considering the connection and succession between the above two types of basic flowfield, only the verification of the basic forebody-inlet flowfield presented in Fig. 6 is implemented. As shown in Fig. 20, a structured grid of 1,017,651 cells is used to validate the basic forebody-inlet flowfield solved using the MOC. In addition, the design parameters of the basic forebody-inlet flowfield presented in Fig. 20 are listed in Table 2. The unstructured grid generated for the numerical computation of the inviscid flowfield of the integrated waverider vehicle is shown in Fig. 23. In addition, the boundary condition of inlet and outlet are set as far field pressure and outlet pressure, respectively. Due to the size of the test case, only half of the entire symmetrical flow field is employed for computation to reduce the considerable number of grid cells, which may reach the magnitude of ten million. And, the number of grid cells used for calculation is 12,799,343. As shown in Table 1, the free-stream boundary conditions for computation are listed. And the free-stream pressure (P0) and temperature (T0) uses the atmosphere parameters at the height of 25km. 3.3. Code validation According to the numerical computational results of the space shuttle [33] and the overall inlet geometry [34]-[35] in Ref. [16], the numerical method and an unstructured grid were verified as being able for the 12

simulation of airbreathing hypersonic vehicle with acceptable error tolerance. As mentioned in Ref. [37], the gird independency of structured grid employed in the space shuttle was verified and the grid scale makes only a slight difference. In addition, the comparisons [16] have been made to assess the influence of unstructured grid and structured grid on the viscous aerodynamic performance of hypersonic. It turns out that, when the angle of attack is no more than 15°, both the unstructured grid and the structured grid are in good agreement with the aerodynamic performance of the experiment in Ref. [33]. Considering the complex geometrical structure of the integrated waverider vehicle, the unstructured grid, which is much more efficient from a grid-generation standpoint, will be used for the verification of the design methodology in this study. For the verification of generation method of the unstructured gird and the the accuracy of the numerical methods employed in this study, experiment model of the space shuttle [33] (shown in Fig. 18) in a wind tunnel is applied for validation. As shown in Table 3, the numerical computation’s free-stream boundary conditions are set up based on the experiment [33]. As shown in Fig. 19. By comparing the results shown in Fig. 19, it is also found that, the aerodynamic performance calculated by the turbulence model, namely k-ω SST, closely match the experiment’s result [34]. In that, the unstructured gird-generation method and the viscous numerical methods are useful in this study.

4.

Results and discussion In this part, the basic axisymmetric integrated flowfield next to an integrated waverider vehicle as verified

through a numerical simulation is described. In addition, the numerical simulation method used for the validations are discussed before analyzing the predicated results. 4.1. Verification of the basic integrated axisymmetric flowfield generation The verification of the MOC used for the calculation of the basic flowfield is carried out by the comparing the Mach contour lines calculated by MOC with the ones by Euler code based on the commercial software 13

FLUENT which has been verified in various studies [16]. As shown in Fig. 21, the cowl shock wave and the body shock wave solved whether by the Euler code or the MOC are nearly identical. In addition, there are no important differences between the Mach number distributions in the ADEFGC region obtained from the MOC and by Euler code. As presented in Fig. 22, the green dots represent the streamline-traced points along the streamline originating at point S in the ADEFGC region. In addition, the black curve with arrows is the streamline starting at the same point S, and it is obtained in the post-processing software TECPLOT. As Fig. 22 indicates, the streamline points solved through the streamline tracing technique clearly fit well with the streamline obtained by the post-processing software TECPLOT. In view of the above analysis, the MOC and streamline tracing technique used in the study are proved to be effective. 4.2. Verification of vehicle generation As shown in Fig. 24, the shock wave at different x-coordinate planes is attached to the leading edges of different conbination parts including forebody-inlet and the body-wing. As mentioned in Ref. [16], the above vehicle, at least the outflow component, is proved to meet the the basic design requirement of an integrated waverider vehicle. Next, a detailed verification of the inlet and the isolator generation, especially the shock wave patterns of the flow field, is provided. As the Mach contour lines shown in the two sliced meridian planes (expressed as Φ ) in Fig. 25, the locations of predicted shock wave including the forebody-inlet shock wave and body shock wave are nearly identical to the designed ones. The meridian plane at Φ =0o is the symmetric plane. The purple plane is another meridian plane at Φ =15o . In addition, the shock patterns of the two meridian planes are identical. In that, the flow field of the meridian plane at Φ =15o is selected for analysis in detail. By comparison, the shock patterns exhibited in the meridian plane at Φ =15o of Fig. 25 are well matched with the shock wave PD and the cowl shock wave DS of the forebody-inlet basic flowfield, as shown in Fig. 14, as well as

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the shock wave DR of the basic airframe flowfield depicted in Fig. 9. As illustrated in Fig. 26(a) and (b), the dashed lines serve as the designed shock wave. By contrast, the shock wave patterns including the cowl shock wave of the predicted ones and the designed ones are in good agreement. Moreover, the cowl shock wave is almost entirely called off on the centre body. On different x-direction and two meridian planes sliced from the flow field by numerical computation, the observed shock wave pattern and locations are identical to the designed ones. Thus, the design procedure is proved to be effective under the design condition. 4.3. Analysis on the viscous effects and performance of the integrated waverider vehicle

A. Viscous effects analysis As shown in Fig. 27, the assessment of the viscous effects are baesd on the non-dimensional pressure contours at two sliced meridian planes. In this part, the comparison of the predicted shock wave locations and the designed ones signified by the dashed lines will be discussed. In addition, several evaluation criterions in aerodynamic performance of airbreathing hypersonic vehicle, shown in Table 4, are adopted to quantitatively evaluate the viscous effects. In Table 4, area-weighted average values [16], such as Me, Pe/P0, Te/T0, Pe,t/P0,t, m&, and σ are used to estimate the effect of viscosity on the performance evaluation of the inlet relative to the inviscid aerodynamic performance. Considering the overall aerodynamic performance, the general parameters [16] including CL, CD, L/D, and Cmz are adopted to evaluate the performance of the entire vehicle. A comparison between viscous and inviscid computation case would find out that, a similar cowl shock wave pattern, as depicted in Fig. 27 (a), is also observed. However, a remarkable drift of the end position of the cowl shock is identified. Hence, the slight variation of the cowl shock wave distinguishes the viscous result from the inviscid case shown in Fig. 27 (a). In addition, the impinging position of the cowl shock wave deviates upstream,

15

and it causes the cowl shock wave uncancelled. Specifically, the reflected shock wave is created, and a subsequent shock wave train is developed in the inlet isolator. Due to the viscous effect, the generated boundary layer and the shock wave/boundary layer interactions are the reasons. As discovered in another meridian plane of Φ = 30°, shown in Fig. 27 (b), the deviation of the cowl shock wave does not lead to a reflected shock wave due to the reduced shock wave strength. In short, the boundary layer caused by the viscosity appears in the flow field is the main reason for the slight drift of the cowl shock wave at the end position. As Table 4 suggests, the mainly affected evaluation parameters are the ones for the inlet, such as Me, Pe/P0, Te/T0, Pe,t/P0,t, and the ones for the entire vehicle, that is CD, Cmz, and L/D. The above parameters are sensitive to the viscous effect accordingly. However, the results in Table 4 also implies that the parameters, such as m&, σ change very little. Thus, it can be inferred that the captured air flow of the integrated waverider vehicle almost remains unchanged or little decreases when considering viscous effect. Due to the pressure rise of the captured air, the lift of the entire vehicle (CL) even increases with nearly 10%. But the augmented pressure on the wall also causes a negative effect, that is an increased drag (CD), on the aerodynamic performance of the vehicle.

B. Performance analysis As seen in Fig. 28, the curves of lift-to-drag ratio, lift / drag coefficients and Cmz ratio versus attack angles are given. The reference area and length are the area of the base plane and the length of the vehicle, respectively. And the reference moment point is the geometrical centre of the vehicle. As Fig. 28(c) indicates that the maximal lift-to-drag ratio can get 4.0 at 4° attack angle. As seen in Table 5, some key geometric parameters of test case shown in Fig. 15 are listed. In Table 5, the width (W) and the length (L) of the vehicle are predefined. After the generation process of the whole integrated waverider vehicle, the internal volume (Vol) and the wet surface area (Swet) can be calculated by CAD software. In

16

addition, η namely the volumetric efficiency defined by Eq. (19) will be obtained based on the above two geometrical parameters.

η=Vol2/3/Swet

5.

(19)

Conclusions Based on a novel inlet–airframe integrated methodology, the drip-like intake is integrated to the vehicle. For

the validation of the design methodology, the on-design flow field of an integrated waverider vehicle obtained by numerical computation is applied for verifications. At last, a few conclusions are drawn based on the investigations into the flow field and the performance of the test case.




The flowfield structures solved by two different CFD namely the MOC and Euler code, are nearly identical. In addition, the streamline points solved through the streamline tracing technique clearly fit well with the streamline obtained by the post-processing software TECPLOT. In that, the MOC and streamline tracing technique used for designing the proposed methodology are proved to be effective.




On different x-direction and two meridian planes sliced from the flow field through numerical computation, the observed shock wave pattern and locations are identical to the designed ones. Thus, the design procedure is proved to be effective under the design condition.




The viscous effects mainly affect the flowfield in the inlet. And the boundary layer along the wall brings the deviation of the cowl shock wave. Thus, the reflected shock wave and the shock train are generated in the inlet and isolator.




Based on the quantitative analysis of the viscous and inviscid results, it is concluded that the mass flux of the flow captured by the inlet nearly remains stable. However, the viscous effect will reduce the aerodynamic performance of an integrated waverider vehicle including the entire vehicle’s lift-to-drag ratio and the 17

compressed air-flow quality for the engine.

6.

Further studies The improvement from a drip-like intake being introduced into an integrated waverider vehicle requires

further investigation. Considering the practicality of the application in a hypersonic cruise vehicle design, the unitary design methodology, including the combustor and nozzle, is a key research subject. Thus, optimisation of the basic axisymmetric flowfield is another study direction towards the achievement of future applications. In the future, the experiments should be carried out for further validation and some detailed researches.

Acknowledgements The authors express their gratitude for the financial support provided by the National Natural Science Foundation of China (grant number 11702322) and the Natural Science Foundation of Hunan Province of China (grant number 2018JJ3589). The authors are also extremely grateful to the reviewers for their constructive comments and suggestions.

18

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[15] X.-d. Wang, J.-f. Wang, Z.-j. Lyu, A new integration method based on the coupling of multistage osculating cones waverider and Busemann inlet for hypersonic airbreathing vehicles, Acta Astronautica, 126 (2016) 424-438. [16] F. Ding, J. Liu, C.-b. Shen, W. Huang, Novel inlet-airframe integration methodology for hypersonic waverider vehicles, Acta Astronautica, 111 (2015) 178-197. [17] T.R.F. Nonweiler, Delta wings of shapes amenable to exact shock-wave theory, Journal of the Royal Aeronautical Society, 67 (1963) 39-40. [18] W. Huang, L. Ma, Z.G. Wang, M. Pourkashanian, D.B. Ingham, S.B. Luo, J. Lei, A parametric study on the aerodynamic characteristics of a hypersonic waverider vehicle, Acta Astronautica, 69 (2011) 135-140. [19] M.J. Lewis, Application of waverider-based configurations to hypersonic vehicle design, AIAA Paper 91-3304, 1991. https://doi.org/10.2514/6.1991-3304 [20] F. Ding, J. Liu, C.-b. Shen, Z. Liu, S.-h. Chen, X. Fu, An overview of research on waverider design methodology, Acta Astronautica, 140 (2017) 190-205. [21] F.S. Billig, A.P. Kothari, Streamline tracing: Technique for designing hypersonic vehicles, J. Propul. Power, 16 (2000) 465-471. [22] A.S. Konstantinos Kontogiannis, N. Taylor, On the conceptual design of waverider forebody geometries, 53rd AIAA Aerospace Sciences Meeting, Kissimmee, Florida, AIAA Paper 2015-1009, 2015. https://doi.org/10.2514/6.2015-1009 [23] M.A. Lobbia, Multidisciplinary Design Optimization of Waverider-Derived Crew Reentry Vehicles, Journal of Spacecraft and Rockets, 54 (2017) 233-245.

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[24] L. Rana, T. McCally, J. Haleyz, B. Chudoba, A parametric sizing study on the effects of configuration geometry on a lifting-body reentry vehicle, AIAA SPACE and Astronautics Forum and Exposition, AIAA Paper 2017-5356, 2017. https://doi.org/10.2514/6.2017-5356 [25] M.J. Zucrow, J.D. Hoffman, Gas Dynamics, Vol. 2: Multidimensional Flow, John Wiley and Sons, Inc., New York, 1977. [26] Fluent Inc., ANSYS, Inc. ANSYS FLUENT 13.0 Theory Guide, 2010. [27] F. Ding, J. Liu, C.-b. Shen, W. Huang, Simplified Osculating Cone Method for Design of a Waverider, Volume 1 Aircraft Engine Fans and Blowers Marine, 2015. [28] W. Huang, Z. G. Wang, J. P. Wu, S. B. Li, Numerical prediction on the interaction between the incident shock wave and the transverse slot injection in supersonic flows. Aerospace Science and Technology, 28(1), 91–99, 2013. [29] H. Li, J. Tan, D. Zhang, J. Hou, Investigations on flow and growth properties of a cavity-actuated supersonic planar mixing layer downstream a thick splitter plate, International Journal of Heat and Fluid Flow, 74 (2018) 209-220. [30] F. Ding, J. Liu, W. Huang, C. Peng, S. Chen, An airframe/inlet integrated full-waverider vehicle design using as upgraded aerodynamic method, The Aeronautical Journal, 123 (2019) 1135-1169. [31] W. Huang, W.D. Liu, S.B. Li, Z.X. Xia, J. Liu, Z.G. Wang, Influences of the turbulence model and the slot width on the transverse slot injection flow field in supersonic flows, Acta Astronautica, 73 (2012) 1-9. [32] X.Q. Chen, Z.X. Hou, J.X. Liu, X.Z. Gao, Bluntness impact on performance of waverider, Computers & Fluids, 48 (2011) 30-43.

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[33] S.X. Li, The flow characteristics for the typical model in hypersonic flows, National Defence Industry Press, Beijing, 2007. [34] D.M. Schmitz, N.C. Bissinger, Design and testing of 2-D fixed-geometry hypersonic intakes, Proceedings of the AIAA Paper 98-1529, 1998. [35] B.U. Reinartz, C.D. Herrmann, J. Ballmann, Aerodynamic performance analysis of a hypersonic inlet isolator using computation and experiment, J. Propul. Power, 19 (2003) 868-875. [36] F. Ding, C.-b. Shen, J. Liu, W. Huang, Influence of surface pressure distribution of basic flow field on shape and performance of waverider, Acta Astronautica, 108 (2015) 62-78. [37] F. Ding, C.-b. Shen, J. Liu, W. Huang, Comparison between novel waverider generated from flow past a pointed von Karman ogive and conventional cone-derived waverider, Proceedings of the Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering, 229 (2015) 2620-2633.

23

Figure captions Fig. 1 Schematic illustration of integrated waverider vehicle with drip-like intake and basic flowfield (isentropic view). Fig. 2 Schematic illustration of the basic airframe flowfield. Fig. 3 Schematic illustration of the basic forebody-inlet flowfield. Fig. 4 Schematic illustration of the solution step to determine the cowl shock wave DC. Fig. 5 Schematic illustration of the solution step to determine wall DE and region DCE. Fig. 6 Schematic illustration of the solution step to determine cowl exterior EF and region CGFE. Fig. 7 Schematic illustration of the integrated waverider vehicle with a drip-like intake (planform view). Fig. 8 Schematic illustration of the streamline of cowl exterior (planform view). Fig. 9 Schematic illustration of the streamline of cowl exterior in the basic airframe flowfield (meridian plane). Fig. 10 Schematic illustration of the streamline of wing (planform view). Fig. 11 Schematic illustration of the streamline of wing in the basic airframe flowfield (meridian plane). Fig. 12 Schematic illustration of the streamline of cowl interior (planform view). Fig. 13 Schematic illustration of the streamline of cowl interior and forebody-inlet (planform view). Fig. 14 Schematic illustration of the streamline of cowl interior and forebody-inlet in basic forebody-inlet flowfield (meridian plane). Fig. 15 Geometric model of the test case (a) top view, (b) upward view (without cowl exterior), and (c) upward view. Fig. 16 Shape and dimensions of the test case (unit: mm) Fig. 17 Schematic illustration of input parameters of leading-edge planform curves: (a) forebody and cowl lip, (b)

24

wing Fig. 18 Experimental space shuttle model used for wind tunnel experiments. Fig. 19 Comparison of viscous aerodynamic performances of the space shuttle as calculated using numerical computation and measured during the wind tunnel experiment. Fig. 20 The structured grid of the basic forebody-inlet flowfield on the symmetric plane of the test case Fig. 21 Comparison of Mach number contour lines of the basic integrated axisymmetric flow obtained using the Euler code and MOC Fig. 22 Comparison of streamline and streamline points obtained in TECPLOT and using the streamline tracing technique Fig. 23 Unstructured mesh of the test case. Fig. 24 Inviscid Mach number contour lines on different x-direction planes under the design condition (M0 = 6,

α = 0°). Fig. 25 Inviscid Mach number contour lines on two meridian planes under the design conditions (M0 = 6, α = 0°). Fig. 26 Inviscid non-dimensional pressure contour lines on meridian planes of integrated waverider vehicle under the design condition (M0 = 6, α = 0°). Flow fields at (a) on the symmetric plane of Φ = 0° and (b) on the meridian plane of Φ = 15°. Fig. 27 Viscous non-dimensional pressure contour lines on meridian planes of integrated waverider vehicle under the design condition (M0=6, α = 0°): flow fields (a) on the symmetric plane of Φ = 0° and (b) on the meridian plane of Φ = 30°. Fig. 28 Inviscid aerodynamic performances of test case. (a) Lift coefficient, (b) drag coefficient, (c) lift-to-drag ratio, and (d) pitching moment coefficient.

25

Table captions Table 1 Input parameters applied in the basic airframe axisymmetric flow model Table 2 Input parameters applied in the basic forebody-inlet axisymmetric flow model Table 3 Boundary conditions for the free stream applied in the experiment [34] Table 4 Comparison of inviscid and viscous performance of integrated waverider vehicle Table 5 Geometric parameters of integrated waverider vehicle

26

Fig. 1 Schematic illustration of integrated waverider vehicle with drip-like intake and basic flowfield (isentropic view).

Fig. 2 Schematic illustration of the basic airframe flowfield. 27

Fig. 3 Schematic illustration of the basic forebody-inlet flowfield.

Fig. 4 Schematic illustration of the solution step to determine the cowl shock wave DC.

28

Fig. 5 Schematic illustration of the solution step to determine wall DE and region DCE.

Fig. 6 Schematic illustration of the solution step to determine cowl exterior EF and region CGFE.

29

Fig. 7 Schematic illustration of the integrated waverider vehicle with a drip-like intake (planform view).

Fig. 8 Schematic illustration of the streamline of cowl exterior (planform view).

30

Fig. 9 Schematic illustration of the streamline of cowl exterior in the basic airframe flowfield (meridian plane).

Fig. 10 Schematic illustration of the streamline of wing (planform view).

31

Fig. 11 Schematic illustration of the streamline of wing in the basic airframe flowfield (meridian plane).

Fig. 12 Schematic illustration of the streamline of cowl interior (planform view).

32

Fig. 13 Schematic illustration of the streamline of cowl interior and forebody-inlet (planform view).

Fig. 14 Schematic illustration of the streamline of cowl interior and forebody-inlet in basic forebody-inlet flowfield (meridian plane).

33

Fig. 15 Geometric model of the test case: (a) top view, (b) upward view (without cowl exterior), and (c) upward view.

34

Fig. 16 Shape and dimensions of the test case (unit: mm)

35

Fig. 17 Schematic illustration of input parameters of leading-edge planform curves: (a) forebody and cowl lip, (b) wing

36

Fig. 18 Experimental space shuttle model used for wind tunnel experiments.

37

(a) Lift coefficient

(b) Drag coefficient

(c) Lift-to-drag ratio

(d) Pitching moment coefficient

Fig. 19 Comparison of viscous aerodynamic performances of the space shuttle as calculated using numerical computation and measured during the wind tunnel experiment.

38

Fig. 20 The structured grid of the basic forebody-inlet flowfield on the symmetric plane of the test case

Fig. 21 Comparison of Mach number contour lines of the basic integrated axisymmetric flow obtained using the Euler code and MOC

39

Fig. 22 Comparison of streamline and streamline points obtained in TECPLOT and using the streamline tracing technique

Fig. 23 Unstructured mesh of the test case.

40

Fig. 24 Inviscid Mach number contour lines on different x-direction planes under the design condition (M0 = 6, α = 0°).

Fig. 25 Inviscid Mach number contour lines on two meridian planes under the design conditions (M0 = 6, α = 0°).

41

a

b

Fig. 26 Inviscid non-dimensional pressure contour lines on meridian planes of integrated waverider vehicle under the design condition (M0=6, α = 0°): flow fields (a) on the symmetric plane of Φ = 0° and (b) on the meridian plane of Φ = 30°.

42

a

b

Fig. 27 Viscous non-dimensional pressure contour lines on meridian planes of integrated waverider vehicle under the design condition (M0=6, α = 0°): flow fields (a) on the symmetric plane of Φ = 0° and (b) on the meridian plane of Φ = 30°.

43

Fig. 28 Inviscid aerodynamic performances of test case. (a) Lift coefficient, (b) drag coefficient, (c) lift-to-drag ratio, and (d) pitching moment coefficient.

44

Table 1 Input parameters applied in the basic airframe axisymmetric flow model

M0

6.0

P0(Pa)

xA

rA

δA

xR

rR

δR

xB

δB

(m)

(m)

(°)

(m)

(m)

(°)

(m)

(°)

0.5

0.12

14.0

10.0

2.37

14.0

10.0

0

T0(K)

2511.18

221.649

Table 2 Input parameters applied in the basic forebody-inlet axisymmetric flow model

θ DC ,2 ( x ) (deg.)

δ CG ( x ) (deg.)

MCG(x)

xCF(m)

3.0

3.0

MC

0.01

Table 3 Boundary conditions for the free stream applied in the experiment [33] Ms

Res

P0,s/Mpa

T0,s/K

8.04

1.13×107/m

7.8

892

Table 4 Comparison of inviscid and viscous performance of integrated waverider vehicle Me

Pe/P0

Te/Te

Pe,t/P0,t

m&(kg/s)

σ

CD

CL

Cmz

L/D

Inviscid

3.9359

9.8446

2.0097

0.8298

17.3908

0.9913

0.0752

0.1273

0.0339

1.6927

Viscous

2.7885

17.7787

3.2569

0.2948

16.2216

0.9247

0.1317

0.1397

0.0457

1.10611

-29.2

80.6

62.1

-64.5

-6.7

-6.7

75.1

9.7

34.8

-34.7

Increment percentage (%)

45

Table 5 Geometric parameters of integrated waverider vehicle

Case

L (m)

W (m)

Vol (m3)

Swet (m2)

η

7.2

4.0

5.6734

43.1471

0.0737

46

Highlight
A new axisymmetric basic flowfield generated by shock wave is adopted.
The leading-edge planform curves are used for an inlet-airframe integration waverider vehicle characterised by a drip-like intake.
The validations of both the basic flowfield and the vehicle design process are executed.

1

The authors express their gratitude for the financial support provided by the National Natural Science Foundation of China (grant number 11702322) and the Natural Science Foundation of Hunan Province of China (grant number 2018JJ3589). The authors are also extremely grateful to the reviewers for their constructive comments and suggestions.