###### Simplifications and Stages of Numerical Methods

#### Engine Combustion

Combustion is a complex phenomena involving fluid flow, all three modes of heat transfer, structural severity, lubrication, emissions and very short duration phenomena. Typically, such simulations are performed in specialized programs such as KIVA. However, to gain deeper insight into the physics, CFD tools have now been widely and successfully exploited in a staged manner.

###### Oil Filter - Flow through Porous Domain

The performance of oil filter (pressure drop and flow uniformity across filter) can be optimized using numerical fluid dynamic calculations. The filter can be used as porous domain whose porosity can be varied as the particulate matters get trapped during actual use.

###### Component Level Appliations

There always exist a scope of improvement in the performance of individual components. The power of numerical simulations can be exploited without costly prototypes. For example, the location on inlet and outlets of a radiator is constrained by performance requirement as well as layout inside the engine compartments. The flow distribution inside the radiator tubes can be improved for different location of the inlet and outlet as well as shape and size of headers.

###### Fundamentals: Working Principle and Design Ratios

The conversion of rotating motion to translating motion using a slider-crank mechanism is explained in the following figure. The locus of some of the points which is translating as well as rotating is also shown.

- Length of the stroke = diameter of the crank pin = D
_{CP}. Piston travel per revolution = 2 * D_{CP}. Distance traveled by crank pin per revolution = π * D_{CP}. Hence, the ratio of average piston velocity to that of crankshaft pin = 2 * D_{CP} / π * D_{CP} = 2/π.

###### Slider Crank Mechanism Animation

The video can be accessed here: Slider Crank at YouTube. The Octave script used to create this animation is as follows:
clc; clear;
% Define constants - use consistent units: mm, rad, s
N = 5; % [rpm] - crankshaft rotation speed
R = 0.075; % [m] - Crank Radius
L = 0.200; % [m] - connecting rod length
w = 2*pi*N/60; % [rad/s] - angular speed
tau = 2*pi/w; % Time for one complete rotation of crankshaft
dq = pi/30;
Lp = 0.010; % Piston Length
Db = 0.020; % Bore diameter = piston diameter
%------------------------------------------------------------------------------
% Define parameters, calculate functions and plot
%
x(1) = 0.0;
y(1) = 0.0;
xMax = L + 2*R + Lp; xMin = -2*R; yMin = -2*R; yMax = 2*R;
figure; axis([xMin xMax yMin yMax]); hold on; daspect([1 1 1]);
plot(x(1), y(1), 'o');
for q = [0: dq : 2*pi]
x(2) = R * cos(q);
y(2) = R * sin(q);
% Location of piston centre with crank angle q.
x(3) = R * cos(q) + sqrt(L^2 - R^2 * sin(q) * sin(q));
y(3) = 0;
x(4) = x(3) - Lp/2.0; y(4) = 0.0;
x(5) = x(4); y(5) = -Db/2.0;
x(6) = x(3) + Lp; y(6) = y(5);
x(7) = x(6); y(7) = y(6) + Db;
x(8) = x(4); y(8) = y(7);
x(9) = x(4); y(9) = 0;
%
% Time derivative of x - excluding q_dot term
n = L/R;
xp = -R * sin(q) - R * sin(2 * q) / sqrt(n^2 - sin(q) * sin(q) );
%
% Piston velocity
V = xp * w;
plot(x(2), y(2), 'o'); plot(x(3), y(3), 'o');
plot(x, y, "linestyle", "-", "linewidth", 2, "color", 'k');
xlabel('x'); ylabel('y');
%grid on; % should be placed only after the plot command
xtick = get (gca, "xtick");
xticklabel = strsplit (sprintf ("%.2f\n", xtick), "\n", true);
set (gca, "xticklabel", xticklabel)
ytick = get (gca, "ytick");
yticklabel = strsplit (sprintf ("%.2f\n", ytick), "\n", true);
set (gca, "yticklabel", yticklabel);
pause (0.0001); cla; plot(x(1), y(1), 'o');
axis([xMin xMax yMin yMax]); daspect([1 1 1]);
end
plot(x, y, "linestyle", "-", "linewidth", 2, "color", 'k');
plot(x(2), y(2), 'o'); plot(x(3), y(3), 'o');

Combustion is on the most complex thermo-chemical phenomena known to us. This is much more than fluid mechanics and heat transfer and hence a typical method of CFD simulations does not fulfill the requirements. The complexity of combustion is described by following slides.

#### Types of Combustion

#### Non-Premixed Combustion

#### Premixed Combustion

#### Partially Premixed Combustion

#### Combustion Phenomena in Engines

#### Combustion: CI vs. SI Engines