Showing papers on "Velocity gradient published in 1970"

Experiments on nearly homogeneous turbulent shear flow

Abstract: With a transverse array of channels of equal widths but differing resistances, we have generated an improved approximation to spatially homogeneous turbulent shear flow. The scales continue to grow with downstream distance, even in a region where the mean velocity gradient and one-point turbulence moments (component energies and shear stress) have attained essentially constant values. This implies asymptotic non-stationarity in the basic Eulerian frame convected with the mean flow, behaviour which seems to be inherent to homogeneous turbulent shear flow.Two-point velocity correlations with space separation and with space-time separation yield characteristic departures from isotropy, including clear ‘upstream–downstream’ unsymmetries which cannot be classified simply as axis tilting of ellipse-like iso-correlation contours.The high wave-number structure is roughly locally isotropic although the turbulence Reynolds number based on Taylor ‘microscale’ and r.m.s. turbulent velocity is only 130. Departures from isotropy in the turbulent velocity gradient moments are measurable.The approximation to homogeneity permits direct estimation of all components of the turbulent pressure/velocity-gradient tensor, which accounts for inter-component energy transfer and helps to regulate the turbulent shear stress. It is found that its principal axes are aligned with those of the Reynolds stress tensor. Finally, the Rotta (1951, 1962) linear hypothesis for intercomponent energy transfer rate is roughly confirmed.

Case Studies of a Convective Plume and a Dust Devil

Abstract: The paper describes the characteristics of a convective plume and a dust devil from measurements made at 5.66 and 22.6 m above a flat uniform site in Kansas. The velocity fluctuations were measured with a continuous-wave, three-component sonic anemometer and the temperature fluctuations with a fine platinum wire thermometer. The data show that the plume is basically a non-rotating system; it is more tilted in the downwind direction than the dust devil, travels at a lower velocity than the mean wind speed at 0.5 m, and requires vertical stretching for its maintenance in the presence of wind shear. The dust devil shows a down-draft in the middle, travels at a higher velocity than the mean wind at 32 m, and derives much of its stability from rotation. Both systems tend to transport momentum upward, against the velocity gradient, which probably accounts for the very low and sometimes negative stresses observed during unstable conditions.

Turbulence and Flocculation

Abstract: Designers of flocculators are required to select the residence time, the number of flocculation compartments, the stirrer characteristics and the energy requirements, such that these function in an optimum manner in the treatment of a particular water. This paper presents a rational performance equation incorporating these parameters and demonstrates its validity with measurements employing a continuously operating model flocculation apparatus. Performance is shown to be determined by both the energy dissipation rate and the type of stirring equipment, but excessive energies result in floc breakup and reduced performance. At any particular performance a minimum residence time is shown to exist corresponding to an optimum energy dissipation. Anemometric measurements demonstrate a linear relationship between the mean square fluctuating velocity and the root mean velocity gradient computed from energy measurements. Whereas different stirrers have similar turbulence spectra, they display quite different performance coefficients.

Capillary flow instability of ethylene polymer melts

Abstract: The capillary flow instability resulting in extrudate distortion has been studied for ethylene polymer melts using a molecular structure approach. It is found that the instability initiates at a critical value of elastic strain energy independent of (average) molecular weight for linear polyethylene. Once the flow breaks down, a slip interface within the melt is formed near the capillary wall, causing an abrupt increase in volumetric throughput. The velocity gradient within the melt remains continuous through the instability, however. Low molecular weight species present in the molecular weight distribution of linear polyethylene tend to suppress slip. Blends of linear and branched polyethylene exhibit instability behavior characteristic of both components throughout the entire range of composition. Results are discussed in terms of specific molecular mechanisms.

The limiting behaviour of the turbulent transverse velocity component close to a wall

Abstract: Electrochemical techniques are used to measure the circumferential component of the velocity gradient sz at the wall of a pipe through which a turbulent fluid is flowing. The ratio of the root-mean-squared value of sz to the time-averaged velocity gradient is found to be 0·09 or 0·1, depending on whether corrections are made for frequency response. The frequency spectrum is similar to that for the component of the wall velocity gradient in the direction of mean flow. The amplitude distribution function for sz is very roughly approximated by a Gaussian distribution.

Relation of turbulent mass transfer to a wall at high Schmidt numbers to the velocity field

Abstract: Turbulent mass transfer to a wall at high Schmidt numbers is controlled by the velocity field within the viscous sublayer. Measurements have been obtained of the root-mean-square fluctuating mass transfer coefficient and the frequency spectrum of the fluctuating mass transfer coefficient for a Schmidt number of about 2300. From an order-of-magnitude analysis it is concluded that flow fluctuations in the direction of mean flow have little effect on the mass transfer fluctuations. A comparison of the mass transfer spectrum with the spectrum of the component of the velocity gradient in the transverse direction sz reveals that the high-frequency portion of the sz spectrum is not effective in transferring mass. Approximate relations between the mass transfer spectrum and the sz spectrum are developed for high frequencies and for low frequencies.

Torques in Sheared Nematic Liquid Crystals: A Simple Model in Terms of the Theory of Dense Fluids

Abstract: A fluid of equally and rigidly oriented molecules interacting through a smooth ellipsoidal two‐body potential is considered. We derive the ratio of the shear‐torque coefficients and the ratio of the shear‐viscosity coefficients for two orientations of the unique axis, one parallel to the flow and the other parallel to the velocity gradient. In addition, we confirm the validity of an Onsager relation. Given one of the four coefficients, the other three can be calculated if the axial ratio of the prolate ellipsoids of revolution is known. In accordance with the theory of dense fluids, it is assumed that intermolecular forces rather than molecular motion dominate momentum transfer.

Velocity effects on the profiles of Hα and two FeI lines

Abstract: Profiles are computed for Ha and two Fei lines for a differentially moving atmosphere. The results show that the profiles are asymmetric and that velocity measurements made in the Doppler cores will often lead to erroneous results when the velocity gradient is significant in the regions of the atmosphere where the core forms.

Turbulent flow regions with shear stress and mean velocity gradient of opposite sign

Abstract: An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.

Chemical reaction in a turbulent flow field with uniform velocity gradient

Abstract: A simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner. This theory, which is based on the concept of the generalized Brownian motion, instead of Navier‐Stokes equation, is completely self‐containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large. The latter requirement restricts the theory to the flow region outside of the laminar sublayers. The homologous flow and concentration fields are first analyzed for the chemically frozen case. From the analyses, the relationships between the mean velocity and concentration gradients, and the Reynolds stress, turbulence energy, turbulent transport of chemical species, and the mean square fluctuation of the species concentration are established. Comparison of the present results with the available experimental data is made, which shows a satisfactory agreement. The nonequilibrium chemical reaction is then analyzed and is found to create an inhomogeneity in the concentration field which, among other things, causes the mean square fluctuation to vary nonuniformly with respect to the Damkohler number and the flow region.

Bottom‐Reflection‐Loss Model with a Velocity Gradient

Abstract: Theoretical bottom‐reflection losses are computed using a multilayered model of the ocean bottom in which the layers are considered to be absorbing liquid sediments with velocity gradients. The sound velocity of each sediment layer is assumed to be a nearly linear function of depth z. In this case, the acoustic field in the sediment layers can be represented as a linear combination of Airy functions. Comparisons of theoretical and measured bottom‐reflection losses are made for three areas at frequencies from 0.1 to 1.6 kHz.

Optico-hydrodynamic properties of high molecular weight DNA from steady-state flow birefringence and viscosity at extremely low velocity gradients.

Abstract: The flow birefringence, extinction angles, and shear-dependent viscosity over a velocity gradient range of approximately 0.1–3 sec−1 have been obtained for T2 bacteriophage DNA at low concentration in neutral aqueous buffer. The data are found to be interpretable and self-consistent in terms of subchain dynamical theory, including hydrodynamic, interactions and excluded volume, and the parameters characterizing these phenomena are in good agreement with the results of other hydrodynamic experiments and theoretical calculations. No necessity for modification of the subchain model in terms of limited extensibility or internal viscosity is found for high molecular weight DNA at the velocity gradients studied, although the latter cannot be ruled out on the basis of the present data. The Kuhn statistical segment length is determined from the intrinsic optical anisotropy and is estimated as 930 A. Implications of these findings and their relation to appropriate dynamical models for DNA are discussed.

The effect of Brownian coagulation, gradient coagulation, turbulent coagulation, and wall losses upon the particle size distribution of an aerosol☆

Abstract: Numerical solutions have been obtained for the particle size distribution of an aerosol undergoing (1) Brownian coagulation plus wall loss, (2) gradient coagulation, (3) Brownian coagulation plus gradient coagulation, and (4) turbulent coagulation. The initial aerosols had a modal radius aM = 0.250 mμ or 0.500 mμ and zeroth order logarithmic breadth parameters σ0 = 0.10 or σ0 = 0.20 with initial concentration N = 107cm−3. The various constants (e.g. wall loss constant, velocity gradient, turbulent constant) were varied over a range sufficient to give effects which caused the half-time times and the size distributions to vary significantly from purely Brownian coagulation. Each mechanism of coagulations results in qualitatively similar results. For the aerosols under consideration a velocity gradient of 104 min−1 or a turbulent constant of 107 cm−1 min−1 is needed to produce effects which are appreciable compared to purely Brownian coagulation.

Flow Light Scattering. I. Theoretical Principles of the Effect and Apparatus for Its Measurement

Abstract: A brief introduction is given into the theory of radiation scattering by rigid spheroids and deformable random coils dispersed or dissolved in a liquid medium subjected to flow at a well‐defined velocity gradient. The theory is limited, in the former instance, to spheroids whose largest dimension does not exceed 13 of the wavelength of the incident radiation. It is shown that the radiation scattering increment produced by flow makes it possible to determine not only the axial ratio, as obtainable by streaming birefringence, but also the numerical values of semimajor and semiminor axis of a spheroid provided two orthogonal components of incident linearly polarized light are used. Essentials of the construction and operation of an apparatus designed for the study of hydrodynamic radiation scattering are described.

Application of a new effective viscosity model to turbulent plane Couette flow

Abstract: AjC — constants occurring in semi-logarithmic laws for turbulent layers Cf = skin-friction coefficient, rwl\pu^ h = half width of channel Re = Reynolds number based on half width, huc/v S = dimensionless centerline velocity gradient, (h/uc)du/dy)c u = velocity in streamwise direction u* = friction velocity, (r^/p) u = dimensionless velocity, ufu* U = relative velocity between planes of the Couette flow system y = coordinate normal to wall y + = dimensionless wall distance, yu*/v z = dimensionless wall distance, y/h 7 = dimensionless ratio of effective to kinematic viscosity p = fluid density T = shear stress v = kinematic viscosity

Stress Relaxation in Solutions of Linear Macromolecules

Abstract: The rigid dumbbell model has been used to derive expressions for the relaxation of shear and normal stresses after the cessation of steady shearing flow. It is found that the shear stresses relax more rapidly than the normal stresses, and that all stresses relax more rapidly as the velocity gradient during the prior steady state shearing flow increases; this behavior is in qualitative agreement with experimental data. The results further show that the integral under the shear‐stress relaxation curve is simply related to the normal stress in steady flow. The elastic dumbbell model, with a Gaussian spring, gives results inconsistent with experiment.

Velocity And Concentration Distribution InSlurry Pipe Flow

Abstract: This paper presents theoretical analysis and experimental verification of the velocity and concentration fields in a low concentration steady slurry turbulent flow in a horizontal pipe. The velocity distribution was obtained by the integration of the linear momentum equation. The velocity gradient was considered as the result of the gravitational force, hindered turbulent motion, concentration distribution of the solid particles and mixing effects due to the interaction of the liquid and the solid particles. The obtained explicit algorithm does not require system of equations to be solved. An experiment was designed and carried out to test the theoretical model. Using sand-water suspension of up to 10% solid concentration and an average velocity of up to 2.4 m/s in a 18.35 m length and 33 mm I.D. pipeline. Concentration distribution was measured using gamma-ray absorption principle. Velocity profiles were measured using Pitot-tube system. The results of the experiment showed that the theoretical model is able to reflect particle and fluid property effects on the prediction of the flow velocity distribution for low volumetric concentration of steady slurry flow.

Acoustic Streaming as a Mechanism in the Treatment of Suspensions

Abstract: Hydrodynamical shearing of droplets occurs when sufficiently high‐velocity gradients exist [F. D. Rumscheidt and S. G. Mason, J. Colloid Sci. 16, 238–245 (1961)]. Theory for acoustic microstreaming near a gas bubble indicates that large velocity gradients can exist in the boundary layer. Comparison of such gradients with hydrodynamic theory leads to the prediction that acoustic streaming can be an important mechanism in the disruption of suspensions. For example hydrodynamic theory predicts that a velocity gradient of 2.5 × 104 sec−1 existing in a fluid with a viscosity of 20 cP is sufficient to shear a droplet of radius 10 μ and a surface tension of 10 dyn/cm. A velocity gradient of this magnitude exists near a resonant 20‐kHz bubble oscillating with an amplitude of 20 μ. Under suitable experimental conditions, such amplitudes can be achieved using a single controlled oscillating bubble. Data obtained from such an arrangement substantiate aspects of the theory. [This investigation was supported by a Nati...

Closed Solution for the Initial Target‐Acquiring Angle at the Source Depth in a Linear‐Gradient Ocean

Abstract: A closed solution for the initial target‐acquiring angle θ0 at the source depth in a linear‐gradient ocean is obtained for the case involving no surface or bottom reflections. The solution for θ0 is a function of the known source and target coordinates in the ray‐path plane, the ray velocity at the source, and the velocity gradient. The equation for the intensity at the moment of acquisition is derived in a closed form through the use of the above acquiring‐angle solution.

Flow Induced Ordered State of Helical Poly-Benzyl-L-Glutamate

Abstract: Dielectric constant of α-helical poly-benzyl-L-glutamate (PBLG) is measured in the presence of a velocity gradient using rotating cylindrical electrodes. The electric field is applied across the annular gap between electrodes and the vectors of the mechanical and the electrical forces are perpendicular to each other. The dielectric constant decreases with the increasing velocity gradient, as long as the frequency is sufficiently low. When the frequency is increased, the dielectric constant increases slightly and moreover, the dielectric constant is no longer affected by the velocity gradient if the frequency is further increased. In the presence of a sufficiently high velocity gradient, PBLG solutions exhibit a considerably different dielectric relaxation from that without the velocity gradient. A semi-empirical explanation is presented to account for the behavior of polar molecules in a mechanical field and an electrical field.