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The net heat release rate, denoting the rate at which work was done on the piston plus the rate of sensible internal energy change of the cylinder contents, was calculated according to the first law of thermodynamics, the law of conservation of energy. The net heat release rate (Qn) was considered as the difference between the chemical energy released to the engine cylinder contents by combustion (Qch) and the heat transfer (energy dissipation) from the engine cylinder contents (Qht), as shown in equation (E5). The in-cylinder contents were assumed to be at uniform pressure and temperature and were modelled as an ideal gas. These assumptions allowed the net heat release rate to be calculated as a function of the in-cylinder pressure (p), engine cylinder volume (V) and crank angle (𝜃), according to the equation (E5). Time was defined in equation (E5) as crank angle degrees (𝜃) of the engine cycle (from 0 to 720 CAD) and engine cylinder volume (V) at any given crank angle was calculated according to the equation (E6). Values of the ratio of the specific heat (𝛾) suggested by Heywood [1] were applied: 1.35 during the compression stroke and 1.28 during the expansion stroke. In the equation (E6) 𝑉_{𝑐𝑙𝑒𝑎𝑟} is the clearance volume, 𝐴_{𝑏𝑜𝑟𝑒} is the surface area of the bore, 𝑙_{𝑐𝑜𝑛𝑟𝑜𝑑} is the length of the connecting rod, 𝑟_{𝑐𝑟𝑎𝑛𝑘} is the radius of the crank shaft rotation and the distance between the crank axis and the piston crank pin axis (𝑙_{𝑐𝑎,𝑝𝑝𝑎}) was calculate according to equation (E7) [1].

𝑑𝑄𝑛

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𝑉(𝜃) = 𝑉_{𝑐𝑙𝑒𝑎𝑟}+ [𝐴_{𝑏𝑜𝑟𝑒}(𝑙_{𝑐𝑜𝑛𝑟𝑜𝑑}+ 𝑟_{𝑐𝑟𝑎𝑛𝑘} − 𝑙_{𝑐𝑎,𝑝𝑝𝑎})] (E 6)

𝑙_{𝑐𝑎,𝑝𝑝𝑎} = acos( 𝜃) + √𝑙_{𝑐𝑜𝑛 𝑟𝑜𝑑}²− 𝑟_{𝑐𝑟𝑎𝑛𝑘}²sin²( 𝜃) (E 7)

3.7.2 Ignition delay

Ignition delay was defined as the time interval, in CAD, between the start of injection (SOI) and the start of combustion (SOC). SOI was considered to occur when the injector actuating signal was sent via EmTroniX to the injector. The heat transfer from the cylinder gases (heat dissipation) during the combustion process is a relatively small fraction (about 10-15%) of the released fuel energy and therefore the SOC was defined as the time of the minimum cumulative heat release rate value, as shown in Figure 14. The heat losses become significant after combustion has been completed and the piston travelled down the engine cylinder, causing a reduction in the cumulative heat release rate within the engine cylinder. Hence, the end of combustion (EOC) was considered to be the time of the maximum cumulative heat release rate value (Figure 14).

Figure 14. A typical cumulative heat release rate diagram for diesel fuel combustion.

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3.7.3 Combustion phasing

The combustion split into the premixing-controlled and the diffusion-controlled combustion phases was carried out by a graphical method based on the HRR curve.

Premixed fuel-air burns rapidly at the beginning of combustion, while the diffusion controlled phase that follows occurs over a longer period of time with lower heat release rate. Therefore, the time at which the premixing controlled phase ended was defined as the highest maximum value of the second derivative of HRR (ddHRR), an example of which is shown in Figure 15. The percentage of fuel burned during the premixing controlled phase, usually denoted as the premixed burnt fraction or the premixed phase, was calculated as the ratio of the cumulative HRR that occurred between SOC and the end of the premixed phase to the measured chemical fuel energy injected during the engine cycle.

Figure 15. A typical heat release rate diagram with the first (dHRR) and second (ddHRR) derivatives (the vertical line indicates the switch-over point between the combustion phases).

3.7.4 Maximum average in-cylinder temperature

The maximum average in-cylinder temperature, also known as global gas temperature, was calculated from the instantaneous in-cylinder temperature (𝑇_𝑐𝑦𝑙), which in turn was calculated for any given time using the ideal gas law as shown in equation (E 8). In the equation (E8) 𝑝_𝑐𝑦𝑙 is the cylinder pressure, 𝑉_𝑐𝑦𝑙 is the cylinder

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volume, 𝑛_𝑎𝑖𝑟 is the amount of air in the combustion chamber and R is the gas constant. Combustion conditions were assumed to be lean and the number of air moles present in the engine cylinder were estimated by the air flow rate measurement (see subsection 3.4). The recorded values of in-cylinder temperature for hundred consecutive engine cycles were averaged for the calculation of the maximum average in-cylinder temperature value.

𝑇_𝑐𝑦𝑙 = ^{𝑝𝑐𝑦𝑙∗ 𝑉𝑐𝑦𝑙}

𝑛_𝑎𝑖𝑟∗𝑅 (E 8)

3.7.5 Adiabatic flame temperature

The adiabatic flame temperature at constant pressure was calculated from the iteration of the equivalence of the absolute enthalpy of the reactants (𝐻_{𝑟𝑒𝑎𝑐𝑡}) at the initial in-cylinder temperature (𝑇_𝑖) and that of the products (𝐻_{𝑝𝑟𝑜𝑑}) at the adiabatic flame temperature (𝑇_𝑎𝑑), as shown in equation (E9)

𝐻_{𝑟𝑒𝑎𝑐𝑡}(𝑇_𝑖, 𝑝) = 𝐻_{𝑝𝑟𝑜𝑑}(𝑇_𝑎𝑑, 𝑝) (E 9)

The iteration was conducted as presented by Turns [162]. The initial temperature was defined as the minimum average in-cylinder temperature during the ignition delay period and the change in the enthalpy during complete combustion was calculated according to the Joback method [228].

3.7.6 Indicated mean effective pressure

IMEP was calculated as the ratio of the indicated work output per engine cycle (𝑊_𝑖) and the swept volume (𝑉_{𝑠𝑤𝑒𝑝𝑡}) according to the equation (E 10) [1]. The indicated work output per cycle (𝑊_𝑖) was calculated as the integral of in-cylinder pressure (p) with respect to the cylinder volume (V), whereas the swept volume (𝑉_{𝑠𝑤𝑒𝑝𝑡}) was

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The repeatability of the combustion experiments and the exhaust gas composition analysis were estimated from repeated experiments with the reference diesel fuel.

Reference diesel properties are presented in Appendix I. The repeated tests with reference diesel fuel on different days and at the same engine running conditions, allowed evaluation of average values, standard deviation and the standard error of the mean of the exhaust gas emission measurements. A similar approach was used for the valuation of the repeatability of the engine thermal efficiency measurements.

These repeatability values are quoted in the various chapters of the thesis, where appropriate. To minimize repeatability errors, each test series was conducted within as short a time period of time as possible. That is, for example, tests of a homologous set of fuels were conducted on consecutive days and in as small a number of days as possible. In the limited number of days, when some data appeared to be outlying on result plots, the tests for an outlying data point were repeated to confirm or otherwise of the outlying point was there due to an experimental malfunction. Only in a very limited number of a handful of cases, an outlying point was found to be due to a malfunction of equipment or an operation error.

3.9 Constant injection timing test conditions

All combustion experiments of this PhD project were conducted with constant injection timing. Initial tests with some of the oxygenated fuel molecules, which were assumed to be difficult to ignite, showed that an injection timing of 7.5 CAD before TDC allowed long enough air-fuel mixing time for these difficult-to-ignite molecules to ignite. Therefore, an injection timing of 7.5 CAD BTDC was used throughout the