JOURNAL OF

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Journal of Wind Engineering ~ ~ and Industrial Aerodynamics 62 (1996) 259-277 ELSEVIER

The influence of wind on the performance of forced draught air-cooled heat exchangers

K. Duvenhage, D ,G . Kr6ger* Department of Mechanical Enyineering, University of Stellenbosch, Stellenbosch, South Africa

Received 5 January 1996; accepted 18 November 1996

Abstract

The influence of wind on fan performance and recirculation in a forced draught air-cooled heat exchanger (ACHE) bank is investigated numerically. Winds blowing across and parallel to the longitudinal axis (long axis) of an ACHE bank are considered. It is fotmd that cross winds significantly reduce the air volume flow rate that is delivered by the up-wind fans, while winds along the longitudinal axis cause increased hot plume air recirculation along the sides of the ACHE bank.

Keywords: Air-cooled heat exchanger; Air flow about heat exchangers; Wind effects; Recirculation; Fan performance

Nomenclature

A area ACHE air-cooled heat exchanger C chord C1, C2, Cu constants in turbulence equations CD drag coefficient CL lift coefficient Cp specific heat d diameter e effectiveness Eu Euler number F force or fan 9 gravitational acceleration G production term h heat transfer coefficient H height k turbulent kinetic energy

* Corresponding author.

0167-6105/96/$15.00 Copyright @ 1996 Elsevier Science B.V. All rights reserved. PH S01 67-6105(96)00082-7

260

K m n

P Pr

Q

; S t T u V

V u

x, y>z

; r e

P P 0

4 Y

K. Duvenhage, D.G. Krdgerl J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

pressure drop coefficient mass flow rate number pressure Prandtl number torque or heat transfer radius or recirculation factor gas constant source term thickness temperature or thrust overall heat transfer coefficient velocity volume flow rate velocity vector coordinates or distance dissipation rate of turbulent kinetic energy relative angle diffusion coefficient relative angle dynamic viscosity density Prandtl number for k and E general variable rotor solidity

Subscripts

a aa B C

do e f Fb fr Fr he

id m 0

r ref

sys

air ambient air buoyancy contraction down-wind effective fluid fan blade frontal fan rotor heat exchanger inlet ideal mean outlet relative or recirculation reference system

K. Duvenhaye, D.G. Kr6ger/J. Wind Eng. Ind Aerodyn. 62 (1996) 259-277 261

t turbulent tb tube bundle up up-wind w wind x, y, z coordinates 0 angle tp related to specific variable

I. Intreduction

A thorough understanding of the flow field and associated phenomena around an air- cooled heat exchanger (ACHE) is important for the optimal design of such a system. Most major air flow losses in the ACHE system are well documented [1]. One of the air flow phenomena in the system that is poorly documented is the effect of wind on the overall performance of an ACHE. This effect can be divided into essentially two coupled categories.

The first category is plume recirculation. Plume recirculation occurs when a part of the hot buoyant plume or jet, exiting the ACHE, is drawn back into its inlet. This portion of the inlet air does not contribute effectively to the heat exchange resulting in reduced performance of the ACHE. Du Toit and Krrger [2] reported a numerical and ana]ytical investigation on recirculation in windless conditions. This research was extended by Duvenhage and Krrger [3] and an empirical correlation was introduced with which plume recirculation in windless conditions can be predicted for different forced draught ACHE geometries.

Several other studies of plume recirculation have also been reported in the literature. Most of these studies are experimental investigations performed on heat exchangers having specific geometries and operating under prescribed conditions [4-7, 8].

Because of the complexity of the phenomenon, numerical studies are very limited. Becker et al. [9] describe a two-dimensional numerical method to model wind-induced plume recirculation. The model yields results which are in good agreement with phys- ical intuition and compare well with basic theory and reported laboratory and field results.

The Cooling Tower Institute (CTI) [10,11] was formed in 1951 with the primary purpose of measuring plume recirculation in mechanical draught cooling towers. The test procedure consisted of field tests on 30 cooling towers of various manufacturers. An empirical correlation was derived, based on those test results that gave the maximum plume recirculation for each tower tested. The results indicated that plume recirculation was predominantly a function of tower length. Twenty-eight of the 30 towers tested were induced draught systems. The correlation is thus primarily applicable to induced draught cooling towers and for winds that blow in the longitudinal direction. However, the authors stated that they expected the maximum plume recirculation of a forced draught ,;ystem to be twice the value predicted by the correlation.

The second category is the influence of wind on fan performance. During tests on a full-scale ACHE, Turner [12] observed flow separation at the fan inlet cone due to

262 K. Duvenhage, D.G. Kr69erlJ. Wind Eng. Ind. Aerodyn. 62 (1996) 259 277

\ \, PLAN

Longiu!ai-~) wind ~ \ ~ ~ t........._J

I

SIDE EI..EVATION

F..ND ELEVATION

Fans

/ j : Heat exehange~ ~--- Plenum

Inlet shroud

- - Towex support

Fig. 1. Diagram of a part of a long ACHE bank.

the prevailing wind. This separation causes a maldistribution of air at the fan inlet with a corresponding reduction in fan performance. The influence of wind on fan performance appears to exhibit features similar to the influence of fan platform height on fan performance. A numerical and experimental investigation on the latter is reported by Duvenhage et al. [13].

A numerical and experimental investigation on the influence of crossflow on fan performance is reported by Thiart and Von Backstr6m [14]. They observed a significant reduction in fan performance due to crossflow.

As previously mentioned, the two effects due to wind are inherently coupled. Du Toit et al. [15] reported a numerical investigation in which the influence of wind on both plume recirculation and fan performance was investigated simultaneously. The authors concluded that the heat transfer of an ACHE should be based on local flow conditions and that the influence of the flow field on fan performance and recirculation should be taken into account.

Forced draught ACHEs in the petroleum and chemical industries are usually erected in the form of long banks. A bay usually consists of two side-by-side tube bundles with two axial flow fans, with their axes in the vertical position, fitted to each bay. Such bays are then placed side-by-side to form an ACHE bank. Sets of bays, 16 or more long are very common. Fig. 1 shows a part of a long (essentially two-dimensional)ACHE bank.

The aim of the present paper is to determine the influence of two wind directions on the heat transfer of a typical ACHE bank at a petrochemical plant.

2. Numerical model

The general purpose code, PHOENICS [16-18], for numerical simulations of fluid flow, heat transfer and chemical-reaction processes is used to simulate the air flow

K. Duvenhage, D.G. Kr6ger/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277 263

pattern about and through a typical ACHE bank. Two wind directions are considered namely, wind across and wind parallel to the longitudinal axis of the ACHE. It is assumed that the wind profile can be described by a power law [19], i.e.

vw = Vwref , (1)

where Vwref is the reference wind velocity at the reference height Zre f. The reference height is taken as the ideal fan platform height of the particular ACHE in windless conditions [13], i.e. 5.7 m above ground level. The value of the exponent b is taken as 0.2 as recommended by VDI 2049 [20].

2.1. Governing equations

The F'HOENICS code provides solutions to the discretized version of sets of differ- ential equations having the general form:

d iv (pv - F grad ) = S, (2)

where p is the density, v the velocity vector, = 1, Vx, Vy, Vz, T, k and e, F~ the diffusion coefficient and S the source term.

The expressions for S and F are specific to a particular meaning of and are given in Table 1.

The fi)rces exerted by the fan blades on the air as well as the pressure drop through the tube bundles are incorporated in the force terms Fx, Fy and Fz.

Table 1 The forms of the diffusion coefficient and the source term in Eq. (2)

1 o o

T 7

k G -- pe ~---~ c~ k

e }(Cl G - C2p~) ~

where

G=pe 2 ~x +t '~/ ) +1 ay) ) +! t& + ay.] +t & + ,y ] +

264 K. Duvenhage, D.G. Kr69er/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

The effect of the buoyancy force on the air is modelled via the Boussinesq variable density model and is incorporated in the body force term, FB:

FB = g(p -- Pref). (3)

With the reference density, Pref, equated to the ambient density, Paa, this equation gives the buoyancy force that arises from the differential variation of the density field about this mean. This has the effect of implicitly removing the hydrostatic variation of pressure from the pressure field. The absence of the hydrostatic component in the pressure field also simplifies the specification of the pressure boundary conditions, for often the so-called "reduced pressure" is constant at the boundaries [21].

It is assumed that the k-e model of Launder and Spalding [22] satisfactorily describes the turbulent nature of the flow.

The effective viscosity, #e, is given by

]Ae = ]A -[- ]At, (4)

where ]A is the laminar dynamic viscosity of air and ]A t the turbulent eddy viscosity. The turbulent eddy viscosity is expressed as follows:

k 2 ]At = C#P T . (5 )

The Prandtl number in the temperature equation is taken as Pr = 0.71 and the empirical constants which appear in the turbulence equations are assigned the values shown in Table 2 [23].

The governing equations are discretized using the finite volume method as described by Patankar [24]. PHOENICS employs a staggered grid formulation and also uses the SIMPLEST pressure correction algorithm as described by Spalding [25]. A full description of PHOENICS is given by Rosten and Spalding [16-18].

Under-relaxation, using the false-time-step mode on the momentum, temperature, k and ~ equations and linear under-relaxation on the pressure and the other algebraically calculated values of density and turbulent eddy viscosity, are employed to ensure convergence.

2.2. Cross wind model

A fan bay which is a part of a long, essentially two-dimensional ACHE bank as shown in Fig. 1 is considered. The ACHE bay has a frontal tube bundle area of 7.07 10.2 = 72.12 m 2 per bay, a tube bundle height of 0.72 m, a plenum height of 3.0 m. Each bay contains two 6 blade, 4.31 m diameter axial flow fans with

Table 2 Values of the constants in the turbulence equations

Cp C1 C2 ak ae

0.09 1.44 1.92 1.0 1.3

K. Duvenhage, D.G. Kr6gerlJ. Wind Eng. Ind Aerodyn. 62 (1996) 259-277 265

zl Y

Ple~ama

3.0

Hh e

5.1 ~ Heat exchanger

- ll:allnl n lmm j

0 4.31 Cylindrical shroud

Bay length = 7.07

Fig. 2. Section through a single bay of an ACHE bank (dimensions in meters).

cylindrical inlet shrouds. The main dimensions of a bay of the ACHE bank are shown in Fig. 2.

Because the influence of wind on fan performance seems to exhibit the same features as the influence of fan platform height on fan performance, the same numerical model, which produced reliable results in Ref. [13], is used.

The axial fan is modelled with the aid of the blade element theory as described by Ref. 1114]. This theory which is commonly employed for aircraft and ship propeller calculations was adapted by Thiart and Von Backstrrm [14] and successfully employed in simulating the flow field near an axial fan operating under distorted inflow conditions.

The influence of the fan blades are modelled as body forces exerted on the air. Each blade element between two radii r and (r + 8r) experiences a lift force, 8L, and a drag force, 5D. It is assumed that there are no radial forces. These two forces are, respectively, normal and parallel to a relative velocity vector, yr. This relative velocity vector is composed of the axial velocity component and the azimuthal velocity component of the air relative to the blade element. By decomposing the lift and drag forces into axial and azimuthal components, the thrust and torque exerted by the blade element on the air are obtained. Body forces appear in the Navier-Stokes equations as forces per unit volume. The thrust and torque per unit volume exerted by a blade element on the air are given by, respectively,

01" 1 2 ~ - - "~p.Vr 7[CL cos/~ - CD sin/~], (6)

aV tFr

~Q_ 1 v,

~/" ~ - tT Fr

266 K. Duvenhage, D.G. Kr69er/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

with

nFbfFb T - -

2~zr '

7 j is the solidity of the rotor and fl is the angle between the relative velocity vector and the plane of rotation of the blade element.

In the numerical model the pressure drop through the ACHE is modelled as a force exerted on the air in a direction opposite to the air flow direction. From design data for the modelled ACHE the pressure drop for normal flow conditions through the finned tube bundles is determined from the Robinson-and-Briggs correlation [26] for a six-row tube bundle with round finned tubes in a staggered tube layout, i.e.

Ap (Ac) 2 = 120.016 = [ ma ] -0316

Eu paV2r \Afr// [. ~-~fr J " (8)

To determine a pressure drop coefficient, based on the frontal velocity of the ACHE, Eq. (8) can be rewritten in the following form:

(Afr "~ 2 [paVfr ] -0"316 /(he = 2Eu \~-c J = 928.873 (9)

[~a J

Incoming flow streamlines approach the finned tube bundles at an angle and are then directed by the closely spaced fins to leave the finned tube bundles normal. The entering flow tends to separate at the leading edge of the tube fins, which results in an additional pressure loss. Moore and Torrence [27] quantified this pressure loss as follows:

gio= 1 _1 , (10)

with 0 the angle between the approach velocity and the tube bundle. The value of Kio is restricted to Kio

I~ Duvenhage, D.G. Kr6gerlJ. Wind Eng. Ind Aerodyn. 62 (1996) 259-277 267

relation [29] for cross flow conditions.

Ta~= The- (The- Tai)exp ( -Cp~a) . (12)

The performance characteristics of the heat exchanger bundles are incorporated into the numerical model by expressing the overall heat transfer coefficient as a function of the air mass flow rate. The air-side heat transfer coefficient in terms of the frontal velocity of the ACHE is determined with the aid of the Briggs-and-Young correlation [30] while the process fluid-side heat transfer coefficient, hf, is assumed to be constant. With Cp also kept constant Eq. (12) can be rewritten as follows:

( (1/108392.6053v~ 681 +1/223.19hf)-1~ Tao = The -- (The -- Tai) exp 36.06CpPaVfr j . (13)

The atmosphere is considered to be an infinitely large volume of air of homogeneous composition in a uniform gravitational field. The air is assumed to be incompressible and the local density is determined according to the ideal gas law:

P (14) P = ~-~,

where R is the gas constant. All calculations were done for The=371.15 K, Cp=I007.2 J/kgK and h f=

1208W/m 2 K. The computational domain is constructed in such a way that the physical dimension of height, /-/he, could easily be changed. The other geometrical dimensions of the ACHE are kept constant.

A body-fitted non-orthogonal coordinate system is used, consisting of 28 138 98 cells in the x-, y- and z-direction, respectively. The grid is non-uniformly spaced so as to have a greater concentration of cells near the ACHE and the buoyant plume where ~aore detailed information is required. The fan and the fan inlet shroud are modLelled in a grid area of 20 20 10 cells which are adapted to form a cylindrical pipe. A section of the computational grid around the fan is shown in Fig. 3.

The free atmospheric boundaries are placed far away from the ACHE so as not to influence the flow field around the ACHE.

2.3. Lor,~gitudinal axis wind model

Becau:~e of the symmetry plane along the longitudinal axis of the ACHE, only half of the ACHE bank needs to be considered. The edition of PHOENICS used, does not provide Jbr local grid refinement. If all the fans in the considered half of the ACHE are to be modelled extensively, as described in the cross wind model, the computational domain will get unrealisticly large.

In the case of the longitudinal axis wind the fans are modelled with a simplified fan model as; described in Ref. [3]. The volume flow rate through each fan of the ACHE bank is assumed to be uniform. The upper surface of the ACHE is modelled as a

268 K. Duvenhage, D.G. Kr69er/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

L x Y

Fig. 3. A section of the computational grid around the fan.

source and the bottom surface as a sink. It is assumed that the pressure rise due to the fans is cancelled by the pressure drop over the ACHE. It is further assumed that only the fans of the first two bays at the up-wind side of the ACHE bank are influenced by the wind, The cross wind solutions are used to prescribe the volume flow rate of the fans in the first two up-wind bays, while the other fans are assumed to deliver the same volume flow rate as in windless conditions.

The heat transfer to the air by the ACHE is calculated in the same manner as described in the cross wind model.

The computational domain is constructed in such a way that the number of bays in the ACHE bank could easily be changed. The fan platform height is kept constant at I0.7 m.

A body-fitted non-orthogonal coordinate system is used, consisting of 43 x 128 x 70 cells in the x-, y- and z-direction, respectively. The gird is non-uniformly spaced so as to have a greater concentration of cells near the ACHE and the buoyant plume where more detailed information is required. The free atmospheric boundaries are placed far away from the ACHE so as not to influence the flow field around the ACHE.

2.4. Boundary conditions

A dual temperature boundary condition is applied at all the atmospheric boundaries. A zero gradient is prescribed at any point where outflow over the boundary occurs. When inflow over the boundary is encountered the temperature is assumed to be equal to the ambient temperature. A zero gradient boundary condition is also prescribed for the variables, Vx, Vy, Vz, k and e, while a zero value is assigned to the pressure, p, at the atmospheric boundary.

K. Duvenhage, D.G. Krdger/J. Wind Eng. Ind Aerodyn. 62 (1996) 259.-277 269

A zero gradient boundary condition is prescribed for all the variables at these sym- metry planes.

Wall functions as described by Launder and Spalding [22] are used to calculate values of variables near solid surfaces.

3. Results

The investigation to determine the influence of cross wind on the performance of the ACHE is started by calculating the fan performance and recirculation of an ACHE bay in windless conditions. To eliminate the influence of fan platform height in windless conditions on fan performance, the fan platform height is taken at 5.7 m above ground level [13]. The volume flow rate through a single fan in windless conditions is then considered to be the ideal volume flow rate of the fans used (146.6m3/s). In this paper the performance of the fans in different wind conditions will be evaluated relative to this ideal volume flow rate.

The effectiveness of an ACHE with recirculation is defined as

heat transfer with recirculation Qr Tmao -- Tmai e~ = heat transfer with no recirculation Q Tao - Taa ' (15)

where Tma i and rma o are, respectively, the mass averaged inlet and outlet air tem- peratures of the heat exchanger. Tao is calculated from Eq. (13) for which the inlet temperature is taken as the ambient temperature.

For the first investigation the ACHE fan platform height is kept constant at //he = 5.7 m. The influence of different wind speeds on fan performance and plume recircu- lation are presented in Figs. 4 and 5. The following convention is used in presenting

100

90

80 T

-o 70

;> 60

50

40

30

~- . . . . . . . . . . . , . _ . _ , . . . . . . . . . . . . . . .

, ' l ' do

- - .

I I I '~uo .

0 0.5 1 1.5 2 2.5 3

Wind velocity at a refereaee height of 5.7 m, Vwref lm/s]

Fig. 4. The influence of cross wind on the fan performance of an ACHE bay with a platform height of 5.7m.

270 K. Duvenhage, D.G. Kr6ger/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

1

0.98 ,.._.--- - - " - - ' - ' - " " - " " - ' " - " - - " "4"" - - ' - " " " " - "~""~

o ~ 0.96

0.94

0.92

0.9

0 0.5 1 1.5 2 2.5

Wind velocity at a reference height of 5.7 na, vwref [m/sl

Fig. 5. The influence of cross wind on plume recirculation at an ACHE bay with a platform height of 5.7m.

the results: Fup up-wind fan; Fdo down-wind fan; Fm mean volume flow rate of each fan in the bay.

In Fig. 4 a drastic decrease in fan performance of the up-wind fan is observed with an increase in wind velocity, while the performance of the down-wind fan increases to above 100%. For the case of wind profiles with reference velocities above 3 m/s and an ACHE with a fan platform height of 5.7 m the numerical fan model could not cope with the cross flow. A vector diagram in the region of the ACHE bay with a fan platform height of 5.7 m and a wind profile with a reference velocity of 3.0 m/s at a reference height of 5.7 m is shown in Fig. 6. The severe distorted flow profile along the up-wind inlet edge of the ACHE and under the up-wind fan gives an indication of the flow conditions the fans have to deal with. The influence of recirculation in cross wind conditions on the heat transfer performance of the ACHE is small com- pared to the influence due to the reduction in fan performance in cross wind conditions. In Fig. 5 an increase in effectiveness due to a decrease in recirculation compared to windless conditions is observed for a slight increase in wind velocity. The effective- ness decreases due to increasing recirculation at higher wind speeds. This trend can be ascribed to the phenomenon that in windless conditions recirculation occurs at both sides of the ACHE bay. A slight cross wind will prevent recirculation from occur- ring at the down-wind side of the ACHE bay with the result that there is a decrease in recirculation. With a further increase in wind velocity the amount of recirculation at the up-wind side of the ACHE bay will increase. A temperature distribution in the region of the ACHE bay for a wind profile with a reference velocity of 3.0 m/s at a reference height of 5.7 m and an ACHE with a fan platform height of 5.7 m is shown in Fig. 7. It can clearly be seen in Figs. 6 and 7 that recirculation only occurs at the up-wind edge of the ACHE. This result corresponds to the results of Du Toit et al. [15].

The fan platform height is systematically heightened to 10.7m while the wind profile is kept constant with a reference velocity of 3.0 m/s at a reference height of 5.7 m.

K. Duvenhaoe, D.G. Kr69er / J . Wind Eng. Ind. Aerodyn. 62 (1996) 259-277 271

. . . . . . . . . . . . . . . H / / / I / I I / / / / / / / /

. . . . . . . . . . . . . . , H/H/ I / I / I I I l I / I I

. . . . . . . . . . . . . . ~ H/t/ / l i t / t i l l / I l l

. . . . . . . . . . . . . . ~ l l l l l / ? l / l l l l l l l l

. . . . . . . . . . . . . ~ t l l l t l f l l l l l l l l l l l

. . . . . . . . . . . . . I I I l l l l f l l l l l l l l l ) ' l "

. . . . . . . . t ) P I I I P I I I I I I I I I I I I . . . . . . . ~I I I11 l l l l l l l l l l l | [

, ~ ~ , ,+( , I l l l l l l l l l l l l l l

11tt ~ + ' ' + ' . . + I l l l l l l l l l l l l l l " ' " + ' ' '+ ' . ~ I I I I I I I I/Ill . . . . . . . . . . . - ,.,~,,+J:,.+.~tT+l..~,JJJ,._"+.:'+2"~..~'~ ~ ~ K L ~ , L g C , ' ? ' / Z Z / / / / / / / ." ." ....... , . .

% % ~ . . . , '++. .~, . , . . - -~ . .~ J ]# ' .~ . .~ ' / / ' , ,+ '2" / .+ ' / / / - . . , * / . . . * . / / / / / / / /

Fig 6. Vector diagram for air flow in the region of an ACHE bay in a cross wind of 3.0 m/s.

!01.15 K

"L Ground level y

Fig. 7. Temperature distribution in the region of an ACHE bay in a cross wind of 3.0 m/s.

272 K. Duvenhage, D.G. Kr6yer/J. Wind En9. Ind. Aerodyn. 62 (1996) 259-277

90

50

8O

7O

6o

40 . -~o

30

IF t in 100

. . , ,

. . .

..x .... . .- ,r~Fu p

. - " " I . . - I

. ~ . . . - "

5 6 7 8 9 10 11

Platform height [m]

Fig. 8. The influence of platform height on the fan performance of an ACHE bay in a cross wind of 3.0m/s.

1

0.98

0.96

0.94

0.92

0.9

I

r i 5 6 7 8 9 10 11

Platform height [m]

Fig. 9. The influence of platform height on recireulation at an ACHE bay in a cross wind of 3.0 m/s.

The influence of this change on fan performance and effectiveness due to recirculation can be seen, respectively, in Figs. 8 and 9.

The ACHE is a flow obstruction in the way of the wind. The warm rising plume adds an additional wall-like obstruction with the result that the wind accelerates to flow underneath the fan platform and over the deflected plume. Flow separation occurs at the up-wind side of the ACHE influencing the performance of the up-wind fan. By increasing the height of the fan platform the flow passage underneath the platform is enlarged. The flow separation at the up-wind side of the ACHE weakens and the performance of the up-wind fan increases.

In Fig. 9 it can be seen that there is a slight increase in recirculation with an increase in the height of the fan platform. This trend can be ascribed to the wind

K. Duvenhage , D.G. Krroer/J. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277 273

profile that is kept constant at a reference height of 5.7 m. Because of the power law describing the wind profile, the wind velocity experienced by the fan platform will increase as the height of the fan platform is increased. This increase in wind velocity at fan platform height will increase the plume reeirculation at the up-wind side of the ACHE.

Only plume recirculation is investigated for the case of a longitudinal axis wind and not the influence of wind on fan performance. The fan platform height is kept constant at 10.7 m, the plenum height is 3.0 m and two wind profiles are considered, i.e. Vwrer = 3.0 m/s and Vwref ----- 5.0 m/s both at Zref = 5.7 m. The fans of the ACHE are not modelled extensively and the volume flow rate through each fan of the ACHE bank is assumed to be uniform. The cross wind solutions for fan performance are used to prescribe the volume flow rate of the fans in the first two up-wind bays, while the other fans are assumed to deliver the same volume flow rate as in windless conditions. For instance the performance of the fans in the first two ACHE bays, in a wind with a reference velocity of 3.0m/s at a reference height of 5.7m, are, respectively, taken as VIVid = 69.20% and VIVid = 104.36% (see Fig. 8). For a wind profile with a reference velocity of 5.0 m/s at a reference height of 5.7 m, the performance of the fans are, respectively, taken as V/Vid = 50.00% and V/Vid = 101.14%.

During the investigation the number of bays in the ACHE bank is systematically increased from 3-6 bays. The recirculation at each bay is calculated according to Eq. (15). The recirculation of the ACHE bank is taken as the mean of the recirculation occurring at the bays. In order to compare the results with the CTI [10, 11] correlation a recirculation factor, r, is defined as follows:

r = 1 -er . (16)

The recirculation results for different lengths of the ACHE bank are shown in Fig. 10. The trerLd is similar to that obtained by the CTI [10, 11]. Although the CTI correlation has mainly a bearing on induced draught cooling towers the authors state that they expect the maximum plume recirculation of a forced draught system to be twice the value predicted by the correlation.

In Figs. 11-13 a temperature distribution and vector diagrams of the air flow in the region of an ACHE bank, consisting of 6 bays, are shown. The wind deflects the plume of warm air in a horizontal direction onto the ACHE bank with the result that reeirculation at the sides of the bank increase drastically. This recirculation region along the sides of the bank can clearly be seen in Fig. 12.

The flow distribution at the up-wind side of the ACHE can be seen in Fig. 13. This corresponds well to the up-wind distribution in cross wind conditions. The fan perform.'mce results from cross wind conditions can thus be used with confidence in the simplified fan model.

To de.termine the combined influence of recirculation and fan performance on the heat transfer of the ACHE bank a system effectiveness is defined:

Q es:~s -- Qid' (17)

274 K. Duvenhage, D.G. Kr6gerlJ. Wind Eng. Ind. Aerodyn. 62 (1996) 259-277

0.14

0.12 ~.~I - "-.

0.1 f " "~'~" . . I

o.o8 / , ' " ~" 0.06 f 3m~ ;'~..*--- ,-'r"~-- . . . . . . .

/ j...~.. ~ ..... CT~ [lO, ll 1 0.04 / j . . . .7~ 7 . - "-

0.02 / ~ "'' "='

0

5 10 15 20 25 30 35 40 45 50

ACHE length [m]

Fig. 10. The influence of a longitudinal axis wind on recirculation for different lengths of an ACHE bank.

301.15 K

/ A

Y Ground level

Fig. 11. Temperature distribution in the region of a ACHE bank in a longitudinal axis wind of 3.0 m/s.

where Q is the numerically determined heat transfer in windy conditions and Qid is the heat transfer of the same system in windless conditions. Qid can be calculated as follows:

Qid : maidCpa(Tao -- Yaa),

where maid is the ideal volume flow rate in windless conditions and in the absence of recirculation, Tao can be calculated according to Eq. (13) and Taa is the ambient

I( Duuenhage, D.G. Kr6ger/J. Wind Eng. Ind Aerodyn. 62 (1996) 259-277 275

l i t I l l

I t !

l i t l i e

i t ! I l l t i t t t t

I I / I I / / / / / t /~ . . . . . . .

I l / / / / / / / / /~

I / / / / / / / / / .~ .~/ . . . . . . . .

I I / I I / / / / / / . .~- . : . . . . .

I I I / / t l / t / /~-~ . . . . .

I I I I I I f / / /~ .~

ACHE !': : :- ' ; ; . - '~.~ I I I I

. . . . . . . . . . . . . . . . . . . . . . . . . x

Fig. 12. Vector diagram for air flow at a cross section of an ACHE bank in a longitudinal axis wind of 3.0 m/s.

. . . . x . . - . \N \ \ \ \ \ "~xN\ \ \ \ \ \ \ \ \ \ \ \ * ' -x*x 'x . -x -x .~. , , . . . . . . . .~- . . . . . : : - . _ ~ : . . . . . . . . :

. . . . .~ . . \ \ \ \ \ \ '~ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ' x . , . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . : : : : : . ~ ~

Nig llillli)]!llliii ' Ground level y

Fig. 13. Vector diagram for air flow at a longitudinal section of an ACHE bank in a longitudinal axis wind of 3.0 m/s.

276 K. Duvenhage, D.G. Krdger/J. Wind Eng. Ind Aerodyn, 62 (1996) 259 277

temperature. The total influence of cross wind can now be compared to the total in- fluence of the longitudinal axis wind. However, it is important to remember that end effects are not taken into account at cross wind conditions and that the influence of wind on fan performance in the case of the longitudinal axis wind is approximated with the aid of the cross wind results. In the case of a fan platform height of 10.7 m, a plenum height of 3.0 m, an ACHE bank consisting of 6 bays and a wind profile with a reference velocity of 3.0 m/s at a reference height of 5.7 m the following comparison can be made:

cross wind:

longitudinal axis wind:

esys = 83.53% (primarily due to reduced air flow, %

due to recirculation = 3.1%).

esys = 89.50% (primarily due to plume recirculation,

% due to fans = 4.0%).

In both cases it can be seen that wind has a significant influence on the heat transfer of a typical ACHE bank.

4. Conclusions

In this study the flow field and associated phenomena about a typical forced draught ACHE bank under the influence of wind is investigated numerically. Both winds across and parallel to the longitudinal axis of an ACHE bank are investigated. It is found that cross wind mainly leads to the reduction in air volume flow rate delivered by the up- wind fans, while the wind along the longitudinal axis leads to an increase in plume recirculation along the sides of the ACHE bank. The influence of both wind directions on heat transfer of an ACHE bank consisting of 6 bays, are significant and care must be taken when designing an ACHE to take this effect into consideration.

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