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1、.专业整理.CFD simulation in Laval nozzleSIAE 090441313AbstractWe aim to simulate the quasi one dimension flow in the Laval nozzle based on CFD computation in this paper .We consider the change of the temperature ,the pressure ,the density and the speed of the flow to study the flow.The analytic solution
2、 of the flow in the Laval nozzle is provided when the input velocity is supersonic.We use the Mac-Cormack Explicit Difference Scheme to slove the question.Key words :Laval nozzle ,CFD,throat narrow.Contents Abstract .1Introduction .2Simulation of one-dimensional steady flow.3 Basis equations .3Dimen
3、sionless .10Mac -Cormack Explicit Difference Scheme.11Boundary conditions .13Reference .13Annex .14IntroductionLaval nozzle is the most commonly used components of rocket engines and aero-engine, constituted by two tapered tube, one shrink tube, another expansion tube.Laval nozzle is an important pa
4、rt of the thrust chamber. The first half of the nozzle from large to small contraction to a narrow throat to the middle. Narrow throat and then expand outwards from small to big to the end. The gas in the rocket body by the front half of the high pressure into the nozzle, through the narrow throat t
5、o escape by the rear half. This architecture allows the speed of the air flow changes due to changes in the jet cross-sectional area, the airflow from subsonic to the speed of sound, until accelerated to transonic. So, people flared nozzle called transonic nozzle. Since it was invented by the Swedis
6、h Laval, also known as Laval nozzle. Analysis of the principle of the Laval nozzle. The rocket engines of the gas flow in the combustion chamber under pressure, after the backward movement of the nozzle into the nozzle . At this stage, the gas movement follow the principle of the fluid moves in the
7、tube , the small cross-section at the flow rate large sectional large flow velocity, thus accelerating airflow.Laval nozzle When you reach the narrow throat, the flow rate has exceeded the speed of sound. Transonic fluid movement they no longer follow the principle of cross-section at small velocity
8、, at a flow rate of small cross-section large, but on the contrary the larger cross-sectional flow faster. The gas flow speed is further accelerated to 2-3 km / sec,equivalent to 7-8 times the speed of sound, thus creating a great thrust. The Laval nozzle fact played the role of a flow rate Enlargem
9、ent Device. In fact, not just rocket engines, missile nozzle is this horn shape, so the Laval nozzle weapons has a very wide range of applications.Simulation of one-dimensional steady flow1.Basis equationsAs we know,Laval nozzle is a zooming nozzle flow channel to narrow further expansion.Allows the
10、 airflow to further accelerate to reach the speed of sound at the throat into a supersonic flow.Now,we want to simulate the quasi one-dimension flowing.Firstly,we will analysis on theory.The flow is isentropic,so we can apply the following equations.(1)Continuity equation:In the flow, we need to con
11、sider the following physical quantities.The pression ,the temperature ,the speed of the fluid and the cross-section .They are respectively represented by P,T,u,A. We apply the conservation of the mass.we will obtain this equation.And then we get(2)Equation of momentum(in the direction of the axis)Ac
12、cording to the theory of momentum:The simplification of this equation is (3)Energy equationIdeal gas equation of stateR is ideal gas constant,R=8.314J/g/K.M is the masse per mole.(4)The equation of ThermodynamicsBecause the flow is isentropic,so dS=0And we use the equation of momentum,we haveCombine
13、 with others equations,we result withWe called u the speed of sound,we noted a. We apply the continuity equationWe defined the Mach number If we have the relation as We have the figure So M1,supersonicIf dA0.If dA0,we have du0.M1,subsonicIf dA0.If dA0,we have du0.This is the reason why this architecture allows the speed of the air flow changes due to changes in the jet cross-sectional area, the airflow from subsonic to the speed of sound, until accelerated to transonic.We have the consequence as followsThen we replace P and T in this equation.Th
