Turbulent Advection Research Articles

Turbulent heat transfer of highly buoyant supercritical CO2 flow in various horizontal pipes

Supercritical CO2 (sCO2) is considered as an ideal heat transfer fluid for power cycles adapted to a wide range of heat sources. This paper employs computational approach based on Reynolds-Averaged Navier-Stokes (RNAS) modelling to study highly buoyant turbulent sCO2 flow and heat transfer heated in various horizontal tubes with diameter of 4.57 mm, 13.39 mm, and 22.14 mm. The conditions with relatively high ratio of heat flux q to mass flux G are simulated. The chosen AKN k − ε low-Reynolds number turbulence model is rigorously validated against experiments and DNS covering a wide range of operation conditions and exhibits quite satisfactory consistencies on the strong buoyancy reproductions of horizontal supercritical flows. With sCO2 heat transfer data presented, details about the coupled turbulent flow characteristics have been discussed. It has been observed that in various size horizontal geometries, not only the local sCO2 heat transfer along the tube top surface, but also the overall performance within the liquid-like region near Tpc is greatly degraded by the strong buoyancy, and the deterioration regime expands with decreasing pipe diameter. For the highly buoyant horizontal sCO2 flows, a backflow vortex appears near the top wall then a second velocity peak forms which locates further into the core flow section for larger diameter pipes; The radial velocity profile of the top wall has been flattened even distorted into “half-M” shape that the turbulence statistics decline remarkably then the turbulent activities and thermal advection are attenuated. With sCO2 heated into the gas-like regime, the heat transfer recovers because of the reduced buoyancy effects.

Strongly Nonlinear Diffusion in Turbulent Environment: A Problem with Infinitely Many Couplings

The field theoretic renormalization group is applied to the strongly nonlinear stochastic advection-diffusion equation. The turbulent advection is modelled by the Kazantsev–Kraichnan “rapid-change” ensemble. As a requirement of the renormalizability, the model necessarily involves infinite number of coupling constants (“charges”). The one-loop counterterm is calculated explicitly. The corresponding renormalization group equation demonstrates existence of a pair of two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant), the critical dimensions of the scalar field Δθ, the response field Δθ′ and the frequency Δω are nonuniversal (through the dependence on the effective couplings) but satisfy certain exact identities. For the second surface (advection is relevant), the dimensions are universal and they are found exactly.

Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise: Emergence of Induced Nonlinearity

We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f(t,x) is specified by the pair correlation function ⟨f(t,x)f(t′,x′)⟩∝δ(d)(x−x′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε=4−d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.

Stochastic Modeling of a Lifted Methane/Air Jet Flame with Detailed Chemistry

AbstractThis preliminary numerical study investigates a lifted methane/air jet flame in a vitiated coflow by means of the One‐Dimensional Turbulence (ODT) model. In the considered Cabra Burner configuration [Combust. Flame 143 491‐506 (2005)], a jet flame issues from a central nozzle into a vitiated coflow of hot combustion products from lean premixed hydrogen/air flames. ODT is a map‐based model for turbulent flow simulations which uses a stochastic formulation for the turbulent advection. The diffusion and reaction effects along the one‐dimensional domain are considered by temporally advancing deterministic evolution equations. ODT simulations are performed with a representation of the methane/air chemistry by a reduced 19‐species mechanism with 15 reactions and a detailed 53‐species mechanism with 325 reactions. In this work, we present centerline profile of temperature and species concentrations obtained from ODT simulations using a cylindrical ODT‐formulation. Additionally, two‐dimensional renderings of the temperature distribution are shown. Although the simulation of reactive jet configurations by means of ODT is not novel, the complex stabilization region depending on the flow conditions represents a challenge for the model. Considering the reduced order of the model, ODT is able to predict the flow characteristics and reasonably matches the existing experimental data.

Characteristics and Scaling of the Stable Marine Internal Boundary Layer

AbstractThe characteristics of a stable internal boundary layer (SIBL) offshore of Duck, North Carolina documented during CASPER‐EAST have been examined using surface layer‐resolving large eddy simulations. Under the influence of steady offshore winds, a SIBL develops over the coastal waters with its depth growing with the offshore advection time (TA) as ∼. The SIBL includes an internal equilibrium layer above the surface where the heat and momentum fluxes linearly decrease with height and a transition layer aloft. The offshore area can be partitioned into three distinct zones, namely, a nearshore zone (NSZ, TA < Td/3), an intermediate offshore zone (IOZ, Td/3 < TA < Td), and a far‐offshore zone (FOZ, TA > Td), where Td is the vertically‐averaged turbulent dissipation time. The advection of turbulence from land plays a significant role in the momentum and scalar budgets over the NSZ. Consequently, the Monin‐Obukhov similarity theory (MOST) becomes invalid, and local similarity theory is applicable only above the SIBL in the NSZ. In the IOZ, the advection of turbulence from land is less important but still non‐negligible. As a result, while the dimensionless standard deviations of winds and potential temperature converge toward the MOST curves, the dimensionless gradients are smaller than their counterparts in the FOZ. In the FOZ, the advection from land becomes negligible, and MOST is applicable throughout the constant flux layer. Over the IOZ and the FOZ, LST works reasonably well within the SIBL.

Numerical Prediction of the Boundary-Layer Flow Over the Bolund Hill: Assessment of Turbulence Models and Advection Schemes

The WindStation software package is applied to simulate the wind field over the Bolund hill. The standard, ReNormalization Group (RNG), realizable, and limited-length k−e turbulence models are tested, along with the quadratic upstream interpolation for convective kinetics (QUICK) and hybrid advection schemes. Comparisons with experimental results are made for the speed-up and turbulence kinetic energy (TKE) increase. The adopted mesh is Cartesian uniform in the horizontal plane and terrain following with a variable expansion factor in the vertical direction. The QUICK advection scheme leads to better agreement with the experimental data than the hybrid scheme, in particular for the TKE increase. The RNG and standard k−e turbulence models show the best performance for speed-up and for TKE increase, respectively.

The influence of turbulent transport in reactive processes: A combined numerical and experimental investigation in a Taylor-Couette reactor

Turbulent reactive flows are ubiquitous in industrial processes. Decoupling transport effects from intrinsic chemical reactions requires an in-depth understanding of fluid flow physics; computational fluid dynamics (CFD) methods have been widely used for this purpose. Most CFD simulations of reactive liquid-phase flows, where the Schmidt numbers are large, rely on isotropic eddy viscosity models. However, the assumption of turbulent isotropy in most stirred reactors and wall-bounded flows is fundamentally incorrect and leads to erroneous results. Here, we apply a systematic CFD approach to simulate liquid-phase diffusive and convective transport phenomena that occur in a Taylor-Couette (TC) reactor. We resolve the turbulent flow by extracting statistics from large eddy simulation which is used to tune the anisotropic Reynolds stress model. In addition, we conducted a series of turbulent precipitation and mixing studies in a TC reactor that was designed and fabricated in-house. The numerical model is successfully validated against a published torque correlation and it is found to accurately describe the advection and diffusion of chemical species. The validated model is then used to demonstrate key flow properties in the reactor. We define new local turbulent Peclét numbers to characterize the relative increase in diffusivity from turbulent advection and observe a 29% increase in the turbulent contribution as Reynolds number is doubled. Both reactive simulations and experiments show an increase in overall reaction rates with increased turbulence. The results from reactive simulations provide a deeper understanding of flow-kinetics interactions at turbulent conditions.

Hierarchy of coherent structures and real-space energy transfer in turbulent channel flow

Abstract

A convective analytical model in turbulent boundary layer on a flat plate based on the unifying heat flux formula

The two-dimensional (2D) convective heat fluxes are formulated for quasi-steady incompressible turbulent thermal boundary layer flow over a flat plate based on the unifying heat-flux formula developed previously. It is indicated that the total turbulent convection heat flux is the combination of three heat transport mechanisms: conduction due to random molecular motion, laminar advection due to time-averaged motion of fluid bulk and turbulent advection due to fluctuations of velocity and temperature. The interdependent relationship between two heat flux components in different directions is obtained for the quasi-steady turbulent boundary layer flow, which is proved to be equivalent to the turbulent differential and integral energy equations with constant physical properties, respectively. The turbulent thermal boundary layer is divided into laminar sublayer and turbulent layer, in which the linear and one-seventh-power temperature (velocity) profiles are adopted, respectively. Considering the different thicknesses of turbulent thermal and velocity boundary layers, the explicit analytical expression of convective turbulent heat transfer coefficient, as well as the simplified analytical expressions of boundary layer thickness ratio, is proposed based on the total turbulent convection heat transfer structure. The suggested analytical turbulent convective heat transfer coefficients (or Stanton numbers) for air and water are validated by comparing with those of previous theories and experimental measurements. Relevant key characteristics and physical insights of the turbulent structure on the flat plates are revealed in virtue of 2D analytical convective heat fluxes proposed.

Low complexity model to study scale dependence of phytoplankton dynamics in the tropical Pacific.

We demonstrate that a simple model based on reaction-diffusion-advection (RDA) equation forced by realistic surface velocities and nutrients is skilled in reproducing the distributions of the surface phytoplankton chlorophyll in the tropical Pacific. We use the low-complexity RDA model to investigate the scale relationships in the impact of different drivers (turbulent diffusion, mean and eddy advection, primary productivity) on the phytoplankton chlorophyll concentrations. We find that in the 1/4^{∘} (∼25km) model, advection has a substantial impact on the rate of primary productivity, while the turbulent diffusion term has a fairly negligible impact. Turbulent diffusion has an impact on the phytoplankton variability, with the impact being scale propagated and amplified by the larger scale surface currents. We investigate the impact of a surface nutrient decline and some changes to mesoscale eddy kinetic energy (climate change projections) on the surface phytoplankton concentrations. The RDA model suggests that unless mesoscale eddies radically change, phytoplankton chlorophyll scales sublinearly with the nutrients, and it is relatively stable with respect to the nutrient concentrations. Furthermore, we explore how a white multiplicative Gaussian noise introduced into the RDA model on its resolution scale propagates across spatial scales through the nonlinear model dynamics under different sets of phytoplankton drivers. The unifying message of this work is that the low-complexity (e.g., RDA) models can be successfully used to realistically model some specific aspects of marine ecosystem dynamics and by using those models one can explore many questions that would be beyond computational affordability of the higher-complexity ecosystem models.

Stochastic Modeling of a Lifted Methane/Air Jet Flame with Detailed Chemistry

AbstractThis preliminary numerical study investigates a lifted methane/air jet flame in a vitiated coflow by means of the One‐Dimensional Turbulence (ODT) model. In the considered Cabra Burner configuration [Combust. Flame 143 491‐506 (2005)], a jet flame issues from a central nozzle into a vitiated coflow of hot combustion products from lean premixed hydrogen/air flames. ODT is a map‐based model for turbulent flow simulations which uses a stochastic formulation for the turbulent advection. The diffusion and reaction effects along the one‐dimensional domain are considered by temporally advancing deterministic evolution equations. ODT simulations are performed with a representation of the methane/air chemistry by a detailed 53‐species mechanism with 325 reactions. In this work, we present centerline profile of temperature and species concentrations obtained from ODT simulations using a cylindrical ODT‐formulation. Additionally, a two‐dimensional rendering of the temperature distribution is shown. Although the simulation of reactive jet configurations by means of ODT is not novel, the complex stabilization region depending on the flow conditions represents a challenge for the model. Considering the reduced order of the model, ODT is able to predict the flow characteristics and reasonably matches the existing experimental data.

Effects of Turbulent Environment on Self-Organized Critical Behavior: Isotropy vs. Anisotropy

We study a self-organized critical system under the influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [Phys. Rev. Lett.62: 1813 (1989)]. The motion of the environment is modelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressible fluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form ∝δ(t−t′)/kd+ξ, where k is the wave number and ξ is an arbitrary exponent with the most realistic values ξ=4/3 (Kolmogorov turbulence) and ξ→2 (Batchelor’s limit). Using the field-theoretic renormalization group, we find infrared attractive fixed points of the renormalization group equation associated with universality classes, i.e., with regimes of critical behavior. The most realistic values of the spatial dimension d=2 and the exponent ξ=4/3 correspond to the universality class of pure turbulent advection where the nonlinearity of the Hwa–Kardar (HK) equation is irrelevant. Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equation and the (isotropic) advecting velocity field are relevant also exists for some values of the parameters ε=4−d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specific universality class, different types of scaling behavior (ordinary one or generalized) are established.

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier–Stokes equation

The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent motion is described by the stochastic Navier–Stokes equation with the random stirring force whose correlation function includes two terms that allow one to account both for a turbulent fluid and for a fluid in thermal equilibrium. The renormalization group analysis performed in the leading order of perturbation theory (one-loop approximation) reveals six possible types of scaling behaviour (universality classes). The most interesting values of the spatial dimension d = 2 and 3 correspond to the universality class of a pure turbulent advection where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant.

Application of masked two-dimensional Fourier spectra for improving the accuracy of STIV-based river surface flow velocity measurements

Space-time image velocimetry (STIV) is a well-established image-based technique for measuring river surface flow from videos or image time series. Because the fundamental measurement mechanism is relatively simple, STIV has been used widely in research and for practical purposes in Japan and other countries. The advantage of STIV over other imaging techniques such as large-scale particle image velocimetry (LSPIV) is its robustness. More specifically, the streamwise velocity component can be efficiently estimated by simply measuring the slope appearing in a space-time image (STI) that represents the advection of surface textures. However, in the course of practical applications cases occur in which STIV yields erroneous results when the measurement conditions at the river site are not satisfactory for accurate measurements, such as when the water surface includes textures other than those directly related to turbulent advection. In this research, surface textures are classified into ten types and image filters based on wavenumber–frequency spectra are developed to improve the quality of the STI so that the texture contains only those features that represents the advection of surface turbulence. The quality of the STI can be improved with the filters and thus further increase the robustness of the measurement technique.

One-dimensional turbulence: Application to incompressible spatially developing turbulent boundary layers

A map-based stochastic approach, One-Dimensional Turbulence (ODT), is applied to analyze the incompressible spatially developing turbulent boundary layer (SBL). In the present study, the SBL is formed by a plane moving wall and a free stream at rest. The flow variables are resolved on all scales along a 1-D domain. A deterministic process represents the molecular diffusion and a stochastic process is modeling the effect of turbulent advection and pressure fluctuations. Due to the reduced dimensions in the model, it achieves major cost reductions as compared to the full 3-D simulations and is, thus, able to explore large parameter regimes. The simulations are presented for momentum thickness Reynolds numbers, Reθ, varied in the range Reθ≈1968-8000. We have investigated various features related to the SBL, such as mean, root mean square, Reynolds shear stress, skewness, flatness and pre-multiplied velocity profiles and skin friction coefficient and shape factor, all for two bulk velocities using ODT and compared our results to the available reference Direct Numerical Simulations (DNS) and large-eddy simulations (LES) results. We have further compared the results for spatial and temporal ODT formulations used to investigate the turbulent boundary layer with the reference data at matched Reθ. The comparison presented suggests that ODT is a reasonably accurate approach for the simulations of the spatially developing turbulent boundary layers which can be further improved to yield accurate statistics at high Reynolds number by implementing Fourier transformation of the kernels which in the present formulation of the model is not implemented.

Universality Classes of the Hwa-Kardar Model with Turbulent Advection

Self-organized critical system in turbulent fluid environment is studied with the renormalization group analysis. The system is modelled by the anisotropic stochastic differential equation for a coarse-grained field proposed by Hwa and Kardar [Phys. Rev. Lett. 62, 1813 (1989)]. The turbulent motion of the environment is described by the anisotropic d-dimensional velocity ensemble based on the one introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990)] and modified to include dependence on time (finite correlation time). Renormalization group analysis reveals three universality classes (types of critical behavior) differentiated by the parameters of the system.

ПРО "КОРОЛІВСЬКУ ЗОНУ" СОНЯЧНИХ ПЛЯМ І ПОДВІЙНИЙ МАКСИМУМ СОНЯЧНОГО ЦИКЛУ

Cyclic regeneration of the large-scale magnetic field of the Sun underlies all the phenomena known collectively as “solar activity”. The sunspot cycle is arguably the best known manifestation of the solar magnetic cycle. We outlined here the scenario of reconstructing of toroidal magnetic field in the solar convection zone (SCZ), which, on our opinion, may help to understand why magnetic fields rise to the solar surface only in the sunspot “royal zone” and what is reason of the phenomenon of double maximum of sunspots cycle. The effect of magnetic pumping (advection) caused by radial inhomogeneity of matter with taking into account Sun’s rotation, in conjunction with deep meridional circulation, play a key role in proposed scenario. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the SCZ. Therefore, we examined two “antibuoyancy” effects: macroscopic turbulent diamagnetism and magnetic advection caused by radial inhomogeneity of fluid density in the SCZ, which we call as the ∇ρ effect. The Sun’s rotation substantially modifies the ∇ρ effect. The reconstructing of the toroidal field was examined assuming the balance between mean-field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. We found that the reconstructing of large-scale magnetism develops differently in the near-polar and equatorial domains of the SCZ. In the near-polar domain, two downward pumping effects (macroscopic diamagnetism and rotational pumping) act against magnetic buoyancy and, as a result, they neutralize magnetic buoyancy and block the toroidal field (which is generated by the Ω effect) near the tachocline. Therefore, these two antibuoyancy effects might be the reason why sunspots at the near-polar zones are never observed. In other words, strong deep-seated fields at high latitudes may well be there, but they not produce sunspots. At the same time, in the deep layers of the equatorial domain, the rotational turbulent pumping due to the latitudinal convection anisotropy changes its direction to the opposite one (from downward to upward), thereby facilitating the migration of the field to the surface. We call this transport as first (upward) magnetic advection surge. The fragments of this floating up field can be observed after a while as sunspots at latitudes of the “royal zone”. Meanwhile, a deep equator-ward meridional flow ensures transporting of deep-seated toroidal field, which is blocked near pole in tachocline, from high latitudes to low ones where are favourable conditions for the floating up of the strong field. Here this belated strong field is transported upward to solar surface (the second upward magnetic advection surge). Ultimately, two time-delayed upward magnetic surges may cause on the surface in the “royal zone” the first and second maxima of sunspots cycle.

Momentum Transport in Shallow Cumulus Clouds and Its Parameterization by Higher‐Order Closure

AbstractIt is challenging to parameterize subgrid vertical momentum fluxes in marine shallow cumulus layers that contain a jet in the profile of horizontal wind. In a large‐eddy simulation of such a layer, it is found that the momentum flux in the direction of strongest wind magnitude has a three‐layer structure. The lowest layer, from the ocean surface up to the jet maximum, has downgradient momentum flux. The middle layer, from the jet maximum up to an altitude several hundred meters above, has upgradient (i.e., countergradient) momentum flux because of transport of low‐magnitude momentum upward through the jet maximum. In the upper layer, the layer‐average momentum flux is weak. The budget of momentum flux shows that in the middle and upper layers, both the buoyancy production term and turbulent advection (i.e., third‐order flux‐of‐flux) terms are important.To parameterize the profile of momentum flux in a single‐column model, the momentum flux is prognosed in this study. The buoyancy production and flux‐of‐flux terms are parameterized by integrating them over a subgrid probability density function with an assumed normal‐mixture shape. The resulting parameterized fluxes and mean‐wind profiles are demonstrated to be comparable to those produced in large‐eddy simulations, both for two marine shallow cumulus cases with upgradient fluxes and for a continental cumulus case and two stratocumulus cases with downgradient fluxes. In the two marine shallow cumulus cases, the parameterization is able to capture the upgradient momentum flux above the jet maximum and the weak momentum fluxes aloft.

Hierarchical Parcel‐Swapping: An efficient mixing model for turbulent reactive flows

AbstractHierarchical Parcel‐Swapping (HiPS) developed by A.R. Kerstein [J. Stat. Phys. 153, 142‐161 (2013)] is a computationally efficient and novel model for the effects of turbulence on time‐evolving, diffusive scalar fields. The characteristic feature of HiPS is the interpretation of the one‐dimensional flow domain or a state space as a binary tree structure. Every tree level corresponds to a specific length and time scale, which is based on a turbulence inertial range scaling. The state variables reside at the base of the tree and are interpreted as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion time scales. In this work, we investigate the influence of turbulent time scale variations on an isothermal series‐parallel reaction scheme. The production of a desired chemical species is evaluated by means of a defined selectivity and is strongly affected by the underlying mixing time scales.

One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS

ABSTRACTThe incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range using fixed model parameters. The influence of the model parameters is analysed for and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows.