Integrated Optimization Design of Hypersonic Cruise Vehicle ++

Che Jing* and Tang Shuo†

College of Astronautics, Northwestern Polytechnical University, Xi’an, Shannxi,710072, China

Optimization design is the most important key technique of Air-breathing Hypersonic Cruise Vehicle (HCV). To improve the design level and get better integrated performances of HCV, this paper researches the integrated optimization design method of waverider hypersonic cruise vehicle. In the optimization design, Multi-Objective Genetic Algorithms (MOGA) is selected as the optimization algorithm, and the shape parameters of aircraft are as design variables. Some performances, such as aerodynamics, aeroheating, radar cross section (RCS), airframe/scramjet integration, and volume of airframe, trimmed characteristic, static stability and maneuverability at cruise stage are selected as the objectives. When the optimization process finishes, the Pareto front side is got, in which many Pareto solutions whose integrated performances are more excellent than basic configuration are found. According to the design idea, we choose a Pareto solution from the Pareto front side as the recommended shape configuration for further research. To validate the aerodynamics of recommended HCV, wind tunnel test is done. And the comparison results show that the optimization design is successful.

Nomenclature

trimα = trimmed angle of attack = root chord of wing 0wbCd = drag coefficient = tip chord of wing 1wbCF = thrust coefficient wc = relative thickness of wing

Ma = Mach number = span of wing wlnyk = longitudinal available overload 0wχ = leading edge sweep angle of wing

nzk = lateral available overload = height of H and O point OHYTs = stagnation temperature = height of G and O point OGYRCS = radar cross section 1δ = the first wedge angle of forebody

ztrimδ = trimmed deflection angle of pitching rudder 2δ = the second wedge angle of forebody

maxzδ = maximal deflection angle of pitching rudder 3δ = the third wedge angle of forebody

maxγ = maximal rolling angle cδ = chord angle of nozzle Vb = airframe volume CL = lift coefficient

cX = longitudinal static stability ϕ = azimuth angle of incidence radar

sX = lateral static stability θ = pitching angle of incidence radar

* Postgraduate, College of Astronautics of Northwestern Polytechnical University, Xi’an Shannxi, 710072, China. † Professor, College of Astronautics of Northwestern Polytechnical University, Xi’an Shannxi, 710072, China. ++ Support by National Natural Science Foundation of China(10572115)

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46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-142

Copyright © 2008 by Northwestern Polytechnical University of China. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

I. Introduction ir-breathing hypersonic cruise vehicle(HCV) is one of the most important configurations of hypersonic vehicles. This configuration takes scramjet as its power device and can fly in high velocity from 5Ma to 10Ma for long

times and distances. Commonly, its cruise range is over 1000Km. Because of these advantages, HCV has become the research emphasis all over the world. Optimization design is a key technique of HCV, but due to the mutative flight environment and rigid work condition of scramjet, the optimization design aimed at integrated performances is very difficult.

A

In the optimization design of HCV, the main research work is now focus on airframe/scramjet integration, especially on forebody/inlet integration1, 2 and aftbody/nozzle integration3, 4, or aerodynamics/propulsion integration5, which arrive far from at the integration of total performances. To improve the design level and get better integrated configurations of HCV, this paper researches its integrated optimization design method. In the optimization design, Multi-Objective Genetic Algorithms (MOGA) is adopted as the optimization tool, and the shape parameters of HCV are selected as design variables. The integrated performances, including aerodynamics, aeroheating, radar cross section (RCS), airframe/scramjet integration, and volume of airframe, trimmed characteristic, static stability and maneuverability are considered to be design objectives.

II. Optimization Model and Optimization Algorithms In the optimization design work, one basic configuration of HCV is presented It is a quasi-waverider

configuration shown as Fig.1. And the airframe has a lift-body characteristic of two dimensional, which is fit for airframe/scramjet integration.

Figure 1. The shape of basic Configuration.

A. Optimization Design Variables To optimize the shape of basic configuration of HCV, first step is building the parametric modeling of aircraft.

For basic shape, 21 parameters are chosen as the optimization design variables including 5 variables of upper body, 4 variables of forebody/inlet, 3 variables of aftbody/nozzle, 5 variables of wing, and 4 variables of relative position relationship of wing-body. These variables can describe the shape of HCV completely.

B. Optimization Design Objectives At cruise flight stage, the integrated performances include aerodynamics, aeroheating, RCS, airframe/scramjet

integration, and volume of airframe, trimmed characteristic, static stability and maneuverability performances. Some of them are selected as objectives, and others as restrictions.

Aerodynamics: The lift-drag-ratio CL/Cd is taken as the aerodynamic objective, it is hoped maximal. Aeroheating: The highest temperature of body will lie in the stagnation point. So, stagnation temperature

sT is taken as the aeroheating objective, it is hoped minimal. Airframe/scramjet integration: At design condition, airframe and scramjet should be integrated design, and

all shock waves of forebody should converge at point D shown as Fig.1. On the base of airframe/scramjet integration, thrust-drag-ratio CF/Cd is another objective, it is hoped maximal.

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Effective volume of airframe: Volume of airframe is an important performance of aircraft. Waverider is

too small to bring many limitations. In optimization design, a bigger is hoped. bV

bV bV RCS performance: The most dangerous direction of RCS is in the range of of lateral direction,

especially at of lateral direction, the dihedral corner reflectors made up of wing-body and wing-wing joints are the most important scattering sources. So, reducing RCS at this direction is one of optimization aims.

030±030+

C. Restrictions In the optimization design, some restrictions are required. They are:

Variables limitations: These limitations are explicit limitations. Before optimization begins, these limitations have been given.

Airframe/scramjet integration: To ensure the rigid work condition of scramjet, in the airframe/scramjet integration design, some implicit limitations are required, such as the flow flux of inlet, Mach number of inlet, and the length of forebody and so on.

The flight task and aerodynamic parts limitations: such as the trimmed angle of attack 05trimα ≤ , the

deflection angle of pitching rudder , the rolling angle of aircraft , even when aircraft is maneuvering.

0max 20zδ ≤ 0

max 90γ ≤

Trimmed characteristic: In longitudinal plane, trimmed angle of attack trimα and deflection angle of

pitching rudder ztrimδ stand for trimmed characteristic, they will be limited to a range.

Static stability: Static stability includes longitudinal static stability cX and lateral static stability sX . They are expressed by the relative distance of center of mass and center of lift or center of lateral force, and will be limited to a range.

Maneuverability: Maneuverability is scaled by longitudinal available overload ykn and lateral available

overload . For the basic configuration of HCV, BTT control system may be adopted, and the lateral

force is offered by the lateral component of lift. In this optimization, zkn

ykn and will be limited to a range. zkn

D. Multi-Objective Genetic Algorithms Genetic Algorithms (GA) is a global optimization algorithm, which is widely applied in the design field of

aircraft. Because Simple GA (SGA) has only a frame and has some shortages such as Hamming Cliff problem, GA Block, GA Deceptive and so on6, this paper modifies some key techniques in SGA, and develops a new optimization tool called Multi-Objective GA (MOGA). The main key techniques include:

Encoding: Real number encoding is adopted to avoid Hamming Cliff problem in binary encoding method. Crossover: Arithmetic Crossover. Mutation: Gaussian Mutation. Reproduction: Steady reproduction with no uniform individuals to accelerate the convergence of population

and improve the efficiency of GA. Niche: Niche based on sharing mechanism to keep the diversity of population. Restriction: Accurate penalty strategy. Multi-objective strategy: The concept of Pareto adopted to get the Pareto front side of final population. Local search: Simple simulated annealing algorithm to strengthen local search.

The process of MOGA is shown as Fig.2.

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Figure 2. The Process of MOGA.

III. The Engineering Method of Main Objectives In the integrated optimization design, aerodynamics, aeroheating, scramjet and RCS are the most important of all

objectives, and they are complex to compute. To be fit for optimization work, this paper builds their engineering models.

Aerodynamics7. The computation of aerodynamics is partitioned into three parts of work. First work is the computation of hypersonic inviscid aerodynamics based on hypersonic inviscid flow theory. With triangle surface element taken as to approach the vehicle’s shape configuration, Dahlem-Buck formula, Prandtl-Meyer formula, tangent cone formula and expansion wave formula are adopted respectively to calculate inviscid aerodynamics according to windside or leeside status. Second work is the estimation of viscid drag. We estimate the skin friction and base drag of HCV with experiential formula. Finally, the aerodynamic interactions of vehicle parts are considered by interaction factors. The main aerodynamic interactions include body-horizontal wings, and horizontal wings-sideling wings.

Aeroheating8. To calculate the aeroheating of HCV, reference temperature and experience formulas are adopted. With aerodynamic heating, thermal radiation and heat exchange of skin, the thermal flux equation is built. Through supposing the material parameters of surface skin, the temperature of an arbitrary point of vehicle can be got. In the engineering method, the transition of boundary-layer is considered.

Scramjet performance9. To build the engineering model of scramjet, this paper computes respectively the flow fields of forebody/inlet, combustor and aftbody/nozzle. In forebody/inlet, one-dimensional oblique shock wave formula is the main method. And in combustor, quasi-one dimensional flow model including chemical combustion, mass projection, and friction effect is built. In aftbody/nozzle, the method of two-dimensional characteristics is taken as to compute the flow field.

RCS10. The computed model of RCS can be partitioned to three aspects of work. One is the mirror reflection of slick surface, which can be computed by Physical Optics (PO) method. The second is wedge scattering such as the edge of wings, which can be computed by the method of equivalent currents (MEC). And the last is the dihedral corner reflector such as wing-body and wing-wing joints, which can be computed by Geometrical Optics (GO) method, PO, the method of complex ray expansion and so on. In the

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computation of dihedral corner reflector, combined with the engineering RCS formula of ideal dihedral corner reflector, we define a concept of equivalent illumination area (EIA). And to improve the accuracy of computed method, the shadowing relationship of facet is analyzed by the method of backward surface identification and depth-buffer is considered.

IV. Integrated Optimization Design As an example, the basic shape of HCV has been optimized. The design conditions and GA parameters are:

Design conditions: flight height KmH 30= , flight velocity 6Ma = . GA parameters: the population size is 300; the probability of crossover is 0.8; the probability of mutation is

0.3, and the maximal generation is 300. When population is convergent, we get the Pareto front side. The boundary of Pareto front side is shown as

Table 1. Table 1 The boundary of Pareto front side

Performances Configuration

FC RCS,dBsm bV ,m3

sT ,K ykn zkn cX sX dC trimα ,0

Basic shape 0.0229 20.618 1.487 1368 1.810 1.509 -5.32％ 11.22% 0.01540 2.593

Max FC 0.02467 -10.712 1.664 1354 2.021 1.756 -5.47％ 6.30% 0.01264 2.068

Min σ 0.02309 -15.577 1.580 1339 1.887 1.600 -3.43％ 10.03% 0.01328 2.300Max bV 0.02194 -5.066 1.806 1341 1.909 1.626 -3.06％ 8.34% 0.01286 2.200

Min sT 0.02168 -5.313 1.574 1299 1.778 1.470 -0.40％ 5.26% 0.01477 2.397

Max ykn 0.02467 -10.712 1.664 1354 2.021 1.756 -5.47％ 6.30% 0.01264 2.068

Max 1cX 0.02029 1.106 1.529 1319 1.858 1.566 1.16％ 14.00% 0.01287 2.019

Max zkn 0.02467 -10.712 1.664 1354 2.021 1.756 -5.47％ 6.30% 0.01264 2.068

Min dC 0.02190 -6.092 1.383 1382 1.903 1.619 -4.26％ 9.75% 0.01081 2.352

From Table 1, we find that the integrated performance of basic configuration is not ideal. Except X s , its other performances are far lower than Pareto solutions. But the performances of boundary Pareto solutions are not still the best because their objectives distribution is not in balance. That is, some objectives are good and others are so bad. In the design of HCV, we expect to find a configuration whose all objectives are the best. But this is not possible because these objectives are conflict each other. So the balanced Pareto solutions whose all objectives are not bad are our chief choice. Fortunately, in the Pareto front side, there are many Pareto solutions which have the balanced performances. These Pareto solutions stand for better integrated configurations, such as the following three configurations listed in Table 2 and Table 3, which have all better objectives than basic shape except sX .

Table 2 Partial Design Variables of balanced Pareto solutions and basic shape No.

1δ ,0 2δ ,0 3δ ,0 cδ ,0 OHY ,m OGY ,m 0wb ,m 1wb ,m wl ,m wc 0wχ ,0

Basic shape

0.636 1.728 5.634 8.000 0.0785 0.140 1.200 0.350 0.940 12.0% 65.18

1 4.343 1.877 2.382 8.506 0.0901 0.1282 1.103 0.311 0.910 7.61% 52.842 4.199 1.368 3.367 8.206 0.0623 0.1265 1.295 0.280 0.836 9.36% 68.043 5.280 1.946 1.991 6.288 0.0593 0.1531 1.253 0.250 0.941 6.32% 42.42

Table 3 Design Objectives of balanced Pareto solutions No.

FC RCS,dBsm bV ,m3

sT ,K ykn zkn cX sX dC trimα ,0

1 0.02392 -4.258 1.606 1346 1.891 1.605 -3.52% 7.17% 0.01317 2.2822 0.02448 -7.205 1.563 1350 1.987 1.717 -4.64% 10.08% 0.01376 2.1603 0.02230 -12.36 1.715 1363 2.002 1.735 -3.64% 19.44% 0.01220 2.050

Besides the performances comparison on-design, the integrated performances of configurations No.1, No.2 and No.3 at off-design conditions are computed. We find that they not only have balanced performances at cruise flight stage, but also have better integrated performances than basic configuration at wide Mach numbers, wide angles of

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attack, and wide incidence directions of radar wave. Fig.3-Fig.6 show their partial performance comparisons at off-design conditions. In fact, there are many other solutions like them in Pareto front side.

Figure 3. Lift-drag-Ratio Comparisons at Ma=6. Figure 4. Thrust-drag-Ratio Comparisons at Ma=6.

Figure 5. Temperature Comparisons of Center Line of Figure 6. RCS Comparisons at Lateral Upper

Body at Ma=6. Direction.

V. The aerodynamics validation of No.2 configuration Because No.2 configuration has balanced integrated performances and its all design objectives exceed the

optimization goals, it has been recommended to the optimum configuration for further research. To validate its aerodynamics, we do the wind tunnel test before and after optimization. The test results are shown as Fig. 7-Fig.8. From these figures, it is evident that the aerodynamic characteristic of No.2 configuration (after optimization) is better than basic configuration (before optimization). So, we consider that the optimization design is credible.

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Figure 7. Wind tunnel Test Comparisons at 05−=zδ .Figure 8. Wind tunnel Test Comparisons at 00=zδ .

VI. Conclusion HCV is a complicated system, and the integrated optimization design on HCV is a very important and

significative work. This paper has adopted MOGA and engineering computation models to optimize the integrated performance of HCV, and has got its Pareto front side. In the Pareto front side, many better and more balanced solutions than basic configuration are found. As a fruit, one Pareto solution is recommended and the wind test validation is done, which shows that the optimization work can improve the design level of aircraft, and can get configurations with better integrated performances. As an optimization idea, our method can be applied in the multi-objective optimization design of aircraft field. To get a more credible result, the more accurate computation models of objective performances should be introduced.

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