Journal of Aerospace Technology and Management ISSN: 1984-9648 [email protected] Instituto de Aeronáutica e Espaço Brasil
Zakeri, Mostafa; Nosratollahi, Mehran; Novinzade, Alireza Multi-Disciplinary System Design Optimization of a Launch Vehicle Upper-Stage Journal of Aerospace Technology and Management, vol. 9, núm. 1, enero-marzo, 2017, pp. 48-62 Instituto de Aeronáutica e Espaço São Paulo, Brasil
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Multi-Disciplinary System Design Optimization of a Launch Vehicle Upper-Stage Mostafa Zakeri1, Mehran Nosratollahi1, Alireza Novinzade2
ABSTRACT: The design method presented in this paper is related to the upper-stage system and its instrumentation, INTRODUCTION expedition and facilitation so as to transfer the satellite from the destination orbit to the target orbit. We used an In a article named “Technologies for future precision strike integrated design method with a structure based on multi- disciplinary system design optimization and developed missile systems - missile design technology” (Fleeman 2001), a simple systematic interference method for designing there is a survey of missile technology concepts, influential aerospace products. The subsystems’ convergence in an parameters in design, and balance among subsystems, using optimized environment, matrix relationship, and integration of new technologies with lower weight and cost communicating the subsystems’ parameters and presentation of design give results while meeting all requirements and considering the with the launcher. Overall configuration as well as missile limitations of the design were the main aims of the research. simulation results from such a design method. The detailed Instead of a merely mathematical optimization design, in explanations for the study are available in his book of Tactical the present study a new design method with a systematic multipurpose optimization approach was designed. In this con- Missiles Design. It needs to be mentioned that design depth is text, the optimization means the parameters are optimized limited in the method yet the functional area is high while lack as a result of the design convergence coefficients. Validation of of integration and systemic communications implementation are the design method was not only obtained through comparison the biggest weak points in this method which he explains and with a specific product but also with the systematic parameters of all upper-stage systems with a similar operation through completes in his 2012 edition of the book. It is claimed in the the results of statistical design graphs. The approximate study that all main parameters of a missile at conceptual design similarities of the results indicate an acceptable and genuine are taken into consideration while the missile has operational design with a quite systematic approach which is better than capability. Operational capability as well as systemic relation an unreal and merely optimized design. integration is the first act in the current study. Keywords: Upper stage, Systems design, Multidisciplinary The history of transition from classic design to modern design optimization, Systems integration. design is not accountable in this study, however, some developed countries have been able to take advantage of system design and multidisciplinary optimization methods to improve conceptual design process through considerable savings in design time and costs (Olds 1993). Brown and Olds (2006) surveyed multi-objective optimization techniques of collaborative optimization (CO), modified collaborative optimization (MCO), bi-level integrated system synthesis (BLISS), and all at once (AAO) on a reusable satellite. The study claims that the best design method cannot be chosen since such activities are for research
1.Space Research Institute – System Engineering Department – Space System Design Laboratory – Tehran/Tehran – Iran. 2.Khaje Nasir Toosi University of Technology – Faculty of Aerospace – Systems Division – Tehran/Tehran – Iran. Author for correspondence:Mostafa Zakeri | Space Research Institute – System Engineering Department – Space System Design Laboratory | Postal Address: 1316943551 – Tehran/Tehran – Iran | Email: [email protected] Received: May 07, 2016 | Accepted: Sep. 08, 2016
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purposes only and require various studies on the results. Conceptual design in the current study is optimized through Systemic design activities are briefly mentioned in this a genetic algorithm. study while most of the activities are focused on comparing It could be claimed that creation of a systematic approach 3 design techniques. In the final conclusion, a comparison and transforming MDO to multi-disciplinary system design is made among design methods based on running time as optimization (MSDO) includes development of MDO well as quality comparisons, which could be said that BLISS methods which develops operational capability based on designed outputs have higher quality. MDO. MSDO approach is available in a limited number Balesdent et al. (2011) surveyed various multipurpose of the articles. optimization methods in space systems design quantitatively. According to Wronski and Gray (2004), one can verify a Various MDO methods to design satellite missiles are sur- comprehensive MSDO implementation in a specific case in veyed in the study and some features, such as strength, price the Massachusetts Institute of Technology (MIT). The specific calculations, flexibility and convergence speed and problem importance of the study is that it gives a true expression of implementation are taken into consideration so as to select MSDO systematic design, multipurpose optimization and the most suitable design method in designing launch vehicle. an obvious process of the algorithm. Mathematical equations of optimization of every method as well Additionally, design and multipurpose optimization of an as main profile of the algorithm with optimization activities of aircraft was studied through implementation and integrated every method are mentioned briefly. Selection of the optimal design tools so as to predict and optimize the implementa- method to design space system based on the mission and va- tion and related expenditures of commercial aircrafts design rious situations such as implementation time, cost, complexity, and production with the aim of reducing the noise through etc. is the final conclusion of the study (Balesdent et al. 2011). accurate selection of configuration and mission parameters Riddle (1998) states that using MDO in designing complex (Diedrich et al. 2006). After surveying some design samples, systems comes with 2 obstacles. One of them originates a brief look to upper stage activities are made. from disconnected and nonlinear essence of design process Engine and trajectory design in Casalino and Pastrone most of mathematical optimization methods are facing. One (2010) is optimized simultaneously. Systematic design is brief other unattractive point of MDO methods is design teams’ in the study and it could be included among the optimization unwillingness to use it and similarity of automatic decision- articles with systematic approach for propulsion engine. making with creative process of innovative design. An upper stage activity is presented with a brief look at Tsuchiya and Mori (2002) claimed that in spite of the upper stage engine of solid fuel engine (Casalino and Pastrone higher speed of MDO with parametric methods, and based 2010). Adami et al. (2015) designed an upper stage performed on which studies are reported to improve system and des- through three forms of MDO. Mathematically, a detailed tination optimization for reusable launch vehicles (RLV), comparison among the three design methods is presented. they are still recognized unsuitable for space systems design, The optimal proof of choice is surveyed mathematically. especially satellite-carrying missiles which are essentially more After considering the aforementioned articles in addition complicated in configuration steps and trajectory design. to their quantitative and qualitative analyses, Table 1 presents The need to design with a systematic approach in addition a summary of their features. to design implementation based on physics of an aerospace product attracts some researchers to optimized systematic design. Aldheeb et al. (2012) tried to create an optimized design METHODOLOGY for a Micro Air Launch Vehicle. In the present study, optimization and trajectory design Designing an optimized multidisciplinary system is a are done through a design algorithm with systematic modern example of aerospace product design. MSDO can approach to reduce payload mass. The look on functional be complex product design process and multidisciplinary design physics in the main algorithm of the article and engineering systems. In this method, the subsystems are model of subsystems is clear. Villanueva et al. (2013) used a related to each other and to a system in an optimized and systematic approach in an article to design solid fuel engine. converging space. Also the main feature of this method is the
J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.48-62, Jan.-Mar., 2017 Zakeri M, Nosratollahi M, Novinzade A 50
Table 1. Distribution of mass components.
Balanced Requirement Subsystems Imbedded Design Physics-based Mathematical-based Full subsystems meeting between design baseline methods methods methods configuration (converge) subsystems depth statistics data Conceptual design classic × _ × _ _ × × System design optimization × × _ × _ × × MDO _ × × _ × _ × MSDO (this study) × × × × × × × presence of human expert in the Designing tool environment • Restrictions: diameter, orbital altitude, payload. and integration of all designing subdivisions. The aim of • Combined merit functions: aiming at minimizing the this approach is the creation of sophisticated and advanced total mass and designing the best way of sending engineering systems that are competitive not only in terms of the satellite to the target orbit. performance but also in terms of value of life cycle. The most important specifications of the MSDO algorithm The most important properties of MSDO method can be are as follows: stated as follows: • Offering new approaches in systematic design derived • Deal with design models of realistic size and fidelity from MSDO designing method. that will not lead to erroneous conclusions. • Using statistical processing in the design process • Reduce the tedium of coupling variables and results (increasing accuracy and rapid convergence). from disciplinary models. • Offering innovative convergence methods. • Allow for creativity while leveraging rigorous, • Optimizing system and subsystems’ design parameters quantitative tools in the design process. Hand-shaking: by using communication matrixes. qualitative versus quantitative. • Convergence of designing upper stage with previous • Data visualization in multiple dimensions. stages of the rocket. • Incorporation of higher-level upstream and downstream • Integrating all the design parameters and meeting all system architecture aspects in early design: staged the restrictions and requirements. deployment, safety and security, environmental • Ability to enter any new special requirement in the sustainability, platform design, etc. way of designing. In this procedure, design algorithm similar to other Algorithm design of upper stage includes the following: design algorithms is not of tree type or merely a mathematical • Statistical designing and analysing statistical data. optimization. The MSDO algorithm is designed to link all the • Designing the layout of subsystems and subdivisions. subdivisions directly to each other and the best convergence • Dynamics and trajectory design. is applied according to physics and subdivisions. In this way, • Propulsion system design and tank design. the designer can easily put all the limitations and restrictions • Feeding system design. of design to work. In this paper, the concepts of design and • Analysis of mass-dimensions and mass associated with multistep optimization are used in a strategic computing the previous stage of launch vehicle design. environment to design upper-stage which transfers from • Structural design and stiffener. parking orbit to the target orbit. Presented parameters in this • Systematic analysis (configuration, integrating and procedure are classified as: optimization). • Design or independent variables: including fuel mass All the requirements and limitations of designing the ratio, engine structural mass ratio to the whole engine, upper stage is done based on the objectives, bottlenecks, and etc. administrative constraints. These constraints are applied in • Simple limitations: including mass ratios, Isp, etc. all the phases with the presence of the designer in the design
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environment. All the requirements and restrictions can be of the communication of the propulsion system components. classified as follows: The most important design matrix is the comprehensive design • The requirements of trajectory. matrix which is shown in Fig. 2. Only the main parameters of • The requirements of the launch vehicle and launch. design are mentioned in the matrixes. • The requirements of subsystems and subdivisions. In designing the MSDO algorithm, several optimization • The requirements of construction and assembly. and convergences were used. The goal of optimization is to • The limitations in choosing the hardware. achieve the least amount of goal parameters; however, the goal Basic hypotheses regarding the design of upper stage are of convergence is to converge all design parameters within each as follows: other as well as meeting all the requirements and limitations. • Payload. Optimization includes: • Parking orbit and target. • Optimizing comprehensive design matrix based on • Mechanical properties. the MSDO and through genetic algorithm. • Helium mechanical properties. • Optimizing trajectory through genetic algorithm. • The characteristics of the chosen fuel. • Optimizing propulsion system through genetic • Safety factors. algorithm. • Temperature of tanks and the flame. • Optimizing total mass through genetic algorithm. The main body of the communication among subsystems, • Optimizing the thickness of the crust and stiffener based within each other, and the system is created according to on the buckling test and through genetic algorithm. the design matrix. Design matrixes are the designer’s guide In Table 2, one can see the above-mentioned optimization for displaying design communications and the effects of properties. Design convergence items in MSDO algorithm the parameters on each other (Peoples and Schuman 2003). include the acceleration of design process according to the The communicative matrix between the components of statistical equations (reducing the time while increasing propulsion system is shown in Fig. 1 due to the importance accuracy).
Propellant and βi Pc Pe γ, ∆Vi Pc L* θ Ftu fs MP Ftu Pblow system Optimizer
βi + – βi ≤ ε
Isp tt β M T Isp ε ε, MC tt i + p Ballistic
V L m ∆Ph c c t Nuzzle and chamber R h R h M M Vto Vtf Pb tf tf to to o f Tank mhe mth Vth Nh mh Ullage
Pc and Pe: Chamber and exit pressure; Pblow: Blow tanks pressure; Ph: Distribution of the pressure gradient;
L*: Combustion characteristic length; ΔVi : Energy change in each burn tt:
Burn time distribution; Rt and ht : Radius and height of the tank;
Vth and mth: Volume and mass of the helium tanks’
mh: Blow rate; Nh: Number of blowing tanks; Vto, Vtf and Vc: Fuel tank capacity oxidation and combustion;
ε: Expansion ratio; T and Isp: rust and specic impulse; Lc: Combustion chamber length;
Ftu: Yield stress; fs: Reliability factor; ts: ickness of body structures; tsm: Maximum thickness of body structures.
Figure 1. Propulsion system matrix.
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. System ∆Vi, ti, m*, T*, OF P h, ti fs, nx, ny β* Ms* Mp* L*, D* and trajectory
Engine Main PTox, PTfu Pc m , m , m A , L , R , h , ε speci cation engine/oxidant e Tox Tfu t t t t and fuel tank
Ullage system . m n , V speci cation m he th b h Ullage system
Crust structure and sti ener Crust structure speci cation Nxula, Nxhea, f I, J, mcr, mst tcr, lmax and sti ener Receiving systematic data systematic Receiving
Mass distribution msub m (x) Con guration mass
Size distribution Rsub, hsub D, L dx, dy Con guration size
OF: Oxide fuel ratio; Rsub and hsub: Subsystem dimensions; At, Lt ,Rt, and ht: Engine size distribution;
nx and ny: Axial and lateral acceleration coe cients; dx and dy: Dimension distribution;
m0(x) and msub: Mass distribution and mass of the subsystems; me and mT: Mass of the engine and of the tanks;
Nequ: Equivalent stress distribution; Vb: Volume of gas tanks.
Figure 2. Design correlations matrix.
Primary values for design are obtained with statistical In Fig. 3, it is presented the interference between convergence equations. Propulsion system convergence through propulsion ! system mass factor is defi ned as (Motlagh et al. 2013): System optmizer:System ropt, Rim, Rizer:!" ,!#$%&#' ! System optimizer:! ,e!# ox &#f Subjected to: minimizing" M$%, L' /D sp e +e β = M / (M + M ) (1) ( & "- s s p Subjected to :MMininmimiz+ii"zningg: : )* , MinimiziPropulsionng: ( )* &system- , " " β
input algorithm Initial (2) βn = βn – 1 < ε
βn a l Th e convergence of upper stage compared with the previous 0 i n p u t I n i t Propulsion system β stage launch vehicle is: n alg –o rit h≤m βn βn–1 ε N α = M / M (3) p1 p2 Y
(4) αn – αn – 1 < ε Figure 3. Interference between convergence and optimization. n n Table 2. Optimization properties.
System optimizer Subjected to Generations Population Crossover Mutation . / 0 . 1/ 0 2 3 4!
MSDO optimization Min: Mt and L/D 100 100 Scattered Uniform (0.2) Y Orbital optimization 100 20 Scattered Uniform (0.2) Min: Mp Propulsion optimization 100 100 Scattered Uniform (0.2) Min: Msp and Le/De Total mass optimization 100 20 Scattered Uniform (0.2) Min: Mt
Structure optimization Min: Mst 100 20 Scattered Uniform (0.2)
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and optimization of the algorithm (Fig. 4). Design variables are • Systematic parameters of upper stage. described in Table 3. • Subdivisions’ mass-dimension distribution. Design output includes the following: • Systematic data of subdivisions.
Table 3. Design variables. Design System optimizer Subjected to Name Unit Limitation Description variables Chamber pressure bar – Pc 5 < Pc < 15 Min: Mt OF Oxide to fuel ratio – 3.5 < OF < 4.5 MSDO Optimization and According to fuel N Number of helium tanks – 2 < N < 12 L/D h h N Thrust to weight ratio – 1.5< n <4.5 According to configuration r Transfer orbit Perigee Orbital Optimization Min: M pt km 200 ...36000 According to orbit design sp Transfer orbit Apogee rαt Nozzle exit re re < D Propulsion Min: M sp Oxidizer tank profile m – Rox Rox < D – ts Optimization and Le/De Fuel tank profile Rf Rf < D – ts Total mass Min: M – Selection of components – – According to data feasibility Optimization t
t Body thickness m t – 2 < t < t – Structure s sm s sm Min: M J Stiffener rigidity m4 Stiffener selection Optimization st – – Structural Materials – – – Propulsion system β – β < ε β Propulsion Mass factor – 0.8 < β < 1.5 According to statistical data convergence n n–1 Stages fuel mass ratio α – α < ε α Stages mass factor – 0.08 < α < 0.3 According to statistical data convergence n n–1
Mass and total length Feasibility Payload mass Statistical Mass-dimensions components Mission Mass analysis Basic dimension Total mass con guration as Mass Feasibility estimation estimation previous stage distribution Layout type Layout Mass-dimensions con guration Design P c Mission O/F M Fuel mass X = S J = c Orbital Nh L/D System optimizer: rpt, rαt fuel mass dynamics α convergence αn – αn–1 ≤ ε n Previous stage Minimizing: Mp
System optimizer: Select Components rust - Time pro les Fuel mass con guration Propulsion system Propulsion Minimizing: Mt rust - Time criterions
Loading distribution within the stream components Body exact e mass Simulation Motor Combustion chamber pressure structures Feeding Tanks e decision to decision e
Stiener pro les designing continue Structural Result system stieners discussion Propulsion system mass-dimensions speci cations Structural arrangement End β convergence Propulsion system System optimizer: Mechanical properties, t, J System optimizer: r , R , R e ox f con guration Minimizing: Mt Minimizing: Msp, Le/De
Figure 4. MSDO algorithm.
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However, the most important outputs of the algorithms (15) include the following: • Multidisciplinary optimization system. (16) • Adaptation of all design parameters. • Meeting all the requirements and limitations. 16
14 deSIGN MeTHodoLoGy oF SUBSySTeMS 12 Statistical Design Preliminary estimation of systematic parameters in upper 10 [ton] k stage design process is of utmost importance due to the M 8 following reasons: creating a basic confi guration for upper 6 stage and faster convergence and more optimal design. In statistical design via obtained data, the created population 4 and needed graphs were extracted to create initial input 2 4 6 8 10 12 M [ton] (Mirshams and Khaladjzadeh 2010). For instance, 2 sample pay graphs are given in Figs. 5 and 6. Th e payload mass is the fi rst Figure 5. Dry mass versus payload mass. and the most important input in designing an upper stage.
9 (5) 9
where: Mk and Mpay are the fi nal and payload mass. 7 Th e thrust to weight relative to burn time is represented by: 6 n [Kn/s]
(6) 5
4
500 600 700 800 900 1000 1100 Statistical equations are derived as follows: μp and μf payload t [s] mass ratio and dry mass ratio. Figure 6. Thrust/weight versus burn time. (7) Trajectory Simulation and Design (8) In this study, trajectory design (Fig. 7) is done based on Hahman’s approach as well as 2 references (Chobotv 1996; (9) Curtis 2005).
(10) Parking orbit Trajectory design Target orbit Trajectory Number of reburns (11) Inclination change design Amount of energy required Equipment's lifetime Trajectory time (12)
Figure 7. Trajectory design algorithm. (13) Mass Analysis (14) Acc ording to statistical studies, linear relationship between the dry mass of the rocket block with the portable
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mass of the same rocket block represents the similarity and the way to achieve them are illustrated. Final mass of of mass ranges of the whole subsystems and their subcategories the upper stage is achieved via the table and considering in each block with the same objectives. Thus, determining all the mass parameters. The final mass of upper stage mass ranges of the main subcategories based on the main can be achieved with all mass parameters presented in effective parameters is viable. In Table 4, all the objects Table 4.
Table 4. Distribution of the mass components.
Upper Stage Estimated mass Computational mass Selective mass
Satellite installation stand × Body structure × Tank protector × Structure Motor holder × Nacelle × Motor front and back flange × Separation equipment × Helium × Feeding system Helium tank × Other equipment × Fuel tank × Oxidant tank × Connection tunes × Propulsion Motor elements × Combustion chamber × Nozzle × Other components of motor × Flight computer × Guidance control block ×
Guidance and Inertia measurement block × control hardware Valves × Accessories × Telemetric system × Electromechanical actuators × Cables and electrical connections × Actuators Thrusters × Braking motor × Acceleration motor × Central computer × Cases guidance Sensors × Gyro planes ×
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Propulsion Subsystem Analysis After propulsion system design convergence, the amount Different specifications of a space propulsion system of optimal fuel mass in every engine-on status is achieved. with other propulsion systems of a rocket are summarized as In the present study, the optimal propulsion system design (Friedman and Kenny 1965): is achieved through converging the structural convergence • Different outside conditions (space conditions). factor (β). Using upper stage mass in every design loop, • On-Off numbers (based on the trajectory design). all subsystems’ propulsion design is achieved and then • Less thrust-to-weight ratio. the new value for fuel mass and convergence factor is • Th e use of pressure feed system (high accuracy but obtained. low thrust) (Sutton and Biblarz 2001). Figure 8 shows the propulsion analysis algorithm. (22)
Trajectory design System
where: j is the integration loop counter design; Msh, Mse, and
MsT are dry mass of subsystems. Th e equation for convergence Determine internal ballistic initial coeffi cient (β) is defi ned as follows: parameters
Determine area of the throat and (23) average thrust according to nozzle external diameter
Th e internal relations of the propulsion system are shown Calculate nozzle external diameter and number of motors on burn time in Fig. 1.
Calculate sprinkle system Feeding System Analysis Controlling pressure in fuel tanks is easily possible using the Calculate mass-volume of nozzle pressure system feed. Furthermore, the simplicity of adjusting and combustion chamb pressure in pressure system feed determines its high reliability, Figure 8. Propulsion sub-algorithm. thus the process of switching and fl ow control is easily possible. Output fl ow could be controlled with installing a heater or pressure Propulsion System Convergence control valves. Generally, the concurrent process of disembarkation In the fi rst design loop, the amount of fuel mass and the of capsules containing compressed gas and fi lling propellant tanks fi nal mass of upper stage in every burning is calculated through could be shown via Eqs. 24 and 25 (Huzel et al. 1992). the following equations: High-pressure tanks (capsules):
(17)
(24) (18)
(19) Propellant tanks:
(20) (25)
(21)
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where: Q is heat transfer between the gas blowing and its According to blow subsystem sub-algorithm, numbers of environment; Z is the gas compressibility factor; V is the volume blow tanks are selected considering confi guration and layout. . . control; T is the temperature; P is the pressure; mi . md are Th e fi nal mass of feeding system is calculated by the following blowing gas mass fl ow rate input and output volume control; hi equation: and hd are blowing gas enthalpy entry and exit control volume. Th e sub-algorithm of feeding system is shown in Fig. 9. (29)
InitialInitial llayoutayout ooff bblowlow Tanks Analysis subsystemsubsystem Fuel and oxidant tank Th e shape of the tank is a function of weight, leakage rate, dimensions tank volume, and locating restrictions. Spherical tanks have Fuel and oxidant tank Initial inputs Initial inputs Tanks'dim eoutletnsion s ow rate the best empty weight-to-loaded weight ratio (Hutchinson and Tanks outlet flow rate Tanks' volume Olds 2004). Tank design sub-algorithm is shown in Fig. 10. Initial layout and estimation of blow change in on/o Other elements such as control valves are selected according tanks'Initial volumelayout a nusingd esti midealatin ggas blo equationw tanks motor number to input pressure and fl ow rate. volume using ideal gas equation of cycles Tanks volume Temperature and pressure changes inside and oxidant ctankshange in on/off TempCalculateerature an dblow pres pressuresure chan ofge stanks insid eat a eachnd ox momentidant motor number of Check all e ective requirements in volume and structure of tanks tanks cycles Checking all effective requirements Calculating blow pressure to tanks at each moment in volume and structure of tanks Mixing ratio Calculate pressure drop (transfer, dynamic head, vents and ...) Calculate required propellant's volume and types of Calculating pressure drop Calculate nal tank's mass propulsion Select tolerable pressure Calculate(tr instantaneousansfer, dynami c ow hea drate, vents and …) of the helium tanks Mixing ratio and and required helium volume Calculating required propellant volume Select the best layout and dimension design of tanks types of Selecting tolerable Calculating instantaneous calRecalculateculating fin nalal ta nvolumek mass pressure of the helium propulsion Selecflo wtall ra trequirede and req elementsuired tanks helium volume n = n +1 Shear and compressive forces during time n = 2 Selecting best layout and dimension design of tanks Accepting suitableSelecting all reqVuihr e=d V th / 1.05 n Recalculating final volume locating elements Calculate nal pressure and thickness of the propellant tanks Calculating thickness and mass of each tank
Shear and compressive forces Final mass-dimension con guration of blown= 2subsystem Calculate nal mass and con guration of the tanks n=n+1 during time V V = th FigureAcc e9.pti nBlowg suit asystemble sub-algorithm.h Figure 10. Tank design sub-algorithm. locating 1 . 05 Calculating final pressure and Structureth iAnalysisckness of the propellant tanks Volume, thickness, andCal ctheulat imassng thi cofkn eeveryss helium tank is obtained from the followingand mequationsass of each (Humbletank et al. 1995): In structural analysis, providing stability and structural strength to deal with all external pressures is the main goal. In Calculating final mass and Final mass-dimension order to determine the mass of the structure, at fi rst, the loads configuration of blow subsystem (26) configuration of the tanks on each section of the structure shall be determined via diff erent stages of preparation to the end of the fl ight. Loads on each (27) section mean axial force, shear force and bending torque which is applied under external loads during structure mission. Critical load for each section is occurred based on existing experiences in any of the selected above stages. Loading sub-algorithm and (28) the thickness of the body structure is shown in Fig. 11. Aft er calculating longitudinal and lateral load fl ow, equivalent stresses are obtained and exerted to the structure which
where: Vh, tG and MTh are volume, thickness, and mass determines the thickness of the body (Ardema et al. 1996; of blowing tanks; σhw and ρhw are the mechanical properties. Crawford and Burns 1963).
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(30) Stiff ener rigidity and then the shape of the stiff ener profi le can be selected through the following equation: (31) (34)
(32) where: J is the rigidity stiff ener.
(33) Dimension Design Dimension design is achieved with 2 diff erent assumptions which, in one, upper stage diameter was determined and, in the where: N is the axial force; M is the bending moment. other, it was calculated in the output. Th e calculation of the length According to the critical situation exerted on the upper stage and diameter can be achieved through the following equation: structure, lateral stiff eners with low number could be used to strengthen body structure. Design algorithm for strengthening (35) stiff eners is shown in Fig. 12. (36)
Dimensions, mass distribution and block layout
Identify critical conditions Inner and outer atmosphere RESULTS SAMPLe SoLUTIoN
Calculate center of gravity and extracting force equilibrium A sample solution for upper stage design is presented in equations in each critical condition this section to generally introduce the design method: 1. Mission defi nition Calculate axial and lateral acceleration factor and • Payload mass is 1.5 tones with parking orbit which graphs of shear and axial force and bending moment is 200 KMs and destination orbit is 36000 KMs with inclination of 45 degrees change. Calculate equivalent force in each condition f = 1.5 • and determine maximum thickness Other design inputs are based on requirements and limitations. Figure 11. Body structure sub-algorithm. 2. Results of supplying design initial inputs are shown in Table 5. Body skin thickness Table 5. Initial input. Calculate maximum step Input variable Values Calculate number of sti eners β 0.162 Calculate new step T (kn) 48.36 Increase number Decrease body Perform buckling test of rein forces or thickness μp 0.75 Increase skin Calculate critical pressure thickness MP (ton) 10.23
pcr > p MF (ton) 3.47
M0 (ton) 13.70 p < 7p/6 cr Speci cations of pro les of the 3. Trajectory design: Calculate rigidity of sti eners sti eners • Hohmann’s transfer (3 times Re burn). Select shape of pro le • Determining transfer orbit (according to energy Figure 12. Stiffener structure sub-algorithm. limitation and optimized mode).
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4. Determining material and construction inputs of the 9. Design of tanks: mass and volume of tanks (Table 8). subsystem: Table 8. Tank parameters. • Used mechanical properties, environmental conditions, used fluid properties. Parameter name Values • Determining fuel and oxidizer (hydrogen/oxygen). Oxidant volume 7.050 m2 5. Initial feasibility based on ability to transport about Oxidant mass 9.669 ton 13 tones to the parking orbit through stages of launcher Fuel volume 4.2827 m2 rocket. Fuel mass 3.581 ton 6. System design: Oxidant tank radius 1.1895 m • Determining configuration parameters according Fuel tank radius 1.1895 m to Table 4. Oxidant tank pressure 12 bar • Selecting initial mass factor. Fuel tank pressure 11.2 bar 7. Propulsion design parameters (Table 6). Fuel tank thickness 0.72257 m Table 6. Propulsion engine parameters. Oxidant tank thickness 3.801 mm Parameter name Input variable Values Fuel tank thickness 3.5485 mm
Thrust factor Cf 1.68 Nozzle expansion ratio ε 37 10. Body structure: determining body thickness and Specific impulse Isp 326 stiffener which requires determining critical modes properties of previous steps, fairing and types of stiffener. Burning time tb (s) 680 11. Mass distribution: Thrust T (kn) 60 . • Determining mass distribution (Table 9). Propulsion flow rate m (kg/s) 20.52 • Upper stage primary masses. Motor mass mm (m) 497 Motor diameter d (m) 0.852 m Table 9. Other components mass distribution.
Motor length Lm (m) 2.04 Parameter name Values (kg) Nozzle length Ln (m) 1.14
Nozzle outlet diameter de (m) 0.78 Control block 245.88 Actuators 94.56 8. Feeding system design (Table 7): Cables 113.48 Body 189.1397 Table 7. Feeding system parameters. Telemetry 151 Parameter name Input variable Values Stand 150
Blowing system mass mh (kg) 66 Disposal system 60
Cases blowing mass MTh (kg) 34.5 Engine maintenance 28.28
Helium mass mhe (kg) 20.6 Control segments 18.91
Thickness of helium tanks th (mm) 4.45 Long tube 31
Radius of helium tanks rh (mm) 257 Flanges 28.28
Number of helium tank Nh 6 Separation 75 Gyro planes and IMU 35 a. Selecting pressure-feed system. b. Calculating pressure drop in fuel flow which is 12. Upper stage mass and dimensions: 3.2 bars and for oxidant is 4 bars. • Upper stage dimensions (Table 10). c. Fuel tank pressure 11.2 bars and oxidant 12 bars. • Upper stage primary masses (Table 11).
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Table 10. Diameter and total length. In Table 13, the errors in the statistical design methods and MSDO compared to the systematic data of Cent. D-5 upper stage Parameter name Values system. As shown in Table 5, errors of fuel mass, dry mass and Dimensional ratio 2.7812 total mass in MSDO design are decreased by 9 to 16% com- Diameter (m) 2.4921 pared with Cent. D-5. Furthermore, the accuracy of primary Total length (m) 6.9314 data derived from the statistical design is obvious in this table.
Table 11. Mass parameters. 3,000
Parameter name Values
Fuel mass 13.249 2,000 Final mass 3.391 Structure mass 1.891 t [s] 1,000 Total mass 16.64 dIFFeReNT VARIANTS ANd VALIdATIoN 0 0.5 2.5 4.5 Technology for constructing a launch vehicle in countries n [N/kg] varies from each other, however, the statistical graphs indicate the approximate similarity of systematic parameters Figure 14. Comparative curve of burn time due to T/W. for upper-stage systems. For instance, Fig. 13 shows the relationship of payload mass and dry mass in the upper- 0.11 stage system. The real samples are circular and the samples 0.1 derived from this paper for UDMH/N204 fuel are square- shaped. The comparative curve of burn time due to thrust/ 0.09 weight is presented in Fig. 14. Convergence factors (α and α 0.08
β) are illustrated in Figs. 15 and 16. 0.07 The close similarity of these graphs is the main reason 0.06 to validate the results derived from the study. At this 0.05 point another validation was compared with Cent.D-5 0 2 4 6 8 10 12 14 16 upper-stage of Atlas V (401) which is presented in Table Number of rounds design
12. Problem inputs: Mpay = 4.75 ton; D = 3.05m and Figure 15. Convergence factor Isp = 4378 N*s/kg. α.
12 0.15 0.14 8 0.13 0.12 β [ton] f 0.11
M 4 0.1 0.09 0 0.08 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Number of rounds design Mpay [ton]
Figure 13. Final mass versus payload mass. Figure 16. Convergence factor β.
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Table 12.Comparation of validation to Cent D-5 upper-stage.
Output data (ton) n (N/kg) Mp M0 (ton) µf µp β System parameters Cent. D-5 19.65 26.78 0.266 0.18 0.10 3.64 Statistical design 16.8 23.66 0.29 0.2 0.11 3.88 MSDO 18.93 26.01 0.27 0.182 0.109 3.61
Table 13. Methods errors compared to the systematic data • Presenting a sample upper stage according to different of Cent. D-5 upper stage system inputs. Design type Propellant Dry weight Lift off • Logical convergence of parameters to logical values. method weight [%] [%] weight [%] • Ability of performing general feasibility. Statistical 11.6 11.3 14.5 • Extensibility to accurate initial design. MSDO 0.2 2.1 3.66 • Ability of networking the design under supervision 0.27 0.182 0.109 3.61 of the system. • Designing systematic sample of upper stage. • General guideline based on implementation of detail design (limitations of methods and range of CONCLUSION parameters). • All the important design points are specified in order Design processes of all elements are done simultaneously to divide the algorithm for performing different in this paper. In each design loop, calculations become more projects. accurate and results of each section, more suitable according to other systems. In this design method, a mistake can be found by system (because it affects all elements) and it would be easier AUTHOR’S CONTRIBUTION to fix it. The main results are: • Proportional with technology and ability for cons- Zakeri M has provided the article’s text; Nosratollahi M and truction. Novinzade A carried out the guidance and control of the paper; • Logical relation of all segments and subsystems. the final set was conducted by Zakeri M and Nosratollahi M; • Developing a national design and method. the idea was developed by all authors.
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J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, No 1, pp.48-62, Jan.-Mar., 2017