Investigation of Thermopressor with Incomplete Evaporation for Gas Turbine Intercooling Systems

Abstract

One of the promising ways to increase fuel and modern gas turbine energy efficiency is using cyclic air intercooling between the stages of high- and low-pressure compressors. For intercooling, it is possible to use cooling in the surface heat exchanger and the contact method when water is injected into the compressor air path. In the presented research on the cooling contact method, it is proposed to use a thermopressor that implements the thermo-gas-dynamic compression process, i.e., increasing the airflow pressure by evaporation of the injected liquid in the flow, which moves at near-sonic speed. The thermopressor is a multifunctional contact heat exchanger when using this air-cooling method. This provides efficient high-dispersion liquid spraying after isotherming in the high-pressure compressor, increasing the pressure and decreasing the air temperature in front of the high-pressure compressor, reducing the work on compression. Drops of water injected into the air stream in the thermopressor can significantly affect its characteristics. An increase in the amount of water increases the aerodynamic resistance of the droplets in the stream. Hence, the pressure in the flow parts of the thermopressor can significantly decrease. Therefore, the study aims to experimentally determine the optimal amount of water for water injection in the thermopressor while ensuring a positive increase in the total pressure in the thermopressor under conditions of incomplete evaporation. The experimental results of the low-consumption thermopressor (air consumption up to 0.52 kg/s) characteristics with incomplete liquid evaporation in the flowing part are presented. The research found that the relative water amount to ensure incomplete evaporation in the thermopressor flow part is from 4 to 10% (0.0175–0.0487 kg/s), without significant pressure loss due to the resistance of the dispersed flow. The relative increase in airflow pressure is from 1.01 to 1.03 (5–10 kPa). Based on experimental data, empirical equations were obtained for calculating the relative pressure increase in the thermopressor with evaporation chamber diameters of up to 50 mm (relative flow path length is from 3 to 10 and Mach number is from 0.3 to 0.8).

1. Introduction

Currently, the world’s leading industrial companies are developing new-generation engines. Such engines should have low environmental penalties and high fuel efficiency. A promising direction in achieving low environmental penalties is using new types of fuels [1] and fuel emulsions [2].

Greening of heat engines contradicts their energy efficiency because measures to reduce emissions require additional external energy costs. The peculiarities of the formation of nitrogen oxides, NOx, require the need to reduce the maximum fuel combustion temperature, but on the other hand, reducing this temperature reduces the fuel-energy efficiency of the engine [3,4,5]. Therefore, it is urgent to develop environmentally friendly and energy-efficient technologies that would ensure the reduction in emissions and, at the same time, eliminate the negative impact on the fuel and energy efficiency of the engine [6,7].

The low fuel efficiency of power plants based on existing internal combustion engines and gas turbines is due to the significant waste heat amounts, which exceed half the primary fuel heat [8,9]. Waste heat utilization in most power plants is limited to using waste gas heat for heat production in steam boilers, which is seasonal [10,11]. The high cost of replacing existing power plants with modern steam and gas turbines is challenging [12,13]. In addition, the modern power plant’s efficiency depends on climatic conditions and decreases significantly with increasing ambient temperature: every 10 °C increase in air temperature at the engine’s inlet causes an increase in fuel consumption from 0.5 to 0.7% [14,15]. Therefore, the obvious way forward is using energy-saving technologies to ensure low-potential waste heat utilization [16,17] and compensate for the rising ambient air temperature’s negative impact on the power plant’s fuel efficiency [18,19].

One of the effective ways to improve modern gas turbine energy efficiency is to use intercooling cycle air [20,21]. Such cooling is carried out between low- and high-pressure compressors [22,23]. Intercooling can be carried out using two methods [24,25]: a surface cooler (plate or tubular-plate heat exchanger) or contact cooling due to injected water evaporation. The use of surface heat exchangers is accompanied by significant aerodynamic losses [26,27]. It is simpler and more effective to use water injection into the high-pressure compressor air part [28,29]. Special high-pressure nozzles are most commonly used for water injection, but many problems exist, in particular the drops’ separation of injected water on the blades and the compressor housing [30]. Therefore, modern injection methods and preparation of the dispersed flow should provide an average droplet diameter of less than 20 to 25 μm [31].

One of the promising directions is the use of a thermopressor for cooling cycle air [29,32]. The thermopressor implements a thermo-gas-dynamic compression effect to increase the pressure during cooling in the high-dispersed liquid evaporation process, which is injected into the transonic gas flow [33].

It is necessary to use incomplete water evaporation in the thermopressor flowing part for the preparation of highly dispersed and homogeneous spraying of water [34]. When providing effective highly dispersed liquid sprays with less than 20–25 μm droplet size, there is more efficient compression process isotherming in the high-pressure compressor. Compensation for aerodynamic losses in the compressor air path and reducing the work on compression in the compressor stages is provided by increasing the pressure in the thermopressor while increasing the working fluid consumption and, consequently, increasing efficiency with decreasing specific fuel consumption [35].

However, the efficient technology-based development of the thermopressor is constrained by sufficient data from experimental tests as a cooling system part.

2. Literature Review

The main goal of developing water injection technologies in the compressor is to reduce air compression work [36,37]. In this case, the changing character and the influence of climatic and hydrometeorological conditions should be considered [38,39]. One of the first developments in this area is the Brown Boveri water injection system for gas turbine plants (1968) [40]. An exciting direction is water injection after the gas turbine compressor stage, effectively implemented in systems such as the Humidified Advanced Turbine or Humidified Air Turbine (HAT) [28]. Further developments of technologies for water injection were based on multi-stage air compression and gas expansion—Cascaded Humidified Advanced Turbine (CHAT) [41].

For an experimental two-shaft gas turbine plant AGTJ-100A, experimental studies of the contact intercooling characteristics were carried out (Japan, 1984). The relative humidity in the wind was 90% after evaporative cooling.

A promising two-stage compression technology with contact intercooling of cycling air (SPRINT) was developed by General Electric (Boston, MA, USA). Developments in this field began long ago. General Electric successfully uses the patented SPRINT technology, which provides intercooling of the working fluid by injecting dispersed water between compressors of the low- and high-pressure gas turbine LM6000 PC, one of the most popular conversion gas turbines in the range from 40 to 50 MW [42]. SPRINT technology makes it possible to increase the total gas turbine plant capacity by 8%. At the same time, the effective efficiency was 32% at an inlet air temperature of 32 °C [43]. To improve the capacity produced for hot summer days, Hitachi Ltd. (Ibaraki, Japan) developed a special water injection system for the compressor flow part (“Water Atomization Cooling”). The WAC system increases the gas turbine engine capacity by cooling the compressor air from 5 to 10%. Other advantages include reducing the exhaust gases’ nitrogen oxide concentrations and cleaning the compressor blade’s surface. The water amount supplied does not exceed 1% of the working fluid mass flow rate through the compressor.

In real conditions, effective intercooling achievement is associated with the need to solve a number of engineering problems due to the presence of the negative factors associated with the water injection into the compressor air duct [44]:

(1)

Providing highly dispersed and homogeneous injected water sprays [37,45].

(2)

Injected water drop separation on the blades and the compressor casing and related possible complications in its operation [46,47]. Due to insufficiently efficient spraying of the injected water, already in the compressor’s first stages (according to the injection area) there is an intensive drop separation on the working blades with the liquid layer formation. Moving layers are torn from the edges of the blades, resulting in the formation of so-called secondary drops, which are separated on the compressor housing [48].

(3)

Providing sufficient intensity of injected water evaporation and cooling the compressed airflow [49]. Several times less moisture evaporates from the surface of the droplets in the airflow (the evaporation share from the surface of the droplets is usually less than 20%) than from the liquid layer surface on the blades and compressor housing [50].

(4)

Mechanical losses due to the drop acceleration of the flow and rotating blades’ deceleration of the impellers drop by their repeated deposition and surface failure of the blades and housing, as well as friction, liquid layer on the blades’ surface, and compressor housing [22,51]. As a result, the stage’s internal efficiency and the compressor are reduced [52].

(5)

Blade surface protection from drop erosion when injected water collides with them [49,53].

An effective way to prevent the droplet’s separation on the blade’s surface is the implementation of an injected liquid highly dispersed spray, in which the droplets can move in the airflow to flow around the blades without colliding with them. During the liquid droplets’ evaporation of dispersed flow, the heat transfer intensity increases with a decrease in the average droplet diameter to 3 μm. This determines the compression process efficiency. This requires the implemented injection technologies to provide a highly dispersed spray of injected water in mist form [54,55].

Another effective spraying method for a highly dispersed flow is using a liquid that is superheated relative to the saturation temperature. At the same time, the spray efficiency is ensured by the instantaneous evaporation process and, as a result, the liquid droplet’s effective crushing [51,56].

Several leading modern companies (Bete Fog Nozzle (Greenfield, MA, USA), Spraying Systems Co. (Wheaton, IL, USA), and Amfog Nozzle Technology (Scottsdale, AZ, USA)) have proposed their developments to solve the problem of efficient liquid spraying. Still, the most interesting development belongs to Mee Industries Inc. (Irwindale, CA, USA). The proposed technology uses impact-type nozzles with a high-pressure water supply and provides a dispersion of less than 30 μm, which increases the gas turbine efficiency by 2% [57,58].

Another relevant concept is the use of technologies based on TOPHAT (Alpha Power Systems, Tampa, FL, USA). Its essence is to inject water superheated relative to the saturation temperature at the compressor inlet through centrifugal nozzles. When this water outflows the nozzle duct, its pressure drops sharply, and explosive boiling occurs in the volume of the formed drops, which are crushed into smaller drops [59]. The efficiency analysis and gas turbine-specific power show that the TOPHAT cycle has significantly higher efficiency (57.4%) and specific power (430 kW/kg) compared to simple cycles. In 2001, this technology was first used at a power plant in the Netherlands and is currently being implemented in many gas turbine energy systems [60].

The most intensive droplet evaporation process occurs directly in the sprayed water fluent [36]. In particular, it is known that in the first second, a drop having an initial diameter of 14 μm has time to decrease to a size less than 5 μm. In addition, in experimental studies, it was found that if the droplet diameter does not exceed 10 μm, the centrifugal energy effect on the droplet is nearly negligible, and the droplets move in the direction of the airflow. The installed nozzles of the “wet compression” system form droplets with a diameter not more than 20 to 25 μm at the inlet to the compressor [54,56].

The considered analysis of the technologies of cyclic air intercooling of gas turbines proves the practicality of these systems and can be used for the increase in operational characteristics and the reliability of gas turbine engine work.

Other researchers previously conducted studies of thermopressor characteristics under incomplete evaporation conditions in the flow part. Still, they did not aim to use the thermopressor to organize and prepare a highly dispersed stream. Such research has shown that there are optimal values of the injected water amount to ensure the maximum increase of pressure during incomplete evaporation. The experimental research results of the thermopressor characteristics are shown in [34] and are presented in Figure 1. Data are grouped relative to the relative water injected amount, g_w, at different Ma numbers and different initial temperatures. It can be seen that at the cost of g_w > 15%, a decrease in the total pressure increase is observed, and the largest increase in pressure corresponds to when g_w is 15 to 25% and ε_tp is 1.00 to 1.01.

Accordingly, we have formulated the following hypotheses:

(1)

Cyclic air intercooling the gas turbine by a thermopressor provides an increase in power by increasing the working fluid mass flow rate, increasing efficiency and reducing fuel consumption by reducing the compressed air temperature, and, consequently, reducing the compression power cost.

(2)

Intercooling of the gas turbine cycle air by a thermopressor provides increased power due to more efficient liquid spraying in the thermopressor itself by providing incomplete droplet evaporation and reducing droplet diameter (dispersion) to less than 30 μm, consequently decreasing relative fuel consumption by reducing power consumption in the compressor since the compression process is approximately isothermal.

(3)

A thermopressor is a multifunctional device that implements three main functions: air (gas) compression–compressor; air (gas) cooling–heat exchanger; and providing an effective liquid (water) spray nozzle. This versatility allows, on the one hand, to increase the power plant efficiency, reduce fuel consumption, and increase power by reducing the cost of compressing the working fluid, therefore increasing the working fluid consumption in the cycle.

These hypotheses determine the following research direction—ensuring efficient energy transformation using a thermopressor for evaporative intercooling cyclic air to increase efficiency and reduce fuel consumption for the gas turbine.

Design factors that affect energy consumption to overcome frictional forces and local resistances in the flow part of the thermopressor (receiving chamber, evaporation chamber, confuser, and diffuser) have a significant influence on the work processes in the thermopressor. The gas velocity in the vaporization chamber of the thermopressor should be in the range of 0.5–0.9 Ma to ensure a positive increase in pressure. However, at such speeds, the hydrodynamic resistance of the flow part of the thermopressor increases significantly.

One of the ways to increase the efficiency of the thermopressor (relative pressure increase) is to inject more liquid into the flow part than is necessary for evaporation. This method ensures the availability of a dispersed flow regime along the entire length of the thermopressor. At the same time, this will reduce pressure losses in the flow part due to the presence of two-phase flow and related processes of aerodynamic resistance and heat and mass transfer. However, the aerodynamic resistance of the liquid drops injected into the airflow will also increase when the liquid is injected over the necessary amount.

Thus, it is necessary to specify the methodology for determining total aerodynamic resistance to determine losses from aerodynamic resistance in thermopressors of low flow rates (up to 1 kg/s). The definition of such dependencies will allow for determining the optimal design characteristics of the thermopressor when the maximum value of the pressure increase is reached.

At the same time, determining the relative and total pressure increase in the flow part of the thermopressor, considering water injection by experiment, will make it possible to specify the design methodology of the thermopressor as a part of power plants based on gas turbines.

3. Materials and Methods

The study of the thermopressor characteristics was carried out on a specially designed experimental setup (Figure 2). The experimental unit was designed to model the thermopressor for intercooling air of the gas turbine (the thermopressor module part consists of the thermopressors set with a common water injection system).

The developed experimental setup works as follows: the air was purified in a filter (Caterpillar-4N-0015 CAT) and then compressed in an Atlas Copco HA 85-3 screw compressor (0.6 MPa, 6 m³/h) and pumped to the thermopressor. Fog-type nozzles (Figure 3a) was used to spray the liquid. The design of the thermopressor (Figure 3b) includes the following parts: receiving (inlet) chamber (Figure 3c); liquid injection system (Figure 3d); confuser (Figure 3e); evaporation chamber (Figure 3f); and diffuser (Figure 3g). All thermopressor elements are variable, which made it possible to conduct investigations of thermopressors with variable geometric characteristics.

The principle of operation of the experimental setup was as follows: after cleaning the air filter, air followed the screw compressor (maximum discharge pressure is 0.6 MPa, capacity is 6 m³/h), where it was compressed and pumped to the air receiver. After deep cleaning in a three-section moisture–oil separator, the air was heated in a channel gas air heater to a temperature of t₁ = 50–180 °C. After preparation (approaching the parameters of cyclic air: the initial pressure at the input to the receiving chamber of the thermopressor P₁ up to 0.32 MPa; the flow velocity in the evaporation chamber w_air = 0.4–0.9 Ma), the air followed to the experimental thermopressor. Water for injection was pumped up from a distilled water supply tank and was supplied by a low-consumption high-pressure pump.

The error of the experimental results is determined by the error of measuring devices and methodical and systematic errors. The measurement of a physical quantity is based on the measurement method used, the measuring instrument, and the method of recording the result.

The Student’s distribution was used to assess the accuracy of the measurement results, which is recommended for a small number of observations, n ≤ 20, provided that the error distribution of individual measurements follows the normal distribution. In the case of applying the two-sample criterion for independent samples, the condition of variance equality was also observed.

The methodological error was determined with consideration of thermal inertia. MathLab and SigmaPlot software were used to estimate errors and obtain empirical dependences of thermopressor characteristics. Measuring the temperature took into account heat dissipation along the heat removal and thermal inertia.

Air is heated to the set temperature by a heat exchanger (Figure 4). The heat source is a gas burner set. Heat supply was carried out externally using a special thermal shield to reduce environmental losses. To increase efficiency, the heat exchanger has an internal fin located inside the device’s main part of the spiral. Finning is made of steel rods with a diameter of 8 mm. The heat exchanger capacity is G_a = 0.35–0.55 kg/s, while providing the temperature at the inlet T_a1 = 10–40 °C and at the outlet T_a2 = 50–190 °C.

The data collection of the experimental unit parameters was carried out with a measurement interval τ = 1 s, and each parameter was covered by no less than 15 measurements.

The air temperature was measured by resistance temperature sensors, which were set to measure the air temperature along the airflow:

(1)

At the entrance in front of the air filter;

(2)

After compressing the air in the compressor and cleaning from oil and moisture;

(3)

After heating the air in the duct air heater at the entrance of the thermopressor;

(4)

In the thermopressor evaporation chamber;

(5)

At the thermopressor diffuser outlet (the discharge pipe).

To measure the injected water temperature into the thermopressor, submerged resistance temperature sensors were installed in the distilled water supply tank.

The airflow pressure measurement was performed by pressure sensors of the model A-10 (WIKA).

Pressure sensors were installed in front of the thermopressor inlet chamber to measure the discharge pressure after the compressor, along the airflow of the apparatus flowing parts, and at the thermopressor diffuser outlet.

The temperature and pressure measurement data were recorded by an 8-channel I8-TC (for temperature sensors) and an I8-AT (for pressure sensors) by the company RegMik. Measuring instruments are designed to receive and convert sensor signals and display them on the built-in digital indicator. Since the maximum temperature of the measuring medium for sensors of this type was 80 °C, a radiator (cooler) was used to ensure correct readings, which was installed together with a pressure sensor.

The rotameter for measuring the volumetric flow of homogeneous flows with a measurement range of up to 25 m³/h and the permissible measurement error of ±4% were used to measure airflow.

The measuring system automatically monitors the condition of the sensors and determines the measured temperature and pressure of the set measuring range. The measurement data were also recorded in the measurement protocols and in readings graphs. This created an appropriate database for data entry and processing.

The measuring system automatically monitors the condition of the sensors and determines the measured temperature and pressure in the set measurement range. The principle of operation is as follows: the signal from the sensor with a current output makes a voltage on a precision resistance dependent on the measured value of the object, which is fed to a specialized controller through an instrumental amplifier. The source code is processed by a specialized controller, which, in particular, calculates the temperature or pressure of the object based on the entered transformation characteristic and then displays its values on indicators.

The PY485/USB, RS485 communication interface converter is used, which converts USB interface signals (compatible with USB 1.1 and USB 2.0) into RS-485/RS-422/V.11 interface signals (EIA-485 and EIA-422A) to collect and transform information. Figure 5 shows the connection diagram of the PI485/USB communication interface with a computer and two eight-channel meters I8-TS (for resistance thermoconverters) and I8-AT (for measuring pressure converters).

The received information from the measuring system was transmitted directly to the PC and processed using the software SSD 3.5 of the company Regmik. The obtained measurement data were also recorded in special measurement tables and data graphs. An appropriate database was created for processing data results.

4. Results and Discussion

The use of incomplete evaporation to reduce pressure losses along the length of the thermopressor’s working part can result in an opposite effect than the one intended, with an increase in the diameter and drop number. An increase in the injected liquid amount keeps increasing hydraulic resistance from liquid droplets and, as a result, decreases the positive effect of the thermo-gas-dynamic compression effect. To investigate this process in more detail, the effect of the relative water injected amount under different evaporation chamber operating conditions (relative velocity Ma and mass flow rate G_w) was studied.

In the first stage, the influence of the relative increase in pressure ε_tp of the thermopressor as a function of the velocity airflow Ma and mass water flow consumption G_w was studied. The following input parameters were adopted for the study: the air temperature was T_a1 = 155 °C; water consumption G_w = 0.0175, 0.0407, and 0.0487 kg/s; the water pressure P_w was 7.5 to 8.0 MPa; and air consumption G_a was 0.32 to 0.52 kg/s. The evaporated liquid amount was 15 to 70% of the total amount.

Experimental determinations of pressure losses in the flow part of the thermopressor were carried out for several values of the mass flow of water (Figure 6). Pressure losses for a thermopressor without liquid injection at inlet pressure P₁ = 150–300 kPa can reach ΔP_tp.r = 20–70 kPa (δ_tp.r = 10–27%). When injecting liquid G_w = 0.0175 kg/s (2%), pressure losses decrease—ΔP_tp.r = 20–55 kPa (δ_tp.r = 6–22%). However, with an increase in the amount of injected liquid, pressure losses increase: at G_w = 0.0407 kg/s (8%)—ΔP_tp.r = 20–60 kPa (δ_tp.r = 7–24%) and at G_w = 0.0487 kg/s (12%)—ΔP_tp.r = 20–65 kPa (δ_tp.r = 9–26%). This confirms that with a gradual increase in the flow of liquid, the pressure loss of the flow increases.

Further injection of water into the flow already leads to the opposite effect—hydraulic losses due to the resistance of the drops dominated the positive effect of reducing pressure losses in the dispersed flow, and as a result, pressure losses increase more than for a “dry” thermopressor. Thus, it can be concluded that the optimal relative amount of water that can be injected to ensure incomplete evaporation in the flow part of the thermopressor with the maximum effect of reducing hydraulic pressure losses is g_w < 10%. Therefore, it is important to experimentally define the optimal range of relative water flow for injection in the thermopressor.

Thermopressor parameter measurements at various relative velocities Ma of the airflow showed that with increasing relative speed Ma from 0.28 to 0.95, the relative increase in pressure increases. Thus, at G_w = 0.0175 kg/s, ε_tp increases from 0.97 to 1.04, and pressure losses, ΔP_tp, are −10 to −8 kPa (a minus sign means that there is an increased total pressure); at G_w = 0.0407 kg/s, the increase in ε_tp is from 0.88 to 1.01, and the pressure loss, ΔP_tp, goes from 0 to 16 kPa. At G_w = 0.0487 kg/s, the increase in ε_tp is from 0.82 to 0.97, and the pressure loss ΔP_tp is from 16 to 28 kPa (Figure 7). The largest value of ε_tp matches the nozzle with a flow rate of 0.0175 kg/s, and ε_tp is from 1.02 to 1.03. The decreased relative increase value of the pressure with increasing water flow G_w is due to an increase in the droplet number in the flow and, consequently, an increase in drag resistance at the initial evaporation sector of the flowing part.

The liquid droplet’s initial velocity at the nozzle exit impacts the initial droplet resistance in the flow and depends on the airflow velocity ratio. The closer the value (v_w/v_a) is to 1.0, the lower the initial resistance. In this study, the value equals the value (v_w/v_a) > 0.3.

Analysis and comparison of the obtained experimental data show that at some Ma numbers (the lower permissible limit of the thermo-gas-dynamic effect occurrence), the relative increase in the flow pressure in the thermopressor is completely levelled by hydraulic losses of the flow path. This phenomenon is observed at G_w = 0.0175 kg/s (Ma = 0.28); G_w = 0.0407 kg/s (Ma = 0.32); and G_w = 0.0487 kg/s (Ma = 0.38).

It was also found that the relative temperature (T₁/T₂) is from 1.36 to 1.41 (Figure 8), and the cooling air temperature at the thermopressor outlet is from 301 to 307 K (i.e., 28 to 34 °C). The cooling process is determined by the temperature of the wet bulb thermometer, and the relative humidity j is 100%.

Data analysis of Figure 7 by the approximation method makes it possible to propose several empirical relations. It describes the dependence of the thermopressor relative pressure increase ε_tp on two parameters: the relative velocity in the working chamber Ma and the water injected total flow rate G_w (

Table 1. Approximation functions and their coefficients for Figure 7.

Equation	Coefficient						R	R2
	y0	x0	a	b	c	d
Plane: $\mathrm{z}={\mathrm{x}}_0+\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}$	1.0101	–	0.1745	−3.8608	–	–	0.9255	0.8566
Paraboloid: $\mathrm{z}={\mathrm{y}}_0+\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}+\mathrm{c}{\mathrm{x}}^2+\mathrm{d}{\mathrm{y}}^2$	0.7985	–	0.3159	9.7491	−0.1479	−209.01	0.9832	0.9667
Gaussian: $\mathrm{z}=\mathrm{a}{\mathrm{e}}^{-0.5\left[{\left(\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{b}}\right)}^2+{\left(\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{c}}\right)}^2\right]}$	0.0237	1.0174	1.0859	1.7044	0.0465	–	0.9820	0.9533
Lorentzian: $\mathrm{z}=\frac{\mathrm{a}}{\left[1+{\left(\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{b}}\right)}^2\right]\times \left[1+{\left(\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{c}}\right)}^2\right]}$	0.0240	0.9934	1.0880	2.2880	0.0611	–	0.9820	0.9641

). Table 1 shows that the largest regression coefficient corresponds to the paraboloid equation—R = 0.9832 (R₂ = 0.9667). Thus, the empirical equation for determining the relative pressure increase ε_tp can be represented as follows:

$${\epsilon }_{tp}=0.7985+0.3159Ma+9.7491G_w-0.1479M{a}^2-209.01G_w{}^2$$

(1)

The second stage in this study is outlined as follows: the relative flow rate in the thermopressor evaporation chamber Ma was fixed, and the variation in the relative pressure increase ε_tp from the relative amount of injected water g_w was determined (Figure 9 and Figure 10). It can be seen that at Ma = 0.37 in the area of g_w being 4 to 8%, the relative increase in pressure decreases slightly, and ε_tp is 1.00 to 1.03. At values g_w > 8%, the pressure loss ΔP_tp decreases sharply (up to 16 kPa). The same can be seen for Ma = 0.53, wherein in the area g_w = 5–9%, the relative increase in pressure decreases slightly and ε_tp = 0.97–1.03. However, at values g_w > 9%, the pressure losses decrease sharply (ΔP_tp = 5–26 kPa), and for Ma = 0.82 in the area g_w = 6–10%, the relative increase in pressure decreases slightly and is ε_tp = 0.92–0.96. Values g_w > 10% decrease P_tp = 14–27 kPa sharply. From this, we can conclude that the water injection’s positive effect for the required amount of excess for evaporation will be only in the area g_w = 4–10%, and a further increase in g_w will result in a decrease in ε_tp. Moreover, increasing the relative velocity in the evaporation chamber changes the limit value of g_w to a smaller value and can reach g_w = 6–8%.

The total thermopressor outlet pressure increase will be small for ε_tp = 1.01–1.03 (1–3%). However, this makes it possible to ensure effective liquid high-dispersion sprays in the airflow with simultaneous cooling.

The Student’s distribution method was used to determine relative pressure measurement errors. In this case, the error deviations δ_tp ranged from ±1.81% to ±4.00%. The obtained measurement accuracy determines the reliability of the obtained experimental data.

Due to the increased pressure e_tp when excess water is injected in the working chamber, gw can be presented as a two-variable function (Figure 11). Analysis of these data points by the approximation method makes it possible to obtain empirical equations for determining e_tp (

Table 2. Approximation functions and their coefficients for Figure 11.

Equation	Coefficient						R	R2
	y0	x0	a	b	c	d
Plane: $\mathrm{z}={\mathrm{x}}_0+\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}$	1.0808	–	0.0048	−1.1982	–	–	0.9299	0.8647
Paraboloid: $\mathrm{z}={\mathrm{y}}_0+\mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}+\mathrm{c}{\mathrm{x}}^2+\mathrm{d}{\mathrm{y}}^2$	1.0664	–	0.0961	−1.3433	−0.0869	0.6821	0.9307	0.8663
Gaussian: $\mathrm{z}=\mathrm{a}{\mathrm{e}}^{-0.5\left[{\left(\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{b}}\right)}^2+{\left(\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{c}}\right)}^2\right]}$	−3.0078	0.5553	6.7176	2.1882	1.5781	–	0.9312	0.8672
Lorentzian: $\mathrm{z}=\frac{\mathrm{a}}{\left[1+{\left(\frac{\mathrm{x}-{\mathrm{x}}_0}{\mathrm{b}}\right)}^2\right]\times \left[1+{\left(\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{c}}\right)}^2\right]}$	−0.6391	0.5568	1.8002	3.0152	0.7955	–	0.9313	0.8673

). The regression coefficients for the selected functions are approximately the same. The paraboloid function is chosen for simplicity and corresponds to the changes observed in the experimental curves in Figure 11. It is worth noting that the regression coefficients for the selected functions are approximately the same. The paraboloid function is chosen for simplicity and corresponds to the changes observed in the experimental curves in Figure 11.

Accordingly, the obtained coefficients of the empirical equation function to determine the relative pressure increase ε_tp:

$${\mathsf{\epsilon }}_{\mathrm{t}\mathrm{p}}=1.0664+0.0961\mathrm{M}\mathrm{a}-1.3433{\mathrm{g}}_{\mathrm{w}}-0.0869\mathrm{M}{\mathrm{a}}^2+0.6821{\mathrm{g}}_{\mathrm{w}}{}^2$$

(2)

It should be noted that using empirical Equations (1) and (2) to determine the pressure relative increase ε_tp makes it possible to clarify the calculation method of thermopressor characteristics with incomplete evaporation of water in the working chamber. The initial operating thermopressor conditions correspond to the contact intercooling systems for cyclic air of heat engines. Empirical relations are applicable for a low-consumption thermopressor with an air consumption G_a from 0.32 to 0.52 kg/s, a working chamber diameter D_ch from 25 to 50 mm, and a relative flow path length l_tp from 3 to 10. At the same time, the operating air temperature at the inlet T_a is at least 100 °C.

5. Conclusions

• The use of incomplete evaporation in a thermopressor to provide contact cooling of the cycled air of gas turbines makes it possible to obtain a highly dispersed flow before going into the high-pressure compressor.
• It was determined that the increase in pressure due to the effect of thermo-gas-dynamic compression depends on the influence of the aerodynamic resistance of the dispersed flow droplets in the thermopressor evaporation chamber. Water injection has a positive effect over the necessary amount for evaporation, but only in the area g_w = 4–10% (0.0175–0.0487 kg/s), and a further increase in g_w will result in a decrease in relative increase pressure ε_tp. Moreover, the increased relative velocity in the evaporation chamber (up to Ma = 0.74) shifts the limit value of g_w to a narrower range of g_w = 6–8%.
• It has been experimentally shown that excessive liquid injection into the thermopressor for air cooling makes it possible to increase the relative pressure in the thermopressor to ε_tp = 1–3% (5–10 kPa). However, this makes it possible to ensure effective liquid high-dispersion spraying in the airflow with simultaneous air cooling up to 301–307 K.
• The highly dispersed flow thus acquired with the use of the thermopressor can be pre-evaporated in the high-pressure compressor stage. This will allow the compression process to operate closer to an isothermal process.
• The maximum error value of the increased pressure in the thermopressor during measurements, corresponding to the Student’s dispersion, does not exceed δtp = ±4.00%.
• Based on experimental data, empirical equations are obtained for calculating the relative pressure increase in the thermopressor for intercooling systems of power plant engines’ cyclic air. The equation can calculate the thermopressor characteristics under incomplete water evaporation (up to g_w = 10%) in the flowing part.
• The obtained data on the optimal amount of water for injection and empirical equations for determining the pressure increase in the thermopressor correspond to low-consumption thermopressors with an airflow rate of up to 0.52 kg/s, evaporation chamber diameters of up to 50 mm (relative flow path length ltp is from 3 to 10), and a Mach number from 0.3 to 0.8.