Structural Analysis Of Rocket Nozzle

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International Journal of Science and Research (IJSR)ISSN (Online): 2319-7064Index Copernicus Value (2016): 79.57 Impact Factor (2017): 7.296Structural Analysis of Rocket NozzleMohan BanothDepartment of Mechanical Engineering, Jawaharlal Nehru Technological University College Of Engineering (JNTU CEJ), Jagital,Telangana, IndiaAbstract: A solid rocket motor nozzle is an essential component housed in the rear end of the rocket. The basic purpose of having thiscomponent is the conversion of the thermal energy into kinetic energy thereby imparting thrust to the missile. Nozzle Geometr y is ofparamount importance to understand the performance of a missile. The performance can be modified by changing the geometricaldesign, so as to achieve maximum effective velocity of the rocket. Nozzle design is a complex, multi- disciplinary and an iterative process.Aerodynamic, thermodynamic, structural and fabrication considerations are manipulated within the constraints to produce apreliminary nozzle configuration. The configuration thus produced is then rigorously analyzed for thermal and structural defe cts andalso its contribution on the rockets overall performance. The iterative process is continued until a thermally and structurally adequatenozzle is obtained within the required rocket constraints. Two basic exit configurations are considered in the design process, contouredand conical. The contoured nozzle turns the flow so that the exhaust products exit in a more or less axial direction thereby reducingdivergences losses. The conical nozzle on the other hand is considered due to its ease of fabrication. In this report the design andanalysis of a contour nozzle for optimizing thrust as per the requirements and constraints is carried out. The design process is carriedout as per the GVR Rao method which has now become an aerospace industry standard due to its ease of use and accuracy.1. Introduction to Rocket Nozzle1.1 IntroductionA jet engine uses a nozzle to accelerate hot exhaust tosupply thrust as delineated by Newton's third law of motion.The study of the high-temperature gas flow in a nozzle hasled to the definition of a certain number of parameters,characteristic serve as a basis for evaluation of a rocketmotor and also for comparison between different systems.So as to attain these parameters mathematically.1.2 Atmospheric useThe best size of a jet engine nozzle to be used among theatmosphere is achieved once the exit pressure equalsatmospheric pressure that decreases with altitude. Forrockets movement from the world to orbit. Slightoverexpansion causes a small reduction in potency, howeverotherwise will very little hurt.For optimal lift-off performance, the pressure of the gasesexiting nozzle should be at sea-level pressure; however, if arocket engine is primarily designed for use at high altitudesand is only providing additional thrust to another "firststage" engine during liftoff in a multi-stage design, thendesigners will usually opt for an over-expanded nozzle (atsea-level) design making it more efficient at higher altitudeswhere the ambient presser is lower. This was the techniqueused on the area shuttle's main engines.1.3 Vacuum useThis was the technique used on the world shuttle's mainengines that spent most of their powered flight in nearvacuum whereas the shuttle's two solid rocket boostersprovided the majority of the ascension thrust.1.4 Optimum shapegases is regenerate into linear motion. The only nozzle formcould be a 12º cone half-angle that is regarding 97economical. Smaller angles offer terribly slightly higherpotency; larger angles offer lower efficiency. They are wideused on launch vehicles and alternative rockets whereverweight is at a premium.1.5 Advanced designsA number of additional subtle styles are projected foraltitude compensation and alternative uses.Nozzles with A part boundary include:a) The Expansion-Deflection Nozzleb) The Plug Nozzlec) The Aero spike Nozzled) Single enlargement Ramp Nozzle (SERN)C-D nozzles are radial out-flow nozzles with the flowdeflected by a center penile.Controlled nozzles:a) The increasing Nozzle,b) Bell nozzles with a removable insert andc) The Stepped nozzles or Dual-bell nozzles.These square measure usually terribly like bell nozzleshowever.Dual-mode nozzles include:a) The dual-expander nozzle andb) The dual-throat nozzle.They would once more enable multiple propellants to beused (such as RP-1) more increasing thrust.India's PSLV calls its design 'Secondary Injection ThrustVector Control System'; a jet engine uses a nozzle toaccelerate hot exhaust to provide thrust as delineated byNewton's third law of motion.The shape of the nozzle additionally with modesty affectshowever with efficiency the enlargement of the exhaustVolume 7 Issue 7, July 2018www.ijsr.netLicensed Under Creative Commons Attribution CC BYPaper ID: ART20183795DOI: 10.21275/ART20183795300

International Journal of Science and Research (IJSR)ISSN (Online): 2319-7064Index Copernicus Value (2016): 79.57 Impact Factor (2017): 7.296A nozzle could be a comparatively straightforward device,simply a specially formed tube hot gases flow. During a C-Drocket nozzle.2. Review of LiteratureThe length and therefore the exit space area unit famed ofthe nozzle so as to urge a fascinating thrust. First the exitconditions are defined and after that only the coordinates arefound by using the MOC method that would meet thedesired exit conditions. Since there's a awfully high rate giftwithin the exhaust gases and there are finite reaction ratesthat are gift which build the method of finding thecoordinates of nozzle. George P. Sutton and Osca Biblarz.“Rocket Propulsion Elements, a Wiley-IntersciencePublication. The method of coming up with the exhaustnozzle contour for optimum thrust by variational strategies.However, an answer that's shock-free isn't attainable bythese strategies. It is obtained for the case of equilibrium andfrozen chemistry. D.R. Bartz “Turbulent Boundary LayerHeat Transfer from Rapidly Accelerating Flow of RocketCombustion Gases and of Heated Air”. Jet PropulsionLaboratory. Many nozzle contours are designedmistreatment this approach and also the correspondingvacuum performance is given.M. Barrere, and J. Vandenkerckhove, “Rocket Propulsion”,Elsevier Publishing Company, Amsterdam, 1960. Thedevelopments of the supersonic jets from these nozzles areexamined in under expanded, perfectly expanded and overexpanded conditions.As a consequence, there‟s no absence of shock noise at orclose to the planning condition. These nozzles manufactureshock cells 9%-25% shorter than cells from a comparableswimmingly contoured nozzle. The Experimental/Numericalproject sponsored by the Swedish Defense MaterielAdministration (FMV) to apply flow control techniques toreduce the noise from high performance military aircraftsuch as the Saab Gripes. At University of metropolischevrons and trailing-edge fluidic injection were tested andcompared with secondary flow simulating forward flight. AtChalmers University identical conditions were simulatedwith giant Eddy Simulation and G. R. Kirchhoffmethodology.G.V.R. Rao method, Exhaust Nozzle Contour forOptimization thrust, jet propulsion, June, 1958. The problemof high-speed compressible flow through focused roundshape nozzles is studied computationally mistreatment thefinal purpose ANSYS Fluent. A pressure-based coupledsolver formulation with weighted second-order centralupwind spatial discrimination is applied to calculate thenumerical solutions. 15 , 25 and 40 axis symmetric conicalnozzles and a reference nozzle with a circular arc crosssection are considered.different systems. So as to make these parametersmathematically, it‟s necessary to form U.S.E of asufficiently easy model showing varied phenomenaconsidered; this leads us to form various assumptions, thevalidity of that should be even.3.1 Assumptions and fundamental equationsAllow us to contemplate a perfect rocket motor assumption.1) The combustion gases are homogeneous.The combustion gases law:p ρRT(3.1)P/ (ρ) RT(3.1.1)WhereR is the Specific gas constant (R R0 /m, R0 being theuniversal gas constant and m the molecular mass)2) The particular heats of the gas don‟t vary withtemperature and pressure.3) The flow is meant to be one-dimensional, steady andphysical property.It states that the decrease in enthalpy in the nozzle is equal toincrease in kinetic energy. Indicating the initial state withinthe chamber by the subscript c, it is written:2𝑉𝑐2 𝑐𝑝 𝑇𝑐 𝑉22 𝑐𝑝 𝑇(3.2)This relation expresses the fact that the total or stagnationtemperature 𝜏tot remains constant. Stagnation temperature isoutlined because the temperature obtained by deceleratingthe flow to rest through an adiabatic transformation with orwhile not losses.Τtot τ (V2/ (2CP )) τ (1 (γ-1)/2 M2)(3.3)From equation (3.2), a limiting rate VL will be outlined it‟sthe speed that might be reached by increasing isentropicallyinto vacuum:𝑉𝐿 2𝑐𝑝 𝜏𝑡𝑜𝑡(3.4)The second fundamental equation is that of continuity𝑚 ̇ 𝜌𝑉𝐴(3.5)WhereA is that the space of section thought-about. Finally thephysical property flows square measure characterized by therelationship:𝑝𝜌 𝛾 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡From that we tend to deduce:𝑇𝑇𝑐𝑝𝛾 1𝛾 ( )𝑝𝑐𝜌 ( ) 𝛾 1(3.6)𝜌0Total pressure is sometimes used and is defined asthe pressure obtained by decelerating the flow to restthrough an isentropic transformation.𝛾𝜏 𝑡𝑜𝑡 𝛾 1)𝜏𝑝𝑡𝑜𝑡 𝑝( 𝑝(1 𝑉22𝑐 𝑝 𝜏𝛾)𝛾 1 𝑝 (1 𝛾 12𝛾𝑀2 )𝛾 1(3.7)3. Nozzle Theory3.1 Introduction3.2 Aerodynamic choking of nozzleThe basic parameters function a basis for analysis of a rocketmotor and conjointly for comparison between totallyIf the initial velocity VC is zero, one can easily deduce fromequations (3.2), (3. 5) and (3.6), the link that links the massVolume 7 Issue 7, July 2018www.ijsr.netLicensed Under Creative Commons Attribution CC BYPaper ID: ART20183795DOI: 10.21275/ART20183795301

International Journal of Science and Research (IJSR)ISSN (Online): 2319-7064Index Copernicus Value (2016): 79.57 Impact Factor (2017): 7.296flow per unit space (m/A) ̇ with the upstream conditions andalso the reciprocal of the growth ratio; it is:𝑚̇𝐴2𝛾 𝛾 12𝑝𝑝𝛾 1𝛾𝑝𝑐 𝜌𝑐 [( )𝛾 ( )𝑝𝑐nd𝑝𝑐](3.8)The 2 member of this equation is adequate to zero once p pc or p 0.Let the subscript t indicate the crucial conditions: the crucialpressure quantitative relation is often found by golf shotcapable zero the spinoff of m ̇ /A with relation to p/pc, andthat we get:𝑝𝑡𝑝𝑐And consequently𝛾𝛾 12 (𝛾 1𝜏𝑡(3.10)𝛾 1The essential pressure magnitude relation pt/pc so separates2 sorts of nozzles.If (pe/pc) (pt/pc), the nozzle designed to provide a givenmass flow m̊ is entirelyIf (pe/pc) &let; (pt/pc), the nozzle designed to drop thepressure of flow( m) ̇ to close should be initial of decreasingsection, Such a nozzle is termed a Convergent-Divergent orFirst State Laval Nozzle.𝛾𝑝𝑡𝜌𝑡 𝛾𝑅𝜏𝑡 𝑎 𝑡(3.11)The nozzle is claimed to be saturated or obstructed and itsmass flow is entirely. Relations (3.9), (3.10) and (3.11) stayvalid for physical property nozzles during which the body ofwater speed isn‟t zero.3.3 Mass flow through a nozzleThe mass flow m ̇ through a nozzle , expressed as a operateof the measurable existing within the combustion chamber(pc, τc) and of the throat space At, may be determined asfollows.𝑎𝜌𝑡𝑚̇ 𝜌𝑡 𝑎 𝑡 𝐴𝑡 𝜌𝑐 𝐴𝑐 𝑡𝐴𝑡(3.12)𝑎𝑐𝑉𝐿Equation (3.18) is very often used in a particularly simpleform by introducing the mass flow factor CD or thecharacteristic velocity c* defined as follows:1Г𝐶𝐷 (3.20)𝑐𝑅𝜏 𝑐Equation (12) can be written:𝑚̇ 𝐶𝐷 𝑝𝑐 𝐴𝑡 𝑝 𝑐𝐴𝑡(3.21)𝑐 Nozzle exhaust velocityVelocity Vc being assumed negligible and, taking intoassount relation (3.6) which characteristics isentropicprocesses, the energy qquation (3.2) can be given.2𝑉𝑐2𝑝𝛾 1𝛾 𝑐𝑝 𝜏𝑐 𝜏𝑒 𝑐𝑝 𝜏𝑐 [1 ( 𝑒 )𝑝𝑐As we realize that:𝛾 𝑐𝑝𝑐𝑣and 𝑅 𝑐𝑝 𝑐𝑣 Where R0 is that the universal R:2𝛾2𝑐𝑝 𝜏𝑐 𝑅𝜏𝑐 𝛾 12𝛾 𝑅0𝛾 1 𝑐 At the throat, it is often without delay;𝑉𝑡 𝛾 1(3.9)2 𝜏𝑐)The mass flow m ̇ may be expressed as a operate of thelimiting rate VL given by(3.4)2𝛾 𝑝 𝑐 𝐴 𝑡𝑚̇ Г(3.19)2𝛾 𝑅0𝛾 1 𝑚𝑝𝛾 1𝛾𝜏𝑐 [1 ( 𝑒 )𝑝𝑐Introducing the limiting speed VL outlined by equation (4)we are able to write relation (3.26) in significantly easy form𝑝𝛾 1𝛾𝑉𝑒 𝑉𝐿 1 ( 𝑒 )(3.27)𝑝𝑐Equation (3.26) brings out the different variables thatinflence the exhaust velocity Vc they are the pressure ratiopc/p e, the initial temperature in the chamber 𝜏𝑐 , the molecularweight m of the gases, and their specific heat ratio 𝛾.(A) Increasing the chamber presure, however, reduces.Despite its favourable influence, pressure increase islimited by practical design considerations𝜌𝑐By neglecting the velocity VC at the nozzle inlet, quitejustified relations (3.10) and (3.11) give as:𝑎𝑡𝑎𝑐𝜏1𝜏𝑐12 ( 𝑡 )2 (𝛾 1)2(3.13)Now, isentropic and relations (6), (10) lead to:𝜌𝑡𝜌𝑐1𝜏2 ( 𝑡 )𝛾 1 (𝜏𝑐𝛾 11)𝛾 1(3.14)Thus, by eliminating 𝜌𝑡 /𝜌𝑐 and at /ac, we get:𝑚̇ 𝜌𝑐 𝑎 𝑐 𝐴𝑡 (12𝛾 1)𝛾 1 12(3.15)By replacing ac by the expression:𝑎 𝑐 𝛾𝑅𝜏𝑐(3.16)By eliminating 𝜌𝑐 by means of the perfect gas law (3.1.1) andby plase:Г 𝛾(We ultimately get:𝑚̇ Г2𝛾 1𝑝 𝑐𝐴𝑡𝑅𝜏 𝑐𝛾 1)2(𝛾 1)(3.17)(3.18)Figure 3.1: Variation of the ratio Ve/VL as a function ofpressure ratio pc/pe for several values of 𝛾(B) Velocity Ve varies as the square root of the combustiontemperature 𝜏𝑒 ; it is thus describle to choose propellantsthat give a high value of 𝜏𝑐 . This limits set practically atbetween 2750 to 3500 degrees Kelvin. Only a fewchemical reactions give higher temperatures at the priceof considerable difficulties (for instance the reactionfluorine-hydrogen gives 𝜏𝑐 5000 ͦ K).(C) This molecular weight m of the reaction are be possible.(D) The specific heat ratio 𝛾 both factors of equation (3.27).Volume 7 Issue 7, July 2018www.ijsr.netLicensed Under Creative Commons Attribution CC BYPaper ID: ART20183795DOI: 10.21275/ART20183795302

International Journal of Science and Research (IJSR)ISSN (Online): 2319-7064Index Copernicus Value (2016): 79.57 Impact Factor (2017): 7.296The first corresponds to the initial enthlpy Cp τc, i.e. to thelimiting rate, it decreses once γ will increase (Figure 3.2)𝐴𝑒𝐴𝑡Г 1𝑝𝑒 𝛾𝑝𝑐2𝛾𝛾 1𝛾 1𝑝[1 ( 𝑒 ) 𝛾 ]𝑝𝑐 Г2(3.33)1𝑝𝑒 𝛾 ̇𝐶𝐹𝑝𝑐Also, conversely the ratio pe/pc is completely determinedwhen Ae/At is fixed, as long as no flow separation takes placewithin the divergent.Figure 3.2: Variation of the exit velocity Ve , of the limitingvelocity VL and of the ratio Ve/VL as functions of thespecific heat ratio in the case: pc/pe 20, and m 25The second factor,𝑝𝛾 1𝛾1 ( 𝑒)(3.28)𝑝𝑐Corresponds to the expansion and increase together with 𝛾).The real process lies in between the so-called “FROZENFLOW” in which the composition has no time to vary andthe so-called “EQUILIBRIUM FLOW” in which physicaland chemical equilibrium exists at all times.Figure 3.4: Variation of the area ratio Ae/At as a function ofpressure ratio pc/pe, for several valuesEquation (16) will be employed in a very easy kind by aparameterof 𝛾. (𝑝𝑒 /𝑝𝑐 )𝛾 can easily readily obtained from:𝐶𝐹̇ Г2𝛾𝛾 1𝛾 1𝑝𝑒 𝛾[1 ( )𝑝𝑐](3.29)Figures 3.4 (3.3) and 3.5 give the values of the area ratioAe/At as a function of pressure ratio pc/p e, for different values11𝑝( 𝑒 )𝛾𝑝𝑐 𝑝𝑒𝑝𝑐𝛾 1𝑝𝑒 𝛾(𝑝 )𝑐Equation (3.15) can be written:𝑉𝑒 𝑐 𝐶𝐹̇(3.30)Figure 3.3 represents 𝐶𝐹̇ as a function of pc/pe for fivevalues of 𝛾. Equation (3.30) terribly is incredibly typicallyused as a result of it results in very straightforwardexpression of the thrust.3.4 Area ratio (ae/at )Indeed, continuity of the mass between the throat and exitspace is written:𝜌𝑒 𝑉𝑒 𝐴𝑒 𝜌𝑡 𝑉𝑡 𝐴𝑡(3.31)And by mistreatment a similar transformations as with in thepreceding sections𝐴𝑒𝐴𝑡 𝜌 𝑡 𝑉𝑡 𝜌 𝑡 𝑎 𝑡 𝜌𝑐 𝑎 𝑐𝜌 𝑒 𝑉𝑒 𝜌 𝑒 𝑎 𝑒 𝜌 ͦ𝑒𝑉𝑒1 Г𝑝( 𝑐 )𝛾𝑝𝑒𝑅𝜏 𝑐𝑉𝑒(3.32)Figure 3.5: Variation of the area ratio Ae/At as a function ofpressure ratio p c/pe, for several values of 𝛾.3.5 Thrust and thrust coefficientThe flow of the propellant gases or the momentum flux-outcauses the thrust force on the rocket structure plane of thenozzle could also be totally different from the close pressure.𝐹 𝑚̇ 𝑣2 𝑝2 𝑝3 𝐴2(3.35)Values calculated for optimum operative conditions (p2 p3)for given values of p1,k, and A2/At , the subsequentexpressions could also be used. For the thrust,𝑝𝑝 𝐴𝐹 𝐹𝑜𝑝𝑡 𝑝1 𝐴𝑡 2 3 2(3.36)𝑝1Figure 3.3: Variation of the characteristic thrust coefficientas a function of the pressure ratio pc/pe, for several valuesof.In above relation, 𝑉𝑒 can be replaced by its expression asgiven by equation (3.26), os that:For specific impulse,𝐼𝑠 𝐼𝑆𝑜𝑝𝑡 𝑐 𝜖𝑝2𝑔0𝑝1𝑝 1 𝐴𝑡 𝑝3(3.37)𝑝1If, as an example, the particular impulse for a replacementexit pressure p2 such as a replacement space quantitativerelation A2 /At is to be calculated, the on top of relationscould also be used.Volume 7 Issue 7, July 2018www.ijsr.netLicensed Under Creative Commons Attribution CC BYPaper ID: ART20183795DOI: 10.21275/ART20183795303

International Journal of Science and Research (IJSR)ISSN (Online): 2319-7064Index Copernicus Value (2016): 79.57 Impact Factor (2017): 7.296Equation 3.3 can be modifying and substituting 𝑣2 , 𝑣𝑡and 𝑉𝑡 .𝐴𝑡 𝑣𝑡 𝑣2𝐹 𝑝2 𝑝3 𝐴2𝑉𝑡𝐹 𝐴𝑡 𝑝12𝑘 22𝑘 1 / 𝑘 1𝑘 1 𝑘 11 𝑝2𝑘 1 /𝑘𝑝1 𝑝2 𝑝3 𝐴2(3.38)The pressure quantitative relation the nozzle [p1/p2], heatquantitative relation k, and of the pressure thrust. The thrustconstant CF is outlined because the thrust divided by thechamber pressure p 1 and also the throat space elevation𝑣2 2 𝐴2 𝑝2 𝐴2 𝑝3 𝐴2𝐶𝐹 𝑝1 𝐴𝑡 𝑉2 𝑝1 𝐴𝑡 𝑝1 𝐴𝑡𝐶𝐹 𝐴𝑡 𝑝12𝑘 22𝑘 1 / 𝑘 1𝑘 1 𝑘 11 𝑝2𝑝1𝑘 1 /𝑘 𝑝 𝑝 𝐴23 2𝑝 1 𝐴𝑡(3.39)The thrust constant CF could gas property k,This peak price is thought because the optimum thrustconstant𝐹 𝐶𝐹 𝐴𝑡 𝑝1(3.40)The above equation can be solved for CF and provides therelation for determining the thrust coefficientexperimentally.4. Materials and MethodsMaterials usedThe solid propellant rocket nozzle mainly uses four differentcomposites namely Aluminum 7075, Silica-Phenolic,Carbon Phenolic, Graphite.Table 4.1: The Variation of Thermal Conductivity andSpecific with respect to TemperatureTemperature(k) 300 1000 1500 2000 2500 3000Thermal0.5424 0.5693 1.875 5.2615 11.619 1443Conductivity(W/ mk)Specific1087.1 1336.9 1426.8 1443 1443 1443heat(J/Kgk)4.2 Silica phenolicDensityUltimate tensile StrengthYoung‟s modulusPoisson‟s ratio: 1350 Kg/ m3: 9 MPa: 1700 MPa: 0.284.3 Carbon phenolicAblative materials are commonly used. Because of theextraordinarily harsh atmosphere within which thesematerials operate, they're worn throughout motor firing witha ensuing nominal performance reduction. The objective ofthe present work is to study the thermo chemical erosionbehavior of carbon-phenolic material in solid rocket motornozzles. The adopted approach relies on a validated fullNavier-stokrs flow solver coupled with a thermo chemicalablation model, which takes into account finite-rateheterogeneous chemical reactions at the nozzle surface, rateof diffusion of the species through the boundary layer,pyrolysis gas and char-oxidation product species injection inthe boundary layer heat conduction inside the nozzlematerial, and variable multispecies thermo physicalproperties.Thermal ConductivitySpecific heatDensityUltimate tensile StrengthYoung‟s modulusPoisson‟s ratio: 0.56 W/m K: 0.177 J/Kg k: 1350 Kg/ m3: 10 MPa: 900 MPa: 0.254.4 GraphiteFigure 4.1 Material Representation of nozzle4.1 Aluminum 7075Aluminum alloy 7075 is AN aluminum alloy. It has lowerresistance to corrosion than several alternative Al alloys;however has considerably higher corrosion resistance thanthe 2000 alloys. 7075 aluminum alloy's composition roughlyincludes five.6–6.1% zinc, 2.1–2.5% magnesium, 1.2–1.6%copper, and less than a half percent of silicon, iron,manganese, titanium, chromium, and other metals.Thermal conductivitySpecific heatDensityUltimate tensile strengthYoung‟s modulusPoisson‟s ratio: 177 W/m K: 890 J/Kg: 2700 Kg/ m3: 42.9 MPa: 7378 MPa: 0.33Graphite archaically stated as plum bago, could be acrystalline kind of carbon, a semimeta

Heat Transfer from Rapidly Accelerating Flow of Rocket Combustion Gases and of Heated Air”. Jet Propulsion Laboratory. Many nozzle contours are designed mistreatment this approach and also the corresponding vacuum performance is given. M. Barrere, and J. Vandenkerckhove, “Rocket Propulsion”,

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