Numerical Simulation of Interior Flow in Evaporation Droplet

Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting FEDSM2014 August 3-7, 2014, Chicago, Illinois, USA

FEDSM2014-22143 NUMERICAL SIMULATION OF INTERIOR FLOW IN EVAPORATION DROPLET

Qingming Dong

Zhentao Wang

Jiangsu University

Jiangsu University

Zhenjiang, Jiangsu, China


Yonghui Zhang

Junfeng Wang

Jiangsu University

Jiangsu University



ABSTRACT

evaporation mainly include two parts: one is about

In this present study, the VOF (Volume of Fluid)

evaporation rate, the other is about internal circulation.

approach is adopted to capture the interface, and CSF

Maxwell presented the first evaporation theory that the simple

(Continuum Surface Force) model to calculate the surface

case of a droplet was considered and its center of mass do not

tension, and the governing equations are founded in numerical

move with respect to surrounding medium[1]. One of the first

simulation of evaporating droplets. In this work, a water

attempting to model droplet evaporation was made by

droplet is assumed to be suspending in high temperature air,

Godsave[2] and Spalding[3] who proposed the well known

and the gravity of a droplet is ignored. During evaporating

“d2-law”.But, the model was based on the assumption that the

process of the droplet, the internal circulation flow will be

droplet temperature was uniform and kept constant in time.

induced due to the gradient of temperature at the droplet

However, the local interface temperature is different

surface. The interface flows from high temperature area to

during droplet evaporation duo to the difference of local

low temperature area, which pulls the liquid to produce

evaporation rate which was presented by Bond and

convective flow inside the droplet called as Marangoni flow.

Struchtrup[4]. A nonuniform temperature distribution at the

Marangoni flow makes the temperature distribution tend to

interface creates a surface tension gradient that produces a

uniformity, which enhances heat transfer but weakens

forcing under which surface fluid is pulled toward region of

Marangoni flow in turn. So, during droplet evaporation, the

higher surface tension(Marangoni flow). The viscous force

internal flow is not steady.

then transports momentum into the interior of the droplet and a convective flow results throughout the droplet. In this work,

INTRDUCTION

the internal circulation in the evaporation droplet is focused

Droplet evaporation occurs in many important natural

on. Some researchers have reported the convection or

and engineering processes. These include such diverse

circulation flow in droplets. Leclair B P etc investigated the

phenomena as cloud physics, combustion of fuel, biological

internal circulation in water drops at terminal velocity in air

crystal growth, heat radiators, et al. The researches of

with theoretical and experimental methods, and also discussed

1

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the effect of internal circulation on drop shape and

of method is used to track the change of gas-liquid interface,

hydrodynamic drag[5]. Hegseth J J etc. experimentally

and the surface tension is described using the continuous

studied the natural convection in droplet evaporation,

surface tension forces model. The internal flows of

observed vigorous convection inside an evaporating droplet,

evaporation droplet are presented and the cause is analyzed.

and also discussed the droplet life time and how the system tended toward a state of marginal stability[6]. Savino R etc

MATHEMATICAL FORMULATIONS AND PHYSICAL

experimentally and numerically investigated evaporating

MODEL

hanging drops of n-octane and water, and the results showed

The simulation of a multiphase flow with free interfaces

that buoyancy and Marangoni convection affected the drop

still is one of the big challenges in CFD despite decades of

evaporation. In stationary droplets Marangoni and buoyancy

work on that topic. Difficulties are, among others, the exact

effects can be important in studies on evaporation or

localization of the interface, calculation of surface tension and

combustion of single stationary droplets[7]. Fabien G etc

the high variation of fluid properties. So, the numerical

numerically investigated the evaporation dynamics and

method should be capable of maintaining a sharp interface.

Marangoni driven convection in small sessile water droplets

The VOF method developed by Hirt and Nichols [12]can

on heating substrates under microgravity conditions[8]. F

model two or more immiscible fluids by solving a single set

Girard, M Antoni and K Sefiane numerically researched the

of momentum equations and the volume fraction of each of

effect of Marangoni flow on evaporation rates of heated water

the fluids throughout the domain, which could track the

droplet and showed that the Marangoni flow contribution to

interface between two phases so that it has been used widely

the evaporation rate of small heat water droplet resting on the

in analyzing various two phase flow system where the change

substrates would be negligible, but it is worth noting that the

of interface is important.

presented results apply to volatile heated drops[9]. Schlottke J

VOF model

and Weigand B directly numerically studied the evaporation of droplets in an air flow, and found that there were two pair

In VOF model, the governing equations are solved using

vortexes that generated by the outer flow adjacent to droplet

the volume fraction in each cell.The summation of the each

surface[10]. Deepak K M and Shamit B experimental

phase’s volume fraction is unity. n

researched internal circulation in a single droplet evaporation in a closed chamber. His work showed that there was

evaporation induced internal circulation within certain

where the volume fraction αk is defined as:

droplets under atmospheric conditions and this circulation

k

k 1

enhanced the evaporation rate significantly as compared to

1

k

(1)

the k phase fluent volume cell total volume

(2)

Figure 1 shows how the volume fraction is marked in each

diffusion-driven evaporation[11]. Above researches are aimed at droplets of resting on the

cell. The cells, αl=1 and αg=0, represent liquid region and gas

heated substrates or hanging on the supporter under

region. And for 0< α