A vortex chamber with an atomizing device is proposed for cooling of return water from industrial plants,

and the effect of design and production parameters are theoretically investigated.

Thermal and nuclear power plants in which cooling towers are widely used in return-water supply circuits make up

the basic part of generating capacities for the power industry of the Russian Federation. As practice indicates, a large portion

of the cooling towers in use were constructed 20–40 years ago, and all these installations are now technically and physically

obsolete. Packed units do not provide the efficiency required for cooling of the water, and the entrainment separators have a

high percentage of carry off of drop moisture. Moreover, ecological problems with operation of the towers, such as carry-off

of drop moisture, discharge of harmful substances (CO2, NOx, SO2), vapor flame, and noise, and also with the proximity of

manufacturing entities to residential development transportation arteries, have begun to appear as the productivity of the

structures and their number on industrial sites continue to grow [1].

Use of vortex chambers with an atomizing device [2] represents a possible solution to the problem of return-water

cooling. In these devices, air, on passing through a tangential vane swirler, acquires a rotational motion. While rotating, the

air flow is displaced toward the center of the vessel, and is removed through a branch pipe. The return water enters the ves-

sel through a branch pipe situated in the lower part of the vessel. Falling onto the atomizing device, the water is repulsed in

different directions, and a three-dimensional spray cone is formed. Moreover, the flow of air breaks the water down into drops

that are taken up into joint rotational motion. This pattern of interaction between the air and water drops results in the for-

mation of a finely disperse rotating trickling layer, increasing the area of contact between the phases, and the intensity of heat

and mass exchange.

To assess the effectiveness of cooling of water by an air flow in a vortex chamber, we theoretically investigated the

effect of design and production parameters. An annular element of a volume with a width dr was conditionally isolated in

the effective zone of the vessel (Fig. 1).

For the isolated element, the heat balance with respect to air with allowance for its longitudinal displacement can be

represented as

(1)G C T Q Q S C DdT

drG C T dT S C D

dT

dr

d T

drdrm G G G G G

Gm G G G G G G

G G+ + + = +( ) + +⎡

⎣⎢⎢

⎤

⎦⎥⎥1 2 1

2

2ρ ρ ,

Chemical and Petroleum Engineering, Vol. 47, Nos. 7–8, November, 2011 (Russian Original Nos. 7–8, July–August, 2011)

COOLING OF RETURN WATER FROM INDUSTRIAL

PLANTS IN VORTEX CHAMBERS

A. V. Dmitriev,1 O. S. Makusheva,2

and N. A. Nikolaev2

Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 7, pp. 19–22, July, 2011.

0009-2355/11/0708-0462 ©2011 Springer Science+Business Media, Inc.462

1 Scientific Center for Power-Industry Problems, Kazan Scientific Center, Russian Academy of Sciences, Russia.2 Kazan State Technological University, Russia.

where DG is the coefficient of molecular diffusion for the air in m2/sec, CG = Ch + Csx is the specific mass heat capacity of

the moist air (at a constant pressure) in kJ/(kg·K) [3], Ch = 1.006 kJ/(kg·K) is the specific mass heat capacity of the dry air

in the temperature interval from –40 to + 60°C at a constant pressure, Cs = 1.8068 kJ/(kg·K) is the specific mass heat capac-

ity of the water vapor, and S = 2πr(h1 + (Ra – r) tanα) and S1 = 2π(rh + (h – r tanα)dr) are the cross-sectional areas of the

effective zone of the vessel at the inlet (outlet), respectively, in the isolated volume in m2.

For the isolated element, the amount of heat that goes over from the water into the air due to heat conduction can be

defined as

Q1 = αG (TL – TG)dF, (2)

and due to evaporation:

Q2 = ISdLm, (3)

where Is = CLTL + r is the enthalpy of the vapor at the temperature of the water in J/kg/K, and r = 2493 kJ/kg is the specific

heat of vapor formation.

The mass flow rate of evaporating water in the isolated element:

dLm = βG(xe – x)dF, (4)

where xe = 0.622ps/(pm – ps) is the equilibrium moisture content in kg/kg, pm is the total pressure of the moist air in kPa, and

ps = 479 + (11.52 + 1.62TG)2 is the partial pressure of the saturated vapor in kPa.

The surface of the drops in the isolated volume in m2:

dF = πa2dN, (5)

where a is the drop diameter in m.

The number of drops in the isolated volume:

(6)

In [4], the fraction of water that exists in drop form within the effective zone of the vortex chamber is determined

from the formula

(7)EL

G

R

rAynm

mbx

a= ⋅⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

−−

5 13 1030 34

0 9

0

1 22

. Re ,.

..

dNE dV

a

yn L=6

3π.

463

Fig. 1. Design dimensions of vortex chamber.

where Rebx = WbxRaρG /μG is the Reynolds number for the air at the inlet to the vortex chamber, μG is the coefficient of

dynamic viscosity of the air in Pa·sec, Wbx = Gv / (2πRah1) is the air velocity at the inlet to the vortex chamber in m/sec,

A = πRa2/(nbh1) is the coefficient of twist of the flow, n is the number of vanes, b is the distance between vanes in m, and h1

is the height of the vanes in m.

The volume of water in the isolated element (for the average distribution of water throughout the effective zone of

the vortex chamber):

(8)

The isolated volume of the effective zone of the vortex chamber:

(9)

Using formulas (6), (8), and (9), formula (5) takes on the form

(10)

The holding capacity of the vortex chamber is determined from a formula derived on the basis of the processing of

experimental data acquired in [5]:

(11)

The volume of the effective zone of the vortex chamber in m3:

(12)

After transformations, Eq. (1) assumes the form

(13)

where PeG = WbxRa /DG is the Peclet number for air.

For the isolated element, the heat balance with respect to the water with allowance for its longitudinal displacement

can be represented as

(14)

where DL is the coefficient of molecular diffusion for water in m2/sec.

= + + − + +⎡

⎣⎢⎢

⎤

⎦⎥⎥

Q Q L C T dT S C DdT

dr

d T

drdrm L L L L L L

L L1 2 1

2

2( ) ρ ,

L C T S C DdT

drm L L L L LL+ =ρ

= − + −( )α βρG G L S Gyn L

G G bx aT T I x x

E V

C aV W R( ) ( )e

,6

1 1 12

21

1 1Pe PeG

G

a a G

Gd T

dr

h

r h R r r h R r

dT

dr+

+ −( ) +⎛

⎝⎜⎜ −

+ −( )⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎞

⎠⎟⎟ =

( ) tan

tan

tanαα

α

V h R r R r R ra a a= − + + −( )πα

33 2 31

202 3

03

02( ) ( ) tan .

V AL

GAL

m

m= ⋅ +( ) ⎛

⎝⎜

⎞

⎠⎟ + +( )⎡

⎣⎢⎢

⎤

⎦⎥⎥

−5 31 10 0 974 7 834 0 3085. ln ( . ln . ln .) ( ) .

dFrE V

aVr R h dr

yn La= − −( )12

1

πα( tan .)

dV r r R h dra= − −( )2 1π α( tan .)

dVV

VdVL

L= .

464

After transformations, Eq. (14) takes on the form

(15)

where PeL = UbxRa /DL is the Peclet number for water, and Ubx is the velocity of the water at the inlet to the vortex chamber

in m/sec.

The material balance for the isolated element can be represented as

(16)

After transformations, Eq. (16) assumes the form

(17)

Let us introduce the dimensionless parameter ξ = r /Ra, where r is the current radius of the vortex chamber in m, and

Ra is the radius of the vortex chamber in m. Ultimately, the system of three equations (13), (15), and (17) for the cooling of

water in the vortex chamber is written as

(18)

System of equations (18) is solved with the following boundary conditions: TL(ξ0) = TL0, TG(1) = TG0, xe(ξ0) = xe,

x(1) = x0, dTL /dξ(ξ0) = 0, and dTG /dξ(1) = 0.

The calculations were performed for a vortex chamber with a radius Ra = 0.26 m, a branch pipe with a radius

r0 = 0.05 m for the discharge of the gas–liquid mixture, and a vane swirler with a height h1 = 30 mm in which the water is

air-cooled. The cooling efficiency of the water was assessed by the parameter ET = 1 – TL /TL0, and the fraction of the water

that has been evaporated by the parameter EL = (1 – Lm /Lm0)·100%.

The calculations indicated that cooling efficiency in the vortex chamber decreases with decreasing air flow, since the

motive force of heat-transfer tends to zero, and cooling of the water is slowed. It should be pointed out that a significant reduc-

dx

d

x x R E V

G aVh RG a yn L

maξ

β ξπξ α=

−+ −( )( )

( ) tan .e 121

2

1

= − + −( )α βρG L G S G

a yn L

L L bxT T I x x

R E V

C a U V( ) ( )e ;

6

11 1 2

1

2

2

1

1Pe

Pe

PeL

LL

m

m

G

L

bx

bxa

L a

Ld T

d

hL

G

W

UR

h R

dT

dξ

ρρ

ξ α

ξ ξ α ξ+

−⎛

⎝⎜

⎞

⎠⎟ + −

+ −( ) =( ) tan

( ) tan

= − + −( )α βρG G L S G

a yn L

G G bxT T I x x

R E V

C a W V( ) ( )e ;

6

1 1 1 2

1

2

21

1Pe

Pe

PeG

G G a

G a

Gd T

d

h R

h R

dT

dξ

ξ αξ ξ α ξ

++ + −

+ −( ) =( ) ( ) tan

( ) tan

dx

drx x

rE V

G aVr R hG

yn L

ma= − − −( )β

πα( ) ( tan .e )

121

G x dL G x dxm m m+ = +( ).

= − + −( )α βρG L G S Gyn L

L L bx aT T I x x

E V

C aV U R( ) ( )e

,6

1 1 12

21

1

1Pe PeL

L

a L

m

m

G

L

bx

bx a

Ld T

dr r h R r

L

G

W

U

h

r h R r

dT

dr+ −

+ −⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜ −

+ −( )⎞

⎠⎟⎟ =

tan

( ) tan ( ) tan

αα

ρρ α

465

466

Fig. 2. Dependence of cooling efficiency of water (a) and fraction of water evaporated (b) on ratio of mass

flow rates of phases and initial air temperature: Wbx = 10 m/sec; tL0 = 50°C; tG0, °C: 1) 40; 2) 20; 3) 10.

Fig. 3. Dependence of cooling efficiency of water (a) and fraction of water evaporated (b) on ratio of mass

flow rates of phases and initial water temperature: Wbx = 10 m/sec; tG0 = 20°C; tL0, °C: 1) 50; 2) 40; 3) 30.

Fig. 4. Dependence of cooling efficiency of water (a) and fraction of water evaporated (b) on ratio of mass flow

rates of phases and air velocity at inlet to chamber: tG0 = 20°C; tL0 = 40°C; Wbx, m/sec: 1) 7; 2) 10; 3) 15.

tion in efficiency is observed when the ratio of the mass flow rates of the phases is more than 0.2 (Figs. 2a, 3a). When the

air temperature changes at the inlet to the vessel, the fraction of evaporation is changed by less than 0.1%, since the time of

contact is essentially independent of this parameter. The fraction of water that has evaporated decreases with increasing ini-

tial air temperature owing to reduction in the motive force of mass transfer as the equilibrium moisture content increases

(see Fig. 2b), and, conversely, the higher the water temperature at the inlet to the vortex chamber, the more vigorous the evap-

oration (see Fig. 3b).

A change in air velocity at the inlet to the vortex chamber has virtually no effect on the cooling efficiency of the

water, since during the short relaxation time of the drops, the coefficient of heat transfer, which depends on the relative

velocity of the drops, remains essentially constant (Fig. 4a). It should be pointed out that a reduction in the fraction of water

evaporated takes place with increasing air velocity at the inlet to the vortex chamber, because the water drops exist in the

effective zone of the vessel for a shorter time when the volume of the chamber is the same (see Fig. 4b).

Thus, return water enters the vessel in the form of drops, uniformly coating the effective zone; this excludes the pos-

sibility that air will pass through without contact with the water, and makes it possible to increase the cooling efficiency of

the return water from industrial plants. A high carrying capacity with respect to air, and also a comparatively low hydraulic

resistance are basic advancements in vortex chambers, and carry-off of droplet moisture is eliminated, rendering the ecolog-

ical situation of industrial regions and regions adjacent to them appreciably improved. When vortex chambers are utilized,

moreover, the electric motor of the fan does not come under the influence of moist flows, as occurs in ventilated evaporative

cooling towers.

The study was conducted with financial support from the Ministry of Education and Science of the Russian Feder-

ation within the framework of implementation of the Federal Targeted Program on Scientific and Teaching Staff for an Inno-

vative Russia in 2009–2013 (State Contracts 02.740.11.0062, 02.740.11.0685, 02.740.11.0753, and P560) and a grant from

the president of the Russian Federation.

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2. O. S. Makusheva, A. V. Dmitriev, and N. A. Nikolaev, Russian Federation Patent No. 89000, MPK V 05 V 1/26,

“Atomizing device,” applicant and patent holder is the Kazan Scientific Center, Russian Academy of Sciences,

No. 2009129889/22, appl. Aug. 3, 2009, publ. Nov. 27, 2009, Byull., No. 33.

3. V. I. Polushkin, O. N. Rusak, and S. I. Burtsev, Heating, Ventilation, and Conditioning of Air [in Russian], Professiya,

St. Petersburg (2002).

4. S. A. Laptev, “Behavior of a gas-liquid flow in vortex chambers,” Sib. Fiz. Tekhn. Zh., No. 5, 131–134 (1992).

5. S. A. Laptev, A. A. Ovchinnikov, and N. A. Nikolaev, “Dynamics of a gas-liquid flow in vortex chambers,” Khim.

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