Mixing quantification by visual imaging analysis

This paper reports on development of a method for quantifying two measures of mixing, the scale and intensity of segregation, through flow visualization, video recording, and software analysis. This non-intrusive method analyzes a planar cross section of a flowing system from an instantaneous data record, thereby eliminating the need for statistical analysis of a large number of point measurements at multiple locations throughout the system to characterize the mixing. The method is applied to a cold flow model of a high temperature, gas/solid reactor so that reactor design and operation can be optimized to promote reaction efficiency. This method may be useful for studying a variety of mixing systems in which multiphase components or tracers are visually distinguishable.List of symbols mixing coefficient (defined by Eq. (17)) - standard deviation - a mixing coefficient (defined by Eq. (16)) - C(k, m) sample grayscale covariance (defined by Eq. (3)) - d distance (defined by Eq. (8)) - D divisor (defined by Eq. (3)) - d ^* value of d for which R _I (d) approaches zero - D ₅₀ mass median diameter - I intensity of segregation (defined by Eq. (20)) - M sample size (defined by Eq. (16)) - n number of contiguous pixels - n ^* value of n for which SSE _Q /SSE _L is maximized - n _c number of columns of pixels - N_R number of rows of pixels - P number of pixels per linear distance - r radius of Cold Flow Model - R(k, m) sample correlation function (defined by Eq. (5)) - R _C (k) column correlation function (defined by Eq. (7)) - R _I (d) isotropic correlation function (defined by Eq. (9)) - R _R (m) row correlation function (defined by Eq. (6)) - SSE _Q residual sum of squared errors from the least squares fit of the quadratic model to Eq. (14) - SSE _L residual sum of squared errors from the least squares fit of the linear model to Eq. (14) - S _y ² sample grayscale variance (defined by Eq. (2)) - S _c column scale of segregation (defined by Eqs. (7) and (13)) - S _D Danckwerts' scale of segregation (defined by Eq. (10)) - S _R row scale of segregation (defined by Eqs. (6) and (13)) - S _s scale measure developed in this paper (defined by Eq. (13)) - V _n sample variance of contiguous pixels (defined by Eq. (11)) - V _n ^* normalized variance function (defined by Eq. (12)) - sample grayscale mean (defined by Eq. (1)) - Y _i,j grayscale value at pixel (i,j)     

Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant-density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have applications to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, we examine the stability of this nonorthogonal flow to self-similar, three-dimensional disturbances. Stability characteristics of the flow are given as a function of the parameters of this study: ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wave number and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case. By use of this scaling, it can be shown that decreasing the angle of attack decreases the wave number and the magnitude of the temporal decay rate, thus making nonlinear effects important. For small wave numbers, it is shown that cooling the plate decreases the temporal decay of the least-stable mode, while heating the plate has the opposite effect. For moderate to large wave numbers, density variations have little effect except that there exists a range of cool plate temperatures for which these disturbances are extremely stable.This work was supported by the National Aeronautics and Space Administration under NASA Contract NAS1-18605 while the authors were in residence at the Institute for Compute Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

Excitation of velocity fluctuations and noise in a wind tunnel

The aim of this paper is to develop a theory, consistent with the observations, of the nature and location of the structures that determine self-excitation and the emission of the narrow-band components of the noise generated by the open working section of wind tunnels. At the same time, the theory is applied by using it as a basis for constructive solutions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 165–173, July–August, 1992.     

Orienting properties of discotic nematic liquid crystals in Jeffrey-Hamel flows

The orienting properties of incompressible discotic nematic liquid crystals for creeping flows between converging and diverging planar walls (Jeffrey-Hamel) are analyzed using the Leslie-Ericksen theory. The dependence of director orientation on the reactive parameter and the flow kinematics is presented. Closed form stationary solutions for the director orientation are found when elastic effects are neglected. Stationary numerical solutions for the velocity and director fields using the full Leslie-Ericksen theory are presented. The director field in converging flow is characterized by azimuthal (radial) centerline orientation, by being asymmetric with respect to the azimuthal (radial) direction, and by having an allowed orientation range that spans two half-quadrants (full quadrants). In the limiting case of perfectly flat disk ( –) the flow-induced director orientation in converging flow is the azimuthal direction, while in diverging flow the director rotates by a full n radians. By reducing the vertex angle between the walls to vanishingly small values, converging flow solutions properly reduce to those of flow between parallel plates, but diverging flows are expected to lead to a new instability.     

An experimental validation of load distribution in screw threads

The thread load distribution has been examined, as is known, in literature both theoretically and experimentally. in the present paper the load distribution is validated by strain-gage measurements. Starting from the theoretical load distribution the stresses on the outer surface of the female member of a threaded connection are calculated. The theoretical and experimental stress values obtained are reasonably close.     

Self-oscillations in an underexpanded jet flowing into a barrier

The distribution of the phases and amplitudes of the static pressure fluctuations with self-oscillations of an underexpanded jet flowing into a barrier is obtained experimentally in the present paper. The distribution of the Mach number in the compressed layer and in the subsonic flow in front of the barrier is shown. The results of the measurements of the characteristics of the self-oscillation process are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 38–43, November–December, 1977.     

Necking of biaxially stretched elastic-plastic circular plates

The necking of an elastic-plastic circular plate under uniform radial tensile loading is investigated both within the framework of the three-dimensional theory and within the context of the plane-stress approximation. Attention is restricted to axisymmetric deformations of the plate. The material behavior is described by two different constitutive laws. One is a finite-strain version of the simplest flow-theory of plasticity and the other is a finite-strain generalization of the simplest deformationtheory, which is employed as a simple model of a solid with a vertex on its yield surface. For an initially uniform plate made of an incompressible material, bifurcation from the uniformly stretched state is studied analytically. The regimes of stress and moduli where the governing axisymmetric three-dimensional equations are elliptic, parabolic or hyperbolic are identified. The plane-stress local-necking mode emerges as the appropriate limiting mode from the bifurcation modes available in the elliptic regime. In the elliptic regime, the main qualitative features of the bifurcation behavior are revealed by the plane-stress analysis, although three-dimensional effects delay the onset of necking somewhat. For the deformation theory employed here, the first bifurcation modes are encountered in the parabolic regime if the hardening-rate is sufficiently high. These bifurcations are not revealed by a plane-stress analysis. For a plate with an initial inhomogeneity, the growth of an imperfection is studied by a perturbation method, by a plane-stress analysis of localized necking, and by numerical computations within the framework of the three-dimensional theory. When bifurcation of the corresponding perfect plate takes place in the elliptic regime, the finite element results show that the plane-stress analysis gives reasonably good agreement with the numerical results. When bifurcation of the corresponding perfect plate first occurs in the parabolic regime, then a bifurcation of the imperfect plate is encountered, that is, the finite element stiffness matrix ceases to be positive definite.     

Recent advances in notch analysis of fracture and fatigue

Summary Neuber's micro- and macrosupport effect theories are applied to obtain on expression for the plastic work required for crack extension. On this basis analytical predictions for fracture toughness, thickness effects and fatigue crack propagation threshold are made and found in very good agreement with experimental results.

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Übersicht Mit Hilfe der Neuberschen Theorie der Mikro- und Makrostützwirkung wird eine allgemeine Formulierung für die Rißerweiterungskraft bei nichtlinearem Werkstoffverhalten hergeleitet. Darauf aufbauend werden die Rißzähigkeit, Dickeneffekte und Rißstop bei Schwingbeanspruchung theoretisch behandelt und eine sehr gute Übereinstimmung mit Versuchsergebnissen festgestellt.

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Dedicated to o. Prof. Dr.-Ing. Dr. rer. nat. h. c. H. Neuber.