CFD multiphase modelling of the acetone condensation and evaporation process in a horizontal circular tube

With increasing demands on energy efficiency, the use of low grade waste heat using vapour absorption refrigeration systems (VARS) are receiving renewed interest. One idea is to use the combination of acetone and zinc bromide as the salt solution, which allows use of temperatures in the order of 10s of  C above ambient conditions. This work numerically models acetone phase change in the evaporator and condenser in order to indicate how improvements can be made in these components of the system. ANSYS® Fluent finite volume method CFD is used to produce volume of fluid (VOF) and mixture multiphase flow models to investigate the evaporation and the condensation of acetone in a horizontal circular tube. Different velocities and temperatures were taken in each process to explore the effect of these variables in the system. A user defined function (UDF) is used to calculate the volume fraction of the phases. For the evaporation case, the heat transfer coefficient increases with increasing velocity and the temperature difference between the inlet flow and the wall, as expected. The mass transfer rate decreases with increasing the flow rate or decreasing the wall temperature, from 0.045 kg/m 3 .s at 0.01 m/s to 0.016 kg/m 3 .s at 0.06 m/s and it drops from 0.044 to 0.023 kg/m 3 .s by changing the temperature just from 300 to 298 K. This demonstrates a reduction in specific heat transfer to the liquid despite the higher wall heat transfer coefficient. In the condenser, vapour quality decreases along the tube as liquid acetone is created with reduced flow rate. Vapour volume fraction at the outlet section drops from 0.74 to 0.168 by increasing the ingoing velocity from 0.01 to 0.06 m/s. Increasing the rate of condensation will increase the liquid in the evaporator, which increase the evaporation rate then increase the performance of the VARS. This demonstrates the importance of controlling the temperature and the flow rate in the VARS for generate more refrigerants.


Introduction
Low grade waste heat (heat produced by system due to a mechanical or chemical processes that use energy) from small industrial and micro-generation plants can be used to generate cooling using vapour absorption refrigeration systems which are suitable for use with low temperature difference between waste heat and ambient temperature. VARS rely on effective evaporation and condensation processes to enhance performance. One particular VARS of recent interest for low grade heat systems uses acetone and zinc bromide salt solution [1][2][3][4]. Most existing research on VARS concentrates on NH3/H2O and H2O/LiBr for the case where higher grade heat is available. Macriss et al. [5] provide a survey of absorption system fluids; they suggest that there are about 40 refrigerants and around 200 absorbents which can be used in absorption systems. H2O/LiBr is used in many literatures for various purposes described in the following [6][7][8][9][10][11][12].
There are no studies found related with the heat and mass transfer for acetone as a refrigerant; however, it has been done for other liquids such as water. For example, Walter et al. [13] studied the heat and mass transfer of the condensation process of water in a square cross section channel, also, there are different studies related to the heat and mass transfer through the evaporation and boiling processes [14][15][16]. The concept of condensation mass transfer was modelled first by Colburn and Hougen [17]. In their study, the mass concentration gradient through a non-condensable gas layer controlled the mass transfer in the condensation process. They defined the heat transfer procedure as the sum of sensible heat and latent heat flows. Li [18] used a computational fluid dynamics (CFD) simulation to study the condensation of water vapour as a turbulent flow in a vertical cylindrical tube. He found that the average axial velocity drops quickly as water vapour is condensed, because the density of the gas mixture increases across the condenser tube and along the condenser.
Padin and Soares [19] studied CFD modelling of steam condensing in industrial tubes. They observed that there was a linear variation of the vapour concentration from the inlet of the pipe along the axial distance when the inlet velocity in the range of 4-5 m.s -1 with two different wall temperature (293.15 K and 343.15 K). Sun et al. [20] modelled condensation and evaporation phase change for water using ANSYS® Fluent based on the volume of fluid (VOF) model. Their simulation showed good agreement with the classical analytical results, their model is suitable for the case with saturated and unsaturated vapour. They developed a phase change model based on the calculation of the heat source term through a UDF code, and obtained a grid independent and accurate outcome, which has been verified by two-phase flow and heat transfer experiments.
Mimouni et al. [21] use NEPTUNE CFD code for wall steam condensation with varying homogeneous flow in a nuclear-pressurized water reactor (PWR) . They found a large amount of steam and hydrogen gas is released within the dry containment of PWR. Their expectation of axial velocity did not agree in some cases because of the turbulence modelling. Nabati [22] investigated numerically the condensation of water from a flue gas with high CO2 content. They found that the total heat transfer rate depends on the inlet velocity and temperature and that the heat transfer coefficient decreases as the CO2 mass fraction increases in the constant wall temperature case. Their results could be use in the condenser's design for oxi-fuel power plants. Hiller and Swift [23] studied the condensation in a steadyflow thermoacoustic refrigerator. They found that the liquid condensate does not show an effect to the oscillating thermoacoustic variables, which can be described by ideal-gas equations, but the condensing water is a large thermal load on the refrigerator. Laguerre et al. [24] studied the water evaporation and condensation in a domestic refrigerator loaded by wet product. They state that the numerical simulation which gives information on temperature, velocity and humidity fields may be used to evaluate risk during food preservation in domestic refrigerator.
Heat and mass transfer during the evaporation process has received much attention. Gao et al. [25] simulated flow and boiling heat transfer in a horizontal tube using the mixture approach and adding user-defined source term functions of mass transfer and energy transfer on phase boundary. Their results show that the heat transfer is enhanced by increasing the velocity and they realised that the superheat of the wall is one of the main factors affecting the heat transfer. Trujillo et al. [26] used Fluent CFD to model the heat and mass transfer process during evaporation of water in a circular tube. They found that the RNG ҡ-ε model using the enhanced wall treatment, taking into consideration the effect of radiation, fits better the experimental data in the case when the wall temperature is higher than the fluid temperature. The CFD model showed that at low Reynolds numbers when the radiative heat is considered the relation ht/hmCp (h: heat transfer coefficient, hm: mass transfer coefficient and Cp: specific heat capacity) is not constant around the cylinder.
Vik and Reif [27] implemented an improved evaporation model in Fluent based on the friction velocity. They found that the normalised evaporation rate is dropped with time and that the evaporation rate is 4.321x10 -11 kg/s for RANS model and 4.01x10 -11 kg/s for the LES model; however, the evaporation rate calculated analytically was 4.12x10 -11 kg/s. Yang et al. [28] investigated numerically and experimentally the two-phase flow during boiling of refrigerant R141B in a coiled tube. They found that the flow velocity is strongly dependent on the phase distribution and both the vapour and liquid interface and the flow rate had a great influence on the variation of the pressure drop and vapour volume fraction.
Falling film heat transfer were studied experimentally in different applications with conflicting results. For example, several studies [29][30][31] stated that with increasing the velocity, the heat transfer coefficient decreases first, and after specific value of velocity it starts increase. as Otherwise, according to [32,33], the heat transfer coefficient always increasing with the velocity. The last two studies also present that for completely wetted surfaces in strictly convective conditions, the heat flux does not affect the heat transfer coefficient and the convective heat transfer coefficient increases with the liquid temperature. Yang and Shen [34] state that with increasing of the heat flux, the heat transfer coefficient increases. According to Parken [33], Armbruster and Mitrovic [35], it appears that the liquid temperature effect is strongly causing to the decrease of viscosity, consequently, dropping in the film thickness.
Vapour absorption refrigeration is dependent on the condensation and evaporation processes on the refrigerant side of the process. In the case of the acetone zinc bromide system, pure acetone is the refrigerant fluid, which is not represented in the literature for heat transfer processes for the particular fluid or at flow rates encountered. Therefore this paper presents a CFD representation of the condensation and evaporation of acetone in a single tube element of a heat exchanger using the volume of fluid (VOF) model for condensation and the mixture model for evaporation. A user defined function (UDF) code developed by Lee [36] in 1979 and written in the C language was used for the mass transfer and the phase change. The effect of varying wall and inlet temperatures and different inlet velocities of the liquid are explored in order to identify how the heat and mass transfer improve.  In the condensation process, the flow was considered to be steady state with a VOF approach and the effect of turbulence was taken into account using the transition SST (Shear Stress Transport Table 1 Mesh independence study for both evaporation and condensation processes (The evaporation process was done with (Tw=300 K, Vel=0.6 m/s) and the condensation process was done with (Tw=290K, Tin=312K, Vel=0.01 m/s and the first layer= 2 * 10-6 m).

Evaporation Process Condensation Process
Axial

Calculation model (Evaporation process)
Evaporation has been modelled as the transient process in different work [20,25,28]. The governing equations used for the evaporation process are continuity, momentum, energy, turbulence and volume fraction models, which are presented in Ansys documentation [38,39] as repeated in the following for convenience.

Continuity
Where ⃗ is the body force and mixture viscosity.
Two-equation turbulence models allow the resolve of both a turbulent length and time scale by solving two separate transport equations. The standard k-ε model in Ansys Fluent falls within this class of models and has become the work-horse of practical engineering flow calculations in the time since it was proposed by Launder and Spalding [39]. The standard k-ε is a model based on transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). The model transport equation for (k) is derived from the particular equation, while the model transport equation for ε was obtained using physical reasoning and bears little resemblance to its mathematically accurate complement. In the derivation of the k-ε model, a fully turbulent flow is assumed and the effects of molecular viscosity are negligible. The standard k-ε model is, therefore, valid only for fully turbulent flows [38].
The turbulence kinetic energy (k) and its rate of dissipation (ε) are obtained from the following transport equations or the Standard k-ε model in Fluent-Solver Theory Guide [39].
From the mixture model a multiphase flow was selected with two fluids: liquid and a vapour.
In addition to the continuity and momentum equation, the mixture model also contains the relative (slip) velocity, which was defined as the velocity of a secondary phase (q) relative to the velocity of the primary phase (p): In order to calculate the phase volume share, the volume fraction expression was used as follows The is an interaction quality transformation source item from liquid to vapour phase.

Condensation process
The volume of fluid (VOF) model used in the condensation process which solves momentum, energy, turbulence and the volume fraction was solved under the steady state condition [18,40]. This method also solves mass, momentum and energy conservation equations for the condensing film. Where is the energy and can calculate by Where for each phase is based on the specific heat of that phase and the shared temperature. for the intermittency is defined as: Where is the wall distance, 1 and 1 are transition sources and 2 and 2 are destruction source; they are defined as: Where S is the strain rate magnitude, ℎ is an empirical correlation which controls the length of the transient region and Ω is the vorticity magnitude.
The condensation process, used an Eulerian modelling wall film, solved mass, momentum and energy conservation equations. Conservation of mass for two dimensional film in three dimensional domain is Where is a mass source per unit area due to droplet collection and phase change, ∇ is the surface gradient operator, ℎ is the film height ⃗⃗ the mean film velocity.
The film momentum conservation is given by The term on the left-hand side is a convective effect. On the right-hand side, the first term is the effect of the vapour pressure, the second term is gravity in a direction parallel to the film, the third term is a viscous shear force at the vapour film interface, the fourth term is viscous force on the film and the last term represents droplet collection. The conservation of film energy is given as Where is the temperature at the film-vapour interface; is the average film temperature; is the wall temperature; is the source term due to liquid impingement from the bulk flow to the wall; is the mass vaporization or condensation rate and is the latent heat associated with the phase change.
It is clear that if a piece-wise linear profile has been assumed: the film temperature varies from to in the lower half of the film and from to in the upper half A UDF code for mass transfer rate and the energy source which (shown in table 2) developed by Lee [36] in 1979 written in the C language, this code has been successfully applied by other researchers [19,20,25] for the boiling, evaporation and condensation's applications. The UDF file is linked with Fluent to calculate the source concentration of each phase. Liquid phase Vapour phase Where SM is the source term in mass conservation equation (kg/m 3 s), SE source term in the energy equation (J/m 3 s), is a time relaxation factor with unit s -1 , which is set equal to 0.1 s −1 (to keep the interface temperature close to the saturation temperature) in both of evaporation and condensation cases, and and are the volume fraction of the liquid and vapour respectively.

Validation and Numerical result
To validate the numerical work for the both processes (condensation & evaporation), two previous studies for each process were repeated with the same geometry and same boundary condition.
Experimental study of falling film evaporation heat transfer of Yang and Shen [34] are replicated using

Evaporation process results
The results of the simulation of the acetone evaporation process in the horizontal tube are         Figure 7a shows that the mean volumetric evaporation rate for the entire tube decreases with increasing velocity for both temperature conditions (298 & 300 K). Figure   7b shows that the volume fraction of the vapour decreases exponentially with increasing velocity of the liquid acetone because by increasing the mass flux, which increases with the velocity, the fluid has decreased energy absorption per unit mass. The mass transfer and the vapour generation rate increase with wall temperature as expected.  temperature distribution. Whereas, the lower side of the tube, which has more liquid phase has lower temperature; this gives the non-circular shape to temperature distribution at the cross section of the tube.

Condensation process results
The  Figure 10 also shows that with decreasing wall temperature, the mass rate increases, because there is a bigger temperature difference between Tsat and Tw. Figure 11 illustrates          The velocity of the flow and temperature difference between the inlet and the wall have a significant influence on the evaporation and condensation process, this behaviour proved by [22]. The slow velocity (low mass flux) of acetone makes the flow gain or release more heat, consequently better opportunity to reach the saturation temperature and achieving the phase change. A high temperature difference between the inlet flow and the wall with a condition of rapprochement between the inlet and the saturation temperature leads to exchange more heat and reaching to the phase change point.

Conclusion
Acetone evaporation and condensation processes in the horizontal tube have been simulated numerically using a commercial code ANSYS® (Fluent). These processes are a part of the vapour absorption refrigeration mechanism work. The simulations were conducted with 28000 Pa for condensation and 22000 Pa for evaporation with corresponding saturation temperature point of 310 and 296 K respectively; these conditions reflect the exchange of heat with ambient heat exchangers. It was found that the heat transfer coefficient for both evaporation and condensation processes increases with increasing velocity of the flow and the heat transfer coefficient at the lower side of the tube is much higher than the upper side which fill with the vapour. The heat transfer coefficient increases with increasing the difference of the temperature between the flow and the wall, also, the phase change rate increases as the velocity decreases and the wall temperature increases (evaporation case) or decreases (condensation case). For the condensation case, the vapour quality decreases as the length of the axial tube increase because there is more condensation by increasing the tube length. On the other hand, in the evaporation process, the liquid quality drops with the length of the tube. Consequently, the vapour volume fraction in the condensation and evaporation processes, decrease and increase respectively, with increasing the length of the tube.
Both of the velocity of the flow and the wall and inlet temperatures have a significant influence on the heat transfer coefficient and the phase change process. In the vapour absorption refrigeration process the velocity of the flow in both evaporator and condenser should be as slow as possible. A high difference between the inlet and the wall temperature gives better results for both process in condition of the inlet temperature should be near to the saturation temperature. Furthermore, it can concluded that the CFD modelling with ANSYS® Fluent is suitable to simulate these processes, but they need to develop an especial user define function for the source phase change.