Turbulent Mixing Rate Research Articles

An Observational Case Study on the Influence of Atmospheric Boundary-Layer Dynamics on New Particle Formation

We analyze the influence of atmospheric boundary-layer development on new particle formation (NPF) during the morning transition. Continuous in-situ measurements of vertical profiles of temperature, humidity and aerosol number concentrations were quasi-continously measured near Melpitz, Germany, by unmanned aerial systems to investigate the potential connection between NPF and boundary-layer dynamics in the context of turbulence, temperature and humidity fluctuations. On 3 April 2014 high number concentrations of nucleation mode particles up to $$6.0 \times 10^4~\text {cm}^{-3}$$ were observed in an inversion layer located about 450 m above ground level. The inversion layer exhibited a spatial temperature structure parameter $$C_T^2$$ 15 times higher and a spatial humidity structure parameter $$C_q^2$$ 5 times higher than in the remaining part of the vertical profile. The study provides hints that the inversion layer is responsible for creating favorable thermodynamic conditions for a NPF event. In addition, this layer showed a strong anti-correlation of humidity and temperature fluctuations. Using estimates of the turbulent mixing and dissipation rates, it is concluded that the downward transport of particles by convective mixing was also the reason of the sudden increase of nucleation mode particles measured on ground. This work supports the hypothesis that many of the NPF events that are frequently observed near the ground may, in fact, originate at elevated altitude, with newly formed particles subsequently being mixed down to the ground.

Observations and environmental implications of variability in the vertical turbulent mixing in Lake Simcoe

Abstract A field study was conducted in Lake Simcoe to examine variations in turbulent mixing rates for a 40-day period in late summer of 2011. High sampling frequency records of water currents and temperature profiles were acquired using an acoustic Doppler current profiler (ADCP) and a chain of fast-response temperature loggers respectively. The acquired data were processed to quantify the relative strengths of the stratification in relation to the velocity shear, expressed by the dimensionless gradient Richardson number ( Ri g ). We then used the calculated Ri g as a proxy to estimate vertical turbulent eddy diffusivity ( K z ) in the stratified water column of the lake. K z exhibited large spatial and temporal variability with frequent high values in the epilimnion ( K z ~ 10 − 5 –10 − 4 m 2 s − 1 ), and relatively low values in the metalimnion ( K z ~ 10 − 7 –10 − 6 m 2 s − 1 ) and the hypolimnion ( K z ~ 10 − 6 –10 − 5 m 2 s − 1 ). We correlated the K z variability with the environmental forcing through the Lake number ( L N ), which expresses the relative strengths of the stratification to the wind forcing. Analysis of the environmental implications of K z variability suggested that vertical turbulent transport of dissolved oxygen was 10% of the total oxygen depleted in the hypolimnion for the observation period. We concluded that at least some of the observed year-to-year variability of hypolimnetic oxygen depletion could be due to the variation in turbulent transport of dissolved oxygen across the thermocline.

Effect of fuel composition and differential diffusion on flame stabilization in reacting syngas jets in turbulent cross-flow

Three-dimensional direct numerical simulation results of a transverse syngas fuel jet in turbulent cross-flow of air are analyzed to study the influence of varying volume fractions of CO relative to H2 in the fuel composition on the near field flame stabilization. The mean flame stabilizes at a similar location for CO-lean and CO-rich cases despite the trend suggested by their laminar flame speed, which is higher for the CO-lean condition. To identify local mixtures having favorable mixture conditions for flame stabilization, explosive zones are defined using a chemical explosive mode timescale. The explosive zones related to flame stabilization are located in relatively low velocity regions. The explosive zones are characterized by excess hydrogen transported solely by differential diffusion, in the absence of intense turbulent mixing or scalar dissipation rate. The conditional averages show that differential diffusion is negatively correlated with turbulent mixing. Moreover, the local turbulent Reynolds number is insufficient to estimate the magnitude of the differential diffusion effect. Alternatively, the Karlovitz number provides a better indicator of the importance of differential diffusion. A comparison of the variations of differential diffusion, turbulent mixing, heat release rate and probability of encountering explosive zones demonstrates that differential diffusion predominantly plays an important role for mixture preparation and initiation of chemical reactions, closely followed by intense chemical reactions sustained by sufficient downstream turbulent mixing. The mechanism by which differential diffusion contributes to mixture preparation is investigated using the Takeno Flame Index. The mean Flame Index, based on the combined fuel species, shows that the overall extent of premixing is not intense in the upstream regions. However, the Flame Index computed based on individual contribution of H2 or CO species reveals that hydrogen contributes significantly to premixing, particularly in explosive zones in the upstream leeward region, i.e. at the preferred flame stabilization location. Therefore, a small amount of H2 diffuses much faster than CO, creating relatively homogeneous mixture pockets depending on the competition with turbulent mixing. These pockets, together with high H2 reactivity, contribute to stabilizing the flame at a consistent location regardless of the CO concentration in the fuel for the present range of DNS conditions.

Determination of Turbulent Mixing Rate for Single-Phase Flow in Simulated Subchannels of a Natural-Circulation Pressure Tube–Type BWR

The Advanced Heavy Water Reactor (AHWR) is a vertical pressure tube–type, heavy water–moderated, boiling light water–cooled, natural-circulation–based reactor. The fuel bundle of AHWR contains 54 fuel rods arranged in three concentric rings of 12, 18, and 24 fuel rods. This fuel bundle is divided into a number of imaginary interacting flow passages called subchannels. A single-phase-flow condition exists in the reactor rod bundle during the start-up condition and up to a certain length of rod bundle when it is operating at full power. Predicting the thermal margin of the reactor during the start-up condition has necessitated the determination of the turbulent mixing rate of the coolant among these subchannels. Thus, it is vital to evaluate the turbulent mixing between the subchannels of the AHWR rod bundle.In this paper, experiments were carried out to determine the turbulent mixing rate in the simulated subchannels of the reactor. The size of the rod and the pitch in the test were the same as those of the actual rod bundle in the prototype. Three subchannels are considered in 1/12th of the cross section of the rod bundle. Water was used as the working fluid, and the turbulent mixing tests were carried out at the atmospheric condition without heat addition. The mean velocity in the subchannel was varied from 0 to 1.2 m/s. The flow conditions were closer to the actual reactor condition. The turbulent mixing rate was experimentally determined by adding tracer fluid in one subchannel and measuring the concentration of that in other subchannels at the end of the flow path. The test data were compared with existing models in literature. It was found that none of the models could predict the measured turbulent mixing rate in the rod bundle of the reactor. This is because the turbulent mixing rate is highly dependent on geometry. An empirical model is derived based on these experimental data, and it is found that this correlation can predict the turbulent mixing rate quite accurately.

Subchannel analysis with turbulent mixing rate of supercritical pressure fluid

The subchannel analysis with turbulent mixing rate law of supercritical pressure fluid (SPF) is carried out for supercritical-pressurized light water cooled and moderated reactor (Super LWR). It is different from the turbulent mixing rate law of pressurized water reactor (PWR), which is widely adopted in Super LWR subchannel analysis study, the density difference between adjacent subchannels is taken into account for turbulent mixing rate law of SPF. MCSTs are evaluated on three kinds of fuel assemblies with different pin power distribution patterns, gap spacings and mass flow rates. Compared with that calculated by employing turbulent mixing rate law of PWR, the increase in MCST is smaller even when peaking factor is large and gap spacing is uneven. The sensitivities of MCST on non-uniformity of the subchannel area and power peaking are reduced.

Influence of turbulence on the wake of a marine current turbine simulator.

Marine current turbine commercial prototypes have now been deployed and arrays of multiple turbines under design. The tidal flows in which they operate are highly turbulent, but the characteristics of the inflow turbulence have not being considered in present design methods. This work considers the effects of inflow turbulence on the wake behind an actuator disc representation of a marine current turbine. Different turbulence intensities and integral length scales were generated in a large eddy simulation using a gridInlet, which produces turbulence from a grid pattern on the inlet boundary. The results highlight the significance of turbulence on the wake profile, with a different flow regime occurring for the zero turbulence case. Increasing the turbulence intensity reduced the velocity deficit and shifted the maximum deficit closer to the turbine. Increasing the integral length scale increased the velocity deficit close to the turbine due to an increased production of turbulent energy. However, the wake recovery was increased due to the higher rate of turbulent mixing causing the wake to expand. The implication of this work is that marine current turbine arrays could be further optimized, increasing the energy yield of the array when the site-specific turbulence characteristics are considered.

Penetration depth of diapycnal mixing generated by wind stress and flow over topography in the northwestern Pacific

AbstractThe role of turbulent diapycnal mixing in the northwestern Pacific was estimated by employing a fine‐scale parameterization method based on 6756 high‐resolution CTD profiles spanning a period of 8 years from the Japan Oceanography Data Center (JODC) and the Kuroshio Extension System Study (KESS). The rate of turbulent mixing in the upper ocean within 300–1800 m depth displayed a distinct seasonal cycle, bearing a statistically significant correlation to wind‐induced near‐inertial energy flux (hereafter denoted by WNEF). Enhanced turbulent mixing was also found near the rough seafloor relative to that over smooth topography. Enhanced dissipation at surface and bottom was found to be able to penetrate the ocean interior up to 1800 m and 3300 m, respectively, with penetration depths varying with the WNEF and topographic roughness. Our study here provides evidence for the important role of near‐inertial energy input from wind stress and the influence of bottom topography in maintaining mixing in the ocean interior.

Extension of the eddy dissipation concept and smoke point soot model to the LES frame for fire simulations

The eddy dissipation concept (EDC) is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence. A series of structure levels are assumed to exist under the filter width “Δ” in the turbulent energy cascade which spans from the Kolmogorov to the integral scale. The total kinetic energy and its dissipation rate are expressed using the sub-grid scale (SGS) quantities. Assuming infinitely fast chemistry, the filtered reaction rate in the EDC is controlled by the turbulent mixing rate between the fine structures at Kolmogorov scales and the surrounding fluids. In order to extend the laminar smoke point soot model (SPSM) to LES, the partially stirred reactor (PaSR) concept is used to relate the filtered soot formation rate to the soot chemical time scale, which is assumed to be proportional to the laminar smoke point height (SPH) of the fuel. The turbulent mixing time scale for soot is computed as a geometric mean of the Kolmogorov and integral time scale. A new soot oxidation model is also developed by imitating the gas phase combustion within EDC. The newly extended EDC and SPSM are implemented in the open source FireFOAM solver and tested with two medium scale heptane and toluene pool fires with promising results.

Intra-colony motility of Microcystis wesenbergii cells

Microcystis is a widely distributed genus of cyanobacteria that often forms surface blooms. The ability of Microcystis colonies to regulate buoyancy in response to variations in nutrients and light, and in the presence of low rates of turbulent mixing, is well described. Here, we report on the movement of individual cells within Microcystis wesenbergii colonies. Cells actively rearranged themselves within colonies, but randomly relative to other cells. Of the known types of cyanobacterial movement, gliding or twitching mediated by type IV pili was deemed the most likely causative mechanism. Transmission electron microscopy showed, however, no pilus-like structures on M. wesenbergii cell surfaces. We speculate that intra-colony movement may optimize colony fitness by helping individual cells to meet specific physiological requirements that may differ between the core and outer parts of the colony. This may increase fitness of cells and explain the recent dominance of M. wesenbergii in some New Zealand lakes.

Assessment and Development of Two Phase Turbulent Mixing Models for Subchannel Analysis Relevant to BWR

Determination of turbulent mixing rate of two phase flow between neighboring subchannels is an important aspect of sub channel analysis in reactor rod bundles. Various models have been developed for two phase turbulent mixing rate between subchannels. These models show that turbulent mixing rate is strongly dependent on flow regimes; their validity was examined against specific or limited experiments. It is vital to evaluate these models by comparing the predicted two phase turbulent mixing rate with available experimental data conducted for various subchannel geometries and operating conditions. This paper describes evaluation of different models for two phase turbulent mixing rate for both gas and liquid phase against large range of experimental data which are obtained from various subchannel geometries. The results indicate that there is large discrepancy between the predicted and experimental data for turbulent mixing rate. This paper provides important shortcoming of the previous work and need for the development of a new model. In the view of this, a two phase flow model is presented, which predicts both liquid and gas phase turbulent mixing rate between adjacent sub channels of reactor rod bundles. The model presented here is for slug churn flow regime, which is dominant as compared to the other regimes like bubbly flow and annular flow regimes, since turbulent mixing rate is the highest in slug churn flow regime. The present model has been tested against low pressure and temperature air-water and high pressure and temperature steam-water experimental data found that it shows good agreement with available experimental data.

Large eddy simulation of a medium-scale methanol pool fire using the extended eddy dissipation concept

The eddy dissipation concept (EDC) is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence. A series of structure levels are assumed to exist under the filter width “Δ” in the turbulent energy cascade which spans from the Kolmogorov to the integral scale. The total kinetic energy and its dissipation rate are expressed using the sub-grid scale (SGS) quantities. Assuming infinitely fast chemistry, the filtered reaction rate in the EDC is controlled by the turbulent mixing rate between the fine structures at Kolmogorov scales and the surrounding fluids. The newly extended EDC was implemented in the open source FireFOAM solver, and large eddy simulation of a 30.5cm diameter methanol pool fire was performed using this solver. Reasonable agreement is achieved by comparing the predicted heat release rate, radiative fraction, velocity and its fluctuation, temperature and its fluctuation, turbulent heat flux, SGS and total dissipation rate, SGS and total kinetic energy, time scales, and length scales with the corresponding experimental data.

Radiative Impacts of Free-Tropospheric Clouds on the Properties of Marine Stratocumulus

Abstract Observations from multiple satellites and large-eddy simulations (LESs) from the Regional Atmospheric Modeling System (RAMS) are used to determine the extent to which free-tropospheric clouds (FTCs) affect the properties of stratocumulus. Overlying FTCs decrease the cloud-top radiative cooling in stratocumulus by an amount that depends on the upper-cloud base altitude, cloud optical thickness, and abundance of moisture between the cloud layers. On average, FTCs increase the downward longwave radiative flux above stratocumulus clouds (at 3.5 km) by approximately 30 W m−2. As a consequence, this forcing translates to a relative decrease in stratocumulus cooling rates by about 20%. Overall, the reduced cloud-top radiative cooling decreases the turbulent mixing, vertical development, and precipitation rate in stratocumulus clouds at night. During the day these effects are greatly reduced because the overlying clouds shade the stratocumulus from strong solar radiation, thus reducing the net radiative effect by the upper cloud. Differences in liquid water path are also observed in stratocumulus; however, the response is tied to the diurnal cycle and the time scale of interaction between the FTCs and the stratocumulus. Radiative effects by FTCs tend to be largest in the midlatitudes where the clouds overlying stratocumulus tend to be more frequent, lower, and thicker on average. In conclusion, changes in net radiation and moisture brought about by FTCs can significantly affect the dynamics of marine stratocumulus and these processes should be considered when evaluating cloud feedbacks in the climate system.

Predictions of CO and NOx emissions from steam cracking furnaces using GRI2.11 detailed reaction mechanism – A CFD investigation

This investigation develops a three-dimensional Computational Fluid Dynamics (CFD) model to simulate the turbulent diffusion flame on the fire-side of the radiation section of a thermal cracking test furnace coupled with a non-premixed low NOx floor burner. When this type of burners which uses the internal Flue Gas Recirculation (FGR) technique is coupled with large scale furnaces, both the turbulent mixing and chemical reaction rates are comparable and hence this should be considered in the model. Different combustion models are used to simulate the turbulence–chemistry interactions for this flame. The CFD model, based on the Eddy Dissipation Concept (EDC) combustion model coupled with the detailed GRI2.11 reaction mechanism, gives the most reasonable predictions compared with the available experimental data or empirical correlations for the diffusion flame in the thermal cracking test furnace, especially for the flame length and the CO and NOx emissions.

Three-dimensional numerical simulation of the operation of a rotating-detonation chamber with separate supply of fuel and oxidizer

A three-dimensional numerical simulation of the operation of an annular rotating-detonation chamber (RDC) with separate supply of combustible mixture components, hydrogen and air, is performed, and the calculation results are compared to available experimental data. The model is based on a system of time-dependent Reynolds-averaged Navier-Stokes equations complemented with a turbulence model and continuity and energy equations for a multicomponent reacting gas mixture. The system is solved using a coupled algorithm based on the finite volume method and particle method. Calculations are for the first time performed with allowance for effects of finite rates of turbulent and molecular mixing of the combustible mixture components with each other and with reaction and detonation products. The calculation results compare favorably with the experimental data obtained at the Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences.

東京湾の現地乱流観測データに基づく鉛直混合スキームの基礎的検討

We describe performance of two vertical mixing schemes based on in-situ measured vertical profiles of turbulent mixing in Tokyo Bay. Three-dimensional hydrodynamic simulations using two turbulence closure schemes, the Mellor-Yamada (MY) model and the k-ε (KE) model, were carried out in the period 2011-2012. In almost all the vertical profiles, the difference in the potential density was insignificant between the two schemes although the turbulent mixing predicted by KE was rather stronger than that by MY. Both models well reproduced the observed turbulent energy dissipation and eddy mixing rates in the whole columns during nearly neutral conditions, but significantly underestimated them in the middle and bottom layers during the strongly stratified conditions.

Argon supersaturation indicates low decadal‐scale vertical mixing in the ocean thermocline

The rate of vertical mixing in the ocean's stratified waters limits the uptake of anthropogenic CO2, influences the strength of the overturning circulation, and regulates the transport of nutrients to the lighted surface waters, controlling global biological production. Despite this fundamental importance, there is a long‐standing conundrum in oceanography that experimentally‐measured rates of turbulent mixing across density surfaces (diapycnal mixing) in the main thermocline cannot support sufficient nutrient fluxes from below to explain rates of biological production measured in the subtropical euphotic zone. Possible solutions to this problem are transport mechanisms that occur intermittently on short time and space scales that would be difficult to observe in tracer‐ release experiments and are not resolved in large‐scale ocean models. We tested this hypothesis by measuring highly‐accurate argon profiles from the subtropical thermocline in the North Pacific Ocean. It has been shown theoretically that the change in argon supersaturation along density surfaces is a measure of diapycnal mixing averaged over the decadal time‐scale of thermocline ventilation. Two different model interpretations of our data indicate that the mean rate of diapycnal mixing on density surfaces betweenσθ = 26.4 – 26.7 (depths 150–600 m) is no more than 0.2 × 10−4 m2 s−1. This supports low diapycnal mixing rates even on decadal time‐scales and rules out enhancement of diapycnal mixing on this density interval by intermittent mixing or mixing at boundaries that propagates into the ocean interior.

Diffusion and hydrodynamic instabilities in gaseous detonations

To clarify the role played by diffusion in detonation structure, two-dimensional numerical simulations are performed by solving the Navier–Stokes equations and considering the single step Arrhenius kinetic as reaction model. The effect of diffusion on the generation of vortices produced by hydrodynamic instabilities (Richtmyer–Meshkov (RM) and Kelvin Helmholtz (KH) instabilities) is investigated. Mixtures with both low and high activation energies, characterized by their regular and irregular detonation structures, are considered. The computations are performed with resolutions ranging from 25 to 103 cells per half reaction length of the ZND structure. Resolution studies of the Navier–Stokes solution for irregular detonations in moderate activation energy mixtures shows that to capture a proper structure, to be at least in qualitative agreement with experimental observations, resolution more that 300 cells per half reaction length is required. However, in mixtures with low activation energy a resolution of 25 cells per half reaction length gives a reasonable physical structure of the detonation. Results provided by very high resolution for irregular structure detonations reveal that the major effect of diffusion occurs at shear layers and unburned pockets boundaries. Diffusion suppresses the small-scale vortices produced by KH instabilities and decreases the turbulent mixing rate of burned and partly burned gases at shear layers. However, behind the shock front, where less concentration of small-scale vortices exist, the diffusion of heat and mass from neighboring hot regions of burned material to the unreacted gases increases the burning rate of the un-reacted pockets. Comparison of the structure obtained by solving the Euler equations with the solution of the Navier–Stokes equations shows that, the strength of the shock front in Navier–Stokes solution is higher than that in Euler solution. Due to the absence of hydrodynamic instabilities behind the main front of regular structure detonations, the results obtained by solving the Euler equations and Navier–Stokes equations are similar for detonations with regular structure even in high resolution simulations.

Unsteady numerical simulations of the single-phase turbulent mixing between two channels connected by a narrow gap

This paper focuses on the unsteady numerical simulation of the turbulent flow in two types of geometry containing a narrow gap with the explicit algebraic Reynolds stress model. The model was first validated through the comparison of simulation results inside a rectangular channel containing a cylinder and the corresponding experimental data. The structures of the oscillation were correctly reproduced. Simulation of turbulent mixing between circular channels connected by a narrow gap was carried out with the validated model. Because of the influence of the strong anisotropic turbulent flow in the gap region, the mixing rate was dramatically enhanced by the cyclic and almost periodic flow pulsation. The calculation results of the turbulent mixing rate showed good agreement with the experiment and the maximum error was less than 15%.

Evaluation of turbulent Prandtl (Schmidt) number parameterizations for stably stratified environmental flows

In this study, we evaluate four different parameterizations of the turbulent Prandtl (Schmidt) number Pr t = ν t / Γ t where ν t is the eddy viscosity and Γ t is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Pr t are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. no extra transport equations are required) turbulence model for ν t in a one-dimensional, turbulent channel flow is considered to evaluate the behavior of the different formulations of Pr t . Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems such as atmospheric boundary layer flows and tidally driven estuarine flows, to quantify the behavior of each of the four formulations of Pr t . We perform model-to-model comparisons to highlight which of the models of Pr t allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Pr t given a model for ν t in stably stratified flows.

WHAT HAPPENED TO THE OTHER MOHICANS? THE CASE FOR A PRIMORDIAL ORIGIN TO THE PLANET–METALLICITY CONNECTION

When a planet falls onto the surface of its host star, the added high-metallicity material does not remain in the surface layers, as often assumed, but is diluted into the interior through fingering ('thermohaline') convection. Until now, however, the timescale over which this process happens remained very poorly constrained. Using recently measured turbulent mixing rates for fingering convection, I provide reliable numerical and semi-analytical estimates for the rate at which the added heavy elements drain into the interior. I find that the relative metallicity enhancement post-infall drops by a factor of 10 over a timescale that depends only on the structure of the host star and decreases very rapidly with increasing stellar mass (from about 1 Gyr for a 1.3 M{sub sun} star to 10 Myr for a 1.5 M{sub sun} star). This result offers an elegant explanation to the lack of an observed trend between metallicity and convection zone mass in planet-bearing stars. More crucially, it strongly suggests that the statistically higher metallicity of planet-bearing stars must be of primordial origin. Finally, the fingering region is found to extend deeply into the star, a result which would provide a simple theoretical explanation of the measurements of higher lithium depletionmore » rates in planet-bearing stars.« less