Orthogonal Mesh Research Articles

PENALTY FUNCTION METHOD FOR MODELING OF CYLINDER FLOW WITH SUBSONIC COMPRESSIBLE FLOW

Numerical modelling of compressible flows around moving solids is important for engineering applications such as aerodynamic flutter, rocket engines and landing gear. The penalty function method is particularly effective when using orthogonal structural meshes within a finite difference scheme and is widely used to solve both laminar and turbulent flow problems. The method is based on the direct application of the Navier-Stokes equations with added sources, which allows the boundary conditions to be set indirectly. This method facilitates the imposition of Dirichlet boundary conditions but complicates the application of Neumann conditions. Nevertheless, the method works well with both types of boundary conditions, making it suitable for thermal and compressible flows where Neumann conditions are often used. Despite its flexibility, the method requires a high degree of data management and additional coding. This paper presents results of a recently developed higher-order method for compressible subsonic flows, demonstrating accurate modeling of moving objects without numerical noise. The method has been tested on stationary and moving objects over a wide range of Reynolds and Mach numbers.

Experimental study on improving the heat transfer performance of large-diameter thin flattened heat pipes

Theoretically, when flattened to the same thickness, thin flattened heat pipes made from thin-walled cylindrical heat pipes with larger diameters have better thermal performance, but the conventional wick structures cannot meet their high-performance thermal requirements. In this study, to improve the heat transfer performance of large-diameter thin flattened heat pipes, composite sintered wick structures with spiral woven mesh and different mesh sizes of orthogonal woven mesh were designed and fabricated. The sizes were 150, 200, and 250 mesh. Four types of wick structures were developed to investigated the effects of the weaving mesh size and the composite sintering of the orthogonal woven mesh on heat transfer performance. The results demonstrated that the sample with the 200-mesh orthogonal woven mesh sintered wick exhibited the most pronounced improvement in thermal performance. The maximum heat transport capacity of the sample was found to be 46 W, representing an increase of 91.67 % compared with the sample utilizing the spiral woven mesh wick. Additionally, the evaporation resistance decreased by 56.24 %, and the total thermal resistance decreased by 53.40 %. These findings are highly conducive to the economic fabrication and performance improvement of large-diameter thin flattened heat pipes.

Mechanical Behaviors of Hybrid Composites with Orthogonal Spiral Wire Mesh and Polyurethane Elastomer

This work aims to significantly improve the mechanical properties of conventional rigid lattice structures under repeatable large deformations. A novel hybrid material is proposed based on the concept of interpenetrating composite materials. The material utilizes a woven TC4 orthogonal spiral wire mesh as the skeleton and PU elastomer (OSWM‐PU) as the matrix. The uniaxial tensile tests demonstrate that OSWM‐PU possesses the excellent load‐bearing capacity, allowing for large deformations (≥60%) while maintaining partial integrity even after matrix fracture. Optical measurements and simulation analysis reveal that Poisson's ratio can be adjusted within a certain range by manipulating the microscopic parameters (p, d) of the longitudinal helical filaments. Cyclic tensile experiments further demonstrate that OSWM‐PU exhibits exceptional energy absorption performance, multiple energy dissipation modes, and a more pronounced Mullins effect. The stress relaxation experiment reveals the significant influence of the volume fraction of the skeleton on long‐term loading conditions. The orthogonal spiral wire skeleton exhibits a superior hooking effect without dividing the matrix, enabling OSWM‐PU to possess enhanced collaborative deformation capability and inherent designability in the orthogonal direction. These characteristics make it highly promising for applications in various robot joints and as flexible aircraft skin, offering excellent prospects for utilization.

Thermal performance of a large-diameter thin flattened heat pipe with novel composite wick structure

Flattening large-diameter cylindrical heat pipes to fabricate thin heat pipes can significantly improve their heat transfer performance in theory, but their appropriate wick structures and thermal performance are still unclear. In this work, a novel composite wick structure sintered from spiral woven mesh and orthogonal woven mesh was developed for large-diameter thin flattened heat pipes. Their diameter and thickness were 8 and 1.0 mm, respectively. Seven types of wick structures for the experimental heat pipes were designed to investigate the effects of the length and position of the orthogonal woven mesh on the thermal performance. The results indicated that based on the spiral woven mesh, sintering the orthogonal woven mesh in the evaporator and adiabatic sections of the heat pipe can significantly improve the thermal performance. Compared with the single spiral woven mesh wick, the maximum heat transport capacity of the experimental heat pipe with optimal composite wick increased by 41.67%, and the evaporation and total thermal resistances decreased by 68.41% and 61.49%, respectively. This study provided very useful guidance for improving the thermal performance of the large-diameter thin flattened heat pipes for cooling laptops.

Path Integral Representation Model to Extend the Analytical Capability of the Nonstandard Finite-difference Time-domain Method

The nonstandard finite-difference time-domain (NS-FDTD) method is a powerful tool for solving Maxwell’s equations in their differential form on orthogonal grids. Nonetheless, to precisely treat arbitrarily shaped objects, very fine lattices should be employed, which often lead to unduly computational requirements. Evidently, such an issue hinders the applicability of the technique in realistic problems. For its alleviation, a new path integral (PI) representation model, equivalent to the NS-FDTD concept, is introduced. The proposed model uses a pair of basic and complementary path integrals for the H-nodes. To guarantee the same accuracy and stability as the NS-FDTD method, the two path integrals are combined via optimization parameters, derived from the corresponding NS-FDTD formulae. Since in the PI model, E-field computations on the complementary path are not necessary, the complexity is greatly reduced. Numerical results from various real-world problems prove that the proposed method improves notably the efficiency of the NS-FDTD scheme, even on coarse orthogonal meshes.

An immersed boundary method‐discrete unified gas kinetic scheme simulation of particle‐laden turbulent channel flow on a nonuniform orthogonal mesh

AbstractParticle‐resolved simulations of turbulent particle‐laden flows provide a powerful research tool to explore detailed flow physics at all scales. However, efficient particle‐resolved simulations for wall‐bounded turbulent particle‐laden flows remain a challenging task. In this article, we develop a simulation approach for a turbulent channel flow laden with finite‐size particles on a nonuniform mesh by combining the discrete unified gas kinetic scheme (DUGKS) and the immersed boundary method (IBM). The standard discrete delta function was modified according to reproducible kernel particle method to take into account mesh non‐uniformity and correctly conserve force moments. Simulation results based on uniform and nonuniform meshes are compared to validate and examine the accuracy of the nonuniform mesh DUGKS‐IBM. Finally, the computational performance of the nonuniform mesh DUGKS‐IBM is discussed.

A finite volume method based multi-group neutron diffusion model for space-time nuclear reactor kinetics problems in RZ geometry

The transient analysis of Fast Breeder Reactor (FBR) requires the development of high fidelity space-time nuclear reactor kinetics codes for the realistic prediction of spatial and temporal behavior of neutron flux and fission power along with the feedback effects. So, a space-time nuclear reactor kinetics model has been developed for solving the coupled time dependent multi-group neutron diffusion equations and the delayed neutron precursor equations in axi-symmetric cylindrical (r-z) geometry. The numerical model employs an orthogonal mesh finite volume method for spatial discretization and implicit method for time discretization. A computer code named MANDIR-KRZ (Multi-group Analysis of Neutron DIffusion in Reactor for Kinetics problems in RZ geometry) has been developed and employed to reconstruct the keff, transient neutron flux and power results of different benchmark problems. Mathematical formulation of the numerical model and results of the code for Dodds and FBR transient benchmark problems are discussed in this paper.

On the discrete Sobolev inequalities

Abstract We prove a discrete version of the famous Sobolev inequalities [1] in R d for d ∈ N ∗ , p ∈ [ 1 , + ∞ [ $\mathbb{R}^{d} \text { for } d \in \mathbb{N}^{*}, p \in[1,+\infty[$ for general non orthogonal meshes with possibly non convex cells. We follow closely the proof of the continuous Sobolev inequality based on the embedding of B V R d into L d d − 1 $B V\left(\mathbb{R}^{d}\right) \text { into } \mathrm{L}^{\frac{d}{d-1}}$ [1, theorem 9.9],[12, theorem 1.1] by introducing discrete analogs of the directional total variations. In the case p > d (Gagliardo-Nirenberg inequality), we adapt the proof of the continuous case ( [1, theorem 9.9], [9, theorem 4.8]) and use techniques from [3, 5]. In the case p > d (Morrey’s inequality), we simplify and extend the proof of [12, theorem 1.1] to more general meshes.

Level set function based on conformal geometry theory: An efficient approach for optimization of shell structure with arbitrary Gaussian curvature

Topology optimization based on the level set (LS) theory is of great significance to shell structure design. However, the Gaussian curvature of the shell structure can turn complex in many cases, and the establishing process of the LS function will become extremely cumbersome, which consumes overmuch time to solve the Hamilton-Jacobi(H-J) equation. In order to improve the efficiency of optimization, an LS function based on the conformal geometry theory (LSF-CGT) is proposed in this paper. Firstly, the shell structure with arbitrary Gaussian curvature is conformally mapped into 2D Euclidean space to generate the orthogonal mesh of the preset initial LS function. Then the barycentric interpolation method is used to reveal the transformation relationship between the orthogonal and shell structure mesh. Finally, the LS function of the orthogonal mesh is assigned to the mapped shell structure, and the LS function of the 3D shell structure is subsequently obtained. Three typical shell structures with positive, zero, and negative Gaussian curvature are used to verify the effectiveness of LSF-CGT in topology optimization. Results show that LSF-CGT can effectively reduce the strain energy of shell structures with arbitrary Gaussian curvatures by more than 30%. As a method for optimizing shell structures with arbitrary Gaussian curvatures, LSF-CGT can not only stably and quickly converge to the optimal structure in the 2D domain but also effectively maintain the initial geometric characteristics of the shell structure.

Punching Shear of Flat Slabs with Pultruded GFRP Stay-in-Place Structural Forms

This paper examines the punching shear behavior of a new concrete flat slab design, incorporating a glass fiber-reinforced polymer (GFRP) stay-in-place (SIP) structural form system and orthogonal GFRP top rebar mesh. The SIP form system comprises I-beams supported on the four sides of a column and flat plates with T-up ribs supported by, and adhesively bonded to, the bottom flanges of the I-beams. The web and top flange of the I-beams are embedded in the slab, thereby providing flexural and shear reinforcement, while the SIP ribbed plates provide the bottom reinforcement. Four full-scale interior slab–column specimens, 2000 × 2000 × 200 mm3, were tested under axial compression applied to the column. The slabs have a central 300 × 300-mm square column extending 300 mm on either side of the slab. The study assessed the contributions to punching shear strength of different components of the GFRP system. The new design experienced a 29% higher punching shear strength than the control slab with GFRP rebar only, and was much more ductile. The load dropped gradually over a large range of deflection, increasing the ductility index from 1.6 in the control slab to 3.1 in the slab incorporating the new design. An analytical model is developed for punching shear strength, accounting for concrete contribution and flexural and web contributions of I-beams. Results agreed with experimental strength, within −6% to +13%. A parametric study examined a range of rebar reinforcement ratios, different GFRP I-beam sizes and a comparable steel I-beam.

Discrete orthogonal structures

To represent smooth geometric shapes by coarse polygonal meshes, visible edges often follow special families of curves on a surface to achieve visually pleasing results. Important examples of such families are principal curvature lines, asymptotic lines or geodesics. In a surprisingly big amount of use-cases, these curves form an orthogonal net. While the condition of orthogonality between smooth curves on a surface is straightforward, the discrete counterpart, namely orthogonal quad meshes, is not. In this paper, we study the definition of discrete orthogonality based on equal diagonal lengths in every quadrilateral. We embed this definition in the theory of discrete differential geometry and highlight its benefits for practical applications. We demonstrate the versatility of this approach by combining discrete orthogonality with other classical constraints known from discrete differential geometry. Orthogonal multi-nets, i.e. meshes where discrete orthogonality holds on any parameter rectangle, receive an in-depth analysis.

Reduced order modeling of modular parameter dependent structures based on proper orthogonal decomposition and mesh tying

AbstractA model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.

A single–region Finite Volume framework for modeling discontinuous magnetic field distributions

In this paper we present a novel method to model discontinuous distributions of magnetic fields. The method is based on a finite volume discretization of a divergence form of the magnetostatic equations. The theoretical framework is written in terms of the vector potential, therefore, the computational implementation is capable of predicting the magnetic field distribution in permeable, permanently magnetized, and current-carrying media. The use of a single-region meshing scheme simplifies the simulation set-up due to the fact that it avoids the use of interface boundary conditions. This renders it computationally more effective than the multi-region counterpart. In order to test the performance of the present approach we execute several numerical experiments and compare the results against a multi-region discontinuous method and a single-region boundary layerless method. The experiments demonstrate that provided the boundary layer complies with certain topological rules, the method gives accurate results of the magnitude and direction of the magnetic field, both near and far from the interfaces. We show that, for orthogonal meshes, the results obtained with a single-region approach using boundary layers are comparable to the results obtained with a multi-region framework that imposes the magnetic field gradient discontinuity as a boundary condition.

Grid ionization chamber based on stainless steel woven wire mesh

The grid electrode of the grid ionization chamber (GIC) is devoted to eliminating the dependence of the anode pulse amplitude on the initial position and orientation of the ionization. The traditional methods of grid production require cumbersome processes and advanced instruments. In this paper, a bonded stainless steel woven wire mesh (SSWWM) grid electrode manufacturing method is proposed. Compared with the traditional grid electrode, the SSWWM grid features the advantages of simple fabrication, low cost, and high mechanical strength. The energy resolutions of the 40-mesh, 60-mesh and 80-mesh SSWWM grids and orthogonal mesh grid realized by the traditional wire winding method were tested using an 241Am source (around 5.486 MeV). The results show that the optimum energy resolution of the SSWWM and orthogonal mesh grids is approximately 47 keV full width at half-maximum (FWHM). The optimal energy resolutions of the 40-mesh and 60-mesh SSWWM grids are comparable, but the initial operating voltages corresponding to the energy resolution plateau are different, mainly because of the effect of the different geometric parameters of the SSWWM grid on the electron transmittance. A simulation program was used to study the electron transmittance of the SSWWM grid. The simulation results are in agreement with the experimental results, indicating that the simulation program can be used as a reference for the selection of the geometric parameters of the SSWWM grid.

Development of unstructured mesh tally capability in cosRMC and application to shutdown dose rate analysis

Accurate estimation of shutdown dose rate (SDDR) is one of the key issues in the neutronics calculation of fusion reactors. cosRMC R2S was developed based on the Rigorous two-step (R2S) method using a mesh tally for shutdown dose rate calculation, which requires higher transport calculation accuracy in complex geometry. However, the traditional method in this approach was based on the orthogonal structured mesh. The orthogonal structured mesh does not necessarily coincide with geometry and material boundaries, which can introduce large errors in activation calculation and reduce the calculation accuracy of shutdown dose rate. To solve this problem, the unstructured mesh tally capability was developed in the Monte Carlo code cosRMC. On this basis, cosRMC R2S was further developed, using unstructured meshes to replace structured meshes. Due to the geometry particularity of the unstructured tetrahedral mesh, the rejection sampling strategy was adopted to sample the position of the decay gamma source. In order to verify the reliability and validity of the code, the verification analyses were carried out on the ITER port plug benchmark and the FNG ITER shutdown dose rate benchmark respectively. The results obtained with unstructured meshes were compared with those obtained with structured meshes, and the reliability of the code was preliminarily verified. The results showed that the maximum discrepancy between experimental results was 10.1% with unstructured meshes, which was closer to experimental results than that with structured meshes, indicating that the computational accuracy of the result was improved effectively. It is demonstrated that the code developed in this paper is capable of accurate shutdown dose field calculations and has the potential to be applied to complex shielding devices.

Numerical Study of Non-Premixed Combustion Characteristics on Supplementary Firing of HRSG

<p dir="ltr"><span>Computational fluid dynamics (CFD) is a simulation model to provide complex processes in the industry that has been widely used to investigate industrial-scale combustion phenomena. Supplementary firing is used to increase steam production. The non-premixed combustion is a type of supplementary firing. Supplementary firing has seven burners arranged vertically. Supplementary firing uses exhaust steam from a gas turbine to ignite the air. This research investigates the combustion characteristics of flame length and exhaust gas emission at burners. The viscous model was observed by using non-premixed modeling. While the absorption of radiation in the combustion residual gas was observed by using the weight sum-gray gases model (WSGGM). This study used the realizable </span><span>k-ε</span><span> model and tetrahedron meshing algorithm to approach the turbulent characteristics. The total nodes and the orthogonal mesh quality in the meshing steps are 1,334,359 and 0.86, respectively. The modeling results show that burners-1 and 7 have longer flame compared to other burners. The combustion exhaust gas has height contents of CO</span><span><span>2</span></span><span> and H</span><span><span>2</span></span><span>O. The velocity near the furnace wall is lower than the center of the furnace, but the pressure is higher. This phenomenon is dominantly influenced by the thermal boundary layer.</span></p><div><span><br /></span></div>

Novel discretization strategies for the 2D non-Newtonian resistance term in geophysical shallow flows

In the context of two-dimensional models for complex geophysical surface flows such as debris flows, muddy slurries, oil spills over land, hyperconcentrated floods, lava flows, etc, depth-averaged rheological models relate the shear stress state within the fluid column to the depth-averaged local flow features. Despite it is the most influencing term on the mobility of complex shallow flows, the numerical treatment of the resistance contribution to the flow momentum is still a challenging topic, especially when dealing with 2D large-scale applications. In this work, two novel strategies for the explicit upwind discretization of generalized non-Newtonian resistance terms in two-dimensional numerical models are proposed, called integral and differential approaches. These new strategies are applicable to generalized rheological formulations in any type of mesh topology. Results from benchmark tests running in orthogonal, triangle structured and triangle unstructured meshes demonstrate that both approaches represent an improvement for the explicit upwind integration of the 2D resistance force compared with previous procedures. It is shown that the alignment of the flow with the mesh main-axis, which has been previously attributed to faults of 2D FV numerical methods and insufficient mesh refinements, is directly related to the loss of the rotational invariance of the integrated resistance force. This is caused by the erroneous procedure for including the 2D resistance term into the local flux balance at the cell edges. Furthermore, a novel implicit centered method for the integration of the 2D resistance force has also been derived for the quadratic frictional non-linear resistance formulation. Despite the implicit procedure fails to converge to steady uniform flow states, the differential explicit upwind and the implicit centered methods show similar level of accuracy, robustness and computational efficiency for transient 2D frictional visco-plastic flows.

Coupled thermal-hydrodynamic-mechanical–chemical numerical simulation for gas production from hydrate-bearing sediments based on hybrid finite volume and finite element method

Gas production from hydrates induced by depressurization is a complex thermal-hydrodynamic-mechanical–chemical (THMC) coupled process. In this paper, we present a THMC coupled model to simulate the fluid flow in hydrate-bearing sediments (HBS) and the geomechanical behavior of HBS. The model is made of two subsystems, which are the fluid part of non-isothermal multi-phase flow with hydrate kinetic and solid part of geomechanical deformation. It accounts for two-way coupling effects between these two subsystems, i.e. the effect of pore pressure and hydrate dissociation on the solid mechanical behavior and the effect of stress on the hydraulic behavior. A new numerical method based on the hybrid control volume finite element method (CVFEM)-finite element method (FEM) is developed to solve the mathematical models. The local conservative CVFEM is used for the fluid part, and the standard FEM for the solid part. In the framework of hybrid CVFEM-FEM, the local conservation is reserved and the primary variables for the two subsystem are co-located. A multi-point flux approximation (MPFA) is adopted without orthogonal meshes so that it is very flexible to build complex geometrical models. The accuracy and reliability of the newly developed simulator QIMGHyd-THMC are tested by comparing with two experimental examples and a large-scale benchmark problem of other popular simulators.

A method for generating moving, orthogonal, area preserving polygonal meshes

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Because Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, a generalization of Voronoi polygon meshes was formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. The advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps.

二次元版UTCartと発見的探索法による形状融通性を活かした翼型最適設計フレームワーク

In this presentation, we introduce a robust and efficient airfoil design method that combines a two-dimensional version of UTCart based on the the Cartesian mesh and global optimization methods based on a heuristic. Since a wide variety of shapes can be generated during the optimization process, the Cartesian mesh method was expected better flow solver for global design optimizations than the body-fitted mesh methods because it uses a hierarchical orthogonal mesh method and the boundaries are handled by embedded boundaries. It was also expected to be easier method to adapt to zero-thickness geometries. In this study, we developed a framework for design optimization flamework using the Cartesian mesh based flow solver and the global optimization based on the metaheuristics such as evolutionary algorithms and Bayesian optimization.