
Roughness Parameter in Simulations of Droplet Sliding and Water Flow on Wall Surface Using Moving Particle Semi-Implicit Method
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The behavior of droplets sliding on surfaces and the flow of water are important in various engineering fields. To improve simulation predictions, a simple unified way of modeling both droplet motion and water flow is proposed and its validity is examined. The Moving Particle Semi-implicit (MPS) method [1] is suitable for modeling the motion of the fluid. When a droplet slides down an inclined surface, the contact angle hysteresis appears, and surface tension acts as resistance. Hattori et al. [2] proposed “dynamic friction model” to replicate this behavior, introducing a roughness parameter. While the sliding speeds matched with experimental values, their method required very small initial particle distance l_0. The present research aims to propose a method that maintains accurate sliding velocities with larger l_0. In the simulations of water flow by Nakajima et al. [3], increasing the effective radius in the MPS method led to a good reproduction of the flow on a vertical wall with a larger l_0. However, this approach increased computational cost and introduced artificial attractive forces between non-contacting droplets. The present study seeks to keep the effective radius small while achieving accurate flow rate and velocity. The motion of a droplet on an inclined surface is simulated. Two distinct modes of the roughness parameter depending on the initial particle distance are identified: "Mode F" for finer resolutions and "Mode C" for coarser ones. The optimal roughness parameter for Mode C is theoretically derived and matches well with the simulation results. Furthermore, applying the roughness parameter from droplet motion to water flow allows consistent velocity reproduction across different resolutions. Validity of the roughness-parameter-based model has been demonstrated in both droplet and water flow simulations, indicating potential applications in evaluating rainwater behavior on building surfaces. However, further optimization of the roughness parameter is needed to enhance its universality. REFERENCES [1] S. Koshizuka and Y. Oka, Nucl. Sci. Eng., 123, 421-434 (1996). [2] T. Hattori, M. Sakai, S. Akaike and S. Koshizuka, Comput. Part. Mech. 5, 477–491 (2018). [3] K. Nakajima, T. Koyama and S. Koshizuka, Annual Meeting of Japan Society of Fluid Mechanics, September 25-27, 2014, Sendai, 1M907-11-05.