Turbulent Mass Research Articles

Turbulent Schmidt and Prandtl Numbers in the Boundary Layer on a Wall with Film Cooling when a Foreign Gas is Injected through a Porous Insert

Variations in the turbulent Schmidt and Prandtl numbers in the boundary layer on a wall with film cooling when helium is injected into xenon flow through a porous insert is investigated numerically using the three-parameter RANS turbulence model supplemented with transport equations for turbulent heat and mass transfer. The results obtained are compared with calculated data for constant turbulent Schmidt and Prandtl numbers.

Multi-scale study of turbulent mass transfer process in different shaped-adsorbent packed bed

Insufficient consideration of the coupled effect of multi-scale and turbulent mass transfer impedes thorough understanding of the dynamic adsorption process in the fixed bed. To solve this problem, a novel PR-CMT model, integrated particle resolution method and computational mass transfer theory, is proposed and verified to simulate the gas adsorption process on particles by combining the computational mass transfer method and the particle dissolution method. The proposed model not only rigorously accounts for the turbulent diffusion by incorporating the equation of concentration variance c2‾ and concentration variance dissipation εc, but also establishes connections between different scales of fixed-bed particle-fluid systems. Through this work, it is found that there is a preferred fluid path in the particle filling structure, which can lead to significant changes in local mass transfer performance. Additionally, the turbulent diffusion enhances the mass and heat transfer between the gas and particles, resulting in a more uniform distribution in the radial direction. Using the proposed model, the effects of the adsorbent characteristics on the multi-scale adsorption process, such as the adsorbent porosity and shape, are further examined. The results indicate that increasing the adsorbent porosity leads to enhanced overall adsorption rate in the fixed bed, and the turbulent diffusion is strongest in the fixed bed with cylinder adsorbents.

Turbulent heat and mass lines in finite difference regime

AbstractFinite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.

Turbulent flow-driven liquid-solid mass transfer in serpentine tube heat exchanger/reactors: applications and implications

ABSTRACT This study examines liquid-solid mass and heat transfer rates in serpentine tube heat exchangers/reactors under turbulent flow using the copper dissolution technique. Key factors include solution flow rate, properties, tube diameter, U-bend curvature, and drag-reducing polymers. An empirical correlation predicts mass transfer coefficients, which are 4.12–5.36 times higher than straight tubes. Serpentine tubes show potential for economically viable diffusion-controlled reactions. Drag-reducing polymer (Polyox WSR-301) reduces corrosion rates by up to 23.3%. The study highlights serpentine tubes’ applicability in catalytic continuous reactors and membrane processes, emphasizing their significance in heat exchanger design and corrosion allowance prediction.

Three Dimensional Natures of Massive Star Envelopes

In this paper, we review our current understanding of the outer envelope structures of massive stars based on three-dimensional (3D) radiation hydrodynamic simulations. We briefly summarize the fundamental issues in constructing hydrostatic one-dimensional (1D) stellar evolution models when stellar luminosity approaches the Eddington value. Radiation hydrodynamic simulations in 3D covering the mass range from 13M⊙ to 80M⊙ always find a dynamic envelope structure with the time-averaged radial profiles matching 1D models with an adjusted mixing-length parameter when convection is subsonic. Supersonic turbulence and episodic mass loss are generally found in 3D models when stellar luminosity is super-Eddington locally due to the opacity peaks and convection being inefficient. Turbulent pressure plays an important role in supporting the outer envelope, which makes the photosphere more extended than predictions from 1D models. Massive star lightcurves are always found to vary with a characteristic timescale consistent with the thermal time scale at the location of the iron opacity peak. The amplitude of the variability as well as the power spectrum can explain the commonly observed stochastic low-frequency variability of mass stars observed by TESS over a wide range of parameters in an HR diagram. The 3D simulations can also explain the ubiquitous macro-turbulence that is needed for spectroscopic fitting in massive stars. Implications of 3D simulations for improving 1D stellar evolution models are also discussed.

Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs

ABSTRACT Turbulence in protoplanetary discs, when present, plays a critical role in transporting dust particles embedded in the gaseous disc component. When using a field description of dust dynamics, a diffusion approach is traditionally used to model this turbulent dust transport. However, it has been shown that classical turbulent diffusion models are not fully self-consistent. Several shortcomings exist, including the ambiguous nature of the diffused quantity and the non-conservation of angular momentum. Orbital effects are also neglected without an explicit prescription. In response to these inconsistencies, we present a novel Eulerian turbulent dust transport model for isotropic and homogeneous turbulence on the basis of a mean-field theory. Our model is based on density-weighted averaging applied to the pressureless fluid equations and uses appropriate turbulence closures. Our model yields novel dynamic equations for the turbulent dust mass flux and recovers existing turbulent transport models in special limiting cases, thus providing a more general and self-consistent description of turbulent particle transport. Importantly, our model ensures the conservation of global angular and linear momentum unconditionally and implicitly accounts for the effects of orbital dynamics in protoplanetary discs. Furthermore, our model correctly describes the vertical settling–diffusion equilibrium solutions for both small and large particles. Hence, this work presents a generalized Eulerian turbulent dust transport model, establishing a comprehensive framework for more detailed studies of turbulent dust transport in protoplanetary discs.

Momentum boundary layers in transcritical channel flows

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. We apply a physically consistent subgrid-scale turbulence model, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. In total seven cases are computed covering different Reynolds numbers, pseudo-boiling positions and pressure values. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum layer thicknesses. All cases feature a turbulent mass flux which is essential in turbulence modelling. Furthermore, we analyse the turbulent kinetic energy budgets, perform a quadrant and octant analysis of the Reynolds shear stress and employ an invariant map to study the anisotropy in transcritical turbulent channel flows.

Turbulent transfer and entrainment in a low-density jet

We investigate the dynamics of a low-density round jet, with a focus on the mechanisms governing the turbulent momentum and mass transfers as well as on the entrainment of ambient fluid. To that purpose, we combine a theoretical analysis, laboratory experiments and numerical simulations. The theoretical analysis relies on a general formulation of the entrainment decomposition for the case of large density differences, revealing the role of the processes contributing to the entrainment: turbulent kinetic energy production and variation in the shape of the mean velocity radial profiles. The spatial evolution of these terms has been evaluated by means of challenging experiments, providing a unique data set of combined velocity and density statistics of a low-density jet and an air jet. The same flows are investigated by means of large-eddy simulation (LES). Other than for providing complementary information on flow statistics, LES is here used to investigate the role of varying conditions imposed at the source, notably concerning the shape of the inlet velocity profile and the presence of a bottom wall surrounding the source. Experimental and numerical results provide clear insight on how a reduced density within the jet enhances the turbulent kinetic energy production (compared to an iso-density jet) and modifies the shape of the mean velocity profiles. Despite its clear influence on the flow statistics, the reduced density has overall little influence on the entrainment rate, which also shows little sensitivity to varying source conditions.

3D hydrodynamic simulations of massive main-sequence stars – I. Dynamics and mixing of convection and internal gravity waves

ABSTRACT We performed 3D hydrodynamic simulations of the inner $\approx 50{{\ \rm per\ cent}}$ radial extent of a $25\,\,\mathrm{\mathrm{M}_\odot }$ star in the early phase of the main sequence and investigate core convection and internal gravity waves in the core-envelope boundary region. Simulations for different grid resolutions and driving luminosities establish scaling relations to constrain models of mixing for 1D applications. As in previous works, the turbulent mass entrainment rate extrapolated to nominal heating is unrealistically high ($1.58\times 10^{-4}\,\,\mathrm{\mathrm{M}_\odot \, {\mathrm{yr}}^{-1}}$), which is discussed in terms of the non-equilibrium response of the simulations to the initial stratification. We measure quantitatively the effect of mixing due to internal gravity waves excited by core convection interacting with the boundary in our simulations. The wave power spectral density as a function of frequency and wavelength agrees well with the GYRE eigenmode predictions based on the 1D spherically averaged radial profile. A diffusion coefficient profile that reproduces the spherically averaged abundance distribution evolution is determined for each simulation. Through a combination of eigenmode analysis and scaling relations it is shown that in the N2-peak region, mixing is due to internal gravity waves and follows the scaling relation DIGW-hydro ∝ L4/3 over a $\gtrapprox 2\,\,\mathrm{\mathrm{dex}}$ range of heating factors. Different extrapolations of the mixing efficiency down to nominal heating are discussed. If internal gravity wave mixing is due to thermally enhanced shear mixing, an upper limit is $D_\mathrm{IGW}\lessapprox 2$ to $3\times 10^{4}\,\,\mathrm{cm^2\, s^{-1}}$ at nominal heating in the N2-peak region above the convective core.

Linking turbulent waves and bubble diffusion in self-aerated open-channel flows: two-state air concentration

High-Froude-number flows become self-aerated when the destabilizing effect of turbulence overcomes gravity and surface tension forces. Traditionally, the resulting air concentration profile has been explained using single-layer approaches that invoke solutions of the advection–diffusion equation for air in water, i.e. bubbles’ dispersion. Based on a wide range of experimental evidence, we argue that the complete air concentration profile shall be explained through the weak interaction of different canonical turbulent flows, namely a turbulent boundary layer (TBL) and a turbulent wavy layer (TWL). Motivated by a decomposition of the streamwise velocity into a pure wall flow and a free-stream flow (Krug et al., J. Fluid Mech., vol. 811, 2017, pp. 421–435), we present a physically consistent two-state formulation of the structure of a self-aerated flow. The air concentration is mathematically built upon a modified Rouse profile and a Gaussian error function, resembling vertical mass transport in the TBL and the TWL. We apply our air concentration theory to over 500 profiles from different data sets, featuring excellent agreement. Finally, we show that the turbulent Schmidt number, characterizing the momentum-mass transfer, ranges between 0.2 and 1, which is consistent with previous mass-transfer experiments in TBLs. Altogether, the proposed flow conceptualization sets the scene for more physically based numerical modelling of turbulent mass diffusion in self-aerated flows.

Theoretical analysis of unsteady buoyant turbulent heat and mass transport from a vertical plate using LRN k-ϵ model

The contemporary analysis has been developed to investigate the transient natural convective combined heat and mass transport of a turbulent flow adjacent to the plate by utilizing the low Reynolds number (LRN) k-ϵ model. The research problem on turbulent flow is assumed to be two dimensional and viscous incompressible. The governing turbulent equations such as continuity, momentum, energy, concentration, turbulent kinetic energy (TKE) and dissipation rate of TKE are considered as per the flow geometry. Due to the non-availability of analytical or direct numerical techniques, the corresponding highly nonlinear PDE’s are solved by adopting the standard implicit type of finite difference method namely Crank–Nicolson scheme. Also, this scheme is unconditionally stable and helps to keep the governing turbulent flow equations in discretized form and are solved via tridiagonal matrix algorithm. The simulated results for several control parameters including turbulent Reynolds number are graphically displayed and also analyzed the flow profiles. To understand the physical phenomenon of turbulent flow, the authors shown the turbulent behavior of average momentum, energy and mass transfer rates. It has been noted that, the average temperature and concentration fields boosted with rising values of . Also, TKE and dissipation rate of TKE profiles increase with enhancing turbulent values. In addition, the simulated turbulent flow results from the LRN k-ϵ model are compared with usual laminar flows as a special case and found to be in respectable agreement.

Study of Stable Stratification in HiRJET Facility With Direct Numerical Simulation

Stable density stratification in a large enclosure could significantly hamper the effectiveness of natural convection cooling in pool-type liquid metal or gas-cooled advanced reactors. In addition, accurate prediction of stratified front behavior remains to be a challenging task for turbulence modeling. With the rapid growth of high-performance-computing capabilities in recent years, conducting high-fidelity simulations for a large-timescale transient has become more affordable and hence a valuable data source to support turbulence modeling as well as to gain further physical insights. In this work, direct numerical simulation is performed at experiment-consistent conditions to simulate the density stratification transient High-Resolution Jet (HiRJET) facility. Specifically, we focus on the case where an injected aqueous sugar solution has 1.5% density higher than that in the enclosure. In the early stage of the transient, the impingement of the denser jet to the bottom surface of the enclosure promoted turbulent mixing locally. This rendered the establishment of the mixture layer, formation and swift upward propagation of the stratified front, and elevation with (locally) the highest vertical concentration gradient. As the front rose, the diminishing turbulent mass flux slowed down the propagation, and a larger vertical concentration gradient was established. In this stage, both the velocity and the concentration scalar showed large-timescale fluctuation behavior around the stratified front. For the concentration time signal, the characteristic frequency in the power spectral density was found to agree well with the Brunt-Väisällä frequency. The preliminary validation endeavor showed that the stratified front location and the corresponding concentration gradient magnitude in the simulation agreed well with the experiment data. Further validation will mainly revolve around benchmarking against high-resolution density measurement and high-order flow statistics.

Turbulent Heat and Mass Transfer about a Cylinder through LRN k-ε Model

Turbulent Heat and Mass Transfer about a Cylinder through LRN k-ε Model

Bejan’s numerical heat and mass flow visualization in turbulent boundary layer regime

Low Reynolds number k-ϵ model is employed to demonstrate the Bejan's numerical heat and mass flow visualization in turbulent boundary layer regime. The governing turbulence kinetic energy and its dissipation rate equations are included along with conservation equations. The turbulent flow equations are highly nonlinear and coupled in nature, hence, an unconditionally stable Crank–Nicolson finite difference approach is deployed. The computer-generated heatlines, masslines, streamlines, and isotherms for different control parameters are analyzed in the turbulent flow regime. Average momentum, thermal, and concentration diffusion rates are increased upon the increment in in laminar regime and are decreasing with rising in turbulent regime. The stream, heat and masslines deviate more in turbulent regime when compared to laminar regime. Further, the kinetic energy and dissipation rate contours are deviated more in turbulent heat and mass flow regime for different values of . Mainly, in this research paper, the authors made an attempt to demonstrate the turbulent heat and mass flow visualization about a vertical plate using boundary layer approximations through LRN k-ϵ turbulence model.

A Turbulent Mass Diffusivity Model for Predicting Species Concentration Distribution in the Biodegradation of Phenol Wastewater in an Airlift Reactor

In this study, a three-dimensional CFD transient model is established for predicting species concentration distribution in the biodegradation of phenol in an airlift reactor (ALR). The gas–liquid flow in the ALR is determined by the Euler–Euler method coupled with the standard k-ε model, and the bubble size is predicted by the population balance model (PBM). A turbulent mass diffusivity model is developed to simulate the turbulent mass transfer process and to predict the species concentration distribution. No empirical methods are needed as the turbulent mass diffusivity can be expressed by the concentration variance c2¯ and its dissipation rate εc. A good agreement is found between simulated and experimental results in the literature. It is not reasonable to assume a constant turbulent Schmidt number because the calculated distribution of turbulent mass diffusivity is not identical to that of turbulent viscosity. Finally, the hydrodynamic characteristics and biodegradation performance of the proposed model in a novel ALR are compared with that in the original ALR.

The Importance of Subsurface Productivity in the Pacific Arctic Gateway as Revealed by High‐Resolution Biogeochemical Surveys

AbstractFollowing sea‐ice retreat, surface waters of Arctic marginal seas become nutrient‐limited and subsurface chlorophyll maxima (SCM) develop below the pycnocline where nutrients and light conditions are favorable. However, the importance of these “hidden” features for regional productivity is not well constrained. Here, we use a unique combination of high‐resolution biogeochemical and physical observations collected on the Chukchi shelf in 2017 to constrain the fine‐scale structure of nutrients, O2, particles, SCM, and turbulence. We find large O2 excess at middepth, identified by positive saturation () maxima of 15%–20% that unambiguously indicate significant production occurring in middepth waters. The maxima coincided with a complete depletion of dissolved inorganic nitrogen (DIN = NO3− + NO2− + NH4+). Nitracline depths aligned with SCM depths and the lowest extent of maxima, suggesting this horizon represents a compensation point for balanced growth and loss. Furthermore, SCM were also associated with turbulence minima and sat just above a high turbidity bottom layer where light attenuation increased significantly. Spatially, the largest maxima were associated with high nutrient winter‐origin water masses (14.8% ± 2.4%), under a shallower pycnocline associated with seasonal melt while lower values were associated with summer‐origin water masses (7.4% ± 3.9%). Integrated O2 excesses of 800–1,200 mmol m−2 in regions overlying winter water are consistent with primary production rates that are 12%–40% of previously reported regional primary production. These data implicate short‐term and long‐term control of SCM and associated productivity by stratification, turbulence, light, and seasonal water mass formation, with corresponding potential for climate‐related sensitivities.

Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

This paper is concerned with the analysis of the long-term regular time series of current velocity and conductivity, temperature, and depth (CTD) profiles, measured with the moored autonomous profiler Aqualog over the upper part of the continental slope at a fixed geographical location in the Northeastern Black Sea. This study focuses on the fine structure of the density profiles to show that the fine-structure Cox number (C) is a power function of the Richardson number (Ri). A similar inverse power relationship with the same exponent was found earlier for the coefficient of vertical turbulent mass exchange (Kρ) and Ri. Based on those results, the analysis indicated a statistically significant correlation between C and Kρ, which suggests that the estimations of Kρ could be conducted from the CTD data only.

Energetics of buoyancy-generated turbulent flows with active scalar: pure buoyant plume

A framework for the budget of Reynolds stress, temperature and density variations, turbulent mass flux and turbulent heat flux is presented for buoyancy-generated turbulent flows with a focus on turbulent plumes. The dynamical interactions between the turbulence generated from the velocity and thermodynamic fluctuations in thermal and heated gas plumes is studied. A large-eddy simulation tool has been used to simulate heavier and lighter than air plumes released from a circular heated source for high Reynolds number (Re). The budget equations are developed using a Favre-averaging approach. Both heated air plumes and heated gas plumes, namely, heated ${\rm SO}_2$ and heated ${\rm CH}_4$ plumes, are included in the study. The study focuses on addressing key questions – does the turbulence kinetic energy (TKE) spectrum follow the classical inertial $-5/3$ spectrum or is there a $-3$ buoyancy regime with a different scaling law? Fundamental pathways for generation of turbulence through velocity fluctuations, and temperature and density fluctuations are discussed. Analysis of the TKE and scalar variance budget equations has demonstrated that multiple mechanisms dominate the transport of Reynolds stresses, and in particular that correlations between the density and the velocity dominates the turbulence production mechanisms. Entrainment is connected to the turbulent transport and pressure-dilation processes.

CONCENTRATION AND TURBULENT DIFFUSIVITY OF SAND PARTICLES IN THE ATMOSPHERE BASED ON MIXTURE MODEL THEORY

The particle concentration is analyzed numerically with a mixture model in multiphase flows. Multiple applications of this model in liquid-particle flows ensure its reliability. In the Aeolian sand transport, the density of the dispersed phase is small (on the order of 10<sup>-5</sup>-10<sup>-4</sup>. The mixture momentum equation and the continuity equation can be approximated using the single phase for an incompressible gas where the dispersed phase slip velocity (<i>u</i><sub>slip</sub>) is relative to the continuous phase. The slip velocity was calculated based on the balancing between the body and drag forces due to the density difference. The simulation results based on the mixture theory were determined in comparison to previous test results. The velocity profiles and particle concentration are presented. The results confirm that particle concentration decreases exponentially with altitude. The variation of the diffusion coefficient of sand particles (<i>D</i><sub>md</sub>) with height direction can be traced as a Gaussian distribution, which is influenced by the transported particle size and its kinetic energy. The smaller particle sizes have a larger diffusion coefficient than those with the larger ones. According to the ratio of Schmidt number, it describes the relationship between the rates of turbulent momentum transport and turbulent mass transport, which can explain the effect of wind kinetic energy on the sand turbulent diffusion profiles. The mixture approach application is in good agreement with previous wind tunnel works. This approach can be applied to study the turbulence properties in the Aeolian sand transport.

Influence of wind direction and source location on peak-to-mean concentration ratios in urban environments

Peak values of concentration can occur during very short time intervals due to atmospheric turbulence. The power law function can be used to relate the mean concentration (C‾(ΔT)) over a longer time period (ΔT) to the maximum mean concentration (C‾(Δτ)max) corresponding to a shorter time period (Δτ); however, it has not yet been fully investigated in urban areas where buildings can affect the turbulent airflow and mass transfer of pollutants. This work examines the power law function exponent (p) considering different urban scenarios: a uniform building height array and a tall building embedded in a regular array, considering different wind directions and source locations. The results show that, increasing fetch, the peak-to-mean concentration ratio usually decreases with increasing averaging time. For the same wind direction, sources located in the urban canyon produce lower |p|-values compared to the source located between buildings. Oblique flows present lower |p|-value comparing to perpendicular direction. It is fair to state that although there is an influence of wind direction and source location, the distance from the source promotes larger variations of p. For the tall building configuration, the peak-to-mean ratios as well as the |p|-values were lower compared with the uniform building height array.