Fundamentals of Heat Engines. Jamil Ghojel

id="ulink_0f551e74-3c5f-5f96-ac32-9b1be410f62e">For the last 200 years or so, humans have been living in the epoch of power in which the heat engine has been the dominant device for converting heat to work and power. The development of the heat engine was for most of that time slow and chaotic and carried out mainly by poorly qualified practitioners who had no knowledge of basic theories of energy and energy conversion to mechanical work. In the field of engineering mechanics, drawings of early steam engines depict various, at times strange, inefficient mechanisms to convert steam power to mechanical power, such as the walking beam and sun and planet gear systems. The piston‐crank mechanism was first used in a steam engine in 1802 by Oliver Evans (Sandfort 1964) despite a design being proposed as early as 1589 for converting the rotary motion of an animal‐driven machine to reciprocating motion in a pump. The first internal combustion engine (ICE) to be made available commercially was Lenoir's gas engine in 1860. This engine was also the first to employ a piston‐crank mechanism to convert reciprocating motion of the piston to rotary motion, which has become, despite its shortcomings, a fixed feature and highly efficient mechanism in modern reciprocating engines. However, engine designers were never fully satisfied with this mechanism due to the need to balance numerous parasitic forces generated during operation and were constantly looking for alternative ways of obtaining direct rotary motion. This is said to have been one of the stimuli to develop steam and gas turbines in which a fluid, flowing through blades, causes the shaft to rotate, thus eliminating the need for a crankshaft. The results are smoother operation, lower levels of vibration, and low‐cost support structures. All of these developments occurred over a very long period of time with advances in the science of engineering mechanics (more specifically, engineering dynamics), together with other engineering science branches such as fluid mechanics and thermodynamics.

      Examples of the principles of fluid mechanics of relevance to the topics of Parts I and II in the book include the momentum equation used to calculate thrust in aircraft gas turbine engines, Bernoulli's equation to calculate flow in the induction manifold of piston engines, and dimensional analysis to determine the characteristics of turbomachinery for gas turbines.

The great scientific breakthroughs in the development of heat‐engine theory came with the development of the science of thermodynamics, starting with the pioneering work of Nicolas Sadi Carnot (1796–1832) and followed by the monumental contributions of Rudolf Clausius (1822–1888) and William Thomson (Lord Kelvin, 1824–1907). Ever since, knowledge of thermodynamics has become essential to improving existing heat engine designs and developing new types of engine processes for superior economy and reduced emissions. At the same time, the heat engine, particularly the reciprocating ICE, has become an ideal tool for teaching mechanical and automotive engineering, as it features, in addition to thermodynamics, fundamental principles of engineering mechanics and fluid mechanics as discussed earlier.

A chapter on thermochemistry (Chapter 2) is included in Part I, dealing with fuel properties and the chemistry of combustion reactions and the effect of control of the combustion temperature through control of air‐fuel ratios in order to preserve the mechanical integrity of engine components. Extensive numerical data on gas properties and adiabatic flame temperature calculations are included, which can be used for preliminary design‐point calculations of practical piston and gas turbine engine cycles.

1 Review of Basic Principles

      1.1 Engineering Mechanics

Mechanics deals with the response of bodies to the action of forces in general, and dynamics is a branch of mechanics that studies bodies in motion. The principles of dynamics can be used, for example, to solve practical problems in aerospace, mechanical, and automotive engineering. These principles are basic to the analysis and design of land, sea, and air transportation vehicles and machinery of all types (pumps, compressors, and reciprocating and gas‐turbine internal combustion engines). A review of some principles relevant to heat engines is presented here.

      1.1.1 Definitions

      Particle. A conceptual body of matter that has mass but negligible size and shape. Any finite physical body (car, plane, rocket, ship, etc.) can be regarded as a particle and its motion modelled by the motion of its centre of mass, provided the body is not rotating. The motion of a particle can be fully described by its location at any instant in time.

      Rigid body. An assembly of a large number of particles that remain at a constant distance from each other at all times irrespective of the loads applied. To fully describe the motion of a rigid body, knowledge of both the location and orientation of the body at any instant is required. Gas turbine shafts are rigid bodies that are rotating at high speeds. The reciprocating piston‐crank mechanism in piston engines is a complex system comprising rotating crank shaft and sliding piston connected through a rigid rod describing complex irregular motion.

      Kinematics. Study of motion without reference to the forces causing the motion and allowing the determination of displacement, velocity, and acceleration of the body.

      Kinetics. Study of the relationship between motion and the forces causing the motion, based on Newton's three laws of motion.

      1.1.2 Newton's Laws of Motion

      According to the first law, the momentum of a body keeps it moving in a straight line at a constant speed unless a force is applied to change its direction or speed.

The second law defines the force that can change the momentum of the body as a vector quantity whose magnitude is the product of mass and acceleration:

      (1.1)

      Another form of this law that is particularly pertinent to gas turbine practice states that force is equal to the rate of change of momentum or mass flow rate

multiplied by velocity change dv (the letter v will be used for velocity exclusively in the mechanics section of this chapter):

      (1.2)

      For an aircraft engine, the air flow into the engine diffuser is equal to the forward flight speed v₁, and engine exhaust gases accelerate to velocity v₂ in the engine nozzle. For a mass flow rate

of the gases, the thrust is therefore

.

      In heat engines, it is often necessary to use vector algebra to resolve the acting forces to determine the forces of interest that can produce work. For example, the pressure force of the combusting gases in the piston engine, which is the source of cycle work, does not act directly on the crank, as a result of which parasitic forces are generated, causing undesirable phenomena such as piston slap. Resolving the forces at the piston pin determines the force transmitted through the connecting rod to the crank, generating a torque. In a gas turbine, the gas force generated during flow through the blades has a component acting parallel to the turbine axis that causes bearings overload and needs to be balanced to prevent axial displacement of the rotor.

      The third law simply states that ‘for every force there is an equal and opposite reaction force’. In an aircraft jet engine, the change in momentum of a large flow rate of gases between the inlet and outlet of the engine generates a backward force known as thrust, which has an equal reaction that propels the aircraft forward.

      1.1.3 Rectilinear Work and Energy

      A force F does work on a particle when the particle undergoes displacement in the direction of the force: