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Numerical Solution of Reynolds Equation for a Compressible Fluid Using Finite Volume Upwind Schemes
Published in Jitendra Kumar Katiyar, Alessandro Ruggiero, T.V.V.L.N. Rao, J. Paulo Davim, Industrial Tribology, 2023
M. Phani Kumar, Pranab Samanta, Naresh Chandra Murmu
The present work, with inspiration from oscillation control schemes which are often used in the CFD analysis of compressible flows, uses an upwind scheme to obtain a stable numerical solution of the compressible Reynolds equation at higher bearings numbers. The governing equations are discretized using the finite volume method as it uses the governing equation in conservative form and ensures the conservation of all properties at control volume. After discretization, a solution was obtained using a first-order three-stage Runge-Kutta method and BiCGSTAB method to solve pressure values at clearance region and porous region, respectively. This solution method was validated by obtaining solution for a porous journal bearing and compared with published literature and the results seem to concur. It is shown that under the proposed method the maximum residual values decrease with iteration. However, the residual values fluctuate during the iterative process when FDM with a Gauss-Seidel method is used. Further, the numerical solution was then used for obtaining steady-state characteristics of externally pressurized porous journal bearings up to a bearing number (Λ) of 150. Steady-state characteristics were presented in graphical form which can be used during the design of such bearings.
Numerical investigation of interference effects for the Delft 372 catamaran
Published in Selma Ergin, C. Guedes Soares, Sustainable Development and Innovations in Marine Technologies, 2022
A. Farkas, N. Degiuli, I. Tomljenović, I. Martić
Equations (1) and (2) represent an unclosed set of equations and in this paper, for their closure, k−ω SST turbulence model with wall functions is utilized. This turbulence model is based on the eddy-viscosity concept, and it represents one of the most applied turbulence models in the field of ship hydrodynamics. Governing equations are discretized using the Finite Volume Method and transformed into an algebraic set of equations. The Volume of Fluid (VOF) method along with the High Resolution Interface Capturing scheme is utilised for tracking and locating free surface. To prevent wave reflections from the boundaries of the computational domain, the damping layer approach is used based on Choi and Yoon method (Choi & Yoon 2009). It should be noted that the damping layer approach is based on the introduction of an additional source term in the z-momentum equation, but only within the cells which are in the damping zone. In this paper, the damping zone included all cells which are away from the inlet, outlet, and side boundaries for one length of the analysed model. More details regarding the damping layer approach can be found in (Farkas et al. 2017).
Prediction of pressure induced by liquid sloshing for LNG carrier
Published in C. Guedes Soares, Y. Garbatov, Progress in the Analysis and Design of Marine Structures, 2017
Ren-qing Zhu, Hai-xiao Ma, Quan-ming Miao, Wen-tao Zheng
ABSTRACT: A numerical technique based on VOF method is introduced to study the sloshing problem in a prismatic LNG tank. With incompressible assumption, the governing equations including Navier-stokes equations and continuity equation for liquid sloshing are described. The equations are discretized by finite volume method and solved by SIMPLE scheme. The free surface is reconstructed by the Volume Of Fluid (VOF) method. The numerical simulation is performed by CFD software—FLUENT. A LNG tank model with 1:55 scale is used for experimental test at China Ship Scientific Research Center (CSSRC). The numerical results including free surface profiles and pressure time histories are provided and compared with the test ones. These comparisons show that the present method can be used to predict the pressure induced by liquid sloshing.
Numerical investigation of photothermal performance of glazed window integrated with airflow channel and phase change material
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
Dai Geng, Xinpeng Yang, Dong Li, RuiTong Yang, Yuxin Ma, Yangyang Wu, Müslüm Arıcı, Changyu Liu
The commercial software FLUENT, which has been widely used in the numerical calculation of windows containing PCM and ventilated envelopes, is employed to simulate the heat transfer of the PCMVW. The meshing software ICEM is utilized for generating structured meshes. The equations are discretized by the finite volume method and then iteratively computed by the implicit method. To ensure calculation accuracy, the momentum, energy, and DO radiation equations are discretized by Second Order Upwind. The momentum equation is coupled with the continuity equation by the SIMPLE algorithm. The radiation equations of each layer are calculated using the DO model, in which the Theta divisions and Phi divisions are both set to 2, and the DO solver is calculated in 10 energy iteration steps. Solar radiation and outdoor ambient temperature are imported into the software as boundary conditions by importing UDF files. The convergence criteria are determined by residuals for each Eq.. In order to ensure the accuracy of the calculation, the calculation is considered convergent on the condition that the residuals of momentum, x-velocity, y-velocity, and DO intensity are less than 10−6, and the residuals of continuity are less than 10−3. Four different grids with 25,600, 82564, 207778, 152495 elements are adopted to verify the independence. Outcomes indicate that grid#2 (82564 elements) saves computing resources with the calculation accuracy requirements.
Numerical method to simulate detonative combustion of hydrogen-air mixture in a containment
Published in Engineering Applications of Computational Fluid Mechanics, 2019
Governing equations are discretized by the finite volume method in which computational domain is divided by finite volumes. Over each finite volume, the governing equations are integrated and volume integrals are converted into surface integrals by Gauss theorem. Discretized forms of convection, diffusion terms of the governing equations require flux terms at faces between two neighboring cells. Variables, its gradients and divergence terms at the faces have to be interpolated from the information of neighboring cell-centered values. Discretized equations are solved iteratively by a segregated manner for which PIMPLE method was employed (Moukalled, Mangani, & Darwish, 2016). Matrices resulted from the discretized equations over the whole domain were solved by a conjugate gradient-based method with a matrix preconditioner. For time advancement, the Euler implicit method was applied. Information about numerical schemes and methods for the OpenFOAM solver are summarized in Table 2.
Numerical investigation of 3D rhombus designed PEMFC on the cell performance
Published in International Journal of Green Energy, 2021
Ali Jabbary, Sadra Rostami Arnesa, Hossein Samanipour, Nima Ahmadi
This section explains the numerical simulation and the algorithm for solving the equations governing the fuel cell. The first step in simulation is to create a computational network. The finite volume method is a technique for determining and evaluating partial differential equations in algebraic equations. Due to many equations and the solution’s complexity, a double-precision model has been used in the software to achieve convincing answers. For numerical simulation, we have to discretize the equations governing the computational field. We used the second-order upwind method for discretization. Each term of the equations is discretized according to the power of its derivatives. The system of equations then enters the matrix and is solved simultaneously.