Fully-developed Flow Research Articles

DNS of turbulent low Mach channel flow under asymmetric high temperature gradient: Effect of thermal boundary condition on turbulence statistics

Direct Numerical Simulations have been performed for a fully-developed low Mach turbulent flow of an ideal gas with thermo-dependent viscosity and thermal conductivity in a flat channel at mean friction Reynolds number Reτ=180 submitted to asymmetric heating with a wall temperature ratio T2/T1=2. Mean and turbulent statistics of the flow have been studied and compared for two different thermal boundary conditions: fixed temperatures on the one hand and fixed heat flux densities on the other hand. The influence of the boundary condition type is studied. Temperature variance is particularly impacted by this choice and exhibits asymmetric profiles with different behavior depending on the boundary condition.

Biomass pyrolysis in fully-developed turbulent riser flow

This work presents a numerical study of biomass pyrolysis in turbulent riser flow. Eulerian–Lagrangian simulations of unbounded sedimenting gas-solid flows are performed to isolate the effects of particle clustering on the production of syngas and tar. This configuration provides a framework to resolve the relevant length- and time-scales associated with thermal, chemical and multiphase processes taking place in the fully-developed region of a circulating fluidized bed riser. A four-step kinetic scheme is employed to model the devolatilization of biomass particles and secondary cracking of tar. Two-way coupling between the phases leads to clusters of sand particles that generate and sustain gas-phase turbulence and transport biomass particles. Neglecting the heterogeneity caused by clusters was found to lead to a maximum over-prediction of syngas yield of 33%. Further, it was found that two-dimensional simulations over-predict the level of clustering, resulting in an under-prediction of syngas and tar yields.

Heat transfer characteristics and entropy generation of electroosmotic flow in a rotating rectangular microchannel

This study aims to investigate thermal transport characteristics and analyze entropy generation of thermally fully-developed electroosmotic flow (EOF) in a rotating rectangular microchannel subject to constant wall heat flux. In the two-dimensional rectangular domain, the solutions for electric potential and flow velocity are obtained in terms of eigenfunction series by means of separation of variables technique, and the temperature field, which takes into consideration the effects of heat convection, Joule heating and viscous dissipation, is numerically solved. Results are generated to show the influences due to various factors, including rotational frequency, depth/width ratio of the rectangular channel, distribution of zeta potentials, strength of Joule heating and magnitude of wall heat flux, on the thermal transport characteristics. In particular, how the Nusselt number and the entropy generation vary with these factors are explored in details. To pursue optimization in energy utilization, an optimal aspect ratio is found at which the minimum entropy generation can be achieved. We believe that the findings in the present study will be useful in the design of energy efficient micro-systems which utilize the dual electrokinetic and centrifugal pumping effects.

Solution of Darcy–Brinkman–Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach

The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy–Brinkman–Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters’ influence on the velocity distributions. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10−5. The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it prevails with regards to giving the required answer for vast estimations of Forchheimer number when shooting technique fails to do as such. The technique can be effortlessly utilized in some other sporadic cross-area channel.

Neutronics modeling of bubbles in bubbly flow regime in boiling water reactors

Abstract This study mainly focused on the neutronics modeling of bubbles in bubbly flow in boiling water reactors. The bubble, ring and homogenous models were used for radial void fraction distribution. Effect of the bubble and ring models on the infinite multiplication factor and two-group flux distribution was investigated by comparing with the homogenous model. Square pitch unit cell geometry was used in the calculations. In the bubble model, spherical and non-spherical bubbles at random positions, sizes and shapes were produced by Monte Carlo method. The results show that there are significant differences among the proposed models from the viewpoint of physical interaction mechanism. For the fully-developed bubbly flow, k inf is overestimated in the ring model by about 720 ± 6 pcm with respect to homogeneous model whereas underestimated in the bubble model by about −65 ± 9 pcm with a standard deviation of 15 pcm. In addition, the ring model shows that the coolant must be separated into regions to properly represent the radial void distribution. Deviations in flux distributions principally occur in certain regions, such as corners. As a result, the bubble model in modeling the void fraction can be used in nuclear engineering calculations.

Effect of Debris on the Local Scour at Bridge Piers

Scour is one of the most recurrent causes of failure of bridge structures in alluvial rivers. There is a variety of formulas for the assessment of bridge scour characteristics and for the design of suitable protection. Nevertheless, current approaches neglect the effect of debris carried by natural streams during floods, even when the accumulation of debris can extremely amplify the action of scouring processes. Until now, very limited efforts have been conducted to systematically investigate these effects. The present study focuses on the effect of debris on the maximum clear-water scour depth at cylindrical piers inserted in uniform, fully-developed turbulent flows in wide rectangular channels with flatbed composed of uniform, non-ripple forming sand. For these purposes, an experimental campaign was carried out by performing 17 long-duration (td = 7 days) experiments. The experimental tests were performed in the hydraulic structures channel at the University of Beira Interior. The channel was 0.83 m wide, 12.0 m long and 1.0 m deep. In the central reach of the flume, a 3.0 m long and 0.30 m deep recess exists where scour is free to develop. The experiments were carried out with a cylindrical pier with 0.05 m diameter and two boxes, each with debris of different dimensions, either of triangular or rectangular shape. The tests were carried out with constant approach flow depth, d = 0.15 m, and average approach flow velocity, U, approximately equal to the average approach flow velocity for the threshold condition of sediment entrainment, Uc ~ 0.31 m/s. For this velocity, the scour depth can be expected to be maximal. The experiments will give a special focus to the development of scour hole as the accumulated debris increase. Moreover, the experimental results will be compared with a reference experimental run without debris, so that the increments on scour depth due to the single debris clusters of different characteristics will be obtained and discussed. The following conclusions were obtained: i) The shape and position of the debris accumulation have a strong influence on the final scour depth. Debris placed on the bottom, upstream of the bridge pier, with a triangular shape, does not induce any increase in scour depths, the values are practically the same as the one obtained for the reference pier (without debris); ii) The method suggested by [3], as modified by [6], performed well, replicating the main trends observed in the experiments; and the influence of the relative submerged ratio of the debris on the scour depth, followed the trend observed previously by [8], with an increasing scour depth up to a critical value of the ratio, and then decreasing scour for ratios higher than this critical value.

Turbulence in a Localized Puff in a Pipe

We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about two pipe diameters long.

Eddy Viscosity and Velocity Profiles in Fully-Developed Turbulent Channel Flows

In this study, we present eddy viscosity formulations based on analytical solutions for turbulent kinetic energy (TKE) in fully-developed turbulent channel flows. Mean streamwise velocities are obtained by solving the momentum equation with the proposed analytical eddy viscosity formulations. Our results were validated by comparisons with DNS data of fully-developed turbulent channel flows for 300 < Reτ < 2000 (where Reτ denotes the friction Reynolds number defined by the friction velocity uτ, kinematic viscosity ν and the channel half-width δ). Our method allows accurate description of mean streamwise velocity profiles and turbulent shear stress outside the log-law layer, in the viscous and buffer layers and in the outer region. The aim of this study is to provide simple analytical tools for turbulent channel flow applications.

Local velocity scaling in upward flow to tooth impeller in a fully turbulent region

The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV). The experiments were carried out in a fully baffled cylindrical flat bottom vessel 400 mm in inner diameter agitated by a tooth impeller 133 mm in diameter. Distilled water was used as the agitated liquid. The velocity fields were investigated in the upward flow to the impeller for three impeller rotation speeds – 300 rpm, 500 rpm and 700 rpm, corresponding to a Reynolds number in the range 94 000 &lt; Re &lt; 221 000. This means that fully-developed turbulent flow was reached. This Re range secures the fully-developed turbulent flow in an agitated liquid. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller Reynolds number. On the basis of the test results the spatial distributions of dimensionless velocities were calculated. The axial turbulence intensity was found to be in the majority in the range from 0.4 to 0.7, which corresponds to the middle level of turbulence intensity.

Effects of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation

The effect of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation is investigated via systematic simulations of fully-developed turbulent channel flow. A total of 16 simulations are conducted using the open-source computational fluid dynamics software OpenFOAM®. Four densities of the computational mesh are considered, with four simulations performed on each, in turn varying in the amount of numerical dissipation introduced by the numerical scheme used for interpolating the convective fluxes. The results are compared to publicly-available data from direct numerical simulation of the same flow. Computed error profiles of all the considered flow quantities are shown to vary monotonically with the amount of dissipation introduced by the numerical schemes. As expected, increased dissipation leads to damping of high-frequency motions, which is clearly observed in the computed energy spectra. But it also results in increased energy of the large-scale motions, and a significant over-prediction of the turbulent kinetic energy in the inner region of the boundary layer. On the other hand, dissipation benefits the accuracy of the mean velocity profile, which in turn improves the prediction of the wall shear stress given by the wall model. Thus, in the current framework, the optimal choice for the dissipation of the numerical schemes may depend on the primary quantity of interest for the conducted simulation. With respect to the resolution of the grid, the change in the accuracy is much less predictable, and the optimal resolution depends on the considered quantity and the amount of dissipation introduced by the numerical schemes.

The role of clusters on heat transfer in sedimenting gas-solid flows

Abstract In this study, Eulerian-Lagrangian simulations of unbounded sedimenting gas-solid flows are conducted to quantify the effect of two-phase flow interactions on thermal transport. Cold particles are initially randomly distributed in a hot gas and settle under gravity for a wide range of volume fractions and Prandtl numbers. Two-way coupling spontaneously generates clusters of particles with a characteristic length scale much larger than the particle diameter, where fluctuations in particle concentration generate and sustain the carrier-phase turbulence. Simulations reveal that the gas phase is cooled relatively fast in the vicinity of clusters while hot spots persist in regions void of particles. This non-homogeneity was found to delay the overall heat transfer by as much as a factor of four compared to systems with a homogeneous particle distribution. To identify the mechanisms responsible for these variations, the spatially-averaged temperature equation is derived for statistically homogeneous (zero-dimensional) time-dependent particle-laden flows. It is found that the local fluid volume fraction-temperature covariance, referred to here as the fluid temperature seen by the particles, is the key term that accounts for the effect of clusters on heat transfer. Next, a framework for studying thermally fully-developed flows is presented, and statistics at steady state are reported. Consistent with previous work, local variations in the interphase heat transfer coefficient are found to vary by several orders of magnitude. Finally, a statistical modeling approach based on the concept of presumed-shape probability distribution functions is proposed.

Fluid-solid conjugate heat transfer modelling using weakly compressible smoothed particle hydrodynamics

To date, the Smoothed Particle Hydrodynamics (SPH) method which is mesh-less and fully Lagrangian in nature has been mainly applied in solving solid heat conduction problem and flow convection problem separately. In the current work, we have implemented the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method to solve internal flow problem involving fluid-solid Conjugate Heat Transfer (CHT). In order to ensure heat flux continuity across the interface separating two different materials, the harmonic mean value of thermal conductivities was adopted when modelling the heat transfer between fluid and solid bodies. On the modelling of non-isothermal hydrodynamically fully-developed channel flow, the Dirichlet inlet temperature boundary condition was implemented without having to build a separate temperature reset zone as proposed in the open literature. From the current study, we have found that the particle shifting algorithm is efficient to address the tensile instability problem encountered when simulating flow at high Reynolds number. The WCSPH results were compared against the established analytical and numerical solutions and good agreement was found. The idea of extending the WCSPH method to simulate the flow and heat transfer in parallel-flow and counter-flow heat exchangers was pursued in the current study as well.

Direct numerical simulations of premixed and stratified flame propagation in turbulent channel flow

Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully-developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the non-stratified, homogeneous mixture case while a U-shaped flame surface, whose leading-edge propagates upstream at the channel centreline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to Karlovitz number and it is shown that a nominal channel-flow Karlovitz number, Kachin, based on the wallnormal variation of canonical turbulence (tη = (ν/e) 1/2) and chemistry (tl = δl/Sl) time scales in fully-developed channel flow, compares well with an effective Karlovitz number, Kachfl, extracted from the present DNS datasets using conditionally sampled values of tη and tl in the immediate vicinity of the flame (0.1 < C < 0.3).

Steady Flow in a Patient-Averaged Inferior Vena Cava-Part I: Particle Image Velocimetry Measurements at Rest and Exercise Conditions.

Although many previous computational fluid dynamics (CFD) studies have investigated the hemodynamics in the inferior vena cava (IVC), few studies have compared computational predictions to experimental data, and only qualitative comparisons have been made. Herein, we provide particle image velocimetry (PIV) measurements of flow in a patient-averaged IVC geometry under idealized conditions typical of those used in the preclinical evaluation of IVC filters. Measurements are acquired under rest and exercise flow rate conditions in an optically transparent model fabricated using 3D printing. To ensure that boundary conditions are well-defined and to make follow-on CFD validation studies more convenient, fully-developed flow is provided at the inlets (i.e., the iliac veins) by extending them with straight rigid tubing longer than the estimated entrance lengths. Velocity measurements are then obtained at the downstream end of the tubing to confirm Poiseuille inflow boundary conditions. Measurements in the infrarenal IVC reveal that flow profiles are blunter in the sagittal plane (minor axis) than in the coronal plane (major axis). Peak in-plane velocity magnitudes are 4.9cm/s and 27cm/s under the rest and exercise conditions, respectively. Flow profiles are less parabolic and exhibit more inflection points at the higher flow rate. Bimodal velocity peaks are also observed in the sagittal plane at the elevated flow condition. The IVC geometry, boundary conditions, and infrarenal velocity measurements are provided for download on a free and publicly accessible repositoryat https://doi.org/10.6084/m9.figshare.7198703 . These data will facilitate future CFD validation studies of idealized, in vitro IVC hemodynamics and of similar laminar flows in vascular geometries.

Thermal-hydraulic performance of printed circuit heat exchangers with zigzag flow channels

Printed circuit heat exchanger (PCHE) is one of the leading candidates to be employed in advanced nuclear reactors and next generation concentrated solar power applications due to its compactness and capability for high-temperature, high-pressure applications with high effectiveness. In the current study, thermal-hydraulic performance of a zigzag-channel PCHE with high-pressure, high-temperature helium on both the hot and cold sides was simulated using a computational fluid dynamics (CFD) software package STAR-CCM + . Comparisons between the experimental data and CFD simulation results showed good agreement with some discrepancies in the pressure drop and heat transfer results. Local thermal-hydraulic performance analyses indicated that a fully-developed flow condition was not observed in the PCHE, mainly due to the nature of the zigzag channels, leading to periodic flow disturbance at each of the zigzag bends. It was also found that the local and global heat transfer coefficients were considerably different in the PCHE. Furthermore, thermal boundary conditions showed that the fluid temperatures and heat fluxes were not uniform along the azimuthal direction of a cross section of the flow channel and that the helium temperature distribution for each segment along the flow direction presented a wavy profile. However, the distribution of the helium bulk temperature along the flow direction was approximately linear. For the heat flux distributions, although they were significantly different at different segments, the trend of the heat flux for each segment along the fluid flow direction was similar. Finally, effects of several parameters on the thermal-hydraulic performance of the PCHE were investigated, including the fluid and solid thermophysical properties, radius of curvature at zigzag bends, channel configuration, channel length pitch in the flow direction, and zigzag pitch angle. No considerable enhancement in the Nusselt numbers was observed when the zigzag pitch angles were greater than 30°.

Extended validation of a developing post-dryout heat transfer correlation over a wide range of pressure conditions

Abstract The present paper deals with the validation of a post-dryout heat transfer correlation, which has been proposed by Nguyen and Moon (2015), to show its extended applicability to developing post-dryout region. It is also shown that the well-known film-boiling look-up table (LUT) method currently having limited application to fully-developed flow can be improved to extend its applicability to the developing post-dryout region. In order to show that the correlation can be utilized for nuclear reactor safety analysis, eight different sets of post-dryout data covering flow conditions both in both large break loss-of-coolant accident (LB LOCA) and prolonged station blackout (SBO) scenarios have been assessed. It turns out that the correlation predicts well the measured wall temperature with a total average error of 3.81% and a root-mean-square error of 13.46% in case of given CHF (dryout) condition. The prediction accuracy of the correlation is strongly influenced by how well the local vapor temperature and the CHF locations can be predicted.

Fully-Developed Flow in Semicircular and Isosceles Triangular Ducts With Nonuniform Slip

A modified Ritz method for solving nonuniform slip flow in a duct is applied to the semicircular duct and the isosceles triangular duct. These ducts are important in microfluidics. Detailed flow fields and Poiseuille numbers show the large effects of nonuniform slip. A rare exact solution for the semicircular duct with nonzero slip is also found.

Entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes

The entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes was numerically performed by using a Reynolds stress model. The simulations were conducted for a smooth tube and five cases of corrugated tubes with Reynolds number (Re) ranging from 10,020 to 40,060 at a constant wall temperature condition. The effects of corrugation pitch and height on the flow patterns as well as local thermal and frictional entropy generation are detailed in the near wall region. The results indicate that the local heat transfer entropy generation is significantly evident at the sub-layer region and the detached vortex region, and the local thermal entropy is improved with increases in the secondary flow. Local friction entropy generation is mainly located at the windward of the corrugation and the severely turbulent fluctuation region and is mainly induced by the velocity gradient. The average friction entropy generation exhibits an exponential growth, while the average heat transfer and the total entropy generation display a linear growth trend with increased Re. The average Bejan number (Be) exhibits an exponential decline, and the minimum value can reach 0.69. From a comprehensive viewpoint, it is optimal for the Re to be lower than 30,050. When Re <20,030, higher and dense corrugations are beneficial. When 20,030 < Re <30,050, low and spare corrugations are more optimal. Besides, the case with Hl/D = 0.08 is not recommended.

Early stages of agglomeration of adhesive particles in fully-developed turbulent pipe flows

We study how changes in particle response time and adhesiveness affect particles agglomeration in fully-developed turbulent pipe flows. For this purpose, particle-particle and particle-wall interactions are fully-resolved using the soft-sphere Discrete Element Method (DEM) modified to include adhesiveness due to van der Waals forces and electrostatic forces through JKR theory. The particulate phase is two-way coupled to the turbulent fluid phase, which is partly resolved using Large Eddy Simulations (LES). First, we validate the simulations by grid refinement and by comparing the statistics of the flow field to experiments in literature. Secondly, we vary the particle response time τp=ρpdp2/(18μ) and observe the largest agglomerates in terms of average number of particles per agglomerate to be formed by primary particles with intermediate Stokes numbers, e.g. Ste=τp/τe≈6.4 where τe=D/U is the eddy-turn over time or StL=τp/τL≈46.4 in terms of the integral time scale of the turbulent flow τL. Then we show how the total fraction of particles contained in agglomerates is almost constant up to Ste=6.4 after which there is a sudden drop in the fraction of particles contained in agglomerates. To investigate the transition from non-adhesive particles to highly adhesive particles, we vary the adhesiveness parameter Ad=γ/(ρpU2dp) to obtain particles that vary from non-adhesive particles where no agglomerates are formed to highly adhesive particles where more than 70% are contained in agglomerates. While varying the adhesiveness of the primary particles for a fixed particle response time, we observe three distinct regimes. For almost non-adhesive particles, the agglomerate number density is highest towards the centre of the pipe with a maximum at 0.2 < r/R < 0.3. Slightly more adhesive particles form an almost uniform agglomerate number density profile, while for highly adhesive particles there is a distinct peak in agglomerate number density at the wall where particles and agglomerates deposit.

Effect of the solvent viscosity on pure electro-osmotic flow of viscoelastic fluids

In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution (β3ɛDeκ2≤2/27), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan–Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model).