IJAET International Journal of Application of Engineering and Technology ISSN: Vol.1 No.1

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IJAET International Jornal of Application of Engineering and Technology ISSN: 395-3594 Vol1 No1 ANALYSIS OF SUPERSONIC FLOWS IN THE E -LAVAL NOZZLE AT 1 INTO A SUENLY EXPANE UCT AT L/=WITH CAVITY

1 IJAET International Jornal of Application of Engineering and Technology ISSN: Vol1 No1 ANALYSIS OF SUPERSONIC FLOWS IN THE E -LAVAL NOZZLE AT 1 INTO A SUENLY EXPANE UCT AT L/=WITH CAVITY ASPECT RATIO 1 USING CF Saket BS Pandey, Pratik Sharma, Moin Khan, Antim Rewapati and A P Singh epartment of mechanical engineering Indore Institte of Science and Technology ABSTRACT This paper presents soltions of spersonic flows in the de -laval nozzle at 1 into a sddenly expanded dct at l/d=with cavity aspect ratio 1 Copled implicit scheme with K-ε model have been sed for modeling of spersonic flow It is observed that de to increase in length of the dct the intensity of compression waves decreases, weak shock waves are generated and hence flow oscillation redces The nozzle is designed for streamline flow and hence the intensity of trblence is less inside the nozzle as compared to the dct in all the cases Moreover, this effect pacifies the flow oscillation and hence it proves the fact that increases in L/ not only redces the intensity of compression wave bt also flow oscillations Keywords: - Spersonic flow, two-dimension, e Laval Nozzle, Mach No, Pressre ratio, flow reversal, stream line, cavity I INTROUCTION Swedish engineer of French descent who, in trying to develop a more efficient steam engine, designed a trbine that was trned by jets of steam The critical component the one in which heat energy of the hot high-pressre steam from the boiler was converted into kinetic energy was the nozzle from which the jet blew onto the wheel de Laval fond that the most efficient conversion occrred when the nozzle first narrowed, increasing the speed of the jet to the speed of sond, and then expanded again Above the speed of sond (bt not below it) this expansion cased a frther increase in the speed of the jet and led to a very efficient conversion of heat energy to motion The theory of air resistance was first proposed by Sir Isaac Newton in 176 According to him, an aerodynamic force depends on the density and velocity of the flid, and the shape and the size of the displacing object Newton s theory was soon followed by other theoretical soltion of flid motion problems All these were restricted to flow nder idealized conditions, ie air was assmed to posses constant density and to move in response to pressre and inertia Nowadays steam trbines are the preferred power sorce of electric power stations and large ships, althogh they sally have a different design-to make best se of the fast steam jet, de Laval s trbine had to rn at an impractically high speed Bt for rockets the de Laval nozzle was jst what was needed Armed with this expertise, the designer of an engineering device is able to choose the optimm design from among a nmber of alternative possibilities and can ensre the desired performance Prediction offer economic benefits and contribte to hman well-being The investigation of flow processes can be done by two main methods namely, experimental, theoretical Experimental investigation offers the most reliable information abot a physical process However, there are serios difficlties of measrements in many sitations and the measring instrments are not free from errors Often sch measrement itself interferes significantly with the process being measred, ths making total experimental knowledge of the process impossible to obtain Theoretical investigation works ot the conseqence of a mathematical model of the process, which often consists of a set of partial differential eqations for the physical qantities of interest These eqations are often of sch complexity that if the methods of classical mathematics were to be sed for solving them there wold be a little hope of predicting many cases of practical interest Fortnately, the development of nmerical methods and the availability of large digital compters allow mathematical model to be solved for many practical problems The advantage of theoretical investigation over a corresponding experimental investigation is its low cost, remarkable speed, detailed and complete information of the process nder different conditions Even with the remarkable sccess of nmerical soltions, few accept 49

them ncritically withot some experimental validation As in the saying by Albert Einstein, A theory is something nobody believes except the person proposing the theory and an experiment is something

dimensions for the incompressible flow of a constant viscosity flid is as follows: Continity A PHYSICAL MOEL The problem being considered is the spersonic flow throgh de Laval nozzle to nmerically

field for Mach no 174And 1 is analyzed for flly nderstand the flow field with U, V v Where is the constant inlet velocity Note that all t,, X x, Y y p, Pn velocities are non-dimensionalised by And v,

with typical components actally encontered in applications The frther approximations and idealizations made for the present investigations are as follows: The flid is Ideal gas The flow is Spersonic

The Length to diameter ratio of the dct in which the analyses are performed is 1,, 4 and 6 Initially the stdy for L/ 6 is discssed below Five common properties like Mach nmber, Total Pressre, Static

2 them ncritically withot some experimental validation As in the saying by Albert Einstein, A theory is something nobody believes except the person proposing the theory and an experiment is something everybody believes except the person doing the experiment II MATHEMATICAL FORMULATION C GOVERNING EQUATIONS The nsteady, conservative and dimensionless form of the nevier-stokes eqations in two dimensions for the incompressible flow of a constant viscosity flid is as follows: Continity A PHYSICAL MOEL The problem being considered is the spersonic flow throgh de Laval nozzle to nmerically simlate the flow U X X- Momentm V Y 0 U ( UU ) ( VU ) Pn X Y X Y-momentm 1 Re U X U Y V ( UV ) ( VV ) X Y P n Y 1 V Re X V Y Figre 1: Physical model of spersonic flow throgh e Laval nozzle The flow field for Mach no 174And 1 is analyzed for flly nderstand the flow field with U, V v Where is the constant inlet velocity Note that all t,, X x, Y y p, Pn velocities are non-dimensionalised by And v, respectively B APPROXIMATIONS AN IEALIZATIONS III RESULTS AN ISCUSSIONS The physical model described in the preceding section is a simplified model, with respect to the srface geometry, when compared with typical components actally encontered in applications The frther approximations and idealizations made for the present investigations are as follows: The flid is Ideal gas The flow is Spersonic The flow is assmed to be two-dimensional The flow is belongs to k-epsilon model The flow analysis is performed in the e Laval nozzle with common properties like aspect ratio one and pressre ratio 65 The Length to diameter ratio of the dct in which the analyses are performed is 1,, 4 and 6 Initially the stdy for L/ 6 is discssed below Five common properties like Mach nmber, Total Pressre, Static Pressre, Static temperatre and Trblent Intensity are analyzed for each L/ and discssed over here At the base, that is near the nozzle exit and in the dct flow reversal is clearly visalized in all the L/ cases The figre 51 shows the reversal of flow at the base The reattachment point can also be determined by comparing the varios reslts obtained for varios L/ 50

Figre 4 Total Pressre Figre - Flow Reversals Length to iameter ratio (ASR1) Mach nmber Actally Most of the flow properties are similar as in case of L/ 1The Mach nmber at nozzle exit is 07 for nozzle

3 Figre 4 Total Pressre Figre - Flow Reversals Length to iameter ratio (ASR1) Mach nmber Actally Most of the flow properties are similar as in case of L/ 1The Mach nmber at nozzle exit is 07 for nozzle which is design for Mach nmber 1; The Mach nmber decreases at the nozzle exit de to the formation of weak and obliqe shock wave Static Pressre The figre reveals the fact that the gas gets over expanded at the nozzle exit plane e to increase in L/, the pressre of the compression wave is not so intense and hence a weak shock wave is generated casing redction in rise in static pressre in comparison to previos reslt Moreover, this effect pacifies the flow oscillation and hence it proves the fact that increases in L/ not only redces the intensity of compression wave bt also flow oscillations Frther downstream the expansion fan effect is observed and the vale of static pressre redces to 637 e +04 Pascal The static pressre of flow then smoothly increases to back pressre Total Pressre Figre 3 Mach nmber The total pressre at the nozzle exit at the centre is 56e+5, while the total pressre in the dct at the centre is 197e+5 There is decrease in stagnation pressre near the nozzle walls de to viscos effects, whereas the stagnation pressre remains almost constant in the centre After over expansion at the nozzle exit, there is a formation of weak shock wave As large amont of losses accompany this shock, decrease in stagnation pressre can be observed Static Temperatre Figre 5 Static Pressre As we have assmed the ideal gas properties, the static temperatre is directly proportional to static pressre Here the min Static temperatre in dct at the centre is 31e+0 while at the nozzle exit 197e+0 The static temperatre decreases in the divergent part of the nozzle corresponding to decrease in static pressre There is formation of shock, the static temperatre increases de to decrease in Mach nmber across the shock The static 51

4 temperatre is higher at the walls as compared to the interior becase the effect of shock is more prononced at the circmference of the jet Trblence Intensity Figre 6 Static Temperatres The nozzle is designed for streamline flow and hence the intensity of trblence is less inside nozzle as compared to compared to dct The trblence intensity has high vale of 494 e +03 (%) at nozzle exit This is becase of the eddy creation and reversal of flow at the base region of circlar dct Frther downstream, as flow gets agitated and the trblence intensity increases Figre 7 Trblence Intensity IV CONCLUSION The flid leaves the nozzle as free jet stream As the flid flows in the dct, Static temperatre in dct at the centre is 31e+0 while at the nozzle exit 197e+0 The static temperatre decreases in the divergent part of the nozzle corresponding to decrease in static pressre and in the cavity flow reversal is visalized The Mach nmber was fond to be very low at base region and in the cavities for all the cases The total pressre was fond to be very high at the nozzle exit compare to the total pressre at the dct exit Near the wall the total pressre rapidly decreases It is observed that de to increase in length of the dct the intensity of compression waves decreases, weak shock waves are generated and hence flow oscillation redces The nozzle is designed for streamline flow and hence the intensity of trblence is less inside the nozzle as compared to the dct in all the cases Moreover, this effect pacifies the flow oscillation and hence it proves the fact that increases in L/ not only redces the intensity of compression wave bt also flow oscillations Frther downstream the expansion fan effect is observed V REFERENCE 1 Wick, RS, The effect of bondary layer on sonic flow throgh an abrpt cross sectional area change, Jornal of the Aeronatical Sciences, Vol 0, p (1953) Korst, H, Comments on the effect of bondary layer on the sonic flow throgh an abrpt cross sectional area change, Jornal of Aeronatical Sciences, Vol 1, p 568 (1954) 3 Hall, WB and Orme, EM, Flow of a compressible flid throgh a sdden enlargement in a pipe, Proceedings of Instittion of Mechanical Engineers, Vol 169, p (1955) 4 BenedictRP and Steltz, WG, A generalized approach to one dimensional gas dynamics, Trans ASME (power), Vol 84, p 44 (196) 5 Anderson, J S and Williams, T T, Base pressre and noise prodced by the abrpt expansion of air in a cylindrical dct, Jornal of Mechanical Engineering Science, Vol 10, No (3), p 6-68 (1968) 6 rstf, Melling, A and Whitelaw, JJ, Low Reynolds nmber flow over a plane symmetric sdden expansion, Jornal of Flid mechanics, Vol 1, No6, p739 (1974) 7 Cherdon, W, rst, F and Whitelaw, JH, Asymmetric flows and instabilities in symmetric dcts with sdden expansions, Jornal of Flid Mechanics, Vol 84, part 1, p13 (1978) 8 Brady, JF and Acrivos, A, Closed cavity laminar flows at a moderate Reynolds nmbers, Jornal of Flid Mechanics, Vol 115, p 47 (198) 9 Yang, BT and Y, M H, The flow field in a sddenly enlarged combstion chamber, AIAA Jornal, Vol 1, No1, p 9-97 (1983) 10 Rathakrishnan, E, Ramanaraj, O V, and Padmanabhan, K, Inflence of cavities on sddenly expanded flow field, Mechanics Research commnications, Vol 16 (3), p (1989) 11 Raghnathan S and Mabey, G, Passive shockwave/bondary-layer control on a wall monted model, AIAA Jornal, Vol 5, No, p (1987) 5

5 1 Raghnathan, S, Pressre flctation measrements with passive shock/bondary layer control, AIAA jornal, Vol 5, No 5, p (1987) 13 Raghnathan, S, Effect of porosity strength on passive shockwave/bondary layer control, AIAA jornal, Vol 5, No 5, p (1987) 14 Wilcox, JF Jr, Passive venting system for modifying cavity flow fields at spersonic speeds, AIAA Jornal, Vol 6, No 3, p (1988) 15 Tanner, M, Base cavities at angles of incidence, AIAA Jornal, Vol 6, No 3, p (1988) 16 Vishwanath PR and Patil, SR, Effectiveness of passive devices for axi symmetric base drag redction at Mach, Jornal of Spacecraft, p 34, (May -Jne 1990) 17 Kriswyk, RW and tton J C, Effect of base cavity on sbsonic near wake flow, AIAA Jornal, Vol 8, No 11, p (1990) 18 [18] Rathakrishnan E, Effect of ribs on sddenly expanded flows, AIAA Jornal, Vol 39, No 7, p (001) 19 Pandey, KM, and Rathakrishnan E, Inflence of cavities on flow development in sdden expansion, International Jornal of Trbo and Jet Engines, Vol 3, p (006) 0 Pandey, KM, and Rathakrishnan E, Annlar cavities for Base flow control, International Jornal of Trbo and Jet Engines, Vol 3, p (006) 53

Flow Analysis and Optimization of Supersonic Rocket Engine Nozzle at Various Divergent Angle using Computational Fluid Dynamics (CFD)

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 11, Issue 6 Ver. IV (Nov- Dec. 2014), PP 01-10 Flow Analysis and Optimization of Supersonic Rocket