**Abstract**

Spark-ignition (SI) engine has a high power density, making it suitable for unmanned aerial vehicles. Normally, gasoline fuel with a high octane number (ON) is used for a spark-ignition engine. However, gasoline fuel is easy to be evaporated and has a low flash point which is unsafe for aviation engines. Kerosene with a high flash point is safer than gasoline. In this chapter, the combustion characteristics of kerosene for a spark-ignition aviation piston engine are analyzed. A three-dimensional (3D) model is setup, and the combustion process of the engine fuelled with kerosene is simulated. Later, the knock limit extension by water injection is evaluated experimentally. The results indicate that water injection can suppress the knock of SI engine with kerosene in some extent and the output power can be improved significantly.

**Keywords:** aviation piston engine, spark ignition, kerosene, knock suppression, water injection

#### **1. Introduction**

Four-stroke spark-ignition (SI) piston engines have advantages of good fuel economy, high power to weight density, low noise, low cost, and easy maintenance, making them suitable for helicopters and unmanned aerial vehicles [1]. However, gasoline is volatile and easy to be ignited, which is not safe as aviation fuel. In contrast, kerosene is safer and has been used widely for airplanes. If gasoline can be replaced by kerosene on a four-stroke SI piston engine, the aviation safety will be improved significantly. Therefore, the combustion characteristics of four-stroke SI piston engine using kerosene as fuel need to be investigated.

The physical properties of kerosene are very different from gasoline. Kerosene has a lower volatility and higher viscosity. Accordingly, the spray penetration, spray velocity, and cone angle are different [2]. As a wide distillation fuel, the chemical properties of kerosene also differ from gasoline. Lots of experiments were conducted to investigate the combustion characteristics of kerosene [3, 4]. For example, the ignition delay time of kerosene was measured as a function of temperature, pressure, and equivalence ratio using a shock tube [5] or laser-induced fluorescence (LIF) imaging [6].

The combustion performance of kerosene has been investigated comprehensively for turbojet and scramjet engines [7, 8]. However, the operation conditions of aviation piston engine deviate from those of turbojets and scramjets significantly. Very few investigations focused on the combustion performance of kerosene for internal combustion engines [9–11]. Fernandes et al. studied the performance of a heavy-duty diesel engine fuelled with JP-8. The torque output and fuel consumption were similar with diesel fuel. However, the injection duration was enlarged to compensate the low fuel density, and the ignition delay time was increased because of a low cetane number. In addition, the emissions of nitrogen oxide (NOx) and particle material (PM) were decreased apparently [12]. Tay et al. developed a reaction mechanism composed of 48 species and 152 reactions for kerosene, and the accuracy was validated in an optical engine [13].

Mass:

Momentum:

Energy:

*∂ ∂t*

Species:

*∂ ∂t*

ð Þþ *<sup>ρ</sup><sup>h</sup> <sup>∂</sup> ∂x <sup>j</sup>*

rate *ε* are expressed by

*ρu*~ *<sup>j</sup> ∂ε ∂x <sup>j</sup>*

**93**

*ρu*~ *<sup>j</sup> ∂k ∂x <sup>j</sup>*

¼ *∂ ∂x <sup>j</sup>*

standard wall functions are used.

¼ *∂ ∂x <sup>j</sup>*

*μt σε* þ *μ* � � *∂ε*

� �

ð Þþ *ρui*

*DOI: http://dx.doi.org/10.5772/intechopen.91938*

*∂ ∂xi*

*<sup>ρ</sup><sup>u</sup> jh* � � <sup>¼</sup> *<sup>∂</sup><sup>p</sup>*

ð Þþ *ρYs*

The enthalpy of the mixture can be calculated as

flow in the cylinder. The turbulent eddy viscosity is defined as

*μt σk* þ *μ* � � *∂k*

*∂x <sup>j</sup>*

� �

*∂ ∂t*

equation of state for gaseous mixture.

*ρuiu <sup>j</sup>* � � ¼ � *<sup>∂</sup><sup>p</sup>*

> *∂t* þ *∂ ∂xi*

> > *∂ ∂x <sup>j</sup>*

*∂ρ ∂t* þ *∂ ∂xi*

*Knock Suppression of a Spark-Ignition Aviation Piston Engine Fuelled with Kerosene*

*∂xi* þ *μ ∂ ∂xi*

> *μ Pr ∂h ∂x <sup>j</sup>* þ *μ Pr*

*ρu jYs* � � <sup>¼</sup> *<sup>∂</sup>*

*<sup>ρ</sup>* <sup>¼</sup> *<sup>p</sup><sup>=</sup> RT*<sup>X</sup>

*<sup>h</sup>* <sup>¼</sup> <sup>X</sup> *N*

*s*¼1

*<sup>μ</sup><sup>t</sup>* <sup>¼</sup> *<sup>C</sup>μρk*<sup>2</sup>

*∂x <sup>j</sup>*

The empirical constants for the standard k-ε model are assigned below: C1 = 1.44, C2 = 1.92, C<sup>μ</sup> = 0.09, σ<sup>k</sup> = 1.0, and σε = 1.3. A nonslip boundary condition is assumed regarding all solid surfaces of the computational domain, and the

� *C*<sup>1</sup> *ε <sup>k</sup> <sup>ρ</sup>* <sup>~</sup> *<sup>u</sup>*<sup>00</sup> *<sup>i</sup> u*<sup>00</sup> *j ∂u*~*i ∂x <sup>j</sup>* þ *μt ρ*2 *∂ρ ∂xi*

The transport equations for the turbulent kinetic energy *k* and the dissipation

� *<sup>ρ</sup>* <sup>~</sup> *<sup>u</sup>*<sup>00</sup> *<sup>i</sup> u*<sup>00</sup> *j ∂u*~*i ∂x <sup>j</sup>* � *μt ρ*2 *∂ρ ∂xi*

� �

The above equations can be used in direct numerical simulation of turbulence, but it is difficult for the actual calculation process because the calculation load is extremely large. In this study, *k - ε* model is employed to simulate the turbulent

*∂x <sup>j</sup>*

ð Þ *Ys=Ms* " #

The density of the fluid is calculated by the following equation according to the

*N*

*s*¼1

ð Þ¼ *ρui* 0*:* (1)

*N*

*:* (3)

þ *ρr*\_*s:* (4)

*:* (5)

*Yshs*ð Þ *T :* (6)

*=ε:* (7)

*∂p ∂xi*

� *C*2*ρ*

*∂p ∂xi* � *ρε*, (8)

*<sup>k</sup> :* (9)

*ε*2

*s*¼1 *hs ∂Ys ∂x <sup>j</sup>*

*∂ui ∂x <sup>j</sup>* þ *∂u <sup>j</sup> ∂xi* � 2 3 *δij ∂uk ∂xk* � �*:* (2)

*Pr Sc* � <sup>1</sup> � �X

*μ Sc ∂Ys ∂x <sup>j</sup>* � �

" #

Generally, the octane number (ON) of gasoline is in the range of 70–97, whereas the octane number of kerosene is much lower as only 20–50. Therefore, the knock phenomenon of kerosene is much severe in an SI engine, which will keep the power and economy of the engine in a low level [14]. To control the knock of an SI engine, various methods can be adopted, for example, postponing ignition time, reducing compression ratio, and using antiknock additives. Recently, water injection got wide attentions to control the super knock of gasoline engine [15]. There are basically two methods: port water injection and in-cylinder direct water injection. When port water injection is employed, water is sprayed into the intake manifold. For direct water injection, water is injected directly into the combustion chamber. For port water injection, it is better to install the injector close to the intake valve. The knock suppression was increased for a mass ratio of water over fuel as 0.3 [16]. An experimental study based on a single-cylinder engine indicated that fuel with a lower octane number could be used if port water injection was installed [17]. Kim et al. performed an experiment, and water was sprayed into the cylinder in a pressure of 5 MPa using a gasoline direct injection (GDI) fuel injector. The knock suppression was observed evidently [18]. Wei et al. investigated the influences of water injection quantity on energy efficiency experimentally, and it was found that the energy efficiency maximized with a mass ratio of 0.15 [19].

For the knock suppression of SI aviation piston engine, Anderson et al. had studied the combustion performance of a Rotax 914 engine fuelled with kerosene blends. The octane numbers of the fuel blends were 87 and 70 via blending 100 ON aviation gasoline and JP-8. The brake mean effective pressure reduced evidently when the octane number of the fuel blends diminished. The effect of adjusting the ignition timing was very small for performance improvement [20]. Subsequently, the influences of mass fraction of JP-8 were investigated. The volume ratio of JP-8 changed from 85–27% blending with an 87 ON fuel. To keep a high engine power output, the volume ratio should be decreased accordingly [21]. Later, they used a pre-chamber jet ignition system to increase the flame propagation speed of kerosene, and the fuel octane number was decreased by about 10 [22].

It is critical to find methods that can suppress the knock for an aviation fourstroke SI engine with kerosene. However, very few investigations were performed currently. In this chapter, the knock suppression of an aviation four-stroke SI engine is investigated numerically at first. Then, port water injection is installed, and the experimental results for knock suppression are measured. The improvement of the indicated mean effective pressure (IMEP) is evaluated.

### **2. Mathematical method**

The combustion of SI piston engine is mainly a turbulent flame propagation process. For the flow process in the cylinder, the mass, momentum, energy, and species conservation equations are modeled in the 3D numerical simulation model. *Knock Suppression of a Spark-Ignition Aviation Piston Engine Fuelled with Kerosene DOI: http://dx.doi.org/10.5772/intechopen.91938*

Mass:

aviation piston engine deviate from those of turbojets and scramjets significantly. Very few investigations focused on the combustion performance of kerosene for internal combustion engines [9–11]. Fernandes et al. studied the performance of a heavy-duty diesel engine fuelled with JP-8. The torque output and fuel consumption were similar with diesel fuel. However, the injection duration was enlarged to compensate the low fuel density, and the ignition delay time was increased because of a low cetane number. In addition, the emissions of nitrogen oxide (NOx) and particle material (PM) were decreased apparently [12]. Tay et al. developed a reaction mechanism composed of 48 species and 152 reactions for kerosene, and the

*Numerical and Experimental Studies on Combustion Engines and Vehicles*

Generally, the octane number (ON) of gasoline is in the range of 70–97, whereas the octane number of kerosene is much lower as only 20–50. Therefore, the knock phenomenon of kerosene is much severe in an SI engine, which will keep the power and economy of the engine in a low level [14]. To control the knock of an SI engine, various methods can be adopted, for example, postponing ignition time, reducing compression ratio, and using antiknock additives. Recently, water injection got wide attentions to control the super knock of gasoline engine [15]. There are basically two methods: port water injection and in-cylinder direct water injection. When port water injection is employed, water is sprayed into the intake manifold. For direct water injection, water is injected directly into the combustion chamber. For port water injection, it is better to install the injector close to the intake valve. The knock suppression was increased for a mass ratio of water over fuel as 0.3 [16]. An experimental study based on a single-cylinder engine indicated that fuel with a lower octane number could be used if port water injection was installed [17]. Kim et al. performed an experiment, and water was sprayed into the cylinder in a pressure of 5 MPa using a gasoline direct injection (GDI) fuel injector. The knock suppression was observed evidently [18]. Wei et al. investigated the influences of water injection quantity on energy efficiency experimentally, and it was found that

accuracy was validated in an optical engine [13].

the energy efficiency maximized with a mass ratio of 0.15 [19].

For the knock suppression of SI aviation piston engine, Anderson et al. had studied the combustion performance of a Rotax 914 engine fuelled with kerosene blends. The octane numbers of the fuel blends were 87 and 70 via blending 100 ON aviation gasoline and JP-8. The brake mean effective pressure reduced evidently when the octane number of the fuel blends diminished. The effect of adjusting the ignition timing was very small for performance improvement [20]. Subsequently, the influences of mass fraction of JP-8 were investigated. The volume ratio of JP-8 changed from 85–27% blending with an 87 ON fuel. To keep a high engine power output, the volume ratio should be decreased accordingly [21]. Later, they used a pre-chamber jet ignition system to increase the flame propagation speed of kerosene, and the fuel octane number was decreased by about 10 [22].

It is critical to find methods that can suppress the knock for an aviation fourstroke SI engine with kerosene. However, very few investigations were performed currently. In this chapter, the knock suppression of an aviation four-stroke SI engine is investigated numerically at first. Then, port water injection is installed, and the experimental results for knock suppression are measured. The improve-

The combustion of SI piston engine is mainly a turbulent flame propagation process. For the flow process in the cylinder, the mass, momentum, energy, and species conservation equations are modeled in the 3D numerical simulation model.

ment of the indicated mean effective pressure (IMEP) is evaluated.

**2. Mathematical method**

**92**

$$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial \mathbf{x}\_i} (\rho u\_i) = \mathbf{0}. \tag{1}$$

Momentum:

$$\frac{\partial}{\partial t}(\rho u\_i) + \frac{\partial}{\partial \mathbf{x}\_i} \left(\rho u\_i u\_j\right) = -\frac{\partial p}{\partial \mathbf{x}\_i} + \mu \frac{\partial}{\partial \mathbf{x}\_i} \left(\frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} - \frac{2}{3} \delta\_{\vec{\eta}} \frac{\partial u\_k}{\partial \mathbf{x}\_k}\right). \tag{2}$$

Energy:

$$\frac{\partial}{\partial t}(\rho h) + \frac{\partial}{\partial \mathbf{x}\_j}(\rho u\_j h) = \frac{\partial p}{\partial t} + \frac{\partial}{\partial \mathbf{x}\_i} \left[ \frac{\mu}{Pr} \frac{\partial h}{\partial \mathbf{x}\_j} + \frac{\mu}{Pr} \left( \frac{Pr}{\mathbf{S}c} - \mathbf{1} \right) \sum\_{s=1}^N h\_s \frac{\partial Y\_s}{\partial \mathbf{x}\_j} \right]. \tag{3}$$

Species:

$$\frac{\partial}{\partial t}(\rho Y\_s) + \frac{\partial}{\partial \mathbf{x}\_j} \left(\rho u\_j Y\_s\right) = \frac{\partial}{\partial \mathbf{x}\_j} \left(\frac{\mu}{\text{Sc}} \frac{\partial Y\_s}{\partial \mathbf{x}\_j}\right) + \rho \dot{r}\_s. \tag{4}$$

The density of the fluid is calculated by the following equation according to the equation of state for gaseous mixture.

$$\rho = p / \left[ \text{RT} \sum\_{s=1}^{N} (Y\_s / \mathcal{M}\_s) \right]. \tag{5}$$

The enthalpy of the mixture can be calculated as

$$h = \sum\_{s=1}^{N} Y\_s h\_s(T). \tag{6}$$

The above equations can be used in direct numerical simulation of turbulence, but it is difficult for the actual calculation process because the calculation load is extremely large. In this study, *k - ε* model is employed to simulate the turbulent flow in the cylinder. The turbulent eddy viscosity is defined as

$$
\mu\_t = \mathbb{C}\_{\mu} \overline{\rho} k^2 / \varepsilon. \tag{7}
$$

The transport equations for the turbulent kinetic energy *k* and the dissipation rate *ε* are expressed by

$$
\overline{\rho}\tilde{u}\_{j}\frac{\partial k}{\partial \mathbf{x}\_{j}} = \frac{\partial}{\partial \mathbf{x}\_{j}} \left[ \left( \frac{\mu\_{t}}{\sigma\_{k}} + \mu \right) \frac{\partial k}{\partial \mathbf{x}\_{j}} \right] - \overline{\rho}u\_{i}^{\tilde{\nu}}u\_{j}^{\prime\prime} \frac{\partial \tilde{u}\_{i}}{\partial \mathbf{x}\_{j}} - \frac{\mu\_{t}}{\overline{\rho}^{2}} \frac{\partial \overline{\rho}}{\partial \mathbf{x}\_{i}} \frac{\partial \overline{\overline{p}}}{\partial \mathbf{x}\_{i}} - \overline{\rho}\varepsilon,\tag{8}
$$

$$\overline{\rho}\ddot{u}\_{j}\frac{\partial\varepsilon}{\partial\mathbf{x}\_{j}} = \frac{\partial}{\partial\mathbf{x}\_{j}}\left[\left(\frac{\mu\_{t}}{\sigma\_{\varepsilon}} + \mu\right)\frac{\partial\varepsilon}{\partial\mathbf{x}\_{j}}\right] - C\_{1}\frac{\varepsilon}{k}\left[\overline{\rho}u\_{i}^{\prime\prime}u\_{j}^{\prime\prime}\frac{\partial\bar{u}\_{i}}{\partial\mathbf{x}\_{j}} + \frac{\mu\_{t}}{\overline{\rho}^{2}}\frac{\partial\overline{\rho}}{\partial\mathbf{x}\_{i}}\frac{\partial\overline{p}}{\partial\mathbf{x}\_{i}}\right] - C\_{2}\overline{\rho}\frac{\varepsilon^{2}}{k}.\tag{9}$$

The empirical constants for the standard k-ε model are assigned below: C1 = 1.44, C2 = 1.92, C<sup>μ</sup> = 0.09, σ<sup>k</sup> = 1.0, and σε = 1.3. A nonslip boundary condition is assumed regarding all solid surfaces of the computational domain, and the standard wall functions are used.

The chemical time scales are assumed being much smaller than the turbulent ones. Therefore, the coherent flame model is used for the turbulent premixed combustion of the kerosene. The mean turbulent reaction rate is defined as

$$
\rho \dot{r}\_{\text{f\u}} = -\rho\_{\text{fr}} \mathbf{y}\_{\text{fu}\,\text{fr}} \mathbf{S}\_L \Sigma,\tag{10}
$$

where

*By* <sup>¼</sup> *Yvs* � *Yv*<sup>∞</sup> 1 � *Yvs*

*Knock Suppression of a Spark-Ignition Aviation Piston Engine Fuelled with Kerosene*

The convective heat flux supplied from the gas to the droplet is denoted by

The KH-RT model is used for the breakup process of the droplets. The wave-

<sup>1</sup> <sup>þ</sup> <sup>0</sup>*:*45*Oh*0*:*<sup>5</sup> � � <sup>1</sup> <sup>þ</sup> <sup>0</sup>*:*4*T*0*:*<sup>7</sup> � �

*g*

<sup>1</sup> <sup>þ</sup> <sup>0</sup>*:*87*We*1*:*<sup>67</sup>

� ��0*:*<sup>5</sup> <sup>0</sup>*:*<sup>34</sup> <sup>þ</sup> <sup>0</sup>*:*38*We*<sup>1</sup>*:*<sup>5</sup>

*<sup>τ</sup><sup>a</sup>* <sup>¼</sup> <sup>3</sup>*:*726*C*2*<sup>r</sup>*

Rayleigh-Taylor disturbances are in continuous competition with Kelvin-Helmholtz surface waves. The RT mechanism is caused by quick deceleration of the droplets, resulting in a growth of surface waves. When the droplet diameter is larger than the wavelength of the critical disturbance wave, the process of droplet breakage caused by RT must be considered. The fastest growing frequency *Ω<sup>t</sup>* and

> 2 3 ffiffiffiffiffi <sup>3</sup>*<sup>σ</sup>* <sup>p</sup>

> > r

Λ*<sup>t</sup>* ¼ *C*<sup>4</sup>

τ*<sup>t</sup>* ¼ *C*<sup>5</sup>

The ATKIM model is used for the ignition process in the cylinder, which considers the charge stratification, the available electrical energy, the heat losses to the

The AnB model is used for the prediction of autoignition of the air-fuel mixture. The autoignition delay time of the combustible air-fuel mixture can be calculated as

<sup>100</sup> � �<sup>3</sup>*:*<sup>4017</sup>

where *ON* is the octane number of kerosene and the parameters *A*, *n*, and *B* are

*p*�*ne B*

s

*Kt* ¼

spark plug, and the influences of turbulence on the early flame kernel.

*<sup>τ</sup><sup>d</sup>* <sup>¼</sup> *<sup>A</sup> ON*

calibrated by the measured data of the in-cylinder pressure.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *gt ρ<sup>d</sup>* � *ρ<sup>c</sup>* j j 3*σ*

> *π Kt*

1 Ω*t*

*gt <sup>ρ</sup><sup>d</sup>* � *<sup>ρ</sup><sup>c</sup>* j j<sup>1</sup>*:*<sup>5</sup> *ρ<sup>d</sup>* þ *ρ<sup>c</sup>*

length *Λ* and wave growth rate *Ω* of the fastest growing wave are

Λ ¼ 9*:*02*r*

<sup>Ω</sup> <sup>¼</sup> *<sup>ρ</sup>dr*<sup>3</sup> *σ*

Ω*<sup>t</sup>* ¼

The corresponding wave length and breakup time are

Then, the breakup time is calculated as

*DOI: http://dx.doi.org/10.5772/intechopen.91938*

wave number *Kt* are

**95**

*:* (17)

*<sup>Q</sup>*\_ <sup>¼</sup> *DdπλNu T*ð Þ <sup>∞</sup> � *Ts :* (18)

� �0*:*<sup>6</sup> *:* (19)

ΛΩ *:* (21)

, (22)

*:* (23)

, (24)

*:* (25)

*<sup>T</sup>*, (26)

*g* ð Þ <sup>1</sup> <sup>þ</sup> *Oh* <sup>1</sup> <sup>þ</sup> <sup>1</sup>*:*4*T*<sup>0</sup>*:*<sup>6</sup> � � *:* (20)

where *SL* is the mean laminar burning velocity and *Σ* is the flame surface density. The transport equation for the flame surface density is

$$\frac{\partial \Sigma}{\partial t} + \frac{\partial}{\partial \mathbf{x}\_j} \left( \overline{\mathbf{u}}\_j \Sigma \right) - \frac{\partial}{\partial \mathbf{x}\_j} \left( \frac{\nu\_t}{\sigma\_2} \frac{\Sigma}{\partial \mathbf{x}\_j} \right) = \mathbf{S}\_\mathbf{g} - \mathbf{S}\_a + \mathbf{S}\_{LAM},\tag{11}$$

where *σ*<sup>Σ</sup> is the turbulent Schmidt number, *vt* is the turbulent kinematic viscosity, *Sg* is the product of the turbulent strain rate and the flame surface, *Sa* is the annihilation of flame surface, and *SLAM* is the contribution of laminar combustion.

The laminar flame speed can be computed as

$$\mathbf{S}\_{L} = \mathbf{S}\_{L0} \left( \mathbf{1} - \mathbf{2}. \mathbf{1} \mathbf{y}\_{\mathrm{EGR}} \right) \left( \frac{T\_{fr}}{T\_{ref}} \right)^{a\_1} \left( \frac{p}{p\_{ref}} \right)^{a\_2},\tag{12}$$

where *Tref* and *pref* are the reference values of the standard state and *a*<sup>1</sup> and *a*<sup>2</sup> are fuel-dependent parameters.

The water injected from the water injector forms small droplets and mixes with the gases in the cylinder. The spray model needs to consider the droplet movement, fragmentation, evaporation, and wall impingement. Considering the movement resistance and buoyancy of droplets in the gases, the following equation for the droplet velocity is obtained.

$$\frac{du\_{id}}{dt} = \frac{3}{4} \mathbf{C}\_{\rm D} \frac{\rho\_{\rm g}}{\rho\_{\rm d}} \frac{\mathbf{1}}{D\_{\rm d}} |u\_{\rm g} - u\_{d}| \left( u\_{\rm ig} - u\_{id} \right) + \left( \mathbf{1} - \frac{\rho\_{\rm g}}{\rho\_{\rm d}} \right) \mathbf{g}\_{i},\tag{13}$$

where *uid* is the particle velocity vector, *uig* is the domain fluid velocity, *CD* is the drag coefficient, *Dd* is the particle diameter, *ρ<sup>g</sup>* and *ρ<sup>d</sup>* are the densities of the gas and the droplet, and *gi* is the gravitational acceleration vector.

The instantaneous droplet position vector can be determined by

$$\frac{d\boldsymbol{\omega}\_{id}}{dt} = \boldsymbol{\mu}\_{id}.\tag{14}$$

The evaporation process of the droplet is described by

$$m\_d c\_{p,d} \frac{dT\_d}{dt} = \dot{Q} \left( 1 + L \frac{\dot{f}\_w}{\dot{q}\_s} \right). \tag{15}$$

Assuming the Lewis number is unity, the flux ratio can be written as

$$\frac{\dot{f}\_{\text{vs}}}{\dot{q}\_{\text{s}}} = \frac{-B\_{\text{y}}}{h\_{\text{os}} - h\_{\text{s}} - \left(h\_{\text{vs}} - h\_{\text{gc}}\right)\left(Y\_{\text{voo}} - Y\_{\text{vs}}\right)},\tag{16}$$

*Knock Suppression of a Spark-Ignition Aviation Piston Engine Fuelled with Kerosene DOI: http://dx.doi.org/10.5772/intechopen.91938*

where

The chemical time scales are assumed being much smaller than the turbulent ones. Therefore, the coherent flame model is used for the turbulent premixed combustion of the kerosene. The mean turbulent reaction rate is defined as

where *SL* is the mean laminar burning velocity and *Σ* is the flame surface density.

*vt σ*Σ Σ *∂x <sup>j</sup>* � �

� � *Tfr*

*ug* � *ud* � � �

The instantaneous droplet position vector can be determined by

*dTd*

Assuming the Lewis number is unity, the flux ratio can be written as

<sup>¼</sup> �*By h*<sup>∞</sup> � *hs* � *hvs* � *hgs*

*dt* <sup>¼</sup> *<sup>Q</sup>*\_ <sup>1</sup> <sup>þ</sup> *<sup>L</sup>*

*dxid*

the droplet, and *gi* is the gravitational acceleration vector.

The evaporation process of the droplet is described by

*mdcp*,*<sup>d</sup>*

\_ *f vs q*\_ *s*

**94**

where *σ*<sup>Σ</sup> is the turbulent Schmidt number, *vt* is the turbulent kinematic viscosity, *Sg* is the product of the turbulent strain rate and the flame surface, *Sa* is the annihilation of flame surface, and *SLAM* is the contribution of laminar combustion.

> *Tref* !*<sup>a</sup>*<sup>1</sup>

� *uig* � *uid*

where *uid* is the particle velocity vector, *uig* is the domain fluid velocity, *CD* is the drag coefficient, *Dd* is the particle diameter, *ρ<sup>g</sup>* and *ρ<sup>d</sup>* are the densities of the gas and

� � <sup>þ</sup> <sup>1</sup> � *<sup>ρ</sup><sup>g</sup>*

\_ *f vs q*\_ *s*

!

� �ð Þ *Yv*<sup>∞</sup> � *Yvs*

*ρd* � �

*dt* <sup>¼</sup> *uid:* (14)

*gi*

*:* (15)

, (16)

, (13)

where *Tref* and *pref* are the reference values of the standard state and *a*<sup>1</sup> and *a*<sup>2</sup> are

The water injected from the water injector forms small droplets and mixes with the gases in the cylinder. The spray model needs to consider the droplet movement, fragmentation, evaporation, and wall impingement. Considering the movement resistance and buoyancy of droplets in the gases, the following equation for the

The transport equation for the flame surface density is

*Numerical and Experimental Studies on Combustion Engines and Vehicles*

*<sup>u</sup> <sup>j</sup>*<sup>Σ</sup> � � � *<sup>∂</sup>*

*SL* ¼ *SL*<sup>0</sup> 1 � 2*:*1*yEGR*

The laminar flame speed can be computed as

*∂x <sup>j</sup>*

∂Σ *∂t* þ *∂ ∂x <sup>j</sup>*

fuel-dependent parameters.

droplet velocity is obtained.

*duid dt* <sup>¼</sup> <sup>3</sup> 4 *CD ρg ρd* 1 *Dd*

*ρr*\_*fu* ¼ �*ρfryfu*,*frSL*Σ, (10)

*p pref*

!*<sup>a</sup>*<sup>2</sup>

¼ *Sg* � *Sa* þ *SLAM*, (11)

, (12)

$$B\_{\mathcal{Y}} = \frac{Y\_{\nu\nu} - Y\_{\nu\infty}}{1 - Y\_{\nu\nu}}.\tag{17}$$

The convective heat flux supplied from the gas to the droplet is denoted by

$$
\dot{Q} = D\_d \pi \lambda \text{Nu}(T\_\Leftrightarrow - T\_s). \tag{18}
$$

The KH-RT model is used for the breakup process of the droplets. The wavelength *Λ* and wave growth rate *Ω* of the fastest growing wave are

$$\Lambda = 9.02r \frac{\left(1 + 0.45 \Omega h^{0.5}\right) \left(1 + 0.47^{0.7}\right)}{\left(1 + 0.87 \, W e\_{\text{g}}^{1.67}\right)^{0.6}}.\tag{19}$$

$$
\Omega = \left(\frac{\rho\_d r^3}{\sigma}\right)^{-0.5} \frac{\mathbf{0}.34 + \mathbf{0}.38 \mathbf{W} \mathbf{e}\_\mathbf{g}^{1.5}}{(1 + \mathcal{O}h)\left(1 + \mathbf{1}.4T^{0.6}\right)}.\tag{20}
$$

Then, the breakup time is calculated as

$$
\pi\_d = \frac{3.726C\_2r}{\Lambda \Omega}.\tag{21}
$$

Rayleigh-Taylor disturbances are in continuous competition with Kelvin-Helmholtz surface waves. The RT mechanism is caused by quick deceleration of the droplets, resulting in a growth of surface waves. When the droplet diameter is larger than the wavelength of the critical disturbance wave, the process of droplet breakage caused by RT must be considered. The fastest growing frequency *Ω<sup>t</sup>* and wave number *Kt* are

$$\mathfrak{Q}\_{t} = \sqrt{\frac{2}{3\sqrt{3\sigma}} \frac{\mathbf{g}\_{t} |\rho\_{d} - \rho\_{c}|^{1.5}}{\rho\_{d} + \rho\_{c}}},\tag{22}$$

$$K\_t = \sqrt{\frac{\mathbf{g}\_t |\rho\_d - \rho\_c|}{\mathbf{3}\sigma}}. \tag{23}$$

The corresponding wave length and breakup time are

$$
\Lambda\_l = \mathcal{C}\_4 \frac{\pi}{K\_l},
\tag{24}
$$

$$
\pi\_t = C\_5 \frac{1}{\Omega\_t}.\tag{25}
$$

The ATKIM model is used for the ignition process in the cylinder, which considers the charge stratification, the available electrical energy, the heat losses to the spark plug, and the influences of turbulence on the early flame kernel.

The AnB model is used for the prediction of autoignition of the air-fuel mixture. The autoignition delay time of the combustible air-fuel mixture can be calculated as

$$
\pi\_d = A \left(\frac{ON}{100}\right)^{3.4017} p^{-n} e^{\frac{\theta}{\pi}},\tag{26}
$$

where *ON* is the octane number of kerosene and the parameters *A*, *n*, and *B* are calibrated by the measured data of the in-cylinder pressure.
