Finite Volume Formulation Research Articles

Numerical Investigation on Roll-Wave Properties: Wave–Wave Interactions, Generality, and Spectrum

Modeling natural roll waves in unstable open channel flows where Froude number F>2 has not been well understood. In this investigation, some evolution properties of natural roll waves are numerically disclosed, with the intention to advance the development of modeling unstable open channel flows. To simulate natural roll waves, the diffusive Saint-Venant equations are solved using a high-resolution scheme based on the finite-volume formulation. The numerical solutions of detailed wave–wave interaction processes, including wave overtaking, absorption, and spawning, are displayed. Wave overtaking and absorption result in the coalescence of multiple waves; wave spawning results in the birth of new waves. The spatial evolution of roll waves always undergoes initial, transition, and final phases. The three phases constitute a generality for roll-wave evolutions. Finally, the spectral analysis along channel reveals that both the wave period and nonperiodicity increase from upstream to downstream channel locations.

Parallel adaptive mesh refinement for large-eddy simulations of turbulent flows

In this paper a parallel adaptive mesh refinement (AMR) strategy for large eddy simulations (LES) of turbulent flows is presented. The underlying discretization of the Navier–Stokes equations is based on a finite-volume symmetry-preserving formulation, with the aim of preserving the symmetry properties of the continuous differential operators and ensure both, stability and conservation of kinetic-energy balance. The conservation properties are tested for the meshes resulting from the AMR process, which typically contain transitions between zones with different level of refinement. Our AMR scheme applies a cell-based refinement technique, with a physics-based refinement criteria based on the variational multi-scale (VMS) decomposition theory. The overall AMR process, from the selection of the cells to be refined/coarsened till the pre-processing of the resulting mesh, has been implemented in a parallel code, for which the parallel performance has been attested on an AMD Opteron based supercomputer. Finally, the robustness and accuracy of our methodology is shown on the numerical simulation of the turbulent flow around a square cylinder at Re=22,000 and the turbulent flow around two side-by-side square cylinders at Re=21,000.

Direct numerical simulation of hypersonic transition induced by an isolated cylindrical roughness element

Hypersonic boundary layer transition induced by an isolated cylindrical roughness element is investigated using direct numerical simulation method based on a finite volume formulation. To simulate the transition procedure by resolving the generation and evolvement of small-scale coherent structures, and capture the shock wave at the same time, high-order minimum dispersion and controllable dissipation scheme is validated and then applied. The results are compared with the available measurements in the quiet wind tunnel, such as the dominated frequency and root mean square of pressure. The computational dominated frequency of 19.23 kHz is very close to the experimental one, 21 kHz. Also, the disturbances of the roughness are mostly generated by the “jet” just before the roughness, and then they travel and develop downstream with the shear layer and vortex shedding. The transition is mainly dominated by the instabilities of both the horseshoe vortex and the shear layer.

Mixing Performance of a Suspended Stirrer for Homogenizing Biodegradable Food Waste from Eatery Centers

Numerical simulation of a suspended stirrer within a homogenizing system is performed towards determining the mixing performance of a homogenizer. A two-dimensional finite volume formulation is developed for the cylindrical system that is used for the storage and stirring of biodegradable food waste from eatery centers. The numerical solver incorporates an analysis of the property distribution for viscous food waste in a storage tank, while coupling the impact of mixing on the slurry fluid. Partial differential equations, which describe the conservation of mass, momentum and energy, are applied. The simulation covers the mixing and heating cycles of the slurry. Using carrot-orange soup as the operating fluid (and its thermofluid properties) and assuming constant density and temperature-dependent viscosity, the velocity and temperature field distribution under the influence of the mixing source term are analyzed. A parametric assessment of the velocity and temperature fields is performed, and the results are expected to play a significant role in designing a homogenizer for biodegradable food waste.

Discontinuous Galerkin flood model formulation: Luxury or necessity?

AbstractThe finite volume Godunov‐type flood model formulation is the most comprehensive amongst those currently employed for flood risk modeling. The local Discontinuous Galerkin method constitutes a more complex, rigorous, and extended local Godunov‐type formulation. However, the practical merit associated with such an increase in the level of complexity of the formulation is yet to be decided. This work makes the case for a second‐order Runge‐Kutta Discontinuous Galerkin (RKDG2) formulation and contrasts it with the equivalently accurate finite volume (MUSCL) formulation, both of which solve the Shallow Water Equations (SWE) in two space dimensions. The numerical complexity of both formulations are presented and their capabilities are explored for wide‐ranging diagnostic and real‐scale tests, incorporating all challenging features relevant to flood inundation modeling. Our findings reveal that the extra complexity associated with the RKDG2 model pays off by providing higher‐quality solution behavior on very coarse meshes and improved velocity predictions. The practical implication of this is that improved accuracy for flood modeling simulations will result when terrain data are limited or of a low resolution.

A Stable Lattice Boltzmann Method for Steady Backward-Facing Step Flow

The severe problem of the most lattice Boltzmann methods (LBM) is the instability within the solution. This paper presents the implementation and applicability of a stable finite volume (FV) formulation of LBM for simulating steady separating and reattaching flow pasts backward-facing step geometry. For simulation purpose, a cell-centered scheme is implemented to discretize the convection operator and new weighting factors are used as flux correctors. Compared with previous FV formulations, a remarkable stability improvement is achieved and the secondary recirculation region is clearly captured for Reynolds numbers higher than 400. The simulation results show good agreement with benchmark data, which demonstrate the trustworthiness of the scheme.

Large Eddy Simulation/Conditional Moment Closure modeling of swirl-stabilized non-premixed flames with local extinction

The Large Eddy Simulation (LES)/three-dimensional Conditional Moment Closure (3D-CMC) model with detailed chemistry and finite-volume formulation is employed to simulate a swirl-stabilized non-premixed flame with local extinction. The results demonstrate generally good agreement with the measurements concerning velocity, flame shape, and statistics of flame lift-off, but the penetration of fuel jet into the recirculation zone is under-predicted possibly due to the over-predicted swirl velocities in the chamber. Localized extinctions are seen in the LES, in agreement with experiment. The local extinction event is shown by very low heat release rate and hydroxyl mass fraction and reduced temperature, and is accompanied by relatively high scalar dissipation. In mixture fraction space, CMC cells with strong turbulence-chemistry interaction and local extinction show relatively large fluctuations between fully burning and intermediate distributions. The probability density functions of conditional reactedness, which shows how far the conditionally-filtered scalars are from reference fully burning profiles, indicate that for CMC cells with local extinction, some reactive scalars demonstrate pronounced bimodality while for those cells with strong reactivity the PDFs are very narrow.

Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

We extend a hybrid finite-volume-element (FVE) method to treat the laminar reacting flow in cylindrical coordinates considering the collocation of all chosen primitive variables. To approximate the advection fluxes at the cell faces, we use the upwind-biased physical influence scheme PIS and derive a few new extended expressions applicable in the cylindrical frame. These expressions are derived for both the Navier-Stokes and reactive flow governing equations, of which the latter expressions are considered novel in the finite-volume formulation. To validate our derived expressions, the current results are compared with the experimental data and other available numerical solutions. The results show that the accuracy of the current expressions is better than those derived by the past similar numerical investigators.

Numerical modeling of coanda effect in a novel propulsive system

Coanda effect (adhesion of jet flow over curved surface) is fundamental characteristics of jet flow. In the present paper, we carried out numerical simulations to investigate Coanda flow over a curved surface and its application in a newly proposed Propulsive system “A.C.H.E.O.N” (Aerial Coanda High Efficiency Orienting jet Nozzle) which supports thrust vectoring. The ACHEON system is presently being proposed for propelling a new V/STOL airplane in European Union. This system is based on cumulative effects of three physical effects such as (1) High speed jet mixing speeds (2) Coanda effect control by electrostatic fields (3) Coanda effect adhesion of an high speed jet to a convex surface. The performance of this nozzle can be enhanced by increasing the jet deflection angle of synthetic jet over the Coanda surface. This newly proposed nozzle has wide range of applications. It can be used in industrial sector such as plasma spray gun and for direct injection in combustion chamber to enhance the efficiency of the combustion chamber. Also, we studied the effect of Dielectric barrier discharge (DBD) plasma actuators on A.C.H.E.O.N system. Dielectric barrier discharge (DBD) plasma actuators are active control devices for controlling boundary layer and to delay the flow separation over any convex surfaces. Computations were performed under subsonic condition. Two dimensional CFD calculations were carried out using Reynolds averaged Navier stokes equations (RANS). A numerical method based on finite volume formulation (FVM) was used. SST k-ω model was considered to model turbulent flow inside nozzle. DBD model was used to model the plasma. Moreover, a body force treatment was devised to model the effect of plasma and its coupling with the fluid. This preliminary result shows that, the presence of plasma near Coanda surface accelerates the flow and delays the separation and enhances the efficiency of the nozzle.

Case Study for Tsunami Design of Coastal Infrastructure: Spencer Creek Bridge, Oregon

The absence of tsunami load provisions in coastal infrastructure design has led to unchecked resistance capacity of bridges against one of the most eminent natural hazards on the U.S. west coast. The Spencer Creek Bridge, which was completely rebuilt on the Oregon coast in 2009, is a unique example to demonstrate development and implementation of site-specific tsunami loads during the design stage. Two tsunami models, the Cornell Multigrid Coupled Tsunami model (COMCOT) and the Finite-Volume Wave model (FVWAVE), defined the flow fields from three rupture configurations postulated for a Cascadia earthquake, which has a moment magnitude of 9.0 consistent with the seismic design of the bridge structure. Although both models produce comparable surface elevations at the site, the finite-volume formulation of FVWAVE provides higher flow speed because of its capability to conserve momentum and mass even with formation of tsunami bores. The FVWAVE results define the input to the computational fluid dynamic module of LS-DYNA. The computed time history of the horizontal and vertical loads on the bridge deck, in turn, provide the input to a finite-element model of the bridge structure for capacity comparisons and damage analysis. It is concluded that the earthquake design specifications used for this particular bridge provide more than sufficient strength to resist the maximum tsunami horizontal force. The margin of safety is much smaller for the uplift force, but still remains in an acceptable range.

Numerical modeling of three‐phase dissolution of underground cavities using a diffuse interface model

SUMMARYNatural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and infrastructures because the underground dissolution may lead to subsidence or collapse (sinkholes). The knowledge of the cavity evolution in space and time is thus crucial in many cases. In this paper, we describe the use of a local nonequilibrium diffuse interface model for solving dissolution problems involving multimoving interfaces within three phases, that is, solid–liquid–gas as found in superficial aquifers and karsts. This paper generalizes developments achieved in the fluid–solid case, that is, the saturated case [1]. On one hand, a local nonequilibrium dissolution porous medium theory allows to describe the solid–liquid interface as a diffuse layer characterized by the evolution of a phase indicator (e.g., porosity). On the other hand, the liquid–gas interface evolution is computed using a classical porous medium two‐phase flow model involving a phase saturation, that is, generalized Darcy's laws. Such a diffuse interface model formulation is suitable for the implementation of a finite element or finite volume numerical model on a fixed grid without an explicit treatment of the interface movement. A numerical model has been implemented using a finite volume formulation with adaptive meshing (e.g., adaptive mesh refinement), which improves significantly the computational efficiency and accuracy because fine gridding may be attached to the dissolution front. Finally, some examples of three‐phase dissolution problems including density effects are also provided to illustrate the interest of the proposed theoretical and numerical framework. Copyright © 2014 John Wiley & Sons, Ltd.

Comparison of mapping operators for unstructured meshes

In this paper, two PDE-based mapping operators for the generation of unstructured meshes are compared. While the Winslow operator allows the construction of valid meshes for most configurations, the functional-based operators based on area, length, orthogonality and their combinations provide a finer control on the resulting meshes. Two distinct discretization methods of the operators are also compared. An original approach using a finite difference scheme on unstructured meshes is implemented and compared to a finite volume formulation. While more complex to implement and control, mainly because of the cross-derivative terms which must be carefully discretized, the finite volume method yields a more robust and stable formulation that allows dealing with sharp curvature variations of the boundaries. Finally, a criterion for the mesh smoothness which has a global definition is presented in order to compare the smoothness of the resulting mesh obtained by different operators.

Finite volume form factors in the presence of integrable defects

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee–Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee–Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found.

Numerical prediction of NOx emissions in a full-scale furnace

The present paper deals with a numerical predic-tion of the thermal level and emission rate of nitrogen ox-ides within an industrial furnace. Favre averaged forms of the governing equations accounting for radiative heat losses are solved via a finite volume formulation. Turbu-lent fluxes are closed using a model for which a limited Pope correction is performed. The relaxation model of Magnussen is used to describe the two-step chemis-try/turbulence interaction for the non-premixed flame. The effect of the swirl number has been also investigated. The predicted static temperature as well as NO emission rate at the furnace exit show good agreement with in-situ meas-urements. In addition, the numerical computation shows that the depression is about 28% for the rate of NO, which it is obtained by adopting a moderate swirl at the primary-air entrance. DOI: http://dx.doi.org/10.5755/j01.mech.20.1.3904

Finite volume formulation of thermal lattice Boltzmann method

Purpose – The main purpose of this paper is to develop a novel thermal lattice Boltzmann method (LBM) based on finite volume (FV) formulation. Validation of the suggested formulation is performed by simulating plane Poiseuille, backward-facing step and flow over circular cylinder. Design/methodology/approach – For this purpose, a cell-centered scheme is used to discretize the convection operator and the double distribution function model is applied to describe the temperature field. To enhance stability, weighting factors are defined as flux correctors on a D2Q9 lattice. Findings – The introduction of pressure-temperature-dependent flux-control coefficients in the streaming operator, in conjunction with suitable boundary conditions, is shown to result in enhanced numerical stability of the scheme. In all cases, excellent agreement with the existing literature is found and shows that the presented method is a promising scheme in simulating thermo-hydrodynamic phenomena. Originality/value – A stable and accurate FV formulation of the thermal DDF-LBM is presented.

Generalized shell heat transfer element for modeling the thermal response of non-uniformly heated structures

A generalized shell heat transfer element is formulated in isoparametric coordinates to simulate the 3D thermal of non-uniformly heated shells with curved geometries. The element uses a combination of finite element and control volume methods to discretize the domain of the element into 2D layers that are coupled by a finite difference calculation. As demonstrated in previous work, the finite element-control volume formulation allows the thermal response to be evaluated with minimal computational expense and the temperature field is calculated in a manner that is compatible with distributed plasticity elements for structural analysis. Although the formulation uses a mixture of finite element and finite difference equations, the element equations are in a form that can readily be implemented in a commercial finite element code. The nine-node quadratic element considered here is implemented in Abaqus as a user-defined element. One-, two-, and three-dimensional verification cases are presented to demonstrate the capabilities of the element. Comparisons between the shell heat transfer element and traditional continuum heat transfer elements illustrate that the shell element converges rapidly and results in significant savings in computational expense.

POROUS SUBSTRATE EFFECTS ON THERMAL FLOWS THROUGH A REV-SCALE FINITE VOLUME LATTICE BOLTZMANN MODEL

In this paper, fluid flows with enhanced heat transfer in porous channels are investigated through a stable finite volume (FV) formulation of the thermal lattice Boltzmann method (LBM). Temperature field is tracked through a double distribution function (DDF) model, while the porous media is modeled using Brinkman–Forchheimer assumptions. The method is tested against flows in channels partially filled with porous media and parametric studies are conducted to evaluate the effects of various parameters, highlighting their influence on the thermo-hydrodynamic behavior.

An accurate finite-volume formulation of a Residual-Based Compact scheme for unsteady compressible flows

The paper discusses the design principles of a Finite-Volume Residual-Based Compact (RBC) scheme for the spatial discretization of the unsteady compressible governing equations of gas dynamics on general structured meshes. Our goal is to develop an accurate and robust approximation methodology, well suited for complex problems of industrial interest. The scheme makes use of weighted approximations that allow to ensure high accuracy while taking benefit from the structured nature of the grid. The accuracy and Cauchy stability properties of the proposed spatial approximation are discussed in detail. Numerical applications to unsteady compressible flows of increasing complexity demonstrate the advantages of the proposed formulation with respect to straightforward extensions of RBC schemes to curvilinear meshes.

An Optimization of Wind Turbine Airfoil Possessing Good Stall Characteristics by Genetic Algorithm Utilizing CFD and Neural Network

In this research, an optimization of a wind turbine airfoil is performed by Genetic Algorithm (GA) as optimization method, coupled with CFD (Computational Fluid Dynamics) and Artificial Neural Network (ANN). A pressure-based implicit procedure is applied to solve the Navier-Stokes equations on a nonorthogonal mesh with collocated finite volume formulation to calculate the aerodynamic coefficients. The boundedness criteria for the numerical procedure are determined by Normalized Variable Diagram (NVD) scheme and the k-e eddy-viscosity turbulence model is utilized. ANN has been used as surrogate model to reduce computational cost and time. Single objective and multi objective optimization of wind turbine airfoil have been performed and the results of optimization are presented. To decrease the number of design variables and producing a smooth shaped airfoil, modified Hicks-Henne functions are applied. In this process, the Eppler E387 airfoil has been applied as the base airfoil. The angle of attack varies from 0 to 20 degrees and Reynolds number of the flow is 460000. The presented technique decreases the time of optimization by 99.5%. Moreover, the results manifest the good agreement of trained ANN outputs and CFD simulation. In addition, the Multi-objective optimization can attain the better solutions than single objective to design a wind turbine airfoil with good stall characteristics.

Non linear schemes for the heat equation in 1D

Inspired by the growing use of non linear discretization techniques for the linear diffusion equation in industrial codes, we construct and analyze various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier’s trick [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 691–695]. They preserve the maximum principle and admit a finite volume formulation. We provide a original functional setting for the analysis of convergence of such methods. In particular we show that the fourth discrete derivative is bounded in quadratic norm. Finally we construct, analyze and test a new explicit non linear maximum preserving scheme with third order convergence: it is optimal on numerical tests.