**3. Application of the anergo-exergy method for evaluating the efficiency of working processes in diesel engines**

The heat generated by the combustion of fuel in the engine cylinders cannot be completely converted into useful mechanical work. In the thermodynamic cycle, the efficiency of converting heat into work is estimated by the thermal efficiency η*t*, which is always less than one as a result of the transfer of part of the heat to a cold source. In a real engine, heat losses increase due to friction, heat transfer, incomplete combustion, and other reasons. In this regard, the effective efficiency of η*<sup>t</sup>* cycle is less important than the value of η*t*.

Currently, there are two directions in the thermodynamics of investigating the efficiency of diesel processes. The traditional direction is that for the thermodynamic study of motors, a heat balance is used, based on the first principle of thermodynamics, when the criterion for the quality of converting heat into work is the effective efficiency (η*е*). The capabilities of the traditional method are limited by the fact that the heat balance only records the final, qualitative result of energy transformations in the internal combustion engine cycle. To implement all the reserves for improving modern internal combustion engines, it is necessary to deeply study the quality of energy transformations in the engine. The anergo-exergetic method of analysis combines the first and second laws of thermodynamics, and the exergy efficiency (ηеx) acts as a criterion for the quality of converting heat into work. Only this method allows to identify the mechanisms of the formation of internal and external ICE losses, assess the possibilities of their reduction, and, therefore, substantiate the ways to achieve optimal heat use in diesel engines.

#### **3.1 Theoretical foundations of the anergo-exergy method**

It is known that heat and internal energy, as forms of energy, determined by the first law of thermodynamics, can only be partially converted into work. Accordingly, in a heat engine (**Figure 3**) it is possible to convert into work only a certain fraction of the energy supplied in the form of heat *Q* [6].

**Figure 3.** *Diagram of the circular process of a heat power plant.*

In a generalized form, a consequence of the second law of thermodynamics is the statement that there are forms of energy that can be converted into any other form of energy. These forms of energy, covered by the general concept "exergy", are completely mutually convertible during reversible processes, and by reversible and irreversible processes they can be transformed into limited convertible forms of energy—internal energy and heat. At the same time, limited convertible forms of energy cannot be converted in any quantities into exergy. All forms of energy that are not transformed into exergy are summarized by the term "anergy".

"Exergy is the maximum possible work that the system can perform in the reversible transition from this state to a state of equilibrium with the environment; anergy is the energy that cannot be converted into exergy" [7].

For all forms of energy, the following general correlation is valid:

Energy ¼ Exergy þ Anergy*:*

According to the principle of irreversibility, all natural, actually occurring processes are irreversible. Thus, in these processes, the supply of exergy decreases due to its transformation into anergy. Part of the exergy that is converted into anergy during irreversible processes is the loss of exergy in the process.

To use the concept of exergy and anergy, it is necessary to know the proportions of these quantities for various forms of energy. When determining exergy, the heat supplied to the heat-power plant is considered, the working fluid of which performs a circular process. The exergy of heat appears here as useful work, and anergy as the unused heat of a circular process. However, the useful work of the circular process coincides with the exergy of the supplied heat under the following conditions:

• the circular process is reversible (otherwise it turns into anergy and useful work will be less than the applied exergy);

• heat removal is carried out at ambient temperature, so that the removed heat consists only of anergy and corresponds to the anergy of the supplied heat (**Figure 3**).

Heat supplied to the working fluid

$$dQ = dE\_Q + dA\_Q \tag{5}$$

As a result of the heat supply *dQ*, perceived at temperature *T*, the entropy of the working fluid will increase.

*dSQ* ¼ *dQ=T*. Since the entropy is not produced in a reversible process, the given heat *dQ*0should be such that the entropy

$$d\mathcal{S}\_{Q\_0} = dQ\_0/T\_0$$

transferred with it is equal to the perceived entropy *dSQ* . From the balanced equation of entropy

$$d\mathbb{S}\_{Q} + d\mathbb{S}\_{Q\_{0}} = \frac{dQ}{T} + \frac{dQ\_{0}}{T\_{0}}\tag{6}$$

for the given heat we get

$$-dQ\_0 = \frac{T\_0}{T} dQ\tag{7}$$

The heat removed to the environment consists only of anergy and represents the desired anergy of heat.

$$dA\_Q = \frac{T\_0}{T} dQ \tag{8}$$

The exergy of heat is manifested as the work of an imaginary reversible circular process

$$d\mathbf{E}\_Q = d\mathbf{Q} - dA\_Q = \left(\mathbf{1} - \frac{T\_0}{T}\right) d\mathbf{Q} \tag{9}$$

If heat is perceived or given off by the system in a certain temperature range, then the exergy of heat perceived or given off with heat *Q*<sup>12</sup> is determined by integrating:

$$E\_{Q\_{12}} = \int\_{1}^{2} (1 - \frac{T\_0}{T}) dQ = Q\_{12} - T\_0 \int\_{1}^{2} \frac{dQ}{T} \tag{10}$$

In a similar way for the anergy of heat

$$A\_{Q\_{12}} = T\_0 \int\_1^2 \frac{dQ}{T} \,. \tag{11}$$

Here *T* is the temperature of the energy carrier that gives or receives heat.

As well as *Q*12, exergy of heat and anergy are characteristics of the process, and not parameters of state. The exergy and anergy of heat depend not only on *T*0, but also on the temperature of the system that receives or gives off heat, which can be seen from expressions (10) and (11). This allows coming to the conclusion that in heat power plants, heat supply to the working fluid must be implemented at the maximum possible temperature for a given installation and to obtain the maximum possible work in the cycle.
