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Analysis of Flow in Convergent-Divergent Rocket Engine Nozzle Using Computational Fluid Dynamics

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Analysis of Flow in Convergent-Divergent Rocket Engine Nozzle Using Computational Fluid Dynamics “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 ROCKET ENGINE NOZZLE 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 pressure of the stream that exhaust from them. Nozzles 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 propellant 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 combustion chamber. After getting heated the propellant first converges at the throat of the nozzle and then expands under constant temperature 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 Mach number 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 2 1 1 M (8) order to obtain maximum thrust. 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 propulsion ve 2 h0 h e (9) system moving through a homogeneous From the isentropic relations the equation atmosphere total thrust and specific impulse becomes: are: 1 F m ve p e p 0 A e (1) 2 RT p v 0 1 e (10) F e 1 M p0 Isp (2) m g0 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 a R T (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 0.53 0.57 (12) p 1 constant in an isentropic flow. Thus, properties 0 along the nozzle are best referenced against T 2 t 0.83 0.91 (13) the stagnation properties. With these T0 1 assumptions of ideal gas and isentropic flow, 1 ratios of pressure, density and temperature can 2 1 t 0.62 0.63 (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 RT0 RTt (15) 1 p0 1 2 1 To attain sonic/supersonic flow: 1 M (6) p 2 1 p 1 1 0 1.75 1.89 (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) m vA constant (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 RT0 p 0 (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 F 1.2MN and v 3500m / s 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). m 342.86kg / s Choking is a compressible flow 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 RTu c p0 A t 2 2 1 m t v t A t Given: 1 RT0 J M 10 ; Ru 287 ; Tc 3000K ; p0 A t kg K m (19) RT 0 1.2 ; Pc 12MPa and putting these values 1 in (23) we get: 2 2 1 2 where At 0.0129m 1 Now by using equation (11) we can get the The area ratio is: value of Ae for 74 : Ae (20) A 0.95m2 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 Ae r e (24) obtaining: re 0,55m developing the wire frame which resembles Convergence area in Nozzle is: the cross-section of the rocket nozzle (figure A 3 A (25) 2). A tri-dimensional geometry of the nozzle c t was created by using the value of A 0.0387m2 c A;r;A;r;Le e t t dn ;A;r;L c c cn ;L;t c wall . Radius of throat: A r t (26) t rt 0.064m Combustion radius: A r c (27) c rc 0.111m 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 Ldn 2.04m 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 Lcn 0.081m start the problem. The mesh created in Length of the combustion chamber: GAMBIT is as shown below figure.3. AL * 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.
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