Analysis of Efficiency of Thermopressor Application for Internal Combustion Engine ^†

Abstract

Contact cooling using thermopressor technologies is a promising direction for the development of energy-efficient technologies. This technology is based on the implementation of the thermo-gas-dynamic compression effect in special contact heat exchangers that consists of increasing the pressure while decreasing the temperature during the evaporation of a finely dispersed liquid injected into a gas flow moving at a speed close to sound. Upon application of the thermopressor for charge air cooling of the engine, the following result was obtained: an increase in the air pressure after the turbocharger by 340 to 480 kPa. The thermopressor can be used as a boost stage after the turbocharger, resulting in the reduction of a basic turbocharger compression work and the increase of engine power output accordingly. Reducing the work allows for the same air flow rate on the internal combustion engine to reduce the compressor power by 10 to 12%. This increases the temperature of the exhaust gases at the inlet of the exhaust boiler by 10 to 15 °C and boiler steam capacity, resulting in an increase in the power output of the utilization turbine generator with a corresponding reduction in the fuel consumption of the diesel generator of the ship power plant by 2 to 3%.

1. Introduction

Thermopressor technologies are based on the implementation of the thermo-gas-dynamic compression effect in special contact heat exchangers (thermopressor or aerothermopressor) that consists in increasing the pressure while decreasing the temperature during the evaporation of a finely dispersed liquid injected into a gas flow moving at a speed close to sound [1,2].

Contact-cooling using thermopressor technologies is a promising reserve for increasing the efficiency of using the secondary heat of power plants based on internal combustion engines, due to highly efficient cooling of the charge air [3].

In research [1] the experimental results and theoretical researches are resulted. They allowed the authors to conclude that an increase in total pressure by 20% is quite achievable. An experimental research of 20 liquid injection systems was conducted. The system of maximum water supply with low speed turned out to be the best. The maximum thermopressor diameter during the experiments was 280 mm. At the same time, an increase in the total flow pressure by 3% was achieved.

Fowle [4] researched the thermopressor operation on the gas turbine exhaust gases. The author designed and researched an experimental thermopressor with gas consumption at 11.5 kg/s. In the experiments, the relative effect of thermo-gas dynamic compression achieved 5%, with the injection of about 8% of water (relative to the flow of gas). The paper obtained data on the pressure loss due to local and hydraulic resistance in thermopressor different parts; the total pressure decrease without liquid injection achieved 14%.

However, in the presented work, a thermopressor was studied that worked with the power plant engine exhaust gases, and the use of a thermopressor for cooling the power plant engine cycle air was not considered.

Low-, medium- and high-speed internal combustion engines are widely used in power plants of transport and stationary energy. The air parameters at the turbocharger (TC) discharge and at the inlet to the cylinders significantly affect the fuel and energy efficiency of the engine. Every 10 degrees, an increase in air temperature causes a decrease in the effective efficiency of marine low-speed diesel engines by 0.5–0.7% [5,6] with a corresponding increase in specific fuel consumption [7,8]. The decrease in engine power is caused by a decrease in the mass air flow in the cylinders, due to a decrease in the air density with an increase in temperature [9,10].

The charge air cooling of the internal combustion engine is carried out in order to ensure normal operating conditions of the turbocharger and to increase the air mass charge in the cylinders. The air can be cooled in refrigerators of various designs: round-tubular, flat-tubular with corrugated common plates, with a surface made of shaped sheets, etc. Cooling the charge air for every 10 K increases the air mass entering the working cylinder by 2.0–2.5% and leads to a decrease in the average temperature of the operating cycle and the heat density of the diesel engine parts at increased boost pressure [11,12].

The increase in air temperature depends on the degree of pressure increase, compressor efficiency and heat exchange with the walls, that is, on the compressor design. Engine intake air temperature can be high at high pressure ratios (unless charge air cooling is used), adversely affecting the engine efficiency [13,14]. Moreover, there is an improvement in the environmental performance of the internal combustion engine as a result of a decrease in the average temperature in the cycle with a decrease in the charge air temperature. Compressors of turbocharging units of modern marine internal combustion engines have relatively high-pressure ratios, ε_c is 3 to 5. In this case, the capacities of the compressor and the turbine are approximately equal, and the turbine uses almost the entire heat drop of the exhaust gases. In this case, additional energy can be obtained only by reducing the compression work in the compressor and thus unloading the turbine [15].

The development of modern energy-efficient technologies for power plants can cause a low level of waste heat use [16,17]: the temperature of gases after the heat recovery boilers is about 180 °C, charge air temperature is 140–220 °C and the temperature of the engine cylinders’ cooling water is 90–120 °C. Heat with such a thermal potential can be used in several ways:

• The use of the combustion products heat for the steam production in the heat recovery boiler (reduction of the specific fuel consumption is 2–3%) [18,19].
• Turning to heat recovery boilers with two-pressure circuits (additionally increases the capacity of the utilization turbine generator by 15–30%) [20,21,22].
• To improve the turbocharge system [23,24].
• The use of the high-temperature cooling method of the internal combustion engine [25,26].
• The use of combined energy production technologies with simultaneous production of heat (steam, hot water), electrical energy (generator, shaft generator) and cold (heat-using ejector and absorption refrigeration machines) [27,28,29].

The most common way to improve the fuel and energy efficiency of a power plant is contact cooling of the air flow by water injection [30,31]. It is promising to cool the charge air of the internal combustion engine with a thermopressor, which provides an increase in efficiency and a reduction in fuel consumption, due to a decrease in temperature and an increase in compressed air pressure. It leads, in turn, to a decrease in the compression power consumption [32]. Changing the operating conditions of power plants and, consequently, the thermopressor thermal load, require rational organization of work processes and the determination of a rational design pressure increase that would provide the maximum effect [33,34]. Further development of this direction is to use the secondary heat of power plants (the heat of air or combustion products compressed by compressors) to accelerate the air (gas) flow to a speed close to the sound one and practically instantaneous (with a minimum length and aerodynamic resistance) evaporation of injected water [4,35].

On the basis of the presented analysis, on the current state of development of technologies for increasing the fuel and energy efficiency of power plants based on internal combustion engines, the main task of the research was formulated: to develop and analyze improved thermopressor systems for utilizing the energy of combustion products with cooling the working fluid (air) of the engines, principles and methods of their implementation.

2. Model of Thermopressor

A comparative–computational research method was used in the work to determine the thermodynamic and energy efficiency of a thermopressor cooling system as part of a power plant. To use this method, a proprietary software package was developed which allows for the following:

• To simulate all working processes in the thermopressor;
• To calculate the main structural elements of the thermopressor;
• To calculate the energy efficiency and main characteristics of the engine with thermopressor cooling systems, taking into account changes in climatic and hydrometeorological conditions, as well as partial operating modes of the power plant.

The characteristics calculation of the thermopressor (air pressure, P_a; air temperature, T_a; air velocity, v_a; water velocity, v_w; etc.) and its basic geometric parameters of the flow path under the given operating conditions of the power plant engine was carried out according to the presented methods [36,37,38]. The calculation took into account the pressure loss in the nozzle part (confuser), working chamber and diffuser, as well as with the frontal resistance of water droplets [39,40,41].

The main parameters calculation of the internal combustion engine was carried out by using the software packages Diesel-RK and CEAS (MAN B&W) [42], taking into account the change in the corresponding parameters of the air at the inlet to the engine cylinders, as well as the partial operating modes. To use the above software systems, an additional control program was developed, in which the parameters of wet air at the inlet and outlet of the turbocharger were determined [43].

The mathematical model of the thermopressor should take into account the following: features of thermo-gas-dynamic compression in the evaporation chamber; evaporation of a drop in a flow of moist air moving at a speed close to sound, features of crushing and transformation of the dispersed flow in the main elements of the thermopressor flow part, features of the liquid injection process into the flow of moist air, friction losses in the elements of the thermopressor flow part and features of the heat transfer processes during the phase transition (boiling) in the evaporation chamber.

Hence, the mathematical model of the thermopressor should include the following components:

(1)

Mathematical model of liquid (water) drop evaporation in a flow of moist gas (air) moving at a speed close to sound;

(2)

Mathematical model of the thermo-gas-dynamic compression working process in the evaporation chamber.

The development of a droplet evaporation mathematical model should describe the processes of liquid leakage and evaporation. Such models should consider workflows that involve a complex of bubbles under conditions of thermodynamic instability. However, the development of such a model requires a separate study with an experiment to determine the dispersion of the flow.

When developing a mathematical model of the thermo-gas-dynamic compression working process in the evaporation chamber, it is advisable to use the classical thermo-gas-dynamic dependences, which were given and tested in known research studies [35,44,45].

The operation of the thermopressor is based on the effect of thermo-gas-dynamic compression—if the gas flow, which moves at a transonic speed, cools, then the pressure will increase. In the real thermopressor (Figure 1), the gas-expansion process occurs in a well-profiled nozzle almost adiabatically. In the narrow part of the nozzle, where the gas flow moves at a speed of (0.5–0.9) Ma, a flow of mechanically finely atomized cooling water is supplied (mode I). In the evaporation area, the interaction of these flows takes place, which is expressed in the acceleration and fragmentation of droplets and some deceleration of the gas flow, heating and evaporation of droplets, and cooling of the gas (mode II). A two-phase flow is formed, moving at a high speed, in which the processes of heat and mass transfer, changes in the composition of the vapor–gas–liquid mixture and all flow parameters take place. These processes continue in the diffuser, where there is a general deceleration of the flow and an increase in static pressure (mode III).

To calculate the characteristics of the thermopressor as part of the engine charge-air-contact-cooling system, it is necessary to use a mathematical model that takes into account the influence of thermo-gas-dynamic compression processes [35,36].

The main assumptions made in the development of the mathematical model of the thermopressor are as follows:

(1)

No heat exchange of the surface of the thermopressor with the environment;

(2)

The air parameters correspond to the parameters on the compressor outlet of the power plant engine;

(3)

The amount of liquid (water) injected corresponds to the modes of operation (including partial modes) of the power plant (temperature, pressure and relative humidity of the engine charge air);

(4)

The modes of power plant operation are influenced by changes in climatic and hydrometeorological conditions (temperature, pressure, relative humidity and moisture of the inlet air);

(5)

The problem of modeling two-phase flows in a thermopressor was set as stationary;

(6)

The problem of heat calculation of the thermopressor with phase transition was solved in conjugate setting—taking into account the decrease of pressure;

(7)

Ehen calculating the pressure decrease (including phase transitions) adopted classic models that take into account the resistances against the flow part walls of the thermopressor, as well as the influence of local resistances (compression, expansion);

(8)

When calculating the resistances losses, the presence of a dispersed flow in the thermopressor flowing part (evaporation chamber, diffuser) was taken into account;

(9)

Liquid droplets evaporation is carried out in the evaporation chamber and the thermopressor diffuser;

(10)

Liquid droplets evaporation is carried out to full saturation of air, i.e., to the value of relative humidity φ = 100%, while evaporation in the whole apparatus may not be complete;

(11)

When determining the parameters of wet gas (air), we considered the boundary conditions of the third kind; that is, the known inlet temperature, pressure, relative humidity and heat-transfer laws determined the heat flux density and heat flow in the tube length dz. From the air heat balance and liquid (water) was its temperature, pressure and relative humidity at the outlet of the section dz, and based on the pressure drop due to hydraulic resistance and pressure increase due to thermo-gas-dynamic compression calculated the pressure at the outlet of the section dz, which served as input parameters for the next section of the thermopressor flow part.

(12)

When numerically integrating the evaporation chamber, the step was chosen so that the pressure increase did not exceed ΔP_tp = (P_tp2/P_tp1) = 1.0001, (0.01%), which allows us to move from the final differences in temperature and pressure to full differentials;

(13)

Water droplets are injected into the moving air flow at transonic speed (Ma = 0.35–0.95);

(14)

The physical properties, flow rate and composition of the gas along the length of the thermopressor flow part remain constant;

(15)

The cross-sectional area of the evaporation chamber is constant (the shape of the chamber is cylindrical).

The input data for the calculation thermopressor cooling system mathematical model are as follows: parameters of the injected water (temperature, T_w1; velocity at the nozzle outlet, v_w; mass flow, G_w; and initial droplet diameter δ_w); parameters of air (pressure, P_a1; temperature, T_a1; relative humidity, φ_a1; moisture content, d_a1; mass flow, G_a; and initial velocity, v_a); and parameters of the thermopressor (the geometry of the flow path is the taper angle of the confuser, α_c; diffuser, β_d; the evaporation chamber diameter, D_ch; the length, L_tp; and the relative length of the main elements, l_tp, and cross-sectional area of the thermopressor flow part F) (Figure 2).

Based on the solution of the differential equations system of flow thermodynamics [35,46,47], equations of the flow velocity, pressure, density and temperature of the flow were obtained under the combined effect of consumption and heat factors.

Equation of mass balance:

$${\mathrm{G}}_{\mathrm{a}}+{\mathrm{G}}_{\mathrm{w}}=\mathrm{G},$$

(1)

where G_a is the air mass flow rate, G_w is the injected liquid mass flow rate and G is the resulting mixture mass flow rate.

Equation for the flow velocity [48]:

$$\left({\mathrm{Ma}}^2-1\right)\frac{\mathrm{d}\mathrm{v}}{\mathrm{v}}=-\left[1-\left(1+\frac{\mathrm{k}-1}{2}{\mathrm{Ma}}^2\right)\mathsf{\sigma }\right]\frac{\mathrm{dG}}{\mathrm{G}},$$

(2)

where Ma is the Mach number:

$$\mathrm{Ma}=\frac{\mathrm{v}}{{\mathrm{a}}_{\mathrm{s}}},$$

(3)

where k is the adiabatic coefficient, v is the flow velocity and a_s is the sound velocity.

The thermopressor criterion characteristic:

$$\mathsf{\sigma }=\left|\frac{\mathrm{d}{\mathrm{T}}_0}{{\mathrm{T}}_0}\times \frac{\mathrm{G}}{\mathrm{d}\mathrm{G}}\right|=\frac{\Delta {\mathrm{I}}_{0\mathrm{w}}}{{\mathrm{c}}_{\mathrm{p}}{\mathrm{T}}_0},$$

(4)

where ΔI_0w is the difference in the total enthalpies of liquid and vapor at the temperature and velocity of their movement, c_p is the heat capacity at constant pressure and T₀ is the flow stagnation temperature.

Equation for the pressure:

$$\left({\mathrm{Ma}}^2-1\right)\frac{\mathrm{d}\mathrm{P}}{\mathrm{P}}={\mathrm{kMa}}^2\left[1-\left(1+\frac{\mathrm{k}-1}{2}{\mathrm{Ma}}^2\right)\mathsf{\sigma }\right]\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}$$

(5)

Equation for the density:

$$\left({\mathrm{Ma}}^2-1\right)\frac{\mathrm{d}\mathsf{\rho }}{\mathsf{\rho }}={\mathrm{Ma}}^2\left(1-\frac{1+\frac{\mathrm{k}-1}{2}{\mathrm{Ma}}^2}{{\mathrm{Ma}}^2}\mathsf{\sigma }\right)\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}},$$

(6)

where ρ is the flow density.

Equation for the temperature:

$$\left({\mathrm{Ma}}^2-1\right)\frac{\mathrm{d}\mathrm{T}}{\mathrm{T}}=-2\left(1+\frac{\mathrm{k}-1}{2}{\mathrm{Ma}}^2\right)\times \left(1-\frac{{\mathrm{kMa}}^2+1}{2}\mathsf{\sigma }\right)\frac{\mathrm{d}\mathrm{T}}{\mathrm{T}},$$

(7)

where T is the flow temperature.

Equations for the air stagnation pressure and density:

$$\frac{\mathrm{d}{\mathrm{P}}_0}{{\mathrm{P}}_0}=\frac{{\mathrm{kMa}}^2}{2}\mathsf{\sigma }\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}=-\frac{{\mathrm{kMa}}^2}{2}\mathsf{\sigma }\frac{\mathrm{d}{\mathrm{T}}_0}{{\mathrm{T}}_0}$$

(8)

and

$$\frac{\mathrm{d}\mathsf{\rho }}{\mathsf{\rho }}=\left(1+\frac{{\mathrm{kMa}}^2}{2}\right)\mathsf{\sigma }\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}=-\left(1+\frac{{\mathrm{kMa}}^2}{2}\right)\mathsf{\sigma }\frac{\mathrm{d}{\mathrm{T}}_0}{{\mathrm{T}}_0}$$

(9)

As a consequence of the law of reversal of influences during contact evaporative cooling of the gas flow, it was found that the main effect is determined only by the thermal effect, which is associated with the heat consumption for the injected liquid evaporation. Therefore, regardless of the criterion value, σ, the parameters of pressure and density grow during the liquid evaporation in a subsonic flow.

The main flow parameters that change as a result of thermo-gas-dynamic compression: P_a, T_a, v_a, G_a, G_w, F, v_w, T_w and δ_w (Figure 2). Basic laws and equations for determining the main flow parameters [49,50]:

• Mass conservation law (continuity equation) for each of the flow components, gas (air) and water;
• Newton’s law of motion (momentum theorem) and the first law of thermodynamics (energy equation) for the flow of liquid and gas;
• Laws of heat transfer, mass transfer and evaporation of droplets;
• Equations of state for a mixture of ideal gases (Gibbs–Dalton law);
• Equations of the laws of gas flow thermodynamics to determine the Mach number, stagnation temperature and pressure of the ideal gas and wet gas (air).

The parameters of the thermopressor working processes change along the flow part, so it is recommended to present them in a differential form.

Continuity equation:

dG_a = 0

(10)

and

$$-\frac{\mathrm{d}{\mathrm{G}}_{\mathrm{w}}}{\mathrm{G}}=\frac{\mathrm{d}{\mathrm{G}}_{\mathrm{a}}}{\mathrm{G}}=\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}=\frac{\mathrm{d}\mathsf{\rho }}{\mathsf{\rho }}+\frac{\mathrm{d}\mathrm{v}}{\mathrm{v}}+\frac{\mathrm{d}\mathrm{F}}{\mathrm{F}}$$

(11)

Momentum conservation equation:

$$\frac{\mathrm{d}\mathrm{P}}{\mathrm{P}}+{\mathrm{kMa}}^2\left(\frac{\mathrm{d}\mathrm{v}}{\mathrm{v}}+\frac{4\Sigma \mathsf{\xi }}{2}\times \frac{\mathrm{d}\mathrm{z}}{{\mathrm{D}}_{\mathrm{ch}}}+\frac{{\mathrm{G}}_{\mathrm{w}}}{\mathrm{G}}\times \frac{\mathrm{d}{\mathrm{v}}_{\mathrm{w}}}{\mathrm{v}}+\left(1-\frac{{\mathrm{v}}_{\mathrm{w}}}{\mathrm{v}}\right)\frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}\right)=0,$$

(12)

where Σξ is the resistance coefficient of the thermopressor flow part surface.

Energy conservation equation:

$$\frac{\mathrm{d}\mathrm{T}}{\mathrm{T}}-\frac{\mathrm{d}\mathrm{q}-\frac{{\mathrm{G}}_{\mathrm{w}}}{\mathrm{G}}\mathrm{d}{\mathrm{I}}_{\mathrm{w}}}{{\mathrm{c}}_{\mathrm{p}}\mathrm{T}}+\left(\frac{{\mathrm{I}}_{\mathrm{w}}^{″}-{\mathrm{I}}_{\mathrm{w}}^{\prime }+\frac{{\mathrm{v}}^2}{2}\left(1-{\frac{{\mathrm{v}}_{\mathrm{w}}}{\mathrm{v}}}^2\right)}{{\mathrm{c}}_{\mathrm{p}}\mathrm{T}}\right)\times \frac{\mathrm{d}\mathrm{G}}{\mathrm{G}}+\left(\mathrm{k}-1\right){\mathrm{Ma}}^2\times \left(\frac{\mathrm{d}\mathrm{v}}{\mathrm{v}}+\frac{{\mathrm{G}}_{\mathrm{w}}}{\mathrm{G}}\cdot \frac{{\mathrm{v}}_{\mathrm{w}}}{\mathrm{v}}\cdot \frac{\mathrm{d}{\mathrm{v}}_{\mathrm{w}}}{\mathrm{v}}\right)=0$$

(13)

where q is the heat amount that is removed during the drop evaporation in an air flow, I′_w is the water enthalpy, I″_w is the steam enthalpy and T is the flow temperature.

By combining the above Equations (2)–(9), we can calculate the behavior of the flow [1,35] (change in Mach number, Ma; total gas-flow pressure, dP/P; gas-flow temperature, dT/T; gas flow inhibition temperature, dT₀/T₀; droplet diameter in gas flow, δ_w; and gas-flow inhibition pressure, dP₀/P₀) under different influences on the local section, dz: cross-sectional area of the thermopressor flow part dF/F, friction against the wall of the flow part ΔPfr, and flow rate and droplets (acceleration) dv, dv_w.

In the case of liquid injection into the air flow at equal air velocities and injected water, the difference between the total water enthalpies and steam, after bringing it to the same temperature and velocity with the air, is approximately equal to the vaporization heat, r:

$$\Delta {\mathrm{I}}_{0\mathrm{w}}={\mathrm{I}}_{\mathrm{w}}^{″}-{\mathrm{I}}_{\mathrm{w}}^{\prime }\approx \mathrm{r}$$

(14)

Hence, it follows that the thermopressor criterion characteristic is calculated as follows:

$$\mathsf{\sigma }\approx \frac{\mathrm{r}}{{\mathrm{c}}_{\mathrm{p}}{\mathrm{T}}_0}$$

(15)

By solving Equation (9), we obtain the following:

$$\frac{\mathrm{d}{\mathrm{P}}_0}{\mathrm{P}}=-\frac{{\mathrm{kMa}}^2}{2}\mathsf{\sigma }\frac{\mathrm{d}{\mathrm{T}}_0}{{\mathrm{T}}_0}$$

(16)

By solving Equation (16), using the quadrature method, we obtain the following:

$${\displaystyle \int \frac{\mathrm{d}{\mathrm{P}}_0}{{\mathrm{P}}_0}}=-\frac{{\mathrm{kMa}}^2}{2}\mathsf{\sigma }{\displaystyle \int \frac{\mathrm{d}{\mathrm{T}}_0}{{\mathrm{T}}_0}}$$

(17)

By solving this equation, the equation for an ideal thermopressor is determined, i.e., without taking into account the friction forces:

$$\frac{{\mathrm{P}}_{02}}{{\mathrm{P}}_{01}}={\left(\frac{{\mathrm{T}}_{02}}{{\mathrm{T}}_{01}}\right)}^{-\frac{{\mathrm{kMa}}^2}{2}\mathsf{\sigma }},$$

(18)

where T₀₁ and T₀₂ are the stagnation flow temperature in the inlet and outlet thermopressor; P₀₁ and P₀₂ are the stagnation flow pressure in the inlet and outlet thermopressor.

The mathematical model must take into account the presence of two-phase flow in the thermopressor evaporating chamber. To determine the speed of sound in a two-phase medium, the equation for water and steam is used [37,48]:

$${\mathrm{a}}_{\mathrm{s}}=\sqrt{\frac{1}{\mathrm{x}\left(1+\frac{\left(1-\mathrm{x}\right){\mathrm{v}}_{\mathrm{w}}}{\mathrm{x}{\mathrm{v}}_{\mathrm{w}}}\right)}\times \mathrm{k}\frac{\mathrm{p}}{\mathsf{\rho }}},$$

(19)

where x is the degree of dryness for the evaporation chamber inlet:

$$\mathrm{x}=\frac{{\mathrm{G}}_{\mathrm{a}}}{{\mathrm{G}}_{\mathrm{a}}+{\mathrm{G}}_{\mathrm{w}}},$$

(20)

To determine the friction pressure loss, we must determine the total hydraulic resistance in the thermopressor flow part:

$$\Delta {\mathrm{P}}_{\mathrm{loss}}=\Delta {\mathrm{P}}_{\mathrm{loc}}+\Delta {\mathrm{P}}_{\mathrm{fr}}+\Delta {\mathrm{P}}_{\mathrm{w}}=\left({\mathsf{\xi }}_{\mathrm{loc}}+\Sigma \mathsf{\xi }\frac{{\mathrm{L}}_{\mathrm{tp}}}{{\mathrm{D}}_{\mathrm{ch}}}+{\mathsf{\xi }}_{\mathrm{w}}\right)\frac{\mathsf{\rho }{\mathrm{v}}^2}{2},$$

(21)

where ΔP_loc is the thermopressor local resistance, ΔP_fr is the friction resistance; ΔP_w is the hydraulic resistance of liquid droplets and L_tp/D_ch is the relative length (caliber) of the evaporation chamber.

The local resistance coefficient depends on the geometric parameters of the thermopressor elements—confuser and diffuser:

$${\mathsf{\xi }}_{\mathrm{loc}}={\mathsf{\xi }}_{\mathrm{loc}.\mathrm{d}}+{\mathsf{\xi }}_{\mathrm{loc}.\mathrm{c}},$$

(22)

where ξ_loc.d is the diffuser local resistance coefficient, and ξ_loc.c is the confuser local resistance coefficient.

The local coefficient of confuser resistance is determined by the following formula [37,44]:

$${\mathsf{\xi }}_{\mathrm{loc}.\mathrm{c}}=\left(\frac{{\mathsf{\lambda }}_{\mathrm{c}1}}{8sin\frac{\mathsf{\alpha }}{2}}\right)\times \left(1-\left(\frac{{\mathrm{d}}_{\mathrm{ch}}^4}{{\mathrm{d}}_{\mathrm{c}}^4}\right)\right),$$

(23)

where λ_c1 is the average value of the hydraulic resistance coefficients at the beginning (λ₁) and at the end (λ₂) of the confuser (λ_c1 = (λ₁ + λ₂)/2); α is the angle of conicity, ° (accepted α = 40°); d_c is the confuser diameter, m; and d_ch is the evaporation chamber diameter, m.

Local coefficient of diffuser resistance [37,44]:

$${\mathsf{\xi }}_{\mathrm{loc}.\mathrm{d}}=\left(\frac{{\mathsf{\lambda }}_{\mathrm{c}2}}{8sin\frac{\mathsf{\beta }}{2}}\right)\times \left(1-\left(\frac{{\mathrm{d}}_{\mathrm{ch}}^4}{{\mathrm{d}}_{\mathrm{d}}^4}\right)\right)+sin\mathsf{\beta }\times {\left(1-\left(\frac{{\mathrm{d}}_{\mathrm{ch}}^2}{{\mathrm{d}}_{\mathrm{d}}^2}\right)\right)}^2,$$

(24)

where λ_c2 is the average value of the hydraulic resistance coefficients at the beginning λ₁ and at the end λ₂ of the diffuser; β is the angle of conicity, ° (accepted β = 10°); and d_d is the diffuser diameter, m.

It is also necessary to take into account the hydraulic resistance coefficient of liquid droplets injected into the flow, ξ_w (the flowing part section of the thermopressor, which corresponds to mode I (Figure 1)—acceleration or deceleration of the drop—depending on the initial speed at the exit of the nozzle):

$${\mathsf{\xi }}_{\mathrm{w}}=\left(\frac{16}{\mathrm{Re}}+\frac{2.2}{{\mathrm{Re}}^{0.5}}+0.32\right)\times \left(\frac{1.5{\mathsf{\mu }}_{\mathrm{w}}+{\mathsf{\mu }}_{\mathrm{a}}}{{\mathsf{\mu }}_{\mathrm{w}}+{\mathsf{\mu }}_{\mathrm{a}}}\right),$$

(25)

where Re is the Reynolds number for a flow, μ_w is the fluid dynamic viscosity coefficient and μ_a is the dynamic viscosity coefficient for air.

To assess the efficiency of the thermopressor used, we need to calculate the degree of pressure increase:

$${\mathsf{\epsilon }}_{\mathrm{tp}}=\frac{{\mathrm{P}}_{\mathrm{tp}2}}{{\mathrm{P}}_{\mathrm{tp}1}}$$

(26)

The value of the drop aerodynamic resistance largely depends on the drop diameter. The recommended droplet diameter should be less than 50 μm. In this case, the smaller the drop diameter, the lower the aerodynamic drag on mode I and II. Hence, the degree of pressure increase in the thermopressor will be larger.

Today there are a models number and analytical solutions that describe the processes of liquid outflow (including superheated) and its evaporation. A relatively accurate model is a model that considers the work processes associated with the complex (ensemble) of bubbles in conditions of thermodynamic instability [51].

Furthermore, in the model, it is assumed that the number of bubbles is constant throughout the process. The coagulation processes and crushing of bubbles are excluded. The size, kinematic and thermophysical characteristics of the bubbles are the same. The velocity and pressure fields near each bubble are symmetric.

The efficiency of spraying liquid (water) by the nozzle is determined by the maximum and average drop diameter, the angle and length of the stable spray torch.

The size droplets distribution is determined by the spray spectrum (dispersion). This spectrum is usually determined by the normal distribution law. In the study of injection systems for low-viscosity liquids, the effective droplets’ diameters in the flow were determined [35], and they are equal to about 10 μm (30% of the total number of droplets). Such diameters can be obtained for mechanical (hydrodynamic) injectors at fluid pressures greater than 2–3 MPa.

However, it should be noted that the use of such a model has few problems that can be solved in experimental researches. One of the problems is the large droplets’ evaporation in the flow and their distribution. The use of the model without the drop evaporation kinetics in this case is correct. This is primarily due to the fact that in experimental research, special nozzles of fine spray type “Fog” were used, which provide a dispersion of 10–20 microns. Liquid injection, acceleration and distribution of droplets in the flow are carried out in the receiving chamber. The flow enters the evaporation chamber already prepared. Therefore, we can assume that the dispersed flow consists of very small droplets, which are distributed in the flow evenly at equal distances from each other.

The next step after the working processes of the thermopressor cooling system calculation is to define the working operation characteristics (depending on the type of power plant engine): power, N_e (changes in power ΔN_e); efficiency, η_e (changes in efficiency Δη_e); specific fuel consumption, g_e (changes in specific fuel consumption Δg_e); and others. Depending on the type of power plant, as well as the schematic design with the use of the thermopressor cooling system, the next step in mathematical model calculating is to calculate the parameters and characteristics of heat exchange, electric power and utilization equipment.

A software package that was developed by References [25,36] allows us to calculate the characteristics of equipment or systems and circuit design solutions when used as part of a power plant: an electric generator (based on an internal combustion engine), heat-using refrigeration machines (ejector refrigeration machine and absorption refrigeration machine), a turbine generator or steam generator as part of a trigeneration unit (stationary units) or as part of a turbo-compound unit (power plants of sea vessels), a recovery boiler of one or two pressures and propulsion complex of a ship power plant. Simulation of the thermopressor cooling system operation makes it possible to reveal the efficiency of using such a system as part of a power plant and compare it with traditional methods of cooling and humidifying air (gas).

3. Validation of Thermopressor Model

For the verification of the mathematical model, an experimental setup was developed to determine the performance characteristics of the thermopressor under conditions of contact cooling of the marine diesel engine charge air (Figure 3) [25].

The experimental thermopressor consists of the following elements (Figure 4): a receiving chamber with a nozzle and system for injecting water into the flow, a confuser, an evaporation chamber, a diffuser, nozzles for installing temperature and pressure sensors. All elements of the thermopressor are removable and allowed us to carry out studies for the different geometric characteristics (

Table 1. Geometrical characteristics of the experimental thermopressor.

Parameter	Value
Receiving chamber	Value
Confuser	Diameter D1 = 65 mm; length L1 = 200 mm
Evaporation chamber	Inlet diameter Dc1 = 65 mm; outlet diameter Dc2 = 25 mm; length Lc = 34 mm; convergent angle α = 30°
Diffuser	Diameter Dch = 25 mm; length Lch = 125; 175 mm (relative length lch = 5; 7)
Nozzle	Inlet diameter Dd1 = 25 mm; outlet diameter Dd2 = 65 mm; length Lch = 192 mm; divergent angle β = 6°

).

An information measuring system was developed for the given experimental setup. This system allows for measurements of pressure, temperature and flow rate with simultaneous automatic recording of data into an electronic protocol. The data were recorded by the system at 1.0 s intervals. To determine each operating point, characterizing a certain operating mode of the thermopressor, 10 measurements were carried out. To collect and organize the exchange of information, a PI485/USB RS485 communication interface converter was used. The information received from the measuring system (Figure 5) was transmitted directly to the computer and processed by using the licensed SSD 3.5 software from RegMik. The discharge pressure of the air flow was measured by a pressure-measuring sensor—model A-10, manufactured by Wika, Germany. A ceramic pressure sensor was used as a sensing element. The measurement range was 0–600 kPa.

4. Analysis of Thermopressor Operation

Analyzing the obtained data of mathematical modeling of thermopressor working, the maxima of pressure increase were revealed as a result of the effect of thermogasdynamic compression. With a decrease in the droplet diameter to 3 μm, the maximum pressure value increases that is, the evaporation process proceeds more intensively, occupying a smaller section of the working chamber. The evaporation efficiency increases with an increase in the total surface droplets area.

Depending on the initial parameters (air temperature, Mach number at the evaporation chamber inlet and droplet diameter) (Figure 6 and Figure 7), at Ma = 0.50, the pressure increase is ΔP_tp = 3.0–6.0% (7–17 kPa); at Ma = 0.60, the pressure increase is ΔP_tp = 4.0–8.5% (11–25 kPa); and at Ma = 0.74, the pressure increase is ΔP_tp = 7.0–12.5% (20–40 kPa). It can also be seen that, with an increase in the initial air temperature, the relative increase in total pressure increases.

The nature of the absolute pressure distribution along the length of the chamber for different initial droplet diameters has the same tendency. The larger the droplet diameter, the less the effect of thermo-gas-dynamic compression, which is associated with an increase in the aerodynamic drag of droplets and a decrease in the intensity of evaporation. However, with an increase in the initial air temperature, the diameter of the droplet increases accordingly, with the possibility of obtaining a positive effect from thermo-gas-dynamic compression.

The nature of the relative and absolute temperature distribution of humidified air values is illustrated in the following charts (Figure 8). The temperature decrease occurs more slowly at the initial temperature, T_tp1 = 500 K, and the relative temperature has lower indices, T_tp1/T_tp2 = 1.465–1.472 (Figure 8a). However, with an increase in the initial temperature to T_tp1 = 550 K, the value of the relative temperature is aligned along the evaporation chamber length (T_tp1/T_tp2 = 1.595–1.603 (Figure 8b).

Depending on the initial parameters (air temperature, Mach number at the evaporation chamber inlet and droplet diameter), the humidified air temperature at the evaporation chamber outlet decreases: at T_tp1 = 500 K, it decreases by ΔT_tp = 160–165 K; at T_tp1 = 550 K, by ΔT_tp = 207–212 K.

The amount of water injected into the air flow (Figure 9) does not exceed 10%, and, accordingly, the amount of water required for complete evaporation at the initial temperature, T_tp1 = 500 K, is the relative water amount, g_w = 5.40–5.47 %; at T_tp1 = 550 K—g_w = 6.55–6.60%.

For effective heat transfer between phases, it is necessary to maintain the maximum value of the relative temperature at the outlet of the thermopressor. That is, at the beginning of the process of spraying water for more intense evaporation, the Mach number should reach the maximum values for a subsonic flow Ma = 0.95. However, the increase in Mach numbers continues in the process of liquid evaporation, which is associated with an increase in the vapor-air flow density. This fact should be taken into account when designing the thermopressor flow paths to prevent the flow from going to supersonic speeds. For the investigated evaporation chamber at the initial air flow temperature T_tp1 = 500 K, the Mach number increases by 11% and reaches the value of Ma = 0.85–0.92; at T_tp1 = 550 K, the Mach number increases by 12% and reaches the value of Ma = 0.71–0.83.

The main characteristics of the water evaporation process in the low-flow thermopressor working chamber (G_a = 1.0–1.5 kg/s), as obtained by mathematical modeling (Ma = 0.50), are illustrated in the following charts (Figure 10). It can be seen that, in the presence of incomplete evaporation, it is possible to provide a droplet diameter of less than δ_w = 20 μm at the thermopressor outlet.

It should be noted that, with an initial droplet diameter of more than 20–30 microns, the achievement of a positive effect from thermo-gas-dynamic compression is possible only at high initial temperatures above T_tp1 = 450 K (177 °C), which is possible when cooling the air between gas turbine compressor stages or behind the ICE compressor; in addition, such conditions must correspond to the modes in the exhaust gas systems of gas turbine and internal combustion engines.

The further development of the method designing consists in rational distribution of the overall design refrigeration capacity between two ranges. The ambient air processing is considered as a two-stage one and includes a fluctuation range as the high-temperature and stable range as the low-temperature stage.

A diagram with the use of the thermopressor as a charge air cooler (CAC) for a turbocharger of a low-speed internal combustion engine with a waste-gas-heat-recovery system in a waste-heat-recovery boiler of the same pressure is shown in Figure 11. The efficiency analysis was carried out in relation to the standard traditional scheme of charge air cooling of a ship’s internal combustion engines. The calculations were performed for a low-speed main engine, 5S50MC-C (MAN B&W) (N_e = 8300 kW, n = 105 rpm). The calculation of the thermopressor parameters is carried out taking into account its joint work with the turbocharger.

The increase in pressure in the thermopressor, ΔP_tp, significantly depends on the value of the temperature decrease during cooling, T_tp. The temperature at the thermopressor inlet corresponds to the air temperature at the discharge of the turbocharger. In the scheme with one-stage compression, the temperature at the thermopressor inlet is T_c2 = 190–270 °C (Figure 12). The higher the temperature at the suction temperature and the degree of pressure increase in the TC ε_c, the higher the temperature according to the turbocharger. Since a thermopressor cooling system, in fact, is a two-stage air compression (the first degree is TC, the second degree is a thermopressor), then the degree of pressure increase ε_c will be lower (Figure 12); therefore, T_c2 = T_c2′ = 170–250 °C. Then the temperature in front of the thermopressor decreases and, accordingly, the degree of pressure increase ε_tp will be lower.

For a system with total ε_c.tp = 4.25, the decrease in compression work is Δl_c = 10–13 kJ/kg; at ε_c.tp = 4.00, the decrease in compression work is Δl_c = 9.0–12.5 kJ/kg; and at ε_c.tp = 3.85, the decrease in compression work is Δl_c = 8.5–12.0 kJ/kg (Figure 13a,b). A decrease in work l_c allows, at the same, air-flow rates on the internal combustion engine to reduce the compressor power by ΔN_c = 100–200 kW (10.0–11.5%) (Figure 13b).

At the minimum temperature at the thermopressor outlet, t_tp2, the temperature was taken to be 2–3 °C higher than the dew point temperature. It was taken into account that water injection continues in the thermopressor until the air is completely saturated, that is, φ = 100%. The decrease in the air temperature is Δt_tp = 110–160 °C, which makes it possible to increase the air pressure by ΔP_tp′ = 520–670 kPa (15–18%) (Figure 14 and Figure 15) with “ideal” compression (without taking into account losses friction against the channel walls), and ΔP_tp = 340–480 kPa (10–13%) is the actual compression in the thermopressor (Figure 15 and Figure 16). In this case, the degree of the air temperature decrease in the thermopressor will be T_tp1/T_tp2 = 1.30–1.45 (Figure 16). The thermopressor uses as a second stage of compression in the pressurization system, and therefore it is appropriate to evaluate its efficiency by the degree of pressure increase, ε_tp = 1.10–1.13.

A check was carried out for the adequacy of the theoretical calculated data of the pressure degree increasing in the thermopressor obtained during the simulation. The degree of discrepancy with the experimental data shows from +7% to −6% (Figure 17), which can be considered satisfactory.

The obtained result of experimental data comparison and calculated data makes it possible to state that the mathematical model is effective and can be used for the analysis of thermopressor circuits.

5. Analysis of Thermocompressor Application for Exemplary Internal Combustion Engine

The next analysis of the results shows the following. A decrease in the air temperature and an increase in pressure (Figure 15) in the thermopressor are quite significant, which, accordingly, affects the decrease in the flow rate in the TC; as a result, the temperature of the exhaust gases through the utilization turbine (UT) increases (Figure 18). Thus, at a constant temperature of gases at the inlet to the UT (T_g1 = 300–400 °C), the temperature of the exhaust gases will be T_g2 = 205–285 °C, and when using the scheme with TP—T′_g2 = 220–300 °C, which is 15 °C higher than for the basic scheme.

Our comparison of the thermopressor from the point of view of a heat exchanger (charge air cooler) with a stationary air cooler shows that the thermal load on the thermopressor is Q_tp = 1600–3700 kW. However, the air temperature at the discharge of the thermopressor (Figure 19) is still high (t_tp = 65–85 °C). Therefore, it is advisable to install an additional charge air cooler behind the thermopressor. The heat load on such a CAC is Q_cac2 = 200–1200 kW; hence, the total heat load on the TP and the additional CAC will be Q_tot = 2000–4800 kW (Figure 20), which is less than for the standard charge-air-cooling system Q_cac = 2400–5200 kW (more by 7–15%). The lower thermal load in the proposed scheme can be explained by the fact that the air temperature at the TC when working together with the TP is 20–25 °C lower.

It would be appropriate to evaluate the thermopressor efficiency by taking into account the energy consumption for the supply of fresh water for injection into the thermopressor (Figure 21). According to calculations, the water consumption for injection is G_w = 0.6–1.2 kg/s (2.2–4.3 m³/h), while the water pump power is N_w = 0.3–0.7 kW. The moisture content of the air increases by Δd_tp = 40–60 g/kg. Consequently, the power of the injection pump is rather small (0.3–0.5%) in comparison with the decrease in the compressor power ΔN_c = 100–200 kW.

The use of the thermopressor leads to a decrease in the TC power, and then the unnecessary heat drop (work) of the TC turbine decreases; the required turbine power and the required gas flow rate also decrease. Hence, it is appropriate to pass (bypass) the excess amount of gas past the turbine, due to which the exhaust gases temperature is increases. The gases’ thermal potential is increased, so they can be used in a waste heat recovery boiler. Thus, the temperature at the recovery boiler inlet increases by almost ΔT_rb = 10–15 °C (Figure 22), taking into account that the temperature gases at the recovery boiler outlet is constant and equal to T_rb2 = 160 °C. The additional heat load (with the corresponding additional consumption steam) is ΔQ_rb = 150–300 kW (10–15%).

As shown by the thermal scheme calculations, the amount of steam produced in the recovery boiler is more than enough for needs of this dry cargo ship. Therefore, it is advisable to use the obtained additional steam to drive a utilization turbine generator (UTG), thereby reducing the load on the ship’s power plant, with a corresponding decrease in fuel consumption for diesel generators.

A scheme of a thermopressor charge-air-cooling system with a comprehensive utilization of the exhaust gases heat in the recovery boiler with two circuits of high and low pressure and UTG is shown in Figure 23.

An analysis of the UTG operation was carried out (Figure 24 and Figure 25); it can be seen that an increase in the thermal power in the recovery boiler of two pressures allows an increase in steam production by ΔD_utg = 0.07–0.12 kg/s (250–430 kg/h), which, in turn, increases the power of the UTG by ΔN_utg = 45–90 kW.

It was proposed to install two MAN B&W 7L16/24 diesel generators on the ship with a rated power N_e = 770 kW and a specific fuel consumption g_e = 195 g/(kW∙h). Reducing the load on the ship power plant when the UTG is used (Figure 26) reduces the specific fuel consumption up to Δg_e = 4–7 g/(kW∙h), while temporarily reducing the fuel consumption ΔG_e = 10–18 kg/h (240– 430 kg/day). The analysis of economic feasibility shows that the reduction in fuel consumption per voyage within 28 days will be ΔG_e.v = 7–12 tons. Taking into account the annual operation of the vessel, the reduction in fuel consumption per year will be ΔG_e.y = 90–150 tons (Figure 27).

6. Conclusions

Circuit solutions to use the thermopressor technologies for charge air cooling of engines were studied and analyzed. We determined that the load reduction on the ship power plant with a corresponding reduction in the fuel consumption of diesel generators is 2–3%. This was achieved by using the thermopressor as a boost stage (second compression ratio in the supercharging system) after the turbocharger, resulting in a reduction of a basic turbocharger compression work by 10 to 12% and increase of engine power output accordingly. Reducing the load on the ship power plant when the utilization turbine generator is used reduces the specific fuel consumption on 4 to 7 g/(kW∙h).

With an initial droplet diameter of more than 20–30 μm and Mach number of Ma = 0.50, the achievement of a positive effect from thermo-gas-dynamic compression is possible only at high initial temperatures above T_tp1 = 450 K (177 °C). In this case, the increase in charge air pressure reaches 12%.

The branches of the predominant application of thermopressor technologies include plants of stationary and marine power energy based on internal combustion engines and gas turbine engines. The use of thermopressor technologies provides a significant reduction in fuel consumption.

Directions for future research in this area are as follows: the research of droplet evaporation thermophysical processes in the working chamber of a thermopressor, and the thermopressor research under the condition of incomplete evaporation of water in the flow path.