Turbulent Momentum Transfer Research Articles

Heat and momentum transfer for magnetoconvection in a vertical external magnetic field.

The scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)JFLSA70022-112010.1017/S0022112099007545] for turbulent heat and momentum transfer is extended to the magnetoconvection case in the presence of a (strong) vertical magnetic field. A comparison with existing laboratory experiments and direct numerical simulations in the quasistatic limit allows us to restrict the parameter space to very low Prandtl and magnetic Prandtl numbers and thus to reduce the number of unknown parameters in the model. Also included is the Chandrasekhar limit, for which the outer magnetic induction field B is large enough such that convective motion is suppressed and heat is transported by diffusion. Our theory identifies four distinct regimes of magnetoconvection that are distinguished by the strength of the outer magnetic field and the level of turbulence in the flow, respectively.

Air–Sea Interactions in Light of New Understanding of Air–Land Interactions

Abstract Air–sea interactions are investigated using the data from the Coupled Boundary Layers Air–Sea Transfer experiment under low wind (CBLAST-Low) and the Surface Wave Dynamics Experiment (SWADE) over sea and compared with measurements from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) over land. Based on the concept of the hockey-stick transition (HOST) hypothesis, which emphasizes contributions of large coherent eddies in atmospheric turbulent mixing that are not fully captured by Monin–Obukhov similarity theory, relationships between the atmospheric momentum transfer and the sea surface roughness, and the role of the sea surface temperature (SST) and oceanic waves in the turbulent transfer of atmospheric momentum, heat, and moisture, and variations of drag coefficient Cd(z) over sea and land with wind speed V are studied. In general, the atmospheric turbulence transfers over sea and land are similar except under weak winds and near the sea surface when wave-induced winds and oceanic currents are relevant to wind shear in generating atmospheric turbulence. The transition of the atmospheric momentum transfer between the stable and the near-neutral regimes is different over land and sea owing to the different strength and formation of atmospheric stable stratification. The relationship between the air–sea temperature difference and the turbulent heat transfer over sea is dominated by large air temperature variations compared to the slowly varying SST. Physically, Cd(z) consists of the surface skin drag and the turbulence drag between z and the surface; the increase of the latter with decreasing V leads to the minimum Cd(z), which is observed, but not limited to, over sea.

Two-Dimensional Thermohydraulic Module of the Integrated Code Sokrat-BN: Mathematical Model and Computational Results

The two-dimensional thermohydraulic model used in the thermohydraulic module of the SOKRAT-BN code is described and the computational results obtained by using it are presented. The thermohydraulic model is based on the solution of two-dimensional equations using empirical correlations for determining the intensity of the turbulent transfer of mass, energy and momentum in the radial direction. The experiments performed in the 19- and 37-pin assemblies on the Siena stand in Japan and in the 37-pin assembly in the KNS stand in Germany were calculated. The average deviations of the computed values do not exceed 10%.

An anisotropic turbulent mass transfer model for simulation of pilot-scale and industrial-scale packed columns for chemical absorption

An anisotropic turbulent mass transfer model, namely the Reynolds mass flux model (RMF), for simulating the chemical absorption process in packed column is introduced by the use of combined computational methodology. With the present model, the concentration and temperature as well as velocity distributions can be simultaneously obtained. The feature of the proposed model is that the modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation so that the Boussinesq’s postulation is abandoned and consequently the anisotropy of turbulent mass diffusion can be characterized. The present model is accompanied by the formulations of computational fluid dynamics (CFD) and computational heat transfer (CHT). In mathematical expression of CFD and CHT, the Reynolds stress and Reynolds heat flux equations are used to close the turbulent momentum and heat transfer equations. The simulated results are validated with experimental data for pilot-scale and industrial-scale packed columns and satisfactory agreement is found between them. Furthermore, the Reynolds mass flux and the anisotropic turbulent mass diffusion are characterized and discussed.

A Reynolds mass flux model for gas separation process simulation: I. Modeling and validation

Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux (RMF) model. With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerically. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation, while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and momentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To validate the presented RMF model, simulation is carried out for CO2 absorption into aqueous NaOH solutions in a packed column (0.1m id, packed with 12.7mm Berl saddles up to a height of 6.55m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temperature distributions. The sequel Part II extends the model application to the simulation of an unsteady state adsorption process in a packed column.

High Temperature Oxidation Stability of Aerodynamically Optimised Riblets for Blades of Aero-engine Applications

The mechanism of nature’s way of friction reduction and aerodynamical optimisation is applied worldwide. There is ample literature on investigations and measurement of skin friction reduction in the boundary layer over flat plates and on turbo machinery type blades. When using a surface with riblet structures, the turbulent momentum transfer at the wall which is responsible for the skin friction is hampered. This paper deals with the oxidation and characterisation of riblets with micrometer dimensions for aerodynamically optimised high temperature turbine applications. Riblets were fabricated on EB-PVD NiCoCrAlY coatings by using a pico-second laser. The high temperature oxidation stability of the riblets was tested by conducting cyclic oxidation tests. The temperatures were selected as 900 and 1100 °C and the time of oxidation was varied between 1 and 1,000 cycles. The thermocyclic tests at 900 °C proved that the riblets are stable even after 1,000 cycles and at 1,100 °C the stability is permitted to until only 100 cycles. With few modifications in the structuring process this stability can be further improved.

Computational fluid dynamics simulation of hydrodynamics and chemical reaction in a CFB downer

A computational fluid dynamics (CFD) model for simulating the chemical reaction process in a gas–particle circulating fluidized bed (CFB) downer is introduced by combining the two-fluid model (TFM) for the gas–particle turbulent flows and the c2¯−εc model for the turbulent mass transfer. With the proposed model, the species concentration and solid volume fraction as well as the velocity distributions along the CFB downer are able to be predicted. In mathematical expression of the proposed model, the recently developed formulations of c2¯−εc is adopted to close the turbulent mass transfer equations so that the turbulent mass diffusivity can be determined without relying on empirical methods. As for the gas–solid two phase turbulent momentum transfer equations, the methodology of kg−εg−kp−εp−Θ is used for their closures. To validate the proposed model, simulation is carried out for the catalytic ozone decomposition in a gas–solid CFB downer. The simulation results are compared with the experimental data and satisfactory agreement is found between them in both axial/radial distributions of concentration and solid volume fraction. Furthermore, the simulations reveal that the turbulent mass diffusivity varies along axial and radial directions, and the turbulent Schmidt number is not a constant throughout the CFB downer.

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 2: Wind–wave spectra

Abstract. Drag and mass exchange coefficients are calculated within a self-consistent problem for the wave-induced air perturbations and mean velocity and density fields using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. This second part of the report is devoted to specification of the model elements: turbulent transfer coefficients and wave number-frequency spectra. It is shown that the theory agrees with laboratory and field experimental data well when turbulent mass and momentum transfer coefficients do not depend on the wave parameters. Among several model spectra better agreement of the theoretically calculated drag coefficients with TOGA (Tropical Ocean Global Atmosphere) COARE (Coupled Ocean–Atmosphere Response Experiment) data is achieved for the Hwang spectrum (Hwang, 2005) with the high frequency part completed by the Romeiser spectrum (Romeiser et al., 1997).

Momentum and mass transfer in developing liquid shear mixing layers

Flow structure in developing mixing layers is experimentally investigated with an emphasis on the second moment terms. Instantaneous streamwise and vertical velocities and concentration are simultaneously measured using a combination of a laser-Doppler velocimeter and a laser-induced fluorescence technique. The results show that the turbulent momentum and mass transfer in developing mixing layers can be negative (counter-gradient flux) at middle and small eddy scales. As a result, the Reynolds shear stress in the developing mixing layer becomes smaller than that in the forcibly developed mixing layer, whereas the momentum production term in the developing mixing layer is larger than that in the developed mixing layer. As the mixing layer develops, the flow gradually becomes turbulent and turbulent momentum and mass transfer becomes positive at small scales. Consequently, the counter-gradient diffusion appears only at the middle scales before it fully develops. With respect to the streamwise mass transfer in the developing mixing layer, the fluid mass at large scales can also be transferred negatively in the off-central region of the mixing layer.

Nonequilibrium thermodynamics of circulation regimes in optically thin, dry atmospheres

An extensive analysis of an optically thin, dry atmosphere at different values of the thermal Rossby number Ro and of the Taylor number Ff is performed with a general circulation model by varying the rotation rate Ω and the surface drag τ in a wide parametric range. By using nonequilibrium thermodynamics diagnostics such as material entropy production, efficiency, meridional heat transport and kinetic energy dissipation we characterize in a new way the different circulation regimes. Baroclinic circulations feature high mechanical dissipation, meridional heat transport, material entropy production and are fairly efficient in converting heat into mechanical work. The thermal dissipation associated with the sensible heat flux is found to depend mainly on the surface properties, almost independent from the rotation rate and very low for quasi-barotropic circulations and regimes approaching equatorial super-rotation. Slowly rotating, axisymmetric circulations have the highest meridional heat transport. At high rotation rates and intermediate-high drag, atmospheric circulations are zonostrophic with very low mechanical dissipation, meridional heat transport and efficiency. When τ is interpreted as a tunable parameter associated with the turbulent boundary layer transfer of momentum and sensible heat, our results confirm the possibility of using the Maximum Entropy Production Principle as a tuning guideline in the range of values of Ω. This study suggests the effectiveness of using fundamental nonequilibrium thermodynamics for investigating the properties of planetary atmospheres and extends our knowledge of the thermodynamics of the atmospheric circulation regimes.

Momentum transfer in a turbulent, particle-laden Couette flow

A point-force model is used to study turbulent momentum transfer in the presence of moderate mass loadings of small (relative to Kolmogorov scales), dense (relative to the carrier phase density) particles. Turbulent Couette flow is simulated via direct numerical simulation, while individual particles are tracked as Lagrangian elements interacting with the carrier phase through a momentum coupling force. This force is computed based on the bulk drag of each particle, computed from its local slip velocity. By inspecting a parameter space consisting of particle Stokes number and mass loading, a general picture of how and under what conditions particles can alter near-wall turbulent flow is developed. In general, it is found that particles which adhere to the requirements for the point-particle approximation attenuate small-scale turbulence levels, as measured by wall-normal and spanwise velocity fluctuations, and decrease turbulent fluxes. Particles tend to weaken near-wall vortical activity, which in turn, through changes in burst/sweep intensities, weakens the ability of the turbulent carrier-phase motion to transfer momentum in the wall-normal direction. Compensating this effect is the often-ignored capacity of the dispersed phase to carry stress, resulting in a total momentum transfer which remains nearly unchanged. The results of this study can be used to interpret physical processes above the ocean surface, where sea spray potentially plays an important role in vertical momentum transfer.

An experimental study of turbulence in a heterogeneous channel

This paper examines the velocity field in an idealised heterogeneous open channel during normal flow conditions, corresponding to two different subcritical flow conditions (discharges of 0·040 m3/s and 0·056 m3/s, with corresponding Froude numbers 0·51 and 0·57). The bed of the channel is formed of two full-length, longitudinal strips of equal width, a smooth section constructed from polyvinyl chloride and a rough section constructed from gravel (d72 = 10 mm). The results indicate that the turbulence appears to propagate vertically from the rough bed and horizontally over the rough–smooth boundary. There is also evidence to suggest that the turbulent momentum transfer is maximised at the rough–smooth boundary. Secondary flow structures are seen to exist due to the rough–smooth boundary and provide another mechanism for momentum transfer. These transfer mechanisms are important in understanding the effect of a heterogeneous channel bed on open-channel flow.

Influence of Spanwise Vorticity on Dissimilarity between Turbulent Momentum and Heat Transfer

Influence of Spanwise Vorticity on Dissimilarity between Turbulent Momentum and Heat Transfer

Effect of the error in determination of the heat transfer coefficient on the simulation data for heat and mass transfer

In a rigorous way, nonstationary problems of convective heat transfer should be treated in the conjugate statement where the condition of conjugation of the heat transfer medium and the channel wall temperature fields at their interface is used [1–3]. However, the difficulties, such as lack, as a rule, of complete data on the distribution of turbulent momentum and heat transfer coefficients over the channel cross-section, inherent restrictions of the existing models of turbulence, and the geometrical complexity of the solution domain, force researchers to consider an alternative approach where the heat transfer from the moving gas medium to the channel walls is described by the Newton–Richman law [4]. In this case, the local coefficient of convective heat transfer is determined by well-known criterial experimental relations, which are valid for a steady flow of the heat carrier [4, 5]. This simplified approach cannot be rigorously substantiated by invoking the quasistationarity principle or by introducing correction factors, and comparison of numerical and experimental data for evaluating the calculation accuracy is not always possible. An attempt is made to determine the domain of applicability of the simplified approach by evaluating the effect of the error that arises in the estimation of the heat transfer coefficient on the parameters of a convective flow.

An equivalent neutral wind observation operator for variational assimilation of scatterometer ocean surface wind data

AbstractThis article describes a new observation operator developed for improved variational data assimilation of scatterometer ocean wind vectors. The forward operator is designed explicitly to take into account the equivalent neutral calibration of scatterometer wind retrievals. The corresponding tangent linear and adjoint (TL/AD) operators are developed for the calculation of near‐surface increments based explicitly on parametrizations of surface‐layer turbulent momentum transfer. Tangent linear and adjoint operators are formulated using the Jacobian of the forward operator estimated using the perturbation method. Various TL/AD configurations are investigated in more detail to assess the impact of sensitivities affecting the vertical gradient of surface‐layer temperature during assimilation of ocean surface wind data. It is argued that these sensitivities should be neglected in the context of a stand‐alone atmospheric prediction system. The complete form of the operator has, however, the potential to be a key component of a coupled atmosphere–ocean data assimilation system. Two data assimilation experiments were performed using distinct scatterometer observation operators, i.e. new equivalent neutral versus the simpler operational configuration using stability‐dependent (real) background winds. Associated medium‐range forecasts were run for a complete impact assessment. The impact of the new operator is tracked through the entire data assimilation and forecast process by comparing analyses and forecasts from both experiments. A significant sensitivity of the data assimilation system to the configuration of the observation operator has been found. Modest but beneficial impacts are obtained with the equivalent neutral wind observation operator with respect to short‐range forecasts of ocean surface winds and medium‐range forecasts of extratropical geopotential heights. © 2012 Crown in the right of Canada. Published by John Wiley & Sons Ltd.

On total turbulent energy and the passive and active role of buoyancy in turbulent momentum and mass transfer.

Measurements of turbulent fluctuations of horizontal and vertical components of velocity, salinity and suspended particulate matter are presented. Turbulent Prandtl numbers are found to increase with stratification and to become larger than 1. Consequently, the vertical turbulent mass transport is suppressed by buoyancy forces, before the turbulent kinetic energy (TKE) and vertical turbulent momentum exchange are inhibited. With increasing stratification, the buoyancy fluxes do not cease, instead they become countergradient. We find that buoyantly driven motions play an active role in the transfer of mass. This is in agreement with trends derived from Monin–Obukhov scaling. For positive Richardson flux numbers (Rif), the log velocity profile in the near-bed layer requires correction with a drag reduction. For negative Rif, the log velocity profile should be corrected with a drag increase, with increasing |Rif|. This highlights the active role played by buoyancy in momentum transfer and the production of TKE. However, the data do not appear to entirely follow Monin–Obukhov scaling. This is consistent with the notion that the turbulence field is not in equilibrium. The large stratification results in the decay of turbulence and countergradient buoyancy fluxes act to restore equilibrium in the energy budget. This implies that there is a finite adjustment timescale of the turbulence field to changes in velocity shear and density stratification. The energy transfers associated with the source and sink function of the buoyancy flux can be modeled with the concept of total turbulent energy.

Thermodynamics of neoclassical and turbulent transport

A variational principle based on the calculation of the entropy production rate is derived, which covers particle, momentum and heat transport. This principle is used to define proper thermodynamical forces and fluxes. When turbulent parallel wavenumbers are small, and fluctuations are ballooned, it is found that the forces are the gradients of density, velocity and temperature normalized to canonical profiles, which are power laws of the magnetic field. The transport matrix is symmetrical for a given background of fluctuations, i.e. if the dependence of the turbulence intensity on gradients is ignored. Minimization of the entropy production rate implies that the profiles tend to relax towards their canonical values, though these values are never reached simultaneously since they are linearly stable. Also it turns out that parallel and perpendicular canonical temperatures are not the same, so that the equilibrium distribution function relaxes towards a two-temperature Maxwellian. When finite turbulence parallel wavenumbers are accounted for, residual fluxes appear. Forces can be redefined to preserve Onsager symmetry but residual heat and momentum sources remain, which correspond to turbulent heating and momentum transfer.

The characteristics of turbulent momentum and heat similarity function and bulk transfer coefficient over grassland surface

The turbulent momentum and sensible heat transfer over land surface have a notable influence on the change of global climate and atmospheric circulation, and Monin-Obukhov similarity function is a most important method to calculate the turbulent momentum and sensible heat flux near the surface, and ascertaining the right bulk transfer coefficient is a most effective way of improving the atmospheric model simulation capabilities. The characteristic of Monin-Obukhov similarity function is analyzed and the empirical formula is fitted, and the changes of bulk transfer coefficients of momentum and sensible heat over grassland with mean wind speed at 10 m high are discussed by using the data of the flux observations over Xilin Gol grassland in Spring 2008. Comparison with the observation values by eddy correlation method shows that the revised Monin-Obukhov similarity function underestimates the momentum flux by 10.8% and over estimates the sensible heat flux by 6.5%, but the typical Businger-Dyer similarity function underestimates the momentum flux by 37.0% and over estimates the sensible heat flux by 16.1%. Under unstable stratification, the bulk transfer coefficients of momentum (CD) and sensible heat (CH) vary with mean wind speed at 10 m high (U) according to the power law, which take the forms CD=0.009U-0.322 and CH=0.184U-1.978 respectively. Under stable stratification, the bulk transfer coefficients are found to increase in the manner of the logarithm law over grassland surface and tend to neutral or nearly neutral values with wind speed increasing. The revised Monin-Obukhov similarity function can significantly improve the accuracy of turbulent momentum and sensible heat flux computed by average gradient data, and the relations between bulk transfer coefficients and wind speed at 10 m high provide the useful parameterization schemes for accurately expressing the transportation characteristics of near surface turbulence.

Turbulent Mixed Convection Inside a Vertical Tube With Wetted Wall

The authors present a numerical investigation of turbulent mixed convection inside a wetted—wall tube. The mixture air and water vapor flows downwards the vertical tube. Turbulent momentum, heat and mass transfer equations combined with a low Reynolds number model are discretized by using the finite volume method. The algebraic system equations deduced from this discretization are solved with the Thomas and Gauss algorithms. Results show that the evaporative cooling of the wetted wall and the air flow through the tube can be produced by low heat flux applied to the tube wall.

Effects of small-scale freestream turbulence on turbulent boundary layers with and without thermal convection

Effects of weak, small-scale freestream turbulence on turbulent boundary layers with and without thermal convection are experimentally investigated using a wind tunnel. Two experiments are carried out: the first is isothermal boundary layers with and without grid turbulence, and the second is non-isothermal boundary layers with and without grid turbulence. Both boundary layers develop under a small favorable pressure gradient. For the latter case, the bottom wall of the test section is heated at a constant wall temperature to investigate the effects of thermal convection under the effects of freestream turbulence. For both cases, the turbulence intensity in the freestream is Tu = 1.3% ∼ 2.4%, and the integral length scale of freestream turbulence, L∞, is much smaller than the boundary layer thickness δ, i.e., L∞/δ≪1. The Reynolds numbers Reθ based on the momentum thickness and freestream speed U∞ are Reθ = 560, 1100, 1310, and 2330 in isothermal boundary layers without grid turbulence. Instantaneous velocities, U and V, and instantaneous temperature T are simultaneously measured using a hot-wire anemometry and a constant-current resistance thermometer. The results show that the rms velocities and Reynolds shear stress normalized by the friction velocity are strongly suppressed by the freestream turbulence throughout the boundary layer in both isothermal and non-isothermal boundary layers. In the non-isothermal boundary layers, the normalized rms temperature and vertical turbulent heat flux are also strongly suppressed by the freestream turbulence. Turbulent momentum and heat transfer at the wall are enhanced by the freestream turbulence and the enhancement is notable in unstable stratification. The power spectra of u, v, and θ and their cospectra show that motions of almost all scales are suppressed by the freestream turbulence in both the isothermal and non-isothermal boundary layers.