Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed. One is based on high-order approximations and upwind-biased discretization of the nonlinear term. Another is consistently of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles. The analysis is conducted using comparison with high-accuracy spectral direct numerical simulations of channel flows with wall-normal and spanwise magnetic fields. Focus of the analysis is on the quality of finite difference approximation in the situation when the magnetic field leads to significant transformation of the flow structure. In the case of turbulent flows at moderate magnetic fields, the conservative scheme approach offers better stability and equal or higher accuracy than the approach based on the upwind discretization. The conservation property is expected to become increasingly important and even indispensable at stronger magnetic fields.     

The uncertainty in conifer plantation growth prediction from multi-temporal lidar datasets

An evaluation of the use of airborne lidar for multi-temporal forest height growth assessment in a temperate mature red pine (Pinus resinosa Ait.) plantation over a five-year period is presented. The objective was to evaluate the level of uncertainty in lidar-based growth estimates through time so that the optimal repeat interval necessary for statistically meaningful growth measurements could be evaluated. Four airborne lidar datasets displaying similar survey configuration parameters were collected between 2000 and 2005. Coincident with the 2002 and 2005 acquisitions, field mensuration for 126 trees within 19 plots was carried out. Field measurements of stem height were compared to both coincident plot-level laser pulse return (LPR) height percentile metrics and stand level raster canopy height models (CHM).The average plot-level field heights were found to be 23.8 m (standard deviation (σ) = 0.4 m) for 2002 and 25.0 m (σ = 0.6 m) for 2005, with an approximate annual growth rate of 0.4 m/yr (σ = 0.5 m). The standard deviation uncertainty for field height growth estimates over the three year period was 41% at the plot-level (n = 19) and 92% at the individual tree level (n = 126). Of the lidar height percentile metrics tested, the 90th (L90), 95th (L95) and maximum (Lmax) LPR distribution heights demonstrated the highest overall correlations with field-measured tree height. While all lidar-based methods, including raster CHM comparison, tended to underestimate the field estimate of growth, Lmax provided the most robust overall direct estimate (0.32 m/yr, σ = 0.37 m). A single factor analysis of variance demonstrated that there was no statistically significant difference between all plot-level field and Lmax mean growth rate estimates (P = 0.38) and, further, that there was no difference in Lmax growth rate estimates across the examined time intervals (P = 0.59). A power function relationship between time interval and the standard deviation of error in growth estimate demonstrated that over a one-year period, the growth uncertainty was in the range of 0.3 m (∼ 100% of total growth) reducing to less than 0.1 m (∼ 6% of total growth) after 5 years. Assuming a 10% uncertainty is acceptable for operational or research-based conifer plantation growth estimates, this can be achieved at a three-year time interval.     

Frequency characteristics of coherent structures and their excitations in small aspect-ratio rectangular jets using large eddy simulation

Large eddy simulations of air jets from small aspect-ratio (AR) rectangular nozzles are performed with the dynamic subgrid-scale closure. Mean streamwise velocity profiles are in good agreement with experimental data. Results indicate that vortices originating from the longer side of the rectangular jet are dominant compared with that from the shorter side. Furthermore, entrainment is slight in the potential core, and significantly increases in the following vortex roll-up region. However, the jet entrains more with smaller AR. Power spectral density of the streamwise velocity indicates that the oscillations consist of a series of sub-harmonic frequencies, with the predominant frequencies reducing along the axial direction. Analysis shows that among multiple frequencies, there is a characteristic one at f = 0.22 which dominates the near field of the rectangular jet. The characteristic frequency is independent of velocity components, aspect ratios of the jet and locations. Based on this characteristic frequency, calculations with different forced frequencies imposed on the inlet nozzle are carried out. Results indicate that when the forced frequency is approximately equal to the characteristic frequency, development of the coherent structures is the most intense in the near field, and exhibits the strongest entrainment.     

CFD simulation and evaluation of controllable parameters effect on thermomagnetic convection in ferrofluids using Taguchi technique

In the present attempt a CFD simulation capable of coupling behaviors from the nano-scale through the full-scale system in which a ferrofluid containing magnetite particles suspended in kerosene carrier liquid is presented. The main objective of the work was to simulate the thermodiffusion and also to evaluate the factors influence on this phenomenon in a cylindrical geometry. In simulations a two-phase mixture model was used to predict the behavior of the system. To optimize the thermomagnetic effect, different parameters including temperature difference across the layer, initial magnetic phase concentration, aspect ratio of the geometry, magnetic field magnitude and diameter of magnetic particles were examined using L₁₆ orthogonal array of Taguchi at four levels. Analysis of the simulation data indicate that the magnetic Soret effect can even be higher than the conventional one and its strength depends on the magnetic field strength, confirmed experimentally by Völker and Odenbach [Völker T, Odenbach S. Thermodiffusion in magnetic fluids. J Magn Magn Mater 2005;289:289-91]. The statistic evaluation shows that temperature and initial concentration of magnetic phase have the maximum and minimum contribution on the thermodiffusion, respectively. According to the results temperature difference 80 K, initial concentration of magnetic phase 0.08, aspect ratio 0.2, magnetic field strength 100 kA/m and magnetic particles diameter 100 nm were obtained as optimum conditions in the presence of natural convection. The same result was gained in the lack of natural convection except the magnetic field strength was 160 kA/m. Finally, based on the primary results, a verification test was also performed to confirm the validity of the used statistical method.     

Dynamic hybridization of MILES and RANS for predicting airfoil stall

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier-Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin-Lomax model with the Degani-Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA63₃-018, NACA63₁-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 10⁶. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.     

Chebyshev wavelet collocation method for magnetohydrodynamic flow equations

This study proposes Chebyshev wavelet collocation method for partial differential equation and applies to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Approximate solutions of velocity and induced magnetic field are obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. Numerical results of the MHD flow problem show that the accuracy of proposed method is quite good even in the case of a small number of grid points. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H_a ≤ 1000.

     

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.     

Towards control of carbon nanotube synthesis process using prediction-based fast Monte Carlo simulations

Precise control of the lengths of carbon nanotube (CNT) and other nanostructures is important for various industrial applications. However, time-resolution (∼1 min) of current in situ measurements does not allow control of lengths to within 20 nm. We present an approach to combine intermittent in situ measurements with length estimates from a fast atomistic Monte Carlo (MC) simulation of CNT synthesis. The MC simulation time was reduced by >70% through prediction of the nonlinear and nonstationary growth increments, and initialization of relaxation process (the most computationally intensive step in MC simulations) with the near-optimum predicted positions, leading to one of the longest (∼194 nm) CNTs from atomistic simulations. A utility function of growth predictions was defined so that its maximization specified the end-point of the synthesis process. Extensive simulation studies indicate that the approach can be used to control CNT lengths to within 1 nm of specifications.     

Efficient parallelization of a parabolized flow solver

This article describes application of our theory of parallelization of implicit ADI schemes to parabolized flows. A parallel multi-domain version of a turbulent developing flow in a straight duct (case A) and viscous flow in a curved duct (case B) are presented. Semi-implicit and explicit methods for the determination of boundary values for the auxiliary ADI functions on the interfaces between the sub-domains are utilized. Numerical runs show that the proposed algorithm is valid in the regions with rapidly varying fields of governing variables (near-entrance region for the case A, region 30°<θ<60° for the case B) as well as in the regions with slow axial modification of the flowfield. The algorithm is suitable for small transverse velocity (case A) and for transverse velocity of order of streamwise velocity (case B). A simplified version of our theoretical model of parallel efficiency is developed and utilized for optimal multidomain partitioning. Computer runs of the multi-domain code are done on a Meiko CS and on a DEC Alpha farm with PVM communication software. The predictions of parallel efficiency obtained by the model compare well with those of actual computer runs. The parallelization parameters obtained are quite different for two considered MIMD machines. This fact confirms the importance of a priori estimation of parallelization efficiency of an algorithm and correct choice of a parallel computer.     

Highly sensitive and selective LPG sensor based on α-Fe2O3 nanorods

The α-Fe₂O₃ nanorods were successfully synthesized without any templates by calcining the α-FeOOH precursor in air at 300 °C for 2 h and their LPG sensing characteristics were investigated. The α-FeOOH precursor was prepared through a simple and low cost wet chemical route at low temperature (40 °C) using FeSO₄·7H₂O and CH₃COONa as starting materials. The formation of α-FeOOH precursor and its topotactic transformation to α-Fe₂O₃ upon calcination was confirmed by X-ray diffraction measurement (XRD), X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) analysis. The α-Fe₂O₃ nanorods exhibited outstanding gas sensing characteristics such as, higher gas response (∼1746-50 ppm LPG at 300 °C), extremely rapid response (∼3-4 s), relatively slow recovery (∼8-9 min), excellent repeatability, good selectivity and lower operating temperature (∼300 °C). Furthermore, the α-Fe₂O₃ nanorods are able to detect up to 5 ppm for LPG with reasonable response (∼15) at the operating temperature of 300 °C and they can be reliably used to monitor the concentration of LPG over the range (5-60 ppm). The experimental results clearly demonstrate the potential of using the α-Fe₂O₃ nanorods as sensing material in the fabrication of LPG sensors. Plausible LP G sensing mechanism of the α-Fe₂O₃ nanorods is also discussed.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Numerical study of the flow over shallow cavities

This paper reports on a series of numerical simulations of both laminar and turbulent flows over shallow cavities. For the turbulent case the influences of the following parameters were considered: (i) cavity aspect ratios, (ii) turbulence level of the oncoming flow, and (iii) Reynolds number. Several important results and conclusions are reported. We have found that for the turbulent case the external flow touches the floor of the cavity, and this depends on a specific value of each of these parameters. This condition has an important impact upon convective effects inside the cavity. The mathematical model corresponds to the incompressible, Reynolds-averaged, Navier-Stokes equations plus a high-Reynolds κ-ε model of turbulence, and the numerical computation is performed using the SIMPLER algorithm.     

Nanostructured spinel ZnCo2O4 for the detection of LPG

Nanostrucutred spinel ZnCo₂O₄ (∼26-30 nm) was synthesized by calcining the mixed precursor (consisting of cobalt hydroxyl carbonate and zinc hydroxyl carbonate) in air at 600 °C for 5 h. The mixed precursor was prepared through a low cost and simple co-precipitation/digestion method. The transformation of the mixed precursor into nanostructured spinel ZnCo₂O₄ upon calcinations was confirmed by X-ray diffraction (XRD) measurement, thermogravimetric analysis (TGA), X-ray photoelectron spectroscopy (XPS) and high resolution transmission electron microscopy (HRTEM). To demonstrate the potential applicability of ZnCo₂O₄ spinel in the fabrication of gas sensors, its LPG sensing characteristics were systematically investigated. The ZnCo₂O₄ spinel exhibited outstanding gas sensing characteristics such as, higher gas response (∼72-50 ppm LPG gas at 350 °C), response time (∼85-90 s), recovery time (∼75-80 s), excellent repeatability, good selectivity and relatively lower operating temperature (∼350 °C). The experimental results demonstrated that the nanostructured spinel ZnCo₂O₄ is a very promising material for the fabrication of LPG sensors with good sensing characteristics. Plausible LPG sensing mechanism is also discussed.     

A LiDAR-derived canopy density model for tree stem and crown mapping in Australian forests

The retrieval of tree and forest structural attributes from Light Detection and Ranging (LiDAR) data has focused largely on utilising canopy height models, but these have proved only partially useful for mapping and attributing stems in complex, multi-layered forests. As a complementary approach, this paper presents a new index, termed the Height-Scaled Crown Openness Index (HSCOI), which provides a quantitative measure of the relative penetration of LiDAR pulses into the canopy. The HSCOI was developed from small footprint discrete return LiDAR data acquired over mixed species woodlands and open forests near Injune, Queensland, Australia, and allowed individual trees to be located (including those in the sub-canopy) and attributed with height using relationships (r² = 0.81, RMSE = 1.85 m, n = 115; 4 outliers removed) established with field data. A threshold contour of the HSCOI surface that encompassed ∼ 90% of LiDAR vegetation returns also facilitated mapping of forest areas, delineation of tree crowns and clusters, and estimation of canopy cover. At a stand level, tree density compared well with field measurements (r² = 0.82, RMSE = 133 stems ha^− 1, n = 30), with the most consistent results observed for stem densities ≤ 700 stems ha^− 1. By combining information extracted from both the HSCOI and the canopy height model, predominant stem height (r² = 0.91, RMSE = 0.77 m, n = 30), crown cover (r² = 0.78, RMSE = 9.25%, n = 30), and Foliage & Branch Projective Cover (FBPC; r² = 0.89, RMSE = 5.49%, n = 30) were estimated to levels sufficient for inventory of woodland and open forest structural types. When the approach was applied to forests in north east Victoria, stem density and crown cover were reliably estimated for forests with a structure similar to those observed in Queensland, but less so for forests of greater height and canopy closure.     

Accurate 2d finite element calculations for hydrogen in magnetic fields of arbitrary strength

Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 10⁵  T (10³  MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers n≤10$n\le 10$. We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths B=0$B=0$ T to B∼10⁹$B\sim {10}^9$ T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of B$B$-splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10⁻⁶ Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths.     

The structure and the small-scale intermittency of passive scalars in homogeneous turbulence

Results generated by direct numerical simulations (DNS) are used to study the structure and the small-scale intermittency of a passive scalar contaminant in a homogeneous turbulent shear flow. Simulations are conducted of flows with and without a constant mean scalar gradient. In all cases, the probability density functions (PDFs) of the scalars adopt an approximate gaussian distribution at the final stages of mixing. In the presence of the mean gradient, the scalar fields yield a nearly identical asymptotic state independent of initial conditions. In these cases, the gradient of the fluctuating scalar field shows preferred directions of orientation with respect to the strain eigenvectors; and the mean transverse velocity conditioned on the scalar is linear. These fields also portray increased flatness and skewness of the scalar-difference field as the separation distance becomes small. Larger than gaussian tails are observed in the PDF of both the velocity- and the scalar-derivatives, and the intermittency of the scalar derivative is shown to be more pronounced in the presence of the mean scalar gradient. Conditional averages of the angle between the scalar gradient and the strain eigenvectors suggest that the scalar field may be viewed as a random gaussian background field superimposed with sporadic scalar structures which are responsible for intermittency. With this view, a Langevin transport equation is proposed for the mapping of the scalar derivative PDF from a gaussian reference field. This is done in the context of the two-fluid model of She (1990). With this model, the PDF of the scalar dissipation is produced and the results are compared with DNS data.     

Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD)

The streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are among the most popular stabilized formulations in finite element computation of flow problems. The discontinuity-capturing directional dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problem a plane channel flow at friction Reynolds number Re_τ = 180.     

A zonal grid algorithm for DNS of turbulent boundary layers

A zonal grid algorithm for direct numerical simulation (DNS) of incompressible turbulent flows within a Finite-Volume framework is presented. The algorithm uses fully coupled embedded grids and a conservative treatment of the grid-interface variables. A family of conservative prolongation operators is tested in a 2D vortex dipole and a 3D turbulent boundary layer flow. These tests show that both, first- and second-order interpolation conserves the overall second-order spatial accuracy of the scheme. The first-order conservative interpolation has a smaller damping effect on the solution but the second-order conservative interpolation has better spectral properties. The application of this algorithm in boundary layer flow separating and reattaching due to the presence of a streamwise pressure gradient reveals the power and usefulness of the presented algorithm. This simulation has been made possible by the zonal grid algorithm by reducing the required number of grid points from about 500 × 10⁶ to 130 × 10⁶ grid cells.     

Cerebral arterial inflow assessment with F-FDG PET: Methodology and feasibility

Positron emission tomography (PET) with ¹⁸fluorodeoxyglucose (¹⁸F-FDG) is increasingly used in neurology. The measurement of cerebral arterial inflow (QA) using ¹⁸F-FDG complements the information provided by standard brain PET imaging. Here, injections were performed after the beginning of dynamic acquisitions and the time to arrival (t0) of activity in the gantry's field of view was computed. We performed a phantom study using a branched tube (internal diameter: 4 mm) and a ¹⁸F-FDG solution injected at 240 mL/min. Data processing consisted of (i) reconstruction of the first 3 s after t0, (ii) vascular signal enhancement and (iii) clustering. This method was then applied in four subjects. We measured the volumes of the tubes or vascular trees and calculated the corresponding flows. In the phantom, the flow was calculated to be 244.2 mL/min. In each subject, our QA value was compared with that obtained by quantitative cine-phase contrast magnetic resonance imaging; the mean QA value of 581.4 ± 217.5 mL/min calculated with ¹⁸F-FDG PET was consistent with the mean value of 593.3 ± 205.8 mL/min calculated with quantitative cine-phase contrast magnetic resonance imaging. Our ¹⁸F-FDG PET method constitutes a novel, fully automatic means of measuring QA.