Keywords

1 Introduction

Complex schemes with cyclic air cooling are usually used in modern gas turbine plants (GTP) to increase fuel and energy efficiency. They are used to bring the process of compressing the working fluid in gas turbine compressors closer to isothermal. It leads to an increase in the thermal efficiency of the cycle and a decrease in specific fuel consumption [1,2,3].

One of the promising areas is the contact cooling of cyclic air by using a two-phase jet apparatus – an aerothermopressor. This device provides efficient evaporative cooling of the gas turbine without loss of total pressure. Pressure losses due to the friction are reduced with the rational organization of work processes and the corresponding development of the apparatus flow part design. By increasing the total air pressure at the outlet, the efficiency of the aerothermopressor is increased up to 30% [4, 5].

2 Literature Review

One of the most common ways to increase the efficiency of gas turbines is to use the cyclic air intercooling in the compression process. Thus, the compressor efficiency increase is achieved by approximating the final compression temperature to the initial temperature (the compression process becomes close to isothermal) [3, 6]. The water injection to the compressor channel is one of the effective ways to increase the power and efficiency of gas turbine plants [3, 7, 8]. The water injection fulfills two functions: it removes the heat from the airflow and returns the heat to the gas turbine cycle.

One of the current directions in increasing the efficiency of power plants is to use the aerothermopressor as a means of efficient water spraying while increasing the mass flow rate of the working fluid in the gas turbine plant [5]. Due to evaporative cooling in the aerothermopressor, an effect of the thermodynamic compression takes place – gas pressure is increased in the process of instantaneous evaporation of water injected into the gas (air) flow accelerated to a speed close to sound [9]. This apparatus combines two working processes: contact cooling of cyclic air and cyclic air pressure increase [4, 9, 10]. The difference of this cooling cyclic air method is that due to the intensive heat and mass transfer processes and a high flow rate, sufficient liquid thin atomization occurs. When injecting more water than is necessary for a complete evaporation, an additional evaporation of the remaining droplets in the airflow compressed in the gas turbine compressor is done. Due to this, the necessary conditions are created to ensure the process of an isothermal compression.

A significant influence on the working processes in the aerothermopressor is carried out by design factors. These factors affect energy consumption to overcome the friction forces and local resistance in the aerothermopressor flow part. To ensure a positive increase in pressure, the gas velocity in the aerothermopressor evaporation chamber should be near the speed of sound. The relative velocity, in this case, is in the range M = 0.5–0.9 Mach number. However, at such gas velocities, the aerodynamic resistance of the aerothermopressor [4, 10] is significantly increased.

The positive effect of using the aerothermopressor is greater the smaller the pressure loss through aerodynamic resistance [5] is. One of the ways to increase the efficiency of the aerothermopressor (relative increase in pressure) is to inject water into the flow part in an amount greater than necessary. This method ensures a dispersed mode of flow along the entire length of the aerothermopressor [11]. To determine the aerodynamic resistance losses in the low-flow aerothermopressor, it is necessary to clarify the methodology for determining the total aerodynamic resistance.

3 Research Methodology

The main objective of the research is to study the effect of the water injection (in excess of the amount necessary for evaporation) into the aerothermopressor flow part on the pressure losses due to aerodynamic resistance and to determine the dependences for calculating such losses.

The calculation model developed by the authors was used considering the calculation features: of gas turbine cycles with the cyclic air intercooler; of the thermodynamic compression effect; of contact cooling processes of moist air. Based on the computational model, a software complex has been developed. It allows determining parameters at the characteristic points of the cycle, GTP efficiency parameters (efficiency, power, specific fuel consumption, etc.), working process parameters in the aerothermopressor, and its geometric characteristics.

The calculation of GTP cycles was carried out according to well-known methods [6, 12] considering the features of processes in moist air [13]. The effect of thermodynamic compression was calculated considering the dependences [4, 9, 10]. The calculation of the evaporation of finely dispersed water was carried out considering contact heat transfer in gas turbine and combined-cycle plants [8, 14, 15].

The reliability of the work results is ensured by the tasks correct formulation of the theoretical and experimental research, the confirmation of the adequacy of the mathematical model with satisfactory agreement between the calculated and experimental data, using modern methods of experimental study and analytical modeling.

To conduct an experimental study, an experimental setup was developed (Fig. 1). The experimental setup is designed to simulate the aerothermopressor operation in the conditions of GTP cyclic air cooling.

Fig. 1.
figure 1

The scheme of the experimental setup.

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The experimental aerothermopressor consists of the following elements: a receiving chamber with a nozzle for injecting water into the flow; a confuser; an evaporation chamber; a diffuser; nozzles for installing temperature and pressure sensors. All elements of the aerothermopressor are removable allowing carrying out studies for the different geometric characteristics: a confuser – inlet diameter Dc1 = 65 mm; a convergent angle α = 30°; an evaporation chamber – diameter Dch = 25 mm; length Lch = 125; 175 mm; a diffuser – length Lch = 192 mm; a divergence angle β = 6°; a nozzle – the distance between the water exit point to the receiving chamber inlet Lf = 5; 65; 125 mm.

In the course of the study, the airflow rate was 6.0 m3/h, at the pressure of 0.32 MPa, with the velocity in the evaporation chamber of 0.4–0.9 M.

All temperature, pressure, and airflow sensors were connected to a developed computerized monitoring system. The parameters were measured with an interval τ = 1 s. To record the readings of measuring instruments, eight-channel meters I8-TS (temperature measurement) and I8-AT (pressure measurement) were used by RegMik. To collect and organize the information about the data, a PI485/USB RS485, a communication interface converter was used.

The error of the experimental results was determined by the error of the measuring instruments, methodological, and systematic errors.

The gas expansion process occurs adiabatically in the aerothermopressor subsonic nozzle. A liquid is supplied to the receiving chamber located up to the confuser, which is mechanically finely atomized with a special nozzle. In the evaporation section, these flows interact, and, as a result, droplets are accelerated, crushed, heated, and evaporated, and gas is also cooled [4]. There are three main operating modes of the aerothermopressor [4]:

  1. 1)

    the influence of the water droplets resistance prevails over the positive effect of evaporation and determines the gas flow behavior. The Mach number is increased, the static pressure of the flow is decreased, and the water temperature is risen approaching the saturation temperature;

  2. 2)

    the water evaporation is predominated. The Mach number is decreased, and the total and static pressure is increased;

  3. 3)

    the surface friction (it was relatively insignificant in the first two modes) becomes the predominant factor. This mode takes place when the liquid is evaporated completely.

This mode takes place when the liquid evaporates completely. When providing the injection of water in an amount more than necessary for the evaporation, the third mode will be absent. This can positively affect the increase in the total pressure of the flow as a result of the thermodynamic effect.

Pressure losses due to the resistance (acceleration or deceleration of the droplet, depending on the initial velocity at the nozzle exit) can be determined by the aerodynamic resistance coefficient of the droplet in the airflow [8, 15]:

$$ \upzeta_{\text{d}} = \left( {\frac{16}{{Re_{\text{d}} }} + \frac{2.2}{{Re_{\text{d}}^{0.5} }} + 0.32} \right) \cdot \left( {\frac{{1.5{\upmu }_{\text{w}} + {\upmu }_{\text{air}} }}{{{\upmu }_{\text{w}} + {\upmu }_{\text{air}} }}} \right), $$
(1)

where μair, μw – dynamic viscosity of air and water.

Reynolds number for a drop moving in the airflow:

$$ Re_{\text{d}} = \frac{{\updelta_{\text{w}} \Delta w_{\text{w}} {\uprho }_{\text{air}} }}{{{\upmu }_{\text{air}} }}, $$
(2)

where ∆ww – droplet velocity relative to air velocity, δw – water droplet diameter.

The local resistance coefficients also determine pressure losses due to aerodynamic resistance in the aerothermopressor flow part: the confuser (nozzle) – ζc; the working chamber (evaporation chamber) – ζch; the diffuser – ζdif.

For a dispersed flow, an equation can be given to determine the hydrodynamic pressure loss. It is used in the phase slip model [17]. The mass flow rates occurring in the evaporation chamber of the low-flow aerothermopressor (with the diameter of the evaporation chamber Dch < 30 mm, Gg < 1.5 kg/s) is (ρw) > 100 [10].

The hydraulic resistance of two-phase flow with phase slip is calculated by the Lockhart-Martinelli method [11, 16]. According to this method, the pressure loss due to the friction of a two-phase flow dP/dZ can be expressed in terms of their value for one phase:

$$ \frac{dP}{dZ} = \varPhi_{\text{w}}^{2} \left( {\frac{dP}{dZ}} \right)_{\text{w}} \,{\text{or}}\,\frac{dP}{dZ} = \varPhi_{\text{air}}^{2} \left( {\frac{dP}{dZ}} \right)_{\text{air}} , $$
(3)

where Martinelli parameter Ф [17]:

$$ \varPhi_{\text{w}} = \frac{{\varPhi_{\text{air}} }}{{X_{\text{tt}} }} = X_{\text{tt}}^{ - 1} + 2.85 \cdot X_{\text{tt}}^{ - 0.48} ;\varPhi_{\text{air}}\, { = 1 + 2} . 8 5\cdot X_{\text{tt}}^{0.523},$$
(4)

Martinelli-Nelson parameter Xtt [18]:

$$ X_{\text{tt}} = \left( {\frac{{\upmu_{\text{w}} }}{{\upmu_{\text{air}} }}} \right)^{0,1} \left( {\frac{1 - x}{x}} \right)^{0,9} \left( {\frac{{\uprho_{\text{air}} }}{{\uprho_{\text{w}} }}} \right)^{0,5} , $$
(5)

where x = Gair/(Gair + Gw) – dryness of the vapor.

Pressure friction losses of the water phase and the gas phase:

$$ \left( {\frac{dP}{dZ}} \right)_{\text{w}} { = }\,\frac{{ \, \upzeta_{{{\text{ch}} . {\text{w}}}} \cdot \left( {\uprho_{\text{air}} w_{\text{air}} } \right)^{2} \left( {1 - x} \right)^{2} }}{{ 2D_{\text{ch}} \uprho_{\text{w}} }}\,{\text{or}}\,\left( {\frac{dP}{dZ}} \right)_{\text{air}} { = }\,\frac{{ \, \upzeta_{{{\text{ch}} . {\text{air}}}} \cdot \left( {\uprho_{\text{air}} w_{\text{air}} } \right)^{2} \left( {1 - x} \right)^{2} }}{{ 2D_{\text{ch}} \uprho_{\text{air}} }}. $$
(6)

The friction coefficient for turbulent flow in the evaporation chamber is found by the Blasius equation [19]:

$$ {\upzeta}_{\text{ch}} = 0.3164 \cdot Re^{ - 0.25} . $$
(7)

The phase with the determining pressure drop must be taken as the one whose pressure gradient is more significant importance for a given vapor content [11], while the total pressure loss is:

$$ \Delta P_{\text{ch}} = \overline{l}_{\text{ch}} \cdot \frac{{\varPhi_{\text{w}}^{2} \cdot \upzeta_{{{\text{ch}} \cdot {\text{w}}}} \cdot \left( {\uprho_{\text{air}} \cdot w_{\text{air}} } \right)^{2} \cdot \left( {1 - x} \right)}}{{2 \cdot \uprho_{\text{w}} }}, $$
(8)
$$ \Delta P_{\text{ch}} = \overline{l}_{\text{ch}} \cdot \frac{{\varPhi_{\text{air}}^{2} \cdot \upzeta_{{{\text{ch}} \cdot {\text{air}}}} \cdot \left( {\uprho_{\text{air}} \cdot w_{\text{air}} } \right)^{2} \cdot \left( {1 - x} \right)}}{{2 \cdot \uprho_{\text{air}} }}, $$
(9)

where lch = (Lch/Dch) – relative length of the evaporation chamber.

To calculate losses from the total resistance for the confuser ζc and the diffuser ζdif using the equation for the local loss coefficient [19]. For aerothermopressor calculated values: ζc = 0.005–0.010; ζdif = 0.01–0.20.

Thus, combining Eqs. (1), (7)–(9) to determine the pressure losses in the aerothermopressor flow part:

$$ \Delta P_{\text{tr}} = \Delta P_{\text{ch}} + \frac{{\left( {\zeta_{\text{d}} \left( {g_{\text{w}} + \Delta g_{\text{w}} } \right) + \zeta_{\text{c}} + \zeta_{\text{dif}} } \right) \cdot \left( {a_{\text{df}} \cdot M} \right)^{2} \rho_{\text{air}} }}{2}, $$
(10)

where adf – sound speed in the two-phase flow; gw – amount of water required for complete evaporation; Δgw – excess water.

Relative pressure losses in the aerothermopressor flow part:

$$ \updelta_{\text{tr}} = \frac{{\Delta P_{\text{tr}} }}{{P_{1} }} = \frac{{P_{1} - P_{2} }}{{P_{1} }}, $$
(11)

where P1, P2 – aerothermopressor inlet and outlet pressure.

4 Results

The experimental determination of pressure losses in the aerothermopressor flow part was carried out for a number of mass flow rates of water and it was compared with the values of pressure loss without water injection (dry aerothermopressor). The dependences plotted from experimental points are shown in Fig. 2.

Fig. 2.
figure 2

The experimental data on the measurement of pressure losses ΔPtr (a) and relative pressure losses δtr (b) in the aerothermopressor flow part on the air pressure at the inlet P1 at various injected water rates Gw: ▲; _______ – 0 kg/s; Δ; ………… – 0.0175 kg/s; ○; _ _ _ _ _ _ – 0.0407 kg/s; ●; __ __ __ __ – 0.0487 kg/s.

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The maximum pressure losses are made for the aerothermopressor without the water injection: at the inlet pressure P1 = 150–300 kPa – ΔPtr = 20–70 kPa (δtr = 10–27%). At the water injection of Gw = 0.0175 kg/s (8%), pressure losses is decreased – ΔPtr = 20–55 kPa (δtr = 6–22%), but with an increase in the amount of the injected water, the pressure losses is increased: at Gw = 0.0407 kg/s (15%) – ΔPtr = 20–60 kPa (δtr = 7–24%), at Gw = 0.0487 kg/s (17%) – ΔPtr = 20–65 kPa (δtr = 9–26%). This is explained by the fact that, with a gradual increase in the water flow rate, the pressure losses also increase due to the droplets resistance in the flow. When the flow rate amounts are gw > 0.2 (20%), the pressure loss becomes equal to or exceeds the losses for the dry aerothermopressor. A comparison of the experimental and calculated dependences (Fig. 3) shows that the calculated line of pressure loss at pressures P1 = 250–300 kPa lies below the line constructed from the experimental data. Moreover, the calculated data are 8–12 kPa less (10–20%).

Fig. 3.
figure 3

Dependences of experimental and calculated data on the measurement of pressure losses ΔPtr in the aerothermopressor on the air pressure at the inlet P1 at various injected water rates Gw: a – 0.0175 kg/s; b – 0.0487 kg/s.

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Equation checking (10) for adequacy with experimental data on the pressure loss ΔPtr shows a discrepancy from + 40% to −20% (Fig. 4), which can be considered satisfactory. However, the discrepancy is quite large, and it might explain the difficulty in determining the initial velocity of the droplet, and therefore underestimated pressure losses due to the droplet’s aerodynamic resistance in the airflow.

Fig. 4.
figure 4

Comparison of the experimental data on the measurement of pressure losses ΔPtr.E in the aerothermopressor flow part with the calculated data ΔPtr.C (Eq. (10)) at various injected water rates Gw: ▲ – 0 kg/s; Δ – 0.0175 kg/s; ○ – 0.0407 kg/s; ● – 0.0487 kg/s.

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To obtain more accurate values of the relative pressure losses δtr in the flow part of the low-flow aerothermopressor, it was proposed to obtain an empirical equation depending on the relative water flow rate gw and the inlet air pressure P1. The equation was determined by the approximation method:

$$ \delta_{\text{tr}} = 0.0457 - 7.3581 \cdot 10^{ - 8} \cdot P_{1} + 0.4682 \cdot g_{\text{w}} + 1.7814 \cdot 10^{ - 12} \cdot P_{1}^{2} - 1.0768 \cdot g_{\text{w}}^{ 2} . $$
(12)

This equation (regression coefficient R = 0.9260) was obtained for the following characteristics of the aerothermopressor: Gair = 0.10–0.52 kg/s; M = 0.4–0.8; P1 = 125–300 kPa; gw = 0–0.4; t1 = 50–180 °C. The deviation of the calculated δtr.C values from the experimental δtr.E is ±15% (Fig. 5), which is more accurate. However, such equation does not make it possible to calculate aerothermopressors with high airflow.

Fig. 5.
figure 5

Comparison of the experimental data on the relative pressure losses in the aerothermopressor flow part δtr.E with the calculated data δtr.C (Eq. (12)) at various injected water rates Gw: ▲ – 0 kg/s; Δ – 0.0175 kg/s; ○ – 0.0407 kg/s; ● – 0.0487 kg/s.

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Thus, at the injected water in an amount greater than necessary for evaporation, the pressure losses in the aerothermopressor is decreased by 15–20% relative to the losses in the dry aerothermopressor. This makes it possible to increase the relative increase in the total pressure in the aerothermopressor (P2/P1)atp. Thus, when simulating the aerothermopressor operation to cooling cyclic air of the gas turbine WR-21 (Fig. 6) from Rolls Royce (Ne = 25250 kW, ge = 0.190 kg/(kW∙h), ηe = 41.2%) without the injection with the excess water – (P2/P1)atp = 1.025–1.060; the injection of the excess water gw = 0.1 (10%) – (P2/P1)atp = 1,045–0,080, so the total pressure is increased by 2%.

Fig. 6.
figure 6

The scheme of the gas turbine with cyclic air cooling by the aerothermopressor: ATP – aerothermopressor; LPC, HPC – low and high pressure compressors; CC – combustion chamber; HPT, LPT – low and high-pressure turbines; PT – power turbine.

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5 Conclusions

An analysis of the obtained experimental data on pressure losses in the aerothermopressor flow part shows that the water injection in an amount gw in excess of necessary for the evaporation provides a decrease in these losses by 15–20% relative to pressure losses in a dry aerothermopressor. A calculation equation to determine the pressure losses in the aerothermopressor flow part is presented; it takes into account the influence of the droplet aerodynamic resistance and the hydrodynamic resistance of the two-phase flow. Checking the calculated equation for adequacy with experimental data shows a discrepancy in a range from 40% to –20%.

An empirical equation is obtained to determine the pressure losses for the low-flow aerothermopressor at the airflow rate of Gair = 0.10–0.52 kg/s. Checking the calculated equation for adequacy with experimental data shows a discrepancy of ±15%.

The application of excessive water injection into the aerothermopressor to cooling cyclic air of the gas turbine allows increasing the relative pressure (P2/P1)atp in the aerothermopressor by 2%.

The study results can be used in the methodology of aerothermopressors rational design to determine the optimal geometric characteristics of the apparatus flow part. The finely dispersed two-phase flow obtained in the aerothermopressor can be further vaporized to the high-pressure gas turbine compressor. This fact will ensure that the compression process is close to isothermal. The application of the principle of the excess water injection in the aerothermopressor is relevant for using at the intercooling of cyclic air of gas turbine plants and the charge air cooling of internal combustion engines.