On the modeling of miscible flow in multi-component porous media

An analytical model of miscible flow in multi-component porous media is presented to demonstrate the influence of pore capacitance in extending diffusive tailing. Solute attenuation is represented naturally by accommodating diffusive and convective flux components in macropores amd micropores as elicited by the local solute concentration and velocity fields. A set of twin, coupled differential equations result from the Laplace transform and are solved simultaneously using a differential operator for one-dimensional flow geometry. The solutions in real space are achieved using numeric inversion. In addition, to represent more faithfully the dominant physical processes, this approach enables efficient and stable semi-analytical solution procedure of the coupled system that is significantly more complex than current capacitance type models. Parametric studies are completed to illustrate the ability of the model to represent sharp breakthrough and lengthy tailing, as well as investigating the form of the nested heterogeneity as a result of solute exchange between macropores and micropores. Data from a laboratory column experiment is examined using the present model and satisfactory agreement results.Roman Letters a rate coefficient of internal flow - b velocity ratio (v ₁/v ₂) - h dispersion ratio (D ₂/D ₁) - c ₁ macropore concentration - c ₂ micropore concentration - ¯c ₁ macropore concentration in Laplace space - ¯c ₂ micropore concentration in Laplace space - c ₁ ⁰ macropore concentration at source location - c ₂ ⁰ micropore concentration at source location - D ₁ macropore dispersion coefficient - D ₂ micropore dispersion coefficient - f fraction of pore space occupied by fluid in primary channel - L length of laboratory sample column - K mass exchange rate - t time from initial stage - v ₁ primary flow channel velocity - v ₂ micropore interstitial velocity - x distance from source - y dimensionless distance Greek Letters equivalent Péclet number - dimensionless time, or injected pore volume     

On the Influence of Pore-Scale Dispersion in Nonergodic Transport in Heterogeneous Formations

Flow of an inert solute in an heterogeneous aquifer is usually considered as dominated by large-scale advection. As a consequence, the pore-scale dispersion, i.e. the pore scale mechanism acting at scales lower than that characteristic of the heterogeneous field, is usually neglected in the computation of global quantities like the solute plume spatial moments. Here the effect of pore-scale dispersion is taken into account in order to find its influence on the longitudinal asymptotic dispersivity D₁₁we examine both the two-dimensional and the three-dimensional flow cases. In the calculations, we consider the finite size of the solute initial plume, i.e. we analyze both the ergodic and the nonergodic cases. With Pe the Péclat number, defined as Pe=U/D, where U, , D are the mean fluid velocity, the heterogeneity characteristic length and the pore-scale dispersion coefficient respectively, we show that the infinite Péclat approximation is in most cases quite adequate, at least in the range of Péclat number usually encountered in practice (Pe > 10²). A noteworthy exception is when the formation log-conductivity field is highly anisotropic. In this case, pore-scale may have a significant impact on D₁₁, especially when the solute plume initial dimensions are not much larger than the heterogeneities' lengthscale. In all cases, D₁₁ appears to be more sensitive to the pore-scale dispersive mechanisms under nonergodic conditions, i.e. for plume initial size less than about 10 log-conductivity integral scales.     

Heat,Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, _m ; solution osmotic pressure head _o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (),T, and C. The thermal vapor diffusivity D _Tv first increased as increased to0.22 m³/m³ then decreased with furtherincreases in . D _Tv was 3 orders of magnitudegreater than either isothermal vapor D _mv orosmotic vapor D _ov , diffusivities at of0.20~m³/m³, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D _Tv decreased with increasing C to a greater extent thanD _mv and D _ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D _d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at of0.20~m³/m³, T of 50°C, and C of 0.001 mol/kg.     

Transport of a Passive Scalar in a Stratified Porous Medium

A uniform and horizontal head gradient J is applied to a stratified formation whose given random conductivity K is function of the vertical coordinate x ₃ only. K is assumed to be stationary and of finite integral scale I _v. By Darcy's law, the velocity field V ₁(x ₃)=JK depicts a fluctuating shear flow. A solute body is injected instantaneously in the formation. In a Lagrangean framework, the second spatial moment of the mean concentration C(x,t) can be related to the one-particle trajectories variance X ₁₁(t,Pe) where Pe = V₁I_v/D _dT and _dT is the transverse pore-scale dispersion coefficient. X ₁₁ was determined in the past by Matheron and de Marsily (1980). The present study is concerned with determining the local concentration variance _C ² , that depends on the two-particles trajectories covariance Z ₁₁(t). The latter is derived exactly and langle Crangle and _C ² are determined by assuming normal or lognormal probability distribution of trajectories. The results are illustrated for small and very large (ergodic) solute plumes. For large travel time the concentration coefficient of variation at the center of the plume tends asymptotically to a constant value, unlike formations with finite horizontal correlation length of the hydraulic conductivity. The results may serve for benchmarking of numerical codes and in applications for short travel distances in highly anisotropic formations.     

A mesomechanical approach to inhomogeneous particulate composites undergoing localized damage:: part I—a mesodomain simulation

This paper presents a mesoscale homogenization methodology to deal with the damage localization in inhomogeneous particulate-reinforced composites. An effective local particle volume fraction, f ^v_loc,eff, which includes the particle size effect is suggested to characterize the damage-inducing aspect of clusters. The clustering regions in a particulate composite accommodating the saturated local damage at an applied stress amplitude are simulated by mesodomains, subdomains of homogeneous medium and homogeneous damage distribution. The size of the mesodomains is determined by the transition condition from local damage to global damage via macro-mechanics. The mesodomain positions are found in a materials science manner by mapping the area contours of f ^v_loc,eff for the composite. Transformation of a clustering composite into a two-homogeneous phase material enables one to appropriately illustrate the local constitutive behaviours, and paves the way to predict saturated local damage life.     

Dispersion in non-Newtonian fluids: Effects of chemical reaction

Summary The dispersion of a solute in non-Newtonian fluids flowing through channels and pipes has been studied by taking into account the homogeneous first-order chemical reaction. It is shown that for the same mean velocity of the flow the equivalent dispersion coefficient decreases as the rate of the chemical reaction increases. This decrease is enhanced due to non-Newtonian nature of the fluid.

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Zusammenfassung Die Verteilung eines gelösten Stoffes in nicht-newtonschen Flüssigkeiten, die durch Kanäle und Rohre fließen, wird unter Zugrundelegung einer homogenen chemischen Reaktion erster Ordnung untersucht. Es wird gezeigt, daß bei gleicher mittlerer Strömungsgeschwindigkeit der äquivalente Verteilungskoeffizient abnimmt, wenn die Reaktionsgeschwindigkeit zunimmt. Diese Abnahme wird bei nicht-newtonschen Flüssigkeiten noch verstärkt.

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Notation c concentration of the solute in the fluid - pressure gradient - D molecular diffusion coefficient - D ^* equivalent dispersion coefficient - J ^* flux used in Fick's law of diffusion - K homogeneous chemical reaction rate constant - L typical length of the system - m consistency of the power law fluid - n flow behaviour index (power law index) - p index for systems - average flux of the solute across a section of the duct - R radius of the tube and half thickness of the channel - (r,z) coordinate system - t time - v velocity component of the fluid alongz-direction - mean velocity of the fluid alongz-direction - shear stress - ₀ yield stress - µ consistency of the fluid (in Bingham and Casson models) With 2 figures and 6 tables     

Travel-time analysis of tracer tests in two geothermal fields

The most important results from a tracer test are whether or not tracer is detected at each observation well and the travel times to the wells that respond. A method developed by the authors for accurately calculating travel times for tracer movement in general flow fields enables the locations of major fractures in a reservoir to be deduced from the travel-time data. The procedure is applied here to data from Wairakei, New Zealand, and Palinpinon, Philippines.Notation H reservoir thickness, m - porosity, dimensionless - Q _c characteristic well volume flow rate, m³ s^-1 - R _c characteristic length, m - t _d time, s - t dimensionless time - t _td tracer travel time (without dispersion), s - t _t dimensionless tracer travel time - v _d background fluid speed, m s^-1 - v dimensionless background fluid speed - x _d Cartesian coordinate, m - x dimensionless Cartesian coordinate, m - y _d Cartesian coordinate, m - y dimensionless Cartesian coordinate     

Dynamic interaction of various beams with the underlying soil – finite and infinite, half-space and Winkler models

Various beams lying on the elastic half-space and subjected to a harmonic load are analyzed by a double numerical integration in wavenumber domain. The compliances of the beam–soil systems are presented for a wide frequency range and for a number of realistic parameter sets. Generally, the soil stiffness G has a strong influence on the low-frequency beam compliance whereas the beam parameters EI and m^′ are more important for the high-frequency compliance. An important parameter is the elastic length l=(EI/G)^1/4 of the beam–soil system. Around the corresponding frequency ω_l=v_S/l, the wave velocity of the combined beam–soil system changes from the Rayleigh wave v_R≈v_S to the bending wave velocity v_B and the combined beam–soil wave has typically a strong damping. The interaction frequency ω_l is found not far from the characteristic frequency ω₀=(G/m^′)^1/2 where an amplification compared to the static compliance is observed for special parameter constellations. In contrast, real foundation beams show no resonance effects as they are highly damped by the radiation into the soil. At medium and high frequencies, asymptotes for the compliance of the beam–soil system are found, u/P(ρv_Paiω)^−3/4 in case of the dominating damping and u/P(−m^′ω²)^−3/4 for high frequencies. The low-frequency compliance of the coupled beam–soil system can be approximated by u/P1/Gl, but it also depends weakly on the width a of the foundation. All numerical results of different beam–soil systems are evaluated to yield a unique relation u/P₀=f(a/l). The integral transform method is also applied to ballasted and slab tracks of railway lines, showing the influence of train speed on the deformation of the track beam. The presented results of infinite beams on half-space are compared with results of finite beams and with infinite beams on a Winkler support. Approximating Winkler parameters are given for realistic foundation-soil systems which are useful when vehicle-track interaction is analyzed for the prediction of railway induced vibration.     

Soil stress state orientation beneath a tire at various loads and inflation pressures

Stress state transducers (SSTs) were used to determine the orientation of the major principal stress, σ₁, in soil beneath the centeline of an 18.4R38 radial-ply R-1 drive tire operated at 10% slip. Two soils, a sandy loam and a clay loam, were each prepared twice to obtain two density profiles. One profile of each soil had a hardpan and the soil above the hardpan was loose. The soil in the second profile was loosely tilled. The stress state was determined at a depth of 358 mm in the sandy loam and 241 mm in the clay loam soil. The tire was operated at two dynamic loads (13.2 and 25.3 kN), each at two levels of inflation pressure (41 and 124 kPa). When the orientation of σ₁ was determined directly beneath the axle, the mean angles of tilt in the direction of travel ranged from 6 to 23 degrees from vertical. Inflation pressure did not significantly affect the angle when the dynamic load was 13.2 kN in the sandy loam soil, and neither inflation pressure nor dynamic load significantly affected the angle in the clay loam soil. When the dynamic load was 25.3 kN in the sandy loam soil, the orientation of the major principal stress determined directly beneath the axle was tilted significantly more in the direction of travel when the tire was at 41 kPa inflation pressure than when at 124 kPa. These changes in stress orientation demonstrate the importance of measuring the complete stress state in soil, rather than stresses along only one line of action. The changing orientation of σ₁ as the tire passes over the soil indicates the soil undergoes kneading and supports future investigation of the contribution of changes in stress orientation to soil compaction.     

On the universality of the velocity profiles of a turbulent flow in an axially rotating pipe

If a fluid enters an axially rotating pipe, it receives a tangential component of velocity from the moving wall, and the flow pattern change according to the rotational speed. A flow relaminarization is set up by an increase in the rotational speed of the pipe. It will be shown that the tangential- and the axial velocity distribution adopt a quite universal shape in the case of fully developed flow for a fixed value of a new defined rotation parameter. By taking into account the universal character of the velocity profiles, a formula is derived for describing the velocity distribution in an axially rotating pipe. The resulting velocity profiles are compared with measurements of Reich [10] and generally good agreement is found.Nomenclature b constant, equation (34) - D pipe diameter - l mixing length - l ₀ mixing length in a non-rotating pipe - N rotation rate,N=Re /Re _D - p pressure - R pipe radius - Re _D flow-rate Reynolds number, - Re rotational Reynolds number, Re =v _w D/ - Re* Reynolds number based on the friction velocity, Re*=v*R/ - (Re*)₀ Reynolds number based on the friction velocity in a non-rotating pipe - Ri Richardson number, equation (10) - r coordinate in radial direction - dimensionless coordinate in radial direction, - v _r ,v ,v _z time mean velocity components - v _r ,v ,v _z velocity fluctations - v _w tangential velocity of the pipe wall - v* friction velocity, - axial mean velocity - v _ZM maximum axial velocity - dimensionless radial distance from pipe wall, - y ⁺ dimensionless radial distance from pipe wall - y ₁ ⁺ constant - Z rotation parameter,Z =v _w/v _* =N Re _D /2Re* - _m eddy viscosity - ( _m )₀ eddy viscosity in a non-rotating pipe - coefficient of friction loss - von Karman constant - ₁ constant, equation (31) - density - dynamic viscosity - kinematic viscosity     

Critical heat flux during natural convective boiling on uniformly heated inner tubes in vertical annular tubes submerged in saturated liquid

An experimental study has been made of critical heat flux (CHF) of natural convective boiling on uniformly heated inner tubes in vertical annular tubes. The experiment was performed at a pressure ofP=0.1 to 3.1 MPa for the clearance of 0.4 to 4.0 mm, the heated tube diameter of 5 to 10.6 mm, the annular tube length ofL=58 to 840 mm and three kinds of liquids. The effects on the CHF are mainly discussed about the pressure in which the density ratio of the test fluid _v / _l varies from 6.24 × 10^–4 to 0.16 and of the ratio ofL/D _he =2 to 500, where an equivalent heated length,D _he , serves as a parameter connecting the clearance with the heated tube diameter. The experiment shows that the CHF obtained depends on the ratio ofL/D _he and then a generalized correlation can be derived predicting the CHF data well.

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Kritische Wärmestromdichte beim Sieden unter natürlicher Konvektion an gleichförmig beheizten Innenrohren vertikaler Ringrohre

Zusammenfassung Die kritische Wärmestromdichte (CHF) beim Sieden unter natürlicher Konvektion an gleichförmig beheizten Innenrohren senkrechter Ringrohre wurde experimentell untersucht, und zwar bei Drücken vonP=0,1 bis 3,1 MPa, Spaltweiten von 0,4 bis 4,0 mm, Durchmessern des beheizten Rohres von 5 bis 10,6 mm, Längen des Ringrohres vonL=58 bis 840 mm und mit drei Arten von Flüssigkeiten. Die Einflüsse auf die CHF werden hauptsächlich in dem Druckbereich diskutiert, bei welchem das Dichteverhältnis der Testflüssigkeit, _v / _l , zwischen 6,24 · 10^–4 und 0,16 variiert und das VerhältnisL/D _he von 2 bis 500 reicht. Die äquivalente beheizte LängeD _he stellt dabei einen Parameter dar, welcher die Spaltweite mit dem Durchmesser des Heizrohres in Beziehung bringt. Die Experimente belegen, daß die erhaltenen CHF-Werte vom VerhältnisL/D _he abhängen, woraus sich eine verallgemeinerte Beziehung herleiten läßt, welche die CHF-Daten gut vorauszuberechnen erlaubt.

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Nomenclature D _he equivalent heated length = {(D _o /D _i )² – 1} ·D _i = 4s/D _i · (1 +s/D _i ) - D _i outer diameter of a heated tube - D _o inner diameter of outertube - g gravitational acceleration - H _fg latent heat of evaporation - K constant (=0.16) - L length of the heated tube or surface in flow direction - P system pressure - q _co critical heat flux for saturated boiling - s clearance of annulus - Kutateladze number - _l density of saturated liquid - _v density of saturated vapor - surface tension     

An analytical approach to coupled heat and moisture transport in soil

The simultaneous diffusion of heat and moisture through soil is described by two coupled partial differential equations in which the diffusion coefficients are highly non-linear functions of the dependent variables. The system has been regarded as analytically intractable for any generality of coupled flow. However, for an asymptotically steady state, the equations show a marked periodic stability. Computer simulation indicates that the behaviour quickly becomes entrained to input boundary periodicity for any initial state, regardless of the detailed functional form of the diffusion coefficients. This property allows an harmonic series solution to be assembled. Factors such as amplitude decay, phase shift and wave form evolution may be evaluated. The solution is adapted to boundary conditions pertaining to arid soils and the results validated against the 1968 field data of Rose and the 1973 experiment by Jackson.Notation gradient operator - divergence operator - _A amplitude of surface moisture content variation - _l volumetric liquid content, m³/m³ - _c value for moisture content, at which vapour diffusivity decays to zero - _M mean of surface moisture content variation - _s saturation value of moisture content - tortuosity factor, m/m - _i eigenvalues of ₀ - hypothetical thermal conductivity, J/m/sec/K - ₀ density of saturated water vapour, kg/m³ - _l density of liquid water, kg/m³ - _v density of water vapour, kg/m³ - surface tension, kg/sec² - matric potential, m - C volumetric heat capacity, J/m³/K - D ^* molecular diffusivity of water vapour in the porous medium, m²/sec - D _atm molecular diffusivity of water vapour in air, m²/sec - D _TV thermally induced vapour diffusivity, m²/sec/K - D _Tl thermally induced liquid diffusivity, m²/sec/K - D _v isothermal vapour diffusivity, m²/sec - D _l isothermal liquid diffusivity, m²/sec - L latent heat of vaporisation, J/kg - P atmospheric pressure at soil surface,Pa - R gas constant of water vapour, J/kg/K - T temperature,K - T _M mean temperature at surface, K - T _A temperature amplitude at surface, K - g acceleration due to gravity, m/sec² - h relative humidity, dimensionless - p partial pressure of water vapour,Pa - q _v water vapour flux, kg/m²/sec - t time, sec - z depth, (measured downwards), m     

Analytical approximation for nonlinear adsorbing solute transport and first-order degradation

Under some constraints, solutes undergoing nonlinear adsorption migrate according to a traveling wave. Analytical traveling wave solutions were used to obtain an approximation for the solute front shape,c(z, t), for the situation of equilibrium nonlinear adsorption and first-order degradation. This approximation describes numerically obtained fronts and breakthrough curves well. It is shown to describe fronts more accurately than a solution based on linearized adsorption. The latter solution accounts neither for the relatively steep downstream solute front nor for the deceleration in time of the nonlinear front.Notation A parameter - c concentration [mol/m³] - c ₀ ^* depth-dependent local maximum concentration [mol/m³] - c; c ₀;c _i concentration difference, feed, and initial resident concentrations, respectively [mol/m³] - D pore scale diffusion/dispersion coefficient [m²/yr] - f adsorption isotherm - f derivative off toc - f second derivative off toc - G ^* parameter - K nonlinear adsorption coefficient [mol/m³)^1–n ] - l column length [m] - L _d dispersivity [m] - m parameter - n Freundlich sorption parameter - P function ofc ₀ ^* - _q change inq [mol/m³] - q adsorbed amount (volumetric basis) [mol/m³] - q derivative ofq toc - R nonlinear retardation factor - retardation factor for concentrationc - R _l linear retardation factor - R(z ^*) depth-dependent average retardation factor, for front at depthz ^* - s adsorbed amount (mass basis) [mol/kg] - t time [years] - u parameter - v flow velocity [m] - z ^* downstream front depth [m] - z depth [m] - transformed coordinate [m] - ^* reference point value of [m] - first-order decay parameter [y^–1] - dry bulk density [kg/m³] - volumetric water fraction - parameter     

Heat,Water, and Solute Transfer in Unsaturated Porous Mdeia: II -- Compacted Soil Beneath Plastic Cover

Soil surface dynamics involve coupled transferof heat, water, and solute. An experimental andtheoretical study of heat, water, and solute transferin closed compacted soil columns under surfacetemperature wave amplitudes is presented. Thetemperature wave amplitudes ranged from 17.9 to 21.0°C. Potassium chloride solution was used tomoisten Clarinda clay and Fayette silty clay loamsoils. Initial water contents of 0.403 and 0.279 andinitial solute concentrations of 0.062 and 0.052 mol kg^-1were used in Clarinda and Fayette soils,respectively. The moistened soils were packed andcompacted in PVC columns (0.075 m diameter and 0.30 mhigh). Bulk densities of the compacted Clarinda andFayette soils were 1403 and 1585 kg m^-3,respectively. The columns were buried in soil suchthat column surfaces were exposed to natural as wellas artificial radiation and thermal conditions. Thecoupled nonsteady-state balance equations of mass andenergy were solved numerically to predict soiltemperature, water content, and solute concentrationdistributions. The theoretical model described soiltemperature, water content, and solute concentrationwell as compared with the measured values. TheFickian diffusive solute flux was one or two orders ofmagnitude greater than salt-sieving and thermal-diffusion solute fluxes.     

In the intermixing region behind circular cylinders with stepwise change of the diameter

The flow within the intermixing region behind circular cylinders with stepwise change of the diameter of diameter ratio d/D of 0.5 has been examined. Based on the statistical analysis and conditional sampling of the velocity fluctuations and of flow visualization, the vortex wakes associated with the big and small cylinders have been established. Both wakes are found under the dominant primary mode, which corresponds to the vortex shedding Strouhal number of two dimensional cylinder, and the less dominant secondary mode. The Strouhal number of the secondary mode of the big vortex wake is higher than that of the primary mode and the opposite is found for the small vortex wake. Both vortex wakes and their modes are found convecting downstream and into region behind the other cylinder. Both wakes are observed to be different from that of two dimensional cylinder.List of symbols D, d diameter of big and small cylinder - f frequency - R ₁₂ (f) cross-power spectral function - R ₁₁, R ₂₂ auto-power functions - Re _D, Re_d Reynolds numbers U ₀ D/v, U ₀ d/v - t time relative to triggering instant - U ₀ freestream mean velocity - U, V, W streamwise, lateral and spanwise mean velocity, respectively - u, v, w streamwise, lateral and spanwise velocity fluctuations, respectively - U _f phase velocity - U _T convection velocity - u _R, v_r recovered u and v velocity fluctuations - uv Reynolds stress - x, y, z streamwise, lateral, and spanwise coordinates, respectively - separation - ₁₂ ² (f) coherence function - _R recovered coherent vorticity fluctuation - phase - ₁₂ (f) phase spectral function     

Minimal cavitation number and cavity width in plane and axisymmetric channels

This paper presents a study of cavity width behind a body in two-dimensional and axisymmetric channels. Equations are given for calculating the minimal cavitation number and also for calculating the dependence of the cavity width on the cavitation number and on the ratio of the transverse dimensions of the body and the channel.Notation v₀ freestream velocity - v velocity at the cavity boundary - p₀ freestream pressure - p pressure in cavity - fluid density - d body width - D₀ channel width - D width of cavity in channel - D width of cavity in unbounded fluid     

Flow about yawed,stranded cables

The development of a steady lift force on a stranded cable, which is yawed with respect to a flow, is a unique characteristic of a cable when compared to a circular cylinder. Comparisons of lift and normal drag coefficients and wake characteristics were made between stranded cable models and the cylinder. These were based upon surface pressure and hot-wire measurements and flow visualization studies conducted in a low speed wind tunnel on rigid cables and cylinders. The models were yawed to four different yaw angles and tested within the Reynolds number range of 5,000 and 50,000. Pressure profiles for the yawed cables indicated that the lift force is directed towards the side where the primary strands are more nearly aligned with the flow. The pressure profiles also indicated that the lift force is generated by asymmetric separation. The small scale irregularities associated with wires within individual strands also appeared to have an effect on the cable's lift and drag characteristics. Results show that cables have significantly different shedding characteristics and near-wake shear layer structure when compared to the circular cylinder. For the flow regime tested, the Strouhal number showed no dependence on Reynolds number nor spanwise position along the cable.List of symbols C _dn normal drag coefficient - C _l lift coefficient - C _p pressure coefficient - D actual diameter, based on circumscribing circle for the cable - f _v shedding frequency - L/D length to actual diameter ratio - ppd peak-to-peak distance, unit span - Re Reynolds number based on actual diameter - S Strouhal number, - V free stream velocity - cable angle - azimuthal angle     

The thermogravitational effect in porous media: A modelling approach

The thermogravitational effect may induce large concentration contrasts, particularly in porous media. This phenomenon arises from a coupling of the Soret effect and convection currents in a temperature field. The present study of this phenomenon is motivated by the safety assessment of nuclear waste repositories, which are sources of thermal energy. Here, we present a modelling approach of laboratory experiments carried out at the University of Toulouse. The results of this model, though more adequate than the analytical solution to account for the influence of permeability, remain far from the experimental ones. In conclusion, it appears that the research must now focus on both a comprehensive phenomenology of the transport processes and experiments with new dimensional constraints.Notation C concentration of the solute - c mass fraction of the solute - D molecular diffusion coefficient - D coefficient of thermodiffusion - F ₁ external forces on the solute - F ₂ external forces on the solvent - g gravity - J _q heat flux - J _l solute mass flux - J _x horizontal mass flux of the solute - k intrinsic permeability - k _L longitudinal permeability - k _T transverse permeability - T ₀ reference temperature - U Darcy velocity - thermal expansion coefficient of the mixture - thermal conductivity - porosity of the medium - dynamic viscosity of the mixture - _T ⁰ dynamic viscosity of pure water atT - _1T dynamic viscosity of 1 atT - _2T dynamic viscosity of 2 atT - ₁ chemical potential of the solute - ₂ chemical potential of the solvent - specific mass of the fluid - ₀ specific mass of pure water atT ₀     

Application of liquid-crystal thermometry to drop temperature measurements

A technique has been developed that enables remote sensing of the temperatures of liquid drops in a medium of an immiscible, transparent liquid with the aid of dispersing microcapsules of thermochromic liquid crystal in each drop under illumination by either a planar floodlight or a light sheet which cuts the drop at a meridian. Based on appropriate hue-temperature calibrations made with an isothermal, stationary drop/medium system, one can analyze spatial and time variations of temperature within drops in motion under transient convective heating (or cooling) from the medium.List of Symbols B tristimulus blue component - D drop diameter - G tristimulus green component - H hue angle - h ₀ constant term in the expression for H - H _m mean value of H over drop surface - h vertical coordinate fixed onto test column - R tristimulus red component - Re drop Reynolds number, UD/v _c - r, g, b chromaticity coordinates - r drop radius - s penetration depth of light into drop - T temperature - T _d instantaneous drop temperature - T _d0 initial drop temperature - T _c continuous-phase temperature - U velocity of rise of drop - z vertical coordinate laid on drop - v _c kinematic viscosity of continuous phase - angle of lighting measured from camera axis - _s local view angle (azimuth) - polar angle     

Effect of measuring volume length on two-component laser velocimeter measurements in a turbulent boundary layer

The effects of finite measuring volume length on laser velocimetry measurements of turbulent boundary layers were studied. Four different effective measuring volume lengths, ranging in spanwise extent from 7 to 44 viscous units, were used in a low Reynolds number (Re=1440) turbulent boundary layer with high data density. Reynolds shear stress profiles in the near-wall region show that u v strongly depends on the measuring volume length; at a given y-position, u v decreases with increasing measuring volume length. This dependence was attributed to simultaneous validations on the U and V channels of Doppler bursts coming from different particles within the measuring volume. Moments of the streamwise velocity showed a slight dependence on measuring volume length, indicating that spatial averaging effects well known for hot-films and hot-wires can occur in laser velocimetry measurements when the data density is high.List of symbols time-averaged quantity - u wall friction velocity, ( _w /)^1/2 - v kinematic viscosity - d _p pinhole diameter - l _eff spanwise extent of LDV measuring volume viewed by photomultiplier - l ⁺ non-dimensional length of measuring volume, l _eff u /v - y ⁺ non-dimensional coordinate in spanwise direction, y u /v - z ⁺ non-dimensional coordinate in spanwise direction, z u /v - U ⁺ non-dimensional mean velocity, /u - u instantaneous streamwise velocity fluctuation, U &#x2329;U - v instantaneous normal velocity fluctuation, V–V - u RMS streamwise velocity fluctuation, u ^21/2 - v RMS normal velocity fluctuation, v ^21/2 - Re Reynolds number based on momentum thickness, U 0/v - R _uv cross-correlation coefficient, u v/u v - R₁₂(0, 0, z) two point correlation between u and v with z-separation, <u(0, 0, 0) v (0, 0, z)>/<u(0, 0, 0) v (0, 0, 0)> - N rate at which bursts are validated by counter processor - T Taylor time microscale, u (dv/dt²)^–1/2