BOILING OF ORGANIC LIQUIDS INDUCED BY BULK ABSORPTION OF CO2 LASER RADIATION

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BOILING OF ORGANIC LIQUIDS INDUCED BY

BULK ABSORPTION OF CO2 LASER RADIATION

R. Joeckle, B. Gautier

To cite this version:

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JOURNAL DE PHYSIQUE _CoZZoque_C9, _{suppZ6ment au nOZ1, Tome 41, novembre 1980, page}_C9-275

R.C. Joeckle and B.G. Gautier.

German-French Research Institute Saint-Louis ( I S L ) , 22, rue de Z71ndustrie, 68301 Saint Louis, France.

R6sum6.- Lorsque d u cyclohexane est chauff6 en profondeur par absorption de rayonnement laser CO _2'

le changement de phase liquide-vapeur sleffectue par un processus d'dbullition. Suivant l'homogdndi- t6 du matdriau, l1dbullition peut Ctre r6guliSre ou d'allure explosive. Des Temperatures plus Blev6es que la tempdrature normale de vaporisation se d6veloppent au sein du liquide.

Abstract.- When cyclohexane is heated in depth by the absorption of C02 laser radiation, its liquid to vapour phase change occurs by a boiling process. According to the homogeneity of the liquid phase, the boiling may be regular or explosive-like. Temperatures higher than the equilibrium vaporization temperature develop in the bulk of the liquid.

IrnDUCT ION

When irradiated with an intense CW-CO; laser beam, most of the materials exhibit an opaque behaviour, that is they vaporize at the surface and the temperature profile decays continuously from the surface to the bulk. Conversely, for chemical lasers wavelengths, several materials like glasses show a significant absorption length; the in-depth heat release may induce other destruction processes than for the opaque behaviour. These processes are difficult to study owing to the high laser intensities required and the high temperatures reached.

Some organic liquids like cyclohexane exhibit an absorption behaviour at CO, laser wavelength; we have studied their liquid to gas phase change in order to establish a physical model of the destruction process typical of absorbing materials [ I ] .

THEORETICAL ASPECTS OF THE PHASE CHANGE

The liquid-to-vapour phase change occurs by a surface vaporization at a liquid-vapour interface. If the heat is released by light absorption in the bulk of the liquid, a subsurface overheating devel- ops while the surface temperature remains fixed at the equilibrium boiling temperature.

Therefore, a heat flux through thermal conduction is initiated, which supplies the latent heat of vaporization Lv to the liquid at the surface where a vapour mass flow takes place.

"

)

Work supported by the D.R.E.T.

Two different situations have to be investigated: 1) The liquid is pure and homogeneous. Then, the

peak temperature under the surface may grow to very high values according to the calculation shown below, until it reaches the "homogeneous nucleation" temperature 121: the probability

for a density fluctuation to grow in a bubble becomes then significant and one no collapsing bubble is formed.

The Laplace relationship describes the behaviour of an equilibrium bubble:

p - p

=Za

b a r

r is the equilibrium radius of the bubble, a is the surface tension, P,, is the actual pressure in the bubble and Pa is the ambient pressure.

If the gas in the bubble is constituted only by the vapour of the liquid, then Pb is equal to PL (vapour pressure of the liquid) and the radius r at equilibrium can take a single value rc (critical radius). This equilibrium state is then unstable, a bubble with a smaller radius collapses and a bubble with a larger radius than the critical one grows fastly: the actual bubble pressure Pb drops and the large difference between PL and Pb yields to a fast vaporization at the wall of the bubble, giving rise to an explosion-like behaviour shown at fig. 1. For cyclohexane, the nucleation temperature is 21g0c, the corresponding vapour pressure is around 40 bar and the normal equilibrium boiling temperature

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JOURNAL DE PHYSIQUE

explosive-like boiling in the clear walls vessel

regular boiling in the porous bottom vessel

Fig. 1: Pictures of the boiling processes obtained with a laser intensity of 30 w/cm2

(free surface vaporization temperature at atmos- pheric pressure) is 81 . ~ O C .

The liquid is not homogeneous, that means tiny bubbles preexist. The Laplace relationship can be applied in its general form. During the liquid temperature rise, the bubbles will begin to expand when the vapour pressure of the surround- ing liquid exceeds the actual bubble pressure. According to Laplace relationship, the latter will then drop and the bubble will grow quickly. Nevertheless, this growing rate will be smaller than for homogeneous nucleation described above. The value of the overheating produced before starting of the boiling process is related to the initial radii of preexisting bubbles. On fig. 1 is shown such a boiling process, called hereafter quiet or regular boiling.

MODELING OF SURFACE VAWRIZATION OF ABSORBING MATERIALS

Ne describe herein the heating and the surface

vaporization of materials which absorb laser radiation in the bulk, up to boiling process appearance.

1) Governing equation

Considering the free surface of a liquid at at- mospheric pressure. A uniform laser beam impinges

the surface in the normal direction. Part of the incident radiation which has not been reflected penetrates the liquid and is gradually transformed into heat according to the Lambert Beer's law.

The decay of the radiation intensity as a function of the depth into the target is:

I (z) = 1, exp[ -b (z-zs)

I

(1 ) where .I is the absorbed power density at the surface, b is the absorption coefficient assumed to be constant, z being the space coordinate normal to the illuminated surface, zs is the abscissa of the surface.

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equation:

where p = liquid density

cp = specific heat

k = thermal conductivity.

Remark: For a liquid it is assumed that heat trans- fer through convective process is negligibly small compared to conduction. This assumption is supported by the fact that times required to bring the liquid at boiling temperature are small enough to preclude noticeable liquid displacement. Assuming constants for p, cD, k, b, equation (2) reduces to:

As soon as the liquid surface reaches the normal vaporization temperature (Tv for p=l atm) after a

time tv, a liquid mass loss occurs through surface vaporization. The free surface begins to move toward the bottom of the vessel at a rate given by:

where Lv is the latent heat of vaporization for normal conditions (p = 1 atm)

.

The above equation takes into account that heat flow is directed toward the illuminated surface from the bulk of the liquid. As the surface temperature cannot exceed the fixed vaporization temperature Tv, the internal heat dissipation builds up a temperature overshoot

(T(z) > T ) leading to boiling of the liquid. v

Boundary conditions associated to equations (3) and (4) are:

where E is the initial liquid thickness. Equation (5) assumes an insulated vessel.

T(z=zs,t) = T

v t > t,

.

(6) Initial condition assumes a uniform temperature liquid layer

T(z, t=O) = To (7)

The set of equations (3)

-

(7) is usually known as the one dimensional Stefan's problem including a single free boundary. It must be solved numerically.

2) Numerical solution of the Stefan's problem Equations (3)

-

(7) are rewritten in tens of the normalized space-time plane x , ~ . Then the numerical solution of these equations is performed through a second order finite element method.

The elements considered are quadrilaterals of the space [x,~] which must be determined for each

time step according to the position a(~) of the free boundary. The normalized heat equation is integrated in a strip G ~ :

n

G"=/[x,TI; Oix<a(~); .r < T < T ~ + ' / of the space$: 3 = I[X,T]; 0 < x <a(-r); -r > 0

1

yielding to a linear system of algebraic equations written in matrix form:

I , , I l 1 1 1= R 1 1 (i ( 1-1 (8)

where I is the number of space divisions, u being the normalized temperature distribution.

The location of the free boundary a('-c) is com- puted at each time step through an implicit formula involving the unknown temperature distribution u.": Therefore an iterative procedure must be used until a convergence criterion is satisfied.

Initial condition must be specified for t=tv(.r=O). The analytical solution of the heat equation with distributed heat source available in ref.[3] provides this condition.

3) Numerical applications

Applications have been performed with cyclohexane (C6H12) as test liquid. Mean values of its thermal properties are summarized in the following table (table 1). Table 1 Density P [g/m31 0. ..78

An initial liquid layer, 5 mm thick at 20°C is illuminated by an uniform laser beam of intensity ranging between 10 and 100 w/m2.

Calculations of temperature profiles together with speed and location of the free surface have been performed.

Typical temperature profiles are shown at fig.2 for a beam intensity I. = 40 141/m2. They exhibit a large subsurface overshoot reaching 138OC above the vaporization temperature after 1.27 s. Fig. 3 is a plot of this peak temperature versus time for beam intensities of 15 to 100 iV/cm2.

Assuming an upper limit of TE=21g0C for the explosion like boiling-up to occur, a cross plot from fig. 3 gives the theoretical explosion delay

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JOURNAL DE PHYSIQUE

as a function of the l a s e r beam i n t e n s i t y . Values of tE have been reported on f i g . 4 (solid l i n e ) .

Fig. 2: Temperature p r o f i l e s calculated f o r d i f f e r e n t illumination times

Fig. 3: Calculated peak temperature versus time f o r d i f f e r e n t l a s e r inten- s i t i e s . Observed regular boiling delays (A)

E X P E R W S

Experiments have been performed with a CIq-C02

l a s e r delivering an optical power of 500 W. A

schematic description of the t e s t s e t up is given i n scheme 1. The t e s t l i q u i d contained i n a small

a t h i n porous ceramic disk placed a t the bottom

Fig. 4: Calculated and experimental explo-

of the vessel. This material contains very small sion o r regular boiling delays

vessel ($3 28.5 mm, h 5 m) i s uniformly illuminated by the l a s e r beam conditioned by ZnSe lenses and a square beam integrator. The incident beam inten-

3- s i t y on the t a r g e t ranges from 10 t o 100 W/cm2.

The vessel i s connected t o a force transducer used

as a dynamic balance allowing f o r continuous 2 -

recording of the l i q u i d mass loss.

The force transducer gives a l s o the time

required t o produce e i t h e r q u i e t boiling o r ex- I-

plosive boiling. The l a s t i s usually observed when a vessel with clean metallic walls i s used to-

./

lnSe lenses

I

.-.

CW-C02 laser vessel "Photon Source"

A

I

_t_[a]

\.

"=

I I---

transducer

gether with beam i n t e n s i t i e s greater than 15 w/an2.

*

mg.boil. ("p.) twpi. boil. (np.1 recorder

0

0 7

---____

Scheme 1: Experimental apparatus

*

0 10 20 30 40 50 60 70 80 W 100

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gas inclusions which are released i n t o the liquid during the t e s t producing tiny bubbles acting as seeds from which boiling i s able to be i n i t i a t e d .

With a "clear wall" vessel explosions delays tE have been measured for several beam intensities. The results have been reported on f i g . 4. Open symbols denote mean values and the bars indicate the absolute scattering of experimental values.

A f a i r l y good agreement has been achieved. The delays of appearance of the regular boiling obtained with the porous bottom vessel a t different laser beam intensities have also been reported on f i g . 4. They are included between the explosion delay obtained f o r the same intensity i n

liquid i s the same f o r regular boiling and f o r surface vaporization with subsurface overheating. CONCLUSION

An explosive-like boiling process has been obtained by bulk absorption of laser radiation i n pure homogeneous liquid. Organic liquids are easily free of bubbles; conversely, solid materials l i k e glasses contain generally t i n y inclusions. Therefore, a regular boiling i s l i k e l y t o be produced when such materials are illuminated by chemical laser radiation.

REFERENCES

a clear wall vessel and the time r e ~ u i r e d by the [TI B. GAUTIER. R. JOECKLE

liquid t o reach the vaporization temperature a t the Explosive Boiling of Cyclohexane Induced by

Absorption of C02 Laser Radiation.

surf ace. Paper presented a t LASER'79, Orlando, 1979

The plot of the calculated peak temperature

[21 V.P. SKRIPOV

variation versus time (fig. 3) can be used t o Metastable Liquids.

evaluate the temperature of the liquid when the John Wiley and Sons, 1974

regular boiling begins. I t has been found a tern- [31 F.W. DABBY, Un CHLTL PAEK

perature ranging from 1 OS°C and 135OC. These values High Intensity Laser Induced Vaporization

and Explosion of Solid Materials.

are depending on the seeding experimental condi- IEEE J1. of Quantum Electronics,

tions used here. QE 8 No. 2, Feb. 1972

Examples of mass losses recorded during t e s t s with clear walls vessel and porous bottom vessel

are compared t o the calculated mass loss on f i g . 5. An electronic f i l t e r allows us to record the mass

loss during the regular boiling period. Good agreement is obtained between theory and measure- ment with clear walls vessel. The regular boiling mass flow i s very close t o the surface vaporization mass flow. Therefore, the energy balance of the absorbed energy shows that the heat stored i n tfie

I

expl. boil. (exp. 0 )

/

rneory

,+

#'+reg. boil. (exp. A )

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t [sl