Turbulent Term Research Articles

Budget analysis of a pseudo-single-phase transport model for slurry flows

This study aims at understanding the influence of the various physical mechanisms involved in the transport of solid particles within slurry flows. The present model simulates such mixtures as pseudo-single-phase fluids. The approach is based on a constitutive equation, which accounts for the shear-induced particle migration. Two supplementary terms are added to this equation to account for particle buoyancy and turbulent dispersion, respectively. The present model is validated against experimental data published in the literature, and the influence of each mechanism is discussed in detail for two particle diameters $$d=125$$ and $$440 \, \upmu \mathrm{m}$$ and bulk Reynolds numbers $$\mathrm{Re}$$ ranging between 46,000 and 109,000. The detailed budget analysis of the present transport equation reveals that the terms accounting for the particle transport due to the viscosity variation and the particle collision frequency variation get preponderant in the near-wall regions. This last term is besides at the origin of the repelling phenomenon. The turbulent agitation term counterbalances the sedimentation effect. When the convective flux term is important in the bulk region, the flow tends to be homogeneous. The present model can be used confidently to model two-phase flows under certain multiphase flow regimes while requiring less computational efforts than other more complex two-phase models.

Analysis of a drag reduced flat plate turbulent boundary layer via uniform momentum zones

High spatial resolution particle-image velocimetry (PIV) and micro-particle tracking velocimetry (μ-PTV) measurements have been performed to analyze the flow structures in a turbulent flat plate boundary layer undergoing spanwise traveling transversal surface waves. The scope of this investigation is to examine the connection between friction drag reduction and the structural properties of the instantaneous flow fields manipulated by the surface wave. The experiments were conducted for a momentum based Reynolds number of Reθ=2250 at dimensionless wave amplitudes of A+=6, 7, 8, and 11, a wave period of T+=94, and a wave length of λ+=3738. Local drag reduction of up to 4.9% at 0.087 boundary layer thicknesses downstream of the moving surface was measured. The Reynolds shear stress in the logarithmic region (50≤y+≤250) is suppressed due to the surface waves, whereas the wall-normal velocity fluctuations are enhanced in the outer layer. The turbulent contribution term in the Fukagata, Iwamoto, and Kasagi (FIK) friction drag decomposition [18] is reduced by 2.7% due to the dampened Reynolds shear stress above the wave crest. The analysis of the large-scale uniform momentum zones (UMZs) indicates that the population of these zones above the wave trough is nearly identical compared to the non-actuated turbulent boundary layer, while above the wave crest the number of UMZs is decreased by 3.5%. The conditional statistics of the modal velocity based on the near-wall velocity fluctuation evidence that there are strong links between the near-wall flow events and the UMZs. The near-wall flow structures of high fluctuating intensity are less correlated to the large-scale UMZs due to the spanwise surface wave motion, which diminishes the momentum transfer from the outer large-scale energetic structures to the near-wall flow, and thus, leads to the friction drag reduction.

Roles of driven current locations on ETB and ITB based on three-field bifurcation concept

This work investigates the roles of external current source on the formation and effectiveness of an internal transport barrier (ITB) and an edge transport barrier (ETB) in fusion plasma using bifurcation approach. Thermal, particle and toroidal momentum transport equations are solved simultaneously for the spatiotemporal profiles of plasma pressure, density and toroidal velocity, respectively. The transport effects include neoclassical and turbulent terms with constant coefficients assumption. The turbulent suppression, leading to intrinsic formation of transport barriers, is driven by the magnetic shear and the flow shear. Residual stress effect is included in this work. Thermal, particle and torques sources are locally provided based on Gaussian shape distribution at plasma center, plasma edge and plasma center, respectively. The effects of off-axis driven current locations on ITB and ETB formations are investigated. In particular, width and height of ETB and ITB are shown to be affected by the source. It is found that off-axis of driven current can increase plasma temperature, density and toroidal velocity at its core because ITB is formed and expanded. However, size of ETB pedestal is slightly affected by the location of driven current. When the location of driven current is changed from r = 0.00 to 0.60, ITB width changes from r = 0.00 to 0.12 of plasma profile and ITB top formation location changes from r = 0.00 to 0.80.

Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzelet al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter$\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption,$\unicode[STIX]{x1D6EC}_{c}$values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form$\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$with the kinematic (incompressible) displacement thickness$\unicode[STIX]{x1D6FF}_{K}^{\ast }$is shown to be a valid parameter of the form$\unicode[STIX]{x1D6EC}_{c}$and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale,$\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the$\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$stress and thus also the wall shear stress$\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of$\text{d}L_{0}/\text{d}x$leads to palpable improvements.

Numerical study on bubble-liquid two-phase turbulent hydrodynamics in extremely narrow shape bioreactor

The main objective of this work was to determine the influence of the bubble-liquid two-phase turbulent hydrodynamics on cell culture in extremely narrow shape bioreactor. An improved second-order moment bubble-liquid turbulent model and built in-house calculation source code were developed to numerically simulate the hydrodynamics that related to cell damage. Two higher gas entrance velocities of 78.3 m/s and 104.4 m/s were employed and their effects on hydrodynamic parameters, such as bubble rising and liquid flow velocities, bubble normal and shear stresses, correlation of bubble-liquid normal stresses, turbulent kinetic energy and turbulent energy dissipation rate of bubble and liquid were investigated details. All increased with gas entrance velocities increase but failed to explain an experimental observation that higher cell death at jetting region. A new correlation definition, bubble-liquid two-phase turbulent energy production term was proposed to successfully elaborate it, as well as the effects of high gas entrance velocities. Simulation results showed turbulent energy production terms are the largest at near gas jetting regions in comparison to those of developed flow regions, which are in good agreements with experimental result. Furthermore, extremely narrow shape deteriorated the cell living environment.

Impact of frontal round jet on vortex synchronization control around a cylinder: a turbulence perspective

The present study demonstrates that a round turbulent jet issued from a cylinder surface towards the upstream against the current can be a controlling parameter for vortex synchronization (VSC) in the wake region (WR) of the vertical cylinder. The results depict that the VSC state can be reached when the jet excitation frequency and the natural shedding frequency (NSF) are almost equal, or the jet excitation frequency is double that of the NSF. Precisely for VSC case, the turbulent production and dissipation terms of the turbulent kinetic energy budget equation contribute majorly to the total energy at the reattachment region with shifting of energy from the pressure and the turbulent diffusion terms. The enhancement of intermittency in turbulence for the VSC cases is also pertinent.

Evaluation of transient effects in the pressure-time method

The pressure-time is a method for measuring the flow rate in closed conduits and is typically used in hydropower applications. The scope of the present paper is to examine the physics of flow during a pressure-time measurement using experimental data and two-dimensional numerical simulations. The Unsteady Reynolds-averaged Navier–Stokes (URANS) equations coupled with the low-Re k-ω SST turbulence model are employed for the simulations. The contributions of inertia, pressure gradient, viscous and turbulent shear stress terms are investigated in the flow during a pressure-time measurement. It is shown that away from the wall and in the initial moments of time, the turbulent shear stress is comparable with the pressure gradient. With increasing time, the contribution of the inertia term becomes progressively significant and comparable with the pressure gradient and turbulent shear stress terms. Close to the wall, both viscous and turbulent shear stresses are the dominant terms which are diminished by increasing the time.

The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions

The effects of incident shock strength on the mixing transition in the Richtmyer–Meshkov instability (RMI) are experimentally investigated using simultaneous density–velocity measurements. This effort uses a shock with an incident Mach number of 1.9, in concert with previous work at Mach 1.55 (Mohaghar et al., J. Fluid Mech., vol. 831, 2017 pp. 779–825) where each case is followed by a reshock wave. Single- and multi-mode interfaces are used to quantify the effect of initial conditions on the evolution of the RMI. The interface between light and heavy gases ($\text{N}_{2}/\text{CO}_{2}$, Atwood number, $A\approx 0.22$; amplitude to wavelength ratio of 0.088) is created in an inclined shock tube at $80^{\circ }$ relative to the horizontal, resulting in a predominantly single-mode perturbation. To investigate the effects of initial perturbations on the mixing transition, a multi-mode inclined interface is also created via shear and buoyancy superposed on the dominant inclined perturbation. The evolution of mixing is investigated via the density fields by computing mixed mass and mixed-mass thickness, along with mixing width, mixedness and the density self-correlation (DSC). It is shown that the amount of mixing is dependent on both initial conditions and incident shock Mach number. Evolution of the density self-correlation is discussed and the relative importance of different DSC terms is shown through fields and spanwise-averaged profiles. The localized distribution of vorticity and the development of roll-up features in the flow are studied through the evolution of interface wrinkling and length of the interface edge, which indicate that the vorticity concentration shows a strong dependence on the Mach number. The contribution of different terms in the Favre-averaged Reynolds stress is shown, and while the mean density-velocity fluctuation correlation term, $\langle \unicode[STIX]{x1D70C}\rangle \langle u_{i}^{\prime }u_{j}^{\prime }\rangle$, is dominant, a high dependency on the initial condition and reshock is observed for the turbulent mass-flux term. Mixing transition is analysed through two criteria: the Reynolds number (Dimotakis, J. Fluid Mech., vol. 409, 2000, pp. 69–98) for mixing transition and Zhou (Phys. Plasmas, vol. 14 (8), 2007, 082701 for minimum state) and the time-dependent length scales (Robey et al., Phys. Plasmas, vol. 10 (3), 2003, 614622; Zhou et al., Phys. Rev. E, vol. 67 (5), 2003, 056305). The Reynolds number threshold is surpassed in all cases after reshock. In addition, the Reynolds number is around the threshold range for the multi-mode, high Mach number case ($M\sim 1.9$) before reshock. However, the time-dependent length-scale threshold is surpassed by all cases only at the latest time after reshock, while all cases at early times after reshock and the high Mach number case at the latest time before reshock fall around the threshold. The scaling analysis of the turbulent kinetic energy spectra after reshock at the latest time, at which mixing transition analysis suggests that an inertial range has formed, indicates power scaling of $-1.8\pm 0.05$ for the low Mach number case and $-2.1\pm 0.1$ for the higher Mach number case. This could possibly be related to the high anisotropy observed in this flow resulting from strong, large-scale streamwise fluctuations produced by large-scale shear.

Numerical analysis of nitrogen oxides in turbulent lifted H2/N2 cabra jet flame issuing into a vitiated coflow

Abstract This paper gives an in-depth insight into NOX (NO, NO2, and N2O) formation of H2/N2 turbulent Cabra jet flame issuing into a hot vitiated coflow. The joint composition probability density function (PDF) was employed to model the combustion and to specify the characteristics of the flame (i.e., scalar variables, concentration of species etc.). The turbulent transport term was modelled by Reynold-Average-Naiver-Stokes (RANS) SSG and molecular mixing was modelled by modified curl model. A combustion mechanism including 13 species and 34 reactions was employed to define the thermochemical state of the flame. The chemical reaction terms were resolved and accelerated by In Situ Adaptive Tabulation (ISAT). The simulation was performed at different equivalence ratios (ER), fuel jet nitrogen content ( Y N 2 , C ), coflow ( T C ) and jet temperatures ( T J ), coflow oxygen ( Y O 2 , C ) and water contents ( Y H 2 O , C ). Results reveal NOX is composed of 30% NO2 and 70% NO in the burner. Reaction rate analysis at different operating points in the ignition kernel demonstrates that N + O H ⇌ N O + H and N O 2 + H ⇌ N O + O H are dominant reactions in NO formation, while N O + H O 2 ⇌ N O 2 + O H is the main reaction in NO2 formation.

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles – II. Contribution of the turbulent term and the potential of the outer shells

In this paper we continue to investigate the energy conservation equation obtained in our previous work. We set ourselves three new goals. The first one is to rewrite the main equations in terms of density profile in order to give more physical insight. The second one is to investigate the significance of two new terms in the energy conservation equation. They originate from the gravity of the outer shells of cloud and the masses outer to the cloud, respectively. The third goal is to investigate the main equation in the case when the kinetic turbulent term scales according to Larson's law and it is independent, formally, of the accretion, in contrast to the previous work. The combination of supersonic turbulence and spherical symmetry raises a caveat which is commented in our conclusions. We obtained two solutions for the density profile. They scale with slopes -2 and -3/2, respectively. The energy balance for the second solution is the same as in the previous paper: this is a free-fall. For the first solution there are two cases. The first one: if the turbulent term does not scale, then it could be important for the energy balance of the cloud. The second one: if the turbulent term does scale, then it is not important for the energy balance of the cloud. The two new gravitational terms don't affect the existence of the two solutions, but the gravitation of the outer masses calibrate the energy balance for the first solution.

Numerical investigation of auto-igniting turbulent lifted CH4/air jet diffusion flames in a vitiated co-flow using a RANS based stochastic multiple mapping conditioning approach

Numerical simulations of auto-igniting turbulent lifted jet diffusion flames of CH4/air fuel issued into a vitiated coflow of lean combustion products of H2/air are performed using Reynolds-averaged Navier-Stokes (RANS) based stochastic multiple mapping conditioning (MMC) approach. A two-dimensional axisymmetric formulation is used to model the fluid flow, where the gas-phase turbulence terms are closed using the standard two-equation k-ε turbulence model with a modified set of constants. A reduced chemical mechanism ARM2 is used which consists of 19 species and 15 reactions derived from the GRI 3.0 mechanism. In MMC, the concept of mapping function is used, which approximates the cumulative probability distribution of the major scalar, namely mixture fraction for nonpremixed combustion. The corresponding variance of the major scalar is modelled by choosing a standard implementation of the major mixing time scale τϕ modelled in terms of the turbulent time scale as τϕ=τt/Cϕ. For all simulations reported herein, the same major mixing time constant Cϕ=3.0 is used. Additionally, in MMC, a minor mixing time scale τmin is introduced which controls fluctuations of scalars relative to the major fluctuations via the minor mixing time constant, Cmin. Three different values of Cmin=(τmin/τϕ)=0.25,0.35and0.50 are used and the corresponding ratios of minor to turbulent time scales are τmin/τt=0.083,0.116 and 0.166, respectively. The conditional and unconditional reactive scalar fields are found to be highly dependent on the choice of Cmin and hence the ratio of the minor and major mixing time scales. The numerical results are thoroughly validated against the experimental measurements. The variation in lift-off height is found to be in good agreement with the experimental data for the entire range of coflow temperature for Cmin=0.25. Also, the predicted conditional and unconditional scalar fields from the present RANS-MMC model shows an excellent agreement with the experimental measurements.

Calculation of cavitation evolution and associated turbulent kinetic energy transport around a NACA66 hydrofoil

The physical mechanism of flow unsteadiness is one of the key problems in cavitating flow. Significant efforts have been exerted to explain the cavitation-vortex interaction mechanism. As well, the process of kinetic energy transport during the evolution of unsteady cavitating flow must be elucidated. In this work, 2D calculations of cavitating flow around a NACA66 hydrofoil were performed based on the open source software OpenFOAM. The modified shear stress transport k-ω turbulence model, which considers curvature and turbulent eddy viscosity corrections, was employed to close the governing equations. The Schnerr-Sauer cavitation model was adopted to capture the cavitation phase change process. Numerical results showed reasonable consistency with the results of the experiments conducted by Leroux et al. (2004). The results showed that cavitation promotes turbulence intensity and flow unsteadiness around the hydrofoil. During the attached sheet cavity growth stage, high-value regions of turbulent kinetic energy are located substantially at the interface of the cavity, particularly at the rear portion of the cavity region. During the cloud cavity shed-off stage, the cavity begins to break off and the maximum value of turbulent kinetic energy is observed inside the shed cavity. Finally, the influence of cavitation on the turbulence intensity is illustrated using the turbulent kinetic energy transport equation, which shows that the pressure diffusion and turbulent transport terms dominate as cavitation occurs. In addition, cavitation promotes turbulence production and increases dissipation with fluid viscosity and flow unsteadiness. The viscous transport term only acts in the cavitation shedding stage under large-scale vortex shedding. Overall, these findings are of considerable interest in engineering applications.

Turbulent mixing and dispersion mechanisms over flexible and dense vegetation

The present study investigates flow turbulence and dispersion processes in the presence of flexible and dense vegetation on the bed. The turbulent dispersion coefficients and the terms of the turbulent kinetic energy equation are determined by using data collected in a straight laboratory channel with living vegetation on the bed. Results show that the turbulent integral lengths assume an order of magnitude comparable to the stems’ characteristic dimension independently by the direction and the turbulence assumes an isotropic behavior. The coefficients of dispersion have a trend similar to that of the turbulent lengths and assume low values in the longitudinal, transversal and vertical directions. Results also show that, in the mixing layer, the shear and wake turbulence production terms balance the dissipation; the turbulent diffusion term also assumes low values and its sign varies along the vertical indicating a transport of turbulent energy both from the vegetation to the free surface and from the free surface to vegetation.

Challenges in Modeling of Turbulence in the Tip Region of Axial Turbomachines

The flow and turbulence in turbomachines are characterized by spatially and temporally nonuniform strain rate fields and tendency to develop partially understood large-scale instabilities. Consequently, the applicability of popular Reynolds stress models in Reynolds-averaged Navier-Stokes simulations of turbomachinery flows is questionable and requires validation under relevant conditions. Experimental studies performed in the Johns Hopkins University optical refractive index-matched facility have investigated the complex flow and turbulence in the blade tip region of several axial turbomachines, including two waterjet pumps and an aviation compressor. The comprehensive databases obtained for different flow conditions and tip geometry using high-resolution particle image velocimetry are used in this article to examine the characteristics of turbulence in the vicinity of the tip leakage vortex (TLV). The results reveal several common features in the spatial distribution of the extremely anisotropic Reynolds stress tensor, suggesting that there are similarities in the mechanisms involved among the different machines. Of the quantities that could be measured accurately, both the local production and mean-flow advection rates appear to govern the evolution of turbulence in the passage. The dissipation rate also appears to be a major factor, but it cannot be measured accurately because of its dependence on motions at small scales that are not resolved by the measurements. The turbulent transport terms are important only in limited cases and locations. The strain rate tensor components, which appear to play primary roles in the production of turbulent kinetic energy (TKE), display common features in the spatial distributions of regions with high contraction, extension, and shear under different conditions. Some but not all of the inhomogeneity and anisotropy in the distributions of Reynolds stresses can be related to the corresponding local production rates. There is disagreement near the TLV core, where the persistent presence of multiple interacting vortices contributes significantly to the elevated TKE there. Lack of a clear functional correlation between the Reynolds stresses and mean strain rates is ubiquitous in all cases, resulting in widely spatially varying positive and negative values for the eddy viscosity. However, surprisingly, results from different machines and conditions have similar spatial distributions of individual stress and strain rate components and, accordingly, the eddy viscosity.

Effect of the turbulent contribution of the interfacial momentum transfer on the bubbles dynamics and void fraction distribution in vertical bubbly jets

A new formulation of the interfacial momentum transfer in two-fluid model for bubbly flows is presented and implemented in a CFD code. The main feature of the interfacial momentum closure lies in an explicit formulation of the turbulent contribution of the added mass force. The two-fluid model with the proposed closure of the momentum interfacial transfer is used to predict vertical bubbly jets. The numerical results show that the turbulent contribution of the added mass force greatly affects the dynamics of the bubbles and the gas distribution. The turbulent contribution of the added mass force has two components: a non-linear turbulent term and a convective acceleration associated to the drift velocity. Each of these turbulent terms can oppose the gravity effect. The simultaneous effects of the two turbulent terms provide an explanation to the deceleration of the bubbles as well as the negative relative velocity reported in the experimental data obtained in vertical bubbly jets. The improvements of the slip velocity prediction appear to have a great effect on the prediction of the lateral void fraction distribution.

Modelling of a planar impinging jet at unity, moderate and low Prandtl number: Assessment of advanced RANS closures

The numerical simulation of turbulent heat transfer in complex industrial flows represents a major challenge for RANS models. The impinging jet configuration is a popular test case for turbulence models, due to both the challenging nature of the flow field for the RANS approach and its widespread use in industrial applications. As a consequence, a large number of studies in the literature is dedicated to the assessment of a broad variety of turbulence models in this configuration. In particular, a significant effort has been put into the assessment of different closures for the turbulent momentum flux. In contrast, relatively little attention has been paid to the modelling of the turbulent heat flux term, and the classical Reynolds analogy is almost universally employed for this purpose despite its well-known limitations. Nevertheless, recently there has been a growing interest towards the development and assessment of more advanced closures for the turbulent heat flux. In this context, in the present work six turbulence models relying on different closures for both the turbulent momentum and heat fluxes have been used to simulate a planar impinging jet at unity, moderate and low Prandtl number and thoroughly assessed against a recently published reference DNS database. It is shown that the use of an advanced differential closure for the Reynolds stresses can result in an improvement in the prediction of the flow field. This, in turn, directly results in a more accurate prediction of the mean temperature at unity Prandtl number when the Reynolds analogy is employed for the closure of the turbulent heat flux. On the other hand, the inadequacy of the latter approach appears evident at low Prandtl values, and the necessity to account at least for the variability of the turbulent Prandtl number is demonstrated. It is then inferred that the most promising approach for such complex cases is represented by the combined use of anisotropic models for both the turbulent flow and the thermal fields.

Application of compressible Reynolds-averaged governing equations to turbulent mixed convection in supercritical fluids in heated vertical tubes

Accurate estimation of thermal-hydraulic characteristics of supercritical flows has long been an attractive but elusive subject to many researchers in spite of tremendous effort devoted to the development of suitable turbulence models. One of the key reasons for the difficulty is a lack of measured turbulence data, which might have been used to formulate adequate turbulence models suitable for highly buoyant fluids. Turbulence models are typically based on the log-law, while the velocity profile in buoyant fluids substantially deviates from the log-law because of significant density variation in a turbulent boundary layer. In this paper, axisymmetric compressible Reynolds-Averaged governing equations were employed together with the property-dependent turbulent Prandtl number to reproduce experimental data representing heat transfer deterioration and consequential sudden temperature increase. The additional turbulence terms associated with turbulent mass flux appeared in the governing equations were modeled using the simple gradient diffusion hypothesis (SGDH). The proposed model successfully reproduced the experimental data. The various turbulence properties are presented and discussed.

Hybrid modeling of flows over submerged prismatic vegetation with different areal densities

In the modeling of vegetated flows an efficient approach is to solve the Double Averaged Navier Stokes (DANS) equations, which are obtained from the spatial and temporal averaging of the Navier Stokes equations. The resistance effects of vegetation are modeled by a drag force density term with an empirical bulk drag coefficient, as well as by turbulence terms characterized by a length scale parameter. These empirical parameters are dependent on the areal density of vegetation and the spatial distribution pattern of vegetation elements and have seldom been studied. In this work the effect of spatial distribution of vegetation elements on the bulk drag coefficient is investigated by computing explicitly the flows around the vegetation elements. The results show that the bulk drag coefficient increases with the longitudinal vegetation element spacing, decreases with the lateral vegetation element spacing and can have multiple values for a given areal density of vegetation. In the DANS model the vegetation induced turbulence is simulated by a novel k-ε type model embracing an empirical length scale parameter. The length scale parameters are calibrated against previous experiments and a new set of experiments with high areal density of vegetation. The DANS model is subsequently verified by two cases with the same vegetation density and different distribution patterns.

NUMERICAL STUDY OF THE WIND TURBINE WAKE FLOW AND EFFECTS OF THE INFLOW TURBULENCE


 
 
 Considering the fact that wind turbines operate at the bottom of the atmospheric boundary layer (ABL) where the turbulence is at a high level, and the difficulty of mesh generation in the fully modelled numerical simulation. It is necessary to carry out researches to study the wake flow of wind turbines with consideration of the inflow turbulence. Therefore, a numerical method generating turbulence was proposed and the results show good agreement with those in experiment, based on which the flow fields in the wake of a wind turbine at two tip speed ratios were examined in detail through three actuator methods, namely, ADM, ADM-R and ALM. The performances of these methods were studied and the error sources for each method are clarified. Moreover, the computational efficiency was revealed and the influencing factor for the efficiency is concluded. Besides, the equilibrium relation of the N-S equation in the wake is revealed, which provides a theoretical basis for the optimal arrangement of the wind turbine. It shows that the mean velocity and fluctuating velocity vary greatly near the wind turbine, and become stable gradually away from the wind turbine. The results of ALM method show the best agreement with the experiment. At near wake region, the turbulent stress term, pressure gradient term and convection term mainly contribute to the equation equilibrium, and convection term is in equilibrium with the turbulent stress term at far wake. The results of ALM method are the most accurate and the most time consuming.
 
 

The Broyden method applied for the analysis of two-phase flow in a BWR fuel bundle based on the drift-flux model

Boiling flows in a BWR rod bundle is studied using the Drift Flux Model solved by the Broyden method. Four constitutive equations in the drift flux model plus auxiliary lateral momentum equations are discretized via the mesh staggered finite volume method. Then, the Broyden method is invoked for solving the resulted nonlinear system of equations. Accurate forms and fast techniques are employed for the solution of equations, especially for vapor generation, drift velocity, exchanges mass, energy and momentum among sub-channels. It was found that the Broyden method used in this study can be much faster in comparison with the Newton method solved through either the inverse Jacobian matrix or the LU factorization of Jacobian matrix. As a major objective, the change in the outlet void fraction is investigated as a function of inlet mass flux, inlet subcooling, and wall heat flux. Important changes e.g. outlet mass flux vs. inlet mass flux and void fraction are analyzed in different sub-channel positions. In comparison, the approach adopted in this article shows better compatibility with the experimental data than other similar works. Results are in generally good agreement with the outcome of F-COBRA-TF code, too, with partial superiority in a number of sub-channels. Also, it is shown that the accurate solution of constitutive equations especially for void drift and turbulent mixing terms that transfers mass, energy and momentum between sub-channels are major contributors to the aforementioned superiority.