Development of Generic Algorithm in Wheel-typed Hybrid Rocket Grain Design for Performance Estimation

Transcription

1 Development of Generic Algorithm in Wheel-typed Hybrid Rocket Grain Design for Performance Estimation RAED KAFAFY 1, MUHAMMAD HANAFI AZAMI 1, MOUMEN IDRES 1, AZAMI ZAHARIM 2 AND KAMARUZZAMAN SOPIAN 2 1 Mechanical Engineering Department, International Islamic University Malaysia P.O. Box 10, Kuala Lumpur MALAYSIA 2 Solar Energy Research Institute (SERI) UniversitiKebangsaan Malaysia UKM Bangi, Selangor MALAYSIA rkafafy@iium.edu.my, hanafee_86@hotmail.com, midres@iium.edu.my, azami.zaharim@gmail.com, k_sopian@yahoo.com Abstract: - Hybrid rockets are featured by restarting capability, increased safety, high performance and moderate cost. These combined unique characteristics pose then as prominent candidates to replace solid rockets in tactical missiles and launch vehicles in the near future. However, the behavior of hybrid rockets is not fully understood, with issues specifically related to combustion instability and lowered regression rate. To investigate the characteristics of hybrid rocket performance we develop generic algorithm code. This script may serve as a valuable teaching resource in hybrid rocket motor design. This paper uses Hydroxyl Terminated Polybutadiene (HTPB) as a solid fuel and liquid oxygen as an oxidizer for evaluation purposes. Later, we introduce the results of the preliminary design and performance analysis of the hybrid rocket system. An interior ballistic model was used for the analysis of hybrid rocket performance. MATLAB environment was used to develop the design and performance analysis codes, and visualize the temporal variation of performance characteristics. Key-words: - Hybrid rocket, interior ballistic model, grain design Nomenclature (m/s) (J/kg.K) kg/kmol (kg/s) (kg/s) (kg/s) (m/s) (kg/(m^2.s)) (kg/(m^2.s)) ISBN:

2 (kg/m^3 ) (m/s) m/s kg/s 1 Introduction A hybrid rocket is comprised of fuel and oxidizer in different physical state. It is well known that hybrid rocket engine offers many interesting features such as better safety, simpler design compared to liquefy rocket, relatively low-cost, shutdown-restart capability and environmental friendly. These features make a hybrid rocket as an alternative and competitive selection for launch vehicles, and thrusters for orbit insertion, transfer and maintenance. In a hybrid rocket, the liquid or gaseous oxidizer feeds into the combustion chamber where it mixes with the solid fuel vaporizing by combustion heat. The combustion process is initiated by ignition and sustained by heat of combustion. This process is similar to the wax in candle [1]. Despite many advantages hybrid technology offers, there are several shortcomings dealing with hybrid rocket in terms of overall performance, reliability and cost effectiveness. The performance will differ slightly due combustion instability. The source of the instabilities is based on a complex coupling of thermal transients in the solid fuel, the wall heat transfer blocking due to fuel regression rate, and the transients in the boundary layer that forms on the fuel surface [2]. The oxidizer and fuel are unable to mix quickly in a typical hybrid rocket motor which results in low propellant burning rates causing a reduction in performance [3]. The hybrid burns as a macroscopic diffusion flame, in which the oxidizer-to-fuel ratio varies down the length of the fuel port [1]. The combustion which occurs in the chamber is influenced by the heat transfer to the solid surface and the heat decomposition of the solid-phase fuel. The combustion zone occurs where the stoichiometric mixture ratio is achieved. The simplified model assumes that diffusion combustion takes place in an infinitesimal layer inside a turbulent boundary layer in which the combustion is fed by fuel gases emerging from the gasifying fuel and oxidizer coming from the core flow by diffusion [4]. Recently, there are several issues addressed during the development period of hybrid rocket technology. Problems related to regression enhancement becoming a main focus to many researchers. Other than that are the issues of fuel web burn out, combustion efficiency, combustion stability, throttling characteristics, and nozzle throat material response [6]. The performance of a hybrid rocket mostly depends on the regression rate of the motor. Interestingly, this parameter is hardly to measure due to high degree of scattering effect. There is no comprehensive theory which predicts this quantity. Therefore, it is normally relies on the results of previous tests. Designing a hybrid rocket, it is also a fundamental need to evaluate the pressure and its temporal changes of the combusting gas in the engine chamber because they are related to various phenomena such as ignition and extinction, shape change of a fuel grain due to the combustion, instability due to vortices, acoustics, and injectors, and so on. According to interior ballistic model, during ISBN:

3 combustion, heat is transferred to the solid surface by convection and radiation where the solid phase fuel is decomposed. A stoichiometric mixture will be formed at the point of flame zone. There is a model developed by Greg Zilliac and M. AriffKarabeyoglu to predict the regression rate behavior. However, the model is applicable to vaporizing fuels in a cylindrical grain configuration that do not form significant char or melt layers [7]. The regression rate can be improved by modifying the geometry grain design. It is believed that the larger surface area is preferable. Designing a hybrid rocket engine is not a straight forward process and it remains challenging because of complexity which involves numerous continuous parameters and variables. There are few published propulsion system design codes available for the industry in which many of it employs exhaustive searches to optimize continuous variables [8]. During engine operations both the exposed surface area and perimeter of fuel ports change with time, the mixture ratio will tend to shift even if the oxidizer mass flow is held fixed. High mass flux is desirable in performance to achieve high volumetric efficiency within the combustion chamber. However, this desire is restricted by the fact that efficient combustion may not be possible at these high mass fluxes and that mixture-ratio shifts become more severe under these conditions [9]. Numerous of analytical works have been conducted to describe the air flow during the combustion. The work had been started by describing the mean gaseous flow in solid rocket motor by Culick in 1966 [10]. J. Majdalani had attempted on analytical modeling of basic flow field in hybrid rockets by employing an arbitrary headwall injection which can be used for benchmarking to test large-scale numerical simulations. However, he added that there many limitations and assumptions should be made because of burning rate sensitivity, complex fluid dynamics and interactions with heat transfer from the flame zone and the fuel surface, viscosity effects on pressure and the mixing of the two streams [11]. At Stanford, a group of postgraduate students had launched their 3 diameter Nitrous Oxide/Aluminized Paraffin Hybrid Rocket. They have optimized their design by using Gauss- Newton Nonlinear Least Squares (NLSQ) algorithm and simulate using a 4th-order Runge- Kutta method to integrate the equation of motion [11]. A genetic algorithm called HYROCS code developed by researchers in Purdue University used different approach to design and optimize hybrid rocket [9]. For this reason, we were motivated to try using other approach to examine and analyzed the performance of a hybrid rocket. The following section provides a brief description of the design code, followed by a description of the generic simulation algorithm to estimate the performance of the designed hybrid rocket. 2 Design and Simulation Algorithm Code Description This code is based on the descriptions of Space Propulsion Analysis and Design by Ronald W. Humble, Gary N. Henry and Wiley J. Larson. It is divided into two main sections which are preliminary design decisions and performance estimation over time. A multiport wheel type fuel configuration is selected for our model. At first, the basic design requirement and reasonable design margins must be selected. Figure 1 below shows the flow of the process to design a hybrid rocket. It starts with thermochemistry evaluation to estimate specific heat ratio, molecular mass of combustion products, flame temperature and characteristic velocity. The thermochemical data for LOX/HTPB selection is based on the previous work. To be more flexible, it is assumed that a frozen-flow approximation will take place and at a specific pressure condition. Other than that, we assume that the regression rate will remain constant throughout the length and oxidizer mass flow rate will be held fix in the combustion process. Sizing the overall propulsion system will need several parameters from mission analysis section. Values such as designed nozzle expansion, chamber pressure, initial payload, nozzle efficiency and thrust to weight ratio approximation are required to decide its performance and exit condition. However, there several design constraints to look into such as the melting point of the material, fuel density, nozzle and combustion efficiency and oxidizer mass flow ISBN:

4 rate. Grain design of wheel type port configurations will be computed from the initial oxidizer mass flux and designed number of ports. The fuel length depends on the desired performance such as the regression rate and the burning time. Geometry relations for triangular ports will be applied to compute the dimension of the triangular ports. A straight base line is designed for more than seven number of ports while fewer ports a curvature type of base line is needed to ensure less slivers left after the combustion takes place. The code will automatically plot and draw the port configuration and the length of the fuel through vector matrices. Generic simulation algorithm shows the analysis performance of the designed hybrid rocket over the time period. The burning web depends on the regression rate. Over the period of time, the surface fuel port area will start to increase. We assumed that the burning surface will burn perpendicularly and the corner of each port started to have a fillet shape. According to interior ballistic model, oxidizer-to-fuel ratio will vary with time and ports geometry. This variation will alter all the thermochemical properties and performances over time. The flow of the code as in Fig. 1. Figure 1 3 Basic Hybrid Rocket Motor Design Hybrid rocket design requires the evaluation of thermochemical properties available from Space Propulsion Analysis and Design by Ronald W. Humble, Gary N. Henry and Wiley J. Larson. Use these themochemical properties and determine characteristic velocity using these relations: (1) Thermochemical data can be obtained using these relations: ISBN:

5 (2) (13) (14) (3) Geometry design of wheel type grain fuel: (15) (16) (4) Exit condition can numerically calculated using the isentropic relation. (17) (18) (19) (20) (5) (21) (6) (22) (23) (24) (7) Performance analysis, we take These values are obtained from previous work. Sizing the system, we used this relation to obtain the geometry of the grain configurations. (9) (8) (10) (26) (25) (27) (28) (11) (12) Generic simulation algorithms started by carefully compute the angle at each corner of a triangular port. These angles are formed by assuming that the two side lines and the base is ISBN:

6 burnt perpendicularly leaving each corner a small fillet. (29) 4 Design of the grain design in Hybrid Rocket Motor (30)..(31) Over the period of time, the web started to decrease forming a new perimeter and area at each port. (32) Fig. 2: MATLAB fuel wheel type grain design with 8 ports. Performance estimation for first 60 seconds: (33) The results of these, oxidizer-to-fuel ratio started to shift and new thermochemical properties will be used. By using an internal ballistic model for a non-circular type of fuel, O/F new can be obtained using this relation: (34) This variation of O/F will have effects on the performance of the hybrid rocket over the time period. Both oxidizer and fuel mass flux are changing due to change in burning area. These changes will vary the regression rate and it starts to decrease over the period of time. For simplicity, the oxidizer mass flow rate will remain constant while fuel mass flow rate will vary according to this relation: Fig. 3: Web thickness variation vs time. Fig. 4: Oxidizer-to-fuel ratio vs time. (35) Other important parameters such as the chamber pressure, exit Mach number, exit pressure, exit velocity, thrust, specific impulse and thrust-to-weight ratio are varied with time. Graphs of O/F, web changes, exit velocity, thrustto-weight ratio, regression rate and specific impulse are plotted with respect to the time. Fig. 5: Thrust-to-weight ratio vs time. ISBN:

7 Fig. 6: Regression rate variation over time. Fig. 7: Exit velocity variation over time. Fig. 8: Specific impulse variation over time 5 Discussion Figure 2 describes the fuel of a wheel typed geometry and its length with dimension. The geometry has been drawn according to our initial design parameters. A separate code is developed to plot the vector array in MATLAB. Eight triangular ports are designed for our discussion. A decrease in web thickness is plotted in Figure 3 due to the burning. The decreasing in web thickness results in the increase of port area. The changes in the geometry will result in the variation of oxidizer-to-fuel ratio as in Figure 4. Notice that oxidizer-to-fuel ratio increases with time as port area increases. This ratio is measured at the length where fuel mass flux is measured. The regression rate has a function of the total mass flux shown in Figure 6. The regression rate decrease exponentially with time because of the changes in mass flux. It is more convenient to have the regression rate constant along the fuel length at each time step because of having small variation of port diameter along the length. Figure 5, 7 and 8 indicate the performance parameter of the designed rocket. The thrustto-weight ratio increases sharply during the early stage because of the rapid increase in O/F and corresponds to the characteristic velocity. This progressive burning is mainly due to the increase in burning area. However, both specific impulse and exit velocity have a maximum point then started to decrease. The increase in specific impulse at the early stage is dominated by the propellant mass flow rate which is low and after the increase in port area, this mass flow rate will started to rise resulting a decrease in the total specific impulse. Same goes to the variation of exit velocity which is highly dependent on the chamber pressure and exit conditions. For the future research and development it is highly recommended to develop new analytical performance estimation for different fuel composition and geometry. This analytical performance estimation and preliminary design code will be one of the tools for scaling-up studies of hybrid rocket motors which have been studied by AlonGany. 6 Conclusion Hybrid rocket motors preliminary design and analytical performance estimation codes have been demonstrated with good success. These successes have lead to more geometry design shape and estimate their performances. It will become a tool for future hybrid rocket designers and more modifications can be ISBN:

8 made to study variety of propellants and geometry designs. Acknowledgements The authors would like to thank the Solar Energy Research Institute (SERI),University KebangsaanMalaysia for funding this research (OUP ). References: [1] Humble, R. W., Henry, G. N., & Larson, W. J., Space Propulsion Analysis and Design. United States: McGraw-Hill, [2] Karabeyoglu, M. A., Zilwa, S. D., Cantwell, B., & Zilliac, G., Modelling of Hybrid Rocket Low Frequency Instabilities. Journal Of Propulsion And Power Vol. 21, No. 6, [3] Jacob, E. J., The Effect of Oxidizer Laced Hybrid Rocket Regression Rates and Performance. American Institute of Aeronautics and Astronautics (AIAA) Southeastern Regional Student Conference. Savannah, Georgia: AIAA, [4] Lazarev, A., & Gany, A., Experimental Investigation of Paraffin-Fueled Hybrid Combustion. Third european combustion meeting ecm [5] David, L., space.com. Retrieved January 10, 2012, from SpaceShipOne Wins $10 Million Ansari X Prize in Historic 2nd Trip to Space: October [6] Venuopal, S., Rajesh, K. K., & Ramanujachari, V., Hybrid Rocket Technology. Defence Science Journal, Vol. 61, No. 3, [7] Zillia, G., & Karabeyoglu, M. A., Hybrid Rocket Fuel Regression Rate Data and Modelling. 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. California [8] Schoonover, P. L., Crossley, W. A., & Heister, S. D., Application of a Genetic Algorithm to the Optimization of Hybrid Rockets. Journal Of Spacecraft And Rockets, AIAA, Vol. 37, No. 5, [9] Vonderwell, D. J., Murray, I. R., & Heister, S. D., Optimization of Hybrid-Rocket-Booster Fuel-Grain Design. Journal Of Spacecraft And Rockets, AIAA, Vol. 32, No. 6,1995. [10] Chiaverini, M. J., & Kuo, K. K., Fundamentals of Hybrid Rocket Combustion and Propulsion. Virginia: American Institute of Aeronautics and Astronautics, [11] McCormick, A., Hultgren, E., Lichtman, M., Smith, J., Sneed, R., & Azimi, S., Design, Optimization, and Launch of a 3 Diameter N2O/Aluminized Paraffin Rocket. AIAA ISBN: