Wet-Bulb Temperature

Wet bulb temperature—the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer by convection equals the rate of mass transfer away from the surface.

From: Fermentation and Biochemical Engineering Handbook (Third Edition), 2014

Chapters and Articles

Power augmentation

A.M.Y. Razak, in Industrial Gas Turbines, 2007

14.5.1 Wet bulb temperature, dry bulb temperature and cooling effectiveness

Wet bulb temperature is the lowest temperature to which air can be cooled by the evaporation of water into the air at a constant pressure. It is therefore measured by wrapping a wet wick around the bulb of a thermometer and the measured temperature corresponds to the wet bulb temperature. The dry bulb temperature is the ambient temperature. The difference between these two temperatures is a measure of the humidity of the air. The higher the difference in these temperatures, the lower is the humidity. Given the wet bulb temperature, dry bulb temperature and ambient pressure, the humidity of the air can be calculated as follows:.

[14.1]p=pw0.00066P(TaTw)(1+0.0115Tw)

where p is the vapour pressure of water vapour, pw is the saturated vapour pressure of water vapour at the wet bulb temperature, P the ambient pressure, Ta is the ambient or dry bulb temperature, and Tw is the wet bulb temperature.

The saturated vapour pressure of water vapour at the wet bulb temperature, pw is given by:

[14.2]pw=6.112×e17.67×TwT+243.5

Also the saturated vapour pressure of water vapour at the dry bulb temperature is:

[14.3]ps=6.112×e17.67×TaT+243.5

Using Equations 14.1 and 14.3, the relative humidity, ϕ, is calculated by:

[14.4]ϕ=pps×100

The specific humidity, ω, can also be determined and is given by:

[14.5]ω=0.622pPp

The dew point can also be determined from:

[14.6]Td=243.5×ln(p6.112)17.67ln(p6.112)

The pressures in Equations 14.1 to 14.6 are in millibars (mb) and the temperatures are in degrees Celsius.

Figure 14.19 shows a schematic representation of an evaporative cooling system. The ambient (warm, dry) airflow enters the wetted media/fogging chamber, where water is added and evaporated. The resultant cooled, moist air leaving the wetted media/fogging chamber enters the engine inlet. As stated above, the cooling effectiveness is a measure of how close the temperature of the moist, cooled, Tcool, air approaches the wet bulb temperature, Tw. The cooling effectiveness, ε, is defined as:

14.19. Schematic representation of a (wetted media) evaporative cooling system.

[14.7]ε=TaTcoolTaTw

Wetted media and chillers may be positioned either upstream or downstream of the gas turbine inlet filter/plenum. If they are positioned upstream of the inlet system, the filters have to be made of synthetic material. If paper filters were to be employed, the cool high humidity air would cause these filters to swell and become damaged.

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Properties of Humid Air

Roger Legg, in Air Conditioning System Design, 2017

The Psychrometric Equation

The psychrometric equation relates the dry- and wet-bulb temperatures with their corresponding vapour pressures and with the atmospheric pressure. To understand this relationship, consider the diagram of the wet-bulb thermometer in Fig. 1.11.

Fig. 1.11. Diagram of a wet-bulb thermometer.

Moisture is being evaporated from the surface of the muslin sleeve into the surrounding air. For evaporation to take place, heat must be supplied, and this can only come from the ambient air in the form of sensible heat, with the temperature of the bulb lower than that of the surrounding air. At equilibrium, the latent heat loss due to moisture evaporation will equal the sensible heat gained. The air film at the surface of the muslin sleeve is considered to be at saturation moisture content gss′. (Note the ′ to indicate that the moisture content is at the wet-bulb temperature.) The latent heat loss is proportional to the moisture content difference between this air film and the ambient air, i.e., gssg. The sensible heat gained is proportional to the temperature difference between the bulb and the ambient air tt, i.e.,

(1.10)Bgssg=Ctt

where B and C are constants related to parameters of heat and mass transfer, e.g., surface area and latent heat of evaporation.

From Eq. (1.6):

g=0.622pspatps

and

g=0.622psspatpss

Since ps and pss′ are very small compared with pat, these equations may be written as:

g=0.622pspatandgss=0.622psspat

Substituting these expressions of moisture content in Eq. (1.10),

0.622Bpatpssps=Ctt

By rearranging the terms and grouping the constants, the psychrometric equation is obtained:

(1.11)ps=psspatAtt

where A is known as the psychrometric constant.

The numerical difference between the dry- and wet-bulb temperatures is known as the wet-bulb depression.

Since the rate of moisture evaporation depends on the speed of the air over the wet-bulb, the wet-bulb temperature will also depend on the air speed. However, the wet-bulb becomes independent of the air velocity above 2 m/s. The two wet-bulb temperatures described above—sling and screen—cater for this with different values for the constant A.

Wet-bulb temperatures are also affected by the air being either above or below freezing point, and again, different values of A are necessary to deal with these conditions. The psychrometric constants for a 4.8 mm bulb diameter are the following:

sling

A=6.66×104Kwhent>0°C
A=5.94×104Kwhent<0°C

screen

A=7.99×104K1whent>0°C
A=7.20×104K1whent<0°C

When working with the psychrometric equation, it is important to remember that the saturated vapour pressure pss′ is taken at the wet-bulb temperature.

Example 1.10

Calculate the vapour pressure for air with the following conditions:

Dry-bulb temperature22%
Wet-bulb temperature (sling)14°C
Atmospheric pressure1013 mbar

Solution

From Table 1.2, the SVP at 14°C = 15.98 mbar. Since the air is above 0°C and the wet-bulb is a sling reading, the psychrometric constant A is 6.66 × 10 4 K.

Using Eq. (1.11):

ps=psspatAttps=15.981013×6.66×104)×2214=11.93mbar

Lines of constant wet-bulb temperature are drawn on the psychrometric chart, as illustrated in Fig. 1.12.

Fig. 1.12. Lines of constant wet-bulb temperature.

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Experimental techniques

Yanqiu Huang, ... Zhixiang Cao, in Industrial Ventilation Design Guidebook (Second Edition), 2021

4.3.6.4 Psychrometers

A psychrometer measures the dry-bulb and wet-bulb temperatures simultaneously (ASHRAE, 1994; ASTM E337-84 & 1996, 1996; Hickman, 1970; Moisture & Humidity, 1985). The measurement of the wet-bulb temperature is achieved by means of a wet wick placed over the thermometer bulb. The thermometer can be practically of any type. A cylindrically shaped sensor is preferred. The wet-bulb temperature-sensing element, covered with the wick, and the dry-bulb temperature sensor, are placed in the airstream to be measured. The stream, generated by a small fan, should have a velocity of 3–5 m s−1 and can be either transverse or axial. The wick-covered sensor is cooled down by evaporation until it reaches a thermal equilibrium state where the (almost only) convective heat transfer is covering the heat required for water vaporization from the wick.

The humidity can be determined using either charts or equations provided by the psychrometer manufacturer. The partial pressure of water vapor provides a more general approach and can be calculated from the “psychrometer equation”

(4.22)Pw=Pws(Tdb)A(TdbTwb)P

where A is the psychrometer constant and Twb is the wet-bulb temperature. The psychrometer constant has values between 5.4 and 6.9 × 10−4 L/K depending on the airstream velocity and some other factors. To reduce the radiative exchange in hot environments, radiation shields should be fitted to both sensors. The thermometers must be adequately spaced from each other to avoid the wetting of the dry bulb. The dry-bulb sensor should not be in the wake of the wet-bulb sensor to ensure that the correct temperature is measured. The water used in the wick should be pure distilled water to stop limescale buildup on the wick.

A psychrometer fitted with a fan is called an aspirated psychrometer or Assmann hygrometer. Another variant is the sling or whirling hygrometer. In this case the wet-bulb and dry-bulb thermometers are attached to a frame with a handle. When measuring the temperatures, the frame is whirled around like a football rattle. The measurement range is dependent on the range of the thermometers but is usually wide enough for ventilation measurements. The response of the psychrometer is slow, taking a few minutes to reach the wet-bulb equilibrium state. Rapidly changing humidity cannot be monitored. The advantage of an instrument of this kind is that its construction and the fundamental nature of the measurement are simple. For this reason, if handled with care, it is a cheap but reliable instrument.

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CURRENT STATUS OF DROPLET AND LIQUID COMBUSTION

G.M. FAETH, in Energy and Combustion Science, 1979

Fluid properties

For volatile fuels at low pressures, the wet-bulb temperature is close to typical injection temperatures, and liquid-phase properties can be assumed to be constant. At higher pressures, however, reduced liquid densities cause the droplet to swell and variable properties must be considered for accurate work.98

Except at high pressures, which will be considered later, the ideal gas assumption is made for the gas phase. A number of analyses have been conducted for variable gas phase property effects on the evaporation process;94,99,100 additional studies for a combusting droplet will be considered later. While early variable property studies only considered variable temperature effects, recent work has also treated variable concentration effects, since the effect of species concentrations can be appreciable, particularly for heavy hydrocarbon fuels which have much different properties than the light gases generally comprising the environment of an evaporating drop.

Hubbard, Denny, and Mills94 considered variable property effects using a complete model which considers both concentration and temperature effects. These results were compared with constant property models using reference conditions recommended by: (a)Knuth;101 (b) Sparrow and Gregg;102 and (c) Law and Williams.103 Best results were achieved using the 1/3 rule of Sparrow and Gregg,102 where average properties are evaluated at the following reference temperatures and compositions

(12)Tr=Ts+1/3(TTS)YFr=YFs+1/3(YFYFs)

These calculated results are for a motionless drop, and the rules can differ in the presence of convection. A number of different treatments will be considered in the context of the convection correlations.

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Refineries

Nicholas P. Cheremisinoff Ph.D., ... Anton R. Davletshin, in Responsible Care, 2008

4.9.10 Cooling Towers

Cooling towers are a major workhorse at any refinery operation. The makeup water source is used to replenish water lost to evaporation. Hot water from heat exchangers is sent to the cooling tower. The water exits the cooling tower and is sent back to the exchangers or to other units for further cooling.

Cooling towers fall into two main subdivisions: natural draft and mechanical draft. Natural draft designs rely on large concrete chimneys to introduce air through the media. Due to the tremendous size of these towers (500 ft high and 400 ft in diameter at the base), they generally are used for water flow rates above 200,000 gal/min. Usually, these types of towers are used only by utility power stations in the United States. Mechanical draft cooling towers are much more widely used and common at refineries. These towers utilize large fans to force air through circulated water. The water falls downward over fill surfaces, which help increase the contact time between the water and the air. This helps maximize heat transfer between the two.

Mechanical draft towers offer control of cooling rates in their fan diameter and speed of operation. These towers often contain several areas (each with its own fan), called cells. Heat is transferred from water drops to the surrounding air by the transfer of sensible and latent heat. Thermodynamics dictate that the heat removed from the water must be equal to the heat absorbed by the surrounding air. The increased heat load causes the hot water temperature to increase considerably faster than the cold water temperature.

Cooling towers are designed according to the highest geographic wet bulb temperatures. This temperature dictates the minimum performance available by the tower. As the wet bulb temperature decreases, so does the available cooling water temperature. The following is the summary of steps in the cooling tower design process in industry:

The plant engineer specifies the cooling water flow rate and the inlet and outlet water temperatures for the tower.

The manufacturer designs the tower to be able to meet this criteria on a “worst case scenario” (i.e., during the hottest months). The tower characteristic curves and the estimate are provided to the plant engineer.

The plant engineer reviews the bids and makes a selection.

Once a tower characteristic has been established between the plant engineer and the manufacturer, the manufacturer must design a tower that matches this value. The required tower size is a function of its

Cooling range.

Approach to wet bulb temperature.

Mass flow rate of water.

Web bulb temperature.

Air velocity through the tower or individual tower cell.

Tower height.

Water losses include evaporation, drift (water entrained in discharge vapor), and blowdown (water released to discard solids). Drift losses are estimated to be between 0.1% and 0.2% of the water supply.

Even during cold weather months, the plant engineer should maintain the design water flow rate and heat load in each cell of the cooling tower. If less water is needed due to temperature changes (i.e., the water is colder), one or more cells should be turned off to maintain the design flow in the other cells. The water in the base of the tower should be maintained between 60°F and 70°F by adjusting air volume if necessary. The usual practice is to run the fans at half speed or turn them off during colder months to maintain this temperature range.

An improperly maintained cooling tower produces warmer cooling water, resulting in a condenser temperature 5–10°F higher than a properly maintained cooling tower. This reduces the efficiency of the chiller, wastes energy, and increases cost. The chiller will consume 2.5–3.5% more energy for each degree increase in the condenser temperature. For example, if a chiller uses $20,000 of electricity each year, it will cost an additional $500–700 per year for every degree increase in condenser temperature. Therefore, for a 5–10°F increase, one can expect to pay $2500 to $7000 a year in additional electricity costs. In addition, a poorly maintained cooling tower has a shorter operating life, is more likely to need costly repairs, and is less reliable. The performance of a cooling tower degrades when the efficiency of the heat transfer process declines. Some common causes of this degradation include:

Scale deposits. When water evaporates from the cooling tower, it leaves scale deposits on the surface of the fill from the minerals dissolved in the water. Scale buildup acts as a barrier to heat transfer from the water to the air. Excessive scale buildup is a sign of water treatment problems.

Clogged spray nozzles. Algae and sediment that collect in the water basin as well as excessive solids get into the cooling water and can clog the spray nozzles. This causes uneven water distribution over the fill, resulting in uneven air flow through the fill and reduced heat transfer surface area. This problem is a sign of water treatment problems and clogged strainers.

Poor air flow. Poor air flow through the tower reduces the amount of heat transfer from the water to the air. Poor air flow can be caused by debris at the inlets or outlets of the tower or in the fill. Other causes of poor air flow are loose fan and motor mountings, poor motor and fan alignment, poor gear box maintenance, improper fan pitch, damage to fan blades, and excessive vibration. Reduced air flow due to poor fan performance ultimately can lead to motor or fan failure.

Poor pump performance. An indirect cooling tower uses a cooling tower pump. Proper water flow is important to achieve optimum heat transfer. Loose connections, failing bearings, cavitation, clogged strainers, excessive vibration, and nondesign operating conditions result in reduced water flow, reduced efficiency, and premature equipment failure.

The cooling tower manufacturer's operation and maintenance instructions should be followed whenever possible. Larger, more complicated cooling towers with special filters or controls demand a comprehensive maintenance program.

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Mixtures of Gases and Vapors

Robert T. Balmer, in Modern Engineering Thermodynamics, 2011

Design Problems

The following are open-ended design problems. The objective is to carry out a preliminary thermal design as indicated. A detailed design with working drawings is not expected unless otherwise specified. These problems do not have specific answers, so each student's design is unique.

53.

Design an electrically driven sling psychrometer to produce the wet and dry bulb temperatures on digital readouts. The finished product must cost less than 30.0 h of minimum wage pay and be battery powered. If possible, fabricate and test your design. (Suggestion: Try designing around inexpensive, “off the shelf” components.)

54.

Design an apparatus to measure the dew point of an air sample based on the cooling of a mirrored surface until it fogs. If possible, build and test this apparatus. (Suggestion: Consider thermoelectric cooling of a polished metal plate.)

55.*

Design a system to remove the respiration carbon dioxide from inside a spacecraft and replace it with oxygen. Use a living quarters volume of 10.0 m3 with the crew generating a maximum of 2.00 × 10−5 m3/s of CO2. Assume the mixture enters your system at 30.0°C and exits it at 20.0°C. Maintain the same oxygen partial pressure in your mixture as that in atmospheric air at 0.1013 MPa and 20.0°C.

56.*

Design a system to remove the respiration carbon dioxide from inside a submarine and replace it with oxygen. The air volume of the submarine is 1000. m3, and the crew can generate a maximum of 1.30 × 10−3 m3/s of CO2. The submarine must be able to achieve a depth of 300. m. Assume the air mixture enters your system at 30.0°C and exits at 20.0°C. Maintain the oxygen partial pressure at all times in your mixture equal to that in atmospheric air at 0.1013 MPa and 20.0°C.

57.*

Cooling towers are large evaporative cooling systems that can be used to transfer heat from warm water to the atmosphere by evaporation of the water to be cooled. Prepare a preliminary design for a cooling tower that will cool 30,000 kg/s of water from 40.0°C to 30.0°C. Atmospheric air enters at 20 ± 10°C with a relative humidity of 45 ± 15%. Establish the overall physical dimensions of the cooling tower, air flow rate, water pumping power, fan power (if forced convection is used), makeup water requirements, air exit conditions, and so forth (Figure 12.15).

Figure 12.15. Problem 57.

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Physical fundamentals

Howard D. Goodfellow, Eric F. Curd, in Industrial Ventilation Design Guidebook (Second Edition), 2020

4.4.3.1 Open recirculation

Open recirculation includes the standard cooling tower, spray pond, or evaporator condenser as shown in Fig. 4.39. An arrangement of this type provides an efficient cooling system. Its main disadvantage is the growth of microorganisms such as the Legionella species. To protect people from these bugs, the biological water treatment represents a very high cost in the operation of the plant. This arrangement is losing favor with many engineers and is being replaced by the less efficient closed systems.

Figure 4.39. Cooling water system (open recirculation).

Typical applications include heat rejection from the refrigeration plant. The highest proportion of cooling takes place by evaporation.

Advantages

1.

It can cool water down to 2°C above the wet-bulb temperature.

2.

Average temperature drop through tower in 10°C–18°C range depends on wet-bulb temperature.

Disadvantages

1.

Corrosion due to absorption from the atmosphere of pollutants as the water droplets pass through the tower.

2.

Fouling of surfaces, resulting in decreased heat transfer efficiency.

3.

Scale buildup, resulting in a reduction of fluid flow through the heat exchanger and loss of effectiveness.

4.

Microbiology problems (such as 2 and above 3) together with corrosion of materials and health hazards.

5.

Decay problems in wooden cooling towers.

6.

Spray water loss, resulting in costly additional water treatment for the makeup water

7.

Spray drift may cause annoyance to people in its path, as well as corrosion of adjacent metals and concrete breakdown; improved design of drift eliminators available (in PVC) for critical control of drift.

The temperature difference between the recooled water temperature and the inlet air wet-bulb temperature is called the approach. The lower the approach, the more complex the tower’s design becomes. The normally used minimum approach temperature is 2°C.

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Definitions of terms used in humidification engineering

B. Purushothama, in Humidification and Ventilation Management in Textile Industry, 2009

Psychrometric tables give the relative humidity in percent considering the dry bulb and wet bulb temperatures. Take the temperature with both dry-bulb and wet-bulb thermometers. Find the difference between the two measurements, and then see where the numbers intersect on the chart below to get the RH%.

Table 15.5. Psychrometric table °F

Temperature on a dry-bulb thermometerTemperature difference between dry-bulb and wet-bulb Thermometers
456789101112
Relative humidity %
406860524537292215 7
50746761554943383227
60787368635853484339
70817772686459555148
80837975726864615754
90858178747168656158

Table 15.6. Psychrometric table °C

Temperature on a dry-bulb thermometerTemperature difference between dry-bulb and wet-bulb thermometers
1.52.02.53.03.54.04.55.07.5
Relative humidity %
10827671656054494419
15858075706661575231
20878278747066625840
25888481777370666347
30898682797673706752
35908784817875726956
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Theoretical Grounds for Humidity

Dario Camuffo, in Microclimate for Cultural Heritage (Second Edition), 2014

2A.9 Wet Bulb Temperature: The Temperature of Evaporation

The wet bulb temperature Tw (or tw) or isobaric wet bulb temperature, is the temperature an air parcel would have if adiabatically cooled to saturation at constant pressure by evaporation of water into it, all latent heat being supplied by the parcel. This temperature is directly measured by the wet bulb of a psychrometer, or can be obtained indirectly by means of a psychrometric diagram or formula, after the dry bulb temperature and any one hygrometric value (i.e. e, MR, SH, AH, RH or DP) are known. From the thermodynamic point of view, Tw is the temperature that an air parcel would have when some liquid water is supplied gradually, in very small quantities and at the same temperature as the environmental air, and then this water is evaporated into the air adiabatically (i.e. the latent heat being supplied by the air) at constant pressure, until saturation is reached. Saturation is reached for the combined action of two factors due to the evaporation: the increase in MR and the drop in T. Consequently, Tw is the lowest temperature that an air parcel would have by evaporating water, the latent heat being subtracted from the air and utilized for the change of state of water from liquid to vapour, until saturation is reached. Tw is also the equilibrium temperature of an evaporating surface of water.

Applying the first law of the thermodynamics to an air parcel formed of 1 g of dry air with a mass of vapour mv, i.e. with mixing ratio w = mυ, and experiencing the above process,

(2A.46)TTwcpm(1+mυ)T=mυmwLυmυ

where cpm is the isobaric specific heat of the moist air that can be expressed in terms of isobaric specific heat of dry air cpd (cpd = 0.240 cal g−1 K−1 = 1.003 J g−1 K−1), i.e. cpm(1+0.8mυ)cpd and Lv is the latent heat. After integration, by dividing both sides by (cpd + <w>c), the wet bulb depression ΔTw = T  Tw is obtained

(2A.47)ΔTw=(msat,wmυ)Lυcpd+<w>cpυ

where <w> is the average mixing ratio during this process, msat,w is the saturation mixing ratio at the temperature Tw and cpv is the isobaric specific heat for the water vapour (c = 1.81 J g−1 K−1). A further approximation of the wet bulb depression is obtained by using the formula (2A.19) for w and considering that cpd + <w>c  cpd (i.e. <w> << 1), so that the wet bulb depression becomes

(2A.48)ΔTw0.622Lυ(ewe)cpdp

where ew is the vapour pressure at Tw. This equation can be solved with successive approximations for every initial set of T, p and e. Graphic solutions are popularly used.

Saturation occurs at temperature Tw for the dynamic equilibrium that follows the increase of MR for the water that is added to the system. From the definition, Tw is conservative with reference to the evaporation of falling raindrops. In the case of an evaporating porous surface, the evaporation rate is generally modest, so that T tends towards Tw but hardly reaches it; the MR increases at the interface, generating a negative gradient of MR (i.e. MR decreasing for diffusion from the surface) and a positive gradient of T in the air close to the evaporating surface. In the opposite case of evaporation occurring in the internal pores of a wall, the latent heat is supplied by the masonry and the air temperature remains unchanged, but the evaporation is still evidenced by a negative gradient of MR.

An analogy exists between DP and Tw: both are based on isobaric cooling until saturation is reached but DP is reached without changes in MR. On the contrary, Tw is reached with the addition of external water, which raises the MR of the air parcel, favouring saturation. For this reason, DP cannot be reached with evaporation cooling, even in the case a forced ventilation is applied. DP is the temperature typical of condensation and Tw is typical of evaporation.

In addition,

(2A.49)DPTwTandΔDPΔTw0

where the identity holds only for RH = 100% when DP = Tw = T.

In atmosphere, saturation is usually found on foggy days or at night when dew is forming. In general, during fog, the RH is 95%  RH  100%. During short rainfalls or showers, saturation is only seldom reached. Summer showers may occur with low RH and the precipitated water then evaporates in a short time.

Tw can be easily measured by means of a psychrometer, which is composed of a couple of ventilated thermometers, i.e. a normal one (i.e. the dry bulb) and another having the bulb (i.e. the wet bulb) covered with muslin, which supplies water adsorbed for capillarity from a reservoir. The speed of blown air generally lies between 3 and 5 m s−1 (see Chapter 12). It is evident that, for a given temperature, the greater the MR, the higher the DP. The same can be said for Tw that lies between T and DP. It is also obvious that Tw is related to the degree of saturation of the vapour in air, in that the higher the RH, the smaller the amount of water that should be evaporated to reach saturation and, consequently, the cooling ΔTw caused by the absorption of the latent heat for vaporization. When the wet bulb is ventilated, its temperature will be lowered until the equilibrium is reached.

The latent heat Qv lost by evaporation from the wet bulb is

(2A.50)Qυ=CLυSewep

where C is a proportionality coefficient, Lv is the latent heat of vaporization, S is the surface area of the evaporating surface, e is the actual vapour pressure, ew = esat(tw) is the saturation vapour pressure at the temperature of the evaporating surface and p is the atmospheric pressure. This equation is known as the Dalton law of evaporation. On the other hand, the sensible heat Qs transferred from the ambient air (at temperature T) to the colder wet bulb (temperature Tw) is

(2A.51)Qs=BS(TTw)

where B is another proportionality coefficient.

At equilibrium, the loss of latent heat Qv equals the gain of sensible heat Qs. Equating the two above equations, the basic psychrometric formula is obtained

(2A.52)e=esat(Tw)Ap(TTw).

where A = (B/C Lv) is the so-called psychrometer coefficient, which is not really a constant and depends, inter alia, on the ventilation rate (see Chapter 12).

In the (2A.30) definition of relative humidity, substituting e with the psychrometric formula, esat with the Magnus and Tetens formula (2A.1), and the coefficient A = 6.667 × 10−4 K−1 and then dividing numerator and denominator by esat(0) = 6.11 hPa, a useful equation is derived

(2A.53)RH=10010atw/(b+tw)1.09×104p(ttw)10at/(b+t)

which allows a precise determination of RH after measurements of t and tw and, consequently, precise calculations of MR (Eqn (2A.33)), e (Eqn (2A.36)), AH (Eqn (2A.38)) and DP (Eqn (2A.28)). This equation has been reported in the form RH versus ΔTw in Fig. 2A.6 for selected values of T.

FIGURE 2A.6. Relative humidity (RH) from psychrometric measurements, i.e. air temperature t and wet bulb depression t  tw. Lines refer to different values of air temperature, i.e. from t = −20 to t = 40 °C. Values below 0 °C (dashed lines) are calculated for vapour in equilibrium with supercooled water.

The ΔTw depression is also calculated after the readings of T and DP with the following empirical formula:

(2A.54)ΔTw=ΔDP(1.281×104t2+0.01786t+0.3682)0.00889ΔDP2.

where the DP spread is computed using Eqn (2A.45) in the case of known RH instead of DP. Conservators do not commonly use this inverse formula because it gives values that they can directly observe with instruments. However, meteorological services furnish the DP instead of the ΔTw or the RH and one could use such data to calculate other basic parameters.

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Cooling tower and cooling water circuits

Alireza Bahadori PhD, in Essentials of Oil and Gas Utilities, 2016

5.3 Design considerations

5.3.1 Design parameters

The parameters involved in the design of a cooling tower are:

1.

ambient wet-bulb temperature;

2.

approach;

3.

cooling range;

4.

circulating water flow;

5.

altitude (considered if more than 300 m above sea level).

An additional parameter in the case of natural draught towers is ambient dry-bulb temperature or, alternatively, ambient relative humidity.

5.3.2 Ambient air temperatures

It is important that the correct design ambient conditions are chosen with care. Generally the hottest period of the year is selected as the critical area to be studied. For climatic conditions the atmospheric information covering the average 5 hot months period inclusive, i.e., last 2 months of spring and summer months (May to Sep. inclusive) are analysed and presented in the form of wet and dry bulb temperature isotherm maps for the different localities.

In general the tower should be designed for a wet-bulb temperature that will not be exceeded more than 2.5% of the time in five hot spring and summer months.

5.3.3 Packings

The function of packing in a cooling tower is:

1.

to increase the duration of contact between the air and the water;

2.

to cause fresh surfaces of water to be formed, thus increasing the rate of heat transfer per unit volume.

5.3.3.1 Types and selection

Packing may be of the two types namely splash packings and film packings. The intended situation of a tower should be considered in deciding on a particular type of packing. In general, the film packings will be more susceptible to fouling by suspended solids, fats and oils, biological growth, or other process contamination. Where fouling may become a problem, the spacing and configuration of the packing elements should be considered regarding the potential for cleaning.

5.3.3.2 Height of packing

The height of cooling tower packing will vary considerably even within the various types of packing according to the design economics relating to any specified requirements. In general, it can be stated that for equivalent duties and fan power requirements the film or extended surface packings will be of lower height than the splash bar type of packing.

5.3.4 Cooling range and water quantity

Cooling range and water quantity variations are usually considered in relation to a fixed heat load and are selected in conjunction with other plant conditions.

5.3.5 Recirculation

The percentage of air recirculating on the leeward side of the cooling tower can vary between 3% and 20%. However, the higher figure is normally associated with installations of one or more large multicell mechanical draught cooling towers.

In general, therefore, recirculation of the warmed air discharged from the cooling towers is relatively insignificant in mechanical draught cooling towers under 0.5 m3/s capacity. For other cases allowance should be made for the maximum anticipated recirculation.

Hydrocarbon detection facilities to be located in cooling tower basins should be provided to account for probable hydrocarbon leakage.

5.3.6 Approach

Approach is a very sensitive design parameter. Closer approaches are limited by practical difficulties such as minimum water loading on the packing.

The cooling tower supplier should be consulted before consideration is given to approaches closer than 3°C for mechanical draught towers or 7°C for natural towers.

At these levels an increase of 1°C in approach may result in a reduction of 20% in tower size and is therefore of considerable economic significance.

A 5.5°C approach between cold-water temperature and wet-bulb temperature should be used unless otherwise specified.

5.3.7 Water loadings

The maximum water loading on a packing is determined largely by the increase in resistance to airflow and by the risk of excessive drift.

Somewhat higher water loadings can in general be used in a cross flow-cooling tower irrespective of the type of packing.

Cooling tower water loadings do not approach the level at which flooding takes place. The only problem with high water loadings is in obtaining adequate airflow and cross flow towers will often therefore be found advantageous.

Water loading should not exceed 407 L/m2 per min (10 gpm/ft.2) of tower cross section area in the horizontal plane.

5.3.8 Windage losses

Typical windage losses, expressed as percentages of the total system water circulation rate, for different evaporative equipment are as follows:

Spray ponds1.0–5.0%
Atmospheric draft towers0.3–1.0%
Mechanical-draft towers0.1–0.3%

5.3.9 Drift losses

Drift losses should not exceed 0.01% of design flow rate. (For further information reference is made to BS 4485:Part 3: 1988)

5.3.10 Effect of altitude

Cooling tower calculations involve the use of published tables of psychometric data that are generally based on a barometric pressure of 1000 mbar (1 mbar = 100 N/m2 = 100 Pa). Barometric pressure falls at a rate of approximately 1 mbar for each 10 m increase in altitude and, although this may be ignored for locations up to 300 m above sea level, appropriate corrections should be applied when designing for sites at higher altitudes.

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