Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements

The information of the wire response is necessary for the estimation of corrections and uncertainty of temperature measurements. This paper describes the theoretical response of cold-wire sensors to temperature fluctuations in a fluid flow. Existing transfer functions of cold wires are approximate and implicit functions of frequency. We present the exact solutions of heat conduction equations for a cold wire and stubs taking account of the prong effect. Because the solutions have simple forms of elementary functions, we can easily calculate the frequency response of cold wires. Sample calculations are given under several typical conditions. Also, the instantaneous temperature profiles of a cold wire are obtained for the first time.     

Improvement of cold-wire response for measurement of temperature dissipation

This work aimed at improving fine-scale measurements using cold-wire anemometry. The dissipation ɛ _θ of the temperature variance was measured on the axis of a heated turbulent round jet. The measurements were performed with a constant current anemometer (CCA) operating fine Pt–10%Rh wires at very low overheat. The CCA developed for this purpose allowed the use of the current injection method in order to estimate the time constant of the wire. In the first part of the paper, it is shown that the time constants obtained for two wire diameters −d=1.2 and d=0.58 μm – compare well with those measured at the same time using two other methods (laser excitation and pulsed wire). Moreover, for these two wires, the estimated time constants were in good agreement with those obtained from a semi-empirical relation. In the second part of the paper, a compensation procedure – post-processing filtering – was developed in order to improved the frequency response of the cold-wire probes. The measurements carried out on the axis of the jet (Re _D =16 500, Re _λ  ≃ 167) showed that the frequency response of the 1.2 μm wire was significantly improved. In fact, the spectral characteristics of the compensated signal obtained with the 1.2 μm wire compared fairly well with those from the 0.58 μm wire. Moreover, the results indicated that the compensation procedure must be applied when the cut-off frequency of the cold-wire f _c is lower than two times the Kolmogorov frequency f _K. In the case where f _c ≃ 0.6f _K, the compensation procedure can reduce the error in the estimate of ɛ _θ by more than 20%. When f _c ≃ 2f _K, the effect of the compensation is reduced to about 5%. Received: 3 November 2000/Accepted: 23 March 2001     

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

The dynamics of homogeneous, isotropic turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the turbulence. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the small-scale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.     

Two-phase flow laden with spherical particles in a microcapillary

Solid–liquid two-phase flow in a finite Reynolds number range (2 < Re < 12), transporting neutrally-buoyant microspheres with diameters of 6, 10, and 16 μm through a 260-μm microcapillary, is investigated. A standard microparticle-tracking velocimetry (μ-PTV) that consists of a double-pulsed Nd:YAG laser, an epi-fluorescent microscope, and a cooled-CCD camera is used to examine the flow. The solid particles are visualized in view of their spatial distributions. We observe a strong radial migration of the particles across the flow streamlines at substantially small Re. The degree of particle migration is presented in terms of probability density function. Some applications based on this radial migration phenomena are discussed in conjunction with particle separation/concentration in microfluidic devices, where the spatial distribution of particles is of great importance. In doing so, we propose a particle-trajectory function to empirically construct the spatial distribution of solid particles, which is well correlated with our experimental data. It is believed that this function provides a simple method for estimating the spatial distribution of particles undergoing radial migration in solid–liquid two-phase flows.     

Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow

The use of hot-wire anemometry in carbon dioxide flow under supercritical conditions has been analyzed and implemented for the first time. A two-sensor probe to simultaneously measure streamwise velocity and temperature in this flow has been designed and constructed. A calibration and test flow loop that can provide supercritical state conditions above the critical point has been also designed, fabricated and tested. The temperature and velocity flow fields of the flow loop can be varied at constant pressure. It has been found that, above the pseudo-critical temperature, the velocity sensor response fits King’s cooling law with a high correlation coefficient. The dependence of the King’s law parameters on temperature can be accurately presented with second or higher order polynomial or exponential fits, depending on the extent of the temperature range. Below the pseudocritical temperature the data is scattered, and the variation with temperature of the King’s law parameters, determined from calibration, is irregular. The influence on this data scatter of the strong variation of the fluid properties near the critical point is analyzed, and a possibility to reduce it is proposed. The temperature sensor response both above and below the pseudocritical temperature is similar to the response under normal conditions. It is linear with a very high correlation coefficient between the calibration data and the fitted curve. It is also shown that the temperature response is not affected by variation of the flow’s speed.     

Investigation of the electrode potential drop at a molybdenum electrode in a flow of argon seeded with potassium

The results of an experimental investigation of the operation of an electrode in argon containing 0.15% of potassium at temperatures from 1400 to 1800 °C and a pressure of 1 atmosphere when the gas and the electrode are in thermal equilibrium are presented. The current-voltage characteristics obtained are compared with the theory of electrode processes developed previously [1, 2]. Good agreement is obtained between the theoretical and experimental data.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1970.     

Synthesis of submicron-sized composite particles with unique morphology by emulsifier-free seeded emulsion copolymerization

Polystyrene (PSt) microspheres with diameter of 375 nm to be used as the seeds for seeded emulsion polymerization were prepared via emulsion polymerization using potassium persulfate (KPS) as initiator in ethanol-water mixed solvents.Emulsifier-free seeded emulsion copolymerization of styrene (St) with acrylonitrile (AN) was carried out in the presence of poly(ethylene glycol) monomethoxymonomethacrylate (PEGm)macromonomer as reactive stabilizer and 2,2'-azobisisobutyronitrile (AIBN) as initiator to obtain submicron-sized PEGm graft poly(styrene-co-acrylonitrile) (PEGm-g-PSAN) composite particles with unique morphology.Scanning electron microscopy (SEM) indicated that St and AN together contributed to forming the unusual morphology.The concentration of St and AN,total monomer concentration,initiator type and the monomer adding method remarkably affected the morphology of the composite polymer particles.     

Synthesis of submicron-sized composite particles with unique morphology by emulsifier-free seeded emulsion copolymerization

Polystyrene （PSt） microspheres with diameter of 375 nm to be used as the seeds for seeded emulsion polymerization were prepared via emulsion polymerization using potassium persulfate （KPS） as initiator in ethanol-water mixed solvents. Emulsifier-free seeded emulsion copolymerization of styrene （St） with acrylonitrile （AN） was carried out in the presence of poly（ethylene glycol） monomethoxymonomethacrylate （PEGm） macromonomer as reactive stabilizer and 2,2＇-azobisisobutyronitrile （AIBN） as initiator to obtain submicron-sized PEGm graft poly（styrene-coacrylonitrile） （PEGm-g-PSAN） composite particles with unique morphology. Scanning electron microscopy （SEM） indicated that St and AN together contributed to forming the unusual morphology. The concentration of St and AN, total monomer concentration, initiator type and the monomer adding method remarkably affected the morphology of the composite polymer particles.     

Hydromagnetic Stokes flow in a rotating fluid with suspended small particles

An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.     

Frequency response of a photo-viscoelastic material

An electromagnetic shaker was used to apply sinusoidal axial displacements to one end of a column of Hysol 4364, an optically sensitive urethane rubber compound of low modulus. The nondriven end of the column was free. The column was excited at frequencies of 81, 244, 424, 603 and 783 cps, corresponding to the first five resonant frequencies of longitudinal vibration. Measurements were made of displacement mode shapes and phase angles, and birefringence modes and phase angles. Measured displacement modes and phase angles were shown to agree with predictions based on a linear one-dimensional viscoelastic theory. The measurements and theory were used to determine the mechanical and optical frequency response of the material for the experimental frequencies. This consisted of determining:

1. 1.
   the dynamic elastic modulus,     
   
   

Multiphase flow with a simplified model for oil entrapment

A computationally simple procedure is described to model effects of oil entrapment on three-phase permeability-saturation-capillary pressure relations. The model requires knowledge of airwater saturation-capillary pressure relations, which are assumed to be nonhysteretic and are characterized by Van Genuchten's parametric model; scaling factors equal to the ratio of water surface tension to oil surface tension and to oil-water interfacial tension; and the maximum oil (also referred to as nonwetting liquid in a three-phase medium) saturation which would occur following water flooding of oil saturated soil. Trapped nonwetting liquid saturation is predicted as a function of present oil-water and air-oil capillary pressures and minimum historical water saturation since the occurrence of oil at a given location using an empirically-based algorithm. Oil relative permeability is predicted as a simple function of apparent water saturation (sum of actual water saturation and trapped oil saturation) and free oil saturation (difference between total oil and trapped oil saturation), and water relative permeability is treated as a unique function of actual water saturation. The proposed method was implemented in a two-dimensional finite-element simulator for three-phase flow and component transport, MOFAT. The fluid entrapment model requires minimal additional computational effort and computer storage and is numerically robust. The applicability of the model is illustrated by a number of hypothetical one- and two-dimensional simulations involving infiltration and redistribution with changes in water-table elevations. Results of the simulations indicate that the fraction of a hydrocarbon spill that becomes trapped under given boundary conditions increases as a nonlinear function of the maximum trapped nonwetting liquid saturation. Dense organic liquid plumes may exhibit more pronounced effects of entrapment due to the more dynamic nature of flow, even under static water table conditions. Disregarding nonwetting fluid entrapment may lead to significant errors in predictions of immiscible plume migration.     

Creeping flow around particles in a Bingham fluid

We revisit the variational setting of the creeping flow of Bingham fluid about a particle. We investigate two problems: the resistance and the mobility problem, which arise in the context of sedimentation. We present results and the general framework for uniqueness, symmetry and reversibility properties of solutions, and clarify the relation between resistance and mobility problems. We also consider general properties of the static stability limit (or load limit). In the second part of the paper we apply insights gained from the first part to the computation of 2D exterior flow around an infinite cylinder with elliptical cross-section. We study the static stability limit and find that the limiting flow solution approaches the perfectly plastic solid solution.     

Pipe flow with solid particles fixed in space

A group of solid particles were hung by slender rods in a pipe to make a model of two-phase flow of coarse particles. Pressure gradient and velocities were measured for different types of the models. The drag on the particles (spheres) were obtained from measurements of pressure gradient with some assumptions. The results are summarized as follows. (1) Mean velocities of fluid are lower in the central part of the pipe than in the circumferential part. Turbulence is remarkably increased by particles. The spectrum distribution of turbulent velocity becomes flatter. These results are similar to the gas-solid flow of coarse particles in a vertical pipe. (2) At a large Reynolds number, the drag coefficient per one sphere in the group is larger than that of a single isolated sphere in a uniform flow. When the spheres are arranged along the same line in the longitudinal direction, the drag coefficient becomes smaller as the longitudinal distance between the spheres is shortened.     

Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles

The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls.     

Dynamics of Brownian particles in a turbulent channel flow

Turbulent channel flows with suspended particles are investigated by means of numerical simulations. The fluid velocity is computed by large eddy simulation. Motion of small graphite particles with diameter of 0.01–10 m, corresponding to the Schmidt number, Sc, of 2.87 × 10²–6.22 × 10⁶ and the particle relaxation time in wall unit, _p⁺, of 9.79 × 10^–5–4.51, is computed by Lagrangian particle tracking. Relation between the particle relaxation time and the computed deposition velocity is found to be in good agreement with an empirical relation. The statistics of the particle motion in the vicinity of the wall are studied. Clear differences are found in dynamical behavior of particles with different sizes. Medium size particles show a strong dependence on the structure of the fluid flow, while small and large particles are considerably less sensitive.     

Gravitational sedimentation of aggregating particles in a shear flow

A theoretical model describing the sedimentation of aggregating particles under the influence of gravity in Couette shear flow is proposed. The relation between the parameters characterizing the dependence of the sedimentation properties on the shear rate and the parameters characterizing the aggregation of the particles is traced.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 95–98, March–April, 1989.The authors wish to thank S. A. Regirer for useful discussions.     

Diffusion of heavy spherical particles in a turbulent flow

A connection is established between the statistical characteristics of a turbulent flow and the coefficient of diffusion of spherical particles suspended in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 142–144, November–December, 1979.