Film flow

A film flow (English flow film ) is a flow associated with a free surface extends approximately in a straight line without entrapped unwetted areas along a body contour. Over the wetted width of the liquid film there is usually a section with an approximately constant film thickness.

If these conditions are not met in a closed flow with a free surface , one speaks of a trickle flow , whereby a straight trickle flow (with a rounded flow cross section) can be viewed as a special case of a film flow. Film flows should not be confused with drag flows between solid boundaries.

Film flow consequently occurs with good wettability of the liquid on the respective solid or with high liquid loads, i.e. overall with good wetting of the liquid on the substrate .

Areas of application

Film flows are applied e.g. B.

• in packed columns during distillation , absorption or condensation
• in thermosiphon systems , cooling towers , heat exchangers and evaporators .

Flow behavior

turbulence

The degree of turbulence can be expressed using the Reynolds number . If the equation is derived from the classical pipe flow , the characteristic length is transferred to the film thickness. This results in:

${\displaystyle {\mathit {Re}}_{1}={\frac {v\cdot d}{\nu }}={\frac {\dot {V}}{b\cdot \nu }}}$.

The symbols stand for the following quantities :

• ${\displaystyle \!\ v}$- characteristic flow velocity of the fluid in relation to the body (ms ⁻¹ )
• ${\displaystyle \!\ d}$ - characteristic film thickness of the fluid (m)
• ${\displaystyle \!\nu }$- characteristic kinematic viscosity of the fluid (m ² s ⁻¹ )
• ${\displaystyle \!\ {\dot {V}}}$- characteristic volume flow of the fluid (l / s)
• ${\displaystyle \!\ b}$ - characteristic film width of the fluid (m)

A Reynolds number range of is given for the transition between laminar and turbulent film flow . From Reynolds numbers of , the film flow is considered completely turbulent. ${\displaystyle {\mathit {Re}}_{1}=75\dotsc 400}$ ${\displaystyle {\mathit {Re}}_{1}=400\dotsc 800}$

It is also possible to derive the equation for the Reynolds number from the channel flow. The above equation corresponds to the hydraulic diameter , which is calculated as follows: ${\displaystyle d}$ ${\displaystyle d_{h}}$

${\displaystyle d_{h}={\frac {4\cdot A}{U}}={\frac {4\cdot b\cdot d}{b}}=4\cdot d}$.

This gives the Reynolds number:

${\displaystyle {\mathit {Re}}_{2}={\frac {4\cdot v\cdot d}{\nu }}=4\cdot {\mathit {Re}}_{1}}$.

The critical Reynolds number ranges for describing the turbulence behavior are accordingly also four times as high. Specifically: a Reynolds number range of is given for the transition between laminar and turbulent film flow . From Reynolds numbers of , the film flow is considered completely turbulent. ${\displaystyle {\mathit {Re}}_{2}=300\dotsc 1600}$ ${\displaystyle {\mathit {Re}}_{2}=1600\dotsc 3200}$

Rip

Various approaches have been developed for calculating the criteria for breaking a film flow. Usually the minimum total energy of the flow is considered. Another method is based on the equilibrium of forces at the stationary tear point of the liquid film. El-Genk and Saber give the following equation to determine the minimum wetting rate:

${\displaystyle \Gamma _{\mathrm {min} }=0{,}67\Delta _{\mathrm {min} }^{2{,}93}+0{,}26\Delta _{\mathrm {min} }^{9{,}51}}$

With:

${\displaystyle \Delta _{\mathrm {min} }=(1-\cos \theta _{0})^{0{,}22}}$.

The symbols represent the following quantities :

• ${\displaystyle \!\ \Gamma _{\mathrm {min} }}$ - minimum wetting rate (dimensionless)
• ${\displaystyle \!\ \Delta _{\mathrm {min} }}$ - minimum film thickness (dimensionless)
• ${\displaystyle \!\ \theta _{0}}$- contact angle in equilibrium

Individual evidence

1. ^ ^{A b c} P. Schmuki, M. Laso: On the stability of rivulet flow. Journal of Fluid Mechanics. 1990, 215, pp. 125-143, doi : 10.1017 / S0022112090002580 . P. 125 f.
2. ↑ ^{a b} A. Doniec: Flow of a laminar liquid film down a vertical surface. Chemical Engineering Science. 1988, 43 (4), pp. 847-854, doi : 10.1016 / 0009-2509 (88) 80080-0 . P. 847.
3. ↑ A. Hoffmann: Investigation of multiphase film flows using a volume-of-fluid-like method. P. 8.
4. ↑ A. Hoffmann: Investigation of multiphase film flows using a volume-of-fluid-like method. Dissertation. Technical University of Berlin, 2010. p. 1 f. ( PDF file; 6.2 kB ).
5. ↑ MS El-Genk, HH Saber: Minimum thickness of a flowing down liquid film on a vertical surface. International Journal of Heat and Mass Transfer. 2001, 44 (15), pp. 2809-2825, doi : 10.1016 / S0017-9310 (00) 00326-4 . P. 2809.
6. ↑ ^{a b} F. Al-Sibai: Experimental investigation of the flow characteristics and the heat transfer in wavy trickle films. Dissertation. RWTH Aachen, 2005. P. 7 ( PDF file; 10.6 kB ).
7. ↑ MS El-Genk, HH Saber: Minimum thickness of a flowing down liquid film on a vertical surface. P. 2819.