**UFBA**

# Propulsion

(Parte **1** de 13)

1 Introduction

1.1 Propulsion

The Random House College Dictionary defines propulsion as "the act of propelling, the state of being propelled, a propelling force or impulse" and defines the verb propel as "to drive, or cause to move, forward or onward. ''1 From these definitions, we can conclude that the study of propulsion includes the study of the propelling force, the motion caused, and the bodies involved. Propulsion involves an object to be propelled plus one or more additional bodies, called propellant.

The study of propulsion is concerned with vehicles such as automobiles, trains, ships, aircraft, and spacecraft. The focus of this textbook is on the propul- sion of aircraft and spacecraft. Methods devised to produce a thrust force for the propulsion of a vehicle in flight are based on the principle of jet propulsion (the momentum change of a fluid by the propulsion system). The fluid may be the gas used by the engine itself (e.g., turbojet), it may be a fluid available in the sur- rounding environment (e.g., air used by a propeller), or it may be stored in the vehicle and carried by it during the flight (e.g., rocket).

Jet propulsion systems can be subdivided into two broad categories: airbreathing and non-airbreathing. Airbreathing propulsion systems include the reciprocating, turbojet, turbofan, ramjet, turboprop, and turboshaft engines. Non-airbreathing engines include rocket motors, nuclear propulsion systems, and electric propulsion systems. We focus on gas turbine propulsion systems (turbojet, turbofan, turboprop, and turboshaft engines) in this textbook. The material in this textbook is divided into three parts:

1) Basic concepts and one-dimensional gas dynamics, 2) Analysis and performance of airbreathing propulsion systems, and 3) Analysis of gas turbine engine components.

This chapter introduces the types of airbreathing and rocket propulsion systems and the basic propulsion performance parameters. Also included is an introduction to aircraft and rocket performance. The material on aircraft perform- ance shows the influence of the gas turbine engine on the performance of the air- craft system. This material also permits incorporation of a gas turbine engine design problem such as new engines for an existing aircraft.

Numerous examples are included throughout this book to help students see the application of a concept after it is introduced. For some students, the material on basic concepts and gas dynamics will be a review of material covered in other

2 ELEMENTS OF PROPULSION courses they have already taken. For other students, this may be their first exposure to this material, and it may require more effort to understand.

1.2 Units and Dimensions

Since the engineering world uses both the metric SI and English unit system, both will be used in this textbook. One singular distinction exists between the English system and SI--the unit of force is defined in the former but derived in the latter. Newton's second law of motion relates force to mass, length, and time. It states that the sum of the forces is proportional to the rate of change of the momentum (M = mV). The constant of proportionality is 1/gc:

~-~F-- 1 d(mV)_ 1 dM (1.1) gc dt gc dt

The units for each term in the preceding equation are listed in Table 1.1 for both SI and English units. In any unit system, only four of the five items in the table can be specified, and the latter is derived from Eq. (1.1).

As a result of selecting gc = 1 and defining the units of mass, length, and time in SI units, the unit of force is derived from Eq. (1.1) as kilogram-meters per square second (kg. m/s2), which is called the newton (N). In English units, the value of g~ is derived from Eq. (1.1) as gc = 32.174 ft. lbm/(lbf- s 2)

Rather than adopt the convention used in many recent textbooks of developing material or use with only SI metric units (gc = 1), we will maintain g~ in all our equations. Thus g¢ will also show up in the equations for potential energy (PE) and kinetic energy (KE):

PE -- mgz gc mV 2 KE= 2go

The total energy per unit mass e is the sum of the specific internal energy u, specific kinetic energy ke, and specific potential energy pe:

V 2 gz e =-- u +ke + pe = u +x--- +-- zgc gc

There are a multitude of engineering units for the quantities of interest in propulsion. For example, energy can be expressed in the SI unit of joule

Table 1.1 Units and dimensions

Unit system Force gc Mass Length Time

SI Derived 1 Kilogram, kg Meter, m Second, s English Pound-force, lbf Derived Pound-mass, Ibm Foot, ft Second, s

INTRODUCTION 3

(1 J = 1 N. m), in British thermal units (Btu), or in foot-pound force (ft-lbf). One must be able to use the available data in the units provided and convert the units when required. Table 1.2 is a unit conversion table provided to help you in your endeavors.

Table 1.2 Unit conversion table

Unit Conversion

Length 1 m = 3.2808 ft = 39.37 in. 1 km = 0.621 mile 1 mile = 5280 ft = 1.609 krn

1 nm -= 6080 ft ----- 1.853 km

Area 1 m 2 = 10.764 ft 2 1 cm 2 = 0.155 in. 2

Volume 1 gal = 0.13368 ft 3 = 3.785 liter 1 liter = 10 -3 m 3 = 61.02 in. 3

Time 1 h = 3600 s = 60 min Mass 1 kg = 1000 g = 2.2046 Ibm = 6.8521 x 10 -2 slug 1 slug = 1 lbf. s2/ft = 32.174 Ibm

Density 1 slug/ft 3 = 512.38 kg/m 3 Force 1 N = 1 kg. m/s 2

1 lbf = 4.448 N Energy 1 J = 1 N. m = lkg. m2/s 2

1 Btu = 778.16 ft. lbf = 252 cal = 1055 J 1 cal = 4.186 J 1 kJ = 0.947813 Btu = 0.23884 kcal Power 1 W = 1 J/s -- I kg. |n2/S 3

1 hp = 550 ft- lbf/s = 2545 Btu/h = 745.7 W 1 kW = 3412 Btu/h = 1.341 hp

Pressure (stress) 1 atm = 14.696 lb/in. 2 or psi = 760 torr = 101,325 Pa 1 atm = 30.0 inHg = 407.2 inH20 1 ksi = 1000 psi 1 mmHg = 0.01934 psi = 1 ton" 1 Pa = 1 N/m 2

1 inHg ----- 3376.8 Pa

Energy per unit mass 1 kJ/kg = 0.4299 Btu/lbm Specific heat 1 kJ/(kg. °C) = 0.23884 Btu/(lbm. °F) Temperature 1 K = 1.8°R K = 273.15 + °C °R = 459.69 + °F

Temperature change 1 °C = 1.8°F Specific thrust 1 lbf/(lbm/s) = 9.8067 N/(kg/s) Specific power 1 hp/(lbm/s) = 1.644 kW/(kg/s) Thrust specific fuel 1 lbm/(lbf- h) = 28.325 mg/(N, s) consumption (TSFC)

Power specific fuel 1 lbm/(hp-h) ---- 168.97 mg/(kW, s) consumption Strength/weight ratio (o/p) 1 ksi/(slug/ft 3) = 144 ft2/s 2 = 13.38 m2/s 2

4 ELEMENTS OF PROPULSION

1.3 Operational Envelopes and Standard Atmosphere

Each engine type will operate only within a certain range of altitudes and

Mach numbers (velocities). Similar limitations in velocity and altitude exist for airframes. It is necessary, therefore, to match airframe and propulsion system capabilities. Figure 1.1 shows the approximate velocity and altitude limits, or corridor of flight, within which airlift vehicles can operate. The corridor is bounded by a lift limit, a temperature limit, and an aerodynamic force limit. The lift limit is determined by the maximum level-flight altitude at a given velocity. The temperature limit is set by the structural thermal limits of the material used in construction of the aircraft. At any given altitude, the maximum velocity attained is temperature-limited by aerodynamic heating effects. At lower altitudes, velocity is limited by aerodynamic force loads rather than by temperature.

The operating regions of all aircraft lie within the flight corridor. The operat- ing region of a particular aircraft within the corridor is determined by aircraft design, but it is a very small portion of the overall corridor. Superimposed on the flight corridor in Fig. 1.1 are the operational envelopes of various powered aircraft. The operational limits of each propulsion system are determined by limitations of the components of the propulsion system and are shown in Fig. 1.2.

The analyses presented in this text use the properties of the atmosphere to deter- mine both engine and airframe performance. Since these properties vary with location, season, time of day, etc., we will use the U.S. standard atmosphere 2 to give a known foundation for our analyses. Appendix A gives the properties of the U.S. standard atmosphere, 1976, in both English and SI units. Values of the pressure P, temperature T, density p, and speed of sound a are given in dimen- sionless ratios of the property at altitude to its value at sea level (SL), the reference value. The dimensionless ratios of pressure, temperature, and density f Helicopter

Lift (stall) limit /" \ ~a~,m~L / ~5 \ ' r°c e 7 "~Upperlimit ~1 / .~

/<, turbofan //

/ \~ \, / Temperature

I Upper-limi~ # limit turboprop I I

(Parte **1** de 13)