# Exergy Analysis of Overspray Process in Gas Turbine Systems

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## Abstract

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## 1. Introduction

## 2. System Analysis

_{0}, pressure of P

_{0}, and relative humidity of RH

_{0}enters the inlet duct of the gas turbine system. At the same time, liquid water droplets are injected into the air stream with initial droplet diameter of D

_{0}at the water injection ratio of f

_{0}, Note that the water injection ratio is defined as mass of liquid water per unit mass of dry air after the injection of water droplets. It is assumed that the small pressure drop occurring in the duct is negligible, thus the pressure of the system remains constant at its initial value during the inlet fogging process. Additionally, water droplets are assumed to be spherical and monodisperse and there are no interactions between the droplets during the process [18]. The present model of overspray process does not take into account the amount of water deposits on the walls of inlet ducts and compressor blade surfaces, which could adversely affect irreversibility and efficiency of the fogging process [8,33,34,35]. Also, the model introduced here in this study may not be accurate if there is substantial diffusion perpendicular to the mean streamlines in compressor channels.

_{0c}is defined as the maximum injection ratio that results in complete evaporation within the compressor. When water injection ratio f

_{0}is lower than f

_{0c}, the injected droplets evaporate completely during the process and no liquid droplet leaves the compressor. Then we expect f

_{3}= D

_{3}= 0. On the contrary, when water injection ratio f

_{0}is higher than f

_{0c}, the air becomes saturated and remained liquid water droplets leave the compressor along with air [14]. In this work the analysis is restricted to the cases of complete evaporation of injected droplets inside a compressor.

_{c}as [17]:

_{s}the temperature of water droplets, J the vapor mass flux away from the droplets, q

_{L}the latent heat flux due to droplet evaporation, q

_{S}the sensible heat flux due to diffusion or convection, and h

_{fg}the latent heat of vaporization.

_{v}the mass diffusion coefficient of water vapor in air, R

_{v}the gas constant of water vapor, and P

_{s}is the saturated pressure at T

_{s}. The solution can be approximated by using the temperature-averaged constant c

_{wet}and temperature-averaged polytropic coefficient n

_{wet}as [24]:

_{c}, irreversibility of inlet fogging process I

_{0}, total irreversibility I

_{tot}, exergy efficiency ${\eta}_{ex}$ are defined as follows [28,29]:

## 3. Results and Discussion

#### 3.1. Effects of Pressure Ratio

_{0}, the pressure ratio R

_{p}, the initial diameter of the droplets D

_{0}, the compression rate C, the polytropic compression efficiency η and the ambient conditions. The basic data for the analysis are as follows: compression rate C = 100 s

^{−1}, polytropic compression efficiency η

_{c}= 80%, water injection ratio f

_{0}= 5%, pressure ratio R

_{p}= 20, initial pressure P

_{0}= P

_{ref}= 1 atm, inlet temperature T

_{0}= T

_{ref}= 15 °C, and relative humidity at inlet RH

_{0}= 60% (ISO condition).

_{0}= 5%. The compression work increases with initial droplet diameter as well as with pressure ratio. It is expected that larger but fewer droplets evaporate more slowly than smaller droplets and the corresponding cooling rate of air due to droplet evaporation is lower than that of smaller droplets. Since the scope of analysis in this work is restricted to the case where all the injected droplets evaporate completely inside a compressor, the evaporation time t

_{evap}should be less than the compression time Δt

_{c}. Then for a given water injection ratio, there exists a lower limit value of pressure ratio under which the complete evaporation of water droplets inside the compressor is impossible. This limit value of pressure ratio increases with initial droplet diameter.

**Figure 2.**Effects of pressure ratio and initial droplet diameter on the compression work at water injection ratio f

_{0}= 5%.

_{tot}and the irreversibility ratio of inlet fogging process to total process I

_{0}/I

_{tot}are shown in Figure 3 and Figure 4, respectively, against pressure ratio for various initial droplet diameters. As observed in the figures, irreversibility or exergy destruction during the process I

_{tot}increases with pressure ratio, for higher pressure ratio results in larger entropy generation during the compression process. The irreversibility ratio of inlet fogging is found to be quite small and it decreases with pressure ratio, since irreversibility of wet compression increases whereas irreversibility of inlet fogging remains unchanged. As initial droplet diameter increases for a fixed pressure ratio and water injection ratio, the irreversibility of the process increases but the irreversibility ratio of inlet fogging decreases. For example, for R

_{p}= 20, the values of the irreversibility are 108.7, 113.7, 119.7, 125.7, and 131.3 kJ/kg for initial droplet diameter of 4, 8, 12, 16, and 20 μm, respectively.

**Figure 3.**Effects of pressure ratio and initial droplet diameter on total irreversibility at water injection ratio f

_{0}= 5%.

**Figure 4.**Effects of pressure ratio and initial droplet diameter on the ratio of inlet fogging irreversibility to total irreversibility at water injection ratio f

_{0}= 5%.

**Figure 5.**Effects of pressure ratio and initial droplet diameter on the exergy efficiency at water injection ratio f

_{0}= 5%.

#### 3.2. Effects of Water Injection Ratio

_{p}= 20. The range of water injection ratio tested here is up to 10%, which is in fact much higher than typical cases of gas turbine water injection. However, it should be noted that this study is seeking potential of overspray process which may allow higher water injection ratio than usual water injection process. Showing the benefit of water droplet injection, increasing water injection ratio reduces the compression work for a fixed value of initial droplet diameter, since evaporation of more droplets results in greater absorption of latent vaporization heat from air and the corresponding cooling rate of air due to droplet evaporation is higher than that of fewer droplets. Similarly with the aforementioned lower limit value of pressure ratio, the water injection ratio has a higher limit value above which the complete evaporation of water droplets inside the compressor is impossible. The limit value of water injection ratio decreases with increasing initial droplet diameter.

**Figure 6.**Effects of water injection ratio and initial droplet diameter on the compression work at pressure ratio R

_{p}= 20.

_{p}= 20, Figure 7 and Figure 8 show the variations of irreversibility during the process I

_{tot}and the irreversibility ratio of inlet fogging process to total process I

_{0}/I

_{tot}, respectively, with respect to water injection ratio for various initial droplet diameters. The total irreversibility during the overspray process I

_{tot}increases almost linearly with water injection ratio, for higher water injection ratio leads greater cooling of air temperature and consequently greater irreversibility during the compression process. The irreversibility ratio of inlet fogging decreases with water injection ratio, which states that the irreversibility of wet compression is dominant, compared to inlet fogging process, and the tendency becomes deepened as water injection ratio increases.

_{p}= 20 and D

_{0}= 12 μm, the exergy efficiencies are 86%, 83%, 80%, 77%, 75%, 72%, 69%, 67% and 64% respectively when water injection ratio increases from 1% to 9%.

**Figure 7.**Effects of water injection ratio and initial droplet diameter on total irreversibility at pressure ratio R

_{p}= 20.

**Figure 8.**Effects of water injection ratio and initial droplet diameter on the ratio of inlet fogging irreversibility to total irreversibility at pressure ratio R

_{p}= 20.

**Figure 9.**Effects of water injection ratio and initial droplet diameter on the exergy efficiency at pressure ratio R

_{p}= 20.

#### 3.3. Results with Saturated Water Injection Ratios

**Figure 10.**Effects of pressure ratio and initial droplet diameter on the saturated water injection ratio.

**Figure 11.**Effects of pressure ratio and initial droplet diameter on total irreversibility at the saturated water injection ratio.

**Figure 12.**Effects of pressure ratio and initial droplet diameter on the ratio of inlet fogging irreversibility to total irreversibility at the saturated water injection ratio.

**Figure 13.**Effects of pressure ratio and initial droplet diameter on the exergy efficiency at the saturated water injection ratio.

## 4. Conclusions

## Acknowledgments

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Kim, K.H.; Kim, K. Exergy Analysis of Overspray Process in Gas Turbine Systems. *Energies* **2012**, *5*, 2745-2758.
https://doi.org/10.3390/en5082745

**AMA Style**

Kim KH, Kim K. Exergy Analysis of Overspray Process in Gas Turbine Systems. *Energies*. 2012; 5(8):2745-2758.
https://doi.org/10.3390/en5082745

**Chicago/Turabian Style**

Kim, Kyoung Hoon, and Kyoungjin Kim. 2012. "Exergy Analysis of Overspray Process in Gas Turbine Systems" *Energies* 5, no. 8: 2745-2758.
https://doi.org/10.3390/en5082745