Multi-Disciplinary System Design Optimization of a Launch Vehicle Upper-Stage

ABSTRACT: The design method presented in this paper is related to the upper-stage system and its instrumentation, expedition and facilitation so as to transfer the satellite from the destination orbit to the target orbit. We used an integrated design method with a structure based on multidisciplinary system design optimization and developed a simple systematic interference method for designing aerospace products. The subsystems’ convergence in an optimized environment, matrix relationship, and integration of the subsystems’ parameters and presentation of design give results while meeting all requirements and considering the limitations of the design were the main aims of the research. Instead of a merely mathematical optimization design, in the present study a new design method with a systematic multipurpose optimization approach was designed. In this context, the optimization means the parameters are optimized as a result of the design convergence coefficients. Validation of the design method was not only obtained through comparison with a specific product but also with the systematic parameters of all upper-stage systems with a similar operation through the results of statistical design graphs. The approximate similarities of the results indicate an acceptable and genuine design with a quite systematic approach which is better than an unreal and merely optimized design.


INTRODUCTION
In a article named "Technologies for future precision strike missile systems -missile design technology" (Fleeman 2001), there is a survey of missile technology concepts, influential parameters in design, and balance among subsystems, using new technologies with lower weight and cost communicating with the launcher.Overall configuration as well as missile simulation results from such a design method.The detailed explanations for the study are available in his book of Tactical Missiles Design.It needs to be mentioned that design depth is limited in the method yet the functional area is high while lack of integration and systemic communications implementation are the biggest weak points in this method which he explains and completes in his 2012 edition of the book.It is claimed in the study that all main parameters of a missile at conceptual design are taken into consideration while the missile has operational capability.Operational capability as well as systemic relation integration is the first act in the current study.
The history of transition from classic design to modern 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 purposes only and require various studies on the results.Systemic design activities are briefly mentioned in this study while most of the activities are focused on comparing 3 design techniques.In the final conclusion, a comparison is made among design methods based on running time as well as quality comparisons, which could be said that BLISS designed outputs have higher quality.Balesdent et al. (2011) surveyed various multipurpose optimization methods in space systems design quantitatively.Various MDO methods to design satellite missiles are surveyed in the study and some features, such as strength, price calculations, flexibility and convergence speed and problem implementation are taken into consideration so as to select the most suitable design method in designing launch vehicle.Mathematical equations of optimization of every method as well as main profile of the algorithm with optimization activities of every method are mentioned briefly.Selection of the optimal method to design space system based on the mission and various situations such as implementation time, cost, complexity, etc. is the final conclusion of the study (Balesdent et al. 2011).
Riddle (1998) states that using MDO in designing complex systems comes with 2 obstacles.One of them originates from disconnected and nonlinear essence of design process most of mathematical optimization methods are facing.One other unattractive point of MDO methods is design teams' unwillingness to use it and similarity of automatic decisionmaking with creative process of innovative design.Tsuchiya and Mori (2002) claimed that in spite of the higher speed of MDO with parametric methods, and based on which studies are reported to improve system and destination optimization for reusable launch vehicles (RLV), they are still recognized unsuitable for space systems design, especially satellite-carrying missiles which are essentially more complicated in configuration steps and trajectory design.
The need to design with a systematic approach in addition 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 for a Micro Air Launch Vehicle.
In the present study, optimization and trajectory design are done through a design algorithm with systematic approach to reduce payload mass.The look on functional design physics in the main algorithm of the article and model of subsystems is clear.Villanueva et al. (2013) used a systematic approach in an article to design solid fuel engine.
Conceptual design in the current study is optimized through a genetic algorithm.
It could be claimed that creation of a systematic approach and transforming MDO to multi-disciplinary system design optimization (MSDO) includes development of MDO methods which develops operational capability based on MDO.MSDO approach is available in a limited number of the articles.
According to Wronski and Gray (2004), one can verify a comprehensive MSDO implementation in a specific case in the Massachusetts Institute of Technology (MIT).The specific importance of the study is that it gives a true expression of MSDO systematic design, multipurpose optimization and an obvious process of the algorithm.
Additionally, design and multipurpose optimization of an aircraft was studied through implementation and integrated design tools so as to predict and optimize the implementation and related expenditures of commercial aircrafts design and production with the aim of reducing the noise through accurate selection of configuration and mission parameters (Diedrich et al. 2006).After surveying some design samples, a brief look to upper stage activities are made.
Engine and trajectory design in Casalino and Pastrone (2010) is optimized simultaneously.Systematic design is brief in the study and it could be included among the optimization articles with systematic approach for propulsion engine.
An upper stage activity is presented with a brief look at upper stage engine of solid fuel engine (Casalino and Pastrone 2010).Adami et al. (2015) designed an upper stage performed through three forms of MDO.Mathematically, a detailed comparison among the three design methods is presented.The optimal proof of choice is surveyed mathematically.
After considering the aforementioned articles in addition to their quantitative and qualitative analyses, Table 1 presents a summary of their features.

METHODOLOGY
Designing an optimized multidisciplinary system is a modern example of aerospace product design.MSDO can be complex product design process and multidisciplinary engineering systems.In this method, the subsystems are related to each other and to a system in an optimized and converging space.Also the main feature of this method is the  presence of human expert in the Designing tool environment and integration of all designing subdivisions.The aim of this approach is the creation of sophisticated and advanced engineering systems that are competitive not only in terms of performance but also in terms of value of life cycle.
The most important properties of MSDO method can be stated as follows: • Deal with design models of realistic size and fidelity that will not lead to erroneous conclusions.

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Reduce the tedium of coupling variables and results from disciplinary models.

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Allow for creativity while leveraging rigorous, quantitative tools in the design process.Hand-shaking: qualitative versus quantitative.

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Data visualization in multiple dimensions.

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Incorporation of higher-level upstream and downstream system architecture aspects in early design: staged deployment, safety and security, environmental sustainability, platform design, etc.In this procedure, design algorithm similar to other design algorithms is not of tree type or merely a mathematical optimization.The MSDO algorithm is designed to link all the subdivisions directly to each other and the best convergence is applied according to physics and subdivisions.In this way, the designer can easily put all the limitations and restrictions of design to work.In this paper, the concepts of design and multistep optimization are used in a strategic computing environment to design upper-stage which transfers from parking orbit to the target orbit.Presented parameters in this procedure are classified as: • Design or independent variables: including fuel mass ratio, engine structural mass ratio to the whole engine, etc.

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Simple limitations: including mass ratios, I sp , etc.

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Combined merit functions: aiming at minimizing the total mass and designing the best way of sending the satellite to the target orbit.The most important specifications of the MSDO algorithm are as follows: • Offering new approaches in systematic design derived from MSDO designing method.

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Using statistical processing in the design process (increasing accuracy and rapid convergence).

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Offering innovative convergence methods.

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Optimizing system and subsystems' design parameters by using communication matrixes.

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Convergence of designing upper stage with previous stages of the rocket.

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Integrating all the design parameters and meeting all the restrictions and requirements.

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Ability to enter any new special requirement in the way of designing.Algorithm design of upper stage includes the following: • Statistical designing and analysing statistical data.

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Designing the layout of subsystems and subdivisions.

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Dynamics and trajectory design.

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Propulsion system design and tank design.

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Feeding system design.

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Analysis of mass-dimensions and mass associated with the previous stage of launch vehicle design.

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Structural design and stiffener.

Systematic analysis (configuration, integrating and optimization).
All the requirements and limitations of designing the upper stage is done based on the objectives, bottlenecks, and administrative constraints.These constraints are applied in all the phases with the presence of the designer in the design environment.All the requirements and restrictions can be classified as follows:

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The requirements of trajectory.

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The requirements of the launch vehicle and launch.

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The requirements of subsystems and subdivisions.

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The requirements of construction and assembly.

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The limitations in choosing the hardware.Basic hypotheses regarding the design of upper stage are as follows: • Payload.

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Parking orbit and target.

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The characteristics of the chosen fuel.

Safety factors.
• Temperature of tanks and the flame.The main body of the communication among subsystems, within each other, and the system is created according to the design matrix.Design matrixes are the designer's guide for displaying design communications and the effects of the parameters on each other (Peoples and Schuman 2003).The communicative matrix between the components of propulsion system is shown in Fig. 1 due to the importance of the communication of the propulsion system components.The most important design matrix is the comprehensive design matrix which is shown in Fig. 2.Only the main parameters of design are mentioned in the matrixes.
In designing the MSDO algorithm, several optimization and convergences were used.The goal of optimization is to achieve the least amount of goal parameters; however, the goal of convergence is to converge all design parameters within each other as well as meeting all the requirements and limitations.Optimization includes:

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Optimizing comprehensive design matrix based on the MSDO and through genetic algorithm.
• Optimizing trajectory through genetic algorithm.

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Optimizing propulsion system through genetic algorithm.
• Optimizing total mass through genetic algorithm.

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Optimizing the thickness of the crust and stiffener based on the buckling test and through genetic algorithm.
In Table 2, one can see the above-mentioned optimization properties.Design convergence items in MSDO algorithm include the acceleration of design process according to the statistical equations (reducing the time while increasing accuracy).

Tank
Ullage    (1) Primary values for design are obtained with statistical equations.Propulsion system convergence through propulsion system mass factor is defi ned as (Motlagh et al. 2013): Th e convergence of upper stage compared with the previous stage launch vehicle is: In Fig. 3, it is presented the interference between convergence β = M s / (M s + M p ) and optimization of the algorithm (Fig. 4).Design variables are described in

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Systematic parameters of upper stage.
• Systematic data of subdivisions.In statistical design via obtained data, the created population and needed graphs were extracted to create initial input (Mirshams and Khaladjzadeh 2010).For instance, 2 sample graphs are given in Figs. 5 and 6.Th e payload mass is the fi rst and the most important input in designing an upper stage.

Trajectory Simulation and Design
In this study, trajectory design (Fig. 7) is done based on Hahman's approach as well as 2 references (Chobotv 1996;Curtis 2005).
where: M k and M pay are the fi nal and payload mass.Th e thrust to weight relative to burn time is represented by: (5)    × mass of the same rocket block represents the similarity of mass ranges of the whole subsystems and their subcategories in each block with the same objectives.Thus, determining mass ranges of the main subcategories based on the main effective parameters is viable.In Table 4, all the objects and the way to achieve them are illustrated.Final mass of the upper stage is achieved via the table and considering all the mass parameters.The final mass of upper stage can be achieved with all mass parameters presented in Table 4.
Table 4. Distribution of the mass components.

Propulsion Subsystem Analysis
Different specifications of a space propulsion system with other propulsion systems of a rocket are summarized as (Friedman and Kenny 1965): • Different outside conditions (space conditions).
• On-Off numbers (based on the trajectory design).
• Th e use of pressure feed system (high accuracy but low thrust) (Sutton and Biblarz 2001).Figure 8 shows the propulsion analysis algorithm.
After propulsion system design convergence, the amount of optimal fuel mass in every engine-on status is achieved.In the present study, the optimal propulsion system design is achieved through converging the structural convergence factor (β). Using upper stage mass in every design loop, all subsystems' propulsion design is achieved and then the new value for fuel mass and convergence factor is obtained.

Propulsion System Convergence
In the fi rst design loop, the amount of fuel mass and the fi nal mass of upper stage in every burning is calculated through the following equations:

Feeding System Analysis
Controlling pressure in fuel tanks is easily possible using the pressure system feed.Furthermore, the simplicity of adjusting pressure in pressure system feed determines its high reliability, thus the process of switching and fl ow control is easily possible.Output fl ow could be controlled with installing a heater or pressure control valves.Generally, the concurrent process of disembarkation of capsules containing compressed gas and fi lling propellant tanks could be shown via Eqs.24 and 25 (Huzel et al. 1992).
High-pressure tanks (capsules): High-pressure tanks (capsules): Propellant tanks: where: Q is heat transfer between the gas blowing and its environment; Z is the gas compressibility factor; V is the volume control; T is the temperature; P is the pressure; m .i .m .d are blowing gas mass fl ow rate input and output volume control; h i and h d are blowing gas enthalpy entry and exit control volume.
Th e sub-algorithm of feeding system is shown in Volume, thickness, and the mass of every helium tank is obtained from the following equations (Humble et al. 1995): where: V h , t G and M Th are volume, thickness, and mass of blowing tanks; σ hw and ρ hw are the mechanical properties.
According to blow subsystem sub-algorithm, numbers of blow tanks are selected considering confi guration and layout.Th e fi nal mass of feeding system is calculated by the following equation:

Tanks Analysis
Th e shape of the tank is a function of weight, leakage rate, tank volume, and locating restrictions.Spherical tanks have the best empty weight-to-loaded weight ratio (Hutchinson and Olds 2004).Tank design sub-algorithm is shown in Fig. 10.Other elements such as control valves are selected according to input pressure and fl ow rate.

Structure Analysis
In structural analysis, providing stability and structural strength to deal with all external pressures is the main goal.In order to determine the mass of the structure, at fi rst, the loads 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 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 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 determines the thickness of the body (Ardema et al. 1996;Crawford and Burns 1963).where: J is the rigidity stiff ener.

Dimension Design
Dimension design is achieved with 2 diff erent assumptions which, in one, upper stage diameter was determined and, in the other, it was calculated in the output.Th e calculation of the length and diameter can be achieved through the following equation:

SAMPLe SoLUTIoN
A sample solution for upper stage design is presented in this section to generally introduce the design method: 1. Mission defi nition

4.
Determining material and construction inputs of the subsystem: • Used mechanical properties, environmental conditions, used fluid properties.

5.
Initial feasibility based on ability to transport about 13 tones to the parking orbit through stages of launcher rocket.

6.
System design: • Determining configuration parameters according to Table 4.

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Upper stage primary masses.

Parameter name Values
Fuel mass 13.249

dIFFeReNT VARIANTS ANd VALIdATIoN
Technology for constructing a launch vehicle in countries varies from each other, however, the statistical graphs indicate the approximate similarity of systematic parameters for upper-stage systems.For instance, Fig. 13 shows the relationship of payload mass and dry mass in the upperstage system.The real samples are circular and the samples derived from this paper for UDMH/N204 fuel are squareshaped.The comparative curve of burn time due to thrust/ weight is presented in Fig.In Table 13, the errors in the statistical design methods and MSDO compared to the systematic data of Cent.D-5 upper stage system.As shown in Table 5, errors of fuel mass, dry mass and total mass in MSDO design are decreased by 9 to 16% compared with Cent.D-5.Furthermore, the accuracy of primary data derived from the statistical design is obvious in this table.
n x and n y : Axial and lateral acceleration coe cients; d x and d y : Dimension distribution; m 0 (x) and m sub : Mass distribution and mass of the subsystems; m e and m T : Mass of the engine and of the tanks; N equ : Equivalent stress distribution; V b : Volume of gas tanks.
derived as follows: μ p and μ f payload mass ratio and dry mass ratio.
where: j is the integration loop counter design; M sh , M se , and M sT are dry mass of subsystems.Th e equation for convergence coeffi cient (β) is defi ned as follows:Propellant tanks: Th e internal relations of the propulsion system are shown in Fig.1.
14. Convergence factors (α and β) are illustrated in Figs. 15 and 16.The close similarity of these graphs is the main reason to validate the results derived from the study.At this point another validation was compared with Cent.D-5 upper-stage of Atlas V (401) which is presented in Table12.Problem inputs: M pay = 4.75 ton; D = 3.05m and I sp = 4378 N*s/kg.

Figure 14 .
Figure 14.Comparative curve of burn time due to T/W.

Table 1 .
Distribution of mass components.
h m h P c and P e : Chamber and exit pressure; P blow : Blow tanks pressure; P h : Distribution of the pressure gradient; L*: Combustion characteristic length; ΔV i : Energy change in each burn t t : Burn time distribution; R t and ht : Radius and height of the tank; V th and m th : Volume and mass of the helium tanks' m h : 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 speci c impulse; L c : Combustion chamber length; F tu : Yield stress; f s : Reliability factor; t s : ickness of body structures; t sm : Maximum thickness of body structures.βi + Figure 1.Propulsion system matrix.

Table 2 .
Optimization properties.Oxide fuel ratio; R sub and h sub : Subsystem dimensions; A t , L t ,R t , and h t : Engine size distribution;

Table 3 .
Design output includes the following:

Table 9 .
Other components mass distribution.
a. Selecting pressure-feed system.b.Calculating pressure drop in fuel flow which is 3.2 bars and for oxidant is 4 bars.c.Fuel tank pressure 11.2 bars and oxidant 12 bars.

Table 8 .
Tank parameters.10.Body structure: determining body thickness and stiffener which requires determining critical modes properties of previous steps, fairing and types of stiffener.11.Mass distribution:

Table 10 .
Diameter and total length.

Table 13 .
Methods errors compared to the systematic data of Cent.D-5 upper stage system