Design optimization of velocity-controlled cruise vehicle propelled by throttleable hybrid rocket motor

https://doi.org/10.1016/j.ast.2021.106784Get rights and content

Abstract

Throttleable engines have greatly raised the technical performances of aircrafts and missiles, particularly for cruise vehicles. The hybrid rocket motor (HRM) combines the advantages of solid and liquid rocket engines, especially the ability of easily throttling and restart. This paper presents a design optimization of an HRM propelled cruise vehicle to explore the throttling ability of HRM on velocity control. First, a theoretical thrust model is presented and revised through several experimental tests. Based on it, a detailed design process of HRM is proposed. Second, the layout of the cruise vehicle, flight trajectory model and a closed-loop PID velocity control method are developed. The differential evolution algorithm is adopted to get the optimal design result, which is used to analyze velocity characteristics by real-time control of the oxidizer flow rate. The results show that the PID-control has good effect on velocity control performance and maintaining small deviation from the target. The influences of aerodynamic and thrust errors are also considered and analyzed. For different types of deviations, including the proportional and periodic perturbations, the PID-controlled scheme shows a good stability under the parameters' deviations, which indicates that the HRM with the real-time throttling thrust has a good capacity of high-precision velocity control when used in rocket propelled vehicles.

Introduction

Recent developments of aerospace vehicles have heightened the needs for the ability of energy management which can effectively increase the range and maneuvering, especially for the missile weapons [1], [2]. Energy management requires the propulsion system with the abilities of thrust throttling and multiple starts, of which the commonly used solid rocket motor (SRM) is nearly incapable, since its solid grain is pre-poured into the chamber and its thrust is preset through grain shape design. Although the SRM thrust control has been realized by some strategies [3], it's not easy to throttle and re-start after extinguishment. Meanwhile, it is also hard to extinguish after ignition before the grain burnt out. Compared to SRM, the hybrid rocket motor (HRM) has the advantages of favorable stability, economical goodness, and characteristics of easy throttling and multiple starts [4], [5], [6]. The liquid rocket engine (LRE) has a high specific impulse, more stable mixture ratio and also has the ability of throttling. However, the liquid engine adopts two propellant feeding systems, and the systems must be simultaneously adjusted at throttling stage, which also increases its complexity. Meanwhile, although the liquid rocket has a better energy characteristic, most of the liquid rockets adopt cryogenic or toxic propellants, which limit its application to a certain extent. The main characteristic of hybrid rocket motor lies between the solid rocket motor and the liquid rocket engine and has both the potential advantages of solid rocket and the liquid rocket. It is an efficient supplement to widely used rockets engines, and has extensive development prospects like sounding rocket, space launch vehicles, sub-orbital spacecraft, target drones, and also shows prominent effect and value in military missiles [7], [8], [9], [10], [11], [12]. Based on the fundamental researches of HRM, exploration of throttleable and multiple-start application also began. In 1980, the Firebolt target drone was developed and its flight envelope was effectively enlarged by its HRM with the throttle ability of 10:1 [7]. The University of Padova conducted a series of deep throttling tests with the deep-throttling range of 3.5:1-12.6:1, and a real-time throttling test of 2.7:1 throttling range [13], [14]. Purdue University developed experimental tests on hybrid rockets to test its restart ability and throttle ability, resulting in 10:1 throttling range, and explore the application of this technology on missiles [15].

Although the HRM is a good supplement to commonly used rocket engines, the burning instability and oxidizer-to-fuel ratio variation [16] restricts its engineering application, therefore the studies on throttle control are essential to release the potential abilities of HRMs. Many researches have been conducted previously, Whitmore et al. [17], [18] presented a closed-loop throttle controller for a laboratory-scale HRM, significantly reduced thrust deviation in burning process, and the deep-throttling research [19] concluded that reducing the oxidizer mass flow rate significantly decrease the effects of combustion instabilities during throttling, which made deep-throttling HRM possible. Tian et al. [20], [21] conducted numerical simulations on a throttleable H2O2/HTPB HRM to explore the regression rate of solid grain and aerospike nozzle in thrust regulation process. Zhao et al. [22] presented a series of simulations and experiments about throttleable catalyst hybrid rocket motor, the results revealed that a delay time was required to readjust the new equilibrium after the oxidizer mass flow rate changed. Most researches above only considered the thrust as a design variable, aiming at thrust control, however, the actual flight gives more emphasis on aircrafts' velocity, altitude and maneuvering, the real velocity control on aircraft could heighten the control precision and robustness, decrease control difficulty and improve competitiveness, which has broadened potential prospects. Based on the advantages of HRM and requirements of velocity maintenance of cruise vehicles, it is essential to develop the application of throttling HRM on velocity-controlled vehicle.

In this paper, the velocity control of an HRM propelled flight vehicle is studied to obtain the theoretical energy management ability of the HRM. The design frameworks of the vehicle and HRM thrust model are developed firstly, then the design optimization of a velocity-fixed high-altitude high-speed flight vehicle with high maneuvering is carried out. Based on the optimal result, the velocity control performance of the HRM is studied in horizontal flight with high maneuvering under aerodynamic and thrust perturbations. The rest of this paper are organized as follows: Section 2 introduces the HRM design process and the revised theoretical thrust model. The detailed vehicle design process is shown in Section 3. Trajectory simulation and PID control theory are presented in Section 4 and Section 5 reveals the optimization model. The optimization results and vehicle performance under different parameters perturbation are discussed in Section 6, and Section 7 is the conclusion.

Section snippets

HRM design model

The HRM designed in this study mainly consists of a pressured gas container, an oxidizer tank, an oxidizer feed system, a catalyst bed, a solid fuel chamber and a conical nozzle, as shown in Fig. 1. In the oxidizer feed system, an electric pump is used to reduce the structure mass and size. A variable area cavitating venturi is designed as a dynamic oxidizer mass flow controller and its performance is detailed in reference [23]. A single port grain which is simple to design is applied in the

Vehicle design

Based on the throttleable characteristics of HRM, a conceptual design and optimization of an HRM propelled vehicle as a target drone, with the cruise flight capacity of high-altitude, high-speed and high-maneuvering, is developed in this paper. The vehicle is set to propel by a solid rocket booster to an initial cruise altitude of 20 km with a velocity of 2.0 Ma and all attitude angles are equal to zero. The flight mission of this drone consists three stages. In the first stage, the vehicle

Trajectory simulation

The vehicle designed in this paper aims at finishing the slope maneuvering flight on horizontal surface, the dynamics and kinematics equation [31] of no-slip and maneuvering flight in trajectory coordinate system is adopted as equation (12) with the assumption of small angle of attack approximation:{dVdt=FXmdϑvdt=gVny3sinγvdxdt=Vcosϑvdzdt=Vsinϑvγv=arccosmg(Fα+Y)=arccos1ny3α=ny3ny3bα where F is the thrust, X is the drag force, m is the vehicle mass, ϑv is the offset angle, g is the

Optimization

To complete the flight mission, a three-stage thrust profile is required. Two oxidizer flow rate parameters, the kmo1 and kmo2 are added as design variables of HRM. The control precision of velocity is neglected during optimization process, after the optimum scheme is obtained, a real-time throttling strategy is used to examine the performance of velocity control through HRM. The detailed control profile is shown in Table 4.

The changing process of lateral overload nz2 is given in equation (19):n

Optimization results

The curve of optimization target varying with evolution is shown in Fig. 11, the vehicle mass decreases at first, and keeps stabilized around 310 kg from about the 600th generations. The design optimization results are shown from Table 5, Table 6, Table 7.

Fig. 12 shows the vehicle shape and size measurements of optimization results. The cruise vehicle has a total mass of 307 kg, the fuselage length, diameter and slenderness ratio are 5.058 m, 0.293 m and 17.3, respectively. The HRM weights 228

Conclusions

In this paper, a detailed design process of HRM and an experimental data revised theoretical thrust model are presented. Based on the modified model, an HRM-propelled high-altitude, high-speed and high-maneuvering flight vehicle is designed and optimized. The performance of velocity control by HRM under proportional and periodic deviations are also analyzed. According to the numerical results above, several conclusions can be drawn out as follows:

  • (1)

    The HRM has strong throttling ability, and a

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the Aeronautical Science Foundation of China (20180151001).

The authors would like to express their sincere thanks the anonymous reviewer #1, reviewer #2, reviewer #3, reviewer #4 and reviewer #5 for their constructive comments which improve this research substantially.

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