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Heat and Mass Transfer of NH3-H2O Falling-Film Absorption on Horizontal Round Tube Banks

The absorption process has been confirmed as the most important process in absorption refrigeration machines in terms of improving their total efficiency. For this reason, absorber structures in general and heat and mass transfers in absorber in particular have attracted the interest of many researchers in this field. Commonly, the falling film absorber structure is the liquid mixture flows over tubes in a film mode. Mathematical model is developed for the falling film flowing on horizontal round tubes absorber derived from the mathematical model of the test volume element. The two-dimensional numerical simulation is written to solve partial differential equations predicting absorption efficiency. For evaluating the parameters which affect the coupled heat-mass transfer as NH3-H2O diluted solution flowing over horizontal round tubes absorb NH3 vapor to become the higher concentration solution. The fields of velocity, temperature, concentration and thickness of the falling film solution varied by the input conditions of diluted solution and cooling water temperature flowing in the tube represented for a test volume element of the tube. The correlations which give the heat transfer coefficient and mass transfer coefficient in the absorption process in range of solution concentration ω = 28% ÷ 31%, solution mass flow rate per unit tube length Γ = 0.001 ÷ 0.015 kgm -1 s -1 , coolant temperature twater = 28°C ÷ 38 o C are set as two functions. The accuracy of numerical model and experiments are compared by the inlet, outlet the tube bundle of cooling water temperatures and absorber heat load. The absorber heat load deviation of the computing program Qa_cumpute and experimental result Qa_meas is 4.3%. The absorber heat load deviation of simulation result Qa_sim and experimental result Qa_meas is 12.3%. The overall heat transfer coefficient k used for simulation result of absorber heat load was taken from the relationship of the heat transfer coefficient k = f(C; Г; T) = f(0.308; 0.008; 306.3) = 0.863 kWm -2 K -1 ). The results were also evaluated with other similar studies by other authors. Based on these simulations, the theoretical studies were done for absorption refrigeration system in order to narrow the working area where the experiments later focused on. The results of this study will be the basis for subsequent application research of falling film absorbers.


Introduction
Heat exchanger plays an important role in chemical processing, refrigeration, petroleum refining, food industries and desalination as evaporators, condensers and absorbers. So falling film technology of heat exchanger has been widely researched by experts. Because compare with the flood exchanger, it provides higher heat transfer coefficient and smaller liquid inventory [1,2]. And Horizontal-tube falling film absorbers can realise high heat and mass transfer rates with compact size and negligible pressure losses [3]. The absorber is usually the largest component in absorption cooling systems. An improvement in the absorption process leads to a reduction in area of the heat exchangers, and therefore a significant reduction in the costs of absorption chillers [4]. Falling film absorber is the most popular due to many advantages of heat transfer efficiency, easy to assemble, easy to manufacture, especially well-suited to Vietnam conditions. This research focuses on the properties of motion, the coupled heat and mass transfer of falling film absorption on the horizontal tubes of the cooling tube bundle.
Two common pairs of working fluid (refrigerantabsorbent) in refrigeration absorption system are H 2 O-LiBr and NH 3 -H 2 O. Testing absorber using dilute solution concentration (NH 3 -H 2 O) distributed evenly from top to form the falling film around the tubes of parallel tube layers, NH 3 vapor go pass through the tube layers from the absorber bottom [5][6][7][8][9]. Dilute solution absorb NH 3 vapor to become stronger solution generating the absorption heat flow. This heat flow go through the tube wall to the cooling water flowing in tubes and carry it away. The falling film covers only one part of the tube depends on the fluid distribution along the tube length and surface tension of the solution, as well as surface roughness of tube.
Solution concentration profile and temperature profile of the film leaving out the cooling tube bottom have decisive role in appropriate choice between adequate absorber size and system operation. Therefore, studying of the influence of solution flow rate, cooling water temperature, solution concentration inlet, and cooling water flow rate on heat and mass transfer coefficients are urgently needed for accurate thermal calculations and applications which is used for designing in falling film absorber.

Model Description
A test volume element has 100% wetted ratio. 3D physical models become 2D physical model has dilute solution flow direction along the tube circumference by coordinate x. Film thickness direction is from the tube center by coordinate y. Any points on the film are determined by coordinate θ, y respectively. Assumptions of 2D physical model 1. The flow is laminar and there are no interfacial waves; 2. Wettability of the solution on the tube surface is 100%; 3. Thermodynamic equilibrium exits at the interface between of solution film and vapor; 4. Heat transfer from interface to vapor phase is negligible; 5. The variation of film thickness due to absorption of NH 3 vapor is negligible; 6. Outside tube surface temperature equals the cooling water temperature.
For a given solution mass flow rate per unit tube length / (kgm -1 s -1 ). Film thickness (m) is expressed as equation (1).
Where υ is kinematic viscosity of solution (m 2 s -1 ) and WR is wetted ratio of the tube (%).
Velocity component u (ms -1 ) along x direction is belong to flow direction as equation (2) Velocity component v (ms -1 ) along y direction is normal to flow direction as equation (3).
The phenomenon of coupled heat and mass transfer in steady state is discribed by energy transport equation (4) and spicies transport equation (5).
Where α and β are thermal diffusivity (m 2 s -1 ) and mass diffusivity (m 2 s -1 ) of solution respectively, while T and ω are corresponding temperature and concentration of solution at the appropriate reference point.
Concentration and temperature boundary conditions at the inlet (6).
Concentration and temperature boundary conditions at the tube wall surface (7).
Concentration and temperature boundary conditions at the liquid-vapor interface (8).
Local heat transfer coefficients from interface to bulk solution along the film flow (9) and from bulb solution to tube wall surface along the film flow (10) in terms of Nusselt number. int . ( Where α ib and α bwall are heat transfer coefficients from interface to bulk and from bulk to wall (Wm -2 K -1 ), while T int , T sb and T wall are temperatures at interface, bulk solution, and tube wall respectively.
Mass transfer coefficient from interface to bulk solution along the film flow (11) in terms of Sherwood number. Where h m is mass transfer coefficient from interface to bulk (ms -1 ), D ab diffusion coeffiction of absorption (m 2 s -1 ).
Total heat transfer coefficient from bulk solution to cooling water (Wm -2 K -1 ) can be expressed as (12).
Where α bwall and α w are convective heat transfer coefficients from bulk solution to wall and for cooling water (Wm -2 K -1 ), while δ wall and λ wall are wall thickness of cooling tube (m) and thermal conductivity of tube wall (Wm -1 K -1 ) respectively.
The physical domain has a complex geometry. Moreover, the film thicness is in micro-size vs half circumference length of the cooling tube is 0.0157 m. This ratio make the domain can not be meshed directly which must be transformed from sliding coordinate xy to non-dimentional coordinate εη making the computational domain rectangular.

Result and Discussion
Parameters used in this study are presented in table 1. Figure  2 shows the mass transfer phenomenon as NH 3 vapor is absorbed in order to become a stronger concentration solution.   Interface temperature is saturated to solution concentration. At tube wall, solution temperature equals wall temperature. When absorption phenomenon occurs, concentration of the liquid-vapor interface increases along ε-axis (x), then diffuses into the tube wall along η-axis (y). This absorption generates heat making liquid-vapor interface temperature increases along ε-axis (x). Due to the temperature difference between the interface and tube wall, heat transfer to the wall along axis η (y).
Average concentration of the film leaves the wall ω = 0.3537; increases 0.0587. Average temperature of the film coming in the tube is 317.6 K (44.5°C), average temperature of the film leaving tube is T = 304.8 K (31.7°C), decreases 12.8°C. Temperature of the liquid-vapor interface coming in the tube is 332 K (58°C), temperature of the liquid-vapor interface leaving the tube is T = 306.5 K (33.4°C), decreased 24.7°C. Difference temperature between liquid-vapor interface leaving the tube and the tube wall is 3.4°C.

The Effect of Solution Flow Rate on Heat and Mass Transfer
Input data as in table 1, tube wall temperature is 303 K, average local temperature at the inlet of falling film on tube is 325 K, solution flow rate Γ are changed: 0.001; 0.005; 0.008; 0.0113; 0.0146; 0.03 kgm -1 s -1 . Figures 3 and 4 show the variation of heat transfer coefficient and mass transfer coefficient with non-dimensional tube half circumference for different solution flow rates, while table 2 presents the thickness variation, the average local velocity, the average local concentration, the average local temperature, the heat transfer coefficient, the mass transfer coefficient of the film.   Figure 3 shows the heat transfer coefficient between the liquid-vapor interface and cooling water flowing in the tube U along ε-axis (x). These coefficients increase in the first quarter of the tube and decrease in the second quarter of tube. This shows absorption rate decreases as heat transfer coefficient decreases. Figure 4 shows the change of the mass transfer coefficient along ε-axis (x). Mass transfer coefficient increases rapidly when the dilute solution just contact the tube wall, then decreases rapidly and fairly flat before leaving the tube wall. When solution flow rate increases, mass transfer coefficient increase, when the increase of flow rate is sizable (Γ = 0.0146 kgm -1 s -1 ) or more, mass transfer increases very small. According to table 2, as solution flow rate distribution decreases 1%, average concentration of the film leaving the tube increases, heat transfer coefficient from interface to wall decreases 0.72%, heat transfer coefficient decreases significantly 0.56%; mass transfer coefficient decreases significantly 3.27%.

The Effect of Cooling Water Temperature on Heat and Mass Transfer
Input data as in table 1, solution flow rate distribution 0.008 kgm -1 s -1 , tube wall temperature are changed: 311; 309; 307; 305; 303; 301 (K). Figures 5 and 6 show the variation of average local concentration and average local temperature with non-dimensional tube half circumference for different tube wall temperatures.  When cooling water temperature decreases, average local concentration increases (Figure 5), average local temperature decreases ( Figure 6). According to table 3, cooling water temperature decreases 1 o C, average concentration of the film leaving the tube increases, average film temperature leaving the tube decreases, heat transfer coefficient increases 0.95%; mass transfer coefficient increases significantly 3.7%.

The Effect of Solution Concentration on Heat and Mass Transfer
Input data as in table 1, solution flow rate distribution 0.008 kgm -1 s -1 , tube wall temperature 305 K. Figures 7 and 8 show the variation of heat transfer coefficient and mass transfer coefficient with non-dimensional tube half circumference for different solution concentrations.  The concentration of the film decreases, the heat transfer coefficient increases; mass transfer coefficient increases. According to table 4, as concentration of the film decreases 1%, average concentration of the film leaving the tube increases, average film temperature leaving the tube increases, heat transfer coefficient increases 1.46%; mass transfer coefficient increases 1.39%.

Heat and Mass Transfer Coefficients
A correlation which gives heat transfer coefficient and mass transfer coefficient in the absorption process in range of solution concentration ω = 28% ÷ 31%, solution mass flow rate per unit tube length Γ = 0.005 ÷ 0.015 (kgm -1 s -1 ), coolant temperature t = 28 o C ÷ 38 o C are set as two funtions.
These functions are derived to estimate the absorber capacity and mass flow rate of NH 3 vapor into NH 3 -H 2 O solution.

Evaluation of Numerical and Experimental Result
The input for the machine compution program are the condensing temperature t c = 30.2°C, absorbing temperature of strong solution leaving the absorber t a = 36°C, evaporating temperature t e = -19°C, and the heat supply capacity Q g = 3.762 kW. The optimal generating temperature will be t g = 120°C.

Conclusion
Solution flow rate increases, average local concentration of the film decreases, average local temperature increases. Heat transfer coefficient increases strongly, mass transfer coefficient increases. When increasing of flow rate is sizable Γ = 0.0146 kgm -1 s -1 or more, mass transfer increases very small.
The effects of the solution concentration ω = 28% ÷ 31%, solution mass flow rate per unit tube length Γ = 0.001 ÷ 0.015 kgm -1 s -1 , cooling water temperature, and cooling water t w = 28°C ÷ 38°C on the heat transfer coefficient U Wm -2 K -1 and mass transfer coefficient h m ms -1 of the absorption process were: a) As solution flow rate distribution decreases 1%, heat transfer coefficient decreases significantly 0.56% and mass transfer coefficient decreases significantly 3.27%. b) As cooling water temperature decreases 1°C, heat transfer coefficient increases 0.95%; mass transfer coefficient increases significantly 3.7%. c) As concentration of the film decreases 1%, heat transfer coefficient increases 1.46%; mass transfer coefficient increases 1.39%. Two functions giving heat transfer coefficient and mass transfer coefficient in the absorption process in range of solution concentration ω = 28% ÷ 31%, solution mass flow rate per unit tube length Γ = 0.001 ÷ 0.03 kgm -1 s -1 , coolant temperature t water = 28°C ÷ 38°C are set as (13) and (14).