**2. Diesel engine concept with inserted PM in head of combustion chamber**

Durst and Weclas described the diesel engine concept with new mixture formation and combustion processes in a PM reactor. Application of PM in diesel engines generates a homogeneous and flameless combustion process accompanied by a near-zero emission level. Heat recovery from the last combustion process in PM increases the temperature end of the compression process, resulting in raised thermal efficiency and reduced fuel consumption. Heat absorption in PM leads to a reduction in combustion temperature and near-zero NOx. There is difference between the combustion processes in conventional diesel engines and PM-inserted diesel engines. These processes are liquid fuel injection directly into PM, causing multi-jet splitting for fuel distribution throughout PM volume, fuel vaporization, and mixing with air, accomplished by thermal ignition and heat release [1, 6–9].

### **2.1 Diesel PM-engine with concept of an open PM chamber**

A diesel PM engine describes as a diesel engine with a homogeneous combustion process in a PM volume. PM engines recognize these processes in PM volume: energy recovery in the cycle, fuel injection in PM, fuel vaporization for liquid fuels, mixing with air, homogenization of air-fuel mixture, self-ignition of the mixture, and homogeneous combustion.

This mathematical modeling of permanent contact between working fluid and PM is schematically studied, as illustrated in **Figure 3**. The PM-combustion chamber is supposed to be inserted in the cylinder head space, and the PM chamber wall is thermally isolated. During the intake process, the PM-heat capacitor has an ignorable effect on the in-cylinder air conditions. Also, during the start of the compression process, a small amount of air is in contact with hot PM. Before TDC, the fuel is injected into PM space, and very fast fuel vaporization for liquid fuels and mixing with air happen in the PM structure. Hence, the fuel is injected close to TDC of the compression process due to high energy storage in PM volume. There is a very complex process during fuel injection, mixture formation, and combustion initiation in the PM structure. The high initial PM temperature (solid-phase temperature of the PM and gas temperature trapped inside PM volume) with mixture formation inside the PM reactor causes self-ignition and volumetric heat release in the combustion process. The reactor heat capacity, pore density, and pore structure can affect the combustion process [2–7].

Solid phase PM has higher heat capacity than fluid flow and high energy storage capability. Correspondingly, its high surface-to-volume ratio leads to considerable

**Figure 3.** *Schematic of a permanent contact PM- diesel engine [8].*

heat exchange. The solid high temperature of PM inside the combustion chamber is a source of the high rate of liquid fuel evaporation and fast mixing with air and selfignition of the mixture. In diesel engines, mixture formation and combustion simultaneously happen, but in PM engines, these processes occur separately.

The ideal thermodynamic model for combustion in diesel engines is an isobar process, but combustion in PM happens inside diesel engines very fast. Combustion in PM intensifies the reaction rate in a short time scale. Hence, volume change can be considered approximately by a combination of isochoric and isothermal processes.

The last case is illustrated in **Figure 3**. During the intake process (**Figure 3a**), PM has not considerably affected the in-cylinder pressure and temperature. Also, during the early compression process, a low quantity of air is in contact with hot PM. In the following compression process, the heat exchange process increases with the motion of the piston to the TDC (**Figure 3b**). At the TDC, total air is collected in the PM volume. Near the TDC of the compression process, the fuel is injected into the PM volume (**Figure 3c**), and vaporization of liquid fuel and mixing with air occur very fast in the PM. A volumetric self-ignition of the fuel-air mixture follows flameless combustion by uniform temperature distribution in the PM chamber (**Figure 3d**). Fuel injection controls combustion initiation timing in the PM volume. The PM structure creates conditions for a homogeneous combustion process and converts the heat into work (**Figure 3e**). The combustion in a PM can be carried out in the PM volume that cannot occur in the free flame combustion process [1–7].

#### **2.2 Mathematical thermodynamic modeling of PM diesel engine**

For an ideal thermodynamic cycle of conventional and PM diesel engines, a closed cycle is assumed, with working fluid as air with no exhaust gases to the environment. The heat capacity of PM is considerably further than that of fluid. Hence, the solid phase temperature of PM is considered constant during the cycle, and heat exchange between the PM and the working fluid does not affect it. Heat losses of the piston,

liner wall, and PM chamber to the environment are ignored, and compression and expansion processes have adiabatically happened.

In the ideal closed cycle energy of a diesel engine (compression ignition engine), combustion occurs at the constant pressure assumed. Heat losses through the combustion chamber to the environment are neglected, and compression and expansion (work) processes happen isentropically. **Figure 4a** and **b** shows the P-V (pressure versus volume) and T-S (temperature versus entropy) diagrams of diesel engine closed cycle analysis. The four processes are:


PM diesel engine in the ideal closed cycle energy of the fuel is added to the air in a combination of isochoric and constant temperature. Heat losses through the PM combustion chamber to the environment are ignored, and compression and expansion (work) processes occur isentropically. **Figure 4a** and **b** shows a closed cycle's P-V and T-S diagrams for permanent contact PM diesel-engine analysis. The five processes are:


#### **Figure 4.**

*(a) P-V diagram of closed cycle of conventional diesel engine and PM engine. (b) T-S diagram of closed cycle of conventional diesel engine and PM engine.*

Compression ratio is defined as *rc*, and *ρ* is the compression ratio during constant temperature heat addition:

$$r\_{\mathfrak{k}} = \mathfrak{v}\_{\mathfrak{1}} / \mathfrak{v}\_{\mathfrak{2}} \tag{1}$$

$$
\rho = \upsilon\_3 / \upsilon\_{3'} \tag{2}
$$

Process 1–2 is isentropic, so:

$$T\_2 = T\_1(r\_c)^2 \tag{3}$$

For PM diesel engines, the energy of fuel is added to air through two process: isochoric process *Cv <sup>T</sup>*<sup>3</sup> ð Þ <sup>0</sup> � *<sup>T</sup>*<sup>2</sup> plus isothermal process *RT*<sup>3</sup> ln *<sup>v</sup>*<sup>3</sup> *v*30 . Heat loss to environment according to conventional diesel engine is *Cv*ð Þ *T*<sup>4</sup> � *T*<sup>2</sup> .

$$q\_{in} = C\_v (T\_{\text{\textdegree}} - T\_2) + RT\_3 \ln \left(\frac{v\_3}{v\_{\text{\textdegree}}}\right) \tag{4}$$

Heat rejection occurs in a constant volume process:

$$q\_{out} = \mathbf{C}\_v (T\_4 - T\_1) \tag{5}$$

Engine thermal efficiency is defined according to Eq. (6):

$$\eta = \frac{w}{q\_{in}} = \mathbf{1} - \frac{q\_{out}}{q\_{in}} \tag{6}$$

Assuming constant specific heat, the thermal efficiency of diesel engine is according to Eq. (7):

$$\eta\_{diel} = \mathbf{1} - \frac{\mathbf{C}\_{\nu}(T\_4 - T\_1)}{\mathbf{C}\_p(T\_3 - T\_2)} \tag{7}$$

Hence, thermal efficiency of PM diesel engine is according to Eq. (8).

$$\eta\_{\text{PM\\_diesel}} = \mathbf{1} - \frac{\mathbf{C}\_{\nu}(T\_4 - T\_1)}{\mathbf{C}\_{\nu}(T\_{\mathcal{Y}} - T\_2) + RT\_3 \ln\left(\frac{\nu\_3}{\nu\_{\mathcal{Y}}}\right)}\tag{8}$$
