“HENRI COANDA” “GENERAL M.R. STEFANIK” AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMANIA SLOVAK REPUBLIC

INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 2015 Brasov, 28-30 May 2015

ANALYSIS OF FLOW IN CONVERGENT-DIVERGENT ENGINE USING COMPUTATIONAL FLUID DYNAMICS

Bogdan-Alexandru Belega*, Trung Duc Nguyen**

*Military Technical Academy, Bucharest, Romania, **Paul Sabatier University, Toulouse, France

Abstract: Nozzle is a device designed to control the rate of flow, speed, direction, mass, shape, and/or the of the stream that exhaust from them. come in a variety of shapes and sizes depending on the mission of the rocket, this is very important for the understanding of the performance characteristics of rocket. By the proper geometrical design of the nozzle, the exhaust of the gases will be regulated in such a way that maximum effective rocket velocity can be reached. Convergent divergent nozzle is the most commonly used nozzle since in using it the propellant can be heated in chamber. After getting heated the propellant first converges at the throat of the nozzle and then expands under constant in the divergent part. In the present paper, flow through the convergent divergent nozzle study is carried out by using a finite volume rewarding code, FLUENT 6.3. The nozzle geometry modeling and mesh generation has been done using GAMBIT 2.4 Software. Computational results are in good acceptance with the experimental results taken from the literature.

Keywords: CFD, fluent, nozzle, Gambit, combustion chamber.

1. INTRODUCTION

The nozzle is used to convert the chemical- thermal energy generated in the combustion chamber into kinetic energy. The nozzle converts the low velocity, high pressure, high temperature gas in the combustion chamber into high velocity gas of lower pressure and temperature. Figure 1 – Convergent-divergent nozzle The general range of exhaust velocity is 2 to 4.5 kilometer per second. The convergent In this project the designing and analysis of and divergent (also known as convergent- CD nozzle geometry is done in the CFD divergent nozzle – figure 1) type of nozzle is (Computational Fluid Dynamics software). known as DE-LAVAL nozzle. [2,3] Firstly the design of nozzle is made in Gambit The inlet is less than one, software and then the nozzle geometry is Convergent section accelerates it to sonic further analyzed in fluent software in order to velocity at the throat and further accelerated to analyze the flow inside the CD nozzle and to supersonic velocities by the diverging section. get the view of the behavior of fluid inside the convergent-divergent section of nozzle. [1,2] 2. NOZZLE GEOMETRY ANALYSIS Additionally, the ratio of the local area to the throat area can be specified by the Mach 2.1 Rocket nozzle equations. The function number: of the nozzle is to accelerate gases produced  1 by the propellant to maximum velocity in A 1  2    1 2    12    1  M  (8) order to obtain maximum . The amount At M   1  2  of thrust produced by the engine depends on In a converging-diverging nozzle a large the mass flow rate through the engine, the exit fraction of the thermal energy of the gases in velocity of the flow, and the pressure at the the chamber is converted into kinetic energy. exit of the engine. The value of these three The flow velocity can be obtained from the flow variables are all determined by the rocket conservation of total enthalpy h : nozzle design. 0 For steadily operating rocket e   hh2v e0  (9) system moving through a homogeneous From the isentropic relations the equation atmosphere total thrust and becomes: are:   1     AppvmF e0ee (1) 2 RT   p    v  0 1   e  (10) F e       1 M p0 Isp  (2)       gm 0   T The first term is the momentum thrust and An increase of the ratio 0 will increase the second term represents the pressure thrust. M The rocket nozzle is usually so designed that the performance of the rocket. The influences the exhaust pressure is equal or slightly higher p of the pressure ratio 0 and of the specific than the ambient fluid pressure. Because p changes in ambient pressure affect the pressure e heat ratio  are less pronounced. thrust, there is a variation of the rocket thrust with altitude (between 10% and 30%). The nozzle area expansion ratio ( ) is an Velocity of sound and Mach number: important nozzle design parameter: A   TRa (3)   e (11) A v t M  (4) The maximum gas flow per unit area a occurs at the throat (critical values): The stagnation properties of a flow are  those properties which would result if the flow p  2   1 is isentropic. Stagnation properties are t   57.053.0 (12) p    1  constant in an isentropic flow. Thus, properties 0  along the nozzle are best referenced against T  2  t   91.083.0 (13) the stagnation properties. With these   T0   1  assumptions of and isentropic flow, 1 ratios of pressure, density and temperature can   2   1 t   63.062.0 (14) be related to the stagnation pressure, density   1  and temperature at a given Mach number. 0   Throat velocity v is: T    1  t 0 1   M 2 (5) T  2  2 vt  0  RTRT t (15)    1 p0    1 2   1 To attain sonic/supersonic flow: 1   M  (6) p  2   1 p   1   1 0   89.175.1 (16) 0    1 2   1 p  2  1   M  (7) e   2  The mass flow rate as a function of nozzle geometry and fluid properties can be found

“HENRI COANDA” “GENERAL M.R. STEFANIK” AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMANIA SLOVAK REPUBLIC

INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 2015 Brasov, 28-30 May 2015

from basic continuity where v the average The velocity ratio is: velocity is, A is the nozzle area,  is the   1  density and m is flowrate: v   1   p     e  1   e  (21)    ttanconsvAm (17) v   1   p   t   0   After substitutions we have De Saint   Venant’s Equation: 2.2 Calculated values for nozzle 2 dimensions and geometry. The dimensions of m 2 1  p  the convergent-divergent nozzle geometry are   p    0   obtained through the following equations A   1 RT  p00  (18) which are used in every spacecraft available   1  during the present day.   p    1    Mass flow in rocket is calculated by:   p   F   0   thrust   m  (22) ve When sonic velocity is reached at the where  MN2.1F and  s/m3500v throat, it is not possible to increase the throat thrust e velocity or the flow rate in the nozzle by Putting the given values in the equation we further lowering the exit pressure (choking the obtain: flow).   s/kg86.342m Choking is a effect that For high altitude (100 km or higher) obstructs the flow, setting a limit to fluid expansion ratio in nozzle, given by (11), are velocity because the flow becomes supersonic between 40 and 200. and perturbations cannot move upstream; in Area of the nozzle throat: gas flow, choking takes place when a subsonic m At  (23) flow reaches M  1.  1 Mass flow rate:  2  1 M  1 Pc       1 TR cu Ap t0   2   12   Avm ttt    Given:    1 RT0   J  10M ; u  287R ; c  K3000T ; Ap t0  Kkg m   (19) RT 0   2.1 ; Pc  MPa12 and putting these values  1 in (23) we get:  2   12 2 where     t  m0129.0A    1 Now by using equation (11) we can get the The area ratio is: value of Ae for  74 : Ae   (20)  m95.0A 2 At 2   1  e 2  p    p    Also the exit area of nozzle is given by:  e  1   e    1  p    p   2  0    0     rA ee (24)   obtaining: e  m55,0r developing the wire frame which resembles Convergence area in Nozzle is: the cross-section of the rocket nozzle (figure  A3A (25) 2). A tri-dimensional geometry of the nozzle tc was created by using the value of  m0387.0A 2 c t;L;L;r;A;L;r;A;r;A wallccnccdnttee . Radius of throat: A r  t (26) t  t  m064.0r Combustion radius: A r  c (27) c  c  111.0r m Given   150 and   600 we can Figure 2 – Nozzle Geometry 3.2 Meshing in Gambit. The next task calculate diverging Nozzle length: was to mesh the geometry created. In Ae 1 GAMBIT the mesh used was tetrahedral mesh Ldn  (28) tan elements and proper care is taken while dn  m04.2L meshing the regions near the walls of the Length of the converging nozzle: nozzle so as to get more refinement in that particular regions. As any computational Ac 1 Lcn  (29) process requires a mesh to carry computation tan  this step is a primary and most important to cn  m081.0L start the problem. The mesh created in Length of the combustion chamber: GAMBIT is as shown below figure.3.  LA * L  t (30) c 2   rc A parameter describing the chamber volume required for complete combustion is the characteristic chamber length, L* , which is given by: V L*  c (31) At where V is the chamber volume (including Figure 3 – Nozzle Geometry (Mesh) c the converging section of the nozzle) and At is We can see that the meshing near the the nozzle throat area. For gaseous boundary of the nozzle is more refined when oxygen/hydrocarbon fuels, an L* of 1.27 to compared to other regions of mesh. The mesh was refined to the third degree using the 2.54 meters is appropriate. For L*  .1 m27 , refinement option of the GAMBIT. After chamber length is: meshing, the inlet, the axis and the outlet  m423.0L c boundaries were named. 3.3 Boundary Conditions used. 3. METHODOLOGY AND Specification of the boundary zones has to be IMPLEMENTATION done in GAMBIT only, there is no possibility to specify the boundary zones in FLUENT. 3.1 Modeling the nozzle. The geometry of Accordingly the geometry of the nozzle is the nozzle was created using the Geometry divided into zones and boundary conditions workbench of GAMBIT modeling package for given to these are: the inside nozzle surfaces

“HENRI COANDA” “GENERAL M.R. STEFANIK” AIR FORCE ACADEMY ARMED FORCES ACADEMY ROMANIA SLOVAK REPUBLIC

INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 2015 Brasov, 28-30 May 2015

are given as WALL; the inlet is given as mass flow inlet; the outlet is given as pressure In figure 4 and figure 5 velocity outlet. With all the zones defined properly the distribution and absolute pressure of nozzle mesh is exported to the solver. The solver used geometry is shown respectively. in this paper is FLUENT. The exported mesh It is clearly seen the velocity is increasing file is read in fluent for solving the problem. along with the length of the nozzle. Due to The fluent conditions to the design nozzle shocking in the nozzle, the velocity decreased geometry are energy equation included, for a while but later began to increase as the viscous model- K epsilon, materials are fluid expanded through the divergent portion. Hydrogen and Titanium for fluid flow and Pressure gradually decreased along the wall respectively, mass flow rate (Inlet) length of the nozzle except a slight rise during 10 s/kg and outlet gauge pressure and the shocking. However, the rise was not temperature are 0 and 273 k respectively. significant comparing to the total fall in 3.4 Solving. After initiating the numerical pressure. According to Bernoulli’s equation, analysis, convergence was obtained after 332th pressure decrease as velocity increases along iteration in case of nozzle analyzed. The the expansion zone. steady axisymmetric implicit formulation with coupled solver with K-e turbulence model is chosen. The mass flow of the burning solid propellant was modeled using a user-defined function. [4, 5]

Figure 6 – Total temperature distribution of nozzle geometry

Figure 4 – Velocity distribution of nozzle geometry

Figure 7 – Wall shear stress distribution of nozzle geometry

In figure 6 and figure 7 total temperature and wall shear stress of nozzle geometry is shown respectively. Figure 5 – Absolute pressure distribution of It is seen that temperature decreased nozzle geometry gradually except a slight increase. The slight increase occurs in the shock zone where rapid Applications. ISSN 2277-3223 Volume 3, change of fluid properties takes place. But the Number 2 (2013), pp. 119-124. rise in temperature was not significant with 2. Mayur Chakravarti - Design analysis of flow respect to the fall in temperature throughout in convergent divergent rocket nozzle - the distance. University of Petroleum and energy studies, Department of Aerospace 4. CONCLUSIONS & Engineering, Dehradun, India, 2011. ACKNOWLEDGMENT 3. Vipul Sharma, Ravi Shankar, Gaurav Sharma, - CFD Analysis of Rocket Nozzle - After successfully completing this University of Petroleum and energy simulation of a design created, the decisions studies, Department of Aerospace were finally confined into the following Engineering, Dehradun, India, 2011. points. 4. Biju Kuttan P, M Sajesh - Optimization of From the analysis, it is clearly observed Divergent Angle of a Nozzle that nozzle created based on exit parameters it Using Computational Fluid Dynamics - is in accord with the scope. The International Journal Of Engineering And Science, volume 2, pages 196-207, REFERENCES 2013, ISSN: 2319 – 1813. 5. MD. Safayet Hossain, Muhammad Ferdous 1. Mohan Kumar G., Dominic Xavier Raiyan, Nahed Hassan Jony - Comparative Fernando, R. Muthu Kumar, - Design and study of supersonic nozzles - International Optimization of De Lavel Nozzle to Journal of Research in Engineering and Prevent Shock Induced Flow Separation - Technology, volume 3, pages 351-357, Advances in Aerospace Science and oct.2014 ISSN: 2319-1163.