Elements of Propulsion: Gas Turbines and Rockets

From the fabric of my life The color and texture you brought into My being. An interesting feature of the first edition was the very extensive foreword by jet engine pioneer Hans Von Ohain.

Background

The ignition of the engine was very similar to the ignition of a gas heating system in the home. The He-280 had severe limitations regarding the distance of the nacelle from the ground.

Fig. 2 Trends of power per weight (hp/Ib) and overall efficiency (r/o) of aeropropulsion systems from 1900 to 2000

Preface

The analysis of gas turbine engines begins in Chapter 4 with the definitions of installed thrust, uninstalled thrust and installation losses. The results of the engine performance analysis can be used to determine component performance requirements.

Acknowledgments

Nomenclature

1 Introduction

Propulsion
Units and Dimensions
INTRODUCTION 3

Operational Envelopes and Standard Atmosphere

INTRODUCTION 5

Airbreathing Engines

INTRODUCTION 7
INTRODUCTION 9
INTRODUCTION 11 subsonic flight. The thrust specific fuel consumption (TSFC, or fuel mass flow
INTRODUCTION 15

Turbojet/Ramjet Combined-Cycle Engine

INTRODUCTION 17 As derived in Chapter 4, the uninstalled thrust F of a jet engine (single inlet

A photo of the J79 turbojet with afterburner used in the F-4 Phantom II and B-58 Hustler is shown in figure. In the turbofan, part of the turbine work is used to provide power to the fan. Further development of the scramjet for other applications (e.g. the Orient Express) will continue if research and development yields a scramjet engine with sufficient performance improvements.

The lift thrust of the JT9D high bypass ratio turbofan engine is given in Fig.

J J2°kft 30kft

INTRODUCTION 19
INTRODUCTION 21
INTRODUCTION 23 Vo = velocity of aircraft
INTRODUCTION 25
INTRODUCTION 27
INTRODUCTION 29

Aircraft Performance

INTRODUCTION 31
INTRODUCTION 33
INTRODUCTION 35 8OOO
SL 10 20 30 36 40 50 kft

The predicted partial throttle performance of the advanced fighter engine is shown under three flight conditions in Fig. The available thermal energy of the fuel is equal to the fuel mass flow rate rnf times the lower heating value of the fuel hpR. With the help of Eq. 1.11), this equation can be written in terms of the specific consumption of propulsion fuel as

For a given engine thrust F, increasing the thrust/weight ratio reduces engine weight.

Fig. 1.14b Uninstalled fuel consumption S of a n advanced a f t e r b u r n i n g fighter engine at m a x i m u m power setting, a f t e r b u r n e r on

Sea /

INTRODUCTION 37

Take-off and landing are two flight conditions in which the aircraft speed is close to the stall speed. For safety, the take-off speed VTo of an aircraft is typically 20% greater than the stall speed, and the landing speed on landing is VTD. The rate of change of the aircraft weight d W / d t is due to the fuel consumed by the engines.

The mass rate of fuel consumption is equal to the product of the installed thrust T and the installed thrust specific fuel consumption.

INTRODUCTION 41

Calculate the stability factor and range factor at 0.8 Mach and 40 kft altitude of the hypothetical HF-1 fighter at 90% maximum gross takeoff weight and a load factor of 1. Determine the difference in stability factor and range factor for two hypothetical aircraft HF-1 and HP-1. a) Combat aircraft (HF-I). Note that the best endurance Mach number (minimum fuel consumption) increases with altitude, and the best fuel consumption occurs at altitudes of 30 and 36 kph. Note that the best cruising Mach number (minimum fuel consumption) increases with altitude, and the best fuel consumption occurs at an altitude of 36 kft and a Mach number of 0.8.

INTRODUCTION 43

Note that the best endurance Mach number (minimum fuel consumption) increases with altitude, and the best fuel consumption occurs at sea level. Note that the best cruise Mach number (minimum fuel economy) increases with altitude, and the best fuel economy occurs at an altitude of 7 miles (11 km) and a Mach number of about 0.83. Because the weight of an aircraft like the HP-1 can vary considerably during a flight, the variation in range factor with cruise Mach number was determined for 95 and 70% of the maximum gross take-off weight (MGTOW) at an altitude of 11 and 12 km . plotted in Fig.

One can see from this discussion that the proper cruise altitude can dramatically affect an aircraft's range.

Fig. 1.32 Endurance factor for HP-1 aircraft.

INTRODUCTION 45

INTRODUCTION 47

Rocket Engines

The grain, usually formed with a hole in the center, called a perforation, is firmly cemented to the inside of the combustion chamber. Liquid rockets, on the other hand, can be stopped and restarted later, and their thrust can be varied slightly by changing the speed of the fuel and oxidizer pumps. A natural starting point in understanding a rocket's performance is to examine its static thrust.

Application of the momentum equation developed in Chapter 2 will show that the static thrust is a function of the propellant flow rate mp, the exhaust velocity Ve and pressure Pe, the exhaust a r e a Ae, and the ambient pressure Pa.

Figure 1.40 shows the essential features of this type of system. In this system, the fuel and oxidizer are mixed together and cast into a solid mass called the grain

INTRODUCTION 51

If the pressure in the discharge plane Pe is the same as the ambient pressure Pa, the thrust is given by F = rhpVe/gc. An estimate of the variation of thrust with altitude for the spacecraft's main engine is shown in Fig. The mass of a rocket vehicle changes greatly during flight due to the consumption of propellant.

The speed that a rocket vehicle reaches during powered flight can be determined by considering the vehicle in Fig.

INTRODUCTION 53

When the output pressure is equal to the ambient pressure. the pulses of the core and the bypass current are given by . where Vce and Vse are the exit velocities from the core and bypass, respectively, Vo is the intake velocity and rnf is the mass flow rate of the fuel burned in the engine core. Estimate the following for the case of output pressures equal to the ambient pressure (Po = Pe): a) The thrust of the engine. Start by taking the derivative of Eq. 1.46) with respect to CL and finding the expression for the lift coefficient that yields maximal CL/Co. Show that for maximum CL/CD the corresponding drag coefficient CD is given by. a) The maximum CL/CD and the corresponding values of CL and CD (b).

The flight height [use Eq. c) The altitude and drag for an aircraft weight of 35,000 lbf at Mach 0.8. d) The range for an installed engine thrust specific fuel consumption rate of 0.8 (lbm/h)/lbf if the 10,000-1bf difference in aircraft weight between parts b and c is due to fuel consumption only. An airplane weighing 110,000 N with a wing area of 42 m 2 is in level flight (n = 1) at the maximum value of CL/Co. a) The maximum CL/CD and the corresponding values for CL and Co. b).

Fig. 1.42b Rocket thrust variation with altitude.

INTRODUCTION 59

You are to determine the thrust and fuel consumption requirements of the two engines for the hypothetical passenger airplane, HP-1. To provide landing gear of reasonable length, the maximum diameter of the engine inlet is limited to 2.2 m. You are to determine the thrust and fuel consumption requirements of two engines for the hypothetical HF-1 fighter jet.

To ensure optimal integration into the airframe, the maximum area of the engine intake is limited to 5 ft 2.

2 Review of Fundamentals

Introduction

From the solution set we can form a table of v and e against specified values of P and T for all states of the system. From these known values of P, T, v and e we can determine every other property of the simple system. If the properties of the fluid at any point i in the control volume do not vary with time, the flow is said to be a constant flow.

Thus, the total flow through a control volume can have more than one dimension and still be uniform (one-dimensional flow) at permeable portions of the control surface perpendicular to the flow direction.

Fig. 2.1 Control volume for steady flow.

Steady Flow Energy Equation

The first step in applying the steady-state energy equation is a clear definition of the control surface 0-. Solution: A graph of the enthalpy equations of state for the reactants and products is given in Figure 2.5 and represents the states of the reactants entering and the products leaving the combustion chamber, respectively.

We can solve this equation for T4, which is the temperature of the product gases leaving the combustion chamber.

Fig. 2.3 Steady flow through control volume ~r.

Steady Flow Entropy Equation

This is the so-called adiabatic flame temperature of the reactants for an air-fuel mixture ratio of 45 : 1. For the analysis in parts of this book, we have decided to avoid the complex thermochemistry of the combustion process and model it as a simple heating process.

Steady Flow Momentum Equation

The propellant supply pipe is very flexible, and the force it exerts on the rocket is negligible. The force read by the scale is 2700 N, the atmospheric pressure is 82.7 kPa, the flow is uniform. Solution: First determine the force on the rocket arm to give a scale reading of 2700 N.

We note that the unbalanced pressure force on the outside of the rocket motor is PaA2, and the internal forces (pressure and friction) are contained in the force Fc~.

Fig. 2.6 Flow through a convergent duct.

Perfect Gas

Substituting the equations for dh and de into Eq. 2.25) gives the ratio of specific heats for a perfect gas. The ratio between the number of moles of component i and the total number of moles in the mixture is called the mole fraction Xi. For an isentropic process between states 1 and 2, equation 2.55), this pressure ratio can be expressed by the reduced pressure Pr a s.

To estimate the properties of these gases, we can use the previous equations based on the ratio between the mass of burned fuel and the mass of air.

Table 2.1 Properties of ideal gases at 298.15 K (536.67°R)

Compressible Flow Properties

The velocity of the gas at each intermediate state y at the nozzle is represented by the vertical distance on the path line from 1 to the state in question. If the divergent channel is frictionless, then the deceleration process from 1 to y is isentropic to the path line C~r in the T-s diagram of the figure. Thus, the pressure corresponding to state Yr of the T-s diagram is the total pressure of the gas in state 1.

The state point Yr is called the total or stagnation state tl of static point 1.

Fig. 2.13 Total temperature minus ambient temperature vs flight speed and vs flight Mach number at 25,000 ft [gcCp is assumed constant at 6000 ft2/(s2-°R); therefore, these are approximate curves]

One-Dimensional Gas DynamicsmFinite Control Volume Analysis and the H-K Diagram

This expression can be rearranged using Eq. 2.82) in the form of the dimensionless static enthalpy cpT/cpTti and the dimensionless kinetic energy V2 / ( 2gccpTti), or. From the definition of the Mach number, isolines of constant Mach number M are given by the straight line. For a given alp, the flow state must be somewhere on this curved line.

The H - K diagram will be used in this text to improve understanding of the flow through naturally aspirated engines.

Fig. 2.22 Finite control volume for one-dimensional gas dynamics.

Nozzle Design and Nozzle Operating Characteristics

The pressure in the receiver is increased to the nozzle outlet face pressure Pe. The loci of this operating condition are located on the normal-shock-on-output line of the nozzle operating diagram (Fig. 2.38). This operating condition is bounded by the sonic limit and the Pn ---- 1 (no flow) lines of the nozzle operating diagram.

The working point of a nozzle is determined by the nozzle pressure ratio Pn and area ratio e.

Fig. 2.31 Control volume for simple nozzle flow.

One-Dimensional Gas Dynamics--Differential Control Volume Analysis

The data in Table 2.4 allow us to locate the operating points of the Saturn and Atlas engines at a given e in the nozzle operating diagram (Fig. 2.38). 2.40, with the presence of the simultaneous effects of area change, heat interaction, and friction, leads to the following set of equations for the infinitesimal element dx. In these equations, heat interaction effects are measured in terms of the total temperature change according to Eq.

General conclusions can be drawn in relation to the variation of the flow properties of the flow with each of the independent variables by the relationships in Table 2.5.