scholarly journals The Influence of Mesh Resolution on 3D RANS Flow Simulations in Turbomachinery Flow Parts

2021 ◽  
Vol 24 (1) ◽  
pp. 13-27
Author(s):  
Serhii V. Yershov ◽  
◽  
Viktor A. Yakovlev ◽  
Keyword(s):  
General Structure ◽  
Complex Structure ◽  
Three Dimensional ◽  
Estimation Method ◽  
Second Order ◽  
Computational Domain ◽  
Time Step ◽  
Multigrid Algorithm ◽  
Grid Convergence ◽  
Number Of Cells

The question of the difference mesh refinement degree influence on the results of calculation of the three-dimensional viscous gas flows in the flow parts of turbomachines using the RANS flow models and second order numerical methods is considered. Calculations of flows for a number of turbine and compressor grids on successively refining grids have been performed. We used H-type grids with approximate orthogonalization of cells in the boundary layer. The calculations were carried out using a CFD solver F with the use of an implicit ENO scheme of the second order, a local time step, and a simplified multigrid algorithm. When calculating the flow on fine grids, the following were used: convergence acceleration tools implemented in the solver; truncation of the computational domain with subsequent distribution of the results based on the symmetry property; the computational domain splitting into parts and computations parallelizing. Comparison of the obtained results is carried out, both in terms of qualitative resolution of the complex structure of three-dimensional flows, and in terms of quantitative assessment of losses. Grid convergence was estimated in two ways. In the first, the characteristic two-dimensional distributions of parameters obtained on different grids were visually compared. The purpose of such comparisons was to evaluate the sufficient degree of solution of both the general structure of the flow in grids and its features, namely, shock waves, contact discontinuities, separation zones, wakes, etc. The second estimation method is based on the grid convergence index (GCI). The GCI calculated from the three-dimensional density field was considered in this paper. It is concluded that for scientific research requiring high accuracy of calculations and detailing of the structure of a three-dimensional flow, very fine difference meshes with the number of cells from 106 to 108 in one blade-to-blade channel are needed, while for engineering calculations, under certain conditions, it is sufficient to use meshes with the number of cells less than 1 million in one blade-to-blade channel.

scholarly journals Domain Decomposition Modified with Characteristic Mixed Finite Element and Numerical Analysis for Three-Dimensional Slightly Compressible Oil-Water Seepage Displacement

2017 ◽  
Vol 9 (1) ◽  
pp. 143
Author(s):  
Yirang Yuan ◽  
Luo Chang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Optimal Error Estimate ◽  
Computational Domain ◽  
Time Step ◽  
Slightly Compressible ◽  
The Method Of Characteristics

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known problem.

Development of a Three-Dimensional Iterative Methodology Using a Commercial CFD Code for Flow Scouring Around Bridge Piers

2012 ◽  
Author(s):  
Phani Ganesh Elapolu ◽  
Pradip Majumdar ◽  
Steven A. Lottes ◽  
Milivoje Kostic
Keyword(s):  
Shear Stress ◽  
Three Dimensional ◽  
Critical Shear Stress ◽  
Shear Stresses ◽  
Computational Domain ◽  
Time Step ◽  
Mesh Morphing ◽  
River Bed ◽  
Scour Hole ◽  
The Stability

One of the major concerns affecting the safety of bridges with foundation supports in river-beds is the scouring of river-bed material from bridge supports during floods. Scour is the engineering term for the erosion caused by water around bridge elements such as piers, monopiles, or abutments. Scour holes around a monopile can jeopardize the stability of the whole structure and will require deeper piling or local armoring of the river-bed. About 500,000 bridges in the National Bridge Registry are over waterways. Many of these are considered as vulnerable to scour, about five percent are classified as scour critical, and over the last 30 years bridge failures caused by foundation scour have averaged about one every two weeks. Therefore it is of great importance to predict the correct scour development for a given bridge and flood conditions. Apart from saving time and money, integrity of bridges are important in ensuring public safety. Recent advances in computing boundary motion in combination with mesh morphing to maintain mesh quality in computational fluid dynamic analysis can be applied to predict the scour hole development, analyze the local scour phenomenon, and predict the scour hole shape and size around a pier. The main objective of the present study was to develop and implement a three dimensional iterative procedure to predict the scour hole formation around a cylindrical pier using the mesh morphing capabilities in the STARCCM+ commercial CFD code. A computational methodology has been developed using Python and Java Macros and implemented using a Bash script on a LINUX high performance computer cluster. An implicit unsteady approach was used to obtain the bed shear stresses. The mesh was iteratively deformed towards the equilibrium scour position based on the excess shear stress above the critical shear stress (supercritical shear stress). The model solves the flow field using Reynolds Averaged Navier-Stokes (RANS) equations, and the standard k–ε turbulence model. The iterative process involves stretching (morphing) a meshed domain after every time step, away from the bottom where scouring flow parameters are supercritical, and remeshing the relevant computational domain after a certain number of time steps when the morphed mesh compromises the stability of further simulation. The simulation model was validated by comparing results with limited experimental data available in the literature.

Semi-Analytical Solution of the Graetz Problem With Uniform Wall Heat Flux Utilizing the Transversal Method of Lines

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Antonio Campo ◽  
Müslüm Arıcı
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Heat Flux ◽  
Complex Structure ◽  
Method Of Lines ◽  
Second Order ◽  
Wall Heat Flux ◽  
Computational Domain ◽  
Temperature Distributions ◽  
Graetz Problem

Abstract This study addresses the second Graetz problem with prescribed wall heat flux employing the transversal method of lines (TMOL), which deviates significantly from the traditional mathematical procedures employed in the past. The wall heat flux is customarily provided by electrical, radiative or solar heating in engineering applications. The TMOL transforms the governing two-dimensional energy equation with temperature-invariant thermo-physical properties into a sequence of adjoint ordinary differential equations of second order with the radial variable as the independent variable. The singular feature in those equations is the embedded axial variable interval. For the implementation of TMOL, a special computational domain consists in a condensed set of transversal lines displayed in the cross section of the tube. An approximate, semi-analytical temperature distribution is obtained with the solution of the first adjoint ordinary differential equation of second order, which is expressed in terms of the Kummer function of first kind M(a,b,c). From here, the approximate, semi-analytical wall and center temperature distributions exhibit excellent quality because the two compare favorably with the exact, analytical wall and center temperature distributions given by the classical Graetz infinite series. As a beneficial consequence, usage of the second adjoint ordinary differential equation of second order having more complex structure becomes unnecessary.

Study of Afterburning in Solid Rocket Booster Jet: Towards a Model for Afterburning in Large Eddy Simulations

2014 ◽  
Author(s):  
Adèle Poubeau ◽  
Roberto Paoli ◽  
Daniel Cariolle
Keyword(s):  
Three Dimensional ◽  
Axial Direction ◽  
Large Eddy Simulations ◽  
Chemical Mechanism ◽  
Computational Domain ◽  
Time Step ◽  
Simple Method ◽  
Large Eddy ◽  
Solid Rocket ◽  
Comparison Of The Results

This paper focuses on two decisive steps towards Large Eddy Simulation of a solid rocket booster jet. First, three-dimensional Large Eddy Simulations of a non-reactive booster jet including the nozzle were obtained at flight conditions of 20 km of altitude. A particularly long computational domain (400 nozzle exit diameters in the jet axial direction) was simulated, thanks to an innovative local time-stepping method via coupling multi instances of a fluid solver. The dynamics of the jet is analysed and comparison of the results with previous knowledge validates the simulations and confirms that this computational setup can be applied for Large Eddy Simulations of a reactive booster jet. The second part of this paper details the implementation of a simple method to study the hot plume chemistry. Despite its limitations, it is accurate enough to observe the various steps of the chemical mechanism and assess the effect of uncertainties of the rate parameters on chlorine reactions. It was also used to reduce the set of chemical reactions into a short scheme involving a minimum of species and having a limited impact on the physical time step of the Large Eddy Simulations.

scholarly journals Wave-Structure Interaction for a Stationary Surface-Piercing Body Based on a Novel Meshless Scheme with the Generalized Finite Difference Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1147
Author(s):  
Ji Huang ◽  
Hongguan Lyu ◽  
Chia-Ming Fan ◽  
Jiahn-Hong Chen ◽  
Chi-Nan Chu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Wave Structure ◽  
Second Order ◽  
Computational Domain ◽  
Ocean Engineering ◽  
Time Step ◽  
Structure Interaction ◽  
Wave Structure Interaction

The wave-structure interaction for surface-piercing bodies is a challenging problem in both coastal and ocean engineering. In the present study, a two-dimensional numerical wave flume that is based on a newly-developed meshless scheme with the generalized finite difference method (GFDM) is constructed in order to investigate the characteristics of the hydrodynamic loads acting on a surface-piercing body caused by the second-order Stokes waves. Within the framework of the potential flow theory, the second-order Runge-Kutta method (RKM2) in conjunction with the semi-Lagrangian approach is carried out to discretize the temporal variable of governing equations. At each time step, the GFDM is employed to solve the spatial variable of the Laplace’s equation for the deformable computational domain. The results show that the developed numerical method has good performance in the simulation of wave-structure interaction, which suggests that the proposed “RKM2-GFDM” meshless scheme can be a feasible tool for such and more complicated hydrodynamic problems in practical engineering.

scholarly journals ParallelN-Body Simulation Based on the PM and P3M Methods Using Multigrid Schemes in conjunction with Generic Approximate Sparse Inverses

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
P. E. Kyziropoulos ◽  
C. K. Filelis-Papadopoulos ◽  
G. A. Gravvanis
Keyword(s):  
Linear Systems ◽  
Nodal Point ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Gravity Potential ◽  
Time Step ◽  
Multigrid Algorithm ◽  
Simulation Based ◽  
Mesh Method ◽  
Large Linear Systems

During the last decades, Multigrid methods have been extensively used for solving large sparse linear systems. Considering their efficiency and the convergence behavior, Multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose two hybrid parallel algorithms forN-Body simulations using the Particle Mesh method and the Particle Particle Particle Mesh method, respectively, based on the V-Cycle Multigrid method in conjunction with Generic Approximate Sparse Inverses. TheN-Body problem resides in a three-dimensional torus space, and the bodies are subject only to gravitational forces. In each time step of the above methods, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body. Then the Velocity Verlet method is used to compute the new position and velocity from the acceleration of each respective body. Moreover, a parallel Multigrid algorithm, with a truncated approach in the levels computed in parallel, is proposed for solving large linear systems. Furthermore, parallel results are provided indicating the efficiency of the proposed MultigridN-Body scheme. Theoretical estimates for the complexity of the proposed simulation schemes are provided.

Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows

2015 ◽  
Vol 18 (3) ◽  
pp. 593-620 ◽  
Author(s):  
Yan Wang ◽  
Chang Shu ◽  
Chiang Juay Teo ◽  
Jie Wu ◽  
Liming Yang
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniform Mesh ◽  
Computational Domain ◽  
Time Step ◽  
Uniform Grids ◽  
Flow Variables ◽  
Thermal Flows ◽  
Cell Interface

AbstractA three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presented in this paper for the simulation of both isothermal and thermal flows. The present solver combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. It applies the finite volume method (FVM) to solve the N-S equations. Different from the conventional N-S solvers, its viscous and inviscid fluxes at the cell interface are evaluated simultaneously by local reconstruction of LBE solution. As compared to the conventional LBE solvers, which apply the lattice Boltzmann method (LBM) globally in the whole computational domain, it only applies LBM locally at each cell interface, and flow variables at cell centers are given from the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS, the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-up of mesh spacing and time step, tedious implementation of boundary conditions, are completely removed. The accuracy, efficiency and stability of the proposed solver are examined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and natural convection. Numerical results show that the LBFS has a second order of accuracy in space. The efficiency of the LBFS is lower than LBM on the same grids. However, the LBFS needs very less non-uniform grids to get grid-independence results and its efficiency can be greatly improved and even much higher than LBM. In addition, the LBFS is more stable and robust.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

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