Drag Reduction on the Basis of the Area Rule of the Small-Scale Supersonic Flight Experiment Vehicle Being Developed at Muroran Institute of Technology (Second Report)

Abstract

A small-scale supersonic flight experiment vehicle named OWASHI is being developed at Muroran Institute of Technology as a flying testbed for verification of innovative technologies for high-speed atmospheric flights. Drag reduction in the transonic and supersonic regimes is quite crucial for attainability of its supersonic flights. This study aims to obtain configuration modification for transonic drag reduction on the basis of the so-called area rule. In order to prevent accumulation of compression waves, various profiles of the bottleneck and the bulge are designed by using arcs with constant and large radii and spline curves approximating them. Their effects are assessed through CFD analysis, wind tunnel tests, and wave drag analysis. As a result, an area-rule-based configuration with a sharpened conical nose and a large-radius bottleneck achieves significant drag reduction in a transonic Mach range, as well as 57-count (57 × 10⁻⁴) reduction at the design Mach number of 1.1. However, the drag reduction effects of bulges are small and apparent only in a narrow Mach range. On the other hand, in the practical vehicle configuration, rearward fuselage extension shows a large amount of drag reduction, whereas the addition of an intake cancels the drag reduction effects of area-rule-based configurations.

1. Introduction

Innovation in technologies for high-speed atmospheric flights is essential for establishment of supersonic/hypersonic and reusable space transportation. It is quite effective to verify such technologies through small-scale flight tests repeatedly in practical high-speed environments prior to installation into large-scale vehicles. Thus, we are developing a small-scale supersonic flight experiment vehicle as a flying testbed. An aerodynamic configuration named M2011 with a single Air Turbo Ramjet Gas-Generator-cycle (ATR-GG) engine [1] has been proposed. Its transonic thrust margin has been predicted to be insufficient, as shown in Figure 1; therefore, drag reduction in the transonic and supersonic regimes is quite crucial for attainability of its supersonic flights.

In the previous study [2], we have proposed configuration modifications for drag reduction on the basis of the so-called area rule. The fuselage shape was modified from the point of view of cross-sectional area distribution; however, its drag reduction was insufficient due to accumulation of compression waves around the fuselage bottleneck with a large curvature. In this study, we propose design modifications to prevent compression wave accumulation and assess their effects through CFD analysis, wind tunnel tests, and wave drag analysis.

In Section 2, the baseline configuration M2011 is outlined. In Section 3, the theory for predicting and reducing wave drag at sonic and supersonic conditions is described, and its drawbacks are discussed. Various shape modifications are proposed for reduction in transonic wave drag in Section 4, and the effects of some of the modifications are predicted preliminarily using CFD analysis in Section 5. The methodology and results of wind tunnel tests in a Mach range of 0.7–1.3 are described in Section 6. In addition, a wave drag analysis in a Mach range of 1.0–2.0 is overviewed in Section 7. Then, Section 8 outlines our conclusions.

2. The Baseline Configuration M2011

The baseline aerodynamic configuration M2011 with a single Air Turbo Ramjet Gas-Generator-cycle (ATR-GG) engine is designed as shown in Figure 2 and

Table 1. Dimensions of the baseline configuration M2011.

Dimension	Value
Wing Span	2.41 m
Wing Area	2.15 m2
Fuselage Diameter	0.3 m
Overall Length	Nose-A: 5.8 m (Propellants 80 kg)
	Nose-B: 6.8 m (Propellants 105 kg)
	Nose-C: 7.8 m (Propellants 130 kg)

. A diamond wing section of 6% thickness is adopted for reduction in wave drag during supersonic flights. Its main wing has a cranked-arrow planform with inboard and outboard leading-edge sweep-back angles of 66 and 61 degrees, respectively, for stable aerodynamic characteristics. A high-wing configuration with a dihedral of 1.0 degree is also adopted in order to attain sufficient roll stability. Three types of fuselage length, 5.8 m, 6.8 m, and 7.8 m, are considered tentatively for various quantities of propellants loaded for various missions.

3. Theory and Method

The area rule was discovered by R. T. Whitcomb [3] through free-fall experiments of slender bodies with very small wings around sonic conditions. It states that, in order to reduce wave drag at Mach 1.0, the cross-sectional area distribution along the body axis should be smoothed. This rule was verified theoretically by the following Karman’s formula on the basis of the slender body theory (i.e., a version of the small perturbation theory of compressible inviscid flows):

$$D_w=-{\displaystyle \frac{\rho V^2}{4\pi }}{{\displaystyle \int }}_0^L{{\displaystyle \int }}_0^L{S}^{″}\left(x_1\right)S^{″}\left(x_2\right)\ln \left|x_1-x_2\right|d{x}_{1}d{x}_2$$

(1)

Here, ρ is the air density, V is the airspeed, x is an arbitrary position along the body axis of the vehicle, and S is the cross-sectional area of the airframe cut with the Mach plane perpendicular to the body axis. In addition, the optimum cross-sectional area distribution was found to be the Sears–Haack curve of Equation (2). Figure 3 shows the curve in a cubic diagram.

$$S\left(x\right)={\displaystyle \frac{16V}{3L\pi }}{\left[4x-4x^2\right]}^{3/2}$$

(2)

Here, x is the nondimensionalized distance from the nose to the cross section (0 ≤ x ≤ 1), V is the body volume, L is the body length, and S(x) is the cross-sectional area at x.

The above theory and treatment are valid strictly for the Mach 1.0 condition only. For larger Mach numbers, the Mach planes are no longer perpendicular to the axis. Then, R. T. Jones [4] adopted the following superposing or averaging calculation with respect to the roll angle of the Mach plane by intuition:

$$D\left(\theta \right)=-{\displaystyle \frac{\rho V^2}{4\pi }}{{\displaystyle \int }}_0^L{{\displaystyle \int }}_0^L{S}^{″}\left(x_1\right)S^{″}\left(x_2\right)\ln \left|x_1-x_2\right|d{x}_{1}d{x}_2$$

(3)

$$D_w={\displaystyle \frac{1}{2\pi }}{{\displaystyle \int }}_0^{2\pi }D\left(\theta \right)d\theta$$

(4)

Here, S is the projected area of the cross section of the airframe cut with the Mach plane with a roll angle θ. This treatment was applied to the numerical wave drag estimation code WAVEDRAG (NASA Langley Program D 2500) [5].

In simplifications of the area rule by Vojin R. Nikolic and Eric J. Jumper, the integral in Equation (4) can be omitted by using the cross-sectional area cut with the Mach cone instead of the average of the cross sections cut with Mach planes with various roll angles [6,7,8].

Physically speaking, the pressure change in supersonic flows propagates along the surface of the Mach cones. Thus, it is also expected by intuition that the wave drag is reduced when the distribution of the cross-sectional area of the vehicle cut with Mach cones emanating from an arbitrary point on the body axis is brought close to that of the Sears–Haack curve.

Therefore, the area rule has two aspects of uncertainty in its validity and applicability. Firstly, is it applicable to practical non-slender winged vehicles? Secondly, is it valid at Mach numbers larger than 1.0? Such validity and applicability must be assessed through case studies for practical winged vehicles at various Mach numbers. One such assessment will be carried out in this study using the proposed supersonic experimental vehicle configuration.

4. The Area-Rule-Based Configurations

The appearance and cross-sectional area distribution of the wind tunnel test model of the baseline configuration M2011 with Nose-C are shown in Figure 4. Here, the cross-sectional area is measured on 3D CAD software SOLIDWORKS 2017 SP5.0. The nose, main wing, and tails are protruded in comparison with the Sears–Haack curve, denoted by the red plot in the figure.

The modification factors are designed for reduction in transonic drag on the basis of the area rule. In particular, several shapes are designed for the bottleneck and the bulge on the mid and rear fuselage, respectively. Their effects are predicted using CFD analysis and then the most favorable shapes are selected as listed in

Table 2. Modification factors for reduction in wave drag of the wind tunnel test model on the basis of the area rule.

Design Item	Parts	Modifications
Nose cone	ARNose-C	Sharpening the conical nose closely to the Sears–Haack curve.
	Bottleneck1	By narrowing the mid fuselage around the main wing, the cross-sectional area of the main wing is canceled partially. R/Df = 5.00, L/Df = 3.11. Proposed in the previous treatment [2].
Fuselage	Bottleneck6 Bottleneck7	Most favorable modifications of Bottleneck1. Smoother shape for preventing compression wave accumulation. R/Df = 15.9, L/Df = 4.57. Bottleneck6: An arc with a constant and large radius. Bottleneck7: A spline curve connecting smoothly to the fore and rear portions of the fuselage.
	Bulge6C Bulge6S Bulge7C Bulge7S	Relaxation of sudden change in the cross-sectional area between the main wing and tails. Most favorable smooth shape for preventing compression wave accumulation. Bulge6C, Bulge7C: Arcs with constant and large radii. Rbulge6/Df = 4.29, Rbulge7/Df = 5.43. Bulge6S, Bulge7S: Spline curves connecting smoothly to the fore and rear portions of the fuselage. Bulge6C,6S: To be used with Bottleneck6. Bulge7C,7S: To be used with Bottleneck7.

. Six patterns of the wind tunnel test model configurations are proposed by combining these factors. Their appearances and cross-sectional area distributions are shown in Figure 5. The design point of these area-rule-based configurations is Mach 1.1.

In addition, the practical vehicle has an intake and engine mount as shown in Figure 6. The shape of the intake is a combination of the air intake itself and a cover for reducing aerodynamic force on the gas generator. The modification factors for such a practical vehicle are listed in

Table 3. Modification factors of the wind tunnel test model for the practical vehicle configuration.

Design Item	Parts	Modifications
Fuselage	Intake	Combination of an air intake and a gas generator cover.
	Fuselage extension	Rearward extension of the fuselage. Corresponding to installation of engine mount.
	Bulge7SN	Modification of Bulge7S. Adapted to fuselage extension. Connected smoothly to Bottleneck7.

. The appearances and cross-sectional area distributions of the wind tunnel test models of area-rule-based practical configurations are illustrated in Figure 7.

5. CFD Analysis

The degrees of compression wave accumulation and zero-lift drag are investigated preliminarily for some of the proposed configurations by CFD analysis, using ANSYS FLUENT R17.2. The primary analysis conditions are listed in

Table 4. CFD analysis conditions.

Governing equation	Three-dimensional Navier–Stokes
Spatial Discretization	Second-order upwind differencing
Fluid	Air/Ideal-gas
Turbulence model	Spalart–Allmaras
Viscosity model	Sutherland
Mach number	1.1
Angle of attack (AOA)	zero

. The physical conditions are adjusted to those of the wind tunnel tests. The angle of attack (AOA) is set to zero; it is quite close to zero-lift conditions because the rigging angles and the cambers of the main wing and the horizontal tail are zero.

As shown in

Table 5. Drag coefficient predicted using CFD analysis for the baseline and area-rule-based configurations.

Configuration		Pressure Drag	Viscous Drag
Baseline configuration M2011 with Nose-C		0.0388	0.0179
Area-ruled configurations
(a)	ARNose-C	0.0350	0.0175
(b)	ARNose-C, Bottleneck1 [2]	0.0353	0.0172
(c)	ARNose-C, Bottleneck6	0.0313	0.0173
(d)	ARNose-C, Bottleneck6, Bulge6S	0.0308	0.0171

, the predicted pressure drag is reduced by Bottleneck6 and by Bulge6S, whereas it is enhanced by Bottleneck1 with a smaller radius. Figure 8 shows the pressure distribution around the area-rule-based configurations. There is a high-pressure region around Bottleneck1 where the accumulation of compression waves takes place [2]. Such compression accumulation is prevented around the redesigned Bottleneck6 and Bulge6S.

6. Wind Tunnel Tests

The wind tunnel tests are carried out using the blowdown-type transonic wind tunnel at the Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (ISAS/JAXA) to acquire aerodynamic characteristic data of the baseline configuration M2011 and the area-rule-based configurations. The overview of the transonic wind tunnel and a vehicle model installation situation are shown in Figure 9 and Figure 10, respectively. The model is designed and manufactured with a scale-reduction ratio of 7/60. The intake part has a flow-through or a closed shape.

Aerodynamic forces are measured using a six-component internal balance. The flow Mach number is 0.7 to 1.3 and the total pressure is 1.5 kgf/cm³. Mach-sweep operations are carried out with an angle-of-attack (AOA) of zero degrees. The drag coefficient obtained is quite close to, and can be taken to be, the zero-lift drag coefficient C_D0, because the rigging angles and the cambers of the main wing and the horizontal tail are zero. In addition, the drag coefficient so obtained is not affected by a small change in lift caused by the fluctuation of AOA in the wind tunnel tests, because it is located around the vertex of the drag polar curve where $d{C}_D/d{C}_L\cong 0$.

Schlieren photos of some of the configurations and the zero-lift drag coefficients C_D0 obtained from the wind tunnel tests are shown in Figure 11 and Figure 12, respectively. Compression wave accumulation is reduced in the configurations with Bottleneck6 or 7 in comparison with that of Bottleneck1, as is predicted by CFD analysis in Section 5. C_D0 of the area-rule-based configurations are significantly smaller than that of the baseline configuration M2011 at Mach numbers above 0.95.

Compared with the pink curve (ARNose-C only) in Figure 11, the brown (ARNose-C, Bottleneck1), blue (ARNose-C, Bottleneck6), and green (ARNose-C, Bottleneck7) curves show the effects of Bottlenecks 1, 6, and 7, respectively. It is clearly shown that Bottleneck1 has a drag enhancement effect due to its compression wave accumulation, as can be observed in the schlieren photo. On the other hand, Bottlenecks 6 and 7 have drag reduction effects in the transonic regime. Their drag reduction at the design point of Mach 1.1 is 57 counts (57 × 10⁻⁴), i.e., 12.7% in comparison with the baseline configuration. However, the drag reduction effects of the bulges are small and apparent only at Mach numbers from 1.0 to 1.1.

As for the practical vehicle configurations, the rearward fuselage extension has 32-count (32 × 10⁻⁴) less transonic drag at Mach 1.1, as shown by the dark green curve G with diamond markers (ARNose-C, Bottleneck7, extended rear fuselage) in Figure 12, i.e., 7.1% drag reduction in comparison with the green curve D (ARNose-C, Bottleneck7). However, the addition of an intake cancels some part of the drag reduction effects of the area-ruled configurations and the fuselage extension. The effects of the bulge are also small in these configurations. Further modification of configuration is necessary; for example, a second bottleneck around the intake would be effective for more drag reduction.

7. Wave Drag Analysis

In order to assess the capability of the conventional wave drag prediction procedure, the wave drag of the baseline configuration M2011 and the proposed area-rule-based configurations are estimated using the calculation program WAVEDRAG (NASA Langley Program D2500) [5]. In this procedure, the wave drag is estimated from Equations (3) and (4) on the basis of the slender body theory; therefore, it can only handle wave drag due to relatively weak compression and expansion waves.

The following ten patterns out of the proposed vehicle configurations are analyzed: the baseline configuration M2011, the area-rule-based configuration adopting only the ARNose-C, and (A) through (H) (closed intake) shown in Figure 4, Figure 5 and Figure 7. The results are shown in Figure 13 and Figure 14 in comparison with the wind tunnel test data.

The estimated wave drag is in relatively good agreement with the wind tunnel test data at Mach 1.0, whereas there is a large discrepancy between them at Mach numbers larger than 1.0. As for comparison among the estimated wave drag for various configurations, characteristics similar to those of the wind tunnel test data can be seen. At Mach numbers around the design point of 1.1, the wave drag of the area-rule-based configurations is significantly smaller than that of the baseline configuration. Configurations with bottlenecks show large wave drag reduction in comparison with the ARNose-C-only configuration.

On the other hand, the drag reduction effects of bulges are not apparent around design point Mach 1.1, differently from the wind tunnel tests. At Mach numbers above 1.1, the addition of bulges has a tendency to increase wave drag.

As for the practical vehicle configurations, the addition of an intake results in a larger wave drag increase than that observed in the wind tunnel tests. Regarding rearward fuselage extension, drag reduction effects do not appear, which is quite different from the wind tunnel tests. This is probably because the conventional wave drag analysis cannot estimate the base drag caused by flow separation, since the analysis procedure is based on the inviscid fluid dynamics.

Then, to clarify the drag reduction mechanism of the rearward fuselage extension, additional CFD analysis was carried out, and its results are shown in Figure 15. It can be seen in Figure 15a,b for a real flight condition (i.e., without a support sting), that the rearward fuselage extension relaxes the pressure drop around the bases of the fuselage and the tail mount, and thus reduces the base drag. It should also be noted that the pressure around the fuselage base is influenced by the support sting in the wind tunnel tests, as shown in Figure 15c,d; The wind tunnel test results for rearward fuselage extension are inaccurate, and the test technique must be improved for prevention of such interference and for precise assessment of drag force.

8. Conclusions

A small-scale supersonic flight experiment vehicle named OWASHI is being developed at Muroran Institute of Technology as a flying testbed for verification of innovative technologies for high-speed atmospheric flights, which are essential to next-generation aerospace transportation systems. Its transonic thrust margin has been predicted to be insufficient. Therefore, drag reduction in the transonic and supersonic regimes is quite crucial for attainability of its supersonic flights. In this study, we aimed to propose configuration modifications for drag reduction on the basis of the so-called area rule. In order to prevent accumulation of compression waves, we designed various profiles of the bottleneck and the bulge by using arcs with constant and large radii and spline curves approximating them. Their effects were assessed through CFD analysis, wind tunnel tests, and wave drag analysis. As a result, an area-rule-based configuration with a sharpened conical nose and a large-radius bottleneck showed significant drag reduction in a transonic Mach range, as well as 57-count (57 × 10⁻⁴) reduction at the design Mach number of 1.1, in comparison with the baseline configuration. However, the drag reduction effects of the bulges were small and apparent only in a narrow Mach number range from 1.0 to 1.1.

On the other hand, in the practical vehicle configuration, rearward fuselage extension showed a large amount of drag reduction. Additional CFD analysis revealed that the distribution of the base pressure changes and the base drag decreases due to rearward fuselage extension. Furthermore, the addition of an intake canceled the drag reduction effects of the area-rule-based configurations. It is necessary to apply additional configuration modifications, for example, the second bottleneck around the intake.