Multidisciplinary Design Optimization of a Two-Stage-to-Orbit Reusable Launch Vehicle with Ethanol-Fueled Rocket-Based Combined Cycle Engines *

Transcription

1 Trans. Japan Soc. Aero. Space Sci. Vol. 6, No. 5, pp , 217 Multidisciplinary Design Optimization of a Two-Stage-to-Orbit Reusable Launch Vehicle with Ethanol-Fueled Rocket-Based Combined Cycle Engines * Takahiro FUJIKAWA, 1) Takeshi TSUCHIYA, 1) and Sadatake TOMIOKA 2) 1) Department of Aeronautics and Astronautics, The University of Tokyo, Tokyo , Japan 2) Kakuda Space Center, Japan Aerospace Exploration Agency, Kakuda, Miyagi , Japan A fully reusable two-stage-to-orbit launch vehicle with ethanol-fueled rocket-based combined cycle (RBCC) engines has been studied in Japan as a promising option for future space transportation system. In this paper, a conceptual design study of such a vehicle is conducted using multidisciplinary design optimization (MDO) techniques in order to clarify a technology goal for related technology development activities. An MDO framework composed of coupled analysis disciplines (vehicle geometry, mass property, aerodynamics, propulsion, and trajectory) is constructed. In particular, consideration is given to the development of a simplified numerical model for evaluating the airframe-propulsion integration that can be incorporated into MDO studies, in contrast to costly CFD simulations. Vehicle design and ascent trajectory are then simultaneously optimized with the aim of minimizing the gross mass of the mated vehicle (booster and orbiter). The gross mass of the obtained optimal design is 581 t for the assumed mission of transporting an 8 kg payload into a low Earth orbit. A detailed inspection of the solution reveals that an external nozzle of the engines enhances not only the propulsion performance, but also longitudinal static stability of the vehicle during hypersonic flight. Key Words: Multidisciplinary Design Optimization, Two-Stage-to-Orbit Reusable Launch Vehicle, Rocket-Based Combined Cycle Engine, Conceptual Design Study, Future Space Transportation System Nomenclature : angle of attack : elevon deflection (positive downward) z: design variables for booster airframe C L : lift coefficient C D : drag coefficient C M;ref : pitching moment coefficient about reference point a: polynomial coefficient in the approximation of aerodynamic coefficient M: pitching moment about center of mass S capt : inlet flow capture area : throttling parameter p: static pressure q: dynamic pressure Ma: Mach number : heat capacity ratio C T : ram thrust coefficient Isp: specific impulse O=F: oxidizer-to-fuel mass mixture ratio T: thrust Subscripts R: embedded rocket in RBCC engine max: maximum 217 The Japan Society for Aeronautical and Space Sciences + Received 18 September 215; final revision received 11 August 216; accepted for publication 3 October 216. Corresponding author, fujikawa.takahiro755@mail.kyutech.jp; Presently, Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Fukuoka , Japan sur: surrogate model 1: free-stream condition in: inlet inflow condition e: exit condition of RBCC combustor A: airframe eng: RBCC engine ext: external nozzle tot: total 1. Introduction Quite high levels of cost efficiency, operability, and reliability are indispensable for future space transportation system in order to attract potential users of outer space and to promote the growth of the space transportation market. Since it is dubious that these requirements can be satisfied by improving expandable launch vehicles, reusable launch vehicles (RLVs) or space planes have been studied for years. An essential effort for realizing RLVs is to perform their conceptual design studies early, and thereby to clarify system goals and associated key technologies. At the Japan Aerospace Exploration Agency (JAXA), the feasibility of fully reusable two-stage-to-orbit (TSTO) systems is currently being investigated as a long-term goal (23s or later). 1) Under a tentative mission plan of transporting eight persons or an 8 kg payload into a low Earth orbit, design studies of two types of booster-stage vehicles equipped with different propulsion systems (rocket engines or airbreathing engines) are underway. This paper focuses on a horizontal takeoff and landing 265

2 RLV with airbreathing engines, which is one of the ideal types of space transportation system that would achieve aircraft-like reliability and operability. Among some airbreathing propulsion options, a rocket-based combined cycle (RBCC) engine 2) is selected here. The RBCC engine is the combination of a dual-mode ramjet/scramjet engine and rocket engines that are embedded in it. A characteristic of the RBCC engine is that it can be operated from sea level to outer space with superior performance to conventional rockets. In this paper, ethanol is adopted as the fuel of the RBCC engine instead of cryogenic liquid hydrogen because it can lead to a compact and easily handled vehicle. In addition, it is assumed that the engine is operated with relatively low combustion pressure aiming to attain high reliability and to prolong operational life. Conceptual design studies of a TSTO RLV with ethanolfueled RBCC engines are challenging tasks, and ongoing studies are still in the early phases. 3 6) Design problems of such airbreathing-powered RLVs contain complex interactions among design disciplines, which makes them difficult to be handled from the viewpoints of solution approaches and computational cost. For example, the substantial interdependence of vehicle design and flight trajectory design originates from the fact that launch vehicles do not have a cruising state unlike aircraft. This means that a steady-state design point for aerodynamic shape and propulsion system cannot be defined. Besides, forebody pre-compression and afterbody exhaust expansion of the propulsion system are related to free-stream conditions and airframe geometry in highly nonlinear manners. Because of such dependence of the performance of airbreathing engines on flight conditions and airframe design, vehicle sizing based simply on velocity increments is unsuitable in contrast to rocket vehicles. In this paper, a multidisciplinary design optimization (MDO) approach is employed so as to overcome the foregoing difficulties. MDO is a design optimization framework where numerical optimization methods are applied to the design problem of a system composed of multiple interacting disciplines. MDO techniques have had significant successes in conceptual design studies of RLVs. 7 1) Coupled analysis disciplines considered in this paper are vehicle geometry, vehicle mass property, propulsion system, aerodynamics, and flight trajectory. With the MDO architecture constructed, optimization is executed to find the vehicle design with the minimum gross mass. Major modifications from a previous research by the authors 6) include the implementation of an airframe-propulsion integrated analysis. This enables more accurate performance evaluation of the RBCC engine considering its interaction with the airframe. Additionally, in the flight trajectory analysis based on point-mass dynamics, some rigid body characteristics of the vehicle (i.e., pitching trim and longitudinal static stability) are also evaluated while taking the influence of RBCC engines into account. The remainder of this paper is organized as follows: Section 2 describes an MDO methodology for the TSTO RLV with RBCC engines. Optimization procedures and numerical models are explained. In Section 3, the optimal solution obtained is presented, and detailed inspections are discussed. Finally, Section 4 summarizes this paper and suggests some future work. 2. A Multidisciplinary Design Optimization Methodology for a TSTO RLV with RBCC Engines The design objective is the minimization of the gross mass of a mated vehicle (booster and orbiter) that transports an 8 kg payload into orbit. While the primary scope of this paper is the conceptual design of the booster vehicle, the performance of the overall TSTO system cannot be evaluated with the booster stage alone. Therefore, the scaling of the orbiter vehicle and the trajectory design of the orbiter are conducted as well Optimization procedures An MDO framework for an RBCC-powered TSTO RLV is constructed as outlined in Fig. 1. Numerical analysis disciplines in this framework are broken up into vehicle geometry and mass property, aerodynamics, propulsion, and flight trajectory. Design variables are composed of sets of variables that specify vehicle design, vehicle performance, and flight trajectory, respectively, as gathered in Table 1. It is noted that an optimization problem arising from this MDO framework is formulated as an augmented optimal control problem. By appending static variables and static constraints regarding vehicle design and vehicle performance to a continuous-time optimal control problem of the vehicle, concurrent design optimization of vehicle and flight trajectory is achieved. Using this formulation, there is no nested iteration loop in the solution procedures, and all the objective and constraints are managed by a single system-level optimizer. Such an MDO architecture is categorized into an all-at-once approach, which is known to have stable and rapid convergence, and to be free from convergence errors between coupling variables in different disciplines. 7) For the optimizer, an off-the-shelf solver named SNOPT, 11) which stands for sparse nonlinear optimizer, is employed. SNOPT is an implementation of a sequential quadratic programming (SQP) algorithm that exploits the sparsity in the constraint Vehicle geometry & Mass property Reference area, length, and point S capt, Ext. nozzle geometry Dry mass, Dry CM position, Tank vol., Prop. CM position Fig. 1. Optimizer (SQP method) Aerodynamics Lift, Drag, Pitching moment Design variables Propulsion Thrust, Isp, O/F, Ext. nozzle performance Objective value (vehicle gross mass), Constraint values Overview of an MDO framework. Trajectory 266

3 Table 1. Design variables. Parameter Unit Associated constraints Vehicle design Booster Length of the fuselage, b l m 3 b l 6 Height of the upper fuselage, b h m :1 b h =b l :5 Inclination of the forebody undersurface, b wed deg 3: b wed 8: Angle of the external nozzle, b ext deg 3: b ext 2: Length of the forebody, b lf m :3 b lf =b l :6 Width of the forebody tip, b wf m :5 b wf =½ð5=1:81Þe h Š:8 Leading-edge position of the exposed wing, w m :25 w =b l :75 Root chord length of the exposed wing, w chrd m :25 w chrd =b l :75 Sweepback of the wing leading-edge, w deg 45 w 7 (Forward, Backward) end of the fore ethanol tank, (t eaf ;t eaff ) m 5: t eaf t eaff (Forward, Backward) end of the LOX tank, (t lo ;t lof ) m t eaff þ :5 t lo t lof (Forward, Backward) end of the aft ethanol tank, (t eaa ;t eaaf ) m t lof þ :5 t eaa t eaaf b l :5 Height of RBCC engines, e h m :2 5:96e h =b l :5 Maximum thrust of RBCC embedded rocket engines, T R,max kn Orbiter Length of the fuselage, o l m 1 o l 3 Backward end of the cabin, cb f m :25 cb f =o l :9 Rocket engine thrust kn Vehicle performance Booster Maximum axial acceleration G Maximum normal load factor G Maximum dynamic pressure, qmax ðbþ kpa q ðbþ max 5 Maximum exerted thrust kn Gross mass t Orbiter Maximum axial acceleration G Maximum normal load factor, lfmax ðoþ G 2:5 lf ðoþ max Maximum dynamic pressure, qmax ðoþ kpa q ðoþ max 5 Maximum exerted thrust kn Gross mass t Flight trajectory Booster Parameterized state variables see Section 2.5. Parameterized control variables see Section 2.5. Switchover times between RBCC engine modes s Staging time s Orbiter Parameterized state variables see Section 2.5. Parameterized control variables see Section 2.5. Terminal time s Jacobian, 11) and it is suited to the present MDO formulation whose constraint Jacobian is highly sparse Vehicle geometry and mass property analysis In this analysis discipline, the geometric design of the booster and that of the orbiter are defined by the design variables. Then, the dry mass of the vehicles, volume of the tanks, and center of mass of the vehicles and propellants are calculated. The basic configuration of the booster is depicted in Fig. 2. In addition to the constraints enumerated in Table 1, some inequality constraints are imposed so that external geometries of the airframe, tanks, and engines are successfully determined by the design variables. Five RBCC engines are installed on the undersurface of the fuselage. The flat undersurface of the forebody is employed to supply uniformly pre-compressed airflow into the engines, and that of the afterbody acts as an external nozzle. The airfoils of the main wing and the vertical tail wing are NACA5, and the taper ratio of the main wing is fixed at.15. Ninety percent of the exposed span from the wing tips and 3% chord from the trailing edge of the main wing are used as elevons. Right and left elevons are deflected in the same direction and Fig. 2. Ethanol tank LOX tanks Ethanol tank Basic configuration and design parameters of the booster. with identical angles (positive downward) to serve as elevators. The tail wings are scaled so that their total area equals 1% of the main wing area. Two integral tanks of ethanol fuel (fore and aft) and cylindrical tanks of liquid oxygen (LOX) are located inside the fuselage. Some control over the position of the center of mass is possible during the flight 267

4 Table 2. Conditions in aerodynamic analysis. Parameter(s) Sample values Unit Ma 1 :2; :6; :9; 1:2; 3:; 5:; 7:; 1:; 15: ð; Þ (, ), (5, ), (1, ), (5, ¹1), (5, 1) (deg, deg) Fig. 3. Cabin LOX tank Ethanol tank Basic configuration and design parameters of the orbiter. by adjusting the ratio of consumption of ethanol fuel between the fore and aft tanks. The volume of the integral tanks is calculated by integrating the fuselage cross section between the forward end and the rear end, times a volume efficiency constant of 8%. It is assumed that the center of mass of the propellant is identical to that of the corresponding tank. The lifting body configuration shown in Fig. 3 is adopted to the orbiter based on Fujii et al. 1) Airframe geometry optimization is not conducted, and rather, only scaling is performed in this paper. It is assumed that every 4.3 m 3 of cabin volume can accommodate a payload that weighs 1 kg. The orbiter is loaded onto the upper surface of the booster at such a position that the center of mass does not move in the axial direction just before and just after the separation of the orbiter. A constraint on the width of the booster fuselage and that of the orbiter is enforced to guarantee the mountability of the orbiter. The dry mass and the center of mass of these vehicles are calculated using HASA, 12) a statistical relationship for estimating the mass of hypersonic vehicles. Cold structures with aluminum alloy are assumed. An input to HASA consists of vehicle geometric parameters such as wetted area, maximum loads such as maximum dynamic pressure, and gross mass. These input values are present in or calculated from the design variables. The mass of the RBCC engines is calculated by adding that of embedded rockets (thrust-to-mass ratio of the rocket engine is assumed to be 5) and that of the dual-mode flow-pass. The structure mass of the flow-pass is estimated with the statistical relation obtained from FEMbased structural analyses. 3) The mass of the thermal protection system is computed assuming a constant areal density based on Tsuchiya and Mori. 8) The resultant gross mass (i.e., the summation of the calculated dry mass and propellant mass before takeoff) must be consistent with the gross mass value specified in the design variables. This consistency condition is enforced as a constraint in the MDO problem Aerodynamic analysis In the aerodynamic analysis, aerodynamic characteristics of the booster, the orbiter, and their mated configuration are calculated when the vehicle shape and flight conditions are specified. In order to calculate the trajectory of the launch vehicle, aerodynamic properties for a wide range of flight conditions are needed. Considering this requirement along with the required fidelity level in the conceptual design study, the following two types of engineering-level CFD methods are utilized depending on the flow speed. In subsonic or supersonic conditions (Ma 1 < 2:), the A52 PAN AIR panel code, 13) whose governing equation is a linearized potential flow equation with compressibility correction, is employed. In hypersonic conditions (Ma 1 2:), the tangent cone method 14) and Prandtl-Meyer expansion flow theory are applied to the windward and leeward regions of the vehicle surface, respectively. Although this hypersonic aerodynamic characterization method is not based on any governing equations, its accuracy is adequate for conceptual design purposes. In both the flow-speed cases, the base pressure of the fuselage is estimated separately with an empirical method, 15) and the skin friction coefficient is calculated using van Driest s formula. 16) The external nozzle ramp is excluded when computing the aerodynamic coefficients of the booster because the forces acting on the ramp are considered in the airframe-propulsion integrated analysis in Section 2.4. In the mated vehicle configuration, it is assumed that the airflow hits the orbiter along its body axis after the free-stream flow passes by the booster upper surface. For the optimization computation, the surrogate model of the above CFD analysis is built based on Yokoyama et al. 9) in order to mitigate the computational burden and to enhance numerical stability. The surrogate aerodynamic coefficients of the booster are the functions of,, Ma 1, and z; that is, C C ; sur ð; ; Ma 1 ; zþ; where represents L, D, orm;ref. In order to train the surrogate models, 2 sample points for z are made in advance via a design-of-experiments algorithm. 9) This is a kind of space-filling design method, and it generates sample points that uniformly fill the constrained design space. In addition to the sample points, 2 test points for cross-validation are prepared using random sampling. Then, the aerodynamic analysis is conducted on these sample and test points under the conditions of,, and Ma 1 shown in Table 2 (45 cases for each z). When z is provided during optimization, the aerodynamic coefficients under the sampled conditions of,, andma 1 are calculated using radial basic function (RBF) networks 17) with the Gaussian basis function in the following manner: " C ; sur ½ð; Þ i ;Ma 1j ; zš ¼ X2 i;j; k exp jjz z 2 # kjj 2 2 ; k¼1 i;j i ¼ 1;...; 5; j ¼ 1;...; 9: Here, i;j; k and i;j are the fitting parameters in the RBF networks that are optimized beforehand based on the input/response of aerodynamic computations at sample/test points by means of simulated annealing. Subsequently, the aerody- ð1þ ð2þ 268

5 namic coefficients are interpolated with respect to Ma 1 using RBF networks with the multiquadric basis function as follows: C ; sur ½ð; Þ i ;Ma 1 ; zš ¼ X9 i;j j¼1 h 2þ i 1=2; Ma 1 Ma 1j 2 i¼ 1;...; 5; i where i;j are other fitting parameters that are calculated from C ; sur ½ð; Þ i ;Ma 1j ; zš; i¼ 1;...; 5; j¼ 1;...; 9 with slight computation cost, and i ¼ :1. The aerodynamic coefficients at the combinations of and shown in Table 2 are obtained. Finally, the surrogate aerodynamic coefficients are constructed as second-order polynomials in terms of and as follows: C ; sur ð; ; Ma 1 ; zþ ¼ a ð;þ þ a ð1;þ þ a ð2;þ where the polynomial coefficients, a ð;þ ð3þ 2 þ a ð;1þ þ a ð;2þ 2 ; ð4þ Thrust to mass ratio ;...;a ð;2þ, are computed via the least squares fit of C ; sur ½ð; Þ i ;Ma 1 ; zš; i ¼ 1;...; 5. The above procedures yield surrogate models whose coefficients of determination are.988 on average and.968 in the worst case, which is an acceptable prediction error Airframe-propulsion integrated analysis In the propulsion analysis, thrust, Isp, O=F, and external nozzle performance are calculated when the engine design, the booster airframe, and flight conditions are provided. Ethanol-fueled RBCC engines, whose conceptual image is illustrated in Fig. 4, are installed on the booster. RBCC engines are operated in ejector-jet (i.e., ducted rocket), ramjet, and scramjet modes, successively in that order. Ejectorjet and scramjet modes are operated by keeping the output of embedded rockets high (rocket chamber pressure is 6 MPa). In ramjet mode, on the other hand, the rocket chamber pressure is reduced to.6 MPa in order to attain better Isp owing to airbreathing effects. The best acceleration performance is achieved by properly switching these operating modes depending on flight conditions. The detailed geometry of the engine flow-pass is fixed: the overall length-to-height and height-to-width ratios of an engine unit are 5.96 and 1.81, respectively, and the throat-to-inlet area ratio is.2. 3) The flow-pass is scaled based on the engine height included in the design variables, and the maximum thrust of the embedded rocket, T R,max, is also variable. An airframe-propulsion integrated analysis, whose overview is shown in Fig. 5, is conducted. The analysis is composed of three calculation steps: pre-compression, RBCC engine, and external nozzle. For simplicity, influence of engine operation on the flow field around the airframe during the subsonic ejector-jet mode is neglected. (1) Pre-compression analysis A shock wave generated from the booster nose before the undersurface is equivalent to an oblique shock wave past a two-dimensional wedge whose angle is ð þ b wed Þ. Equations describing oblique shocks 18) are employed, and inlet inflow conditions to RBCC engines are obtained. (2) RBCC engine analysis The performance dataset of the RBCC engine at a set of representative inflow conditions (Ma in and q in ) and T R =S capt is computed in advance with a quasi-one-dimensional analytical method. 3) It is assumed that q in is bounded to [1, 1] kpa. When T R =S capt is varied, the engine thrust-to-mass ratio in a static condition and Isp in some operating conditions change as shown in Fig. 6. A larger embedded rocket relative to the flow-pass gives a higher thrust-to-mass ratio, while it decreases Isp except in scramjet mode. Then, surrogate models of responses (i.e., C T, Isp, O=F, Ma e, p e, and e ) for each engine operating mode are constructed using an RBF network with the multiquadric basis function. In ejector-jet and scramjet mode, the thrust of the RBCC engine alone, T, is calculated in the following manner: where Fig. 5. Fig. 4. A conceptual image of an RBCC engine. 4) Oblique shock equation RBCC engine model T ¼ C T S capt þ T R ; T R ¼ T R,max : In ramjet mode, on the other hand, Geometry of ext. nozzle Q1D isentropic flow equation Overview of airframe-propulsion integrated analysis. Engine thrust to mass ratio in a static condition Isp(ejector jet mode, Ma in = 2, q in = 5 kpa) Isp(ramjet mode, Ma in = 4, q in = 5 kpa) Isp(scramjet mode, Ma in = 7, q in = 5 kpa) Forces acting on the nozzle T [kn/m 2 R / S capt ] Fig. 6. Effects of T R =S capt on RBCC engine performance. [s] Isp ð5þ ð6þ 269

6 T ¼ C T S capt : Throttling parameter,, is allowed to vary within a range [.5, 1] only in scramjet mode. (3) External nozzle analysis The pressure on the nozzle ramp surface is estimated based on the following numerical model 3) : The exhaust gas of the engine is expanded quasi-onedimensionally along a flow-pass surrounded by the nozzle ramp and an extended line from the engine cowl (the dashed line shown in Fig. 5) in an isentropic manner. Under an over-expansion condition, the exhaust flow goes along the nozzle ramp with static pressure identical to the ambient pressure. The force and pitching moment acting on the external nozzle are obtained by integrating the calculated flow pressure over the entire ramp surface after the free-stream pressure is subtracted. In order to avoid iterative solutions of nonlinear isentropic flow equations during optimization computation, surrogate models of the nozzle performance are constructed beforehand using an RBF network with the multiquadric basis function. Sample points for training the RBF network surrogate models are prepared via an optimized Latin hypercube sampling algorithm. 19) The orbiter is propelled by a rocket engine mounted on the base of the fuselage. Ethanol fuel and LOX are employed, and vacuum Isp, engine thrust-to-mass ratio, and O=F are 32 s, 75, and 1.6, respectively. 1) Effective thrust and Isp are computed considering the effect of atmospheric pressure. It is assumed that the thrust of the rocket engine can be throttled without affecting Isp Flight trajectory analysis In the flight trajectory analysis, it is assumed that the trajectory is restricted to a vertical plane, and two-degreeof-freedom dynamics is employed. A static atmosphere model is built based on U.S. standard atmosphere ) In the context of optimal control, state variables are composed of altitude, velocity, flight path angle, remaining ethanol fuel mass in the fore tank, that in the aft tank, and remaining LOX mass. Control variables consist of angle of attack, elevon deflection angle, throttling parameter, and the consumption ratio of ethanol fuel between the fore and aft tanks. A flight plan is described by the following three phases: (1) Takeoff phase The mated vehicle takes off horizontally from a runway at sea level. No particular launch site is assumed in this paper. The RBCC engines are operated with the maximum thrust, and angle of attack for liftoff is 15 deg. A takeoff analysis 21) is conducted, and the following quantities are computed: takeoff velocity, takeoff distance (ground roll), and the propellant mass consumed during the takeoff phase. The calculated takeoff velocity and distance must be no more than 17 m/s and 4, m, respectively. (2) Mated vehicle ascent phase The mated vehicle is accelerated by the RBCC engines. The rocket engine mounted on the orbiter is not used. Angle ð7þ of attack and elevon deflection are bounded to [¹5, 15] deg and [¹1, 1] deg, respectively. Elevon deflection angle is limited, because a large deflection can lead to flow separation and re-attachment, causing local high heat flux and elevon effectiveness loss. Axial acceleration, normal load factor, dynamic pressure, and exerted thrust must not exceed the corresponding design limits (see Table 1). Since the TSTO RLV investigated is a manned transportation system, total acceleration (the composition of axial acceleration and normal load factor) is restricted to 4. G maximum. At the terminal time of this phase, the orbiter is separated from the booster. This flight phase is further divided into three sub-phases where the RBCC engines are operated in different modes (ejector-jet, ramjet, and scramjet modes in this order). Ramjet mode is available when the engine inflow Mach number, Ma in, is 3. (the designed start Mach number of the inlet) or higher. Switchover times between engine operating modes are included in the design variables, and they are optimized to achieve the best acceleration performance. (3) Orbiter ascent phase The rocket engine on the orbiter is ignited immediately after the staging. Angle of attack is bounded to [, 3] deg, and the throttling parameter must be within a range [.5, 1]. Axial acceleration, normal load factor, dynamic pressure, and thrust must not exceed their corresponding design limits for the orbiter. The total acceleration is limited to no more than 4. G. After the orbiter reaches an altitude of 1 km or higher and the rocket engine is cut off, the trajectory computation is performed based on elliptic orbit equations instead of equations of motion. At the apogee of this coasting trajectory, the orbiter is accelerated again, and it is injected into a circular orbit at 35 km above sea level. The propellant mass needed for this apogee acceleration is calculated by approximating it as an impulsive acceleration whose Isp is 32 s. In addition to the propellant consumed before the orbit insertion, some propellant is reserved for on-orbit and de-orbit operations whose velocity-change requirement is assumed to be 25 m/s in total. The return trajectory of the booster after the staging and that of the orbiter after de-orbit are not considered in this paper. During the mated vehicle ascent phase, a pitching trim condition and a longitudinal static stability condition are imposed in order to ensure the flyability of the vehicle. The trim condition is expressed as follows: M tot :¼ M A þ M eng þ M ext ¼ : Additionally, the following equation describes the non-negative static ð8þ ext : Here, pitching moment in the above equations is calculated about the center of mass, which moves during the flight. It is noted that conventional stability analysis based on the po- 27

7 sitions of stability neutral point and center of mass is invalid, because the magnitude of moment produced by RBCC engines changes depending on aerodynamic attitude. In order to calculate the value tot accurately, analytical differentiation of RBF surrogate models and automatic differentiation 22) of the nose shock wave relations are implemented in the MDO framework. As explained in Section 2.1, the MDO problem for the TSTO RLV with RBCC engines in this paper is formulated as an augmented optimal control problem. In order to discretize state variables and control variables, the Legendre-Gauss pseudospectral method 23) with adaptive mesh refinement 24) is employed. Consequently, these time-dependent variables are parameterized by the values at a finite number of temporal collocation points, and continuous-time equations of motion and path constraints are transcribed into static constraints. It should be mentioned that the MDO problem consists of large numbers of design variables and constraints when it becomes a good approximation to the original continuous-time problem. The number of collocation points and their distribution are automatically and adaptively determined using the mesh refinement algorithm so that a user-defined discretization error tolerance is satisfied. 3. Results and Discussion 3.1. Optimization process The termination criterion of the numerical optimization using SNOPT is that the maximum residual of the Karush- Kuhn-Tucker optimality conditions and the largest constraint violation are both no more than 1: 1 8, which is a morethan-adequate level for engineering purposes The basic configuration of the booster shown in Fig. 2 (fuselage length is 35. m) is used as the initial point for starting optimization. The optimization computation takes about 15 minutes using a Windows 7 machine with an Intel Core i7-493k CPU and 32 GB RAM Optimal vehicle design and flight trajectory The specifications of optimal design obtained are shown in Table 3. The gross mass of the mated vehicle, the design objective to be minimized, is 581 t. This is smaller than the maximum takeoff mass of an An-225 aircraft (6 t 25) ), which may indicate that there is a realistic possibility in the horizontal takeoff of RLVs of this scale. Among the booster-vehicle components, the mass of the landing gear occupies the largest portion, followed by that of the RBCC engines. At JAXA, a fully reusable TSTO launch vehicle with ethanol-fueled rocket engines is under a conceptual design study. The vertical lift-off mass of the rocket-powered system is 788 t, 1) so the RBCC-powered RLV designed in this paper has smaller gross mass. Of course, a simple comparison is rather meaningless since the underlying design assumptions and numerical models differ substantially. Details of the optimal vehicle design are shown in Table 4 and Fig. 7. Since the orbiter is not much smaller than the booster, aerodynamic interference between the vehicles must Table 3. Specifications of the optimal solution. Parameter Unit Booster Orbiter Payload mass kg 8. Mated vehicle gross mass t 58.9 Takeoff velocity m/s 17. Takeoff distance m Maximum axial acceleration G Maximum normal load factor G Maximum dynamic pressure kpa Maximum exerted thrust kn Mass Fuselage t Main wing t 7.9. Tail wing t Tanks t Thermal protection system t Landing gear t RBCC engines t Rocket engine t..5 Thrust structure t The others t Dry gross t Ethanol t LOX t Gross t Table 4. Details of vehicle design in the optimal solution. Parameter Unit Value Booster Fuselage length, b l m 38.4 Fuselage upper height, b h m 1. Forebody undersurface inclination, b wed deg 8. External nozzle angle, b ext deg 14.6 Forebody length, b lf m 13.9 Forebody tip width, b wf m 4.2 Exposed wing leading-edge position, w m 2.6 Exposed wing root chord length, w chrd m 17.8 Wing leading-edge sweepback, w deg 53.4 Fore ethanol tank end (front), t eaf m 5. (back), t eaff m 12.9 LOX tank end (front), t lo m 13.7 (back), t lof m 27.8 Aft ethanol tank end (front), t eaa m 28.3 (back), t eaaf m 37.9 Height of the RBCC engines, e h m 2.2 RBCC embedded rocket thrust, T R,max kn Orbiter Fuselage length, o l m 18.8 Back end of the cabin, cb f m 11.2 Rocket thrust kn be considered in more detail in future work. The optimal value of T R =S capt in the RBCC engine design is 269 kn/m 2. The optimal booster shape has the following notable characteristics in comparison to the basic configuration shown in Fig. 2. The booster fuselage has the minimum width required to load the orbiter on its upper surface. Since the numerical model of the external nozzle in Section 2.4 always produces non-negative thrust, the fuselage base of the booster is fully used as the external nozzle. The inclination of the forebody undersurface is at the upper bound of the design variable. This is because the improvement of the propulsion efficiency due to stronger pre-compression outweighs the increase in the drag of the airframe. The main wing is located at the rear end of 271

8 the fuselage. This moves the neutral point for longitudinal static stability of the airframe rearward and ensures the stability up to a higher Mach number. The flight trajectory of the optimal solution is shown in Fig. 8. After horizontal takeoff, the mated vehicle accelerates and climbs with the RBCC engines at full throttle and with a large angle of attack. Since the vehicle thrust-to-weight ratio at takeoff is.63, which is less than 1, the lift force must play a major role in the takeoff. During ejector-jet mode operation, flight dynamic pressure increases, decreases, and increases again. In contrast to a TSTO RLV with hypersonic Fig m Optimal vehicle shape. turbojet engines, 8) the optimal flight trajectory does not have a dive phase in the transonic region. This dissimilarity can be attributed to the fact that the thrust-to-mass ratio of the RBCC engine is higher than that of the hypersonic turbojet engine. Therefore, the optimal RBCC-powered vehicle has enough thrust performance to pass the transonic drag rise without a dive maneuver. The engine operating mode is switched over to ramjet mode at a flight Mach number of 3.6. This corresponds to the condition where the engine inflow Mach number, Ma in, reaches 3., and ramjet mode becomes available. Ramjet mode is operated at the maximum dynamic pressure prior to 36 s, at which point the dynamic pressure begins decreasing. Subsequently, the RBCC engines are switched to scramjet mode when the vehicle reaches Mach 5.8. During acceleration in scramjet mode, the engines are gradually throttled down. Finally, the vehicle begins a steep climb by raising its angle of attack. In a previous conceptual design study of the TSTO RLV with RBCC engines, 6) in which the airframe-propulsion interaction is neglected, most of the optimal flight trajectory of the mated vehicle lies on the upper dynamic pressure limit. On the other hand, a quasi-one-dimensional model for the external nozzle flow is incorporated in the present study, and the resulting optimal trajectory takes on a more intricate behavior. Since thrust augmentation by the external nozzle in- Altitude [km] Propellant mass [t] Dynamic pressure [kpa] (a) Time history of altitude 25 2 Fore ethanol Aft ethanol 15 LOX Orbiter total (c) Time history of remaining propellant mass Mated (ejector jet) Mated (ramjet) Mated (scramjet) Orbiter (d) Time history of dynamic pressure Mach number AoA [deg] Elevon defl. [deg] Throttling param (b) Time history of Mach number (e) Time history of control variables Fig. 8. Optimal flight trajectory. 272

9 Pitching moment [MNm] Thrust [MN] Ejector jet Ramjet 1 Scramjet T T tot (a) Time history of thrust magnitude (c) Time history of pitching moment M A M eng M ext Specific impulse [s] Stability derivative [MNm] Isp Isp tot (b) Time history of specific impulse M A / α M eng / α M ext / α M tot / α (d) Time history of longitudinal stability derivative Fig. 9. Effect of the external nozzle on the propulsion performance and rigid body characteristics of the vehicle. creases as the ambient pressure drops, the mated vehicle increases altitude without flying along the maximum dynamic pressure around 1 s in order to enhance the overall performance of the RBCC engines. When the propellant in the booster is used up, the orbiter is separated from the booster. At that moment, the Mach number and dynamic pressure are 12.2 and 6.3 kpa, respectively. The orbiter ascends quickly to an altitude of 1 km with maximum rocket thrust, and then it continues to accelerate while descending slightly. At the terminal time, the orbiter is on an elliptic orbit with an apogee of 35 km above sea level. Until 135 s after takeoff, ethanol fuel is consumed only from the aft tank, followed by the consumption almost only from the fore tank until 47 s. After that, the fuel is expended only from the aft tank again. This switching strategy in the fuel consumption maximizes the effectiveness of the elevons while attaining non-negative static stability Effect of external nozzle Time histories of the performance of the RBCC engines and the rigid body characteristics of the vehicle are shown in Fig. 9 with the intent to reveal the effect of the external nozzle. Note that the performance of the total propulsion system including the external nozzle can be calculated as follows: T tot ¼ T þ T ext ; ð1þ! Isp tot ¼ Isp 1 þ T ext : ð11þ T In the early part of the flight (prior to 15 s), the external nozzle has no effect because it is in an over-expansion condition. In reality, however, the nozzle can produce negative thrust in such a condition as experimentally shown by Isono et al. 26) After the altitude becomes sufficiently high and the external nozzle shifts to an under-expansion condition, on the other hand, thrust and Isp are augmented. Between different engine operating modes, there are large differences of pitching moments generated by RBCC engines and the external nozzle. The requirement of maintaining pitching trim throughout multiple engine modes results in the saturation of the elevon deflection angle even though the vehicle has large elevons. If the propulsion system has a gimbal or a thrust vectoring mechanism as in the case of Yokoyama et al., 9) this problem would be solved. The longitudinal static stability of the airframe alone is lost (@M A =@ > ) after 28 s or above Mach 4.3. In addition, eng =@ >, the moment produced by the RBCC engines slightly deteriorates the stability. This is because, a larger angle of attack makes pre-compression prior to the inlet stronger, and as a result, larger thrust and larger positive pitching moment are produced by the RBCC engines. These instabilities are compensated by the moment induced by the external nozzle. Stronger pre-compression increases the exhaust pressure, and hence, the nozzle ramp pressure. This leads to larger negative pitching moment ext =@ < ). In total, positive stability is attained until 395 s and after 445 s, and neutral stability is maintained otherwise Flyability of the booster after staging In the optimal solution, there is no remaining propellant in the booster at the moment of staging. Therefore, the gross mass of the vehicle would increase if the flyback capability of the booster is imposed. To evaluate this increase in mass quantitatively, trajectory optimization for the return flight must be incorporated into the current MDO problem, and this makes its size much larger. In this paper, the flyability of the obtained optimal booster shape after staging is evaluated in terms of pitching trim and longitudinal static stability as a 273

10 CM,cg CM,cg Angle of attack [deg] (a) Clean configuration.5.5 preliminary analysis before designing the return trajectory. The pitching moment characteristics of the booster alone around the center of its dry mass are computed, and it was revealed that static stability cannot be retained above Mach 6.8. The result at Mach 12.2, where the staging is conducted, is presented in Fig. 1(a). In order to remedy this instability, the installation of a body flap (1 m width and 3 m length) at the fuselage base is examined. The effectiveness of the body flap is calculated using the hypersonic aerodynamic model in Section 2.3. The pitching moment curve at Mach 12.2 with the deflection of the body flap (1 deg downward) is obtained as shown in Fig. 1(b), which means that the stability is achieved in a positive angle of attack. Summarizing the above, the flyability of the booster after staging is confirmed in all speed ranges, while higher fidelity analysis is required in future work. 4. Conclusion Elevon defl. = 1 [deg] Elevon defl. = [deg] Elevon defl. = 1 [deg] Elevon defl. = 1 [deg] Elevon defl. = [deg] Elevon defl. = 1 [deg] Angle of attack [deg] (b) Configuration with body flap deflection (1 deg downward) Fig. 1. Pitching moment of the booster alone at Mach In this paper, a multidisciplinary conceptual design study of a horizontal takeoff TSTO RLV with ethanol-fueled RBCC engines was conducted. An MDO framework composed of coupled analysis disciplines was built with the following numerical models: Estimation of the vehicle mass property was based on a statistical relationship. For the aerodynamic analysis, engineering-level CFD methods were used, and surrogate modeling was applied. An analytical model of the interaction between the airframe and the propulsion system was developed, which was composed of pre-compression calculation, an RBCC engine model evaluation, and external nozzle flow computation. This simplified methodology for evaluating the airframe-propulsion integration can be incorporated into MDO studies of RLVs with ease, in contrast to costly CFD simulations. In the flight trajectory computation based on point-mass dynamics, pitching trim and longitudinal static stability were also assessed while taking the influences of the RBCC engines into account. The vehicle design and the ascent flight trajectory of the booster and those of the orbiter were simultaneously optimized in order to minimize the gross mass. Transportation of an 8 kg payload into a low Earth orbit was the assumed mission, and a vehicle with the gross mass of 581 t was obtained as the optimal design solution. The optimal flight trajectory has non-constant dynamic pressure in contrast to the trajectory obtained in a previous study where airframe-propulsion integration was not considered. The fuselage base of the optimal booster shape is fully used as the external nozzle, and it enhances propulsion performance. Additionally, the external nozzle enables longitudinal static stability to be achieved throughout the ascent flight, whereas the vehicle airframe alone cannot retain stability above Mach 4.3. In future work, the following improvements in the accuracy of numerical models and in the problem formulation should be considered for performing more reliable design studies: apply higher fidelity models to the estimation of vehicle mass and aerodynamic forces; employ a more accurate external nozzle flow model; consider the return flight trajectories of the booster and the orbiter; and conduct thermal analysis. Since a gradient-based optimizer is employed in the MDO methodology in this paper, one of its limitations is the lack of the search capability of the global solution. 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