10th INTERNATIONALCONFERENCE AND SEMINAREDM'2009, SECTIONIV, JULY 1-6, ERLAGOL 269

Development of Design Procedure of LiquidMedia Dispenser for the Atomizing Drier

Vladimir N. Khmelev, Senior Member, IEEE, Andrey V. Shalunov,Anna V. Shalunova, Student Member, IEEE

Biysk Technological Institute (branch) ofAltay State Technical University after 1.1. Polzunov, Biysk,Russia

Abstract - In the article the design procedure of liquidmedia dispenser for ultrasonic drying according torequired parameters of atomizing drier is presented.

Index Terms - Dispersion, ultrasonic sprayer, spraychamber, fluid supply.

I. INTRODUCTION

THE DRYING IS REMOVING OF LIQUIDfrom substances and materials by the thermal

means. It is carried out by evaporation of liquid andby formed gas withdrawal during heat supplying to adryable material, more often with the help of so­called drying agent (heated steam, flue gas and theirmixes with air, inert gases, superheated steam).

The spray drying is applied for liquid substancesof the rising viscosity which are sprayed in a flow ofhot drying agent. Due to big specific surface of thesprayed material the process of moisture evaporationoccurs intensively.

Atomizing drying is a set of following processes:dispersion of the material, movement of dispersedmaterial and drying agent and heat-mass exchangebetween them, heat and mass transfer of dryablematerial. Thus, the sizes of drying chamber will bedefined substantially by a root angles milling lossand heat-mass exchange processes, and accordinglyand it will depend on quantity of heat necessary fordrying material.

Efficiency of drying depends on realization ofsprayer unit. Traditionally used sprayer units(pneumatic, mechanical ones) have significant lack,the use of drying reagent. Ultrasonic dispersion ofliquids can be used as an alternative while it has thefollowing advantages:

- low power-consuming;- high efficiency ofthe process;- possibility to receive fme-dispersed spraying;- possibility to receive monodisperse spraying;- possibility to spray high-viscosity liquids

without application ofan additional drying agent;- presence in liquid drops the circulating currents

which accelerate the processes of heat exchange,mass transfer, etc. on a drop surface.

II. INITIAL DATA

As a rule, at designing of an ultrasonic sprayerthe following main parameters are available:

a) liquid parameters: density, a surface tension,the viscosity, the fluid flow rate;

b) sprayer parameters: the angle, the area, slantheight and outer diameter of a sprayer, frequencyand amplitude of ultrasonic vibrations;

c) drying chamber parameters : chamber volume,speed and initial temperature of gas, productivity ofthe dryer according to dry product.

In Fig. I the parameters of atomizing drier arepresented.

s

!LF~l\,/ \.~\

,/ \" \! \

! \( \( \

i II \

I \G

a) b)

a) Chamberparameters: U, - the speed of gas, H - the height

of the chamber, G"" - the fluid flow rate, G - the quantity of dry

powder, Q- the quantityof heat necessaryfor drying material,

b) Spray parameters: S - the surface of the sprayer, ppacn -

the angle of the sprayer, I - slant heightof sprayer surface, do ­

diameterof a nozzlefor fluid supply.Fig. I - Parametersof atomizingdrier.

Regarding all above-listed data it is necessary todetermine such parameters of the ultrasonic sprayer

as the area of dispersion surface, a slope angle f3pacn

of a cone surface generatrix of dispersion anddetermination of amount and location of aperturesfor fluid supply on a dispersion surface.

To solve this problem the following designprocedure is suggested.

978-1-4244-4572-1/09/$25.00 © IEEE

270 10th INTERNATIONAL CONFERENCE AND SEMINAR EDM'2009, SECTION IV, JULY 1-6, ERLAGOL

xFig. 2 - System of the forces acting on a liquid drop after its

(3)

(1)

H

6IIi . fJpacn

max p :JIC 3 Sln-­2 ,

• Ppacn • 3 PpacnSln---Sln --=

2 2

D=

then

r=--­u, ±v2

Therefore it is necessary to describe the speed ofparticles flight. For this purpose Fig. 2 can beconsidered, where the forces acting on a drop of thesprayed liquid left surface of a sprayer areschematically presented.

~ 13 ~

7r 3 8 6 A6ll P 3/ 33,2 max:JIC

The middle surface-volumetric diameter can befound in a following way. So, considering the

general surface of particles F' middle surface­volumetric diameter will equal:

6G83 2

=-,; (7), Fy

where G- quantity of dry product in ml/m 3,y ­relative density of the dryable material in

N/m3, 53,2 - middle surface-volumetric diameter of

liquid drops.The general surface of particles can be calculated

through a total surface ofthe particles being found insuspension state in the drying chamber, whichdepends on duration of falling. Subject to it the

value of F' will be described in the followingexpression (2):

Whence:

III. METHOD PREPARATION

The value of the dispersion surface area can becalculated with the help of expression for defmingthe specific capacity of a sprayer (speed ofdispersion) [1]:

n =~1ra3V1ra ./1/3.yo 3 p

1

S = llmax = 3llmaxP~tt; 3 .!.

2llyoa (1rCF 1)3

where S - the area of dispersion surface m2,

IImax - the demanded productivity of aerosol

formation, IIyo- the speed of dispersion,

a =0,12 , a - a surface tension,1 - frequency of

ultrasonic vibrations, which is defmed as follows.As frequency of ultrasonic vibrations of a

sprayer should provide necessary middle mediandiameter of aerosol, it will be equal:

8Jra 3CF

1=D~alVluP

where Dxannu- middle median diameter of

aerosol drops.Then we defme the angle of an ultrasonic

sprayer. For this purpose it is necessary to findmiddle volume-superficial diameter of liquid drops.In order to fmd the given value it is necessary todetermine such parameters as quantity of heat whichis transferred from gas to solution particles,evaporation and heating of particles, meantemperature difference, volume factor of heatexchange between gases and particles.

For the estimation of middle volumetric-surfacediameter at ultrasonic dispersion the followingformula is offered [2]:

t5 = 0,252 3G:J/C17a3,2 A 3 f3

1iDp~f2gcos ;cnWhere 1] - coefficient of dynamic viscosity in

Pals, p)f(- density of sprayed liquid in kg/nr',

P pacn - the angle between surface generatrix of a2

nozzle and a vertical in degrees, G)K - the fluid flowrate (m3/s), A - vibration amplitude of an ultrasonicsprayer in m, 1 - vibration frequency of a nozzle in11c, o - surface tension coefficient, D - externaldiameter of a working part of a spraying nozzle inm, which can be described in following expression(1):

SHALUNOVA et al.: DEVELOPMENT OF DESIGN PROCEDURE OF LIQUID MEDIA... 271

(6)

separation from a liquidlayercoveringa dispersion surface.

In the initial time drop moves angularly to asurface of the aerosol dispersion, the angle equals to:

, "fJpacna =90-(90-a )=(90--

2-).During the movement of a drop the angle a' will

change according to the following law:

, [Vx(t + ilt)).a =arctg ,vy(t + ilt)

vx(t)sina' - pS2(vx(t))2 CD (M) sinzz ·M .Vx = . ' ,

sinzz

_[_g__ pS2(U/t)YCD(M)] .vy-, i\t + vy(t) ,

cosa m

where m - mass of aerosol drop in kg,

CD(M) - dimensionless function of Mach

number, p - density of air in kg/rrr'; S - cross­

section area of a drop m2•

Then the speed of drop movement in the optionalmoment will be described by the following formula:

vyo, =--,.cosa

As the volume factor of heat exchange isconnected with the factor of heat transfer related tosurface evaporation unit, the total surface ofparticles is described by the following equation (4):

F=av~

am , (4)where V

K- volume of the drying chamber in rrr',

am- heat exchange coefficient in J/m3oS, av ­

volume heat exchange coefficient between gases andparticles in J/m3S.

a = Qv KIK2~tcpVk

where ~t - an mean temperature differencecp

between gas and particles in C, K1

- the factor

considering the decrease of acting force due to themix of gas in the chamber, K

2- compensation factor

on distribution equilibrium of the heat carrier andliquid particles on volume of chambers, Q - the

quantity of heat which is transferred from gas toparticles of the liquid and is neccessary forevaporation and heating ofparticles in J.

Taking into account material and thermal balanceof the dryer the necessary quantity of heat iscalculated by the formula (5):

Q =W(595 +0,47t2 - 9}) + cOG(92 - 9}), (5)

where W - quantity of an evaporated moisture inJ/C, G - productivity of a dryer according to dry

product in ml/nr', t2 - temperature of gases while

drying in °C, 81,82

- temperature according to liquid

and product after drying in °C, CO - a heat capacity

ofa waterless product in JIN°C,

c =c 100-w2 + w2 •

o cyx 100 100'

W2 - fmite humidity of a product in %, Ccyx ­

the thermal capacity of a waterless product in JIN°C.All process of particles heating during drying

can be divided into two main periods: in the firstperiod the temperature of particles is approximatelyequal to temperature of adiabatic evaporation ofpureliquid; in the second one it changes and reachesambient temperature.

The mean temperature differential during thefirst period can be described by the formula (6):

A t} - t 2Dot} =----

It } - tM

n---t; -tm

where 11 - initial temperature of gases, 1M

-

average temperature of the wet thermometer(capability of air to accept a moisture at invariable

heat content, i.e, without heat supply) in "C, I; - the

temperature of gases corresponding to thetermination of the first period ofdrying, °C.

The temperature I; is easy to defme from drying

process according to i - d diagram.The mean temperature differential between

gas and a particle during the second period will beequal:

A _~; -tJ-(t2 -92)tl -t; (7)LJ.t2 - , I

1 t2-t,Mn---

t2 --92

where

92

= ~; - t M) W Z- W2 ,WI - initial humidityw

2-wp

of liquid in %, W2 - the maximum hygroscopic

humidity in % , d l - initial specific humidity of

gases in kg of moisture/kg of a material, Wp ­

equilibrium humidity in %.The mean differential of temperatures between

gas and a particle can be described, if ratio ofduration of drying between the first and the secondperiods of the drying is known. The relation ofdrying duration in the second period to the generaldrying duration can be described by the followingmagnitude:

272 10th INTERNATIONAL CONFERENCE AND SEMINAREDM'2009, SECTIONIV, JULY 1-6, ERLAGOL

x=----r--~,....-----,--­

I + --:>....::...-----".!....::..--'--------"-"'-----

~I +f;XW, -wp)ln w, -wp

w2 -wp

The mean differential of temperatures will beequal to:

«: = M,(1-X)+M2X;

The common expression for fmding middlesurface-volumetric diameter will be following:

6GHamK]K/i.fcp°32=-----~

, r(v. ± v,)av

The final equation for calculation of a angle of asprayer will be expressed as follows :

. f3 pacn • 3 f3 pacnsm---sm --=2 2

~(6GHa K]KZ!i.t )6 13 !.!.3 m cp A 6 Il 3/ 3!t (+) maxP:>cyv._v,av

The received equation is to be solved by themethod ofVieta-Kardano.

The conclusive stage is the calculation ofquantity of necessary apertures . During thecalculations it is supposed that liquid flowed outfrom an aperture is kept by forces of a surfacetension and it spreads on a dispersion surface underthe influence of forces of the radiating pressure (Fig.3).

Fig. 3 - The liquid kept on a dispersion surface under theinfluenceofforces of a superficial tension.

The maximum volume of the kept liquid isdefmed from a condition of equilibrium at themoment of drop separation from the surface andsubject to surface taper:

,....----'----------2ra

R=3 pg(Jrcos2a"(l-sina")+B)'

where

B =!t(l +sina " ) z (~ - .!.. sin a " ) _ .!.. !t cos3 a")·3 3 3

At influence of ultrasonic vibrations radiatingpressure imposes a drop some energy, leading to its

spreading. Expression for the force of radiatingpressure can be presented in a following way:

F,=2slf(krt I 2cos(B) .[C] ;(l+2'q)

where E - time-average energy density offalling wave, r - radius of the drop in m, e - theangle between a direction of wave falling and anormal to interface, p and c - density of the

environment in kg/m' and speed of sound

distribution in km/s, k - wave number m".

C=(q_l+2q )Z+~(I-qY;3qp 9

P=CZ/c1 ,q= pJpz ,Indexes I and 2 deal with environments in which

the falling and passed waves spread.Knowing the value of energy of radiating

pressure it is possible to define the radius of adispersion surface on which the liquid spreads:

1= 2FrJrcosa"" + ~(-2FrJrCoSa")~ -C ;2 ·aJr ·cosa 2 ·aJr·cosa

C = 4· aJrcosa" .(a(!tR z(I +(1 ++sina")z) +

+2!tRzcoszr"· (1- sin a "» + 2FrRcosa")

The area of liquid spreading will equal :

Spacn = Jr [2.

If the area occupied by liquid after its spreading,appears insufficient (i.e. not all surface of dispersionis covered by liquid), it is necessary to executeadditional apertures for fluid supply on thedispersion surface. These apertures should be on thedistance which does not exceed 21 (where 1 is the

radius of the spread drop), Fig. 4.

Fig. 4 - The arrangementof apertureson a dispersionsurface.

If value of distance 21 is bigger than the radius

Rpacn of a dispersion surface apertures should be

made at distance of Rpacn •

2

IV. CONCLUSION

Thus, dependences for a fmding of the area of adispersion surface on the specified productivity ofdispersion, an angle of slope f3pacn of a generatrix of

SHALUNOVA et al.: DEVELOPMENT OF DESIGN PROCEDURE OF LIQUID MEDIA...

cone dispersion surface, quantity and a site ofapertures for fluid supply on a dispersion surfacedepending on the parameters set of drying chambershave been obtained. The given design procedureallows to raise efficiency and safety of ultrasonicspray drying.

ACKNOWLEDGMENT

The work is executed with fmancial support ofCouncil about grants of the President of the RussianFederation for support of young Russian scientists ­candidates of sciences and their supervisors NQ MK­383.2008.8.

REFERENCES

[1] Khmelev, V.N. Ultrasound multipurpose and specializeddevices for an intensification of technological processesin the industries / V.N. Khmelev, A.B. Rascals [etc.]. ­Barnaul: AItSTU, 2007. - 400 p.

[2] Lykov, M.V. The atomizing driers. Bases of the theoryand calculation / M.V. Lykov, B.I. Leonchik - M:mechanical engineering, 1966. - 331 p.

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