Project Report on Analysis of Fluid Flow in Rocket NozzlesBY

A.Venkat (07311A0353) Under the guidance of Mr. V. Vasudeva Rao Principal Sree Nidhi Institute Of Science and Technology

CONTENTS Abstract

Introduction to Fluid Flow Parameters governing the Fluid Flow Brief Introduction to Rocket Nozzles Criterion for 1-D gas flow in Rocket Nozzles Design Of rocket Nozzles based on Nozzle

performance Conclusion References

Abstract The main aim of the project is to analyze the flow

of the fluid(propellants) inside a rocket nozzle. A procedure is outlined for calculating the maximum changes in the exhaust velocity of gases which can be introduced during flow through a rocket nozzle as the result of vibrational time lags.

Introduction to Fluid Flow Fluid flow Fluids (liquids and gases) are a form of

matter that cannot achieve equilibrium under an applied shear stress but deform continuously, or flow, as long as shear stress is applied. The fluid flow means the movement of materials through certain bounded regions (pipe). The study of fluid flow can be divided in to : Fluid Statics : it deals with fluid at rest in equilibrium. Fluid dynamic s: it deals with fluid in motion.

Types of Fluid Flows Steady Flow : In steady flow the velocity of the

fluid particles at any point is constant as time passes. Unsteady Flow : Unsteady flow exists whenever the velocity at a point in the fluid changes as time passes. Turbulent Flow : Turbulent flow is characterized by the irregular movement of particles of the fluid. There is no definite frequency as there is in wave motion. The particles travel in irregular paths with no observable pattern and no definite layers. The flow becomes irregular exceeds a certain velocity any condition that causes abrupt changes in velocity Eddy currents are a characteristic of

Streamline Flow : When the flow is steady,

streamlines are often used to represent the trajectories of the fluid particles. A streamline is a line drawn in the fluid such that a tangent to the streamline at any point is parallel to the fluid velocity at that point. Steady flow is often called streamline flow.

Reynolds Number The flow regime (either laminar or turbulent) is

determined by evaluating the Reynolds number of the flow .The Reynolds number, based on studies of Osborn Reynolds, is a dimensionless number comprised of the physical characteristics of the flow. where: Re = Reynolds number (unit less) V = average velocity (ft/sec) D = diameter of pipe (ft) = absolute viscosity of fluid (lbf-sec/ft2) For practical purposes, if the Reynolds number is less than 2100, the flow is laminar. If it is greater than 4000, the flow is turbulent. Flows with Reynolds numbers between 2100 and 4000 are sometimes referred to as transitional flows. Most fluid systems in nuclear facilities operate with turbulent flow.

Significance of Reynolds Number If the Reynolds number is less than 2100, the

flow is laminar. If it is greater than 4000, the flow is turbulent. Flows with Reynolds numbers between 2100 and 4000 are sometimes referred to as transitional flows. The fluid in the middle of the pipe will be moving faster than the fluid next to the walls. At constant velocity fluid can change from laminar to turbulent if pipe diameters increased. Decrease in viscosity due to temperature change may also show similar effects.

Velocity Distribution The velocity increases from zero at wall to max at

the axis of the tube. For Streamline flow . The graph of velocity Vs Distance from the wall is parabola, sharply pointed at middle. Ave. V = Vmax. For turbulent flow The graph is some what flattened in the middle and Ave. V =0.8 Vmax. Velocity profile for turbulent flow Velocity profile if flow were laminar everywhere

Velocity profile inside a pipe

Bernoullis Theorem Bernoulli's principle states that for an inviscid

flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation.

Simplified form of Bernoullis Equation In many applications of Bernoulli's equation, the

change in the g z term along the streamline is so small compared with the other terms it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the g z term can be omitted. This allows the above equation to be presented in the following simplified form: where p0 is called total pressure, and q is dynamic pressure. Many authors refer to the pressure p as static pressure to distinguish it from total pressure p0 and dynamic pressure q.

The simplified form of Bernoulli's equation can be summarized in the following memorable word equation: static pressure + dynamic pressure = total pressure Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q. Their sum p + q is defined to be the total pressure p0. The significance of Bernoulli's principle can now be summarized as total pressure is constant along a streamline. If the fluid flow is irrotational, the total pressure on every streamline is the same and Bernoulli's principle can be summarized as total pressure is constant everywhere in the fluid flow. It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in flight, and ships moving in open bodies of water. However, it is important to remember that Bernoulli's principle does not apply in the boundary layer or in fluid flow through long pipes.

Compressible flow in fluid dynamics For a compressible fluid, with a barotropic equation of state, and

under the action of conservative forces, (constant along a streamline)where:

p is the pressure is the density , v is the flow speed , is the

potential associated with the conservative force field, often the gravitational potential. In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic. In this case, the above equation becomes (constant along a streamline)where, in addition to the terms listed above: is the ratio of the specific heats of the fluid, g is the acceleration due to gravity ,z is the elevation of the point above a reference plane. In many applications of compressible flow, changes in elevation are negligible compared to the other terms, so the term g and z can be omitted. A very useful form of the equation is then:

where: p0 is the total pressure 0 is the total density

Introduction to Rocket Nozzles A rocket engine nozzle is a propelling

nozzle usually of the de Laval type used in a rocket engine to expand and accelerate the combustion gases, from burning propellants, so that the exhaust gases exit the nozzle at hypersonic velocities.

Figure showing a simple de Laval nozzle

Criterion for 1-D gas flow in rocket nozzles Combustion gas is assumed to be IDEAL GAS. Gas flow is

ISENTROPIC,FRICTIONLESS,ADIABATIC. Gas flow is constant. Gas flow is along a straight line from gas inlet to exhaust gas outlet.(i.e. along the nozzles axis of geometry) Gas flow behavior is compressible since the flow is at very high velocities

Design of Nozzles based on Nozzle performance As the combustion gas enters the rocket nozzle, it is

traveling at subsonic velocities. As the throat contracts down the gas is forced to accelerate until at the nozzle throat, where the cross-sectional area is the smallest, the linear velocity becomes sonic. From the throat the cross-sectional area then increases, the gas expands and the linear velocity becomes progressively more supersonic. The linear velocity of the exiting exhaust gases can be calculated using the following equation

where: Ve= Exhaust velocity at nozzle exit,

m/sT= absolute temperature of inlet gas, K R= Universal gas law constant = 8314.5 J/(kmolK) M= the gas molecular mass, kg/kmol (also known as the molecular weight) k= cp / cv = isentropic expansion factor cp= specific heat of the gas at constant pressure cv= specific heat of the gas at constant volume Pe= absolute pressure of exhaust gas at nozzle exit, Pa P= absolute pressure of inlet gas, Pa

Some typical values of the exhaust gas velocity Ve for

rocket engines burning various propellants are: 1.7 to 2.9 km/s (3800 to 6500 mi/h) for liquid monopropellants 2.9 to 4.5 km/s (6500 to 10100 mi/h) for liquid bipropellants 2.1 to 3.2 km/s (4700 to 7200 mi/h) for solid propellants As a note of interest, Ve is sometimes referred to as the ideal exhaust gas velocity because it based on the assumption that the exhaust gas behaves as an ideal gas.

Specific Impulse Thrust is the force which moves a rocket through

the air, and through space. Thrust is generated by the propulsion system of the rocket through the application of Newton's third law of motion: "For every action there is an equal and opposite reaction". A gas or working fluid is accelerated out the rear of the rocket engine nozzle and the rocket is accelerated in the opposite direction. The thrust of a rocket engine nozzle can be defined as F

and for perfectly expanded nozzles, this reduces to:

F The specific impulse, Isp, is the ratio of the amount of thrust produced to the weight flow of the propellants. It is a measure of the fuel efficiency of a rocket engine.

It is observed exhaust velocity which is the most

prominent factor which governs the design of a nozzle depends on four major factors. 1.Pressure 2.Temperature 3.Friction/Air drag 4.Nozzle geometry

Conclusions I would like to conclude saying that altering

physical parameters like pressure and temperature would enhance the working of a nozzle and thereby also provides a better nozzle efficiency. Better optimization of the physical parameters is a must for the proper working and safety of the nozzle as well as the engine also.