NUMERICAL INVESTIGATIONS ON HEAT TRANSFER IN FALLING FILMS AROUND TURBULENCE WIRES

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1 NUMERICAL INVESTIGATIONS ON HEAT TRANSFER IN FALLING FILMS AROUND TURBULENCE WIRES Abstract H. Raach and S. Somasundaram Thermal Process Engineering, University of Paderborn, Paderborn, Germany Turbulence wires are attached to the vertical heating plate in order to enhance the heat transfer through the falling film. By means of the free CFD software OpenFOAM the optimal distance between the wires is to be found. As a first step, OpenFOAM is assessed for the realistic simulation of two-dimensional wavy laminar falling films comparing the results for the phase velocity and maximal peak height with experimental correlations. Since the results of these tests are satisfactory, we can continue and simulate film flow over two and three turbulence wires. The mean surface temperature of the film is determined in the region downstream the wires at three different times. It is found that the stronger the perturbation the wavier the film and the better the heat transfer. The numerical experiments with two wires are not conclusive. Those with three wires show the best results for a wire distance of 15 and 20 wire radii. 1 Introduction Falling films are frequently employed in process engineering due to their small hold up, large surface and good heat transfer. Horizontal wires are attached to the heating wall in order to improve the heat transfer, cf. figure 1. On the one hand, they homogenise the film preventing it from forming dry patches. On the other hand, they promote turbulence even at lower Reynolds numbers, therefore the name turbulence wires. By the means of Computational Fluid Dynamics (CFD), Raach and Mitrovic (2005) recommended a distance between the wires of 18 wire diameters. In their two-dimensional (2D) numerical experiments, the wires were immersed by the falling water film having a distance of 0.1 mm from the heating wall. This distance was estimated to be the average distance of the wires not being Figure 1: Falling film with turbulence wire

2 perfectly straight. Raach and Mitrovic employed commercial CFD software that made use of the Volume of Fluid (VOF) multi-phase model of Hirt and Nichols (1981) and the Continuum Surface Force (CSF) model of Brackbill et al. (1992) to account for the action of a constant surface tension. Unfortunately, the CSF model could not be used by Raach and Mitrovic, for they encountered huge velocities at the gas-liquid interface that were attributed to parasitic currents, a purely numerical error. Kunugi and Kino (2005) showed that the simulation of wavy falling films by means of the CSF model is possible after all. Since their software is not available, it was our hope, that the new and free CFD software OpenFOAM version 1.3 can do the job. In a first step, it should be tested by performing 2D simulations of laminar, wavy falling water films and comparing the phase velocities and maximal peak heights with correlation obtained experimentally by Nosoko et al. (1996). Then we could continue with wavy falling films around turbulence wires. 2 Assessment of OpenFOAM 2.1 Setup The setup is depicted in figure 2. The x coordinate gives the distance from the inlet at the top, where water at 20 C flows in with constant velocity. The y coordinate is the distance from the wall. The film thickness δ 0 in the beginning is that of a smooth laminar falling film according to Nußelt (1916): Figure 2: Setup of isothermal experiments without wires

3 ν δ 3 0 = Re (1) g In equation (1) ν denotes the kinematic viscosity and g the gravitational acceleration. The inlet velocity is constant along y and modulated with the frequency f: u in = u 0 [ 1+ εsin( 2πft) ], (2) where ε is chosen to be 3% and u 0 is the average velocity of a smooth laminar falling film: 2 1 gδ0 u 0 = (3) 3 ν In the following, the film thickness shall be denoted by δ. 2.2 Isothermal wavy films Isothermal numerical experiments are performed for Re = 25, 40, and 60 and frequencies f = 13 Hz, 20 Hz, and 45 Hz. Further downstream, large solitary waves develop that are superseded by small capillary waves. The phase velocities and the maximal peak heights are determined and compared Figure 3: Comparison of wave phase velocity and peak height between experiment and simulation

4 to a correlation of Nosoko et al. (1996) obtained from experiments. The agreement is very good, cf. figure Non-isothermal wavy films Since the OpenFOAM application interfoam works isothermally, it has to be supplemented by the simplified ( ) energy equation: ρc V T ( r + ρc TU ) V = k 2 t T (4) The setup is changed insofar, that the water inlet temperature is now 60 C and the wall temperature 65 C. The local Nusselt number Nu(x) is determined: 1 3 Figure 4: The local and mean Nusselt number (below) compared to the film thickness (top) ( dt dy) ( T T ) h( x) Nu( ) ν w ν x = = (5) k g w i g In equation (5) the subscript i refers to the interface. In figure 4 the local Nusselt number is displayed together with the film thickness for Re = 75. These results are in good agreement with those of Kunugi and Kino (2005) for a heating wall at constant temperature.

5 Also 3D falling films are simulated. Kunugi and Kino (2005) report that in this case, due to hydrodynamic and numerical instabilities, a 3D flow will evolve. However, in our numerical experiments the deviation from two-dimensionality is so small that a 3D flow can not be observed. 3 Numerical Experiments with Turbulence Wires The experiments with three turbulence wires are performed in the setup described in section 3.1. Those with two wires were not conclusive, so they shall not be mentioned here any more. For a full account, see the diploma thesis of Somasundaram (2007). 3.1 Setup In our numerical experiments, the turbulence wires are half-cylinders attached to the wall. With OpenFOAM, special care has to be taken that dry patches on the film are to be avoided, otherwise the calculation does not converge. The distance between the wires is denoted with l, the wire radius with d chosen to be equal to 0.8 δ 0. The temperature of the water is 60 C, the wall temperature 65 C. The setup is depicted in figure 5. Figure 5: Setup of the numerical experiments with three wires

6 3.1 Optimal wire spacing In these 2D numerical experiments the numerical grid is block-structured. In the region behind the wires the mesh is rectangular. As a measure of a good heat transfer and a presumably high evaporation rate the average temperature at the gas-liquid interface is determined. For practical reason and without loss of significance, this is done in the downstream region behind the wires, where the mesh is rectangular. Three times are chosen at which the average surface temperatures are to be measured: 0.15 s, 0.2 s, and 0.5 s. After the first time interval, 0.15 s, the perturbation by the wires has reached the outlet. After 0.2 s, the wave is fully developed. The last time interval, 0.5 s, is considered to be a very long time. It is found that after 0.15 s and 0.2 s the differences are not very pronounced. Therefore, we should better rely on observations after 0.5 s. Heated as well as insolating wires are taken into account. In the first case, the wires have the temperature of 65 C. In the second case, a zero gradient condition is imposed, where the wires are. Figure 6: The position of the gas-liquid interface is displayed for three different wire distances at Re=73. The perturbation of the falling film by the three wires is largest for a distance between the wires of 15 wire radii (not 10 or 5) after the long time period of 0.5 s.

7 In the cases with heated wires, the chosen Reynolds numbers are 73, 147, and 220. The wire distance is 5d, 10, 15d, 20, and 25d. In the case of 5d and 10d, dry patches occur and we have to set the surface tension to zero for a short time period. However, very large peak heights result, so these experiments are less trustworthy, see Somasundaram (2007) for details. In the cases with insolating wires, we sometimes encounter numerical instabilities due to the nonuniform temperature boundary conditions on the wall. The Reynolds numbers are 73 and 147. The distances between the wires were the same as with heated wires: 5d, 10d, 15d, 20d, and 25d. The general observation is, that the stronger the perturbation, the wavier the film after 0.5 s and the higher the surface temperature. From the numerous results, a certain trend is seen that favour a wire distance of 15 and 20 wire radii. 4 Conclusion From comparison with experiments and research CFD codes, it can be concluded that laminar, wavy falling films are well simulated by OpenFOAM 1.3. From numerical experiments with three turbulence wires, it is seen as a trend that an optimal heat transfer can be obtained by a wire spacing between 15 and 20 wire radii. 4 Acknowledgements The help and friendly support of the Paderborn Center for Parallel Computing (PC 2 ) is gratefully acknowledged. 5 References Brackbill, J.U., Kothe, D.B. and Zemach, C., 1992, A Continuum Method for Modeling Surface Tension, Journal of Computational Physics, 100, Hirt, C.W. and Nichols, B.D., 1981, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, Journal of Computational Physics, 39, Kunugi, T. and Kino, C., 2005, DNS of falling film structure and heat transfer via MARS method, Computers and Structures, 83, Nosoko,T., Yoshimura, P.N., Nagata, T., Oyakawa, K., 1996, Characteristics of two dimensional waves on a falling liquid film; Chemical Engineering Science, 51, Nußelt, W., 1916, Die Oberflächenkondensation des Wasserdampfes, Zeitschrift VDI 60, No. 27, Raach, H. and Mitrovic, J., 2005, Seawater falling film evaporation on vertical plates with turbulence wires, Desalination, 183, Raach, H. and Mitrovic, J., 2007, Simulation of heat and mass transfer in a multi-effect distillation plant for seawater desalination, Desalination, 204,

8 Rusche, H., 2002, Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions, Ph.D. Thesis, University of London / Imperial College of Science Somasundaram, S., 2007, Numerische Untersuchung des Wärmeübergangs in Fallfilmen mit Stolperdrähten, Diploma Thesis, University of Paderborn

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