Physics

This paper introduces a dynamic parametric wind farm model that is capable of simulating floating wind turbine platform motion coupled with wake transport under time-varying wind conditions. The simulator is named FOWFSim-Dyn as it is a dynamic extension of the previously developed steady-state Floating Offshore Wind Farm Simulator (FOWFSim). One-dimensional momentum conservation is used to model dynamic propagation of wake centerline locations and average velocities, while momentum recovery is approximated with the assumption of a constant temporal wake expansion rate. Platform dynamics are captured by treating a floating offshore wind farm as a distribution of particles that are subject to aerodynamic, hydrodynamic, and mooring line forces. The finite difference method is used to discretize the momentum conservation equations to yield a nonlinear state-space model. Simulated data are validated against steady-state experimental wind tunnel results obtained from the literature. Predictions of wake centerlines differed from experimental results by at most 8.19% of the rotor diameter. Simulated wake velocity profiles in the far-wake region differed from experimental measurements by less than 3.87% of the free stream wind speed. FOWFSim-Dyn thus possesses a satisfactory level of fidelity for engineering applications. Finally, dynamic simulations are conducted to ensure that time-varying predictions match physical expectations and intuition.

Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today's computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the understanding of these processes. They serve as a "virtual prototype" of a projected site and support planning in reasonable time. In this contribution, we present a meshfree Generalized Finite Difference Method (GFDM) based on a cloud of numerical points that is able to simulate solution mining processes on microscopic as well as macroscopic scales, which differ significantly in both the spatial and temporal scale. Focusing on anticipated industrial requirements, Lagrangian and Eulerian formulations including an Arbitrary Lagrangian-Eulerian (ALE) approach are considered.

In this article we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg-de Vries (KdV) equation. These quantities can be used to describe the shoaling of cnoidal waves approaching a gently sloping beach. The transformation of these waves along the slope can be described using the shoaling equations, a set of three nonlinear equations in three unknowns: the wave height H, the set-down and the elliptic parameter m. We define a numerical algorithm for the efficient solution of the shoaling equations, and we verify our shoaling formulation by comparing with experimental data from two sets of experiments as well as shoaling curves obtained in previous works.

Thermal energy storage (TES) is increasingly recognized as an essential component of efficient Combined Heat and Power (CHP), Concentrated Solar Power (CSP), Heating Ventilation and Air Conditioning (HVAC), and refrigeration as it reduces peak demand while helping to manage intermittent availability of energy (e.g., from solar or wind). Latent Heat Thermal Energy Storage (LHTES) is a viable option because of its high energy storage density. Parametric analysis of LHTES heat exchangers have been focused on obtaining data with laminar flow in the phase changing fluid and then fitting a functional form, such as a power law or polynomial, to those data. Alternatively, in this paper we present a parametric framework to analyze LHTES devices by identifying all relevant fluid parameters and corresponding dimensionless numbers. We present 64 simulations of an LHTES device using the finite volume method at four values of the Grashof, Prandtl and Reynolds numbers in the phase change material (PCM) and heat transfer fluid (HTF). We observe that with sufficient energy available in the HTF, the effects of the HTF Reynolds number and Prandtl number on the heat transfer rate are negligible. Under these conditions, we propose a time scale for the variation of energy stored (or melt fraction) of the LHTES device based on the Fourier number( Fo ), Grashof number( G r p ) and Prandtl number( P r p ) and observe a G r 1 p and P r (1/3) p dependency. We also identify two distinct regions in the variation of the melt fraction with time, namely, the linear and the asymptotic region. We also predict the critical value of the melt fraction at the transition between the two regions. From these analyses, we draw some conclusions regarding the design procedure for LHTES devices.

The recently introduced harmonic resolvent framework is concerned with the study of the input-output dynamics of nonlinear flows in the proximity of a known time-periodic orbit. These dynamics are governed by the harmonic resolvent operator, which is a linear operator in the frequency domain whose singular value decomposition sheds light on the dominant input-output structures of the flow. Although the harmonic resolvent is a mathematically well-defined operator, the numerical computation of its singular value decomposition requires inverting a matrix that becomes exactly singular as the periodic orbit approaches an exact solution of the nonlinear governing equations. The very poor condition properties of this matrix hinder the convergence of classical Krylov solvers, even in the presence of preconditioners, thereby increasing the computational cost required to perform the harmonic resolvent analysis. In this paper we show that a suitable augmentation of the (nearly) singular matrix removes the singularity, and we provide a lower bound for the smallest singular value of the augmented matrix. We also show that the desired decomposition of the harmonic resolvent can be computed using the augmented matrix, whose improved condition properties lead to a significant speedup in the convergence of classical iterative solvers. We demonstrate this simple, yet effective, computational procedure on the Kuramoto-Sivashinsky equation in the proximity of an unstable time-periodic orbit.

An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is thus devoted to the derivation and validation of a new framework to determine the drag, lift, rotational and pitching torque coefficients for different non-spherical particles in a fluid flow. The motivation for the study arises from medical applications, where particles may have an arbitrary and complex shape. Here, it is usually not possible to derive accurate analytical models for predicting the different hydrodynamic forces. However, considering for example the various components of blood, their shape takes an important role in controlling several body functions such as control of blood viscosity or coagulation. Therefore, the presented model is designed to be applicable to a broad range of shapes. Another important feature of the suspensions occurring in medical and biological applications is the high number of particles. The modelling approach we propose can be efficiently used for simulations of solid-liquid suspensions with numerous particles. Based on resolved numerical simulations of prototypical particles we generate data to train a neural network which allows us to quickly estimate the hydrodynamic forces experienced by a specific particle immersed in a fluid.

A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a pinned contact line. The Navier-Stokes equations in cylindrical coordinates were solved inside the droplet. Galerkin weight residual approach and velocity pressure formulation was used to discretise the governing equations. Six node triangular mesh and quadratic shape functions were used to obtain higher accuracy solutions. Radial velocity profiles in axial directions calculated by the FEM solver were compared with a existing analytical model and were found in excellent agreement. The contours of velocity magnitude and streamlines show the characteristic flow i.e. radially outward inside the evaporating droplet.

A major challenge in flow through porous media is to better understand the link between pore-scale microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of circular obstacles, the size and spacing of which can vary along the length of the porous medium.We use homogenisation via the method of multiple scale to systematically upscale a novel problem that involves cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterized by the local porosity, an effective local anisotropic flow permeability, and an effective local anisotropic solute diffusivity. These macroscale properties depend non-trivially on both degrees of microstructural geometric freedom (obstacle size and spacing). We take advantage of this dependence to compare scenarios where the same porosity field is constructed with different combinations of obstacle size and spacing. For example, we consider scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters, or for studying the impact of deformation on transport in soft porous media.

In this paper, we propose a lattice Boltzmann (LB) model for the generalized coupled cross-diffusion-fluid system. Through the direct Taylor expansion method, the proposed LB model can correctly recover the macroscopic equations. The cross diffusion terms in the coupled system are modeled by introducing additional collision operators, which can be used to avoid special treatments for the gradient terms. In addition, the auxiliary source terms are constructed properly such that the numerical diffusion caused by the convection can be eliminated. We adopt the developed LB model to study two important systems, i.e., the coupled chemotaxis-fluid system and the double-diffusive convection system with Soret and Dufour effects. We first test the present LB model through considering a steady-state case of coupled chemotaxis-fluid system, then we analyze the influences of some physical parameters on the formation of sinking plumes. Finally, the double-diffusive natural convection system with Soret and Dufour effects is also studied, and the numerical results agree well with some previous works.

A novel system has been developed that harnesses the phenomena of vortex-induced vibrations (VIV) from a slow current (<0.5 m/s) of water to generate renewable hydrokinetic energy. It utilizes a single degree-of-freedom pivoting cylinder mechanism coupled with an electromagnetic induction generator. As a result of observation and concept development, the final prototype includes a stationary cylindrical shedder upstream of the oscillator. The system is referred to as "Vortex Assisted Generation" (V.A.G.) throughout the report. Given the novelty of the system, an extensive investigation has been conducted to identify key parameters and functional relationships between system variables, regarding their effect on output voltage, frequency, and power. A range of flow velocities have been established that instigate system lock-in, where the cylinder oscillates at high amplitude and frequency. For the tested prototype up to 37% of system extraction efficiency has been achieved in the lab conditions.