123
Moreover, figure 4.46 highlights a flowing pattern similar to that observed on actual systems. Practically, constant critical thickness model is applied in the first half of the tube while in the second half constant contact angle model is used. The present formulation gives a global wetting ability that can be visualised in figure 4.46.
As a consequence, the sudden change from broken to uniform film configuration is avoided. In fact, this latter behaviour can’t be observed and a gradually increasing wetting ratio is also consistent with the theoretical work of A.
Doniec (1988) 112) about equilibrium shape of liquid cross-section and with the experimental results presented by D. M.
Maron et al., (1982) 92).
Furthermore, in order to employ the model for component analyses, the wetting model needs to be extended considering multiple tubes. Based on visual observations and according to previous models 108) and results 110), the calculation method for wetting ratio should be directly applied only for the tubes at the bottom of the bundle (after 10th tube), while the solution distribution is forced at the first tube. As a consequence, there must be a transition zone, in which wetting ratio decays following a certain law.
( 1) ,j (Re, ) C j
Xβ =B
β
e− β − (4.57)Where j is the index identifying the tube number and B is a coefficient representing Reynolds number influence on the first tube, allowing consistence with the condition of absence of heat transfer in the extreme case of null solution mass flow rate.
, ,
(Re, ) (1 ) Re
j j
Re
b
B β = X
β+ − X
β
(4.59)Where,
4
0Re
bµ
= Γ
(4.59)Accordingly, Cβ is the constant adjusted to give the value of Xβj calculated by the direct application of the wetting ratio model at tube 10.
,10 ,10 ,10
ln (1 ) Re ln
Re 9
b
X X X
C
β β β
β
+ − −
=
(4.60)124
-The partial wetting model and the critical condition show both qualitative and quantitative agreement with experiments and previous theories.
-Furthermore, the hysteresis behaviour of the wetting behaviour with respect to decreasing and increasing flowrates can be described by the present model. The occurrence of this phenomenon is believed to have a major role for the operative control of a system employing falling liquid films as transfer medium.
- Increasing the plain surface width λ and its inclination β the minimum stable thickness δ 0 decreases and wetting ratio at the critical condition X0 increases.
- The bigger the contact angle θ0 the higher the minimum stable thickness δ 0 of the uniform film. Accordingly, film breaking into rivulet occurs at higher Reynolds, but the wetting ratio at the critical condition X0 slightly increases.
As a result, this approach seems to be suitable for the characterisation of thin film hydrodynamics and appears to be promising to be included in heat and mass transfer modelling of processes performed by using thin liquid films flowing on solid surfaces.
Experimental flow visualisation of water on an adiabatic vertical test section, equivalent to a single fin of a liquid desiccant contactor, has been performed as a first comparison and validation of the theoretical analysis. Visual data have been collected, and image binarisation has been used to establish a calculation method of the amount of wetted area.
The film critical condition and the partial wetting model have shown both qualitative and quantitative agreement with experiments. As a result, the current approach appears to be promising for being employed in the optimisation of internally cooled desiccant contactors, as well as in the development of the control method of the whole system, and, can be combined with heat and mass transfer models for an improved characterisation of processes performed by using thin liquid films. On the other hand, further experimental comparisons are envisaged for a refinement of the model and for extending its applicability to different application cases.
Finally, a semi-empirical approach has been used as a criterion for estimating the critical condition for a uniform film, while the energy minimisation principle has been used for describing the tube partial wetting. According to the results obtained and to the model presented in the previous paragraph, the following conclusions can be stated:
The complexity of the flowing film hydrodynamic behaviour has required significant simplifying assumptions, which have brought to neglect important phenomena like Marangoni effect, coupling with mass transfer, turbulence or wavy surface. These considerations suggest that the modelling effort could be extended including the effect of other phenomena and parameters. On the other hand, the model complexity should be compared pragmatically to the accuracy-improvement possibility related to the inclusion of such details and to the practicability of eventual employment of the model in global system simulations. In addition, this first approach can be improved by further experimental comparisons. In particular the estimation of the critical breaking condition and visual observations of partial wetting for an extended range of operative conditions can be critical for refining the model accuracy and extending its applicability.
125
Chapter 4,
Falling film stability and wetting behaviour
126
Chapter 5, Heat and mass transfer characteristics of absorptive falling film on a partially-wetted horizontal tube
Going back to the main objective of this work, a detailed numerical study characterising the absorption process of water vapour in LiBr-H2O solution for different operative conditions, including both partial and complete wetting, is performed and this chapter describes its main results. Consistently with the numerical analysis of the absorption process developed in chapter 3, the model describing partial wetting is based on hydrodynamic description of Nusselt boundary layer integral solution, thus it can be easily adapted to be included in the transfer analysis by acting on the local film thickness. Accordingly, extended maps of heat and mass transfer coefficients of falling film heat exchangers are obtained. The resulting analysis is improved in its accuracy and extended in its applicability to the low Reynolds region.
Due to different dominant hydrodynamic effects, three main regions of the resulting heat and mass transfer coefficients can be identified (Partial wetting, uniform laminar film and film–dominated by velocity field). The influence of operating and geometric parameters is investigated to extract general and detailed observation for actual falling film absorbers design and control. Additionally, a first comparison with experimental data from literature is presented.