Abstract: We propose a relationship between the water surface elevation and the mean water depth for partially wetted rectangular grid cells in the numerical simulation of shallow water flow with complex topography, and apply it to the numerical simulation of shallow water flow to verify the correctness of the relationship. Many natural terrains have complicated surface topography. It is very important to accurately predict the steep-fronted flows that occur after heavy rainfall flash floods or as inundation from dyke breaches. When modeling any terrain, rectangular grid cells are used to facilitate grid generation. In order to achieve a numerical balance of flux gradient and the source terms and to avoid numerical instability, a relationship between the water surface elevation and the mean water depth was derived if wetted and dry parts coexist within a rectangular grid cell. To estimate the momentum flux at the grid cell boundaries, we applied the second-order spatial accuracy Godunov finite volume algorithm with Roe approximation solver using the MUSCL method. Next, these relationships are applied to numerical simulations of three-dimensional shallow water flows with three humps and the validity of the proposed relationship is discussed. The relationship presented in this paper accurately reflects time-varying water regimes and boundaries in flow problems with moving wetting and drying zone interfaces and can be used for numerical simulations of three dimensional shallow water flows with arbitrary topography.Abstract: We propose a relationship between the water surface elevation and the mean water depth for partially wetted rectangular grid cells in the numerical simulation of shallow water flow with complex topography, and apply it to the numerical simulation of shallow water flow to verify the correctness of the relationship. Many natural terrains have complic...Show More
Abstract: Turbulent flow results from the erratic change in velocity and direction of a fluid flow over time. Hence producing irregular mixing and increased transport processes during the flow. Especially for those relying on passive heat transfer methods, designing efficient thermal energy systems requires an awareness of turbulent natural convection. This study aims to find how Rayleigh number affects flow pattern and heat transfer features by focusing on two-dimensional turbulent natural convection within a cylindrical enclosure. The enclosure examined employs Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with the energy equation, turbulence transport equations, and the Boussinesq approximation to represent buoyancy effects. The top wall is maintained at a consistent 298 K (ambient room temperature), while the bottom wall is regularly heated to 320 K; the vertical sidewalls are insulated. To properly represent turbulent features, a two-equation turbulence model appropriate for low Reynolds number flows is used. Numerical simulations are run with the Prandtl number fixed at 0.71—that of air—using a finite difference approach inside ANSYS Fluent. The obtained results revealed that the velocity and temperature decrease with increasing the aspect ratio (AR = 1, 2, 4, 8) at fixed Ra. Both maximum velocity and maximum temperature reduce with AR increase from 0.808 to 0.3090 m/s and from 192K to 55.6 K, while higher AR produces weaker convection, lower turbulence intensity, and more pronounced thermal stratification. Even with uniform Ra, the flow characteristics and heat transfer effectiveness are determined solely by the geometry. This illuminates the controlling influence of aspect ratio in confined natural convection systems.Abstract: Turbulent flow results from the erratic change in velocity and direction of a fluid flow over time. Hence producing irregular mixing and increased transport processes during the flow. Especially for those relying on passive heat transfer methods, designing efficient thermal energy systems requires an awareness of turbulent natural convection. This ...Show More