Tetrahedral Grids Research Articles

NUMERICAL INVESTIGATION OF INFLUENCE OF HEAT EXCHANGER СHANNEL CURVATURE ON HEAT TRANSFER

In this paper the infl uence of the curvature of the portion of the heat exchanger on heat exchange with the use of software systems Salome Meca and Code Saturne is numerically studied the verifi cation of the numerical model by comparing with experimental data of other researchers without taking into account heat exchange is made. The solution is held for an average fl ow rate equal to 11 m/s. To investigate the infl uence on heat transfer of the curvature of the channel carried out the construction of the computational domain in the form of the heat exchanger of the same length with diff erent turn radius. For discretization of the computational domain were used tetrahedral grids containing approximately 850 thousand of elements with local refi nement near the surface of the channel. As a result of simulation values of the fl ow temperature at the outlet of the channels are obtained. It is revealed that the design of heat exchanger channel, of course, aff ects the heat transfer, as well as data on the applicability of diff erent turbulence models for this type of task are collected.

Optimized Reduction of Unsteady Radial Forces in a Singlechannel Pump for Wastewater Treatment

A single-channel pump for wastewater treatment was optimized to reduce unsteady radial force sources caused by impeller-volute interactions. The steady and unsteady Reynolds- averaged Navier-Stokes equations using the shear-stress transport turbulence model were discretized by finite volume approximations and solved on tetrahedral grids to analyze the flow in the single-channel pump. The sweep area of radial force during one revolution and the distance of the sweep-area center of mass from the origin were selected as the objective functions; the two design variables were related to the internal flow cross-sectional area of the volute. These objective functions were integrated into one objective function by applying the weighting factor for optimization. Latin hypercube sampling was employed to generate twelve design points within the design space. A response-surface approximation model was constructed as a surrogate model for the objectives, based on the objective function values at the generated design points. The optimized results showed considerable reduction in the unsteady radial force sources in the optimum design, relative to those of the reference design.

Graph-grammar greedy algorithm for reutilization of partial LU factorization over 3D tetrahedral grids

In this paper, we consider three-dimensional grids with tetrahedral finite elements, and the graph grammar model for mesh generation and adaptation as well as for the simultaneous construction of the element partition tree. The element partition tree defines the ordering to be used by the multi-frontal solver algorithm for efficient LU factorization. Additionally, we present the graph grammar productions for reutilization of the LU factorizations from the previous steps of the computations, when the mesh is h refined. We verify the ordering generated by our graph grammar through the element partition tree by comparing it against AMD, PORD and METIS orderings available through MUMPS interface. We also verify the graph grammar for reutilization by comparing the sequence of computation over 3D grids refined towards point, edge and face singularities, with and without the reutilization technique.

Viscous Resistance Prediction of a Tourist Submarine at Various Speeds

The viscous resistance of a tourist submarine suitable for working in the Red Sea area has been calculated at different speeds using Computational Fluid Dynamics (CFD). The finite volume RANSE code CFX has been used to study the resistance and the hydrodynamic characteristics of the flow around the tourist submarine at different speeds. The Omega Reynolds Stress turbulent model has been used in different numerical simulations. Half of the computational domain was used in this research work due the symmetry of the tourist submarine hull. The mesh generation software of the CFD code has been used for generating the required unstructured tetrahedral grid for the numerical simulations. The numerical results for the tourist submarine viscous resistance are comparable with the available results from other sources.

A staggered space–time discontinuous Galerkin method for the three-dimensional incompressible Navier–Stokes equations on unstructured tetrahedral meshes

In this paper we propose a novel arbitrary high order accurate semi-implicit space–time discontinuous Galerkin method for the solution of the three-dimensional incompressible Navier–Stokes equations on staggered unstructured curved tetrahedral meshes. As is typical for space–time DG schemes, the discrete solution is represented in terms of space–time basis functions. This allows to achieve very high order of accuracy also in time, which is not easy to obtain for the incompressible Navier–Stokes equations. Similarly to staggered finite difference schemes, in our approach the discrete pressure is defined on the primary tetrahedral grid, while the discrete velocity is defined on a face-based staggered dual grid. While staggered meshes are state of the art in classical finite difference schemes for the incompressible Navier–Stokes equations, their use in high order DG schemes is still quite rare. A very simple and efficient Picard iteration is used in order to derive a space–time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems. Formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five-point block system for the scalar pressure, which is conveniently solved with a matrix-free GMRES algorithm. From numerical experiments we find that the linear system seems to be reasonably well conditioned, since all simulations shown in this paper could be run without the use of any preconditioner, even up to very high polynomial degrees. For a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point, the resulting system is, in addition, symmetric and positive definite. This allows us to use even faster iterative solvers, like the conjugate gradient method.The flexibility and accuracy of high order space–time DG methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both, space and time. The proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3D test problems and by comparing the obtained numerical results with available exact analytical solutions, or with other numerical or experimental reference data.To the knowledge of the authors, this is the first time that a space–time discontinuous Galerkin finite element method is presented for the three-dimensional incompressible Navier–Stokes equations on staggered unstructured tetrahedral grids.

Numerical investigation of the aerodynamic and acoustical properties of a shrouded rotor

The problem of shrouded rotor rotation is numerically solved basing on the Navier–Stokes equations in a noninertial coordinate system. The configuration considered is a model helicopter tail rotor.The calculations are performed using edge-based reconstruction (EBR) schemes on unstructured tetrahedral grids with the variables determined at gridpoints. The numerical results on the aerodynamic forces and the acoustic radiation intensity and direction in the far field are presented and analyzed.

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders $$\wp = 3,4,5$$ . We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility.

A computational study of the flow around the KVLCC2 model hull at straight ahead conditions and at drift

The flow around the KVLCC2 model tanker hull at 0°, 12° and 30° drift is investigated using classical Reynolds Averaged Navier–Stokes (RANS) models from two different proprietary codes, hybrid RANS-LES models from one of these proprietary codes, and Large Eddy Simulation (LES) models from a third, semi-proprietary code. Understanding the three-dimensional (3D) flow around a ship hull and in the wake of the hull on straight course or during maneuvering is important for many design and operational aspects, as well as from an environmental perspective. Tetrahedral grids of 13 million and 74 million cells respectively are used for the RANS and hybrid RANS-LES; for the LES, grids of between 120 and 200 million tetrahedral cells are used. The objectives are to generally increase knowledge of the flow past a ship hull both at straight-ahead and at static-drift conditions, and to assess the predictive capabilities of RANS, hybrid RANS-LES and LES computational methods. Using these computational results, the focus is specifically on understanding the complex vortical topology and associated surface-flow characteristics, and how these change when the drift angle increases. The RANS and time-averaged hybrid RANS-LES and LES predictions are compared against each other and against experimental data to further validate the simulation models and to provide additional insight into the flow physics.

A study of high-order grid-characteristic methods on unstructured grids

In this paper, grid-characteristic methods for solving hyperbolic systems using approximation with high-order interpolation on unstructured tetrahedral and triangular grids are studied. Interpolation methods of order from 1 through 5 inclusive are considered. One-dimensional finite difference schemes for these methods are presented. The stability of these schemes is investigated. The grid-characteristic methods on unstructured triangular and tetrahedral grids are successfully used in seismic prospecting, specifically under the Arctic shelf and permafrost conditions. They are also used to solve problems of seismics, dynamic deformation and destruction, and to study anisotropic composite materials.

An octree-based adaptive semi-Lagrangian VOF approach for simulating the displacement of free surfaces

A numerical method based on an adaptive octree space discretization for the simulation of displacement of free surfaces is proposed and applied to 3D free surface flow problems. A VOF approach is combined with a mass-conserving semi-Lagrangian time-stepping scheme. An interface prediction algorithm is used to refine the octree at the predicted location of the interface in order to ensure detail preservation. Subsequently, the fluid is advected and a coarsening algorithm adapts the mesh to avoid excess refinement in non-interfacial regions. SLIC and decompression algorithms are used for post-processing to limit numerical diffusion and correct numerical compression of the VOF function. The scheme is unconditionally stable with respect to the CFL number and does not require solving of a linear system. The octree scheme allows anisotropy and refinement of interfacial cells to an arbitrary level. It does not require a 2:1 cell size ratio condition between neighbouring cells. Numerical validation is done on benchmark test cases and results are compared with the structured analog. The scheme is coupled with a Stokes solver on a tetrahedral grid for solving of time-dependent Navier–Stokes equations and numerical results are compared with experimental water wave profile measurements.

Experimental and numerical study of a generic conventional submarine at 10° yaw

This investigation discusses the flow physics of the fully appended DSTO generic submarine model at both straight ahead conditions and during a 10° side-slip. Reynolds Averaged Navier Stokes (RANS) and Large Eddy Simulation (LES) computations have been performed and are compared with model-scale experiments. The experiments have been carried out in the DSTO Low-Speed Wind Tunnel, with data collected using pressure probes, Particle Image Velocimetry (PIV) and flow visualization using wool-tuft streamers. Computational studies using LES on unstructured meshes of up to 340 million cells provide detailed surface and off-body flow field data, complementing the experimental investigations and providing the opportunity for reciprocal validation of experiments and computations. Surface-flow patterns for the DSTO generic submarine model at 10° yaw and a freestream Reynolds (Re) number, based on wind tunnel speed and hull length, of Re=4.5×106 were obtained. The cross-stream velocity for the DSTO generic submarine model at 10° yaw and Re=2.7×106 was measured using PIV. The in-plane velocity was measured at three streamwise locations corresponding to 65%, 84% and 98% of the submarine model length. LES computations were performed using an incompressible LES flow solver developed using OpenFOAM and unstructured tetrahedral grids generated utilizing a patch-based approach to facilitate high near-wall resolutions and arbitrary refinement for appendage wakes.

Numerical Modeling of Non-destructive Testing of Composites

Low-velocity strikes are considered as one of the most dangerous load types for composites, especially in aviation. They do not lead to an immediate destruction of a whole detail, but inner damage, provoking a delamination between layers or between fiber and matrix, lowers the material strength and may cause a destruction during the flight. This inner damage can only be noticed via complex study, which increases an exploitation cost. Numerical modeling can help to interpret the results obtained from common portable devices, which are currently used for metals. The modification of known methodology can be reliably used for composites. In this research, a hybrid grid-characteristic method of 1-2 order on irregular tetrahedral grid is used. A carbon fiber polymer matrix of unidirectional composite is modeled as a homogeneous orthotropic media with a single distinguished direction along the fiber. As a result, the one-dimensional graphics, which correspond to A-scans in real devices, were obtained. The detailed analysis of received data confirms a rationality of proposed methodoly.

COMPUTATIONAL MODEL OF PLATELET FLOW IN CAROTID ARTERY BIFURCATION

Atherosclerotic plaque tends to occur and develop in carotid artery sinus, where stenoses and other lesions can cause cerebral disturbances. The hemodynamics and the platelet profiles in the carotid artery are simultaneously simulated in the present study to reveal the mechanism of the atherosclerotic plaque formation. Firstly, an unsteady PISO solver on unstructured tetrahedral grids is developed to simulate the hemodynamics of carotid artery bifurcation. And small platelets are treated as spherical solid particle described by Newtonian motion equation in the simulation, including inertial force, drag force, shear lift force, virtual mass force and pressure gradient force. Secondly, the visualization experiment for the platelet flow in the straight micro-channel is setup to validate the numerical model. Using the present method, the platelet flow in a carotid artery bifurcation is analyzed. The results show that the outer vascular wall near the bifurcation is more vulnerable in carotid artery sinus, which is mainly due to the lower wall shear stress (WSS) and platelets backflow in the region.

An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids

A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.

Multi‐method virtual electromagnetic experiments for developing suitable monitoring designs: A fictitious CO2 sequestration scenario in Northern Germany

ABSTRACTWe present a numerical study for 3D time‐lapse electromagnetic monitoring of a fictitious CO2 sequestration using the geometry of a real geological site and a suite of suitable electromagnetic methods with different source/receiver configurations and different sensitivity patterns. All available geological information is processed and directly implemented into the computational domain, which is discretized by unstructured tetrahedral grids. We thus demonstrate the performance capability of our numerical simulation techniques.The scenario considers a CO2 injection in approximately 1100 m depth. The expected changes in conductivity were inferred from preceding laboratory measurements. A resistive anomaly is caused within the conductive brines of the undisturbed reservoir horizon. The resistive nature of the anomaly is enhanced by the CO2 dissolution regime, which prevails in the high‐salinity environment. Due to the physicochemical properties of CO2, the affected portion of the subsurface is laterally widespread but very thin.We combine controlled‐source electromagnetics, borehole transient electromagnetics, and the direct‐current resistivity method to perform a virtual experiment with the aim of scrutinizing a set of source/receiver configurations with respect to coverage, resolution, and detectability of the anomalous CO2 plume prior to the field survey. Our simulation studies are carried out using the 3D codes developed in our working group. They are all based on linear and higher order Lagrange and Nédélec finite‐element formulations on unstructured grids, providing the necessary flexibility with respect to the complex real‐world geometry. We provide different strategies for addressing the accuracy of numerical simulations in the case of arbitrary structures.The presented computations demonstrate the expected great advantage of positioning transmitters or receivers close to the target. For direct‐current geoelectrics, 50% change in electric potential may be detected even at the Earth's surface. Monitoring with inductive methods is also promising. For a well‐positioned surface transmitter, more than 10% difference in the vertical electric field is predicted for a receiver located 200 m above the target. Our borehole transient electromagnetics results demonstrate that traditional transient electromagnetics with a vertical magnetic dipole source is not well suited for monitoring a thin horizontal resistive target. This is due to the mainly horizontal current system, which is induced by a vertical magnetic dipole.

CFD Analysis for Flow of Liquids in Coils

The effects of liquid flow rate, coil diameter, pseudo plasticity of the liquids on the frictional pressure drop for the flow through helical coils have been reported through experimental investigation. Numerical modeling is carried using Fluent 6.3 software to find its applicability in the flow system. The Computational Fluid Dynamics (CFD) simulations are carried out using laminar non-Newtonian pseudo plastic power law model for laminar flow and k-e model for turbulent flow for water. Water and dilute solution of Sodium Carboxy Methyl Cellulose (SCMC) as a non-Newtonian pseudo plastic fluid used for the study. Both hexahedral and tetrahedral grids are used for this simulation. The CFD results show the very good agreement with the experimental values. The comparison of the non-Newtonian liquid flow and water are also reported.

Unstructured hexahedral mesh generation of complex vascular trees using a multi-block grid-based approach

The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid–structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed.

운전조건에 따른 펌프 터빈 시스템의 안정성 연구

Pump-turbine system is widely used by the hydropower industry for stabilizing the electrical grid in the vast growing economy of most developed countries. This study only investigates the Fluid-structure Interaction (FSI) analysis of the pump-turbine system at various operating conditions. The FSI analysis can show how reliable each component of the system is by providing the engineer with a better understanding of high stress and deformation points, which could reduce the lifespan of the pump-turbine. Pump-turbine components are categorized in two parts, pressurized static parts and movable stressed parts. The fixed parts include the spiral casing, top and bottom cover, stay vane and draft tube. The movable parts include guide vanes and impeller blades. Fine hexahedral numerical grids were used for CFD calculation and fine tetrahedral grids were used for structural analysis with imported load solution mapping greater than 90 %. The maximum equivalent stress are much smaller than the material yield stress, and the maximum equivalent stress showed an increasing tendency with the varying of operating conditions from partial to excessive at both modes. In addition, the total deformation of all the operating conditions showed a small magnitude, which have quite small influence on the structural stability. It can be conjectured that this system can be safely implemented.

Workflows for generating tetrahedral meshes for finite element simulations on complex geological structures

Subsurface processing numerical simulations require accurate discretization of the modeling domain such that the geological units are represented correctly. Unstructured tetrahedral grids are particularly flexible in adapting to the shape of geo-bodies and are used in many finite element codes. In order to generate a tetrahedral mesh on a 3D geological model, the tetrahedrons have to belong completely to one geological unit and have to describe geological boundaries by connected facets of tetrahedrons. This is especially complicated at the contact points between several units and for irregular sharp-shaped bodies, especially in case of faulted zones. This study develops, tests and validates three workflows to generate a good tetrahedral mesh from a geological basis model. The tessellation of the model needs (i) to be of good quality to guarantee a stable calculation, (ii) to include certain nodes to apply boundary conditions for the numerical solution, and (iii) support local mesh refinement. As a test case we use the simulation of a transient electromagnetic measurement above a salt diapir. We can show that the suggested workflows lead to a tessellation of the structure on which the simulation can be run robustly. All workflows show advantages and disadvantages with respect to the workload, the control the user has over the resulting mesh and the skills in software handling that are required.

Electromagnetic methods for exploration and monitoring of enhanced geothermal systems – A virtual experiment

We present the concept of virtual electromagnetic experiments, which aims at setting up and optimizing the monitoring design for a potential stimulated geothermal energy reservoir. The concept builds on existing 3D geologic models, which are processed, meshed, assigned realistic electrical parameters and used for our finite element simulations on unstructured tetrahedral grids. The available simulation codes are able to cope with the high degree of geometric complexity in close-to-reality scenarios.To demonstrate the procedure and the capabilities of our method, we show the model preparation and the simulation results for the transient electromagnetic method in the context of a prospective enhanced deep geothermal energy site at the fault ‘Roter Kamm’ near Schneeberg in Saxony/eastern Germany. We show the changes in the measuring signal caused by the stimulated fracture system in more than 5000m depth for a range of electrical resistivity contrasts, which represent different porosity, pore connectivity or fluid resistivity variations. When a borehole receiver is advantageously placed at depth, percentage changes in the measuring signal of 25% can be expected. Our study demonstrates, that the optimal positioning of source and receiver is crucial for a successful monitoring and may only be achieved with advanced simulation techniques.