Experimental Velocity Profiles Research Articles

English

Turbulent flow in a diffuser with swirl occurs in many commonly used fluid mechanicaldevices,eg, diffusers located downstream of a gas turbine, and in certain types of combustionchambers. Diffusers are widely used for converting kinetic energy to pressure, and a reliableprediction method of such flows with the required flow conditions would lead to the design offluid machinery with improved efficiency. As a first step, turbulent swirling flow through a 12oincluded angle conical diffuser for a swirl parameter, m = 0.18 was numerically investigated usingvarious turbulence models like standard k- , RNG-based k- , shear-stress transport (SST) kandReynolds stress model (RSM). Though the comparison between the experimental and thepredicted mean velocity profile by RSM is superior to that by RNG kandSST models, the lattertwo models give closer comparison with the experimental pressure distribution. Subsequently,computation of flow inside a complex duct involving axisymmetric annular diffuser, transitionfrom rectangular to circular cross section, and exit pipe have been carried out using RNG kandSST k models.The comparison of computed and experimental results indicates that theSST k modelgives predictions with reasonable accuracy.

Impinging laminar jets at moderate Reynolds numbers and separation distances

An experimental and numerical study of impinging, incompressible, axisymmetric, laminar jets is described, where the jet axis of symmetry is aligned normal to the wall. Particle streak velocimetry (PSV) is used to measure axial velocities along the centerline of the flow field. The jet-nozzle pressure drop is measured simultaneously and determines the Bernoulli velocity. The flow field is simulated numerically by an axisymmetric Navier-Stokes spectral-element code, an axisymmetric potential-flow model, and an axisymmetric one-dimensional stream-function approximation. The axisymmetric viscous and potential-flow simulations include the nozzle in the solution domain, allowing nozzle-wall proximity effects to be investigated. Scaling the centerline axial velocity by the Bernoulli velocity collapses the experimental velocity profiles onto a single curve that is independent of the nozzle-to-plate separation distance. Axisymmetric direct numerical simulations yield good agreement with experiment and confirm the velocity profile scaling. Potential-flow simulations reproduce the collapse of the data; however, viscous effects result in disagreement with experiment. Axisymmetric one-dimensional stream-function simulations can predict the flow in the stagnation region if the boundary conditions are correctly specified. The scaled axial velocity profiles are well characterized by an error function with one Reynolds-number-dependent parameter. Rescaling the wall-normal distance by the boundary-layer displacement-thickness-corrected diameter yields a collapse of the data onto a single curve that is independent of the Reynolds number. These scalings allow the specification of an analytical expression for the velocity profile of an impinging laminar jet over the Reynolds number range investigated of .

Velocity And Static Pressure Profiles In WideAngled Two-dimensional Stalled Diffuser Flows

Experimental velocity profiles and static pressure recovery data, which were obtained in a 50° included angle diffuser, are presented. The measurements were carried out at Reynolds numbers between 1.07 x 105 and 2.14 x 105 based on inlet hydraulic diameter and centreline velocity. Separation of the attached flow on the stalled wall occurred at a normalized distance of 0.4 from the diffuser entry. On the unstalled diffuser wall, near the diffuser entry, a separation bubble was observed. The flow in this bubble separated from and reattached to the unstalled wall at normalized distances from the diffuser entry of 0.35 and 1.4 respectively. Finally, a method to predict the distance along the wall, on the stalled side of the diffuser, where reverse flow first occurs (point of stall), is proposed.

Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field

This paper presents simulations of the 2d model developed by Poth\'erat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms in the equations of motion accounting for inertia, soften velocity gradients in the horizontal plane, and then we implement the model on a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are closely recovered, and local and global Ekman recirculations are shown to alter significantly the aspect of the flow as well as the global dissipation.

A void coalescence-based spall model

A void coalescence-based spall model is presented using stress relaxation equations based on the assumption that the main effect of the microcracks is to reduce the area over which the stress acts in the early stages and the stress decreases to porosity-dependent value in the void coalescence stages. The stress- (or pressure-) dependent spall porosities given by Thomason, by Tonks et al and by Cochran et al. are, respectively, combined with conservation equations, equation of state and constitutive equations for the damaged aggregate to establish a series of closed equations for all variables including the damage. The void coalescence-based spall model contains only two parameters: the spall strength and critical damage, the values of which can be initially estimated for plate-impact spall tests and be finally determined to make the computed results of spall tests under the initial and boundary conditions consistent with experimental velocity (stress) profile and the observed damage at spall plane in general. The computer simulations of spall experiments for copper, uranium and steel are performed with the one-dimensional Lagrangian finite difference method. The computed results based on the pressure-dependent spall porosities given by Tonks et al., and by Cochran et al., are consistent in general, but different from the computed results based on Thomason's 2D stress-dependent spall porosity to a considerable extent.

CFD simulation of steady state heat transfer in bubble columns

A low Reynolds number k-e computational fluid dynamics (CFD) model has been used for the description of flow pattern near the wall. An excellent agreement has been shown between the predicted and experimental hold-up and velocity profiles. The CFD model has been extended for the prediction of heat transfer for two-phase gas-liquid flows in bubble columns. A comparison has been presented between the predicted and the experimental data.

Universal Velocity Defect Law for the Turbulent Boundary Layer

Turbulent plane boundary layer flows of an incompressible fluid are considered. A refinement of the known Coles wake law is proposed. This refinement makes it possible to ensure the smooth matching of the turbulent boundary layer velocity profile with the outer flow and to extend the range of validity of the law to the case of large positive pressure gradients. The accuracy of the analytical approximation obtained is verified by comparison with the known experimental equilibrium velocity profiles. Using the approximation proposed, a relation for calculating the cross-sectional distribution of the Reynolds stress in the equilibrium boundary layer is derived. The pressure distributions for which the equilibrium turbulent boundary layer flows are single- and two-valued are distinguished.

Development of low field nuclear magnetic resonance microcoils

A miniaturized spiral Helmholtz rf coil was fabricated using standard photolithography and electroplating. A commercial 0.6 T superconductive magnet was used to test the coil performance for both nuclear magnetic resonance (NMR) spectroscopy and imaging applications. NMR spectra of water, methanol, and 1-propanol were obtained as well as static and flow images of a water phantom. The spectral resolution was sufficient to allow chemical identification. Additionally, the viscosity of water was estimated from the experimental velocity profile and was equal to the expected value of 1 cP. Results obtained demonstrated the prospect of using the Helmholtz rf coil as part of a portable low-field NMR system for applications in analytical chemistry and process measurements in industrial settings.

グロー放電トレーサー法による極超音速流中の境界層内速度分布測定

Spark-tracer technique using glow discharge is presented to measure velocity profiles across boundary layers around models in hypersonic flows. At first, a high voltage and high frequency discharge circuit and a discharge electrodes system used in the measurement are described. Next, to demonstrate the capability of the technique, the measurement of a velocity profile across a flat plate boundary layer is performed. The experimental result agrees well with the computational one based on the Navier-Stokes equations. Moreover, to clarify characteristics of the high frequency glow discharge generated in hypersonic flows, discharge gap voltage and current measurement is carried out and the follows are concluded. A positive column region is used as a tracer in the technique. Its characteristics are affected by retained ions in the column and also by the column length. Finally, from the fact that the experimental and numerical velocity profiles agree well, we may conclude that 1mJ of electric energy which is released in an impulsive discharge does not disturb the flow.

Hydrodynamic effects on the oscillations of supported bubbles: implications for accurate measurements of surface properties

Oscillating bubble techniques are commonly used to infer dynamic surface tensions (DST) from the measurements of the dynamic pressure differences across an interface. In inferring DST from such measurements, it is assumed that hydrodynamic efects either are negligible or can be approximated. In virtually all previous studies, the dynamic bubble shapes, which are set by the requisite balance of forces at the bubble surface, are taken to be nearly spherical and assumed to be governed by the static Young–Laplace (Y–L) equation alone. To examine these assumptions, the Navier–Stokes and continuity equations governing the flow of a liquid outside an axisymmetric bubble supported by a narrow capillary are solved simultaneously by a rigorous finite element method. Cases of constant surface tension (pure liquids or solutions with very fast adsorption) are tested to focus on understanding the effects of fluid motion on surface tension measurements. To test the capability of the computational algorithm on describing the hydrodynamics, computed and experimental velocity profiles are compared and found to be consistent, as are the apparent surface tensions. Parameters such as forcing frequency, forcing amplitude, chamber dimensions, and surface tension and viscosity of the liquid are varied to find the limits where pulsating bubbles depart from spherical and where hydrodynamic effects impact the determination of surface tension. In the commercial pulsating bubble surfactometer (PBS), the bubble shapes remain nearly spherical for low pulsation or oscillation rates ( ≤ 100 Hz) with moderate volume amplitudes. Under these conditions, however, two major hydrodynamic effects, due to the inertia of the bulk liquid, or to the liquid viscosity and the viscous forces acting on the chamber walls, are found to be important and can cause large errors in the surface tension measurements. For measurements of low surface tensions ( ≤ 5 mN/m) in a PBS, oscillating bubble methods that do not take into account shape deformations from the spherical are found to be inaccurate, and the results from dynamic bubble shape analysis (solving the Y–L equation for a nonspherical axisymmetric surface) are shown to provide another approach to obtain accurate results provided that hydrodynamic effects can be neglected. At higher frequencies ( ≥ 200 Hz), because of strong convection around the surface of the bubble, the bubble shapes become highly deformed. Further extensions of this algorithm are needed, to include the surfactant diffusion and adsorption effects by which the surface tension may change with time.

EHD flow in air produced by electric corona discharge in pin–plate configuration

The electrohydrodynamic flow in air produced by the electric corona discharge in the pin–plate and pin–grid configurations has been investigated numerically and experimentally in this paper. The numerical algorithm based on the boundary and finite element methods and the method of characteristics is employed to obtain the distributions of the electric field, the electric potential and the space charge density. After the volume force has been calculated, the commercial FLUENT software is used to solve the airflow. Experimental axial velocity profiles outside the ground grid obtained with a hot-wire anemometer reasonably validate the simulation results.

Kinematics of extreme waves in deep water

The velocity profiles under crest of a total of 62 different steep wave events in deep water are measured in laboratory using particle image velocimetry. The waves take place in the leading unsteady part of a wave train, focusing wave fields and random wave series. Complementary fully nonlinear theoretical/numerical wave computations are performed. The experimental velocities have been put on a nondimensional form in the following way: from the wave record (at a fixed point) the (local) trough-to-trough period, T TT and the maximal elevation above mean water level, η m of an individual steep wave event are identified. The local wavenumber, k and an estimate of the wave slope, ϵ are evaluated from ω 2/( gk)=1+ ϵ 2, kη m =ϵ+ 1 2 ϵ 2+ 1 2 ϵ 3, where ω=2π/ T TT and g denotes the acceleration of gravity. A reference fluid velocity, ϵ g/k is then defined. Deep water waves with a fluid velocity up to 75% of the estimated wave speed are measured. The corresponding kη m is 0.62. A strong collapse of the nondimensional experimental velocity profiles is found. This is also true with the fully nonlinear computations of transient waves. There is excellent agreement between the present measurements and previously published Laser Doppler Anemometry data. A surprising result, obtained by comparison, is that the nondimensional experimental velocities fit with the exponential profile, i.e. e ky , y the vertical coordinate, with y=0 in the mean water level.

Flow of Some Carboxymethylcellulose Solutions Through Abrupt Axisymmetric Contractions. Experimental Study and Modelling of Shear Thinning and Elongational Effects

Abstract The focus of this paper will be on the modelling and simulation of contraction flow, with marked aspect ratio β = 6, 9, 12. Two fluid families are considered: a glycerol Newtonian solution and carboxy-methyl-cellulose (CMC) solutions which present particular rheological properties. Their shear thinning character are modelled by a Cross formula over a large scale of shear rates. The elongational properties are taken via a simplified Ericksen model into account. Experimental velocity profiles are determined using the Laser Doppler Anemometry (L.D.A) technique. They are found to be in good agreement with numerical velocity profiles obtained using a finite volume method with extra source terms traducing the particular rheological behaviour proposed here. The simulations allow to determine the different values of an elongational parameter μ3. Then, some numerical results concerning the total energy losses are presented using the usual concept of the equivalent length.

An analytical–numerical approach to the hydraulics of floating debris in river channels

A new simplified approach is developed for the channel flow dynamics under woody debris transport. A continuous carpet of debris is considered, covering a uniform stationary current. Due to the floating debris the shear stresses in the fluid domain are affected. As a result, the velocity profile is different from the free surface flow. The simple model proposed here is able to capture the essential features of flow response to woody debris transport. Velocity and stress profiles are analytically derived for laminar flow and compared with the zero debris condition. More realistic turbulent currents are simulated with the Reynolds equations where turbulent stresses are modeled by the simple mixing length concept. Validation is carried out by comparison with experimental velocity profiles and with direct numerical simulation of the Navier Stokes Equations. Synthetic diagrams are proposed for the calculation of the flow velocity and the bed shear stresses in terms of the relevant non-dimensional parameters.

Tomographic Techniques for Measuring Fluid Flow Properties

ABSTRACT:Experimental fluid velocity profiles can be readily obtained by using tomographic techniques. Combining measurements of a fluid velocity profile with a simultaneous pressure drop permits the evaluation of rheological properties. In order to control a process and to assure product quality, it is useful to monitor the rheological properties in‐line or on‐line. Two tomographic techniques, magnetic resonance imaging (MRI) and ultrasonic Doppler velocimetry (UDV), were used to obtain velocity profiles for a 65.7 °Brix corn syrup solution and a 4.3 °Brix tomato juice. The UDV technique provided velocity profiles that compared well with the MRI method. For the corn syrup, the shear viscosity of 1.37 Pa‐s (UDV) and 1.51 Pa‐s (MRI) agreed well with the offline measurement of 1.57 Pa‐s. The tomato juice was best characterized as a Bingham plastic fluid. The yield stress ranged from 4.44 Pa to 4.70 Pa, which matched well with the off‐line value of 4.50 Pa. The strengths and limitations of both techniques are presented.

Granular flow in equilibrium with the bottom: experimental analysis and theoretical prediction

Abstract. The paper presents measurements performed on the granular flow that develops in a drum partially filled with sand grains and rotating at various speeds. The aims of the paper are: to provide experimental evidence and measurements on grain flow in a drum; to compare theoretical and experimental velocity profiles; to point out discrepancies among theory and experiments. Velocity and "temperature" profiles were obtained with a Laser Doppler Anemometer (LDA) in the mid-section of the stream, where the flow is usually uniform; image analysis and visual observations of the flow were also carried out to evaluate the local slope, the depths of the characteristic flow regions and the concentration of the granular material. A semi-empirical relation that fits the experimental velocity profiles is presented and compared with Takahashi's velocity distributions for rigid and erodible bed. As proven by the distributions of free surface elevation, velocity, volumetric concentration and grain size across the drum, the three-dimensional nature of the flow field is not negligible. By increasing the drum rotation speed, in correspondence with critical and supercritical flows, changes in the flow regime are observed with formation of quasi-stationary surface waves. Wave development is described by analysing the extension and form of the experimental and theoretical velocity profiles. Wave effects on measurements are quantified and checked comparing the free-surface velocity-discharge relation obtained from experiments and from Takahashi's model for erodible bed.

A low Reynolds number k– ε model for the prediction of flow pattern and pressure drop in bubble column reactors

A low Reynolds number k– ε CFD model has been used for the description of flow pattern near the wall. An excellent agreement has been shown between the predicted and experimental hold-up and velocity profiles over a wide range of superficial gas velocity ( V G ), column diameter ( D), column height ( H D ) and the nature of gas–liquid system (bubble diameter and their rise velocity). The CFD model has been extended for the prediction of pressure drop for two-phase gas–liquid flows in bubble columns. A comparison has been presented between the predicted and the experimental data over a wide range of superficial gas and liquid velocities and for three gas–liquid systems.

Determination of elastic parameters in isotropic plates by using acoustic microscopy measurements and an optimization method

The determination of elastic constants in isotropic solids by line focus acoustic (LFA) microscopy is discussed. A velocity corresponding to a global resonance of leaky Lamb waves has been obtained for different frequencies of excitation ( f) from the V( z, f) curves. This fact is analysed by using a Kushibiki spectrum analysis. The elastic constants are determined from the comparison between measured and calculated velocities. The principle is based on the minimization of the summation of the square difference ∑| V f c− V f m| 2 by using an algorithm based on the simplex method. This paper deals with the case of isotropic plates such as glass and aluminium plates. The influence of the initial values of c ij on the final result is discussed in these cases. Experimental velocity profiles are measured on glass and aluminium plates as a function of the frequency varying from 8 to 17 MHz which corresponds to the bandwidth of the used transducer. The problem of geometric V G( z) and measured V( z) curves fitting is also discussed.

Acoustic microscopy measurement of elastic constants by using an optimization method on measured and calculated SAW velocities: effect of initial cij values on the calculation convergence and influence of the LFI transducer parameters on the determination of the SAW velocity

Abstract The determination of elastic constants in anisotropic solids by line-focus acoustic microscopy (LFAM) is discussed. The velocity of leaky surface acoustic waves (SAWs) has been obtained for different directions of propagation ( φ ) from the V ( z ) curves. The elastic constants are determined from the comparison of measured and calculated velocities. The principle is based on the minimization of the summation of the square difference ∑| V Φ c − V Φ m | 2 , by using a Simplex method. This paper deals with the case of cubic-crystallite solids defined by three independent elastic constants. The influence of the initial values of c ij on the final result is discussed in the case of MgO substrate and TiN deposited on MgO substrate. Experimental SAW velocity profile is measured on (100) silicon substrate as a function of φ between [100] and [010] directions. The influence of the transducer parameters and defocusing distance are also discussed.

Bubble velocity profile and model of surfactant mass transfer to bubble surface

Single bubble velocity profiles for a 0.8 mm diameter bubble in solutions of Triton X-100 are simulated by solving the Navier–Stokes equation combined with the Marangoni effect under pseudo-steady state conditions assuming the stagnant cap model and applying different mass transfer control steps. The fit between the experimental and simulated velocity profiles indicated that the mass transfer mechanism for Triton X-100 from bulk solution to the surface of a rising bubble is boundary layer mass transfer controlled.