Transport Equation Model Research Articles

Influence of Residence and Scalar Mixing Time Scales in Non-Premixed Combustion in Supersonic Turbulent Flows

In high Mach number turbulent reactive flows, spontaneous ignition appears as a key ingredient for the stabilization of combustion. In our previous analyses devoted to such conditions, chemical kinetics as well as associated finite rate chemistry effects have already received considerable attention. However, the representation of flow time scales, such as residence and mixing time scales, still requires further work. The present modeling study is devoted to this peculiar point. Hence, a transport equation for the quantity of residence time is considered to evaluate the mean residence time associated with both oxidizer and fuel injection streams, while a modeled transport equation for the mean scalar dissipation rate (SDR) is considered to estimate the scalar mixing time scale. This allows us to improve the description of turbulent mixing, including the large-scale engulfment processes through the consideration of the residence time scale, as well as the small-scale molecular mixing processes, the intensity of which is set by the integral scalar (mixing) time scale. Some insights are gained from the analysis of the evolution of the different production terms that appear in the mean SDR transport equation. The model capabilities are evaluated through a comparison between numerical results and the data obtained from experimental studies devoted to supersonic coflowing jets of hydrogen and vitiated air. The first simulated test case corresponds to a detailed experimental database that includes Raman scaterring and laser-induced pre-dissociative fluorescence measurements. Albeit less documented, the second test case is retained to confirm the relevance of the proposed closure. Finally, the comparisons performed with the two distinct sets of experimental data establish that the main physical processes are well-described by the proposed approach.

Numerical simulation of cavitation around a two-dimensional hydrofoil using VOF method and LES turbulence model

In this paper simulation of cavitating flow over the Clark-Y hydrofoil is reported using the large eddy simulation (LES) turbulence model and volume of fluid (VOF) technique. We applied an incompressible LES modelling approach based on an implicit method for the subgrid terms. To apply the cavitation model, the flow has been considered as a single fluid, two-phase mixture. A transport equation model for the local volume fraction of vapour is solved and a finite rate mass transfer model is used for the vapourization and condensation processes. A compressive volume of fluid (VOF) method is applied to track the interface of liquid and vapour phases. This simulation is performed using a finite volume, two phase solver available in the framework of the OpenFOAM (Open Field Operation and Manipulation) software package. Simulation is performed for the cloud and super-cavitation regimes, i.e., σ=0.8, 0.4, 0.28. We compared the results of two different mass transfer models, namely Kunz and Sauer models. The results of our simulation are compared for cavitation dynamics, starting point of cavitation, cavity’s diameter and force coefficients with the experimental data, where available. For both of steady state and transient conditions, suitable accuracy has been observed for cavitation dynamics and force coefficients.

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.

Pollutant Effect on the Pedestrians and Bicyclists for the Different Setting of Bus Lanes in Urban Street Canyons

In order to study the pollutant effect on the pedestrians and bicyclists for the different setting of bus lanes, the numerical simulation of pollutant dispersion for isolated street canyon was conducted based on a two dimensional k-ε turbulence model and species transport equation. The simulation results fit well with the corresponding wind tunnel tests. The analysis result shows that the pollutant concentration at the leeward side is evidently higher than that of the windward side in the isolated street canyon. The pollutant concentration for the bicycle lane is obviously higher than that of the sidewalk near the ground at the leeward side. As the height increases, the pollutant concentration for the sidewalk is higher than that of the bicycle lane instead. The pollutant concentrations for the sidewalk and the bicycle lane are nearly the same, and almost no change with the height increases at the windward side. When the density of bus lane is low, the emission intensity of the bus lanes is lower than that of the vehicle lanes, and setting of outside bus lanes will have less pollution to the pedestrians and bicyclists. And when the density of bus lane is high, the emission intensity of the bus lanes is higher than that of the vehicle lanes, and setting of inside bus lanes will have less pollution to the pedestrians and bicyclists.

Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619–1627 (2011)]10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

Predicting the mean and RMS fields in subsonic hydrogen jet fires

In this paper two modelling approaches for predicting the mean and root mean squared (RMS) fields of turbulent hydrogen jet fires are evaluated. This is of interest if the turbulence–radiation interaction in such jets is to be modelled rigorously. One of the modelling strategies is based on calculating the variance of the fields of interest from a prescribed probability density function (PDF) and the second is to solve a modelled transport equation for field variances. In addition three different PDFs are considered: a β PDF, a clipped Gaussian PDF and a truncated Gaussian PDF. The different modelling strategies are evaluated using a number of experimental jet fires taken from the open literature. The conclusions of the study are the PDF approach for predicting the RMS fields are superior to solving a transport equation for the variance of the field variables of interest. Of the PDFs considered the β PDF and truncated Gaussian PDF give similar predictions of the jet fire structure being more accurate than the clipped Gaussian PDF.

Optimization and Numerical Simulation of the Flow Characteristics in SCR System

Selective Catalytic Reduction (SCR) DeNOx is the main flue gas denitrification technology, and the efficiency of SCR DeNOx system depends on whether the flue gas and ammonia distributions of the velocity and concentration fields are uniform in the reactor. Combined with the porous medium model and component transport equations, the numerical simulations were carried on for the SCR system of the 1000MW coal-fired station, and the velocity fields and concentration fields in different cases were obtained. The results showed that: the corner vane cascades and rectifier grills installed, the non-uniformity of flue gas velocity is less than 15% at the catalyst inlet within the reactor. Under the premise of the best flow field, the vortex mixers can ensure the full blending of the ammonia and flue gas in the reactor. The reliability of numerical simulation is verified through the cold model test, and then the design of the SCR system is guided effectively by the numerical simulations.

Computational Analysis of Flow Field on the Propulsion Nozzle of a Micro-Turbojet Engine

The purpose of this paper is to analyze the flow field on the propulsion nozzle of a micro-turbojet engine in function of the velocity. The 2D axisymmetric numerical simulation was made by using commercial software FLUENT?. A micro-turbojet engine was also employed for this study and it has the following characteristics: 100 N thrust, 130,000 rpm, mass flow rate 0.2650 kg/s, weight 1.2 kg. This engine is operating in Mexico city under the following conditions: P0, 78,000 Pa T0, 300 K, πc, 2.1 and a turbine entry temperature of 1000 K; it is considered that the nozzle is not choked. For this study, the viscous standard k- model, a semi-empirical model based on transport model equations for the turbulent kinetic energy (k) and its dissipation rate, is used. The transport model equation for k is derived from the ex-act equation, while the transport model equation for is obtained by using physical reasoning and bears resemblance to its mathematically exact counterpart. The employed grids are structured and the boundary conditions are obtained from a thermodynamic analysis. The results that are obtained show an increment of the velocity of 6.25% to the exit propulsion nozzle.

RANS canopy constants from weak turbulence regime

A Taylor series expansion was used to model the effect of forest canopies in the k − ϵ RaNS model transport equation for the turbulent kinetic energy. The model assumes that the turbulent kinetic energy is smaller than the kinetic energy of the mean flow (weak turbulence regime). Comparisons with large eddy simulations showed that a second-order approximation is able to account for 80% of the total canopy effect, while including third- and forth-order terms increases this value to 98

Tuning of dimensionless figure of merit via boundary scattering in In2O3-δ

In this paper, the dimensionless figure of merit (ZT) is optimized using the scattering in nanocrystals (NCs) of Zr-doped In2O3-δ. The effect of boundary scattering on the thermoelectric properties of the NCs was analyzed using the Boltzmann transport equation and Debye-Callaway model. A ZT map computed based on these theories determined the optimum material parameters to improve the transport properties of the NCs. A theoretically predicted enhancement in ZT of ∼40% can be reproduced experimentally, indicating that engineering of ZT using NCs is promising.

Classification of bubbles in vertical gas–liquid flow: Part 2 – A model evaluation

Three-fluid model along with two-group average bubble number density equations have been applied for the classification of bubbles in vertical gas–liquid flow. The current study focused on (i) consideration of three-fluid model transport equations governing the conservation of mass and momentum, (ii) formulation of two-group averaged bubble number density equations, (iii) classification of bubble interaction between spherical bubbles (Group-1) and cap bubbles (Group-2), (iv) consideration of source and sink terms via the proposal of Hibiki and Ishii (Nuclear Engineering and Design 202, 39–76) in the averaged bubble number density equations and (v) assessment by means of the experimental data sets at the bubbly-to-cap flow transition. Reasonable agreement has been achieved between the measured and predicted local and axial distributions of void fraction, interfacial area concentration (IAC) and volume equivalent bubble diameter. This preliminary assessment demonstrated the capability of the current approach in capturing the interfacial transport of bubbly to cap flow transition.

A Hybrid Transport Point-Kinetic method for simulating source transients in subcritical systems

Abstract This paper describes a novel hybrid technique for the solution of the time-dependent neutron transport equation in source switch-on transients. The Hybrid Transport Point Kinetics (HTPK) method is derived from a multi-collision description of the transport equation and is based on the observation that the external source mainly influences the first few neutron generations and, through collisions and multiplications, an ensemble behavior statistically emerges at higher order. The HTPK is designed to separately describe the propagation phenomenon from the ensemble response of the system, using both the rigorous transport equation and simplified kinetic models. Numerical simulations performed on a typical acceleration driven system configuration confirm the basic physical intuition of HTPK and show a significant gain in accuracy when compared to classical point kinetics. The proposed HTPK technique is also shown to be attractive because of its flexibility and competitive computational effort.

A transport equation model and diffusion approximation for the walk of whirligig beetles

The circular walk of whirligig beetles, in the absence of swarming behaviour, is described by a coupled system of transport equations. For this system, an approximate description is derived in the form of coupled damped wave equations and ultimately in the form of a scalar diffusion equation. The resulting diffusion coefficient is quite different from what one would get for a walk on straight lines with tumbling (as in bacterial motion).

A Comprehensive Modelling Approach for the Neutral Atmospheric Boundary Layer: Consistent Inflow Conditions, Wall Function and Turbulence Model

We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard \(k-{\varepsilon}\) turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the \(k-{\varepsilon}\) model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard \(k-{\varepsilon}\) model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant Cμ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.

Effects of non-uniform inlet boundary conditions and lift force on prediction of phase distribution in upward bubbly flows with Fluent-IATE

This study investigates the profile effects of the boundary conditions in two-phase flows, such as the inlet void fraction, interfacial area concentration, and phase velocity, on the predictions of flow behaviors downstream. Simulations are performed for upward air–water bubbly flows in a 48.3-mm inner diameter pipe by employing Fluent's two-fluid model together with an interfacial area transport equation (IATE) model. The IATE was developed in the literature to model the interfacial area concentration by taking into account the bubble coalescence and disintegration, and phase change effects. In this study, two types of inlet boundary conditions are considered, one being a uniform-profile boundary condition in the radial direction with area-averaged experimentally measured values while the other being a non-uniform profile condition based on the actual measured profiles at the inlet. The numerical predictions of downstream profiles of the phase distributions indicate that the two types of boundary conditions yield similar results for the downstream flow behaviors for the bubbly flow conditions investigated. In addition, the results with and without the lift force demonstrated that the lift force is essential to obtain accurate lateral phase distribution.

Convected level set method for the numerical simulation of fluid buckling

Abstract‘Fluid buckling’ is a phenomenon characterized mainly by the existence of fluid toroidal oscillations during flow. It appears when a high viscosity fluid flows vertically against a flat surface and may occur in industrial applications, as in injection molding of a propergol in complex‐shaped cavities. These coiling or folding oscillations appear during the mold filling stage, leading to air entrapment. To understand and to model this free surface flow problem, a convected level set method is proposed. First, a sinus filter is applied to the distance function to get a smooth truncation far from the interface. Second, the reinitialization is embedded in the transport equation model, avoiding it as a separate step during calculation. In order to validate the method, numerical results are presented on classical interface capturing benchmarks. Finally, results are shown on two‐dimensional and three‐dimensional viscous jet buckling problems. Copyright © 2010 John Wiley & Sons, Ltd.

Uncertainty Quantification of Turbulence Model Coefficients via Latin Hypercube Sampling Method

The article is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are obtained through experiments performed on elementary flows, and they are subject to uncertainty. In this work, the widely used k-ɛ turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and the rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for a flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise mean velocity in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly influenced by the uncertainties of the coefficients.

Influence of Interface Arrangement on Phonon Heat Transfer in Nanocomposites

The influence of interface arrangement in two- and three-dimensional silicon–germanium nanostructures on heat transfer is investigated by phonon Boltzmann transport equation model. For all nanocomposites studied here, the thermal conductivity decreases monotonically with increasing interface density and decreases monotonically with decreasing characteristic size. The interface density plays an important role to correlate the size effect of phonon transport. Another factor called structure efficiency, which taking into account both the structure dimensions and the interface arrangement, is also found to affect significantly the thermal conductivities of the nanocomposites. For the structure efficiency of a composite structure, it is found that the superlattice structure has the best structure efficiency in transverse transport and the compacted-wire structure has the best structure efficiency in longitudinal transport. High-dimensional (wire and particle) structures contain large interface density which is beneficial for reducing thermal conductivity. At the same characteristic size, the compacted-particle structure can yield the lowest thermal conductivity in transverse transport and the compacted-wire structure can yield the lowest thermal conductivity in longitudinal transport. The obtained results may provide essential information for the development of bulk-nanostructured thermoelectric devices.

Influence of Interface Arrangement on Phonon Heat Transfer in Nanocomposites

The influence of interface arrangement in two- and three-dimensional silicon–germanium nanostructures on heat transfer is investigated by phonon Boltzmann transport equation model. For all nanocomposites studied here, the thermal conductivity decreases monotonically with increasing interface density and decreases monotonically with decreasing characteristic size. The interface density plays an important role to correlate the size effect of phonon transport. Another factor called structure efficiency, which taking into account both the structure dimensions and the interface arrangement, is also found to affect significantly the thermal conductivities of the nanocomposites. For the structure efficiency of a composite structure, it is found that the superlattice structure has the best structure efficiency in transverse transport and the compacted-wire structure has the best structure efficiency in longitudinal transport. High-dimensional (wire and particle) structures contain large interface density which is beneficial for reducing thermal conductivity. At the same characteristic size, the compacted-particle structure can yield the lowest thermal conductivity in transverse transport and the compacted-wire structure can yield the lowest thermal conductivity in longitudinal transport. The obtained results may provide essential information for the development of bulk-nanostructured thermoelectric devices.

Transition prediction in transonic turbine configurations using a correlation-based transport equation model

The Menter correlation-based transition model has been implemented in the CFD code elsA. The model is a framework for taking into account laminar/turbulent transition effects into CFD simulations. The model has been evaluated on two-transonic turbine configurations experimented at the Von Karman Institute. The first case is the well-known 2D Nozzle Guide Vane LS89; the second test case is the CT3 stator/rotor configuration on which quasi 3D computations have been accomplished. Results obtained with the Menter transition model pointed out real improvements in terms of heat transfer predictions. The laminar zones and the transition onset are well-captured and the early transition situated on the rotor leading edge for the CT3 case is also well-produced.