Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence

Inviscid regularization modeling of turbulent flow is investigated. Homogeneous, isotropic, decaying turbulence is simulated at a range of filter widths. A coarse-graining of turbulent flow arises from the direct regularization of the convective nonlinearity in the Navier–Stokes equations. The regularization is translated into its corresponding sub-filter model to close the equations for large-eddy simulation (LES). The accuracy with which primary turbulent flow features are captured by this modeling is investigated for the Leray regularization, the Navier–Stokes-α formulation (NS-α), the simplified Bardina model and a modified Leray approach. On a PDE level, each regularization principle is known to possess a unique, strong solution with known regularity properties. When used as turbulence closure for numerical simulations, significant differences between these models are observed. Through a comparison with direct numerical simulation (DNS) results, a detailed assessment of these regularization principles is made. The regularization models retain much of the small-scale variability in the solution. The smaller resolved scales are dominated by the specific sub-filter model adopted. We find that the Leray model is in general closest to the filtered DNS results, the modified Leray model is found least accurate and the simplified Bardina and NS-α models are in between, as far as accuracy is concerned. This rough ordering is based on the energy decay, the Taylor Reynolds number and the velocity skewness, and on detailed characteristics of the energy dynamics, including spectra of the energy, the energy transfer and the transfer power. At filter widths up to about 10% of the computational domain-size, the Leray and NS-α predictions were found to correlate well with the filtered DNS data. Each of the regularization models underestimates the energy decay rate and overestimates the tail of the energy spectrum. The correspondence with unfiltered DNS spectra was observed often to be closer than with filtered DNS for several of the regularization models

Capturing aerosol droplet nucleation and condensation bursts using PISO and TVD schemes

A mathematical model for single-species aerosol production and transport is formulated, and solved using an adapted PISO algorithm. The model is applied to a laminar flow diffusion chamber, using a finite volume method on a collocated grid. In tran- sient simulations, a sharp scalar front (e.g., vapor mass fraction), is shown to introduce unphysical oscillation in the solution, when applying a second order linear interpolation in the convective terms. At increased grid resolution, these oscillations are strongly at- tenuated. When applying a TVD scheme (here the MUSCL scheme), a time-accurate monotonicity-preserving solution is obtained. The numerical dissipation introduced by the MUSCL scheme implies increased spatial resolution to restore high accuracy levels. We develop a one-dimensional grid refinement algorithm, which relates the grid density in one direction to the magnitude of the scalar gradient. In combination with the MUSCL scheme, this gives accurate results, with a significant reduction in computational effort, in comparison with a uniform fine grid

Improved PISO algorithms for modeling density varying flow in conjugate fluid–porous domains

Two modified segregated PISO algorithms are proposed, which are constructed to avoid the development of spurious oscillations in the computed flow near sharp interfaces of conjugate fluid–porous domains. The new collocated finite volume algorithms modify the Rhie–Chow interpolation to maintain a correct pressure–velocity coupling when large discontinuous momentum sources associated with jumps in the local permeability and porosity are present. The Re-Distributed Resistivity (RDR) algorithm is based on spreading flow resistivity over the grid cells neighboring a discontinuity in material properties of the porous medium. The Face Consistent Pressure (FCP) approach derives an auxiliary pressure value at the fluid–porous interface using momentum balance around the interface. Such derived pressure correction is designed to avoid spurious oscillations as would otherwise arise with a strictly central discretization. The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow. The robustness of the proposed algorithms is additionally demonstrated for strongly reduced viscosity, i.e., higher Reynolds number flows and low Darcy numbers, i.e., low permeability of the porous regions in the domain, for which solutions without unphysical oscillations are computed. Both RDR and FCP are found to accurately represent porous media flow near discontinuities in material properties on structured grids

Characteristics-based sectional modeling of aerosol nucleation, condensation and transport

Aerosols can be generated by physical processes such as nucleation, conden- sation and coalescence. To predict spatially varying statistical properties of such aerosols, e.g., the size distribution of the droplets, these processes must be captured accurately. We model nucleation using classical nucleation theory, whereas the con- densational growth is captured with a molecular diffusivity model. The droplet size distribution is discretized using a sectional approach, in which droplets are charac- terized in terms of a number of fixed droplet size bins. Often, in such a formula- tion, the numerical time step restrictions arising from condensation and nucleation are more pronounced than those of the corresponding fluid flow, thereby signifi- cantly limiting the global time step size. We propose a moment-conserving method in which this limitation is avoided, by utilizing the analytical solutions of the spa- tially homogeneous nucleation-condensation subproblem. The method is validated against experimental and numerical data of a laminar flow diffusion chamber, and shows an excellent agreement while being restricted only by a flow-related time step criterion

Modeling turbulence in complex domains using explicit multi-scale forcing

A new computational framework for the numerical simulation of turbulent flows through complex domains and along irregular boundaries is presented. The geometrical complexity is included by introducing explicit fractal forcing. This involves the agitation of a spectrum of length-scales and forms an integral part of the flow modeling. The potential application of such a modeling approach is illustrated by the evaluation of the turbulent mixing of a passive scalar field, driven by this turbulent flow. The surface-area and wrinkling of level-sets of the scalar field are monitored showing the influence of the forcing localization on the mixing efficiency

Control over multiscale mixing by broadband-forced of turbulence

The effects of explicit flow modulation on the dispersion of a passive scalar field are studied. Broadband forcing is applied to homogeneous isotropic turbulence to modulate the energy cascading and alter the kinetic energy spectrum. Consequently, a manipulation of turbulent flow can be achieved over an extended range of scales beyond the directly forced ones. This modifies transport processes and influences the physical-space turbulent mixing of a passive scalar field. We investigate by direct numerical simulation the stirring-efficiency associated with turbulence modified by forcing. This is quantified by monitoring the surface-area and wrinkling of a level-set of the passive scalar field. We consider different forcing to manipulate the quality and rate of mixing. The instantaneous mixing efficiency measured in terms of surface-area or wrinkling is found to increase when additional energy is introduced at the smaller scales. The increased intensity of small scales significantly influences the small-scale mixing characteristics depicted by wrinkling, while the forcing of large scales primarily affects the surface-area. Evaluation of geometrical statistics in broadband-forced turbulence indicates that the self-amplification process of vorticity and strain is diminished. This leads generally to smaller extremal values of the velocity gradients but higher average values as a result of the competition between the natural cascading processes and the explicit small-scales forcin

Mixing in manipulated turbulence

A numerical investigation of turbulent flow, subject to deterministic broad-band forcing, is presented. Explicit forcing procedures are included that represent the simultaneous agitation of a wide spectrum of length-scales, including both large scales as well as a band of much smaller scales. Such forcing induces a multiscale modulation of turbulent flow that is motivated by flow through complex objects and along irregular boundaries. Two types of forcing procedures are investigated; with reference to the collection of forced modes these procedures are classified as ‘constant-energy’ or ‘constant-energy-input-rate’. It is found that a considerable modulation of the traditional energy cascading can be introduced with a specific forcing strategy. In spectral space, forcing yields strongly localized deviations from the common Kolmogorov scaling law, directly associated with the explicitly forced scales. In addition, the accumulated effect of forcing induces a significant non-local alteration of the kinetic energy including the spectrum for the large scales. Consequently, a manipulation of turbulent flow can be achieved over an extended range, well beyond the directly forced scales. Compared to flow forced in the large scales only, the energy in broad-band forced turbulence is found to be transferred more effectively to smaller scales. The turbulent mixing of a passive scalar field is also investigated, in order to quantify the physical-space modifications of transport processes in multiscale forced turbulence. The surface-area and wrinkling of level-sets of the scalar field are monitored as measures of the influence of explicit forcing on the local and global mixing efficiency. At small Schmidt numbers, the values of surface-area are mainly governed by the large scale sweeping-effect of the flow while the wrinkling is influenced mainly by the agitation of the smaller scales

Intermittency effects in rotating decaying turbulence

Rotation modulates turbulence causing columnar structuring of a turbulent flow in case of sufficiently strong rotation. This yields significant changes in the flow characteristics and dispersion properties, which makes rotational turbulence modulation particularly relevant in the context of atmospheric and oceanic flows. Here we investigate the canonical flow of turbulence in a periodic box, subjected to rotation about a fixed vertical axis. As point of reference we consider direct numerical simulations of homogeneous isotropic turbulence. Modulation due to rotation at various rotation rates (i.e., different Rossby numbers) is investigated. Special attention is paid to the alteration of intermittency, which is measured in terms of changes in the scaling of the structure functions. A reduction of intermittency quantified with the longitudinal structure functions in the direction perpendicular to the rotation axes will be presented. These numerical findings correspond well to recent results obtained in experiments by Seiwert et al. (2008).Comment: 6 pages, 9 figures, submitted to TSFP6 Conference, 2009, Seoul, Kore