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Introduction
Turbine performance utilities require performance enhancements due to the rapid and unforgiving increase in energy demands calling upon engineers to design and develop energy efficient techniques to optimize power output for energy producing utilities. Among the most reliable technologies for enhancing gas turbine performance in hot and humid climates is the technique of cooling the inlet air using techniques such as fogging and evaporative cooling as discussed in this report. It is clearly a technical and performance advantage to cool air at the inlet leading to the modification of the density of air at the inlet with the aggregate effect of improving the performance of a turbine or power generation utility. That is in consideration of the fact that temperature rises during summer in hot climate regions impair the performance of a power generating utility by reducing the density of air at the intake. One characteristic influencing factor as to the choice of cooling technique to adopt is the ambient ratio of the humidity of air and the density as critical factors. Among the technique is the fogging technique and evaporative cooling as discussed in this paper.
Inlet Air Cooling Systems in Hot and Humid Climates
Gas Turbine Fogging
An extensive application of the fogging technique particularly in power generation utilities leads to the optimization of power production with a rapid payback particularly when using the fogging technique at the inlet of a gas turbine. The impact on the performance of a fogged inlet turbine is influenced by a number of performance determining parameters. Holman (1997) and Johnson (1989) concur that these parameters include the temperature at the inlet of a turbine, the mechanical efficiency of a gas generator, the optimum speed that can be attained by the gas turbine, the temperature of exhaust gases, and the pressure at which the turbine compressor discharges gas in relation to the rate at which fogging is applied at the inlet of the gas turbine. Further arguments by the Technical specification of the project, design, manufacturing, and installation of media evaporative
cooling system for 6 units of Fars combined cycle power plant (2002) report indicates that gas turbine fogging draws on the use of demineralized water with the objective to reduce the applied water into minute droplets using specially engineered nozzles for the purpose of producing atomized water droplet sprays at very high pressures. The technique is aimed at producing fog at the inlet of a turbine during the evaporation process with the consequent objective of cooling the air at the inlet as illustrated below (Cortes, & Willems, 2003).
It has been demonstrated that the cooling efficiency due to fogging at the inlet of a turbine is close or at least almost one hundred percent effective. However, the resulting cooling efficiency is also influenced by the design constraints of the inlet of a turbine and other design variables such as the typical design of the compressor aimed at achieving efficient wet-bulb temperature values. Johnson (1989) provides an overview of a typical high pressure gas turbine (Chaker, Meher-Homji, Mee, 2002).
Johnson (1989)s argument is based on a typical fogging system design that consist of high pressure pumping compartments organized sequentially to provide high pressure water to several nozzles designed to provide excellent fogging effects on the high pressure water from the array of high pressure reciprocating pumps. As an engineering requirement, high pressure plays the critical role of forcing the demineralized water into droplets through the application of very high pressures on the atomizing nozzles. In response to the high pressure water, the fogging effect results from the creation of a large number of droplets whose physical characteristics are influenced by a number of parameters such as the pumping pressure, the number of nozzles in the arrangement of nozzles, and the orientation of the turbine itself to the nozzles (Technical specification of the project, design, manufacturing, and installation of media evaporative cooling system for 6 units of Fars combined cycle power plant, 2002) and (Brooks, n.d).
Bradury, Hancock and Lewis (1963) demonstrate the fact that in a typical fogging environment, large gas turbines show the need to be equipped with a large number of nozzles with the overall effect of creating a fogging effect equivalent to the fogging demands on the turbine inlet to optimize the density of the inlet air. Moreover, the use of demineralized water is critical to avoid the possibility of fouling compressor blades and the aggregate corrosion effect of mineral water and high temperature gases on a turbines construction materials. A typical example of a gas turbine is illustrated below (Grabe & Chappell, 1974).
The above diagram demonstrates a practical application of the fogging effect in the respective engineering fields of application. It can be clearly discerned in the diagram that the turbine is a two shaft design with the effect of applying the fogging technique at the inlet to improve its performance (Brooks, n.d). Typically, the turbine is largely used in gas or oil industries. In addition to that, it provides a basis for further studies on the application and enhancement of turbine performance using the fogging effect on the inlet gases in the discussion, as an industry application (Grabe & Chappell, 1974).
Analytically, it is worth noting that the performance of a two shaft turbine is strongly correlated with the compressor and the respective turbine efficiency. The correlating or matching variables are defined by the gaseous flow in the turbine, the temperature of the flow and pressures that can be achieved in the turbine. That also relates to the equilibrium conditions that are attained between the compressor and the turbine. Other influencing variables include work output, the degree of compatibility of the flow, and optimum speeds achieved by the rotating turbine and the compressor (Boonnasa, Muangnapoh & Namprakai, 2006).
The speed of the rotating turbine and the compressor in all types of engines such as a multiple spool and free spool engines must be in equilibrium for efficiency to be attained. Besides that, the flow of gas in a turbine is continuous hence the demand for compatibility in the flow. There is also need to establish an equilibrium condition between power outputs from the compressor and the input torque from the driver shaft. A typical example of the arrangement is illustrated in the above diagram.
Different turbine designs used in different environments demand varying conditions and equilibriums conditions. In addition to that, an overall critical factor in the performance of these varied models is the relationship between the ambient temperature and the maximum speed that can be attained at optimum working conditions. However, some turbines and engines are designed based on ISO standards. In that case, the ambient temperature is a function of the optimum rotational speed that can be attained by the turbine. As the ambient temperature rises, the driver turbines power experiences a decrease. However, the driver turbine efficiency curve can be improved by orienting the geometry of the turbine to optimize power outputs in relation to the effects of the ambient temperature. Therefore the overall effect of the ambient temperature on the performance of a turbine is worth discussing here (Arrieta & Lora, n.d).
The Effect of the ambient Temperature
It has been demonstrated that the ambient temperature attained by a gas has a mathematically inverse relationship with the inflow rate and the drop in temperature of the inlet gas. Arrieta and Lora (n.d) note that the drop in temperature has the effect of increasing the density of the flow with the ultimate effect on the volume of the flow and power output. From a practical perspective, lower temperatures causes an increase in mass flow influencing an increase in power output. However, it has been observed that as the operating conditions become intense, nozzles choke and the increase in mass flow appreciates the pressure ratio of the operating environment leading o the overall drop in performance of the give machine (Boonnasa, Muangnapoh & Namprakai, 2006). However, a practical evaluation of the operating environment indicates that maximum operating pressures can be attained irrespective of the level to which the inlet air is cooled. The limiting variables are defined by the degree of compressor discharge pressure that can be attained by the compressors mechanical speed, and the temperature of the turbine blades. It is a practical consequence to realize that power drops can be experienced to a minimum knee point for some turbines particularly aero-derivative propulsion machines. However, experimental evidence indicates that power drops are significant when the ambient temperature appreciates under a range of temperature values. However, under practical working conditions, a number of issues have to be considered when designing an inlet fogging system with the aim of improving the ultimate performance of a turbine in a typical environment (Cortes & Willems, 2003).
Practical Considerations
One of the critical elements to consider is the effect of foreign object damage. Under practical working conditions, it has been demonstrated that the possibility of damage due to icing at the inlet cooling point is rive. For that reason, the fogging system should be designed and inculcated with the ability to cease from fogging the inlet gas in the event of icing at the inlet. The icing is commonly caused by temperature that reaches a statically depressive state with the accelerating air as the driving force (Cortes & Willems, 2003).
Another critical engineering factor to consider is the effect of duct drainages (Shah, 1978). This element plays a critical role based on their strategic positioning in relation to the bell mouse and the silencer components. The design has an overall impact on the performance of a turbine therefore calling on careful design considerations. It is important to mention here that the design should be drawn from experience, actual turbine configurations, and other restrictions that might eventually cause water to accumulate at the duct. It is also important to consider incorporating silencers that have draining capabilities built into them (Shah, 1978).
It has been demonstrated that the nozzles have to be oriented as discussed above to achieve optimal fog distributions. That is in addition to determining the arrangement of the array of nozzles that are used in the fogging process as illustrated below (Fairman, 1962).
In a typically practical environment, it is important to consider issues such as nozzle distribution, appropriate location for nozzles in a fogging system, and the distribution of nozzles within the fogging system with the sole aim of optimizing the efficiency of the fogging system. In the views of Shah (1978), practical studies indicate that the design of the nozzle, it orientation, and other engineering considerations are aimed at achieving a uniform distribution of droplets with the ultimate goal of achieving uniform distribution of the inflow mass. However, the orientation of nozzles in a fogging system is critically influenced by the inflow velocity of the air mass, the line separating the nozzles, pressures that are achieved at the mouth of the nozzle and the respective spray patterns, and the geometry of the respective duct (Shah, 1978).
Empirical evidence demonstrates that nozzles can vary in their orientation. It has been shown that these orientations vary between zero degrees and 90 degrees in relation to the inflow mass. However, for practical applications, research shows that a 90 degree orientation and orienting a nozzle towards the inflow mass are not viable options and should be avoided. It has been recommended that an orientation between zero and 60 degree are viable and practical options. Experimental results are illustrated on the behavior of the fogging spray below.
Compressor surge is another factor to consider for optimizing the performance of a turbine in relation to the fogging effect more particularly for the engineering systems that are fog inter-cooled. Engineering estimates clearly indicate that the spraying effect at the inlet for a fog inter-cooled turbine causes an overspray above the value that is allowed under the turbines operating requirements. The overall effect moves the compressors operating points and an engines operating point towards the surge line. Even with heavy duty gas turbines, the surge line shifts by a specific value. In addition to that, a number of factors influence the surge condition. Among the critical factors include the design of the gas turbine blades and the overall fouling effect on the blades. A typical arrangement of high pressure design is illustrated below.
Engineers know quite well that any engineering project must have goals that strategically focus on the needs of the customer and the user of the technology under consideration. To that end, therefore, fog cooling must be characterized by goals that focus on attaining the best benefits from the cooling system. Therefore, fog cooling comes with specific goals. Among these goals are selecting the best option to achieve the best investment. In addition to that, the technology should achieve the best financial benefits with the shortest payback period, user and needs driven designs, excellent fabrications on a system, and a clear and comprehensive maintenance strategy to optimize on the performance the system (Alhazmy & Najjar, 2004).
With such goals identified and being the driving factors behind, it is of critical importance to consider how fog cooling works by considering models of the fogging systems (Ameri & Hejazi, 2004).
Fog-Cooling modeling
The performance of gas turbines is adversely affected by a rise in ambient temperatures in a gas turbine as discussed above. In addition to that, dusty conditions and humidity are other variables that greatly lay penalties on the working efficiency of a gas turbine (Air Quality Data., 1978).
Boonnasa, Muangnapoh and Namprakai (2006) reinforce the fact that it is important as an engineering approach to model the effect of different factors that influence the performance of the fogging effect on the overall performance of a turbine. Besides that, the modeling can lead to the evaluation of the amount of revenue generated due to improved turbine performance due to the cooling effect on the inflow mass. The models are based on the following figure.
A mathematical model based on the principles of physics with the assumption that the fogging is adiabatic, is related to the expression, mw (hv3 hw2) = ma (ha1 ha3) + É1 ma (hv1 hv3). An adiabatic relation draws on the fact that the total amount of energy gained by the sprayed air is cancelled by the amount of energy lost by dry air under ideal conditions therefore establishing an energy equilibrium energy transfer condition. In this relation, the mass transfer of the cooling water is mw whose enthalpy is hw2. On the other hand, (ha3 ha1) provides a relation on the enthalpy of dry air whereas the relation (hv1 hv3) being the enthalpy due to the cooling water. In the equation, É1 provides a value of the humidity ration that can also be obtained from the mathematical relation; É1= (0.622 pv)/ (p1-p2). pv is the pressure that is achieved partially and p1 and p 2 are pressures due to water vapor and the atmosphere respectively (Air Quality Data., 1978).
According the laws of physics, mass can neither be created nor destroyed and based on the law of mass conservation, the amount of sprayed water at the inlet is equivalent to the mass of water at any specific point along the turbine, assuming the rate of mass transfer is constant for this case. However, under practical conditions, the rate of mass transfer may drastically vary along the turbine. The relation can be modeled mathematically as follows; mw = (É3 É1) ma. It is important to note that the relation is defined by a variable of the humidity ration of the air after it has been cooled. In addition to that, it is possible to calculate the partial pressures based on the relations mathematically illustrated below;
pv1 = Æ1 Psat1 and pv3 = Æ3 Psat3.
Noteworthy are the variables in the equations where Æ1 is the relative humidity in the mathematical model while the rest of the variables are the partial pressures that are achieved during the cooling of the mass flow. In addition to that, in the mathematical relation, Psat1 and Psat3 represent the pressures that are attained and defined at temperatures T1 and T2. As mentioned above, the modeling is assumed to be ideal, therefore pressure losses are assumed not to have occurred during the process. Hence, it is assumed that pressure P1 is similar to pressure P2. However, it is important to use a computer to get a number of comparative values with varying temperature ranges as mentioned elsewhere. It is however, important to determine the power performance of a turbine and the heat rating of the turbine after the above cooling has been achieved. That can be modeled based on the Power-Augmentation Sub-model discussed below (Boonnasa, Muangnapoh & Namprakai, 2006)
Powers-Augmentation Sub-model
A turbines performance characteristics as demonstrated by Brooks (n.d)s illustration of the performance curves shown below are a good pointer to the two variables of heat and power discussed above. A typical example of a turbine under consideration is the ABB GT13 Gas-Turbine. As illustrated in the diagram below, the power output of the turbine under consideration and the heat rate attained by the inflow masss air temperature, T, is calculated from the mathematical relations; (1) PO = åPos, and (2) HR = HRs/µ. The variables, POs and HRs, represent the power output of the turbine and the temperature attained by the inflow mass respectively. For the turbine under consideration, the temperature of attained is estimated to be 15.6º C, being the standard temperature T mentioned above. The constant values used in the equations, the relative thermal efficiency of the system (µ) and the relative power of the system (³) can be calculated based on the characteristics of the performance curves illustrated below (Air Quality Data., 1978) and (Dunn, n.d).
Deducing from the above graphs, the values of (µ) and (³) can be calculated from the above graphs as demonstrated here, ³ = 1.1007953 0.0068486514T 9.6865641T² /10 pow7 from fig 1 and · = 1.0276476 0.0018092128T 1.105712T²/10 pow5 from fig 2. In addition to the above mathematical models, it is important to briefly provide mathematical models for conducting a cost benefit analysis of the fog-cooling strategy due to the cost benefits gained to justify the implementation or integration of the fog-cooling system into the inlet of a turbine (Nabati, Soltani, Hosseini & Ameri, 2003).
It has been demonstrated that fog-cooling can attract revenue that can be calculated based on an hourly basis from the relation, RMe = (PO3 PO1) Ce. In this relation, Ce is based on the cost of energy to the customer and
PO3 and PO1 are respective values of power output when the system is subjected to cooling and when it is not subjected to cooling respectively. On the other hand, the hourly rate at which fuel can be saved is based on the following relation, RMf = PO3 (HR1 HR3) Cf. From the mathematical relation, HR1 and HR3, are values of the heat rates that are calculated or obtained based on the ambient temperature (T1), and the temperature attained by the fog-cooled inflow mass (T3).
Analytically it is important for engineers to verify any model as it has practical implications on the performance of any specific turbine. Comparative studies have shown the importance of manufacturers of specific turbines to provide data on the performance of the turbines they have manufactured. These values can are critical in evaluating the above models for obtaining rough estimate data on various performance issues. A critical analysis, however, show that the mathematical derived above provide good estimates of the performance of different types of turbines with minor deviations from the actual values due to design and manufacturing issues (Air Quality Data., 1978.
It is important, therefore, for manufacturers and user of fog cooled turbines to note that the models can provide estimate values on the effect of cooling on the performance of a gas turbine when subjected to cooling at the inlet. However, it is important for the models to be specifically tailored to specific turbines due to variations in design and manufacturing issues and operating conditions (Air Quality Data., 1978).
Gas Turbine Thermodynamics
It is of critical importance to understand the thermal dynamic cycles and principles upon which gas turbines operate. Principally, the cycle is known as the Brayton cycle (Lane, n.d). The Brayton cycle is defined by two key parameters, the ration between the pressure in the turbine and the temperature at which firing takes place. In an argument presented by Javadi (n.d), in a typical environment, the pressure ratio is characterized by two pressure points expressed as a ratio of the discharge pressure of the compressor and the pressure at the inlet. The discussion is illustrated in the diagrams below for a typical turbine (Lane, n.d).
Ameri, Hejazi and Montaser (2005) theoretically model the Brayton cycles as discussed above. The impact of the parameters considered in the process play a critical role in determining the outcome of the calculations and other turbine performance issues. However, it is important to consider both practical and ideal situations under which the analysis below is conducted. One of the critical considerations is that the flow mass is air throught the analysis, the air used in the process behaves perfectly, the flow of fuel and its effect is constant throughout the Brayton cycle, the compressor and the turbine are both 100 % efficient, there are no pressure losses incurred during the inflow of the air mass, during the combustion process, and during the exit of the gases (Punwani, Pierson, Bagley & Ryan, 2001). In addition to that, the turbine is assumed to be in a state where it is not cooled. It has been and will be demonstrated below that the thermal efficiency of the Brayton cycle relies on the pressure ratio attained in the turbine (Air Quality Data., 1978).
Theoretically, the Brayton cycle is principally based on an isentropic cycle, the isobaric process, and the adiabatic processes. The cycle is defined by compressions, addition of heat into the inflow mass, expansion of the inflow and outflow mass, and the rejection of heat in the whole process. In addition to that, the Brayton cycle can ideally be calculated based on the mathematical relation, µ=1=T1/T2=1-(P1/P2) å-1)/å
Theoretically, the firing temperature is reached when the highest value for the temperature has been recorded. In addition to that, a comparison of two approaches as illustrated below indicates that the firing temperature causes a rise in the value of the temperature that is achieved in the process under the Brayton cycle.
Modeling of the open turbine cycle
Based on the Brayton cycle, it is important to conduct an analysis of the cycle. Theoretically, the model is a close loop based on standard considerations of an ideal behavior of the gas in the model. It is assumed that the compression of the gas involved in the process and its expansion remains constant. The whole Brayton cycle is an aggregate of four processes that are designated as internally irreversible. The whole of the four parametric considerations and heat considerations fall into the isentropic compression process in the turbine, an increment of heat at a constant rate, an expansion in the turbine that is isentropic, and the injection of constant pressure into the turbine (Ameri, Hejazi & Montaser, 2005). It is important to note that gas turbines influence a large amount of mass flow through the basic cycles at tremendous velocities. It has been demonstrated that the movements are within the gas turbines are smooth for the greater percentage of the motion of a gas turbine. That calls for an accurate and balanced design of the turbine blades to minimize and essentially do away with any potential to be damaged in the operational process. The air standards are theoretically taken to be adiabatic processes where a balance in pressure is achieved throughout the system as mentioned elsewhere. In addition to that, the irreversible process that is internally considered for the process is a thermodynamic condition in which specific operating temperatures of a gas turbine can be achieved with the overall effect of reversing the whole Brayton cycle with the aggregate effect of improving the efficiency of a turbine in relation to a state of equilibrium that can be achieved in the process. As illustrated in the above diagrams (fig 3), the Brayton cycles are clearly demonstrated. It is assumed that a steady flow is achieved in the process with the objective analyzing the whole cycle based on the steady flow state (Krulls & Lastella, n.d).
In the model Ameri, Hejazi and Montaser (2005) confirm that the flow of mass within the system makes the whole system gain energy equilibrium state per unit mass based on the following expression, (qin-q0ut) + (win-wout) =hexit-hin. Further analysis leads to the Brayton equation as stated below:
·th, Brayton=1-1/(k-1)rp*k, where rp=p2/p1 (k, the ration used as a specific value).
It can therefore, be analogously deduced that the specific heat ratio and the ratio of the pressure of a gas determine the thermal efficiency if the Brayton cycle. It can be noted that the thermal efficiency of a turbine appreciates as the both parameters mentioned above increase (Dunn, n.d).
Ameri and Hejazi (2004) analytical views of the T-s and P-v diagrams illustrated above indicate that the specific heat capacity of the materials used in the design and construction of the turbine have been assumed to be constant. However, based on practical analysis of the behavior of the specific heat capacity of a material with rising temperature, it has been shown that the specific heat capacity varies with varying temperatures. Ameri and Hejazi (2004) observe that changes in the specific heat capacity have a strong influence on the behavior of a turbine and its power production efficiency. However, it worth noting that the temperature of the inflow mass increases at the outlet and is low at the inlet, therefore influencing the Brayton to a minimal extent. However, it has been demonstrated that the Brayton cycle calculations sometimes differ from practical values by a given margin. This can be calculated based on adiabatic considerations in the design and comparison process (Ameri & Hejazi, 2004).
Thermodynamic analysis
A thermodynamic analysis of the whole system leads to a critical evaluation of the Brayton cycle based on the parameters that influence the whole cycle as illustrated below.
Johnson (1994) illustrates that increasing the firing temperature at which firing occurs varies the efficiency of the turbine in relation to the power output and the respective pressure ratios. However, certain factors influence the design of a turbine. It has been demonstrated that the rate of mass flow and the output per unit volume determines the size of the turbine. A smaller design indicates that when the output per unit volume is high, the size of the turbine decreases. In addition to that, the thermal efficiency of a turbine directly impacts on the fuel efficiency and power output from a turbine. Based on the above diagram, pressure ratios vary between different points in the whole cycle (Johnson, 1994). One important point in the design is that as higher pressure ratios are attained, there is a proportional rise in the efficiency and performance of a turbine. However, it can be demonstrated that the efficiency of a turbine are strongly related to the firing temperature. In addition to that, specific pressure ratios lead to optimal output as variations in output efficacy vary with temperatures (Alhazmy & Najjar, 2004).
It can be deduced from the above diagram that when the firing temperature appreciates, the power output increases at specific pressure ratios. However, it
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