Quality and reliability of LES of convective scalar transfer at high Reynolds numbers

Numerical studies were performed to assess the quality and reliability of wall-modeled large eddy simulation (LES) for studying convective heat and mass transfer over bluff bodies at high Reynolds numbers (Re), with a focus on built structures in the atmospheric boundary layer. Detailed comparisons were made with both wind-tunnel experiments and field observations. The LES was shown to correctly capture the spatial patterns of the transfer coefficients around two-dimensional roughness ribs (with a discrepancy of about 20%) and the average Nusselt number (Nu) over a single wall mounted cube (with a discrepancy of about 25%) relative to wind tunnel measurements. However, the discrepancy in Re between the wind tunnel measurements and the real-world applications that the code aims to address influence the comparisons since Nu is a function of Re. Evaluations against field observations are therefore done to overcome this challenge; they reveal that, for applications in urban areas, the wind-tunnel studies result in a much lower range for the exponent m in the classic Nu∼Re m relations, compared to field measurements and LES (0.52–0.74 versus≈ 0.9). The results underline the importance of conducting experimentalor numerical studies for convective scalar transfer problems at a Re commensurate with the flow of interest, and support the use of wall-modeled LES as a technique for this problem that can already capture important aspects of the physics, although further development and testing are needed

Improving the representation of convective heat transfer in an urban canopy model

The urban street canyon has been widely recognized as a basic surface unit in urban micrometeorological studies. Urban canopy models (UCMs), which quantify the exchange of energy and momentum between the urban surface and the overlying atmosphere, often adopt this type of street canyon representation as the fundamental surface element. Since UCMs can be coupled to regional-scale weather and climate models such as the Weather Forecast and Research Model (WRF), parametrizations of the surface momentum and scalar fluxes in UCM are of paramount importance. However, many current single-layer UCMs rely on empirical relations that were obtained over 80 years ago and often invoke the exponential wind profile derived from the existing literature for vegetation canopy. In this study, we conducted wallmodeled large-eddy simulations (LES) to study the forced (very weak buoyancy) convective heat transfer over idealized two-dimensional street canyons. It shows that the transfer efficiency computed following commonly applied resistance formulations can be one order of magnitude lower than LES results. The main reasons for the deviation include inaccurate wind speed parameterization and the use of a log-law based formulation for turbulent heat exchange between canyon air and the flow above

Modeling Flow around Bluff Bodies and Predicting Urban Dispersion Using Large Eddy Simulation

Modeling air pollutant transport and dispersion in urban environments is especially challenging due to complex ground topography. In this study, we describe a large eddy simulation (LES) tool including a new dynamic subgrid closure and boundary treatment to model urban dispersion problems. The numerical model is developed, validated, and extended to a realistic urban layout. In such applications fairly coarse grids must be used in which each building can be represented using relatively few grid-points only. By carrying out LES of flow around a square cylinder and of flow over surface-mounted cubes, the coarsest resolution required to resolve the bluff body’s cross section while still producing meaningful results is established. Specifically, we perform grid refinement studies showing that at least 6-8 grid points across the bluff body are required for reasonable results. The performance of several subgrid models is also compared. Although effects of the subgrid models on the mean flow are found to be small, dynamic Lagrangian models give a physically more realistic subgridscale (SGS) viscosity field. When scale-dependence is taken into consideration, these models lead to more realistic resolved fluctuating velocities and spectra. These results set the minimum grid resolution and subgrid model requirements needed to apply LES in simulations of neutral atmospheric boundary layer flow and scalar transport over a realistic urban geometry. The results also illustrate the advantages of LES over traditional modeling approaches, particularly its ability to take into account the complex boundary details and the unsteady nature of atmospheric boundary layer flow. Thus LES can be used to evaluate probabilities of extreme events (such as probabilities of exceeding threshold pollutant concentrations). Some comments about computer resources required for LES are also included

Plume or bubble? Mixed-convection flow regimes and city-scale circulations

Large-scale circulations around a city are co-modulated by the urban heat islandand by regional wind patterns. Depending on these variables, the circulations fall into different regimes ranging from advection-dominated (plume regime) to convection-driven (bubble regime). Using dimensional analysis and large-eddy simulations, this study investigates how these different circulations scale with urban and rural heat fluxes, as well as up stream wind speed. Two dimensionless parameters are shown to control the dynamics of the flow: (1) the ratio of rural to urban thermal convective velocities that contrasts their respective buoyancy fluxes and (2) the ratio of bulk inflow velocity to the convection velocity in the rural area. Finally, the vertical flow velocities transecting the rural to urban transitions are used to developa criterion for categorizing different large-scale circulations into plume, bubble or transitional regimes. The findings have implications for city ventilation since bubbleregimes are expected to trap pollutants, as well as for scaling analysis in canonical mixed-convection flows.Peer ReviewedPostprint (author's final draft

Large Eddy Simulations of complex turbulent flows

In this dissertation a solution methodology for complex turbulent flows of industrial interests is developed using a combination of Large Eddy Simulation (LES) and Immersed Boundary Method (IBM) concepts. LES is an intermediate approach to turbulence simulation in which the onus of modeling of “universal” small scales is appropriately transferred to the resolution of “problem-dependent” large scales or eddies. IBM combines the efficiency inherent in using a fixed Cartesian grid to compute the fluid motion, along with the ease of tracking the immersed boundary at a set of moving Lagrangian points. Numerical code developed for this dissertation solves unsteady, filtered Navier-Stokes equations using high-order accurate (fourth order in space) finite difference schemes on a staggered grid with a fractional step approach. Pressure Poisson equation is solved using a direct solver based on a matrix diagonalization technique. Second order accurate Adams-Bashforth scheme is used for temporal integration of equations. Dynamic mixed model (DMM) is used to model subgrid scale (SGS) terms. It can represent large scale anisotropy and back-scatter of energy from small-to-large scale through scale-similar term and maintain the energy drain through eddy viscosity term whose coefficient is allowed to change with in the computational domain. This code is validated for several bench-mark problems and is demonstrated to solve complex moving geometry problem such as stator-rotor interaction. A number of parametric studies on jets-in-crossflow are performed to understand complex fluid dynamics issues pertaining to film-cooling. These studies included effects of variation of hole-aspect ratio, jet injection angle, free-stream turbulence intensity and free-stream turbulence length scales on the coherent structure dynamics for jets-in-crossflow. Fundamental flow physics and heat transfer issues are addressed by extracting coherent structures from time-dependent three dimensional flow fields of film-cooling by inclined jet and studying their influence on the film-cooled surface heat transfer. A direct method to perform heat transfer calculations in periodic geometries is proposed and applied to internal cooling in rotating ribbed duct. Immersed boundary method is used to render complex geometry of trapped vortex combustor on Cartesian grid and fluid mixing inside trapped vortex cavity is studied in detail

Fourier spectral computation of geometrically confined two-dimensional flows

Large-scale flow phenomena in the atmosphere and the oceans are predominantly two-dimensional (2D) due to the large aspect ratio of the typical horizontal and vertical length scales in the flow. The 2D nature of large-scale geophysical flows motivates the use of a conceptual approach known as "2D turbulence". It usually involves the (forced/damped) Navier-Stokes equations on a square domain with periodic boundaries or on a spherical surface. This setup may be useful for numerical studies of atmospheric flow. For the oceans, on the other hand, geometrical confinement due to the continental shelves is of crucial importance. The physically most relevant boundary condition for oceanographic flow is probably the no-slip condition. Previous numerical and experimental studies have shown that confinement by no-slip boundaries dramatically affects the dynamics of (quasi-)2D turbulence due to its role as vorticity source. An important process is the detachment of high-amplitude vorticity filaments from the no-slip sidewalls that subsequently affect the internal flow. The first part of the thesis concerns the development and extensive testing of a Fourier spectral scheme for 2D Navier-Stokes flow in domains bounded by rigid noslip walls. An advantage of Fourier methods is that higher-order accuracy can, in principle, be achieved. Moreover, these methods are fast, relatively easy to implement even for performing parallel computations. The no-slip boundary condition is enforced by using an immersed boundary technique called "volume-penalization". In this method an obstacle with no-slip boundaries is modelled as a porous medium with a small permeability. It has recently been shown that in the limit of infinitely small permeability the solution of the penalized Navier-Stokes equations converges towards the solution of the Navier-Stokes equations with no-slip boundaries. Therefore the penalization error can be controlled with an arbitrary parameter. A possible drawback is that the sharp transition between the fluid and the porous medium can trigger Gibbs oscillations that might deteriorate the stability and accuracy of the scheme. Using a very challenging dipole-wall collision as a benchmark problem, it is, however, shown that higher-order accuracy is retrieved by using a novel 159 post-processing procedure to remove the Gibbs effect. The second topic of the thesis is the dynamics of geometrically confined 2D turbulent flows. The role of the geometry on the flow development has been studied extensively. For this purpose high resolution Fourier spectral simulations have been conducted where different geometries are implemented by using the volumepenalization method. A quantity that is of particular importance on a bounded domain is the angular momentum. On a circular domain production of angular momentum is virtually absent. Therefore the amount of angular momentum carried by the initial flow has important consequences for the evolution of the flow. The results of the simulations are consistent with previous numerical and experimental work on this topic performed in a lower Reynolds number regime. The typical vortex structures of the late time evolution of the flow are explained by means of a minimum enstrophy principle and the presence of weak viscous dissipation. For an elliptic geometry it is shown that strong spin-up events of the flow occur even for small eccentricities. The spin-up phenomenon can be related to the role of the pressure along the boundary of the domain. It is found that the magnitude of the torque exerted on the internal fluid can be scaled with the eccentricity. Furthermore, it is observed that angular momentum production in a non circular geometry is not restricted to moderate Reynolds numbers. Significantly higher Reynolds number flow computations in a square geometry clearly reveal strong and rapid spin-up of the flow. Finally the scale-dependence of the vorticity and velocity statistics in forced 2D turbulence on a bounded domain has been studied. A challenging aspect is that a statistically steady state can be achieved by a balance between the injection of kinetic energy by the external forcing and energy dissipation at the no-slip sidewalls. It is important to note that on a double periodic domain a steady state is usually achieved by introducing volumetric drag forces. Several studies reported that this strongly affects the spatial scaling behaviour of the flow. Therefore it is very interesting to quantify the small-scale statistics in the bulk of statistically steady flow on a domain with no-slip boundaries in the absence of bottom drag. It is observed that the internal flow shows extended self-similar, locally homogeneous and isotropic scaling behaviour at small scales. It is further demonstrated that a direct enstrophy cascade develops in the interior of the flow domain. Some deviations from the classical scaling theory of 2D turbulence developed independently by Kraichnan, Batchelor and Leith may be associated to the presence of coherent structures in the flow. It is, however, anticipated that higher-resolution simulations are required in order to draw more decisive conclusions. The parallel Fourier spectral scheme with volume-penalization is very suitable for pursuing such simulations on high performance machines in the near future. In summary the thesis contributes to both the development of numerical techniques and understanding of wall-bounded two-dimensional flows. The Fourier spectral scheme with volume-penalization is found very suitable for pursuing direct numerical simulations in complex geometries. The high-resolution simulations considered in the thesis clearly reveal that spontaneous production of angular momentum due to interaction with non-circular domain boundaries is present for significantly higher Reynolds numbers than considered previously