Fundamentals of Rocket Propulsion

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ADVANCED ROCKET NOZZLE 110

THRUST COEFFICIENT 120

FORCES ACTING ON A VEHICLE 130

THE ROCKET EQUATION 133

SPACE FLIGHT AND ITS ORBIT 140

INTERPLANETARY TRANSFER PATH 147

THERMAL MODEL FOR SOLID-PROPELLANT

INTERNAL BALLISTICS OF SPRE 225

MODELING OF FLOW IN A SIDE BURNING

HEAT TRANSFER ANALYSIS FOR COOLING SYSTEMS 297

BASIC PRINCIPLES OF ELECTRICAL

A bird's eye view of non-chemical rocket engines is provided in this chapter so that students can measure the entire range of rocket propulsion. The basic principles of rocket propulsion, fundamentals of thermodynamics, chemistry and gas dynamics are briefly discussed in this chapter.

P. Mishra

BASIC PRINCIPLE OF PROPULSION

We can recall that the principle of Newton's laws of motion is the basis of the theory of jet propulsion. According to Newton's third law of motion, we know that for every acting force there is an equal and opposite reacting force.

BRIEF HISTORY OF ROCKET ENGINES

Two tubular pipes attached to the boiler head lead the steam to two nozzles. Even von Braun's entire research team moved to the United States and provided leadership in the development of the ambitious American space program.

Figure 1.1 shows a schematic of the aeropile of Hero, which is considered to be the first device in the world to illustrate the reactive thrust principle much before Newton, who established the third law of motion

CLASSIFICATION OF PROPULSIVE DEVICES

In addition, jet engines, which are mostly used for rocket applications, fall under the category of air-breathing engines. Let's compare both air-breathing and non-air-breathing (rocket) engines, as listed in Table 1.1.

TYPES OF ROCKET ENGINES

Of course, the propellant delivery system, along with the propellant mass, contributes significantly to the mass of the engine, but it is significantly less compared to the total mass of an SPRE. In fact, the mass of the nozzle for deep space applications is sometimes comparable to the mass of the propellant and its feed system in the case of an LPRE.

FIGURE 1.5 Three types of chemical rocket engines: (a) solid propellant, (b) liquid propellant, and (c) hybrid propellant.

APPLICATIONS OF ROCKET ENGINES

Based on the energy source, these engines can be broadly divided into three categories: (1) electric rocket engines, (2) nuclear rocket engines, and (3) solar rocket engines. Rocket engines have been used for numerous other civilian applications depending on people's imaginations.

BASIC PRINCIPLES OF CHEMICAL THERMODYNAMICS The term thermodynamics is a combination of two Greek words, namely,

The system can be easily classified into three categories: (1) closed system, (2) open system, and (3) isolated system. But in an open system, both matter and heat energy can flow across the boundary of the system.

THERMODYNAMIC LAWS

The heat added to the system and the work done by the system result in a change in energy in the system. The process can take place either in the direction of increasing entropy or in the direction of constant entropy of the system and its surroundings.

FIGURE 2.1 Schematic of thermodynamic systems: (a) piston cylinder arrange- arrange-ment and (b) rocket engine.

REACTING SYSTEM

Note that the properties of a mixture can be discovered by assuming that it is an ideal gas. We know that the partial pressure of the species in a mixture can be expressed in terms of their respective molar friction as given by.

TABLE 2.1 Heat of Formation of Some Important Species Chemical

BASIC PRINCIPLES OF GAS DYNAMICS

Similarly, the integral form of momentum equation for steady one-dimensional flow in CV can be expressed as. The Mach number downstream of the shock can be easily evaluated using geometry, shown in Figure 2.9, as.

FIGURE 2.3 Control volume for one-dimensional steady flow.

The natural gas from Mahanadi field is used in a combustor that operates with an oxygen concentration of 5% in the flue gas. If the

Hydrogen gas tank at pressure of 100 MPa and temperature 300 K has a hole of 1 mm. Determine the velocity and the mass flow rate of

The combustion products from thrust chamber of rocket engine at 4.5 MPa and 3100 K is expanded through a CD nozzle. If the back

We learned in Chapter 1 that both air-breathing and non-air-breathing (rocket) engines operate on the principle of jet propulsion, but the air-breathing engine differs from the rocket engine in that it carries both fuel and oxidizer. during his flight. Since the processes involved in a rocket engine are quite complex, certain assumptions are made for an ideal engine.

IDEAL ROCKET ENGINE

Uniform conditions in the chamber at the entrance to the nozzle; the properties of the flow, namely pressure, temperature and density remain constant. These simplifying assumptions are very useful in deriving simplified performance parameters that are helpful in characterizing a chemical rocket engine.

THRUST EQUATION OF ROCKET ENGINES

We can also note from equation 3.4 that the thrust of a rocket engine is independent of flight speed, unlike a gas turbine engine. Assuming one-dimensional flow at the nozzle exit and assuming the ideal gas law, we can estimate the discharge velocity from the exit mass flow rate as .

FIGURE 3.2 Variation of thrust of a typical rocket engine with altitude.

ROCKET PERFORMANCE PARAMETERS

It can be noted that specific impulse Isp can be easily estimated from the thrust coefficient CF and mass flow coefficient Cm data. Hence, specific propellant consumption (SPC) for the rocket engine can be defined as the amount of propellant weight consumed per total impulse delivered.

TABLE 3.1 Typical Values of Specific Impulse I sp

A rocket vehicle has the following data

Derive his expression for the rocket engine and compare it with that for an air-breathing engine. Determine the mass ratio, propellant mass fraction, propellant flow rate, thrust-to-weight ratio, and impulse-to-weight ratio of the vehicle.

In a rocket engine with nozzle exit diameter of 105 mm, hot gas at 2.5 MPa is expanded to exit pressure and temperature of 85 kPa and

The hot propellant gas at chamber pressure of 3.5 MPa with a flow rate of 5.5 kg/s is expanded fully through a CD nozzle with throat

The main purpose of the nozzle in a rocket engine is to expand the high-pressure hot gases generated by burning the propellant to a higher jet velocity to produce the required thrust. To have a large value of specific thrust, the kinetic energy of the exhaust must be large enough to produce a higher exhaust velocity.

BASICS OF CD NOZZLE FLOW

The variation in the velocity ratio Ve/Ve,max for three specific conditions is depicted in figure 4.3 with the pressure ratio above the nozzle. The variation in the non-dimensional mass flux through the nozzle is depicted in Figure 4.5.

FIGURE 4.1 Flow through convergent–divergent nozzle.

CD NOZZLE GEOMETRY

Then, with a smooth increase in the cross-sectional area, the divergent section emerges from the throat to create a supersonic flow in the rocket nozzle. It can be seen that the angle down from the throat of the bell nozzle is much greater than 30°.

FIGURE 4.9 Schematic of a conical CD nozzle.

EFFECT OF AMBIENT PRESSURE

Meyer-type expansion downstream of the nozzle exit in the free jet wave as shown in Figure 4.11a. As a result, the nozzle exit pressure remains the same as the design value for isentropic flow.

FIGURE 4.11 Flow pattern downstream of the nozzle exit under (a) underexpan- underexpan-sion and (b) overexpanunderexpan-sion.

ADVANCED ROCKET NOZZLE

In the case of an aerospear nozzle, an aerospear/aerodynamic plug is placed in the center of the nozzle as shown in Figure 4.14b. Therefore, the nozzle with a truncated aerospike, as shown in Figure 4.14b, is designed to overcome this problem.

FIGURE 4.13 Schematic of (a) an extendible nozzle and (b) a dual bell–shaped nozzle.

THRUST-VECTORING NOZZLES

Additionally, jet tabs are used for thrust vectoring due to their low propulsion power and light weight. A typical Vernier rocket system for thrust vectoring is shown in Figure 4.15d in which four small rocket nozzles can be used to provide vectoring of thrust produced by the engine.

FIGURE 4.15 Schematic of (a) a gimballing system, (b) jet vanes and jetavator, (c) a side liquid injection system, (d) a Vernier rocket nozzle, and (e) a flexible nozzle.

LOSSES IN ROCKET NOZZLE

As a result, the nozzle is rotated at an angle from 4° to 7°, making the nozzle flexible. Prolonged combustion in the nozzle can change the flow characteristics, which can change the production of the ideal nozzle.

PERFORMANCE OF EXHAUST NOZZLE

Note that the discharge coefficient CD depends on the flow Reynolds number, which ultimately depends on the Pt2/Pe pressure ratio across the nozzle. In the case of a rocket motor, the mass flow rate through the nozzle is governed by the chamber pressure and the area of ​​the nozzle orifice.

FIGURE 4.16 The expansion processes in a T-s diagram.

THRUST COEFFICIENT

Therefore, the area ratio Ae/At for the nozzle CD must be properly selected to avoid separation of the flow in the nozzle during overexpansion. Note that a design table has been created for the thrust coefficient CF with respect to the pressure ratio Pc/Pa and the area ratio Ae/At, which can be used for the design and development of rocket engines.

FIGURE 4.18 The variation of C T against A e /A t . (From Sutton, G.P. and Biblarz,  O.,  Rocket Propulsion Elements, 7th edn., John Wiley & Sons Inc., New York, 2001.)

Assuming that flow is isentropic, determine (1) the exit Mach number, (2) the maximum exit mass flow rate passing through this nozzle, and (3) the exit area. If the mass flow rate happens to be 4.3 kg/s, determine the exit velocity, exit temperature and thrust coefficient.

A rocket engine has the following data

The data for a rocket engine are as follows

If expansion in the rocket nozzle occurs at an ambient pressure of 533.59 N/m2, calculate the nozzle throat area, thrust, thrust coefficient, characteristic velocity, exhaust exit velocity, and maximum possible exhaust velocity.

Calculate the thrust, effective jet velocity, and specific impulse of a rocket operating at an altitude of 20 km with the following data

A rocket engine burning liquid oxygen and kerosene operates at a mixture ratio of 2.26 and a combustion chamber pressure of 50

A convergent–divergent nozzle has an area ratio of 4 and is designed to expand the hot gases at total pressure and temperature of 5.5 MPa

A convergent–divergent nozzle is designed to expand the hot gases at total pressure and temperature of 4.5 MPa and 2830 K, respectively

But the regime of deep space must be considered for flights to the moon, Mars and other planets. In this book we will limit our discussions to the simplified flight performance of a rocket engine.

FORCES ACTING ON A VEHICLE

But when the vehicle is near the earth, the gravitational pull of the planets and other bodies is extremely small compared to the earth's gravitational force. Note that the duration of the flight in the earth's atmosphere is quite small and will not affect the effect of gravitational acceleration in the estimation of the increase in thrust and speed.

FIGURE 5.1 Variation of C D and C L with Mach number for a typical missile for two angles of attack α = 3° and 10°.

THE ROCKET EQUATION

We know that the mass of the vehicle is reduced when the propellant is ejected through the nozzle of the rocket engine to produce propulsion. Note that if the vehicle is launched vertically, it will not have a gravitational turn.

FIGURE 5.3 Variation of velocity increment with mass ratio MR.

SPACE FLIGHT AND ITS ORBIT

A satellite is placed in a circular orbit at a height of 250 km from the surface of the earth. Note that the orbital velocity of the satellite (Vp) reaches maximum value at perigee while it reaches minimum value at apogee (Va).

FIGURE 5.5 Flight trajectory around a circular orbit.

INTERPLANETARY TRANSFER PATH

Note that the Hohmann transfer circuit is reversible in nature and can be used to bring the spacecraft back from the target planet to the launch planet orbit by firing the rocket motor in the opposite direction [3,4]. Note that the spaceflight along the Hohmann transfer orbit takes about 259 days from Earth back to Earth.

SINGLE-STAGE ROCKET ENGINES

It indicates the load mass that can be carried compared to the thrust and structural mass. The part of the load can be expressed in terms of the velocity increase and Veq and SF:.

FIGURE 5.10 Variation in LF with velocity increment ratio ΔV/V eq for two values of SF.

MULTISTAGE ROCKET ENGINES

If the speed gain AV1 is contributed by the first stage and AV2 is contributed by the second stage, then the total speed gain at the end of the second stage of the operation is equal to AV1 + AV2. Three of the most popular multistaging types are (1) tandem, (2) parallel, and (3) piggyback, which are shown schematically in Figure 5-11.

FIGURE 5.11 Three types of multistaging: (a) tandem, (b) parallel, and (c) piggyback.

Determine the velocity and period of revolution of an artificial satellite orbiting the earth in a circular orbit at an altitude of 200 km

A single-stage rocket engine during its vertical flight can withstand maximum acceleration of 10g. It can produce a thrust of 110 kN with

A single-stage rocket engine with a mass of 12,000 kg and specific impulse of 290 s during its vertical flight consumes 9,500 kg of pro-

Derive the expression for burn time for maximum acceleration and maximum height neglecting drag forces. The following data shall be used to determine (1) structure mass fraction of each stage, (2) payload mass fraction, and (3) total velocity increment.

A three-stage rocket is to be designed to place 750 kg satellite in low earth orbit of 400 km. The booster (first) stage is ignited along with

If the first stage is fired for 45 s, determine the acceleration rate during takeoff, assuming that the propellant mass flow rate is constant.

P. MISHRA 6.1 INTRODUCTION

• CLASSIFICATION OF CHEMICAL PROPELLANTS
• GENERAL CHARACTERISTICS OF PROPELLANTS
• SOLID PROPELLANTS
• LIQUID PROPELLANTS

It can be used as a liquid fuel in the rocket engine, but it is quite toxic and unstable in nature to be used as a coolant. It decomposes easily in the presence of a suitable catalyst and can therefore be used as an excellent monopropellant.

FIGURE 6.1 Classification of chemical propellants.