Experimental Research of Heat Transfer in Cooling Tower

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It should be noted that the processes of: air cooling at dew point with water heating, adiabatic saturation and air cooling without changing water temperature, isothermal saturation of the air with water cooling are not used in engineering applications. Therefore, we will further study processes of air saturation which can take place in cooling towers of different types (labeled D and J in Figure 1).

3. Experimental Unit and Results

The processes of air humidification in the cooling tower mode with cooling down hot water by means of air ^[15] are shown at Figure 2.

Figure 2. Structure of the experimental unit (1, 3 – rotameters, 2, 4 – electrical heaters, 5 – experimental area, 6 – thermocouples)

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The unit worked as follows. Air and water with certain mass flow and temperatures are fed to the experimental area which is a model of cooling tower with corrugated netting packing and countercurrent flow shown at Figure 3. Movement of heat transfer agents is reverse. Absolute moisture content is calculated from the heat balance.

As a result of the unit testing the range of the heat transfer agents is established, heat losses in the mode of work without area with corrugated netting packing for all the air velocities are evaluated.

The experiment was conducted according to the standard plan and consisted of the air loss variation at the stable input water and air temperatures.

Figure 3. Corrugated netting packing for model of cooling tower

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Main operating and geometrical parameters are specified in Table 1.

As a result of this the mass transfer coefficient value is established using the technique mentioned above.

Table 1. Main Parameters

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Knowing the input parameters of water and air, area of the contact device and final parameters of the heat transfer agents we can determine the mass transfer coefficient in the contact device.

If the water temperature is higher than the air temperature due to the difference of temperatures the water is heated and moisturized because of the difference of partial pressures.

The research data obtained includes losses of water and air at the output (measured with the rotameters), temperatures of water and air at the input and output (measured with the dry thermocouples). Sometimes the thermocouple at the output was wetted and therefore it screened. The results of experiment are specified in Table 2.

The research data is processed according to the following pattern.

Table 2. The Results of Experiment

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Output relative humidity which depends on velocity is calculated. So the amount of the water evaporated was determined from the heat balance

(8)

where are the heat losses.

The output absolute humidity, output steam pressure, maximum steam pressure in the air at the output air temperature is calculated as follows

(9)

where , , . Relative humidity is .

Further the correlation of from was checked. Type of correlation dependence is selected based on the available results and the data which was reducing the R – Pearson’s correlation coefficient – were rejected. In particular, the data of experimental research at the air velocity m/s reduced R substantially and that is why is excluded from the consideration.

Figure 4 shows the dependence according to the air humidity at the experimental area on the air velocity and input water temperature.

The calculated value of the correlation coefficients is shown in the figure and is R = 0.92 and 0.98. As it can be seen from Figure 4 the results at the input water temperature of have the relative humidity which is explained by the experiment error.

Also, according to Figure 4, the increase of velocity reduces the relative humidity of air which is not able to become saturated with vapor. And the increase of input water temperature increases the evaporation and saturation efficiency. The data specified are processed in the further researches.

Also, according to Figure 4, the increase of velocity reduces the relative humidity of air which is not able to become saturated with vapor. And the increase of input water temperature increases the evaporation and saturation efficiency, relative deviation of points from the presumptive straight line does not exceed 25%. This data is processed in future.

Figure 4. Dependence of the output relative humidity on the air velocity and input water temperature

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4. Research Results of Polytropic Air Saturation and Heating with Water Cooling

The process considered is characterized by the gradients of temperature and pressure being directed air, which accelerates cooling of water in cooling towers.

As water temperature is higher than the air t₇> t₀ (t₇ - t₀) the latter is heated and due to the partial pressure gradient (p₇ - p₀), the air is saturated and water is decreased. The equation of heat balance in the cooling tower: the heat to the water = heat of the evaporation + heat received by the air

(10)

Calculation of experimental heat transfer coefficient as

(11)

where the heat received by the air

(12)

In the equation (11) it is assumed that the middle air temperature near the water equals the temperature of water. And so instead of air temperature the average water temperature is taken.

To compare calculation of heat transfer coefficient in air, let’s theoretically. Assume the thickness of the heat layer in the air to equal thickness of boundary layer for air

(13)

– the thickness of boundary layer for air from the Navier-Stokes equations.

The experimental and theoretical calculation of heat transfer coefficient in the air , depending on the water temperature and the velocity of the air is shown in Figure 5. The upper curve is experimental and lower curve is theoretical calculation of heat transfer through the thickness of the layer displacement. It is seen that the boundary layer thickness at low air velocity m/s equals experimental results. But in the case of high velocity of air m/s theoretical thickness is higher than experimental, as , а Wt/K/m².

Figure 5. Dependency of the heat transfer coefficient on the air velocity and the initial temperature of water (dots – experiment, lower curve – theory)

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Figure 6 illustrates the heat of evaporation and heat received by the air depending on air velocity and initial water temperature

The heat of the evaporation, Wt

(14)

The heat received by air is calculated by equation (12).

As shown in Figure 6, the heat of the evaporation greatly exceeds the one received by air in the full range of water temperature and air velocity. In addition, the growth of temperature by 35% (from 63 to 85C) increases the heat of evaporation twice and heat received by the air by 40% only.

The heat transfer coefficient in air is calculated by equation (11).

To calculate the heat transfer coefficient in the water film the thickness of displacement layer is determines theoretically.

Figure 6. Dependencies of specific heat spent on evaporation (two upper curves) and heat received by the air (two lower curves) on air velocity and initial temperature

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At the water flow kg/h and wetted perimeter m, as twice for corrugated netting packing, we have water concentration of g/m/s. Reynolds number for the water film

(15)

As , where – area of cross section and ≈ 5 s/sec – velocity of gravity flow of water film from Nusselt equation. The thickness of the film is calculated from equation

(16)

For calculating heat transfer coefficient in water film, let us determine the film thickness (or half thickness), since the film is symmetric.

Figure 7. Dependency of half a water film thickness on the input water temperature and the air velocity

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The experimental results are illustrated in Figure 7 with water concentration g/(m c). Half of thickness depends on the temperature of input water as the water film thermal properties change and practically does not depend on the air velocity.

Half the thickness of the water film was compared to the thickness of the displacement layer in it. Let us calculate thickness of the displacement layer theoretically ^[16].

(17)

As calculated, the thickness of the displacement layer of water film greatly exceeds the experimental thickness of the film. That is, the processes of heat transfer in the film take place entirely within the boundary layer and the transfer zone in the water film which equals half the thickness of the film .

Using the boundary layer density in water film let us calculate the heat transfer coefficient in the water film .

Compare to the heat transfer coefficient in the film ^[9]

(18)

where , , – wetted perimeter.

Has shown in Figure 8 the heat transfer coefficient depends on the input temperature of the water and practically doesn’t depend the air velocity at constant water concentration as shown in Figure 5. The heat transfer coefficient increases with increase of input water temperature as change thermal properties of water film. The good deviation the known heat transfer coefficient in the film and the experimental results does not exceed 24% in the range of air velocities and an input water temperature.

Figure 8. The heat transfer coefficient in water film depending on the air velocity and the input water temperature (down two lines – calculation from [7])

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Let us determine experimentally the difference of temperature at the center and edge of the water film from the heat balance (3) , Wt.

According to 's heat law

(19)

where the heat transfer coefficient calculated in the water film using half of the water film’s thickness.

Figure 9 illustrates the increase of the difference temperature at growth of the initial temperature of water film and air velocity.

The growth in is from 0.52 to 0.68 C (at input water film temperature 63C) and from 1.13 to 1.27C (at input water film temperature 85C) at water concentration g/m/s and at diapason of the air velocity 1.3…2.8 m/s.

Figure 9. The dependency of the difference of temperature in the water film on the air velocity and input water film temperature

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The difference of temperature in the air flow is calculated experimentally , where the temperature of air at the edge of air flow equals the average temperature of water. The Figure 10 illustrates the dependency of it on the air velocity and input water film temperature. The growth of air velocity from 1.3 to 2.8 m/s increases the temperature gradient normal to the air flow from 31.9 to 44.1C, or 44.2 to 54.3C at the input water film temperature 63, or 85C. That is much more than in the water film.

A comparison of the difference of temperature in Figure 9-10 illustrates that the difference in the water film is more dependent on air velocity and water film temperature as a result of influence of mass transfer on heat transfer.

Figure 10. Dependency of difference in the air temperature on the air velocity and input water temperature

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