Turbulent Production Rate Research Articles

Development of modeling and simulation of bubble‐liquid hydrodynamics in bubble column

AbstractIn the present work, the investigation on strategies to alleviate the cell death in terms of bubble‐liquid two‐phase hydrodynamics in bubble column was performed using the modeling and numerical simulation approaches. A multifluid bubble‐liquid turbulent model based on the second‐order moment algorithm was developed to predict turbulent hydrodynamics. In this model, the anisotropic characteristics of Reynolds stresses and the interactions between bubble and liquid phases are considered by means of the defined bubble‐liquid two‐phase fluctuation velocities correlation. Hydrodynamic parameters such as turbulent energy dissipation rate, the turbulent kinetic energy, the distributions of bubble normal and shear stresses, and the operation conditions of gas entrance velocity and height to diameter of column are accurately simulated. A proposed correlation named turbulent energy production rate is revealed successfully the higher cell death rate at the gas inlet regions that cannot be verified by the rest of the two‐phase hydrodynamics. Superficial gas velocity is the predominant influence on this value distribution as smaller the ratio of height to diameter of bubble column, which reduced by two order of magnitude under decreased by one level of gas velocity. Near inlet region with large height‐to‐diameter ratio, this value is always larger than those of small one.

Droplets in homogeneous shear turbulence

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

Transition control in a three-dimensional boundary layer at elevated free stream turbulence using dielectric barrier discharge

The results of an experimental study of the effect of dielectric barrier discharge (DBR) actuator on laminar-turbulent transition in a three-dimensional boundary layer under influence of elevated free-stream turbulence are presented. The travelling cross-flow instability modes are dominated in transition in a base configuration. Their characteristics do not depend on a spanwise position. The DBD-actuator that generated stationary cross-flow vortices with the predefined spanwise wavelength when turned on was capable to reduce a turbulent spots production rate in comparison to the base regime.

Parametrical study and turbulence analysis of high-speed flows around an open cavity using large eddy simulation

Large eddy simulation is used in this work to simulate the three-dimensional turbulent flow in an open cavity, with special attention paid to the parametrical effect and turbulence analysis. The effect of mesh resolution, the sub-grid model and the advection scheme on the resolved flow structure is discussed in detail. Then, the mechanism of flow-induced pressure fluctuation associated with the primary and secondary vortex in the shear layer is clarified quantitatively and qualitatively. Finally, the turbulent kinetic energy and turbulence production rate, the contribution of three components to total turbulence production rate and the main single contributor are analyzed systematically. The present simulations are performed for two Reynolds numbers and the results show that the flow is more turbulent with the increase in Reynolds number, but the general flow morphology is almost the same. It is expected that the basic founding is useful for understanding such similar flows and will provide some guidelines for controlling the vortex-induced flow instability in engineering applications.

Correlations for the Prediction of Intermittency and Turbulent Spot Production Rate in Separated Flows

Experimental data describing laminar separation bubbles developing under strong adverse pressure gradients, typical of ultra-high-lift turbine blades, have been analyzed to define empirical correlations able to predict the main features of the separated flow transition. Tests have been performed for three different Reynolds numbers and three different free-stream turbulence intensity levels. For each condition, around 4000 particle image velocimetry (PIV) snapshots have been acquired. A wavelet-based intermittency detection technique, able to identify the large scale vortices shed as a consequence of the separation, has been applied to the large amount of data to efficiently compute the intermittency function for the different conditions. The transition onset and end positions, as well as the turbulent spot production rate, are evaluated. Thanks to the recent advancements in the understanding on the role played by Reynolds number and free-stream turbulence intensity on the dynamics leading to transition in separated flows, guest functions are proposed in the paper to fit the data. The proposed functions are able to mimic the effects of Reynolds number and free-stream turbulence intensity level on the receptivity process of the boundary layer in the attached part, on the disturbance exponential growth rate observed in the linear stability region of the separated shear layer, as well as on the nonlinear later stage of completing transition. Once identified the structure of the correlation functions, a fitting process with own and literature data allowed us to calibrate the unknown constants. Results reported in the paper show the ability of the proposed correlations to adequately predict the transition process in the case of separated flows. The correlation for the spot production rate here proposed extends the correlations proposed in literature for attached (by-pass like) transition process, and could be used in γ–Reϑ codes, where the spot production rate appears as a source term in the intermittency function transport equation.

Profile features of dissipation rates of turbulence in Lake Taihu and possible mechanism

湍流不仅是导致物质、动量等在水-气交界面的交换、水柱内部输送的关键过程，也是促进浅水湖泊中底泥再悬浮及水生生态系统演变的驱动力；其中湍流动能耗散率（ε）不仅是描述湍流动能变化的关键物理量，也是刻画水体中湍流产生机制的关键过程.基于2017年10月29日-11月2日位于太湖梅梁湾采集的高频三维流速廓线和水温廓线观测资料，结合东山气象站同期的风场和辐射等气象资料，探讨太湖中ε的分布特征及其变化的可能机制.结果表明，0.7 m深度以下水平方向上ε介于10^-8~10^-7 m²/s³之间，比垂直方向大一个数量级左右.尽管大型浅水湖泊几何深度浅，但其ε的深度廓线依然存在典型的3层：ε随深度递减的风浪直接作用层，深度从水面至1.0 m左右；ε基本不随深度变化的常数层，分布区间为水深1.0~1.9 m；随后是ε随深度递减的底边界混合层.热力分层的强弱（垂向温差）、位置对常数层和底部边界中ε的贡献显著，甚至造成ε的常数层起始深度下移.本研究有利于进一步理解大型浅水湖泊的动力学过程及其对水生生态系统演变的驱动效应.;Turbulence is a key process regulating the exchange of matter and momentum not only across the water-gas interface, but also within water columns. It is also a driving force for the resuspension of sediments and the evolution of shallow lake ecosystems. The dissipation rate of the turbulent kinetic energy (ε) is a key physical quantity which depicts the evolution of the turbulent kinetic energy, and discriminates turbulence production rate from mechanisms in water bodies. Based on observations for profiles of three-dimensional currents using Acoustic Doppler Current Profiles (ADCP) and records on water temperature and the wind field in Lake Taihu from October 29, 2017 to November 2, 2017, the profile features of ε in this large-scale shallow lake were explored. The horizontal ε is about 10^-8-10^-7 m²/s³ below 0.7 m water depth, about one order of magnitude larger than the vertical ε. Despite the shallowness of the lake, there are still three typical layers of ε for u',v', and w':the wind-wave layer, where the water depth is shallower than 1.0 m, exhibits that ε decreases with depth due to wind forcing, Langmuir turbulence and wave breaking; constant layer, in the range of 1.0 m to 1.9 m or so, shows that ε is little variation with the depth; bottom boundary mixed layer, below the constant layer, exhibits that ε decreases with depth. In Lake Taihu, the strength and location of stratification significantly contribute to ε in the constant layer and the bottom boundary, and even cause the initial depth of the constant layer of ε to move downward. This study will help to further understand the kinetic process of large shallow lakes and their evolutionary effects on aquatic ecosystems.

Investigation of persistent coherent structures along the Southern Brazilian Shelf

Abstract The freshwater-influenced region of the Patos Lagoon discharge to the Southern Brazilian Shelf (SBS) is a region of complex fluid dynamics. Seasoning and synoptic variable winds and coastal current conditions create an alternating flow pattern. The aim of this paper was to investigate the occurrence of persistent coherent structures in this environment. A numerical approach was chosen to describe the main hydrodynamic features of the region during a climatological year. The open-source finite-element code Telemac-Mascaret was applied to the three-dimensional domain. In addition the two-equation k-epsilon model described the turbulence mechanisms. The presence of persistent high-turbulent structures was identified within the study area. These occur as a strong curvilinear disturbance characterized by higher turbulent production and dissipation rates, which increase local mixture. As a result, upward circulation flow was observed, which may be due to irregularities in bottom topography associated with wind-induced stress forces. These results increase the information about the circulation structures of the study area by means of numerical modelling analysis.

Near‐Bed Turbulent Kinetic Energy Budget Under a Large‐Scale Plunging Breaking Wave Over a Fixed Bar

AbstractHydrodynamics under regular plunging breaking waves over a fixed breaker bar were studied in a large‐scale wave flume. A previous paper reported on the outer flow hydrodynamics; the present paper focuses on the turbulence dynamics near the bed (up to 0.10 m from the bed). Velocities were measured with high spatial and temporal resolution using a two component laser Doppler anemometer. The results show that even at close distance from the bed (1 mm), the turbulent kinetic energy (TKE) increases by a factor five between the shoaling, and breaking regions because of invasion of wave breaking turbulence. The sign and phase behavior of the time‐dependent Reynolds shear stresses at elevations up to approximately 0.02 m from the bed (roughly twice the elevation of the boundary layer overshoot) are mainly controlled by local bed‐shear‐generated turbulence, but at higher elevations Reynolds stresses are controlled by wave breaking turbulence. The measurements are subsequently analyzed to investigate the TKE budget at wave‐averaged and intrawave time scales. Horizontal and vertical turbulence advection, production, and dissipation are the major terms. A two‐dimensional wave‐averaged circulation drives advection of wave breaking turbulence through the near‐bed layer, resulting in a net downward influx in the bar trough region, followed by seaward advection along the bar's shoreward slope, and an upward outflux above the bar crest. The strongly nonuniform flow across the bar combined with the presence of anisotropic turbulence enhances turbulent production rates near the bed.

LES study of near-seabed tide-induced turbulence in the East China Sea

Near-seabed turbulent properties observed in the East China Sea were investigated using a large eddy simulation (LES) model. Tidal forcing estimated from the observed tidal current is imposed to the LES model assuming a flat seabed. Turbulence stirred by tidal currents near the seabed is simulated and compared to observed turbulence. The observed tide is dominated by the M2 constituent. The energy dissipation rate evolves with a quarter-day period near the seabed, whereas the dissipation rate evolves with a diurnal period in the upper part of the boundary layer. Salinity also oscillates diurnally. Thickness of the boundary layer related to K1 is thicker than that of M2. Orientation of the major axis of M2 in the tidal ellipse does not change downward, but that of K1 rotates counterclockwise. The vertical structure difference of two constituents is attributable to the observation site latitude, which is approximately the critical latitude of K1. All of these features are simulated in the LES model. Particularly, results show that the interference of M2 and K1 induces diurnal variation of the turbulent dissipation rate in the upper part of the boundary layer through the turbulent energy production rate controlled by the vertical shear. A hypothetical simulation without horizontal advection demonstrate that this process can contribute more to the diurnal variation in the upper part of the boundary layer than stratification stability control owing to salinity advection through tidal straining.

Large eddy simulation of dam‐break‐driven swash on a rough‐planar beach

Turbulence characteristics in the swash zone are investigated using a 3-D large eddy simulation model. The numerical model is implemented based on OpenFOAM which solves the filtered Navier-Stokes equations for two immiscible fluids with a standard Smagorinsky subgrid-scale closure. The numerical model is validated with laboratory data for swash flow driven by a dam-break apparatus. The model results demonstrate that the main characteristics of turbulence in the swash zone are different from those in the surf zone, which are mainly induced by surface wave breaking. During uprush phase, bore-generated turbulence has 2-D turbulence characteristics because of limited water depth. Near-bed-generated turbulence is mainly observed during backwash. Turbulence production and turbulent dissipation rate estimated from the model results indicate an imbalance, possibly due to advection at swash front and large roughness used. Touching down of turbulent coherent structure (TCS) is observed during uprush, which drives intense bed shear stress. During the backwash, interaction between TCS and bed is less clear. However, finger-like patterns in the spatial extent of bed shear stress and vertical components of vorticity are predicted during the backwash. The location of the strongest finger patterns in the vertical direction is collocated with that of maximum turbulence production. These finger patterns are likely caused by boundary layer instabilities injected vertically from the bed.

On the accuracy of measurement of turbulent velocity gradient statistics with hot-wire probes

A very high resolution minimal channel flow direct numerical simulation was used to examine, virtually, the ability of various multi-sensor hot-wire probe configurations to measure the statistics of velocity gradient components. Various array and sensor configurations and the spatial resolution of probes with these configurations were studied, building on designs and investigations of various authors. In contrast to our previous studies, which focused on turbulent vorticity, vorticity-velocity correlations, dissipation and production rate, here the measurement accuracy of each component of the velocity vector gradient tensor is analyzed separately. The results of the study show that the virtual experiments compare well with a physical experiment, and that such virtual experiments are a powerful tool to examine the accuracy of velocity gradient measurements. The cross-stream gradients needed to determine the vorticity components can be measured with sufficient accuracy with most of the array and sensor configurations of vorticity probes used so far. A systematic error of some of the gradient measurements can appear due to the array or sensor configurations. None of the examined probe designs can measure, with sufficient accuracy, the streamwise velocity gradients, directly or indirectly, using the continuity equation.

A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method

Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

Direct numerical simulation analysis of spanwise oscillating Lorentz force in turbulent channel flow at low Reynolds number

Direct numerical simulations of a turbulent channel flow at low Reynolds number (Re_{tau } = 180, based on the driving pressure gradient and channel half width) are performed. Some results are also presented for Re_{tau } = 400. In this work we apply an idealized spanwise Lorentz force near the lower wall of the channel and compare the results for the applied force and no-force cases in both the upper half and the lower half of the channel. We have studied two-point correlations to explain the effect of the Lorentz force on streamwise vortices and streaky structures. Despite the observation of clear stabilization of the streaky structures in the vicinity of the wall, the existence of the streamwise vortices is explained by the well-known turbulence regeneration cycle, which improves the understanding of streaky and streamwise vortex structure formation on turbulence generation. Spanwise oscillating Lorentz force effects on the Rankine vortex structures are investigated. Our results lead us to establish an explanation on the effect of sweep and ejection events on the mean vortex structures in the flow field. A mean vortex structure is defined by the time-averaged location of the local minimum and maximum of the streamwise r.m.s. vorticity. We also depict turbulence production rates for both cases and compared the lower and upper half of the channel.

Combustion via multiple pairs of opposing premixed flames with a cross-flow

A cylindrical burner accommodating stoichiometric fuel–air mixture combustion via multiple pairs of opposing jets and a cross-flow provided heat intensification and duplication of the stagnation impact for extending the firing limits and maximizing the power density. Six pairs of circumferentially opposing stoichiometric mixture jets sustained bulk injection velocities as high as 21.8 m/s and were associated with NOx emissions of 22 ppm, while emissions of 10 ppm were recorded upon reaching a lean limit equivalence ratio of 0.59. A stoichiometric mixture jet issuing perpendicular to the opposing jets at a momentum flux ratio of 0.3 increased the turbulence production rates to the extent that increased the maximum bulk injection velocity to 28.3 m/s and reduced the NOx emissions to 17 ppm. Since the recirculation zones between the two stagnation centers got compressed by increasing the momentum flux ratio to 0.8, the corresponding residence time reduction decreased the NOx emissions to 12 ppm. As the cross-flow mixture was made fuel–lean, dilution of the stoichiometric mixture by the fuel–lean mixture combustion products made it possible to get NOx emissions of single digit ppm. Emissions of 9 ppm resulted from using the cross-flow fuel–lean mixture jet due to compromising the flame stability limit extension and the temperature reduction in the post flame region. Such emissions, in turn, decreased to 4 ppm as the momentum flux ratio increased to 1.7 at which the stoichiometric mixture flames shrank into their ports. A minimum NOx emission index of 0.27 g/kg fuel was thus obtained at a volumetric heat release of 50.4 MW/m3. The momentum flux ratio corresponding to merging the two stagnation zones was correlated with Reynolds and Froude numbers, the jets’ separation as well as the density and viscosity values pertaining to the lean and stoichiometric mixtures’ flame temperatures.

Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10−4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.

Large eddy simulation of turbulent flow and heat transfer in a square duct with unstable natural convection on the cross section

In this paper, large eddy simulations with the dynamic Smagorinsky eddy viscosity model are performed for a fully developed turbulent flow and heat transfer in a square duct with unstable natural convection on the cross section at a turbulent Reynolds number of 400, a Prandtl number of 0.7 and different Grashof numbers from 105 to 5×107. The MPI parallel programming language is implemented to speed up the calculations. The influences of the buoyancy force on the mean flow and heat transfer, turbulent intensity and Reynolds stresses are analyzed. The results show that the mean velocity decreases while the subgrid viscosity, turbulent intensity and heat transfer increase obviously with the increase of Grashof number. The turbulent intensity in the streamwise direction decreases considerably in the near-wall region while the turbulent intensity in the spanwise direction increases clearly in almost whole regions with an increase in Grashof number. The spatial distribution of Reynolds stresses are mainly influenced by the thermal buoyancy force. The turbulence production rate and the buoyancy force production term of Reynolds stress component 〈v′v′〉 increase with the increase of Grashof number.

Combustion performance of eccentrically rotated flames

Experimental/computational work highlighted the combustion performance with eccentric blockage rotation in the reactive flow passage to augment the turbulence production rates in the flame for acquiring high power to weight ratios and effective heat transfer in industrial applications. The temporal/spatial velocity gradients stimulated around the reactive stream boundaries enhanced the turbulence development in both premixed and non-premixed flames. The eccentric shapes included circular, elliptical, squared and triangular shafts as well as a triple/straight blade rotor. The design was further developed to incorporate simultaneous rotation of the eccentric blockage around its axis via a planetary gear assembly to duplicate the vortical structure. While the premixed flames responded to such cyclic action by having a mixture velocity of 16.8 m/s, the non-premixed flames acquired an increase of 341% in the largest eddy size and a flame length reduction by 42%. Increasing the Strouhal number to 0.94 and the swirl ratio to 0.78 increased the turbulent kinetic energy to 9.1 m2/s2. By controlling the drag coefficient and wake vorticity for the solid shapes, the triangular rotor enhanced the combustor outward heat flux to exhibit a heater efficiency of 36.8% in the premixed flame mode and reduced the HC and CO emissions, respectively, to 0.1% and 513 ppm for non-premixed flames. Decreasing the reactive stream cross-section favorably increased the flow shearing effects, while the elliptical shape showed the highest sensitivity to axes’ orientation with respect to the direction of rotation. Due to the reduction in peak temperatures via increasing the turbulence intensity and heat transfer rate from the flame, the NO x exhaust concentrations decreased to a minimum value around 10 ppm. The combustion efficiency of diffusion flames was optimized with the fuel port central positioning in the burner, where the planetary gear design provided a turbulence intensity of 13.7% by the triple blade rotor.

A Free-Floating PIV System: Measurements of Small-Scale Turbulence under the Wind Wave Surface

Abstract An in situ free-floating underwater miniature particle image velocimetry (UWMPIV) system is developed and applied to measure the structure of turbulence in the aqueous side of the wind wave surface boundary layer. The UWMPIV system provides a direct way to measure the aqueous side turbulence dissipation rate and vortex structures immediately below the air–water interface, which are important parameters that determine the gas exchange rate across the air–water interface subjected to a low-to-moderate wind shear. The impact of platform motion on the measurement of small-scale turbulence is discussed and found to be insignificant. A series of field experiments under a near “zero-fetch” wind wave condition and one open water experiment under a low wind condition were conducted on Lake Michigan to demonstrate the capabilities of the free-floating particle image velocimetry (PIV) system. The dissipation rate estimated with a “direct method” and with a “spectra fitting” method are compared. Vertical profiles of the turbulence dissipation rate suggest a power-law dependency with depth below the water surface. Surface shear velocities estimated through the aqueous side Reynolds stress distribution agreed well with wind stresses estimated by the classic drag law for zero-fetch wind wave conditions, where the primary source of turbulence was wind shear. For the open water experiment under a very low wind condition, a high dissipation rate was observed near the water surface, suggesting a high turbulence production rate by surface waves, and the profile of dissipation rate showed a slower decay rate with depth in the presence of waves.

Turbulent flow characteristics in a randomly packed porous bed based on particle image velocimetry measurements

An experimental study was undertaken to better understand the turbulent flow characteristics within a randomly packed porous bed. A relatively low aspect ratio bed (bed width to spherical solid phase particle diameter of 4.67) with the fluid phase refractive index matched to that of the solid phase was used to obtain time resolved particle image velocimetry data. Care was taken to assure that data were outside of the wall affected region, and results are based on detailed time dependent velocity vector maps obtained at selected pores. In particular, four pores were identified that display a range of very disparate mean flow conditions which resemble channel-like flow, impinging flow, recirculating flow, and jet like flow. Velocity data were used for a range of pore Reynolds numbers, Repore, from 418 to 3964 to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra. The pore Reynolds number is based on the porous bed hydraulic diameter, DH = ϕDB/(1 − ϕ) where ϕ is bed porosity and DB is solid phase bead diameter and average bed interstitial velocity, Vint = VDarcy/ϕ, where VDarcy = Q/Abed, with Q being the volumetric flow rate and Abed the bed cross section normal to the flow. Results show that when scaled with the bed hydraulic diameter, DH, and average interstitial velocity, Vint, these turbulence measures all collapse for Repore, beyond approximately 2800, except that the integral scales collapse at a lower value near 1300–1800. These results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like DH and Vint characterizes their magnitudes despite very different mean flow conditions.

Inert-droplet and combustion effects on turbulence in a diluted diffusion flame

The inert-droplet and combustion effects on turbulence in a diluted diffusion flame are investigated using direct numerical simulation (DNS) through parametric study. The computational configuration is a temporally-developing reacting mixing layer laden with close to 17×106 inert evaporating droplets. The gas phase is described in the Eulerian frame while the discrete droplet phase is traced in the Lagrangian frame, with strong two-way coupling between the two phases through mass, momentum, and energy exchange. In the two-way coupling, distributing droplet source terms onto the Eulerian grids is a key procedure. Different distribution methods are compared to examine its impact on the statistics, including correlations between droplet source term and gas phase flow variables. The physical parameter considered is the characteristic droplet evaporation time, which is varied with the latent heat of vapourisation and plays a crucial role in both dynamic and evaporation effects of droplets on the turbulent reacting flow. To detail the analysis, the transport equation for the turbulence kinetic energy (TKE) is employed, in which the droplet contributions are categorised into three terms. The direct droplet and combustion effects on the TKE and their effects on the turbulence production and dissipation rate, pressure-dilatation are then scrutinised and compared to analyse the interactions among turbulence, combustion, and inert droplets in the multi-phase reacting flow.