Design And Flow Simulation Of Truncated Aerospike Nozzle
IJRET: International Journal of Research in Engineering and Technology eISSN:2319-1163 pISSN: 2321-7308DESIGN AND FLOW SIMULATION OF TRUNCATED AEROSPIKENOZZLEVinay Kumar Levaka1, Srinivasa Reddy K21Student, Aerospace dept., Aurora’s Scientific and Technological Institute, Hyderabad, Telangana, India2Professor, C.M.R. Engineering College, Hyderabad, Telangana, IndiaAbstractAerospike nozzles are being considered in the development of the Single Stage to Orbit launching vehicles because of theirprominent features and altitude compensating characteristics. This paper presents the design of aerospike nozzles usingcharacteristic method in conjunction with streamline function, and performance study through numerical simulation usingcommercial Computational Fluid Dynamics (CFD) code ANSYS FLUENT. For this purpose nozzles with truncation lengths of25%, 40%, 50% are choosen, because of the thermal and structural complications in the ideal aerospike nozzle. Simulation of theflow is carried out at three different altitude conditions representing Under-expansion, Ideal, and over-expansion conditions ofthe flow. FLUENT predictions were used to verify the isentropic flow assumption and that the working fluid reached the designexit Mach number. The flow-fields obtained through the numerical simulation are analysed to know the effect of truncation on theperformance of aerospike nozzle. Optimum percentage of the truncation is selected by the comparison of nozzles with differentlengths of truncation under various altitude parameters. The results show that the flow pattern of the nozzles under differentaltitude conditions are almost similar. The 40 % truncated nozzle is found to give optimum performance and it has achieved thedesired exit Mach number in all the three altitude conditions.Keywords: Aerospike Nozzle, Single Stage to Orbit (SSTO), Linear Aerospike, Truncation and Rocket ----------------------------------------------1. INTRODUCTION1.1 Aerospike nozzleEver since jet and rocket propulsion systems have emerged,researchers have invented and implemented many types ofnozzles, mainly to increase the thrust performance ofnozzles in off-design working conditions. Among thesevarious designs, features of the aerospike nozzle haveattracted researchers since mid-1950s. Many theoreticalstudies of the aerospike nozzle have been carried out in1960s. In early 1970s, thermal and strength problems of theaerospike nozzle and development of more efficientmethods for fabrication of conventional nozzles led to adecline in research activities in this field. Development ofthe nozzle with the capability of producing optimumamounts of thrust in wide ranges of altitude has been asubject of continuous dedicated efforts within thecommunity of rocket propulsion.An aerospike nozzle has a spike in the center of the nozzle.Aerospike nozzle can be described as an inverted bell nozzlewhere the flow expands on the outside of the nozzle insteadof being completely constrained by the nozzle walls. Fromthe throat, the innermost streamlines of the flow follow thecontours of the spike, gradually being turned in the axialdirection. Aerospike rocket nozzles are designed forconsistent performance over a wide range of ambientpressures.The phenomenon of producing optimum amounts of thrustby a rocket nozzle in off-design conditions is called asaltitude compensation. Nozzles with the altitudecompensation characteristics are basic feature in realizingthe development of Single Stage to Orbit (SSTO) vehicles.Reusable SSTO vehicles offer the promise of reducedlaunch expenses by eliminating recurring costs associatedwith hardware replacement inherent in expendable launchsystems.The most popular altitude compensating rocketnozzle to date is the aerospike nozzle, the origin of whichdates back to Rocketdyne in 1950s.Traditional converging-diverging nozzles have a singleambient pressure at which the rocket exhaust gases areneither over-expanded nor under-expanded. As the operatingconditions move away from the design nozzle pressure ratio(NPR), a shock or an expansion fan will form at the exitplane of the converging-diverging nozzle. These result inreductions in the efficiency of the nozzle. An aerospikenozzle does not have a solid geometry defining the outerlimits of the flow path in the supersonic region of the flow.Instead it allows the exhaust gases to expand freely beyondthe throat, via the mechanism of a Prandtl-Meyer expansionfan.1.2 AdvantagesSmaller nozzle: The truncated spike can be far smaller thana typical bell nozzle for the same performance, as shownbelow. In addition, a spike can give greater performance fora given length.Volume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org122
IJRET: International Journal of Research in Engineering and Technology eISSN:2319-1163 pISSN: 2321-7308Flight experience: No aerospike engine has ever flown in arocket application. As a result, little flight design experiencehas been gained.2. DESIGN METHODOLOGYFig-1: Size comparison of a bell and a plug nozzleSuperior performance: Altitude compensation may resultin greater installed performance.Lower vehicle drag: The aerospike nozzle fills the baseportion of the vehicle thereby reducing a type of drag calledbase drag.Modular combustion chambers: The linear aerospikeengine is made up of these small, easier to develop, lessexpensive thrusters that give the engine greater versatility.Thrust vectoring: Because the combustion chambers canbe controlled individually, the vehicle can be maneuveredusing differential thrust vectoring. This eliminates the needfor the heavy gimbals and actuators used to vary thedirection of traditional nozzles.Design of the aerospike nozzle mainly refers to the design ofthe central spike and the determination of angle of theprimary nozzle. Method of characteristics in conjunctionwith the streamline conditions of A.H.Shapiro is used for thedesign of aerospike nozzle contour. A point on thecharacteristic line where it satisfies streamline condition willbe the point on spike contour. Since the method ofcharacteristics solution is based upon a start line slightlygreater than Mach number equal to one, it is apparent thatthe complete supersonic flow field and the nozzleperformance is governed by this parameter.The gas expansion process in the flow field of the plugnozzle is assumed to be isentropic, adiabatic, andfrictionless. The method of characteristics is logically andphysically applicable for determining pertinent parametersthroughout the flow field of a supersonic isentropic plugnozzle. Expansion process is determined by the PrandtlMeyer expansion function, which follows the belowequationBecause of the aerospike nozzle geometry, the physicalnozzle throat area is not normal to the engine centerline butis inclined by a specific angle. Because of the nozzlecontour geometry, the combustion products are accelerateddifferently such that an axisymmetric sonic line shape, evenwith regard to the nozzle throat centerline, is not formed.The flow direction at the throat is set at an angle equal to thePrandtl-Meyer expansion angle associated with the userdefined exit Mach number. The Prandtl-Meyer expansionfan is centered at the tip of the cowl and its location is userdefined. Fig-3 shows the schematic of the aerospike nozzledisplaying the characteristic lines representing PrandtlMeyer expansion waves.Fig-2: Aerospike thrust vectoring controlLower vehicle weight: Even though the aerospike tends tobe heavier than the bell nozzle, it shares many majorstructural elements with the vehicle reducing overall weight.1.3 DisadvantagesCooling: The central spike experiences far greater heatfluxes than does a bell nozzle. This problem can beaddressed by truncating the spike to reduce the exposed areaand by passing cold cryogenically-cooled fuel through thespike. The secondary flow also helps to cool the centerbody.Manufacturing: The aerospike is more complex anddifficult to manufacture than the bell nozzle. As a result, it ismore costly.Fig-3: Schematic of the axisymmetric aerospike nozzleVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org123
IJRET: International Journal of Research in Engineering and Technology eISSN:The technique used in this paper to calculate the contours ofthe aerospike nozzles are similar to the technique outlinedby Lee and Thompson, 1964 [4]. For the traditionalaerospike nozzle, the technique used in this paper definesthe location of the ends of the throat and sets the flowdirection at the throat equal to the Prandtl-Meyer expansionangle associated with the desired exit Mach number. Unlikethe technique outlined by Lee and Thompson [4], thecalculations used in this paper step forward through theexpansion fan by a user-defined Prandtl-Meyer expansionangle increment. The intersection of the characteristicsemanating from the expansion point on one end of the throatand the Stream Function originating from the last pointcalculated on the nozzle’s contour define the nozzle’scontour. The Prandtl-Meyer expansion fan is steppedthrough until the Mach number along the characteristicbeing analyzed is greater than or equal to the desired userdefined exit Mach number, in which case, the intersection ofthe Stream Function and characteristic signify the locationof the last point on the nozzle’s contour. The geometry of anaerospike nozzle and the parameters involved can be seenfrom Fig-4.2319-1163 pISSN: 2321-7308Mach number is greater than the point’s Prandtl- Meyerexpansion angle, the program sets the upper limit of therange equal to the guess Mach number. If the Prandtl-Meyerexpansion angle of the guess Mach number is less than thePrandtl-Meyer expansion angle of the point, set the lowerlimit of the range equal to the guess Mach number. If thedifference between the Prandtl-Meyer expansion angle ofthe guess Mach number and the point’s Prandtl-Meyerexpansion angle is greater than abs(1e-10), recalculate a newguess Mach number using the new range limits. If thedifference in Prandtl-Meyer expansion angles is less thanabs(1e-10), the guess Mach number will be the point’s Machnumber.3. NUMERICAL SIMULATIONThis section describes numerical modeling and analysis ofexternal flow of the aerospike nozzle with different plugshapes using a commercial CFD code ANSYS FLUENT.The objective of the analysis is comparison of flow patternsproduced by aerospike nozzles with different plug shapes.Numerical modeling also helps us to validate the design ofthe Aerspike nozzle by comparing the expected Machnumber with the Mach number obtained from the numericalsimulation3.1 GeometryUsing the design theory mentioned in the previous sectionAerospike nozzle contours with the nozzle lengthpercentages of 25, 40, and 50 are designed. The parametersused as input for the determination of the contour coordinates are as followsExpected exhaust Mach number: Me 3Fig-4: Geometry of an aerospike nozzlePropellant: Ethanol-Oxygen, 1.21This method becomes more accurate as the number ofcharacteristics used in the calculation increases, whichmeans choosing less value for the change in Prandtl-Meyerangle. The increased number of characteristics also results ina smoother contour.Throat Radius: rt 0.0508 m 2 inch2.1 Mach Number CalculationThe work presented in this paper uses the Bisection Methodto calculate the Mach number associated with each flowfield point’s Prandtl-Meyer expansion angle. The programsets the lower limit of the range to a Mach number of 1 andthe upper limit to a 100 times the desired exit Mach number.The program then calculates an initial guess Mach numberby averaging the range’s limits.Change in Prandtl-meyer angle Δ 0.005Truncation values are taken in accordance withconsiderations regarding the thermal and structuralcapabilities of the nozzle. But the increased amounts oftruncation leads to the larger base radius which in turn leadsto the larger Throat radius, so the design uses constant throatradius. The Co-ordinates of the expansion points and thethroat angle which is equal to the max are calculated usingthe Prandtl-Meyer equation.Expansion point: (1.778, 13.3099)Throat Angle: t 62.7508oCalculate the Prandtl-Meyer expansion angle of the guessMach number using Prandtl-Meyer expansion function andcompares it to the Prandtl-Meyer expansion angle of thepoint. If the Prandtl-Meyer expansion angle of the guessVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org124
IJRET: International Journal of Research in Engineering and Technology eISSN:Fig-8: Grid for analysis of 25% nozzleFig-5: Geometrical model of the 25% nozzleFig-9: Grid for analysis of 40% nozzleFig-6: Geometrical model of the 40% nozzleFig-10: Grid for analysis of 50% nozzleFig-7: Geometrical model of the 50% nozzleUsing the co-ordinates of expansion point, nozzle contourco-ordinates, and Throat angle that are calculated,geometrical models are developed and meshed using theGAMBIT, a commercial modeling and meshing tool. Coordinate data obtained from the design calculations is tocreate the contour surface of the nozzle. The primary nozzleis created by using the two geometrical arcs approximatingthe convergent section at the throat.2319-1163 pISSN: 2321-73083.3 Boundary ConditionsThe condition implied at the inlet of the convergent sectionis inlet with specified mass flow, with the followingboundary values, these values are taken from the Reference[5]Mass flow rate (m) 3.25757 kg/sTemperature (T) 1577.826 K3.2 MeshThe solution domain, in all the cases, is discretized using astructured grid of quadrilateral cells. As the geometricvariations in regions surrounding to the nozzle surface makeit impossible to generate a structured grid with acceptablequality, domain has been divide into two different faces.Different geometries of the truncated aerospike nozzlescause the solution domain to have different number of cells.Total number of grid cells for the 25%, 40%, and 50% casesare 6566, 7388, and 7241, respectively.Pressure (P) 2045430 N/m2Volume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org125
IJRET: International Journal of Research in Engineering and Technology eISSN:2319-1163 pISSN: 2321-7308surface, which can be roughly estimated using onedimensional isentropic flow relations, have been used todefine custom field functions describing initial values ofaxial velocity, pressure and temperature in regionssurrounding the nozzle.3.5 Analysis FeaturesFig-11 Solution domain and boundary conditionsBoundary values are calculated using the nozzle designparameters mentioned belowChamber Pressure: P1 2067857 N/m2Design Altitude: h 3657.6 mMass Flow: m 3.25758 kg/sThree different cases of atmospheric conditions (Patm/Pdes)have been analyzed, which correspond to different workingconditions (including over-expansion, optimum andunderexpansion). Boundary values imposed at pressurefarfield and pressure outlet boundaries in the 3 cases arepresented in Table-1. Apart from case 2, which correspondsto the nozzles’ optimum working condition, the other caseshave been chosen hypothetically to test the effect oftruncation on nozzle performance. Supersonic Machnumbers of external flow has been selected for all cases inorder to facilitate convergence criteria. Atmosphericconditions at the design altitudes are given as input pressureand temperature at farfield and pressure outlet conditions.Table-1: Values imposed at farfield boundariesPatm/PdesOutleCASEPExitTemp. at t(N/m2) Mach Farfield Temp(K). (K)11.57101325 e nozzle contours were built on the assumption ofinviscid, irrotational, isentropic flow. So In CFD Simulationthe fluid is considered as inviscid. The isentropicassumption, which implies irrotationality, was achieved byassigning the specific heat at constant pressure as a constantproperty of the working fluid. Combustion products havebeen assumed to behave as a compressible ideal gas(P RT). The coupled implicit method has been used forsolution of the four governing equations (continuity,conservation of momentum in longitudinal and radialdirections, and conservation of energy), considering severecompressibility effects existing in the solution domain.Fluxes of convected variables at cell walls are approximatedby the first order upwind scheme. Courant’s number hasbeen set to 0.5 for all the cases. This criterion has beenposed for convergence. One is reduction of the globalresidual of solution of all governing equations to the orderof 10-5, and the other is establishment of mass balancebetween inlet, far-field and outlet boundaries, which ischecked by integration of mass flow through the mentionedboundaries at each iteration. In all cases, the solutionprocess has been continued until both criteria have beensatisfied.4. RESULTS AND DISCUSSIONSTotal study is divided into three different cases whichrepresent to under-expansion, ideal/ designed conditions andover-expansion conditions.Exhaust flow of the aerospike nozzle is characterized byformation of a series of expansion waves, which originatefrom the upper lip of the convergent section. Since theexhaust flow is not bounded by a solid wall, these expansionwaves can adjust their intensity and domain to match theexhaust flow with the external flow, which gives anadvantage of the altitude compensation in contrast to theconventional nozzle.4.1 Over Expansion Conditions3.4 Initial ConditionsNumerical values of flow variables vary greatly in differentregions of the solution domain in analysis of a nozzle withexternal flow. For example, while values close to stagnationproperties prevail at the inlet of the convergent section, theexternal flow might involve substantially lower pressuresand higher (even supersonic) Mach numbers. In suchcircumstances, initialization of a flow variable with aconstant value throughout the entire domain can makeconvergence difficult or sometimes impossible. To deal withthis problem, properties at nozzle inlet, throat and exhaustThis case corresponds to the simulation of 25%, 40%, and50% nozzles in the over-expansion conditions where thepressure ratio Patm/Pdes 1.57. In this case we can observethat the expansion waves originating from the upper lip ofthe convergent primary nozzle extend even after the surfaceof the nozzle meeting at the midpoint of the base, and thesecondary expansion can be observed at the tip of thetruncated portions. These expansion waves continue theirway in spite of the larger amounts of the compression whichleads to the over-expansion conditions. The effect of overexpansion can be clearly seen in Fig-12(b), 12(d), and 12(f)showing path-lines of the exhaust flow in the region beforeVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org126
IJRET: International Journal of Research in Engineering and Technology eISSN:2319-1163 pISSN: 2321-7308the stagnation point. After the stagnation point the exhaustgases flow parallel to the axis of symmetry. The stagnationpoint in all three nozzles, with varying truncationpercentages, is nearer to the surface of the truncation basereducing the area of recirculation region where the twovortices are formed. This phenomenon can be clearlyobserved in the above mentioned figures.where the flow properties are nearer to the ideal flowconditions. This phenomenon is due to the formation of twosymmetric vortices in the base of the plug, which counteractthe effect of each other at two locations, one of which islocated at the center of the plug base, where the stagnationconditions prevail. This can be noticed in the Fig-14(b),14(d), and 14(f) showing the pathlines.An oblique shock can be seen in this case, which can beobserved in Fig-12(a), 12(c), and 12(e) showing the Machnumber contours, nearer to the surfaces surrounding theupper lip of the primary nozzle. These waves arecharacterized by high velocities and expansion. But in allthe cases the effect of the shock waves on the exhaust flowis in negligible range. In comparison between all the threenozzles, it is observed that effect of shock waves is more inthe 25 % nozzle.In this case it is clearly visible that the series of expansionwaves started at the upper lip of the primary nozzle gotcompressed by the atmosphere; this compression ischaracterized by increase in the density and reduction in thevelocity of the exhaust flow. Effect of these expansion andcompression waves on pathlines is such that the exhaustflow leaves the exit surface straight after the point ofstagnation the exhaust gases flow parallel to the axis leavingno residuals, thus producing a great deal of thrust. This canbe observed in the Fig-14(b), 14(d), and 14(f) showing thepathlines colored by density.In the Fig-12(a), 12(c), and 12(e) showing the contours ofMach number it is observed that the velocity of the flow inall the cases is within the expected range. Velocity of flow isgradually increased to give the optimum Mach number atthe end of the nozzle after the stagnation point. Machnumber of the exhaust flow of the three cases are obtainedas 2.6 in 25 % nozzle, 3.15 Mach in 40 % nozzle, 3.2 Machin the 50% nozzle.From the contours of Mach number in Fig-14(a), 14(c), and14(e) we can observe that velocity of the flow during theexpansion after leaving the primary nozzle is high and thisvelocity is later reduced by the compression of flowachieving a Mach number of 1.5, 3.5, and 1.72 at the nozzleexit for 25%, 40%, and 50% nozzles respectively.4.2 Ideal Conditions4.4 Comparison of ResultsIn this case discussion is about the results of simulation ofaerospike nozzle with varying truncation amounts at designaltitude.In all the cases exhaust flow of the aerospike nozzle ischaracterized by formation of a series of expansion waves,which originate from the upper lip of the convergent section.Since the exhaust flow is not bounded by a solid wall, theseexpansion waves can adjust their intensity and domain tomatch the exhaust flow with the external flow, which givesan advantage of the altitude compensation in contrast to theconventional nozzle.At this condition the flow density pattern is same to that ofthe previous case but the flow keeps on diverging even afterthe stagnation point. But this divergence is contained by thesurrounding domain. From the Fig-13(b), 13(d), and 13(f)showing the path-lines colored by density it is observed thatexpansion characterized by decrease in density occurs at thetip of the primary nozzle and again at the tip of the truncatedportion of the nozzle. This expansion is followed by thecompression of exhaust gases by the surrounding domain.From the Fig-13 the position of the stagnation point and therecirculation area forming two vortices at the base oftruncated nozzle can be observed. And the expansion wavesare extended even after the end of the nozzle surface. Butfrom the contours of Mach number shown in the Fig-13(a),13(c), and 13(e) it is observed that velocity of the exhaustflow is gradually increasing even during the compressionphase reaching the maximum Mach number of 3.2, 3.7 and3.5 Mach for 25 %, 40% and 50% nozzles respectively atthe exit of the nozzle.4.3 Under Expansion ConditionIn this case the expansion waves originated from the upperlip of the primary nozzle face the truncated portion of theplug. The flow facing the truncation first encounters a sharpexpansion, then by continuing its way to the centre of theplug base. From this point flow passes through compressionby the atmosphere and the flow meets at the stagnation pointIt should be pointed out that regardless of the amount oftruncation and the extent of the plug base area, the flowparameter distribution pattern is the same. Figures showingpathlines clearly show the above-mentioned process in formof path-lines colored by density for different plug shapes. Itshould also be noted that in spite of existence of rotationalflow at the base area, path-lines will continue their wayparallel to the axis of the plug after the longitudinal positioncorresponding to the end of a virtual ideal plug, even for the25% truncated aerospike nozzle. In order to understand theconcept of thrust delivery by different truncated aerospikenozzles in under-expansion conditions, design conditionsand in over-expansion conditions, it is necessary to approachthe thrust components differently. Dividing thrust into thethree following components, explains this phenomenonmore clearly1) Thrust produced by the nozzle convergent section2) Thrust produced by the plug surface3) Thrust produced by the plug baseIn under-expansion conditions, when the plug is truncated,its lateral area decreases. Therefore the pressure thrustproduced by the plug reduces. On the other hand, thrustVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org127
IJRET: International Journal of Research in Engineering and Technology eISSN:generated by the base region increases because of theincrease of the base area. These two effects compensateeach other, and the total nozzle thrust becomes almost thesame for different nozzle truncation. This effect can be seenmost clearly for the 25% plug.But in over-expansion conditions, the situation is totallydifferent. In these conditions, as the nozzle length becomesshorter, hence decreasing the plug area, thrust produced bythe plug still decreases, while as the atmosphere pressure ishigher than the exhaust pressure thrust produced by the base2319-1163 pISSN: 2321-7308pressure would have a negative value. So by increasingtruncation, the negative value of base thrust will increase,hence decreasing total thrust in over-expansion conditions.It can be concluded that for the 25% plug, total thrust islowest. At low altitudes (i.e., over-expansion conditions)base pressure linearly increases as atmospheric pressureincreases. At high altitudes, pressure at the base remainsconstant despite variation of altitude. As the altitudeincreases, atmospheric pressure decreases and the differencebetween base pressure and atmospheric pressure increases,hence increasing the base thrust.(a) Contours of Mach Number, 25% nozzle(c) Contours of Mach Number, 40% nozzle(b) Pathlines, 25% nozzle(d) Pathlines, 40% nozzleVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org128
IJRET: International Journal of Research in Engineering and Technology eISSN:(e) Contours of Mach Number, 50% nozzle2319-1163 pISSN: 2321-7308(f) Pathlines, 50% nozzleFig-12: Flow pattern of the ideal and truncated aerospike nozzles in over-expansion conditions (Patm/Pdes 1.57)(a) Contours of Mach Number, 25% nozzle(b) Pathlines, 25% nozzle(c) Contours of Mach Number, 40% nozzle(d) Pathlines, 40% nozzleVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org129
IJRET: International Journal of Research in Engineering and Technology eISSN:(e) Contours of Mach Number, 50% nozzle2319-1163 pISSN: 2321-7308(f) Pathlines, 50% nozzleFig-13: Flow pattern of the ideal and truncated aerospike nozzles in design conditions (Patm/Pdes 1.00)(a) Contours of Mach Number, 25% nozzle(c) Contours of Mach Number, 40% nozzle(b) Pathlines, 25% nozzle(d) Pathlines, 40% nozzleVolume: 03 Issue: 11 Nov-2014, Available @ http://www.ijret.org130
IJRET: International Journal of Research in Engineering and Technology eISSN:(e) Contours of Mach Number, 50% nozzle2319-1163 pISSN: 2321-7308(f) Pathlines, 50% nozzleFig-14: Flow pattern of the ideal and truncated aerospike nozzles in under-expansion conditions (Patm/Pdes 0.10)6. CONCLUSIONSThe results clearly indicate that the aerospike nozzle iscapable of producing the optimum performance at differentaltitudes.From the simulation results we know that the base pressurecompensates the loss of thrust in under-expansionconditions, plug truncation has minor effect on the loss ofthrust in these conditions. But in over-expansion, thrust losswill increase with the increase of truncation. Base pressurethrust is closely related to variation of base pressure withatmospheric pressure. Base pressure is constant in underexpansion conditions, but increase with the increase of theatmospheric pressure in over-expansion conditions.Based on the observed behavior of the exhaust flow, it canbe concluded that the 40 % truncated nozzle isrecommended. Because its flow pattern shows the signs ofoptimum performance and it has achieved the desired exitMach number in all the three altitude conditions.REFERENCES[1]. Angelino G., “Approximation Method for Plug NozzleDesign”, AIAA Journal, Vol. 2, No. 10, Oct. 1964, pp. 18341835.[2]. Gross, Klaus W., "Performance Analysis of AerospikeRocket Engines," 1972.[3] Lee, C. C., “Computation of plug nozzle contours by theRao’s optimum thrust method”, NASA CR-21914 R-61,1963.[4]. Lee, C. C., Inman. S. J., “Numerical analysis of plugnozzles by the Method of characteristics”, NASATECHNICAL NOTE R-10, 1964.[5]. Besnard, E., H. H. Chen, T. Mueller and J. Garvey,“Design, Manufacturing and Test of a Plug Nozzle RocketEngine”, AIAA Paper 2002-4038, 2002.[6]. Naghib Lahouti, A., Nazarinia, M. and Tolouei, E.,“Design and numerical analysis of aerospike nozzles withdifferent plug shapes to compare their performance with aconventional nozzle”, The Eleventh Australian InternationalAerospace Congress, Melbourne, Australia, 13-17 March(2005).[7]. Tomita, T. et al., Nobuhiko, K. and Ogawara, A., "Aconceptual system design study for a linear aerospike engineapplied to a future SSTO Vehicle," The 46thAIAA/ASME/SAE/ASEE Joint Propulsion Conference andExhibit, AIAA-2010-7060, 2010.[8]. Sakamoto, H., Takahashi M., Sasaki, M., Tomita, T.,Kusaka K. and Tamura H., “An Experimental Study on a14KN Linear Aerospike Nozzle Combustor”, AIAA Paper99- 2761, 1999.[9]. Chang Hui Wang, Yu Liu, Li Zi Qin, “Aerospike nozzlecontour design and its performance validation”, ActaAstronautica 64 1264-1275, 2009.BIOGRAPHIESL. Vinay Kumar pur
2. DESIGN METHODOLOGY Design of the aerospike nozzle mainly refers to the design of the central spike and the determination of angle of the primary nozzle. Method of characteristics in conjunction with the streamline conditions of A.H.Shapiro is used for the design of aerospike nozzle contour. A point on the
If Flow Simulation is not available in the menu, you have to add it from SOLIDWORKS menu: Tools Add Ins and check the corresponding SOLIDWORKS Flow Simulation 2017 box under SOLIDWORKS Add-Ins and click OK to close the Add-Ins window. Select Tools Flow Simulation Project Wizard to create a new Flow Simulation project. Enter Project name:
SolidWorks Flow Simulation 2014. box. Select . Flow Simulation Project Wizard. to create a new Flow Simulation project. Enter Project name: " Flat Plate Boundary Layer Study ". Click on the . Next button. Select the default . SI (m-kg-s) unit system and click on the . Next button once again. Figure 2.12a) Starting a new Flow Simulation .
The Introduction to Flow Analysis Applications with SolidWorks Flow Simulation and its supporting materials is designed to assist you in learning SolidWorks Flow Simulation in an academic setting. Online Tutorials The Introduction to Flow Analysis Applications with SolidWorks Flow Simulation is a companion resource and
This product provides a local flow indication and automatically signals the operator or PLC if flow is too high or too low. Uses of the Flow-Alert flow meter include: bearing lubrication, case drain verification, gun drill cooling, pump flow confirmation, etc. FLOW-ALERT FLOW SWITCH 6000 PSI / 414 BARS MAX GPM LPM OIL FIGURE 1- Flow-AlERt Flow .
simulation grid cells. Figure 6 shows the distribution of upscaled geology, compare with Figure 4. This downscaling and upscaling process is repeated for each flow simulation grid network. Flow simulation is performed using the upscaled geology on each of the 15 flow simulation grid networks. A single 500m long well pair is used.
SolidWorks Flow Simulation 2013. box. Select . Flow Simulation Project Wizard. to create a new Flow Simulation project. Create a new figuration named " Flat Plate Boundary Layer Study ". Click on the . Next button. Select the default . SI (m-kg-s) unit system and click on the . Next button once again. Figure 2.12a) Starting a new Flow .
n Simulation and embedded system design ufunctional simulation uperformance simulation ŁPOLIS implementation Łpartitioning example uimplementation simulation Łsoftware-oriented Łhardware-centric n Summary Cycle-based, logic simul. Design flow Behavior capture Mapping (partitioning) Architecture capture Functional simul. Architecture simul .
Simulation is a process of emulating real design behavior in a software environment. Simulation helps verify the functionality of a design by injecting stimulus and observing the design outputs. This chapter provides an overview of the simulation process, and the simulation options in the Vivado Design Suite. The process of simulation includes:
