Implicit Flow Solver Research Articles

Melting and energy storage characteristics of macro-encapsulated PCM-metal foam system

In this study a novel encapsulated phase change material (PCM)-metal foam hybrid system is proposed for energy storage applications. The idea is to improve the melting rate of PCM in encapsulated PCM systems with the introduction of metal foam structures inside the capsules. The main objective of the work is to develop a numerical model which can simulate the melting of PCM in this hybrid system due to the flow of heat transfer fluid (HTF) around the capsule with the resolution of the metal foam geometry at the pore-scale level. The developed model couples geometry creation, phase change and fluid flow models. The foam geometry is created using overlapping circular pores with random location, radii, and overlap. The phase change model is developed by modifying the enthalpy method to incorporate the presence of four phases – HTF, metal, solid PCM, and liquid PCM. This is coupled with an implicit flow solver within a finite volume framework. An in-depth analysis of a base case is conducted by fixing different geometrical parameters such as capsule size, porosity, pore size distribution and shell thickness. The results of the base case are then compared in subsequent parametric studies, by varying one geometrical parameter at a time. The parametric studies reveal that the structure of the metal foam plays an important role in determining the melting pattern and the energy storage characteristics because of its net-like large inner surface area. It is found that the melting time is reduced for lower capsule size, lower porosity, and higher shell thickness. The average pore size and range are crucial in determining the rate of melting.

Forced convection heat transfer around a circular cylinder in laminar flow: An insight from Lagrangian coherent structures

The Lagrangian coherent structure (LCS) method is introduced to the convection heat transfer problem, and the forced convection heat transfer around a circular cylinder in laminar flow regime is analyzed from the Lagrangian viewpoint. First, the mechanics model of forced convection heat transfer around a circular cylinder is introduced along with the mathematical formulations. Subsequently, an implicit flow solver based on the characteristic-based split finite element method and the dual-stepping method is proposed to solve the flow and heat transfer equations, and the computation of LCS employing the finite-time Lyapunov exponent is discussed in detail. The accuracy and stability of the flow solver are examined carefully utilizing the data reported in the literature, and the grid-independence test is conducted. Finally, the mass and energy transport features around the circular cylinder at Pr (Prandtl number) = 0.7 and Re (Reynolds number) = 20–180 are investigated by relating the instantaneous thermal and vorticity patterns, lift coefficient, drag coefficient, and Nusselt number to the LCSs in the flow field. The results obtained may improve the existing understanding of forced convection heat transfer around a circular cylinder and pave the road for the application of LCSs in convection heat transfer problems.

Quality-Preserving Linear Elasticity Mesh Movement Algorithm for Multi-Element Unstructured Meshes

A linear elasticity mesh movement algorithm is presented for unstructured computational aerodynamic meshes consisting of multiple element types. An adaptive method for incrementally stiffening mesh elements is proposed based on mesh element quality. Mesh element quality is defined as the condition number of the coordinate mapping from the element at the previous increment to the current increment. This definition is adopted because it is applicable to elements of arbitrary shape or size. Augmenting the linear elasticity algorithm with this quality metric is demonstrated to improve the success rate of an implicit flow solver on the moved mesh for two practical three-dimensional test cases of industrial relevance and scale.

Scalable Implicit Flow Solver for Realistic Wing Simulations with Flow Control

Massively parallel computation provides an enormous capacity to perform simulations on a timescale that can change the paradigm of how scientists, engineers, and other practitioners use simulations to address discovery and design. This work considers an active flow control application on a realistic and complex wing design that could be leveraged by a scalable, fully implicit, unstructured flow solver and access to high-performance computing resources. The article describes the active flow control application; then summarizes the main features in the implementation of a massively parallel turbulent flow solver, PHASTA; and finally demonstrates the methods strong scalability at extreme scale. Scaling studies performed with unstructured meshes of 11 and 92 billion elements on the Argonne Leadership Computing Facility's Blue Gene/Q Mira machine with up to 786,432 cores and 3,145,728 MPI processes.

Compact Implementation Strategy for a Harmonic Balance Method Within Implicit Flow Solvers

A two-step approximate factorization technique for implementing a computationally stable nonlinear unsteady frequency-domain harmonic balance solution method within existing implicit computational fluid dynamic flow solver codes is presented. The approach uses an explicit discretization of the harmonic balance source term, and no new implicit code development is required. Both of these features enable the harmonic balance method to be implemented within existing implicit flow solver codes with minimal modification necessary to the underlying flow solver code. The resulting harmonic balance solver can then be used for modeling nonlinear periodic unsteady flows. The methodology is applied to the NASA OVERFLOW flow solver code, and results are presented for transonic viscous flow past an unsteady pitching airfoil section.

Performance of numerical integrators on tangential motion of DEM within implicit flow solvers

Abstract This study examines the behaviour of continuous time integration schemes over discontinuities in the tangential forces typical in an oblique impact within a Discrete Element Simulation (DEM). High order schemes are associated low error and efficient computation, however, for DEM this is not always the case. The simulations consist of a particle impacting tangentially with a plane and sliding along it, this makes the numerical integration independent of errors from the normal force integration. Three possible force regimes that occur in the tangential motion of an oblique impact are explored; frictional, elastic and elastic-to-frictional. Tests are conducted to explore the effects of the location of the discontinuity within the time step and to examine scheme order through varying time step resolution. For certain scenarios the tangential motion contains elastic and then frictional forces, this presents a second discontinuity between these force regimes. The effects of this second discontinuity are also presented. It was found that all schemes were limited to 1st order by at least one of the conditions tested. The Symplectic Euler is recommended as it is found to be of generally higher accuracy than other 1st order schemes in these tests, as was found in a similar study regarding normal impacts.

Computational simulation of model and full scale Class 8 trucks with drag reduction devices

Numerical solutions of the unsteady Reynolds-averaged Navier–Stokes equations using a parallel implicit flow solver are given to investigate unsteady aerodynamic flows affecting the fuel economy of Class 8 trucks. Both compressible and incompressible forms of the equations are solved using a finite-volume discretization for unstructured grids and using Riemann-based interfacial fluxes and characteristic-variable numerical boundary conditions. A preconditioned primitive-variable formulation is used for compressible solutions, and the incompressible solutions employ artificial compressibility. Detached eddy simulation (DES) versions of the one-equation Menter SAS and the two-equation k − ϵ/ k − ω hybrid turbulence models are used. A fully nonlinear implicit backward-time approximation is solved using a parallel Newton-iterative algorithm with numerically computed flux Jacobians. Unsteady three-dimensional aerodynamic simulations with grids of 18–20 million points and 50,000 time steps are given for the Generic Conventional Model (GCM), a 1:8 scale tractor–trailer model that was tested in the NASA Ames 7 × 10 tunnel. Computed pressure coefficients and drag force are in good agreement with measurements for a zero-incidence case. Similar computations for a case with 10° yaw gave reasonable agreement for drag force, while the pressure distributions suggested the need for tighter grid resolution or possibly improved turbulence models. Unsteady incompressible flow simulations were performed for a modified full scale version of the GCM geometry to evaluate drag reduction devices. All of these simulations were performed with a moving ground plane and rotating rear wheels. A simulation with trailer base flaps is compared with drag reduction data from wind tunnels and track and road tests. A front spoiler and three mud-flap designs with modest drag reduction potential are also evaluated.

On the optimal numerical time integration for Lagrangian DEM within implicit flow solvers

We investigate a selection of nominally first, second and fourth order time integration schemes with application to particle collision simulation using the discrete element method (DEM). The motivation being the typical requirement to efficiently two-way couple a continuum flow obtained with a finite volume solver employing an iterative implicit solution method to Lagrangian DEM. Using the linear force model to simulate particle repulsion, the actual order of accuracy with respect to initial separation (‘free motion’), timestep, stiffness, damping and impact velocity is investigated. Due to the discontinuities of the inter-particle repulsive force upon contact, we find that without damping, the numerical schemes tested are generally limited to second order accuracy. The addition of damping can reduce actual order of accuracy further depending on the inter-particle free motion. This finding is compared against a continual interaction case (without free motion) where it is found that the expected higher order accuracy is recovered.

Finite elements in CFD: What lies ahead

AbstractThe current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.