Research Article Multidisciplinary Design Optimization and ...

Research ArticleMultidisciplinary Design Optimization and Analysis ofHydrazine Monopropellant Propulsion System

Amirhossein Adami1 Mahdi Mortazavi1 Mehran Nosratollahi2

Mohammadreza Taheri3 and Jalal Sajadi4

1Amirkabir University of Technology Tehran 15875-4413 Iran2Space Research Institute Tehran Iran3Malek Ashtar University of Technology Tehran Iran4Department of Aerospace Engineering Shahid Beheshti University Tehran Iran

Correspondence should be addressed to Amirhossein Adami ahaaerospaceautacir

Received 30 January 2015 Revised 16 June 2015 Accepted 17 June 2015

Academic Editor Martin Tajmar

Copyright copy 2015 Amirhossein Adami et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Monopropellant propulsion systems are widely used especially for low cost attitude control or orbit correction (orbit maintenance)To optimize the total propulsion system subsystems should be optimized Chemical decomposition aerothermodynamics andstructure disciplines demand different optimum condition such as tank pressure catalyst bed length and diameter catalyst bedpressure and nozzle geometry Subsystem conflicts can be solved by multidisciplinary design optimization (MDO) technique withsimultaneous optimization of all subsystems with respect to any criteria and limitations In this paper monopropellant propulsionsystem design algorithm is presented and the results of the proposed algorithm are validated Then multidisciplinary designoptimization of hydrazine propulsion system is proposed The goal of optimization can be selected as minimizing the total mass(including propellant) minimizing the propellant mass (maximizing the Isp) or minimizing the dry mass Minimum total massminimum propellant mass and minimum dry mass are derived using MDO technique It is shown that minimum total massminimum dry mass and minimum propellant mass take place in different conditions The optimum parameters include bed-loading inlet pressure mass flow nozzle geometry catalyst bed length and diameter propellant tank mass specific impulse (Isp)and feeding mass which are derived using genetic algorithm (GA)

1 Introduction

A single propellant is used to produce thrust forces inmonopropellant propulsion systems Hydrazine (N

2H4) is

known as themost commonly usedmonopropellant Isp levelis generally considered as the performance of the propulsionsystem [1ndash3] In this regard hydrazine has a performance ofabout 20 higher than hydrogen peroxide as a monopropel-lant Hydrazine monopropellant thrusters have been appliedto satellites [4ndash6] upper stages and launching vehicles andnew interest is grownup for small reentry vehicles application[7 8] Hydrazine is readily decomposed into ammoniumhydrogen and nitrogen through exothermic reactions whenit is injected into a specific catalyst Because hydrazineexothermic reaction starts immediately after contacting with

the catalysts hydrazine monopropellant thrusters have anadvantage in quick response which is adequate for attitudecontrol system [2 5]

Monopropellant propulsion systems usually use blow-down feeding system which demands lower equipmentDuring thruster activity the decrease in feeding pressuredecreases the thrust level and Isp level Regulators and sepa-rated supply gas tanks are used to keep the performance closeto constant during the activity That means new subsystemis added to the propulsion system Different objective can beconsidered to derive the best solution Higher Isp and lowerstructure mass are the common examples

In this paper the hydrazine monopropellant propulsionsystem breaks down into three more important subsystemsincluding thruster subsystem propellant tank subsystem

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2015 Article ID 295636 9 pageshttpdxdoiorg1011552015295636

2 International Journal of Aerospace Engineering

and pressurized feeding subsystem The design algorithmis introduced based on MDO and the proposed algorithmis validated Then optimization algorithm (GA) is used toderive the optimum solution for every required total impulseand thrust level

2 Multidisciplinary Design Optimization

Higher Isp needs higher nozzle length and higher operatingpressure that leads to increase in the structural mass of thethruster and the supply tanks Although propellant massshould be increased to compensate the increase in dry massthe increase in Isp demands lower propellant masses In viewof system level optimum condition is related to minimumtotalmass of propulsion system (drymass + propellantmass)It means that optimum Isp is not the maximum value andoptimum dry mass is not the minimum value

These conflicts should bemanaged to derive the optimumsolution Multidisciplinary design optimizations (MDO)techniques such as all at once (AAO) collaborative optimiza-tion (CO) bilevel integrated system synthesis (BLISS) andconcurrent subspace optimization (CSSO) can solve theseconflicts and find the optimum solution In this paper everydiscipline is developed based on AAO framework AAOis the most basic MDO technique and has wide industrialacceptance [9] In AAO control is given to a system-leveloptimizer that ensures a global objective is met by havinga single designer control the entire system AAO solvesthe global MDO problem by moving all local-level designvariables and constraints away from each discipline to a newsystem-level optimizer entrusted with optimizing a globalobjective

The hydrazine monopropellant propulsion systemincludes propellant propellant tank pressurized gas tank(constant feeding pressure) thruster (including catalystbed nozzle and injector) electronics valves and theother equipment Three more important subsystems areintroduced as thruster propellant tank and pressurizedfeeding subsystem Modeling of each subsystem andinput-output flow data of every discipline will be introduced

3 Hydrazine Decomposition

Liquid hydrazine has an average density near 1000 kgm3Hydrazine decomposition consists of two important partsOnce in contact with the catalyst the N

2H4propellant

decomposes according to

3N2H4Catalyst997888997888997888997888997888rarr 4NH3 (g) +N2 (g)

+Heat (363 kcal)(1)

Then a part of the ammonia NH3 is further decomposed

via

4NH3 997888rarr 2N2 + 6H2 minusHeat (199 kcal) (2)

0 20 40 60 80 100800

900

1000

1100

1200

1300

1400

1500

1600

1700

Fractional ammonia dissociation ()

Tem

pera

ture

(K)

Adiabatic Kesten

Figure 1 Variation of total temperature with NH3decomposition

percent

Equation (1) shows that heat is released from decomposi-tion process but (2) shows that heat is dropped by decom-position of ammonia The amount of ammonia decompo-sition should be controlled by the design of the catalystbed geometry Lower ammonia dissociation is achieved bymaximum specific impulse while high ammonia dissociationdecreases molecular weight of the gaseous products which isuseful in gas generation applications Accordingly hydrazinedecomposition is presented in

N2H4 997888rarr43NH3 +

13N2 (1)

43NH3 997888rarr 2H2 +

23N2 (2)

from (1)+119909 (2)997888997888997888997888997888997888997888997888997888997888997888997888rarr N2H4

997888rarr

43(1minus119909)NH3 +

13(1+ 2119909)N2 + 2119909H2

(3)

where 119909 is the percent of NH3decomposition Total temper-

ature depends on the percent of NH3decomposition Two

methods namely Adiabatic and Kesten [12] are used toderive the total temperature Figure 1 illustrates the variationof the total temperature with NH

3decomposition present

Molecular mass and 120574 are almost similar in the twomethods as shown in Figure 2

The results of Kestenrsquos method are more acceptableand have reasonable accuracy in experiments as shown inFigure 3

Table 1 presents the relation between temperature molec-ular mass and decomposition percent of NH

3[7]

4 Propellant Tank Modeling

Spherical tanks have lowermass in comparisonwith cylindri-cal types Cylindrical tanks demand lower diameters and sim-pler production procedures Propellant tank configuration islimited with maximum permitted diameter If spherical tank

International Journal of Aerospace Engineering 3

0 20 40 60 80 100115

12

125

13

135

14


AdiabaticKesten

120574

Figure 2 Variation of 120574 with NH3decomposition percent

0 002 004 006 008 01 012 0140

01

02

03

04

05

06

07

KestenExperimental

Frac

tiona

l am

mon

ia d

issoc

iatio

n

Lc (m)

Figure 3 Variation ofNH3decomposition percent with catalyst bed

length

Table 1 NH3 decomposition and Adiabatic temperature

NH3 decompositionpercent 0 20 40 60 80 100

Adiabatic temp (K) 1659 1501 1342 1183 1023 8631Kesten temp (K) 1420 1306 1193 1080 9662 8528Molecular mass 192 1655 1454 1297 1171 1067120574

1169 1203 124 1278 1318 1361

cannot provide the required volumes then cylindrical tankwith maximum permitted diameter and suitable length is

Propellanttank modeling

120588str 120590str

PTank Dmax B

Mpropellant

120575strMtank

Lcyl DTank

Figure 4 Input-output flow data of propellant tank subsystemmodeling

considered Equation (4) presents the calculation of the tankvolume and configuration selection method as follows

if 119881Tank le41205871198773max

3997904rArr 119877Tank =

3radic

3119881Tank4120587

if 119881Tank gt41205871198773max

3

997904rArr

119877Tank = 119877max

119871cyl =(119881Tank minus 4120587119877

3max3)

120587119877

2max

(4)

Propellant tank mass is related to tank configurationtank pressure filling factor and propellant volume Equationsand modeling of the propellant tank are introduced by [7]Aluminum or titanium structures are commonly used forspace application but lower cost of aluminum provides moreinterest Propellant tank mass is estimated by

119872Tank = (41205871198772Tank + 2120587119877Tank119871cyl) 120588str120575Tank

120575sph =119899SF2120590str

119875Tank119877Tank

120575cyl = 2120575sph

(5)

Input-output flow data of propellant tank model is finallypresented in Figure 4

5 Pressurized Feeding Modeling

The feeding subsystem should produce the safe continu-ance or discontinuance propellant flow to the catalyst bed(thruster) A separate gas tank usually helium pressurizesthe hydrazine to flow to the catalyst bed Constant thrustlevel is usually considered in conceptual design phase Itneeds constant feeding pressure and therefore regulator isused to keep the propellant tank pressure close to the desiredvalues The feeding subsystems consist of feed lines (tubesand ducting) regulator valves tank and pressurizer gasSome of these components can be ignored in the conceptualphase because of having the same effect in various concepts[1] Most parts of the feeding subsystem mass (changing byconcepts) are connected to the gas tank mass and pressurizergas mass [1 2] The volume of propellant tank and feedingpressure specify the feeding subsystem geometry and mass


Feedingsubsystemmodeling

120575strMPT MPg

RPress Tank Pmax

120588str 120590str B

PTank VTank

Figure 5 Input-output flow data of feeding subsystem modeling

CatalystPmaxPfeeding Pinject

PTank

PTh PlowastPexit

Figure 6 Introducing pressure of different propulsion system parts

The required radius of the gas tank is derived using (6) Com-pletemodeling of pressure feeding subsystemwas introducedby [7]

119881

(119905=0)PressTank =

119872PG (total) minus 119872(119905=0)PressGas119875maxRT

=

RT (119872PG (total) minus 119872(119905=0)PressGas)

119875max

119877PressTank =3radic

3119881(119905=0)PressTank4120587

(6)

Titanium structure is selected for pressurized tankbecause of high pressure which demands thicker structureMass penalty of using aluminum is considerable Feedingsubsystem mass is estimated from

119872feeding = 119872PT +119872PG

119872PT = 41205871198772PT120588str120575PT

120575PT =119899SF2120590str

119875max119877PT 119875max le 200 (bar)

119872PG =4119875max

3119877gas119879PG120587119877

3PT120588str

(7)

Input-output flow data of feeding subsystem modeling isfinally presented in Figure 5

6 Thruster Subsystem Modeling

Thrusters consist of catalyst catalyst bed and nozzleThruster designing is one of themost important parts of everypropulsion systemThrust level and Isp introduce the thrustersize and performance respectively Pressures of differentparts of propulsion system are introduced in Figure 6 whichwill be used to derive the mathematical model119875Th is the pressure after catalyst bed and before noz-

zle Thrust level and Isp introduce the thruster size and

Table 2 Some properties of the selected catalyst [2]

119871

max119891

(kgm2sdots) sim450

Density (kgm3) sim2450

performance respectively The mentioned parameters arecalculated by

119879vac =119860

lowast119875

119890(120574119872

2119890+ 1)

119872

119890

[

2120574 + 1

(1

+

120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

Ispvac =119879vac1198920

(8)

Steel structure is commonly used for thruster Heatcontrol of hydrazine monopropellant thruster is usuallyignored because of the short time activity and low temper-ature in comparison with bipropellant and solid propellantthrusters

61 Catalyst Catalyst is the most important part of everymonopropellant thruster Actually development of mono-propellant thrusters depends on development of suitablecatalysis Shell Company (1963) introduced the first sponta-neous hydrazine decomposition catalyst It was a ruthenium-iridium catalyst with 21ndash28 active metal on activated char-coal one example consisted of 37 Ru and 43 Ir on acti-vated charcoal The most active catalysts described are thosecontaining iridium or a mixture of iridium and rutheniumas active metals The majority of work on hydrazine decom-position catalyst has been conducted with Shell 405 (32iridium over support of alumina Al

2O3) which is capable

of surviving several hundred cold starts with no significantdegradation It is considered the most successful hydrazinedecomposition catalyst to date thus similar catalyst is con-sidered in this study Cost decreasing of hydrazine catalystis one of the most important objectives in catalysts researchnowadays [13 14] For more information readers are referredto [2 15] The most important characteristic of catalyst isthe ability to decompose propellant flow (named catalystbed-loading factor) with lower required residence timeTable 2 shows some physical parameters of the consideredcatalyst

62 Catalyst Bed Cylindrical bed is considered in this paperLength and diameter of the catalyst bed introduce thegeometry The required thickness is specified by maximumpressure in catalyst bed The important event in catalystbed is pressure drop during the injection and movementthrough the catalyst bed Three more important pressurelosses between propellant tank and thruster are pipe andfeeding pressure drop injector pressure drop and catalyst


pressure drop Equation (9) shows the relation betweenpropellant tank pressure and thruster pressure [7 16 17]

119875Tank = 119875Th +Δ119875ctl +Δ119875inj +Δ119875pipe

Δ119875ctl =2119871119891

120588119903

119901

(

1 minus 120593120593

3 )[

300 (1 minus 120593) 120583119903

119901

+ 175119871119891]119871ctl

119871ctl =647993119871

119891

(1 minus 120593)[(0663 (2119903

119901)

017minus 017)

sdot (

6803119875inj (bar)

)

022

+ 017]minus35714

119871Th = 12119871ctl

Δ119875pipe = 05 bar

119875inj = 119875Tank minusΔ119875pipe

Δ119875inj = 02 (119875Tank minusΔ119875pipe)

(9)

where 120593 is the percent decomposition of NH3 Catalyst bed

length and diameter depend on thruster pressure and massflow but it should be noted that pressure drop in catalystbed is related to bed-loading factor This event conflicts withthruster performance

63 Divergent-Convergent Nozzle High pressure and tem-perature flow exits the catalyst bed and enters the D-C nozzlewhich changes the potential energy to the kinetic energyConical nozzle is selected for conceptual design phasesDivergence half angle of cone diameter of the catalyst bedthroat diameter convergence half angle of cone and theexit diameter introduce the nozzle geometry The geometryparameters are shown in Figure 7

Geometry parameters correlate with thermodynamicparameters Equation (10) presents the relation betweengeometry parameters and thermodynamic parameters

1205791 = 45∘

1205792 = 15∘

119860

lowast=

radic119879

119888119877120574

119875Th(1+

120574 minus 12)

(120574+1)2(120574minus1)

119860

119890=

119860

lowast

119872

119890

[

2120574 + 1

(1+120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

119860

119890= 119860

lowast119885expansion

119871div =119877ctl minus 119877119905tan 1205791

119871div =119877

119890minus 119877

119905

tan 1205792

(10)

Total thruster mass (catalyst catalyst bed and nozzle) isestimated from

Dcomb

1205791 1205792

DtDe

Figure 7 Geometry parameters of the nozzle

Thrustersubsystemmodeling

120588str 120590str 120588ctl Lf

PTh T Zexpansion

120575CombMthruster

Rctl Lctl Re Rt

Isp m

Figure 8 Input-output flow data of thruster subsystem modeling

119872Thruster = 119872Comb +119872Nozzle +119872cat

119872Comb = (2120587119877ctl119871ctl +1205871198772ctl) 120575Comb120588str

119872Nozzle

= [

120587

tan 1205791(119877

2ctl minus119877

2119905) +

120587

tan 1205792(119877

2119890minus119877

2119905)] 120575Comb120588str

120575Comb =119899SF120590str

(

120587119875Th1198772ctl + 119879

120587119877ctl)

119872cat = 120588ctl119860119888119871ctl

(11)

Finally input-output flow data of thruster modeling is pre-sented in Figure 8

7 Validation of the ProposedDesign Algorithm

Modeling of each part of propulsion system should becomplex enough to have an acceptable estimation of thetotal mass geometry and performance Results of the designalgorithm can be converted to real monopropellant thrusterrsquosdata by using some correction factors The correction factors(and suitable values) are presented as follows [18 19]

Thrustreal = 1205821ThrustIdeal

119879

real0 = 120582

22119879

Adiabatic0

119872Total = 119899120590 (119872Thruster +119872feeding +119872Tank)

1205821 = 095 Nozzle Correction Factor

1205822 = 090 Adiabatic Temp Correction Factor

119899

120590= 155 Other Equipment

(12)

Comparison between operational thrustersrsquo data and pro-posed design algorithm is summarized in Table 3 It shouldbe noted that Table 3 shows the redesign results only and


Table 3 Results of comparison of real thrusters and proposed design algorithm [10 11]

Parameters Redesign of 2ndthruster (400N)

2nd existence thruster(400N)

Redesign of firstthruster (10N)

First existencethruster (10N)

Pic mdash mdash

Mass with valve 2506 (gr) 2700 (gr) 190 (gr) 240 (gr)Catalyst bed pressure 26 (bars) 6sim26 (bars) 22 (bars) 55sim22 (bars)Mass flow 196 (grs) 182 (grs) 44 (grs) 44 (grs)Catalyst bed length 59 (cm) sim 2 (cm) 24 (cm)Nozzle length 144 (cm) 82 (cm) 57 (cm) 34 (cm)Catalyst bed diameter 68 (cm) 65 (cm) 19 (cm) 19 (cm)

optimization has not been done yet According to the resultsof Table 3 presented design algorithm has an acceptableaccuracy in modeling mass (gt22) geometry (gt19) andthermodynamic parameters (gt9) The conical nozzle hasalways longer length in compression with bell types so realmodels have shorter nozzle length

As case study following conditions are considered formultidisciplinary analysis of a monopropellant propulsionsystem

119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)

Figure 9 illustrates the variation of propellant mass anddry mass with the pressure of catalyst bed for the followingconditions

According to Figure 9 the minimum total mass solutionis different from the minimum dry mass solution or theminimumpropellantmass solutionThe decrease in drymassoccurs by increase in the pressure of thruster because of 119871

119891

value The increase in dry mass by increase in the pressure ofthruster is seen for low 119871

119891values (119871

119891lt 20) Finally lowest

total mass is achieved by selecting the pressure of the thrusterequal to 1006 bar

It should be noted that although mass per cost ratio ofstructure and propellant may be different in view of thesystem level (what is considered in this paper) the propulsionmass parts (dry mass and propellant mass) have a similareffect in the mission cost Figure 10 illustrates the variationof total mass with Isp for the same conditions

According to Figure 10 the minimum total mass solutionis derived when Isp value equals 2157 and this value is not themaximum value

Now the effects of bed-loading and percent of NH3

decomposition are taken into account Figure 11 shows theeffect of bed-loading on movement of the minimum masspoint According to the results of Figure 11 increase in 119871

119891

leads to having a heavier total mass and the minimum totalmass moves to have lower Isp values Figure 12 illustrates the

2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6

Thruster pressure (bar)

Mas

s (kg

)

X 1006Y 3323

Dry massPropellant massTotal mass

Figure 9 Mass variation with the thruster pressure

effect of percent of NH3decomposition on movement of the

minimummass pointAccording to the results of Figure 12 increase in120593 leads to

having a higher total mass for 120593 gt 04Therefore it should betried to keep this parameter as low as possible to have lowertotal propulsionmass It should be noted that by usingMDOthe best solution is directly derived and such analysis is notrequired The minimum total mass is derived by trading offbetween minimum propellant mass and minimum dry massfor every required total impulse

8 Multidisciplinary DesignOptimization of Hydrazine MonopropellantPropulsion System

Dry mass Isp and geometry are recognized as the mostimportant parameters for every propulsion system Thepropellant mass plays significant role in the cost of


170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323

Figure 10 Total mass variation with Isp

170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104

Figure 11 Movement of the minimum mass point by variation 119871119891

the mission and propellant tank mass The optimumdesign depends on minimum mission cost It is better toconsider the total mass as the cost function in preliminarydesign phases because the total mass is suitable predictionof the mission cost The total mass consists of propellantmass and dry mass Propellant mass is decreased withincrease in pressure or decrease in ammonia decompositionpercent (Isp) but dry mass has an inverse behavior Figure 13illustrates the multidisciplinary design optimization

170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05

Figure 12 Movement of the minimummass by variation of percentof NH

3decomposition

algorithm for monopropellant propulsion system based onAAO framework

As mentioned before it is considered that 120593 = 55 Nowsimilar problem which has been introduced in relation (13) isconsideredThe optimum solution has been derived byMDOand the results have been summarized in Table 4

According to the results of Table 4 the optimum solu-tion has been directly derived with acceptable accuracy incomparison with results of Figures 9 to 11 It is clear that thestructure or pressurizer gas can be simply changed to evaluatetheir effects

9 Summary and Conclusions

In this paper optimum design algorithm of the hydrazinemonopropellant propulsion system is introduced based onall at once (AAO) framework The results of the proposedalgorithm have been justified using some correction factorswhich are derived by comparison between the results ofproposed algorithm and operational thrusterrsquos data Thenthe minimum total mass is derived by trading off betweenthe minimum propellant mass and the minimum dry massfor a case study As the results of this research it is shownthat the minimum total mass solution is derived when Ispis not the maximum value In addition the effects of twodesign parameters have been recognized as follows Increasein 119871119891leads to having a heavier total mass and the minimum

total mass point moves to have lower Isp Increase in 120593 leadsto having a higher total mass for 120593 gt 04 The proposedalgorithm can be used for every required total impulse andthrust level FinallyMDO technique has been used to directlyderive the optimum solution using GA As the results MDOhas acceptable accuracy and directly finds the optimumsolution


Table 4 Results of multidisciplinary design of hydrazine propulsion system

Optimumpressure Optimum Isp Optimum

bed-loadingMinimum total

massOptimum

propellant mass Optimum dry mass

1015 bars 2157 sec 038 334 kg 164 kg 167 kg

Thrustersubsystem modeling

Constant parameter

Feedingsubsystem modeling

System optimizer level(cost function and constrain)

Propellanttank

modeling

VTank RTank

minimizing MTotal

MThruster Isp mDTh LTh

Mtank LcylDTank

(structure Dmax Press Gas)

PTank

Pinjection

PPT

120588Steel 120590Steel 120588Al 120590Al Dmax 120588Ti 120590Ti

PThMpropellant Lf T 120593 Zexpansion

Mfeeding RPress Tank

Figure 13 Multidisciplinary design optimization algorithm for the hydrazine propulsion system

Notations

AAO All at onceCO Collaborative optimizationGA Genetic algorithmMDO Multidisciplinary design optimizationBLISS Bilevel integrated system synthesisCSSO Concurrent subspace optimization120588str Structure density119860

lowast 119877119905 Throat area radius of throat

119875

119890 Pressure at exit of the nozzle

119872

119890 Mach number of exit nozzle

120574 Isentropic exponent Mass Fflow of nozzle1198920 Gravitational acc119879vac Vacuum thrust119860

119890 119877119890 Exit area radius of exit section

119875Th Pressure of catalyst bed119899

120590 Other equipment mass fraction

119881inj Injection velocity of propellant119872Thruster Thruster mass1205791 Convergent angle

1205792 Divergent angle119871Th Thruster length119871

119891 Bed-loading

119881Tank 119877Tank Volume radius of tank119871cyl Cylindrical length of tank119877max Maximum permitted radius119872Tank Mass of the propellant tank119909 120593 Percent of NH3 decomposition120575Tank Propellant tank thickness119861 Filling factor of tank119881PressTank Volume of pressurized tank119877PressTank Radius of pressurized tank119879

infin Initial temperature

119872PG Required mass of pressurizer gas119875max Maximum pressureMPT Mass of the pressurizer tank119877PT Pressurizer tankrsquos radius119871ctl Catalyst bed length119875Tank Tanks pressure1205821 Nozzle correction factor119899SF Correction factor1205822 Temperature correction factor


119872cat Catalyst mass119871con Convergent length of nozzle119871div Divergent length of nozzle119877gas Constant parameter of pressurizer gas

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Adami M Mortazavi and M Nosratollahi ldquoMultidisci-plinary design optimization of hydrogen peroxide monopro-pellant propulsion system using GA and SQPrdquo InternationalJournal of Computer Applications vol 113 no 9 pp 14ndash21 2015

[2] A Adami M Mortazavi and M Nosratollahi ldquoMultidisci-plinary design hybrid optimization of hydrazine monopropel-lant propulsion systemrdquo Aircraft Engineering and AerospaceTechnology In press

[3] A AdamiMMortazavi andM Nosratollahi ldquoA new approachin multidisciplinary design optimization of upper-stages usingcombined frameworkrdquo Acta Astronautica vol 114 pp 174ndash1832015

[4] A-S Yang ldquoSatellite hydrazine propulsion system designtradesrdquo Journal of Da-Yeh University vol 10 no 1 pp 41ndash502001

[5] K-H Lee M-J Yu and J-M Choi ldquoDeveloment of mono-propellant propulsion system for low earth orbit observationsatelliterdquo KSAS International Journal vol 6 no 1 2005

[6] D T Schmuland R K Masse and C G Sota ldquoHydrazinepropulsion module for CubeSatsrdquo in Proceedings of the 25thAnnual AIAAUSU Conference on Small Satellites SSC11-X-4August 2011

[7] A Adami Multidicsiplinary design optimization of reentryvehicle considering guidance algorithm [PhD thesis] AmirkabirUniversity of Technology Tehran Iran 2014

[8] M Rath H D Schimtz and M Steenborg ldquoDevelopment of a400Nhydrazine thruster for ESArsquos atmospheric reentry demon-stratorrdquo in Proceedings of the 32nd AIAAASMESAEASEE JointPropulsion Conference AIAA-96-2866 Lake Buena Vista FlaUSA July 1996

[9] M Nosratollahi M Mortazavi A Adami and M HosseinildquoMultidisciplinary design optimization of a reentry vehicleusing genetic algorithmrdquo Aircraft Engineering and AerospaceTechnology vol 82 no 3 pp 194ndash203 2010

[10] Astrium Propulsion amp Equipment 10N Mono-PropellantThruster AstriumPropulsionamp EquipmentMunich Germany2012


[12] A S Kesten ldquoAnalytical study of catalytic reactors for hydrazinedecompositionrdquo Quarterly Progress Report No 2 ReportE910461-6 United Aircraft Research Laboratories 1966

[13] J N Hinckel ldquoLow cost catalysts for hydrazine monopropellantthrustersrdquo in Proceedings of the 45th AIAAASMESAEASEEJoint Propulsion Conference amp Exhibit AIAA 2009-5232 Den-ver Colo USA August 2009

[14] I-T Kim J-H Jung J-H Kim H-H Lee and J-WLee ldquoPerformance test of hydrazine decomposition cata-lyst formonopropellant thrusterrdquo in Proceedings of the 45thAIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA 2009-5484 Denver Colo USA August 2009

[15] M W Schmidt and M S Gordon ldquoThe decomposition ofhydrazine in the gas phase and over an iridium catalystrdquoZeitschrift fur Physikalische Chemie vol 227 no 11 pp 1301ndash1336 2013

[16] A E Makled and H Belal ldquoModeling of hydrazine decom-position for monopropellant thrustersrdquo in Proceedings of the13th International Conference on Aerospace Sciences amp AviationTechnology Paper ASAT-13-PP-22 Military Technical CollegeCairo Egypt May 2009

[17] R B Bid E W Stewart and E N Lightfoot TransportPhenomena Revised John Wiley amp Sons 2nd edition 2007

[18] M J Sidi Spacecraft Dynamics and Control Cambridge Univer-sity Press 1997

[19] T M Chiasson Modeling the characteristics of propulsionsystems providing less than 10 N thrust [MS thesis] Departmentof Aeronautics and Astronautics Massachusetts Institute ofTechnology 2012

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VLSI Design



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Civil EngineeringAdvances in

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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and pressurized feeding subsystem The design algorithmis introduced based on MDO and the proposed algorithmis validated Then optimization algorithm (GA) is used toderive the optimum solution for every required total impulseand thrust level

2 Multidisciplinary Design Optimization

Higher Isp needs higher nozzle length and higher operatingpressure that leads to increase in the structural mass of thethruster and the supply tanks Although propellant massshould be increased to compensate the increase in dry massthe increase in Isp demands lower propellant masses In viewof system level optimum condition is related to minimumtotalmass of propulsion system (drymass + propellantmass)It means that optimum Isp is not the maximum value andoptimum dry mass is not the minimum value

These conflicts should bemanaged to derive the optimumsolution Multidisciplinary design optimizations (MDO)techniques such as all at once (AAO) collaborative optimiza-tion (CO) bilevel integrated system synthesis (BLISS) andconcurrent subspace optimization (CSSO) can solve theseconflicts and find the optimum solution In this paper everydiscipline is developed based on AAO framework AAOis the most basic MDO technique and has wide industrialacceptance [9] In AAO control is given to a system-leveloptimizer that ensures a global objective is met by havinga single designer control the entire system AAO solvesthe global MDO problem by moving all local-level designvariables and constraints away from each discipline to a newsystem-level optimizer entrusted with optimizing a globalobjective

The hydrazine monopropellant propulsion systemincludes propellant propellant tank pressurized gas tank(constant feeding pressure) thruster (including catalystbed nozzle and injector) electronics valves and theother equipment Three more important subsystems areintroduced as thruster propellant tank and pressurizedfeeding subsystem Modeling of each subsystem andinput-output flow data of every discipline will be introduced

3 Hydrazine Decomposition

Liquid hydrazine has an average density near 1000 kgm3Hydrazine decomposition consists of two important partsOnce in contact with the catalyst the N

2H4propellant

decomposes according to

3N2H4Catalyst997888997888997888997888997888rarr 4NH3 (g) +N2 (g)

+Heat (363 kcal)(1)

Then a part of the ammonia NH3 is further decomposed

via

4NH3 997888rarr 2N2 + 6H2 minusHeat (199 kcal) (2)

0 20 40 60 80 100800

900

1000

1100

1200

1300

1400

1500

1600

1700


Tem

pera

ture

(K)

Adiabatic Kesten

Figure 1 Variation of total temperature with NH3decomposition

percent

Equation (1) shows that heat is released from decomposi-tion process but (2) shows that heat is dropped by decom-position of ammonia The amount of ammonia decompo-sition should be controlled by the design of the catalystbed geometry Lower ammonia dissociation is achieved bymaximum specific impulse while high ammonia dissociationdecreases molecular weight of the gaseous products which isuseful in gas generation applications Accordingly hydrazinedecomposition is presented in

N2H4 997888rarr43NH3 +

13N2 (1)

43NH3 997888rarr 2H2 +

23N2 (2)

from (1)+119909 (2)997888997888997888997888997888997888997888997888997888997888997888997888rarr N2H4

997888rarr

43(1minus119909)NH3 +

13(1+ 2119909)N2 + 2119909H2

(3)

where 119909 is the percent of NH3decomposition Total temper-

ature depends on the percent of NH3decomposition Two

methods namely Adiabatic and Kesten [12] are used toderive the total temperature Figure 1 illustrates the variationof the total temperature with NH

3decomposition present

Molecular mass and 120574 are almost similar in the twomethods as shown in Figure 2

The results of Kestenrsquos method are more acceptableand have reasonable accuracy in experiments as shown inFigure 3

Table 1 presents the relation between temperature molec-ular mass and decomposition percent of NH

3[7]

4 Propellant Tank Modeling

Spherical tanks have lowermass in comparisonwith cylindri-cal types Cylindrical tanks demand lower diameters and sim-pler production procedures Propellant tank configuration islimited with maximum permitted diameter If spherical tank


0 20 40 60 80 100115

12

125

13

135

14


AdiabaticKesten

120574


0 002 004 006 008 01 012 0140

01

02

03

04

05

06

07

KestenExperimental

Frac

tiona

l am

mon

ia d

issoc

iatio

n

Lc (m)


length




1169 1203 124 1278 1318 1361



120588str 120590str

PTank Dmax B

Mpropellant

120575strMtank

Lcyl DTank



if 119881Tank le41205871198773max

3997904rArr 119877Tank =

3radic

3119881Tank4120587

if 119881Tank gt41205871198773max

3

997904rArr

119877Tank = 119877max

119871cyl =(119881Tank minus 4120587119877

3max3)

120587119877

2max

(4)



120575sph =119899SF2120590str


120575cyl = 2120575sph

(5)






120575strMPT MPg

RPress Tank Pmax

120588str 120590str B

PTank VTank



PTank

PTh PlowastPexit



119881



=


119875max


3119881(119905=0)PressTank4120587

(6)


119872feeding = 119872PT +119872PG

119872PT = 41205871198772PT120588str120575PT

120575PT =119899SF2120590str

119875max119877PT 119875max le 200 (bar)

119872PG =4119875max

3119877gas119879PG120587119877

3PT120588str

(7)






119871

max119891

(kgm2sdots) sim450



119879vac =119860

lowast119875

119890(120574119872

2119890+ 1)

119872

119890

[

2120574 + 1

(1

+

120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

Ispvac =119879vac1198920

(8)









Δ119875ctl =2119871119891

120588119903

119901

(

1 minus 120593120593

3 )[

300 (1 minus 120593) 120583119903

119901

+ 175119871119891]119871ctl

119871ctl =647993119871

119891

(1 minus 120593)[(0663 (2119903

119901)

017minus 017)

sdot (

6803119875inj (bar)

)

022

+ 017]minus35714

119871Th = 12119871ctl




(9)





1205791 = 45∘

1205792 = 15∘

119860

lowast=

radic119879

119888119877120574

119875Th(1+

120574 minus 12)

(120574+1)2(120574minus1)

119860

119890=

119860

lowast

119872

119890

[

2120574 + 1

(1+120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

119860

119890= 119860


119871div =119877ctl minus 119877119905tan 1205791

119871div =119877

119890minus 119877

119905

tan 1205792

(10)


Dcomb

1205791 1205792

DtDe



120588str 120590str 120588ctl Lf

PTh T Zexpansion

120575CombMthruster

Rctl Lctl Re Rt

Isp m




119872Nozzle

= [

120587

tan 1205791(119877

2ctl minus119877

2119905) +

120587

tan 1205792(119877

2119890minus119877

2119905)] 120575Comb120588str

120575Comb =119899SF120590str

(

120587119875Th1198772ctl + 119879

120587119877ctl)

119872cat = 120588ctl119860119888119871ctl

(11)





119879

real0 = 120582

22119879

Adiabatic0




119899


(12)








Pic mdash mdash




119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)



119891


119891values (119871







119891


2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6


Mas

s (kg

)

X 1006Y 3323









170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100115

12

125

13

135

14


AdiabaticKesten

120574


0 002 004 006 008 01 012 0140

01

02

03

04

05

06

07

KestenExperimental

Frac

tiona

l am

mon

ia d

issoc

iatio

n

Lc (m)


length




1169 1203 124 1278 1318 1361



120588str 120590str

PTank Dmax B

Mpropellant

120575strMtank

Lcyl DTank



if 119881Tank le41205871198773max

3997904rArr 119877Tank =

3radic

3119881Tank4120587

if 119881Tank gt41205871198773max

3

997904rArr

119877Tank = 119877max

119871cyl =(119881Tank minus 4120587119877

3max3)

120587119877

2max

(4)



120575sph =119899SF2120590str


120575cyl = 2120575sph

(5)






120575strMPT MPg

RPress Tank Pmax

120588str 120590str B

PTank VTank



PTank

PTh PlowastPexit



119881



=


119875max


3119881(119905=0)PressTank4120587

(6)


119872feeding = 119872PT +119872PG

119872PT = 41205871198772PT120588str120575PT

120575PT =119899SF2120590str

119875max119877PT 119875max le 200 (bar)

119872PG =4119875max

3119877gas119879PG120587119877

3PT120588str

(7)






119871

max119891

(kgm2sdots) sim450



119879vac =119860

lowast119875

119890(120574119872

2119890+ 1)

119872

119890

[

2120574 + 1

(1

+

120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

Ispvac =119879vac1198920

(8)









Δ119875ctl =2119871119891

120588119903

119901

(

1 minus 120593120593

3 )[

300 (1 minus 120593) 120583119903

119901

+ 175119871119891]119871ctl

119871ctl =647993119871

119891

(1 minus 120593)[(0663 (2119903

119901)

017minus 017)

sdot (

6803119875inj (bar)

)

022

+ 017]minus35714

119871Th = 12119871ctl




(9)





1205791 = 45∘

1205792 = 15∘

119860

lowast=

radic119879

119888119877120574

119875Th(1+

120574 minus 12)

(120574+1)2(120574minus1)

119860

119890=

119860

lowast

119872

119890

[

2120574 + 1

(1+120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

119860

119890= 119860


119871div =119877ctl minus 119877119905tan 1205791

119871div =119877

119890minus 119877

119905

tan 1205792

(10)


Dcomb

1205791 1205792

DtDe



120588str 120590str 120588ctl Lf

PTh T Zexpansion

120575CombMthruster

Rctl Lctl Re Rt

Isp m




119872Nozzle

= [

120587

tan 1205791(119877

2ctl minus119877

2119905) +

120587

tan 1205792(119877

2119890minus119877

2119905)] 120575Comb120588str

120575Comb =119899SF120590str

(

120587119875Th1198772ctl + 119879

120587119877ctl)

119872cat = 120588ctl119860119888119871ctl

(11)





119879

real0 = 120582

22119879

Adiabatic0




119899


(12)








Pic mdash mdash




119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)



119891


119891values (119871







119891


2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6


Mas

s (kg

)

X 1006Y 3323









170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120575strMPT MPg

RPress Tank Pmax

120588str 120590str B

PTank VTank



PTank

PTh PlowastPexit



119881



=


119875max


3119881(119905=0)PressTank4120587

(6)


119872feeding = 119872PT +119872PG

119872PT = 41205871198772PT120588str120575PT

120575PT =119899SF2120590str

119875max119877PT 119875max le 200 (bar)

119872PG =4119875max

3119877gas119879PG120587119877

3PT120588str

(7)






119871

max119891

(kgm2sdots) sim450



119879vac =119860

lowast119875

119890(120574119872

2119890+ 1)

119872

119890

[

2120574 + 1

(1

+

120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

Ispvac =119879vac1198920

(8)









Δ119875ctl =2119871119891

120588119903

119901

(

1 minus 120593120593

3 )[

300 (1 minus 120593) 120583119903

119901

+ 175119871119891]119871ctl

119871ctl =647993119871

119891

(1 minus 120593)[(0663 (2119903

119901)

017minus 017)

sdot (

6803119875inj (bar)

)

022

+ 017]minus35714

119871Th = 12119871ctl




(9)





1205791 = 45∘

1205792 = 15∘

119860

lowast=

radic119879

119888119877120574

119875Th(1+

120574 minus 12)

(120574+1)2(120574minus1)

119860

119890=

119860

lowast

119872

119890

[

2120574 + 1

(1+120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

119860

119890= 119860


119871div =119877ctl minus 119877119905tan 1205791

119871div =119877

119890minus 119877

119905

tan 1205792

(10)


Dcomb

1205791 1205792

DtDe



120588str 120590str 120588ctl Lf

PTh T Zexpansion

120575CombMthruster

Rctl Lctl Re Rt

Isp m




119872Nozzle

= [

120587

tan 1205791(119877

2ctl minus119877

2119905) +

120587

tan 1205792(119877

2119890minus119877

2119905)] 120575Comb120588str

120575Comb =119899SF120590str

(

120587119875Th1198772ctl + 119879

120587119877ctl)

119872cat = 120588ctl119860119888119871ctl

(11)





119879

real0 = 120582

22119879

Adiabatic0




119899


(12)








Pic mdash mdash




119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)



119891


119891values (119871







119891


2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6


Mas

s (kg

)

X 1006Y 3323









170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Δ119875ctl =2119871119891

120588119903

119901

(

1 minus 120593120593

3 )[

300 (1 minus 120593) 120583119903

119901

+ 175119871119891]119871ctl

119871ctl =647993119871

119891

(1 minus 120593)[(0663 (2119903

119901)

017minus 017)

sdot (

6803119875inj (bar)

)

022

+ 017]minus35714

119871Th = 12119871ctl




(9)





1205791 = 45∘

1205792 = 15∘

119860

lowast=

radic119879

119888119877120574

119875Th(1+

120574 minus 12)

(120574+1)2(120574minus1)

119860

119890=

119860

lowast

119872

119890

[

2120574 + 1

(1+120574 minus 12119872

2119890)]

(120574+1)2(120574minus1)

119860

119890= 119860


119871div =119877ctl minus 119877119905tan 1205791

119871div =119877

119890minus 119877

119905

tan 1205792

(10)


Dcomb

1205791 1205792

DtDe



120588str 120590str 120588ctl Lf

PTh T Zexpansion

120575CombMthruster

Rctl Lctl Re Rt

Isp m




119872Nozzle

= [

120587

tan 1205791(119877

2ctl minus119877

2119905) +

120587

tan 1205792(119877

2119890minus119877

2119905)] 120575Comb120588str

120575Comb =119899SF120590str

(

120587119875Th1198772ctl + 119879

120587119877ctl)

119872cat = 120588ctl119860119888119871ctl

(11)





119879

real0 = 120582

22119879

Adiabatic0




119899


(12)








Pic mdash mdash




119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)



119891


119891values (119871







119891


2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6


Mas

s (kg

)

X 1006Y 3323









170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Pic mdash mdash




119868Total = 4375 (N sdot s)

119879 = 500 (N)

119871

119891= 84

120593 = 40

(13)



119891


119891values (119871







119891


2 4 6 8 10 12 14 16 18 2015

2

25

3

35

4

45

5

55

6


Mas

s (kg

)

X 1006Y 3323









170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










170 180 190 200 210 220 230 2403

35

4

45

5

55

6

Isp (s)

Tota

l mas

s (kg

)

X 2157Y 3323


170 180 190 200 210 220 2306

7

8

9

10

11

12

13

Isp (s)

Tota

l mas

s (kg

)

Lf = 64

Lf = 74

Lf = 84

Lf = 94

Lf = 104



170 180 190 200 210 220 230 2403

4

5

6

7

8

9

10

11

Isp (s)

Tota

l mas

s (kg

)

120601 = 03

120601 = 04

120601 = 06

120601 = 07

120601 = 05


3decomposition











massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













massOptimum


1015 bars 2157 sec 038 334 kg 164 kg 167 kg


Constant parameter



Propellanttank

modeling

VTank RTank

minimizing MTotal


Mtank LcylDTank


PTank

Pinjection

PPT





Notations



119875


119872








119891 Bed-loading








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Multidisciplinary Design Optimization and ...

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