Time Resolved Concentration Measurements in an Axial Flow Mixer

2004 ◽  
Vol 126 (6) ◽  
pp. 981-989 ◽  
Author(s):  
J. E. Campbell ◽  
R. W. Coppom ◽  
J. E. Guilkey ◽  
J. C. Klewicki ◽  
P. A. McMurtry
Keyword(s):  
Pipe Flow ◽  
Velocity Ratio ◽  
Wave Number ◽  
Initial Increase ◽  
Recent Theory ◽  
Far Field ◽  
Flow Loop ◽  
Mixing Rate ◽  
Scalar Concentration ◽  
Concentration Statistics

Experimental results are reported providing information on the downstream mixing evolution in axial pipe flow mixers where a scalar is introduced into the pipe via a coaxial injection tube. Experiments were conducted in a 25.4 mm diameter water pipe flow loop 25,700>RD>28,500, in which a fluorescein dye was coaxially injected. The injection tube diameter was 1.5 mm. Three velocity ratios, VR=0.5, 1.0, and 2.0 were explored, where VR=Vjet/Vmain. The present results indicate that the effects of velocity ratio on the scalar concentration statistics are mainly evident in the first several outer pipe diameters downstream. In the far field, velocity ratio effects are shown to be insignificant on the concentration statistics. All cases showed a similar trend of an initial increase in variance at the centerline as the injected fluid begins mixing with the main pipe flow. This is followed by a region of rapid “exponential-like” decay, followed by a much slower decay rate after approximately 50 pipe diameters. Space-time correlations of the scalar concentration between far field locations verify the low wavenumber motions as predicted by the recent theory of Kerstein and McMurtry [A. Kerstein and P. McMurtry, “Low-wave-number statistics of randomly advected passive scalars,” Phys. Rev. E 50, 2057 (1994)], and are consistent with the slower than exponential downstream mixing rate.

Flow Phenomena and Time Resolved Concentration Measurements in an Axial Flow Mixer

2002 ◽  
Author(s):  
Jared E. Campbell ◽  
Richard W. Coppom
Keyword(s):  
Near Field ◽  
Velocity Ratio ◽  
Axial Flow ◽  
Recent Theory ◽  
Flow Loop ◽  
Time Resolved ◽  
Concentration Variance ◽  
Jet Breakup ◽  
Flow Phenomena ◽  
Concentration Measurements

Experiments were conducted to better understand the flow physics associated with axial flow mixers in pipes. Specifically, the dependence of the downstream mixing evolution on the velocity ratio of the secondary to primary stream was explored. Experiments were conducted in a 25.4 mm diameter water pipe flow loop (25,700 ≤ RD ≤ 28,500), in which a fluorescein dye was coaxially injected. The injection tube diameter was 1.5 mm. Three velocity ratios, VR = 0.5, 1.0 and 2.0 were explored, where VR = Vjet/Vmain. The present results indicate that the effects of velocity ratio on the mean concentration are primarily evident in the near-field flow downstream of the injector, while concentration variance measurements indicate a primary influence at intermediate axial locations. Analysis of higher order moments and flow visualizations suggest that these influences are associated with the injected flow conditions. Two-dimensional LIF analysis of the coherent jet breakup region showed an instability in this transition related to injector flow Reynolds number. The present concentration measurements do not indicate the exponential variance decay commonly used for modelling mixing in pipes. Far field data exhibit low wavenumber motions as predicted by the recent theory of Guilkey et al. (1997).

Ribbing Instability Analysis of Forward Roll Coating

2009 ◽  
Vol 25 (2) ◽  
pp. 167-175
Author(s):  
K. N. Lie ◽  
Y. M. Chiu ◽  
J. Y. Jang
Keyword(s):  
Surface Coating ◽  
Velocity Ratio ◽  
Rolling Process ◽  
Linear Stability Theory ◽  
Wave Number ◽  
Roll Coating ◽  
Critical Capillary Number ◽  
Roll Velocity ◽  
Forward Roll Coating ◽  
Numerical Program

AbstractThe ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.

The low frequency scalar diffraction by an elliptic disc

1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Scattered Field ◽  
Low Frequency ◽  
Field Amplitude ◽  
Wave Number ◽  
Series Expansions ◽  
Far Field ◽  
Scalar Diffraction ◽  
Scattering Cross

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

The analysis of near and far field pattern through mode analysis and FFT in a finite periodic dielectric gratings

2015 ◽  
Vol 17 (1) ◽  
pp. 82-90 ◽  
Author(s):  
Tae-Bong Lee ◽  
Min-Nyeon Kim
Keyword(s):  
Near Field ◽  
Bloch Wave ◽  
Wave Number ◽  
Mode Analysis ◽  
Field Pattern ◽  
Far Field ◽  
Content Type ◽  
Coupled Method ◽  
Field Patterns ◽  
Dielectric Gratings

Purpose – The purpose of this paper is to analyze far and near field emitted field patterns through more exact calculation of the modes formed in finite periodic dielectric gratings. Design/methodology/approach – For the mode calculation, equations are newly defined by applying vertical boundary condition on the assumption that transverse electric modes are generated in the structure. After finding modes, near field patterns are calculated using the wave number and coefficient of the mode. Findings – Additionally, the results from these calculations are compared with that of the rigorous-coupled method. Finally, far field patterns are derived by applying fast Fourier transform to near field patterns and also compared with the results of rigorous-coupled method. Research limitations/implications – For convenience of coordinate, we use rectangular coordinate, though the shape of radome is a hemisphere. Practical implications – In this paper, the authors derive more exact near field patterns without the assumption of infiniteness so that these results can be used practically for a making real frequency-selective structure. Originality/value – Conventional periodic finite dielectric gratings analysis has been done using Floquet–Bloch wave theory, coupled-mode, rigorous-coupled method which is based on the assumption of infiniteness of the structure.

scholarly journals The influence of far field stratification on shear-induced turbulent mixing

2021 ◽  
Vol 928 ◽  
Author(s):  
S.F. Lewin ◽  
C.P. Caulfield
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Richardson Number ◽  
Scaling Laws ◽  
Mixing Efficiency ◽  
Far Field ◽  
Mixing Rate ◽  
Gradient Richardson Number ◽  
Background Density ◽  
Secondary Instabilities

We compare the properties of the turbulence induced by the breakdown of Kelvin–Helmholtz instability (KHI) at high Reynolds number in two classes of stratified shear flows where the background density profile is given by either a linear function or a hyperbolic tangent function, at different values of the minimum initial gradient Richardson number ${{Ri}}_0$ . Considering global and local measures of mixing defined in terms of either the irreversible mixing rate $\mathscr {M}$ associated with the time evolution of the background potential energy, or an appropriately defined density variance dissipation rate $\chi$ , we find that the proliferation of secondary instabilities strongly affects the efficiency of mixing early in the flow evolution, and also that these secondary instabilities are highly sensitive to flow perturbations that are added at the point of maximal (two-dimensional) billow amplitude. Nevertheless, mixing efficiency does not appear to depend strongly on the far field density structure, a feature supported by the evolution of local horizontally averaged values of the buoyancy Reynolds number ${Re}_b$ and gradient Richardson number ${Ri}_g$ . We investigate the applicability of various proposed scaling laws for flux coefficients $\varGamma$ in terms of characteristic length scales, in particular discussing the relevance of the overturning ‘Thorpe scale’ in stratified turbulent flows. Finally, we compare a variety of empirical model parameterizations used to compute diapycnal diffusivity in an oceanographic context, arguing that for transient flows such as KHI-induced turbulence, simple models that relate the ‘age’ of a turbulent event to its mixing efficiency can produce reasonably robust mixing estimates.

scholarly journals The Exciting Forces on Fixed Bodies in Waves

1962 ◽  
Vol 6 (04) ◽  
pp. 10-17 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Wave Amplitude ◽  
Amplitude Ratio ◽  
Exciting Force ◽  
The Body ◽  
Forced Oscillations ◽  
Wave Number ◽  
Far Field ◽  
Two Dimensional ◽  
Calm Water ◽  
Exciting Forces

General expressions, originally given by Haskind, are derived for the exciting forces on an arbitrary fixed body in waves. These give the exciting forces and moments in terms of the far-field velocity potentials for forced oscillations in calm water and do not depend on the diffraction potential, or the disturbance of the incident wave by the body. These expressions are then used to compute the exciting forces on a submerged ellipsoid, and on floating two-dimensional ellipses. For the ellipsoid, the problem is solved using the far-field potentials, and detailed results and calculations are given for the roll moment. The other forces agree, for the special case of a spheroid, with earlier results obtained by Havelock. In the case of two-dimensional motion the exciting forces are related to the wave amplitude ratio A for forced oscillations in calm water, and this relation is used to compute the heave exciting force for several elliptic cylinders. Expressions are also given relating the damping coefficients and the exciting forces. A = wave amplitude A = wave-height ratio for forced oscillations(a1 a2 a3) = semi-axis of ellipsoidBij = damping coefficientsC4 = nondimensional roll exciting-force coefficientDj = virtual-mass coefficients, defined by equations (18) and (19)g = gravitational accelerationh = depth of submergencei = √ — 1j = index referring to direction of force or motionn(z) = spherical Bessel function, K = wave number, K = ω2/gPj = functions defined following equation (17)R = polar coordinateV, = velocity components (x, y, z) = Cartesian coordinatesαi = Green's integrals, defined by equation (20)β = angle of incidence of wave systemθ = polar coordinateρ= fluid densityφj = velocity potentialsω = circular frequency of encounter

Wave Component Analysis of Fluid-Loaded, Finite Cylindrical Shell Response

1995 ◽  
Author(s):  
Karl Grosh ◽  
Peter M. Pinsky
Keyword(s):  
Surface Displacement ◽  
Dispersion Relations ◽  
Wave Number ◽  
Far Field ◽  
Signal Processing Algorithm ◽  
Field Response ◽  
Finite Cylindrical Shell ◽  
Finite Shell ◽  
Complex Dispersion

Abstract In this paper, the surface displacement response of a finite fluid-loaded shell and the resulting far field acoustic pressure are studied. A high resolution signal processing algorithm is applied to the surface displacement to estimate the constituent wave numbers and corresponding amplitudes for these wave components. This parameter estimation technique identifies the fluid-loaded cylinder’s complex dispersion relations from finite shell data; the dispersion relations consist of subsonic, leaky, evanescent and oscillatory-decaying wave-number loci. The identified results are compared to the analytic dispersion relations. The far field pressure radiated due to each wave-number component is computed allowing for the determination of important contributors to the far field response. For the frequencies studied, the subsonic wave dominates the far field response due to the finite length of the shell and large amplitude of this component. The supersonic components have the next largest contribution to the far field pressure.

The Effect of Temperature Gradient on the Stability of Flow between Vertical, Concentric, Rotating Cylinders

1979 ◽  
Vol 21 (6) ◽  
pp. 403-409 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Temperature Gradient ◽  
Velocity Ratio ◽  
Axial Flow ◽  
Wave Number ◽  
Taylor Vortex ◽  
Effect Of Temperature ◽  
Neutral Stability ◽  
Radial Temperature ◽  
Annular Gap ◽  
The Stability

The effect of a radial temperature gradient on the hydrodynamic stability in the annular gap formed by two, vertical, concentric cylinders, the inner being rotatable and the outer both stationary and isothermally heated, was studied for the cases of zero and imposed axial fluid flow in the annular gap. For zero axial flow, it was found that the temperature gradient destabilizes the flow while not affecting the form of the secondary flow, viz. the classic Taylor vortex. For imposed axial flow, the point of neutral stability was modified only when natural convection was strong enough to affect the parabolic velocity profile associated with that flow; the extent of this modification was shown to depend on the direction of the axial flow. Also, the longitudinal temperature gradients within the gap were found to influence the axial wave number and the drift-velocity ratio.

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