Experimental and Numerical Studies on Water Cooling Tower Performance

Theoretical and experimental studies were conducted on forced draft water cooling tower. In such towers, the heat and mass transfer take place from the hot water to the bulk air, which passes through the tower. The theoretical study includes two parts, the first part describes the numerical solution for the water cooling tower governing equations, a two dimension air momentum equation (Navier-Stocks equations) and air enthalpy equation (energy equation), moisture content and water enthalpy equation. The effect of turbulence was simulated using the k-ε model. The packing-air resistance is described and added to the air momentum equation in y-direction only. The second part highlights the use of three different packing types. This includes the use of a ceramic packing in two different heights (0.66, 0.48m) in addition to an aluminum packing. A simple comparison between all the above types of packing behavior is conducted. The experimental study was conducted using Hilton water cooling tower, which is a counter flow type. The variation in many variables, which affect the tower efficiency, are described in this part of the research including variation heating loads, entering water mass flow rates and incoming air volume flow rates. The flow field velocity vector for air through the tower is plotted, and an accurate behavior of both air and water properties was found.

. discuss the limitations of current practices of evaluating thermal performance of wet cooling towers and describes a more advanced mathematical model for mechanical and natural draft cooling towers.Burger, (1989) [2] , studied a various elements of the modern crossflow cooling tower and their upgrading capability.Alwan, (1991) [3] , studied the counter-flow water cooling tower with flat plate asbestos packing.Al.Habobi, (1995) [4] , studied the performance of ceramic blocks and asbestos sheets used as a packing for a counterflow water cooling tower.Mohiuddin and Kant, (1996) [5] , described the detailed methodology for the thermal design of wet, counter flow and crossflow types of mechanical and natural draft cooling towers.Al-Nimr, (1998) [6] , studied a dynamic thermal behavior of a counter-flow cooling tower by proposed a simple mathematical model.Bedekar, et.al, (1998)  [7] , studied experimentally the performance of a counter-flow packed-bed mechanical cooling tower.Gan and Riffat, (1999) [8] , presented a numerical technique for evaluating the performance of a closed wet cooling tower for chilled ceiling systems.Al.Nimr, (1999) [9] , studied the dynamic thermal behavior of counter-flow cooling towers that contain packing materials.Abdula, (2002) [10] , conducted a numerical study for forced draft cooling towers.A forced draft counter flow water cooling towers will be employed.A theoretical and experimental study will be carried out on this tower.In theoretical part a thermal solution (heat and mass balance) will be used to solve many equations using finite difference method based on computational fluid dynamics (CFD) such equations are, Xdirection momentum equation, Y -direction momentum equation, air enthalpy equation, air moisture fraction equation, water enthalpy equation, K-Є model for turbulent flow and equation of state.The effect of packing type heightens air flow rate, water flow rate and heating load on the tower performance will be predicted.Experimentally several tests on a counter-flow cooling tower test plant will be conducted.These tests will quantify the previous effects and justify the CFD program.

GOVERNING EQUATIONS
The basic equations that describe the flow of the fluid, heat and mass transfer between water and bulk air in two dimention with Cartesian coordinate system are the continuity, the Navier-Stokes and energy equations [1] .
Because the density varies along the tower, equation of state should be used.
where C µ is an empirical constant.
The distribution of k and ε over the flow field is calculated from the following semi-empirical transport equations for k and ε [12] .
A-Turbulent Kinetic energy: The empirical constants appearing in the above model are shown in the following table.

Table (1) Empirical constants in the
1.44 1.92 1.00 1.30 Cooling towergoverning equations are non-linear and required to be iterative procedure, However these equations must be written in a general form that is: where Φ is the dependent variable, which may be a directional quantity such as velocity components (u,v) or scalar quantity such as temperature or enthalpy ( ) a h .The left side of equation ( 14) is the convection term which mean the fluid transfer, the right side is the diffusion term which gives the variation in fluid property during the flow, Φ S is the source term which means the source of heat, mass transfer or pressure variation that allows fluid to flow, Φ Γ is the diffusion coefficient which is a dynamic viscosity in momentum equation but effective exchange coefficient in enthalpy and moisture fraction equations [11] , and  14) is solved by using a finite volume method, which divided the flow field in to small volumes, and integration of this equation on the faces of the control volume is the key solution of this method.

NUMERICAL SOLUTION
. The pressure is corrected to satisfy continuity at the end of each iteration.To derive the pressure correction equation we define the following [11]  in solving the steady momentum equations in this step, underrelaxation factor of (0.5) is applied to the velocity components to prevent instability and divergence due to nonlinearity in the Navier-Stokes equation.Also under-relaxation factor of (0.8) is used for pressure correction.After steady state solution is obtained for the flow field [12] .

EXPERIMENTAL WORK
The experimental work was carried out using Hilton water-cooling tower, which is a forced draft counter flow type.The tower was equipped with four heaters (2.5 kw each) to heat the water and that represents the load on it.The tower was equipped also with several measuring devices to express the condition of water and air at inlet, outlet and other five stations along the tower [13] .
The equations reflect mass and heat balance at any point in the tower is: The above two equations are convertible in to one another and independent of real active motion of the two fluids streams.Mathematical integration of the equations is required and the procedure must account for relative motion.In cooling tower practice, the integrated value of equation ( 19) is called "The number of transfer units" or "NTU".This gives the number of times the average enthalpy potential ( In examining equation ( 19), it can be seen that the vertical distance between the two curves represents the enthalpy difference ( ) in the integral of equation ( 19) [14] .Thus a second curve can be plotted for ( ) a sw h h − 1 as a function of the local water temperature, and the value of the integral can be determined by obtaining the area under the curve.
The resulting quantity ( ) known as the tower characteristic, is thus a function of the inlet and exit air wet bulb temperatures and the inlet and exit water temperatures.These can be expressed in terms of the approach temperature, the temperature range of the water, and the ratio of the water flow to the air flow rate.However the log-mean-enthalpy method based on the inlet and outlet enthalpy differences would underestimate the value of the tower characteristic, , the enthalpy correction, h δ , may be defined by The error involved in estimating the tower characteristic using the corrected log-mean-enthalpy method is small and normally acceptable which is about 2 percent.The difference between the use and no use of the corrected log-mean-enthalpy method is about 23 percent.The results are plotted graphically and the best straight line through each set of points is drawn.The values of "n" and " λ " would be approximated to 0.44 and 0.179 respectively and the characteristic equation becomes: The characteristic equations for these two types of packing are presented in equations ( 27) and ( 28) respectively [4] .The above two equations are used in the present theoretical work to predict the air and water properties that flow through these types of packing.This is done under the same inlet conditions (air and water temperatures and velocities) that are used in the experimental work.The theoretical packing-air resistance is similar to the Hilton tower packing-air resistance.Figs.(12 to 14) show the variation in the air enthalpy, moisture content and water enthalpy respectively, along (0.66 m) height ceramic packing [4] .Figs.(15 to 17) show the same above variables variation along (0.48 m) height ceramic packing [4] .Fig. (18)  shows the variation of the water temperatures along the tower stages for the three types of packing.(I.e aluminum, ceramic of 1.27 m height and ceramic of 0.48 m height) it is clear from this figure that the water cooling range for the Hilton packing is greater than that of both ceramic types.This is because the coefficient of performance (ka) for the Hilton packing is greater than the other packing two types.It is found also that the increase in the packing height lead to increase the cooling range, since it allow for much time for direct contact between the warm water and bulk air.
The packing resistance to air flow was calculated and added to the y-direction momentum equation only.This is because of the assumption that there is no heat and mass transfer in the horizontal direction.Fig. (19)  shows the variation of water temperatures with the use of the packing-air resistance.Fig. (20)  shows the variation of the same variable without the use of the packing-air resistance.These two figures represent a simple comparison between the two states.This comparison highlight the effect of this resistance, so that the water cooling range in the first case (use of packing-air resistance) is more than the second case.Many experimental tests are done by using a Hilton water cooling tower.Experimental results are compared with the theoretical results.The variation in the air enthalpy and water temperatures along the tower stages was considered in this comparison.Figs.(21 to 22).show the theoretical and the experimental water temperatures variation along the tower stages at different coefficient of performance (ka) values.The theoretical water cooling range is more than the experimental one in all these figures.This is due to the shape of the packing.That the simulation of this shape in the theoretical work is very complex, therefor the packing-air resistance which used in the numerical solution is not similar to the experimental packing-air resistance that actually exist inside the tower during the tests.However, the use of the theoretical resistance will decrease the difference between theoretical and experimental results.This comparison show a 7.69 % difference between these results.All these figures show that the delivery of experimental water temperature is higher than it in the final stage (one) is Fig. ( 23         Experimental delivary water temperature (c ) ....... .......... .......... ..........
Fig. (1) Configuration of the counter flow water cooling tower. 2 ......( .......... .......... .......... number, which takea unit.Equation ( Fig. (2) shows the variation in water temperature with different heating load along the tower stages.At each tower stage the water in temperature will decrease with increase the air volume flow rate, and this is represented in Fig. (3).At each stage of the tower the temperature of water will increase with increase in the water mass flow rate.This is represented in Fig. (4).The air velocity vector field that is shown in Fig. (5) highlights the air flow along the tower.Fig. (6) shows the moist air density variation as it passes through 520 the Hilton tower.The magnitude of this density depends on the magnitude of the static pressure and air dry bulb temperature.The air enthalpy variation as it passes through the Hilton tower is presented in Fig. (7).The variation in the air moisture content through Hilton tower is exhibited in Fig. (8).The variation in the water enthalpy through Hilton water cooling tower is shown in Fig. (9).The variation in the rates of heat transfer from warm water to bulk air as they flow through the Hilton tower is exhibited in Fig.(10).The variation in mass transfer rate from water to the bulk air as they flow through the Hilton tower is shown in Fig. (11).

Figure
Figure (6): Moist air density contour through the counter flow type water cooling tower.

Figure
Figure (14): Water enthalpy contour through the counter flow type water cooling tower at 0.66 m ceramic packing height.

Figure ( 17
Figure (17): Water enthalpy contour through the counter flow type water cooling tower at 0.48 m ceramic packing height.

Figure
Figure (20): Water temperature contour without using the packing air resistance.
Figure (22): The theoretical and experimental variation of water temperatures along the tower stages at