1. COMPUTATIONAL FLUID DYNAMICS• The physical aspects of any fluid flow are governed by three fundamental principles:• A) Mass is conserved;• B) Newton's second law (force = mass x acceleration); and• C) energy is conserved.

• Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that

• uses numerical methods and algorithms to solve and analyze problems that involve fluid flows.

• Computers are used to perform the calculations required to simulate the interaction of liquids and

• gases with surfaces defined by boundary conditions.

2. Governing Equations

• All of CFD, in one form or another, is based on the fundamental governing equations of fluid• dynamics—the continuity, momentum, and energy equations• They are the mathematical statements of three fundamental physical

principles upon which all of• fluid dynamics is based:• 1. Mass is conserved.• 2. Newton's second law, F = ma.• 3. Energy is conserved

Finite Control Volume

• Let us imagine a closed• volume drawn within a finite region of the flow. This volume defines a

control volume "V~; a• control surface S is defined as the closed surface which bounds the volume.

The control volume• may be fixed in space with the fluid moving through it, as shown in figure in

next slide.• Alternatively, the control volume may be moving with the fluid such that

the same fluid particles are always inside it, as shown at the right of Fig. 2.2a. In either case, the control volume is a reasonably large, finite region of the flow

Physical Boundary Conditions

FLUID MECHANICS • FLUID- A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

• Properties of fluid- In addition to the properties like mass, velocity, and pressure usually considered in physical problems, the following are the basic properties of a fluid- • 1.DENSITY • 2.SPECIFIC WEIGHT • 3.RELATIVE DENSITY • 4.VISCOSITY • 5.REYNOLDS NUMBER

• Types of Fluids- • Fluids can be classified into four basic types. They are: • 1. Ideal Fluid • 2. Real Fluid • 3. Newtonian Fluid • 4. Non-Newtonian Fluid

FLUID DYNAMICS

• In physics, fluid dynamics is a sub discipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. It has several sub disciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion).

Equations of fluid dynamics

• Conservation laws- Three conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form. Mathematical formulations of these conservation laws may be interpreted by considering the concept of a control volume.A control volume is a specified volume in space through which air can flow in and out. Integral formulations of the conservation laws consider the change in mass, momentum, or energy within the control volume

Conservation of momentum

• In the integral formulation of this equation, body forces here are represented by fbody, the body force per unit mass. Surface forces, such as viscous forces, are represented by F(surf) , the net force due to stresses on the control volume surface.

• The differential form of the momentum conservation equation is as follows. Here, both surface and body forces are accounted for in one total force, F. For example, F may be expanded into an expression for the frictional and gravitational forces acting on an internal flow

• Conservation of energy: Although energy can be converted from one form to another, the total energy in a given closed system remains constant.

Types of Flow

• Compressible & incompressible• Viscous vs inviscid flow- • Steady vs unsteady flow • Laminar vs turbulent flow

The Internal Combustion Engine

• The term internal combustion engine usually refers to an engine in which combustion is intermittent, such as the more familiar four-stroke and two-stroke piston engines, along with variants, such as the six-stroke piston engine. A second class of internal combustion engines use continuous combustion: gas turbines, jet engine sand most rocket engines, each of which are internal combustion engines on the same principle.

DIESEL ENGINE

• The internal combustion engine (ICE) is an engine in which the combustion of a fuel (normally a fossil fuel) occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combustion engine the expansion of the high temperature and high-pressure gases produced by combustion apply direct force to some component of the engine. The force is applied typically to pistons, turbine blades, or a nozzle. • This force moves the component over a distance, transforming

chemical energy into useful mechanical energy.

• The image on the left shows a p-V diagram for the ideal Diesel cycle; where ispressure and is specific volume. The ideal Diesel cycle follows the following four distinct processes (The color references refer to the color of the line on the diagram.): • Process 1 to 2 is isentropic compression of the fluid

(blue) • Process 2 to 3 is reversible constant pressure

heating (red) Process 3 to 4 is isentropic expansion (yellow) • Process 4 to 1 is reversible constant volume cooling

(green)

Maximum thermal efficiency

• Factors Affecting Efficiency of Diesel Engine • Inefficient combustion • Friction of moving parts • Heat loss from the combustion chamber • Departure of the working fluid from the thermodynamic properties of an ideal

gas • Aerodynamic drag of air moving through the engine • Energy used by auxiliary equipment like oil and water pumps • Inefficient compressors and turbines • Imperfect valve timing

Real diesel engine cyclic processes

Inlet and Exhaust System

• Four-stroke engines The four-stroke engine of Figure 1.17 is assumed to be of the naturally aspirated type, with the inlet and exhaust manifold pressures approximately constant and equal to atmospheric pressure.