atw 2018-09v3

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atw Vol. 63 (2018) | Issue 8/9 ı August/September 470 AMNT 2018 | YOUNG SCIENTISTS' WORKSHOP | | Fig. 3. Comparison of simulations with empirical contact angle model and the laboratory experiments by Becker Technologies [5] (in false color representation) with mass flow rate ṁ = 11 g/s (ṁ =12 g/s for inclination of 10°), three different inclinations (left 2°, middle 10°, right 20°) and without aerosol loading. given water velocity parallel to the surface such that a specified mass flow rate is achieved. The flat plate is bounded by vertical sidewalls and has an inclination angle α. Material properties of water and air are used. For snapshots of the resulting flow fields see Figure 3. The simulations are conducted with the empirical contact angle model and the filtered initial randomized contact angle field [6]. The contact angle is specified in the boundary conditions of the water field and is taken into account to calculate the curvature of the water-air interface. The contact angle has a huge impact on the formation of rivulets and their stability as shown in previous studies [7]. The empirical contact angle model accounts for the wetted history and therefore enforces a spatially and temporally stable rivulet flow. 4 Simplified geometry This study also considers a simplified geometry with dimensions of 6 cm x 5 cm, 60° inclination and different water loadings. As a first step the simplified geometry, for which additional benchmark data from CFD simulations and experiments are available, is used for the parameter variation to save computational effort and time. Later the findings are transferred to the larger laboratory geometry. Also the experimental data can be used to investigate the empirical contact angle model [6] in another scenario than the laboratory geometry where it was developed. For the simplified geometry Singh et al. [8] provide results of CFD simulations, as do Hoffmann [9] and Iso et. al [10]. Experiments are conducted by Ausner [11]. All of the latter use the identical geometry, but different inlet conditions (overflow weir and feed tube) and various simulation tools (Singh and Iso Fluent, Hoffmann CFX). In the present study simulations with constant contact angle and with empirical contact angle model are performed. The results for different Weber numbers are evaluated and compared to the results of the studies mentioned above for validation. Five different Weber numbers (We = 0.02, We = 0.24, We = 0.47, We = 0.76 and We = 1.10) are investigated, which correspond to an increasing water mass flow rate: We = with liquid density ρ l , inclination angle α, volumetric mass flow rate Q, surface tension σ, plate width W and viscosity μ. As the water load increases, the flow pattern changes from a thin rivulet to a more pronounced rivulet to a fully wetting water film (see Figure 4). The influence of the side walls is also clearly visible and was also observed by Hoffmann [9] and Ausner [11]. With a constant contact angle of 70° (which is the value frequently quoted in the literature for the material combination water on steel) the percentage of wetted area in the present CFD calculations and in the calculations of Hoffmann and Iso tends to be underestimated, whereas the similar setup of Singh yields, for an unknown reason, larger values of wetted area. In Figure 5 the measurements are shown as blue triangles, the results of Hoffmann, Iso and Singh in purple, yellow and green, respectively, and the current calculations with the different contact angles in red, gray and black. The simulations with constant contact angle and empirical contact angle model with 70° for a dry surface and 50° for a wet one still slightly underestimate the wetted surface. With the empirical contact angle model 30°/70° the results are very well within the variation of the experiments. 5 Wash-off model The particle wash-off consists of a two-stage process. First the sedimented particles on the plate floor are | | Fig. 4. Comparison of simulations with empirical contact angle model with θ dry = 70° and θ wet = 30° for different Weber numbers We. The water height is indicated by color. | | Fig. 5. Normalized wetted surface A wn for different Weber numbers. Blue triangles indicate the experimental results; results of CFD simulations are displayed with differently colored lines. AMNT 2018 | Young Scientists' Workshop Development and Validation of a CFD Wash-Off Model for Fission Products on Containment Walls ı Katharina Amend and Markus Klein
atw Vol. 63 (2018) | Issue 8/9 ı August/September resuspended into the water flow, and then they are transported by the water flow down the plate and through the outlet. The model is based on the approach suggested and investigated in [1], which is also implemented in AULA. 5.1 Shields criterion In this section wash-off criteria, i.e. the circumstances that have to be met to resuspend settled particles, are presented. Many forces act upon a particle lying in a sediment bed. The particle starts to move, if the hydrodynamic forces and the buoyancy exceed the forces of gravity, friction, cohesion and adhesion. Shields proposes a criterion, which states, that the incipient motion occurs, when the shear velocity acting on the particle exceeds a critical threshold, the critical shear velocity. This critical shear velocity u c can be approximated with the help of the Shields-Rouse equation [12]. Using the dimensionless Rouse Reynolds number R * (1) (with the specific gravity of sediment , the particle density ρ p , the gravitational acceleration g and the kinematic viscosity of water ν) the critical dimensionless shear stress τ c * and further the critical shear velocity u c can be calculated via . , (2) (3) In this relation the adhesion and cohesion forces are neglected. Thus according to this criterion all particles with the same diameter and density would erode exactly at the same time as soon as u > u c holds. This leads to the so called instantaneous total wash-off. One way to also take the adhesion and cohesion forces into account is to model the wash-off as an exponential decay of the sedimented particle concentration c s (t) with a mass erosion rate r e [13], defined as: ,(4) (5) and erosion constant (or wash-off coefficient) ~ r e [13] which has to be estimated. 5.2 Particle transport The second stage is the transport of the volumetric particle concentration c with [c] = kg/m 3 . It is based on the OpenFOAM solver scalarTransport- Foam, which solves a simple transport equation for a scalar volume field . (6) The resuspended aerosol concentration is treated as massless particles that follow the flow perfectly. The velocity field v, shared by the water and air phase, is set to zero in cells without water. Thus particles are transported only within water and not within air. The concentration of eroded particles in each floor face at each time step serves as the source term S in the corresponding cell above the floor. The result of the simulations Name is the time-resolved particle mass that is transported through the outlet. 6 Results of the parameter variation In this section parameters such as particle density and the wash-off coefficient are varied. Detailed correlations or influences of the parameters on the total washed-off mass are analyzed. Table 1 summarizes the constant particle properties, the initial plate loading and the properties of the water flow. To investigate the influence of the particle density ρ p three different densities are used: 10 000 kg/m 3 which resembles the density of silver, 5000 kg/m 3 and 2500 kg/m 3 which is the effective density of the aerosol. The erosion constant ~ r e is also varied with values of 0.027 s –1 , 0.135 s –1 and 0.27 s –1 . Together with the five different Weber numbers (see Sec. 4) the parameter variation covers a total number of 45 simulations that are evaluated hereinafter. The parameter variation is conducted with the simplified geometry. Three seconds of water field simulations are calculated. The water field is then in a pseudo-stationary state and the water, the velocity and the pressure fields are kept constant. Overall the particle wash-off and Value α Inclination 60° ρ l Density of water 1000 kg/m^3 c s Initial loading 27 g/m^2 θ dry Contact angle dry 70° θ wet Contact angle wet 30° d p Particle diameter 2 μm | | Tab. 1. Parameters for simulations with simplified geometry. 471 AMNT 2018 | YOUNG SCIENTISTS' WORKSHOP | | Fig. 6. Time resolved washed off mass for different Weber numbers. Parameters according to Table 1, ρ p =2500 kg/m 2 and r ~ e = 0.027 s –1 . | | Fig. 7. Time resolved washed off mass for different particle densities. Parameters according to Table 1 and r ~ e = 0.027 s –1 . AMNT 2018 | Young Scientists' Workshop Development and Validation of a CFD Wash-Off Model for Fission Products on Containment Walls ı Katharina Amend and Markus Klein
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