Turbulent Momentum Transfer Research Articles

Flow structure and momentum transport for buoyancy driven mixing flows in long tubes at different tilt angles

Buoyancy driven mixing of fluids of different densities (ρ1 and ρ2) in a long circular tube is studied experimentally at the local scale as a function of the tilt angle from vertical (15°≤θ≤60°) and of the Atwood number [10−3≤At=(ρ2−ρ1)/(ρ2+ρ1)≤10−2]. Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) measurements in a vertical diametral plane provide the velocity and the relative concentration (and, hence, density) fields. A map of the different flow regimes observed as a function of At and θ has been determined: as At increases and θ is reduced, the regime varies from laminar to intermittent destabilizations and, finally, to developed turbulence. In the laminar regime, three parallel stable layers of different densities are observed; the velocity profile is linear and well predicted from the density profile. The thickness of the intermediate layer can be estimated from the values of At and θ. In the turbulent regime, the density varies slowly with z in the core of the flow: there, transverse turbulent momentum transfer is dominant. As At decreases and θ increases, the density gradient β in the core (and, hence, the buoyancy forces) becomes larger, resulting in higher extremal velocities and indicating a less efficient mixing. While the mean concentration varies with time in the turbulent regime, the mean velocity remains constant. In the strong turbulent regime (highest At and lowest θ values), the transverse gradient of the mean concentration and the fluctuations of concentration and velocity remain stationary, whereas they gradually decay with time when turbulence is weaker.

On the theory of turbulent heat and mass transfer with allowance for intermittence effects

A new viewpoint of the mechanism of turbulent heat and mass transfer has been proposed; a mathematical apparatus of statistical theory and a method of construction of mathematical models under the conditions of intermittent dynamic and scalar fields of nonuniform turbulent flow have been developed. A model of a turbulent axisymmetric jet for evaluation testing of the method has been constructed and the conditional and total means of the basic statistical characteristics of the jet have been calculated. It has been shown that the reason for the “different mechanism” of turbulent transfer of momentum, heat, and substance is the intermittence of not coincident dynamic and scalar fields of turbulent flow. An equation for the conditional probability density function of the concentration of a passive impurity has been derived and its solution for the axisymmetric jet in a strongly intermittent region has been given. Good agreement between the performed calculations and experimental data confirms the adopted concept of the transfer mechanism.

Experimental Investigation of Turbulent Momentum Transfer in a Neutral Boundary Layer over a Rough Surface

The turbulent characteristics of the neutral boundary layer developing over rough surfaces are not well predicted with operational weather-forecasting models. The problem is attributed to inadequate mixing-length models, to the anisotropy of the flow and to a lack of controlled experimental data against which to validate numerical studies. Therefore, in order to address directly the modelling difficulties for the development of a neutral boundary layer over rough surfaces, and to investigate the turbulent momentum transfer of such a layer, a set of hydraulic flume experiments were carried out. In the experiments, the mean and turbulent quantities were measured by a particle image velocimetry (PIV) technique. The measured velocity variances and fluxes $${(\overline{{u_{i}^{\prime}}{u_{j}^{\prime}}})}$$ in longitudinal vertical planes allowed the vertical and longitudinal gradients (∂/∂z and ∂/∂x) of the mean and turbulent quantities (fluxes, variances and third-order moments) to be evaluated and the terms of the evolution equations for ∂e/∂t, $${\partial \overline{u^{\prime 2}}/\partial t}$$ , $${\partial \overline{w^{\prime 2}}/\partial t}$$ and $${\partial \overline{{u^{\prime}}{w^{\prime}}}/\partial t}$$ to be quantified, where e is the turbulent kinetic energy. The results show that the pressure-correlation terms allow the turbulent energy to be transferred equitably from $${\overline{{u^{\prime}}^{2}}}$$ to $${\overline{{w^{\prime}}^{2}}}$$ . It appears that the repartition between the constitutive terms of the budget of e, $${\overline{{u^{\prime}}^{2}}}$$ , $${\overline{{w^{\prime}}^{2}}}$$ and $${\overline{{u^{\prime}}{w^{\prime}}}}$$ is not significantly affected by the development of the rough neutral boundary layer. For the whole evolution, the transfers of energy are governed by the same terms that are also very similar to the smooth-wall case. The PIV measurements also allowed the spatial integral scales to be computed directly and to be compared with the dissipative and mixing length scales, which were also computed from the data.

A Simple Model for Turbulent Boundary Layer Momentum Transfer on a Flat Plate

AbstractA simple model is presented for turbulent momentum transfer on a flat plate. The proposed model is based on some polynomial velocity profiles in a laminar sublayer as well as in a fully developed boundary layer and two integral boundary layer equations. The model could be used for the calculation of boundary layer thickness, velocity profile and skin friction factor on the flat plate. The calculated results are in very good agreement with other proposed empirical correlations.

Coherent structures in canopy edge flow: a large-eddy simulation study

Large coherent structures over vegetation canopies are responsible for a substantial part of the turbulent transfer of momentum, heat and mass between the canopy and the atmosphere. As forested landscapes are often fragmented, edge regions may be of importance in turbulent transfer. The development of coherent structures from the leading edge of a forest is investigated here for the first time. For this purpose, the turbulent flow over a clearing–forest pattern is simulated using the Advanced Regional Prediction System (ARPS). In previous studies the code has been modified so as to simulate turbulent flows at very fine scale (0.1h, where h is the mean canopy height) within and above heterogeneous vegetation canopies, using a large-eddy simulation (LES) approach. Validations have also been performed over homogeneous forest canopies and over a simple forest–clearing–forest pattern, against field and wind-tunnel measurements. Here, a schematic picture of the development of coherent eddies downstream from the leading edge of a forest is extracted from the mean vorticity components, the Q-criterion field, the cross-correlation of the wind velocity components and the length and separation length scales of coherent structures, determined by using a wavelet transform. This schematic picture shows strong similarities with the development of coherent structures observed in a mixing layer, with four different regions: (i) close to the edge, Kelvin–Helmholtz instabilities develop when a strong wind gust hits the canopy; (ii) these instabilities roll over to form transverse vortices from around 3h downstream from the edge, characterized by a length scale close to the depth of the internal boundary layer that develops from the canopy edge; (iii) secondary instabilities destabilize these rollers and increase the vertical and streamwise vorticity components from around 6h, and two counter-rotating streamwise vortices appear; (iv) at about 9h the initial rollers have become complex three-dimensional coherent structures, with spatially constant mean length and separation length scales. These four stages of development occur closer to the edge with increasing canopy density. While this average picture of the development of coherent structures is similar to that observed in a mixing layer, the analysis of instantaneous fields shows that coherent structures behind the leading edge appear as resulting from the ‘branching’ of tubes localized in regions of low pressure, where their cores are characterized by high values of enstrophy and Q-criterion.

Direct numerical simulation of stratification effects in a sediment-laden turbulent channel flow

This work presents direct numerical simulations of sediment-laden turbulent channel flows employing an Eulerian–Eulerian approach. The flow is driven by a constant pressure gradient and self-stratifies owing to the presence of settling sediment particles. The study is performed so as to systematically vary the settling velocity of the sediment particles, which is the parameter that controls the stratification of the flow. The effect of stratification is to suppress vertical Reynolds fluxes. For the larger values of settling velocity considered here, the flow relaminarizes below the streamwise velocity maximum, completely suppressing the turbulent vertical mass and momentum transfer. For the cases that remain actively turbulent, Reynolds fluxes are partially suppressed, but remain larger than their viscous counterparts. These cases present a clear pattern of low-speed streaks with a mean separation of approximately 100 wall units. Moreover, for these cases a pattern of high concentration streaks is found to be in high spatial correlation with the low speed streaks.

Features of turbulent momentum and heat transfer in a stably stratified boundary layer over a rough surface

The features of the structure of a stable boundary layer over an urbanized surface are studied using a nonlocal model for the turbulent momentum and heat fluxes, which physically adequately takes into account the effect of buoyancy on turbulent transfer. The transformation of the structure of the boundary layer during transition from a state of convective mixing to a stable state is described by unified expressions for the turbulent momentum and heat fluxes. In some known schemes, different models are used for unstable and stable states. The model reproduces a stable dependence of the Prandtl number on the Richardson number and countergradient heat transfer in a strongly stable boundary layer. The results of numerical simulation are compared to the data of a laboratory experiment and the data obtained using the large-eddy simulation (LES) method.

MHD turbulence in a channel with spanwise field

AbstractWe study turbulent channel flow of an electrically conducting liquid with a homogeneous magnetic field imposed in the spanwise direction. The Lorentz force is modelled using the quasistatic approximation. Direct and large–eddy simulations are performed for hydrodynamic Reynolds numbers Re=10000 and Re=20000 and the Hartmann number varying in a wide range. The main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall–normal direction. Comparing the results from direct and large–edddy simulations we show that the dynamic Smagorinsky model accurately reproduces the flow transformation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Solid–liquid mass transfer analysis in a multi-phase tank reactor containing submerged coated inclined-plates: A computational fluid dynamics approach

Although there is a voluminous literature on the estimation of interphase transport parameters in conventional slurry bubble column reactors, these correlations are inadequate in photoreactors equipped with specialized internals to facilitate light harvesting efficiency of the photocatalyst. This is particularly germane to the present externally illuminated bubble column reactor containing titania-coated plates immersed in the liquid column at different angles of inclination. Thus, a computational fluid dynamics (CFD) procedure utilizing the Eulerian–Eulerian approach has been used to solve the governing differential equations for the solid liquid mass transport problem based on the standard k – ε model incorporating additional terms that take account of the interfacial turbulent momentum transfer. Mass transfer from the surface of the coated-quartz plates to the liquid phase was modeled using the Launder–Spalding wall functions. The plates were coated with benzoic acid as solid substrate with water and air as the liquid and gas phases, respectively. The increase in mass transfer due to reduction of the boundary layer thickness during air-induced liquid recirculation on either side of the submerged inclined plates was correlated with difference between turbulent and molecular Schmidt numbers via an adjustable parameter, A. CFD simulation using the Launder–Spalding wall function (with A = 1.08 ) gave better agreement with experimental transient concentration profiles than calculations based on FLUENT's enhanced wall function for the plate orientations ( θ = 0 ∘ , 22 . 5 ∘ , and 45 ∘ ) studied. The solid-to-liquid mass transfer was higher on the lower-side of the plate than the upper-side. In particular, mass transfer coefficient was higher with the inclined plate than with the vertical or horizontal orientation suggesting an added advantage for the application of the system as a solar photoreactor.

Magnetohydrodynamic turbulence in a channel with spanwise magnetic field

The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of a low magnetic Reynolds number. Direct numerical simulation (DNS) and large eddy simulation (LES) computations are performed for two values of the hydrodynamic Reynolds number (104 and 2×104) and with the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near the wall decrease, and the typical horizontal dimensions of the coherent structures enlarge upon increasing the Hartmann number. Comparison between LES and DNS results shows that the dynamic Smagorinsky model accurately reproduces the flow transformation.

Countergradient heat transfer in the atmospheric boundary layer over a rough surface

The nonlocality of the mechanism of turbulent heat transfer in the atmospheric boundary layer over a rough surface manifests itself in the form of bounded areas of countergradient heat transfer, which are diagnosed from analysis of balance items in the transport equation for the variance of temperature fluctuations and from calculation of the coefficients of turbulent momentum and heat transfer invoking the model of “gradient diffusion.” It is shown that countergradient heat transfer in local regions is caused by turbulent diffusion or by the term of the divergence of triple correlation in the balance equation for the temperature variance.

Intermediate Scaling of Turbulent Momentum and Heat Transfer in a Transitional Rough Channel

The properties of the mean momentum and thermal balance in fully developed turbulent channel flow on transitional rough surface have been explored by method of matched asymptotic expansions. Available high quality data support a dynamically relevant three-layer description that is a departure from two-layer traditional description of turbulent wall flows. The scaling properties of the intermediate layer are determined. The analysis shows the existence of an intermediate layer, with its own characteristic of mesolayer scaling, between the traditional inner and outer layers. Our predictions of the peak values of the Reynolds shear stress and Reynolds heat flux and their locations in the intermediate layer are well supported by the experimental and direct numerical simulation (DNS) data. The inflectional surface roughness data in a turbulent channel flow provide strong support to our proposed universal log law in the intermediate layer, that is, explicitly independent transitional surface roughness. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional type roughness, Colebrook–Moody monotonic roughness, etc. In traditional variables, the roughness scale for inflectional roughness is supported very well by experimental and DNS data. The higher order effects are also presented, which show the implications of the low Reynolds-number flows, where the intermediate layer provides the uniformly valid solutions in terms of generalized logarithmic laws for the velocity and the temperature distributions.

Improved 1-D modelling in compound meandering channels with vegetated floodplains

This paper shows that common open channel flow one-dimensional (1-D) numerical models behave poorly in terms of flow distribution across a section in a naturalized meandering channel with vegetated floodplains.We compared numerical models with new experiments carried out in a physical model on a reach of the Besòs river close to Barcelona that has been restored. The case examined has floodplains with thick vegetation, a low-flow meandering channel and high water depths over the main channel and floodplains. 1-D models overestimate velocities in the main channel but underestimate them on the floodplains. The paper gives a detailed description of an improved 1-D computation method based on the consideration of the total shear stress at the main channel-floodplain interface (the sum of turbulent friction plus lateral momentum transfer) on the one hand, and the influence of upstream velocity distribution with the help of two-dimensional numerical models on the other hand.

Two aerodynamic roughness maps derived from Mars Orbiter Laser Altimeter (MOLA) data and their effects on boundary layer properties in a Mars general circulation model (GCM)

Mechanical (forced convective) and free convective turbulent heat and momentum transfer in the lower atmosphere of a terrestrial planet has some dependence on the roughness characteristics of the surface, often quantified in terms of a single roughness parameter which is then used to calculate the coefficients that govern heat and momentum transport between the surface and the boundary layer. We take two different approaches for deriving this aerodynamic roughness parameter for Martian surfaces using data from the Mars Orbiter Laser Altimeter. We then use these two different roughness maps to force the boundary layer in a Mars general circulation model, primarily investigating differences in temperatures and the pressure cycle between the two simulations. While the pressure cycle does not vary significantly, spring and summer high‐latitude temperatures are somewhat sensitive to the input roughness conditions. Daytime temperatures may vary up to 10 K seasonally, though zonally and annually averaged daytime temperatures vary only by ∼1 K. Our results can be explained by the dominance of mechanical over convective turbulent heat transfer processes on Mars. These simulations, however, use a prescribed atmospheric dust distribution and thus only provide a minimum estimate of the uncertainty in boundary layer temperatures because of this plausible range of aerodynamic roughness parameters. Since surface roughness determines the threshold wind velocity for dust lifting we anticipate a much larger effect of the aerodynamic roughness parameter on temperatures when the dust distribution is allowed to vary according to predicted lifting and transport.

Two-dimensional modeling of water spray cooling in superheated steam

Spray cooling of the superheated steam occurs with the interaction of many complex physical processes, such as initial droplet formation, collision, coalescence, secondary break up, evaporation, turbulence generation, and modulation, as well as turbulent mixing, heat, mass and momentum transfer in a highly non-uniform two-phase environment. While it is extremely difficult to systematically study particular effects in this complex interaction in a well defined physical experiment, the interaction is well suited for numerical studies based on advanced detailed models of all the processes involved. This paper presents results of such a numerical experiment. Cooling of the superheated steam can be applied in order to decrease the temperature of superheated steam in power plants. By spraying the cooling water into the superheated steam, the temperature of the superheated steam can be controlled. In this work, water spray cooling was modeled to investigate the influences of the droplet size, injected velocity, the pressure and velocity of the superheated steam on the evaporation of the cooling water. The results show that by increasing the diameter of the droplets, the pressure and velocity of the superheated steam, the amount of evaporation of cooling water increases. .

A Total Turbulent Energy Closure Model for Neutrally and Stably Stratified Atmospheric Boundary Layers

Abstract This paper presents a turbulence closure for neutral and stratified atmospheric conditions. The closure is based on the concept of the total turbulent energy. The total turbulent energy is the sum of the turbulent kinetic energy and turbulent potential energy, which is proportional to the potential temperature variance. The closure uses recent observational findings to take into account the mean flow stability. These observations indicate that turbulent transfer of heat and momentum behaves differently under very stable stratification. Whereas the turbulent heat flux tends toward zero beyond a certain stability limit, the turbulent stress stays finite. The suggested scheme avoids the problem of self-correlation. The latter is an improvement over the widely used Monin–Obukhov-based closures. Numerous large-eddy simulations, including a wide range of neutral and stably stratified cases, are used to estimate likely values of two free constants. In a benchmark case the new turbulence closure performs indistinguishably from independent large-eddy simulations.

Modeling of the rotational motion of a dispersed phase using the equations of transfer of the second and third moments of pulsations of the translational and angular velocities of particles

This article considers the Eulerian continuum description of turbulent transfer of momentum and moment of momentum in a solid phase on the basis of the equations of transfer of the second and third moments of pulsations of the linear and angular velocities of particles. The pulsating characteristics of a gas are computed using the two-parameter model of turbulence generalized to the case of gas-dispersed turbulent flows.

Calculation of turbulent momentum transfer in a solid phase based on equations for the second and third moments of particle-velocity pulsations

A chain of transfer equations for the second and third moments of dispersed-phase-velocity pulsations in the anisotropic field of energy of random particle motion is obtained based on the computational procedure developed. The interphase and interparticle interactions are allowed for. The turbulent characteristics of the gas are calculated on the basis of a one-parameter turbulence model generalized to the case of two-phase turbulent flows.

F225 DNSによる温度成層を伴う空間発展乱流境界層の研究(乱流・DNS)

This paper presents turbulent structures of thermally-stratified boundary layer using results of direct numerical simulations (DNSs) for a spatially developing boundary layer. In the previous study (Hattori et al., 2007), we indicated fundamental turbulent statistics of boundary layer flow with various thermal stratifications by means of DNS. DNSs show fascinating results, in which the counter-gradient diffusion phenomena (CDP) in turbulent momentum and heat transfer are observed in the strongly-stratified stable boundary layer It is well-known that the counter-gradient diffusion phenomenon disturbs the transport of turbulent quantities due to reductions of the effective diffusivities for momentum and heat. However, it is not yet fully understood how and why CDP occur in strongly-stratified stable turbulent flows. The objectives of this study are to investigate turbulent structure in specially developing thermally-stratified turbulent boundary layers.

Determining factor for the blowoff limit of a flame spreading in an opposed turbulent flow, in a narrow solid-fuel duct

Abstract This study clarified the blowoff mechanism for a flame spreading in an opposed turbulent flow in narrow solid fuel ducts. To clarify this mechanism, two experiments were conducted. The first experiment was to investigate the influence of ambient pressure and fuel duct size on the blowoff limit. The results indicated that the flow velocity at the point when blowoff occurred, V g , t , increased with ambient pressure. This tendency could not be confirmed by a well-known expression for the Damkohler number, which is defined as the ratio of the characteristic flow time to the characteristic chemical time. Subsequently, to clarify the determining factor for the blowoff, the second experiment, which observed the flow field near the flame leading edge, was conducted. The results show that the flow separation in front of the flame leading edge, which provided sufficient residence time of oxidizer and gaseous fuel, is necessary for the flame to spread in an opposed oxidizer flow. From the results, it is found that the oxidizer friction velocity, u ∗ , which is an indicator of the turbulent momentum transfer, is the determining factor for the flame blowoff limit. When the friction velocity is larger than a critical value, flame blowoff occurs in the fuel duct, due to the absence of flow separation.