Transport Equation Model Research Articles

Numerical modeling of turbulence above offshore helideck – Comparison of different turbulence models

The turbulent flow over an offshore oil-rig helideck has been simulated by a commercial engineering CFD code, Star-CCM+, with nine different turbulence models: two Reynolds-stress transport equation (RSE) models, six k–ε models and one k–ω model. Simulations by the same code and models were compared to experimental data for simpler test cases, including flows over a backward-facing step and a surface-mounted cube. The primary aim was to compare RSE models to two-equation models on the background of a new industry standard for helicopter operation with requirements on the vertical velocity variance over the helideck. It was found that RSE models do not outperform two-equation models for separated flows and wakes. The RSE models seem to underpredict the turbulence energy more than the two-equation models and hence, also the vertical velocity variance. Among the two-equation models, the realizable k–ε model and Menter׳s k–ω model performed better than the standard k–ε model, while a cubic k–ε model predicted unphysical, negative normal Reynolds stresses. Attempts on adjusting the coefficients of the k–ε model, as promoted by some authors, worked fine for undisturbed atmospheric flow but quite poor for more complex flows.

Implicit Algebraic Heat Flux Model Linked up with Elliptic Blending Reynolds Stress Transport Equation Model

Implicit Algebraic Heat Flux Model Linked up with Elliptic Blending Reynolds Stress Transport Equation Model

LES of the Sydney piloted spray flame series with the PFGM/ATF approach and different sub-filter models

Detailed numerical investigations of the Sydney spray flame series [1] are presented for ethanol flames referred to as “EtF3, EtF6 and EtF8”, which feature identical ethanol mass flow rates but different carrier gas mass flow rates. Large eddy simulations (LES) are performed, where the gaseous and liquid phases are modeled by an Eulerian/Lagrangian approach. The turbulent sub-filter stresses (sgs) are modeled with Nicoud’s sigma model [2] on grids with two different resolutions. Combustion is modeled with the premixed flamelet generated manifold approach (PFGM), which is combined with the artificially thickened flame (ATF) method. The sub-filter distributions of the control variables are modeled with (a) a β function (β-fdf) and (b) a top-hat function (TH). First, the influence of the variance in the mixture fraction and reaction progress variable is investigated separately, where the variances are either determined from an algebraic model or a transport equation model. Subsequently, the TH model is used to account for the joint impact of Z and Yp. The results are compared against the experimental measurements and reference simulations without sub-filter model. The particle statistics are in good agreement with the experimental data. The variances predicted by the two algebraic models are quite similar, whereas the transport equation model predicts variances which are one order of magnitude higher. The results obtained with the TH and the β-fdf model are comparable. It is found that the impact of the sgs models for the mixture fraction and the progress variable increases with an increasing carrier gas mass flow rate.

Modeling of transient thermoelectric transport in Harman method for films and nanowires

Harman method is a technique with great potential for rapidly scanning the figure-of-merit (zT) of emerging nanostructured thermoelectric materials. In the AC variant of this method zT is determined from the ratio of the electrical resistance measured across a thermoelectric material subjected to a sinusoidal current at high and low frequencies. The low frequency resistance incorporates both ohmic and Peltier responses, while at high frequencies the Peltier component vanishes. This work employs finite element modeling of the transient thermoelectric transport equations in thermoelectric thin films and nanowires to determine the frequency regime for a measurable temperature and voltage response to an applied alternating current. The lower bound for the high frequency requirement was found to depend on nanostructures' geometry (i.e. thin film thickness or nanowire diameter) and thermal properties. It is shown that reducing the thickness of the films or the diameter of the nanowires increases the lower bound for the high frequency regime, often imposing challenging conditions for the measurement of zT. Although heat losses from the sample surface due to natural convection have little effect on measured zT, the electrical contact resistance between the thermoelectric material and the contact electrodes can be the source for large errors. These aspects should be taken into account when performing experiments to characterize zT using the Harman method.

A comparative study of cavitation models in a Venturi flow

This paper presents a numerical study of an aperiodic cavitation pocket developing in a Venturi flow. The mass transfer between phases is driven by a void ratio transport equation model. A new free-parameter closure relation is proposed and compared with other formulations. The re-entrant jet development, void ratio profiles and pressure fluctuations are analysed to discern results accuracy. Comparisons with available experimental data are done and good agreement is achieved.

RANS modelling of a lifted H2/N2 flame using an unsteady flamelet progress variable approach with presumed PDF

An unsteady flamelet/progress variable (UFPV) approach is used to model a lifted H2/N2 flame in a RANS framework together with presumed PDF. We solve the unsteady flamelets both in physical space and in mixture fraction space. We show that in the former case, the scalar dissipation rate profile strongly varies in time (while it is assumed to be fixed in time in the latter). However, this does not result in significant qualitative differences in the corresponding flamelet libraries. The progress variable is carefully defined, including both the main combustion product (H2O) and a key radical species in ignition process (HO2). The presumed-PDF model is proposed in terms of the non-normalised progress variable, without assuming its statistical independence with mixture fraction. We introduce a modelled transport equation for the mean progress variable which is consistent with the basic underlying UFPV assumption, derived from the Lagrangian flamelet model. The influence of different model parameters on the results for the mean temperature and mean species mass fractions and their fluctuations is discussed. Good results are obtained for the conditions of the considered lifted flame where detailed experimental data is available. However, at low coflow temperature the modelled flame lift-off height is shorter than expected.

Electron-transfer kinetics and electric double layer effects in nanometer-wide thin-layer cells.

Redox cycling in nanometer-wide thin-layer cells holds great promise in ultrasensitive voltammetric detection and in probing fast heterogeneous electron-transfer kinetics. Quantitative understanding of the influence of the nanometer gap distance on the redox processes in the thin-layer cells is of crucial importance for reliable data analysis. We present theoretical consideration on the voltammetric behaviors associated with redox cycling of electroactive molecules between two electrodes separated by nanometer widths. Emphasis is placed on the weakness of the commonly used Butler-Volmer theory and the classic Marcus-Hush theory in describing the electrochemical heterogeneous electron-transfer kinetics at potentials significantly removed from the formal potential of redox moieties and, in addition, the effect of the electric-double-layer on the electron-transfer kinetics and mass transport dynamics of charged redox species. The steady-state voltammetric responses, obtained by using the Butler-Volmer and Marcus-Hush models and that predicted by the more realistic electron-transfer kinetics formulism, which is based on the alignments of the density of states between the electrode continuum and the Gaussian distribution of redox agents, and by inclusion of the electric-double-layer effect, are compared through systematic finite element simulations. The effect of the gap width between the electrodes, the standard rate constant and reorganization energy for the electron-transfer reactions, and the charges of the redox moieties are considered. On the basis of the simulation results, the reliability of the conventional voltammetric analysis based on the Butler-Volmer kinetic model and diffusion transport equations is discussed for nanometer-wide thin-layer cells.

Estimation of the accuracy of the microwave FET equivalent circuit using the quasi-hydrodynamic model of electron transport

Computational methods are considered for the time- and frequency-domain simulations of a microwave power amplifier with a transistor built on a diamond-like semiconductor. The first method is based only on a two-dimensional model of the intrinsic transistor that includes the quasi-hydrodynamic model of electron transport and electric field equations. The second method, which is less accurate but much more computer-time-saving, is based on the intrinsic transistor large-signal lumped-element equivalent circuit model with the parameters and spline characteristics calculated by means of the abovementioned two-dimensional model. Using these two methods, the microwave parameters of the amplifier are calculated for frequencies varying from 15 to 90GHz. When using the equivalent circuit at frequencies of up to 60GHz, the calculation error (equal to the difference between the results of the time- and frequency-domain simulations) does not exceed 5% for the input impedance and 0.6dB for the transducer power gain.

New insights into self-heating in double-gate transistors by solving Boltzmann transport equations

Electro-thermal effects become one of the most critical issues for continuing the downscaling of electron devices. To study this problem, a new efficient self-consistent electron-phonon transport model has been developed. Our model of phonon Boltzmann transport equation (pBTE) includes the decay of optical phonons into acoustic modes and a generation term given by electron-Monte Carlo simulation. The solution of pBTE uses an analytic phonon dispersion and the relaxation time approximation for acoustic and optical phonons. This coupled simulation is applied to investigate the self-heating effects in a 20 nm-long double gate MOSFET. The temperature profile per mode and the comparison between Fourier temperature and the effective temperature are discussed. Some significant differences occur mainly in the hot spot region. It is shown that under the influence of self-heating effects, the potential profile is modified and both the drain current and the electron ballisticity are reduced because of enhanced electron-phonon scattering rates.

A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence

This paper puts forth a simplified dynamic eddy-viscosity subgrid-scale model for the vorticity transport equation which is employed in a large eddy simulation study of freely evolving isotropic two-dimensional turbulent flows. The dynamic parameter is averaged in space, thereby retrieving a spatially constant value which only varies in time. The proposed dynamic model is applied to a two-dimensional decaying turbulence problem in a square periodic box, which is a standard prototype of more realistic turbulent flows in the atmosphere and oceans, in order to eliminate any possible errors associated with the boundary conditions or mesh non-uniformities. Compared with high-resolution direct numerical simulations, the performance of the dynamic model is systematically investigated considering various filtering strategies by means of test filters. The effects of the computational resolution and the filtering ratio between the test and the grid filters are also studied by using a huge set of parameters.

Peculiarities of cosmic ray modulation in the solar minimum 23/24

AbstractWe study changes of the galactic cosmic ray (GCR) intensity for the ending period of the solar cycle 23 and the beginning of the solar cycle 24 using neutron monitors experimental data. We show that an increase of the GCR intensity in 2009 is generally related with decrease of the solar wind velocity U, the strength B of the interplanetary magnetic field (IMF), and the drift in negative (A < 0) polarity epoch. We present that temporal changes of rigidity dependence of the GCR intensity variation, before reaching maximum level in 2009 and after it, do not noticeably differ from each other. The rigidity spectrum of the GCR intensity variations calculated based on neutron monitors data (for rigidities > 10 GV) is hard in the minimum and near‐minimum epoch. We do not recognize any nonordinary changes in the physical mechanism of modulation of the GCR intensity in the rigidity range of GCR particles to which neutron monitors respond. We compose 2‐D nonstationary model of transport equation to describe variations of the GCR intensity for 1996–2012 including the A > 0 (1996–2001) and the A < 0 (2002–2012) periods; diffusion coefficient of cosmic rays for rigidity 10–15 GV is increased by ~ 30% in 2009 (A < 0) comparing with 1996 (A > 0). We believe that the proposed model is relatively realistic, and obtained results are satisfactorily compatible with neutron monitors data.

Modelling for isothermal cavitation with a four-equation model

In a recent study, an original formulation for the mass transfer between phases has been proposed to study one-dimensional inviscid cavitating tube problems. This mass transfer term appears explicitly as a source term of a void ratio transport-equation model in the framework of the homogenous mixture approach. Based on this generic form, a two-dimensional preconditioned Navier–Stokes one-fluid solver is developed to perform realistic cavitating flows. Numerical results are given for various inviscid cases (underwater explosion, bubble collapse) and unsteady sheet cavitation developing along Venturi geometries at high Reynolds number. Comparisons with experimental data (concerning void ratio and velocity profiles, pressure fluctuations) and with a 3-equation model are presented.

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.

Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges

Accurate thermal conductivity values are essential for the successful modeling, design, and thermal management of microelectromechanical systems (MEMS) and devices. However, the experimental technique best suited to measure the thermal conductivity of these systems, as well as the thermal conductivity itself, varies with the device materials, fabrication processes, geometry, and operating conditions. In this study, the thermal conductivities of boron doped single-crystal silicon microbridges fabricated using silicon-on-insulator (SOI) wafers are measured over the temperature range from 80 to 350 K. The microbridges are 4.6 mm long, 125 μm tall, and either 50 or 85 μm wide. Measurements on the 85 μm wide microbridges are made using both steady-state electrical resistance thermometry (SSERT) and optical time-domain thermoreflectance (TDTR). A thermal conductivity of 77 Wm−1 K−1 is measured for both microbridge widths at room temperature, where the results of both experimental techniques agree. However, increasing discrepancies between the thermal conductivities measured by each technique are found with decreasing temperatures below 300 K. The reduction in thermal conductivity measured by TDTR is primarily attributed to a ballistic thermal resistance contributed by phonons with mean free paths larger than the TDTR pump beam diameter. Boltzmann transport equation (BTE) modeling under the relaxation time approximation (RTA) is used to investigate the discrepancies and emphasizes the role of different interaction volumes in explaining the underprediction of TDTR measurements.

Joint statistics and conditional mean strain rates of streamline segments

Based on four different direct numerical simulations of turbulent flows with Taylor-based Reynolds numbers ranging from Reλ = 50 to 300 among which are two homogeneous isotropic decaying, one forced and one homogeneous shear flow, streamlines are identified and the obtained space curves are parameterized with the pseudo-time as well as the arclength. Based on local extrema of the absolute value of the velocity along the streamlines, the latter are partitioned into segments following Wang (2010 J. Fluid Mech.648 183–203). Streamline segments are then statistically analyzed based on both parameterizations using the joint probability density function of the pseudo-time lag τ (arclength l, respectively) between and the velocity difference Δu at the extrema: P(τ,Δu), (P(l,Δu)). We distinguish positive and negative streamline segments depending on the sign of the velocity difference Δu. Differences as well as similarities in the statistical description for both parameterizations are discussed. In particular, it turns out that the normalized probability distribution functions (pdfs) (of both parameterizations) of the length of positive, negative and all segments assume a universal shape for all Reynolds numbers and flow types and are well described by a model derived in Schaefer P et al (2012 Phys. Fluids24 045104). Particular attention is given to the conditional mean velocity difference at the ending points of the segments, which can be understood as a first-order structure function in the context of streamline segment analysis. It determines to a large extent the stretching (compression) of positive (negative) streamline segments and corresponds to the convective velocity in phase space in the transport model equation for the pdf. While based on the random sweeping hypothesis a scaling is found for the parameterization based on the pseudo-time, the parameterization with the arclength l yields a much larger than expected l1/3 scaling. A theoretical indication for this finding is given and a scaling of 〈|Δu∥l〉∝l2/3 is found from the DNS.

Mesh Resolution Effects in Simulating Unsteady Sheet Cavitation

We present simulations of the cavitating flow on a NACA0015 hydrofoil in homogeneous and constant inflow. The simulations are performed using an incompressible implicit LES methodology with cavitation modelling based on a one-fluid mixture approach combined with a transport equation modelling including source terms for the mass transfer between the phases. We compare the flow development and spectral content of lift oscillations with experimental results from the literature. The study shows that a good qualitative as well as quantitative agreement is possible but requires a high mesh resolution, primarily in the wall normal direction, to avoid spurious cavitation dynamics in the simulated flow.

Surveyed and modelled one‐year morphodynamics in the braided lower Tana River

AbstractField measurements and morphodynamic simulations were carried out along a 5‐km reach of the sandy, braided, lower Tana River in order to detect temporal and spatial variations in river bed modifications and to determine the relative importance of different magnitude discharges on river bed and braid channel evolution during a time span of one year, i.e. 2008–2009. Fulfilling these aims required testing the morphodynamic model's capability to simulate changes in the braided reach. We performed the simulations using a 2‐D morphodynamic model and different transport equations. The survey showed that more deposition than erosion occurred during 2008–2009. Continuous bed‐load transport and bed elevation changes of ±1 m, and a 70–188‐m downstream migration of the thalweg occurred. Simulation results indicated that, during low water periods, modifications occurred in both the main channel and in other braid channels. Thus, unlike some gravel‐bed rivers, the sandy lower Tana River does not behave like a single‐thread channel at low discharge. However, at higher discharge, i.e. exceeding 497 m3/s, the river channel resembled a single‐thread channel when channel banks confined the flow. Although the spring discharge peaks caused more rapid modifications than slower flows, the cumulative volumetric changes of the low water period were greater. The importance of low water period flows for channel modifications is emphasized. Although the 2‐D model requires further improvements, the results were nevertheless promising for the future use of this approach in braided rivers. Copyright © 2013 John Wiley & Sons, Ltd.

Chaos in semiconductor band-trap impact ionization

We introduce a new spatially-extended semiconductor carriers transport equation model, based on generation–recombination process of the band-trap impact ionization under a longitudinal electric field. By means of numerical studies, we demonstrate the existence of chaos. Also, we present many results such as, the lyapunov spectrum, the bifurcation diagram, the phase portrait and the Poincaré surface of section. In addition the basic electric circuit used is found to be helpful in the implementation of a simple and autonomous chaotic oscillator circuit. Furthermore, the obtained results are interesting in the way that they could be useful in avoiding of undesirable chaotic regime in some switching and memory electronic devices.

An explicit algebraic model for the subgrid-scale passive scalar flux

AbstractIn Marstorpet al. (J. Fluid Mech., vol. 639, 2009, pp. 403–432), an explicit algebraic subgrid stress model (EASSM) for large-eddy simulation (LES) was proposed, which was shown to considerably improve LES predictions of rotating and non-rotating turbulent channel flow. In this paper, we extend that work and present a new explicit algebraic subgrid scalar flux model (EASSFM) for LES, based on the modelled transport equation of the subgrid-scale (SGS) scalar flux. The new model is derived using the same kind of methodology that leads to the explicit algebraic scalar flux model of Wikströmet al. (Phys. Fluids, vol. 12, 2000, pp. 688–702). The algebraic form is based on a weak equilibrium assumption and leads to a model that depends on the resolved strain-rate and rotation-rate tensors, the resolved scalar-gradient vector and, importantly, the SGS stress tensor. An accurate prediction of the SGS scalar flux is consequently strongly dependent on an accurate description of the SGS stresses. The new EASSFM is therefore primarily used in connection with the EASSM, since this model can accurately predict SGS stresses. The resulting SGS scalar flux is not necessarily aligned with the resolved scalar gradient, and the inherent dependence on the resolved rotation-rate tensor makes the model suitable for LES of rotating flow applications. The new EASSFM (together with the EASSM) is validated for the case of passive scalar transport in a fully developed turbulent channel flow with and without system rotation. LES results with the new model show good agreement with direct numerical simulation data for both cases. The new model predictions are also compared to those of the dynamic eddy diffusivity model (DEDM) and improvements are observed in the prediction of the resolved and SGS scalar quantities. In the non-rotating case, the model performance is studied at all relevant resolutions, showing that its predictions of the Nusselt number are much less dependent on the grid resolution and are more accurate. In channel flow with wall-normal rotation, where all the SGS stresses and fluxes are non-zero, the new model shows significant improvements over the DEDM predictions of the resolved and SGS quantities.

Asymptotic preserving numerical schemes for a non-classical radiation transport model for atmospheric clouds

We present numerical schemes for the P1-moment and M1-moment approximations of a non-classical transport equation modeling radiative transfer in atmospheric clouds. In contrast to classical radiative transfer, the photon path-length is introduced as an additional variable and serves as pseudo-time in this model. Because clouds may have optically thick regions, we introduce a diffusive scaling and show that the diffusion limits of the moment models and the original equations agree. Furthermore, we show that the numerical schemes also preserve the diffusion asymptotics as well as the set of admissible and realizable states, both for the explicit and the implicit discretization of the pseudo-time variable. A source iteration-like method is proposed, and we observe that it converges slowly in the optical thick case, but a suitable initialization can help to overcome this problem. We validate our method in 1D and present simulation results in the 2D-case for real cloud data. Copyright © 2013 John Wiley & Sons, Ltd.