Determination of hydraulic resistance of the aerothermopressor for gas turbine cyclic air cooling

One of the promising trends to increase the fuel and energy efficiency of gas turbines is contact cooling of cyclic air by using a twophase jet apparatus – an aerothermopressor. The rational parameters of work processes of the aerothermopressor were studied. The experimental setup was designed to simulate the aerothermopressor operation in the cooling air cycle of the gas turbine and to determine pressure losses in the aerothermopressor flow part. Based on the obtained experimental data, an empirical equation was proposed to determine the hydraulic resistance coefficient of the aerothermopressor flow part, depending on the initial pressure and the amount of water injected. The deviation of the calculated hydraulic resistance coefficient from the experimental ones is ± 25 %. The obtained results can be used in the practice of designing the aerothermopressor for gas turbine cyclic air cooling.


Introduction
To bring the process of compressing air in gas turbine compressors closer to isothermal ones the complex schemes with cyclic air cooling are usually used [1,2]. It results in increasing the fuel and energy efficiency [3,4]. One of the promising trends is contact cooling of cyclic air [5,6]. For this purpose the jet technologies can be used [7][8][9][10]. To provide efficient evaporative cooling of gas turbine cyclic air without total pressure loss the aerothermopressor are quite useful [11]. Due to evaporative cooling in the aerothermopressor, an effect of thermogasdynamic compression is taken 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 [12,13]. An effective water dispersed atomization in the air flow occurs in the aerothermopressor. This ensures efficient evaporation of the water dispersed flow in the flow part of the gas turbine compressor bringing the compression process closer to isothermal.

Literature Review
The aerothermopressor allows to compensate the pressure loss and reduce the work of compression in the compressor and to increase the working fluid flow and, accordingly, the gas turbine power output [11]. In addition, the aerothermopressor is compact and structurally and technologically simple to manufacture in comparison with surface air coolers [12,14,15].
The working processes in the aerothermopressor are considerably influenced by design factors. The total pressure of the gas flow in the aerothermopressor is significantly affected by pressure losses caused by hydraulic and local resistance in the aerothermopressor flow part (confuser, evaporation chamber and diffuser) [13,16]. Therefore for designing the aerothermopressors it is important to determine the rational parameters of working processes in their flow part.
The operation of the aerothermopressor on the gas turbine exhaust gases was investigated in [12]. Data on the pressure loss caused by local and hydraulic resistance were obtained for the experimental aerothermopressor (gas flow rate G g = 11.5 kg/s). It was shown that the total pressure of compressed air and the work of compression correspondingly was decreased by approximately 14 %.
The pressure losses in the aerothermopressor flow part depend primarily on the operating mode nature. The process of accelerating the gas flow to a transonic speed (0.5-0.9 M) occurs in the confuser. To the inlet chamber, located before the confuser, liquid is supplied using a nozzle or other special devices [12,16,17]. In the evaporation section, these flows interact, and, as a result, droplets are accelerated, crushed, heated and evaporated, and gas is also cooled [13]. There are three main operating modes of the aerothermopressor [12,13,17]: 1. The influence of the water droplets resistance prevails over the positive effect of evaporation and determines the gas flow behaviour. The Mach number is increased, the static pressure of the flow is decreased, and the water temperature has risen approaching the saturation temperature.
2. Water evaporation predominates. The Mach number is decreased, and the total and static pressure is increased.
3. Surface friction (in the first two modes was relatively insignificant) becomes the predominant factor. This mode is taken place when the liquid completely evaporates.
All three modes determine the effect of hydraulic resistance on pressure losses. One of the ways to increase the aerothermopressor efficiency is to increase the total pressure by reducing losses due to hydraulic resistance of the flow part. It might be achieved by providing liquid incomplete evaporation -dispersed mode. Incomplete evaporation should provide a greater pressure increase, due to a friction losses decrease in the two-phase flow and it should provide effective fine atomization of water, due to a drop reduction during partial evaporation.
It is known that pressure losses in the two-phase flow (liquid-gas) may be less than pressure losses in the single-phase flow (gas) [18,19,20]. When providing liquid injection through the nozzle in an amount more necessary for evaporation, mode 3 is absent (in this mode, surface friction of the single-phase flow predominates). It positively affects the increase in total flow pressure as a result of the thermogasdynamic effect.
To determine pressure losses in the aerothermopressor, classical methods are used. These techniques are based on the analytical determination of the local and friction resistance coefficients of each of the aerothermopressor elements [21,22]. Pressure losses due to resistance (acceleration or deceleration of the droplet) can be determined by the aerodynamic resistance coefficient of the droplet in the flow  w in accordance with the technique proposed in [21]. Pressure losses in the evaporation chamber determined by the classical Blasius equation for flow in the channels [ Lockcart-Martinelli phases slip model [19,20 for the confuser and diffuser are used equations for the local loss coefficients Thus, the general equation for determining pressure losses in the aerothermopressor:

ΔP
where  ATP -total coefficient of hydraulic resistance in the aerothermopressor flow part; w air -average air velocity in the evaporation chamber; The total coefficient of hydraulic resistance is determined by: The application of the indicated methods for calculating losses by the elements of the aerothermopressor flow part often gives incorrect results. First of all, it is due to the complexity of accounting for the operating modes of the flow in the aerothermopressor.
Even more difficult is to determinate the losses due to the in the confuser and in the evaporation chamber initial part. This is due to the difficulty in determining the initial velocity of the droplet, its diameter, etc. It has been experimentally established that such losses can reach 10-20% [ exact determination of such losses for the aerothermopressor.
Determination of pressure losses in the aerothermopressor flow part experimentally, taking into account water injection, will clarify the design methodology for such jet devices. This will provide an accurate determination of the aerothermopressor effective use as a part of the gas turbine for cooling cyclic air under various operating conditions, as well as in various climatic conditions.

Research Methodology
The installation of the aerothermopressor in the gas turbine cyclic air cooling system is proposed in accordance with the scheme (Fig. 1) [ compressors will reduce the operation of the gas turbine high lower initial temperature of the compression process. This will ensure isothermal compression during the evaporation of the finely dispersed mixture in the high compressor flow part [25]. To conduct an experimental study of determining pressure losses in the aerothermopressor flow part, an experimental setup was developed (Fig. 2). The ]. Pressure losses in the evaporation chamber  ch might be equation for flow in the channels [22] or by the , 20]. To calculate losses from the total resistance for the confuser and diffuser are used equations for the local loss coefficients  с ,  d [22,23].
ral equation for determining pressure losses in the aerothermopressor: total coefficient of hydraulic resistance in the aerothermopressor flow part; average air velocity in the evaporation chamber;  air -air density. The total coefficient of hydraulic resistance is determined by: The application of the indicated methods for calculating losses by the elements of the flow part often gives incorrect results. First of all, it is due to the complexity of accounting for the operating modes of the flow in the aerothermopressor.
Even more difficult is to determinate the losses due to the resistance of the droplet [24] e confuser and in the evaporation chamber initial part. This is due to the difficulty in determining the initial velocity of the droplet, its diameter, etc. It has been experimentally -20% [12,13], but there are no equations for the exact determination of such losses for the aerothermopressor.
Determination of pressure losses in the aerothermopressor flow part experimentally, taking into account water injection, will clarify the design methodology for such jet es. This will provide an accurate determination of the aerothermopressor effective use as a part of the gas turbine for cooling cyclic air under various operating conditions, as well of the aerothermopressor in the gas turbine cyclic air cooling system is proposed in accordance with the scheme (Fig. 1) [11]. This arrangement between the compressors will reduce the operation of the gas turbine high-pressure compressor due to al temperature of the compression process. This will ensure isothermal compression during the evaporation of the finely dispersed mixture in the high-pressure cheme of the gas turbine with cyclic air cooling by the aerothermopressor: low and high pressure compressors; CClow and high pressure turbines; PT -power turbine.
To conduct an experimental study of determining pressure losses in the ermopressor flow part, an experimental setup was developed (Fig. 2). The experimental setup is designed to simulate the aerothermopressor operation in the cooling cycle air of the gas turbine. The simulation of the aerothermopressor operation to cooling cyclic air of the gas turbine WR-21 from Rolls Royce (N e = 25.250 kW, g e = 0.190 kg/(kW•h),  е = 41.2%) were considered.
The principle of experimental setup operation (Fig. 3): after cleaning in the air filter (2) (Caterpillar -4N-0015 CAT), the air was supplied for compression to the screw compressor (3) (Atlas Copco ХА 85), and pumped at 0.6 MPa into the air receiver. After deep cleaning in the three-section moisture separator and oil separator (7), the air was heated in the ducted gas heater (11) to t 1 = 50-180 °C. After preparation (approximation to gas turbine cyclic air parameters), the air entered into the experimental aerothermopressor (19). Water for injection came from a distilled water reserve tank (14) and it was injected by a highpressure pump (18) (STIHL RE 98). Water spray was carried out by nozzles of type FMT. At the pressure of 7.5 MPa, the nozzles provided a water flow rate at the receiving chamber inlet of the aerothermopressor: FMT-43.0 -g w = 0.0175 kg/s; FMT-100.0g w = 0.0407 kg/s; FMT-120.0 -g w = 0.0487 kg/s. The spraying angle was 70-90 ° and the average droplets diameter was  w = 18-20 μm with a maximum diameter of  w = 50 μm.
The experimental aerothermopressor (Fig. 4 a) consists of the following elements: a receiving chamber with a nozzle (Fig. 4 b) and system for injecting water into the flow (Fig. 5 a); confuser (Fig. 5 b); evaporation chamber ( Fig. 6 a); diffuser (Fig. 6 b); nozzles for installing temperature and pressure sensors. All elements of the aerothermopressor are removable allowed to carry out studies for the different geometric characteristics (Table 1).  temperature and pressure sensors; 4 -control valve with a device for trapping droplets; 5three-section moisture separator for air coming from the compressor module; 6 -computer monitoring and control system. -control valves; 7 -three-section moisture separator; 8 -drain oil and moisture; 10temperature compensator; 11 -gas air heater; 12, 13 -inlet and outlet of hot gas; 14water reserve tank; 15 -control valve of the injection system; 16 -return pipeline; 17pipeline for supplying water to the injection system; 18 -high pressure pump; 19experimental aerothermopressor; 20 -control valve at the outlet; 21 -output pipeline; Ppressure sensors; T -temperature sensors.  All temperature, pressure and air flow sensors were connected to a developed computerized monitoring system. The parameters were measured with an interval  = 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 information about the data, a PI485 / USB RS485 communication interface converter was used, which converts USB interface signals (USB 1.1 and USB 2.0 compatibility) to RS485 / RS-422 / V.11 interface signals (EIA-485, EIA-422A).
Testing and measuring devices with a list of the parameters they measure, the measurement range, accuracy classes and measurement errors are given in Table 2. The error of the experimental results was determined by the error of the measuring instruments, methodological and systematic errors.
To determine the local resistance coefficients for the diffuser and confuser, classical dependences of fluid dynamics [13,14] were used. The energy equation (Bernoulli equation for air flow, taking into account mechanical specific losses): where ρgz 1 , ρgz 2 -geometric pressure; p 1 , p 2 -static pressure; Δp t -total losses of total pressure; 2 1 Dividing by ρg: where Δh t -total head losses. The equation for total pressure is: Taking into account the fact that z 1 = z 2 and Eq. (4), the total head losses Δh t : The local resistance coefficient  ATP is:  Based on the obtained experimental data, for different values of the initial pressure at the aerothermopressor inlet P 1 and the relative amount of water injected g w , an empirical dependence was established by approximation to determine the pressure losses coefficient in the aerothermopressor with the flow rate to 0.52 kg/s. The reliability of the work results is ensured by: the tasks correct formulation of the theoretical and experimental research; confirmation of the adequacy of the mathematical model with satisfactory agreement between the calculated and experimental data; using modern methods of experimental research and analytical modeling.

Results
To determine the hydraulic resistance coefficient of the aerothermopressor flow part, a number of experimental measurements of pressure losses P r were carried out under various conditions (Fig. 7, 8): the pressure at the inlet to the receiving chamber -Р 1 = 150; 200; 250; 300 kPa; injected water flow rate relative to the flow rate of the two-phase flowg w = 5-35% (up to 0.0487 kg/s). The measurements are showed: at the inlet pressure P 1 = 300 kPa pressure losses are P r = 55-75 kPa (20-24%), at P 1 = 250 kPa pressure losses are P r = 40-45 kPa (16-18% ), at Р 1 = 200 kPa pressure losses are P r = 22-24 kPa (12-16%). In this case, with an increase in water flow rate g w , pressure losses increase by 2-4%, and when the initial pressure decreases from 300 to 150 kPa, the effect of the amount of injected water gradually decreases. At Р 1 = 150 kPa, pressure losses are P r = 18-20 kPa (11-12%), but with an increase g w to 35% pressure losses remain practically unchanged, the effect of water flow rate on pressure losses ceases. Pressure losses increase P r with injected water flow rate increase g w at inlet pressures P 1 = 200-300 kPa is explained by the greater difference between the initial droplet velocity at the nozzle exit and the air velocity -(w w / w air ) = 1.1-1.3. Hence, there is a greater influence of the droplet resistance. It can reach up to 20% of the total pressure loss in the aerothermopressor. At the pressure P 1 = 150 kPa, the droplet and air velocities are almost equalized and the droplet resistance decreases significantly.  Determination of the hydraulic resistance coefficient  ATP.E for the aerothermopressor based on the data (Fig. 7, 8,9): at P 1 = 300 kPa - ATP.E = 1.15-1.30, at P 1 = 250 kPa - ATP.E = 0.90-1.00 and at P 1 = 200 kPa - ATP.E = 0.70-0.75. The tendency of the hydraulic resistance coefficient behavior is the same as for absolute pressure losses P r , that is, with a water flow rate increase, the hydraulic resistance coefficient  ATP.E increases by 0.05-0.15.  Based on the obtained experimental data, the equations of the dependence of the hydraulic resistance coefficient in the aerothermopressor flow part  ATP were determined by the approximation method according to a number of equations and depending on the initial pressure at the receiving chamber inlet P 1 and the relative water injected flow rate g w . In this case, the plane equations were selected (Fig. 10 This equation (regression coefficient -R = 0.8847; R 2 = 0.7827) is obtained for the following characteristics of the aerothermopressor operation: 1.2 · 10 5 < Re < 3.4 · 10 5 ; M = 0.25-0.65; g w = 0.05-0.35; Р 1 = 150-300 kPa.
The deviation of the calculated values of the hydraulic resistance coefficient  ATP.C (equation (8)) from those obtained during the experimental study  ATP.E is   = ± 25 % (Fig. 11). Based on the calculated values  ATP.C , the absolute pressure loss in the aerothermopressor P r.С was determined (equation (1)) and their comparison with experimental P r.E was carried out. In this case, the deviation of the calculated data with the experimental ones was no more than  P = ± 25 % (Fig. 12). This indicates that the empirical dependence (8) for determining  ATP can be applied to the considered conditions when designing aerothermopressor for gas turbine cyclic air cooling. But it should be noted that experimental data were obtained only at air flow rates to 0.52 kg/s, i.e., it is possible to

Conclusions
The data on hydraulic resistance coefficients for the flow part of the low-flow aerothermopressor were determined experimentally. The experimental hydraulic resistance coefficient  ATP.E = 0.35-1.30, depending on the initial pressure P 1 , and the relative flow rate g w of water injected into the inlet chamber has been received. The absolute values of pressure losses were ΔP r = 18-75 kPa (11-24%).
An empirical equation was proposed to determine the hydraulic resistance coefficient of the aerothermopressor flow part  ATP , depending on the amount of water injected. This coefficient takes into account hydraulic losses: local losses in the confuser and diffuser; friction losses in the evaporation chamber; losses due to resistance of water droplets. The deviation of the calculated hydraulic resistance coefficient  ATP.C from the experimental ones  ATP.E is   = ± 25 %. The deviation of the calculated pressure loss P r from experimental is  P = ± 25 %. This indicates the possibility of applying this dependence under the conditions: 1.2 · 10 5 < Re