Towards the solution of finite plane-strain problems for compressible elastic solids

A new approach to the solution of finite plane-strain problems for compressible Isotropie elastic solids is considered. The general problem is formulated in terms of a pair of deformation invariants different from those normally used, enabling the components of (nominal) stress to be expressed in terms of four functions, two of which are rotations associated with the deformation. Moreover, the inverse constitutive law can be written in a simple form involving the same two rotations, and this allows the problem to be formulated in a dual fashion.For particular choices of strain-energy function of the elastic material solutions are found in which the governing differential equations partially decouple, and the theory is then illustrated by simple examples. It is also shown how this part of the analysis is related to the work of F. John on harmonic materials.Detailed consideration is given to the problem of a circular cylindrical annulus whose inner surface is fixed and whose outer surface is subjected to a circular shear stress. We note, in particular, that material circles concentric with the annulus and near its surface decrease in radius whatever the form of constitutive law within the given class. Whether the volume of the material constituting the annulus increases or decreases depends on the form of law and the magnitude of the applied shear stress.     

Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

Drying performance and surface forces of a pair of impinging radial jets

The drying performance and the forces generated by a pair of radial jets impinging on a plane surface are studied experimentally and compared with a pair of in-line (axial) jets. The reattachment rings of the radial jets are visualized by liquid-crystal-thermography. The results of the drying experiments are presented in terms of Sherwoodnumbers. The results of the surface force measurements are presented in terms of force coefficients. The effects of flow exit angle, exit velocity, horizontal nozzle spacing and vertical nozzle to surface distance on mass transfer and net surface force are discussed. Results show that drying performance of a pair of radial jets with an exit angle towards the surface of 10° is 18% higher than that of a pair of in-line jets. The surface force of impinging radial jets depends on the exit angle. A global pressure force on the surface is typical for jets directed towards the surface, while a global lifting force is found when the jet is initially directed away from the surface. Radial jets have a high potential in drying applications for force sensitive products and when high drying rates and/or small suction forces are of interest.     

Effects of outflow boundary condition on convective heat transfer with strong recirculating flow

Three practices of treating outflow boundary condition were adopted in computations for convective heat transfer of a two-dimensional jet impinging in a rectangular cavity. The three practices were local mass conservation method, local one-way method and fully developed assumption. The numerical solutions of the three methods were compared with test data obtained via, naphthalene sublimation technique. It was found that the fully developed assumption was inappropriate, and the local one-way method could provide reasonably good results for the cavity bottom, while for the lateral wall the results with this method qualitatively differed from the test data. The solution with the local mass conservation method was the best. It thus suggested that for a problem expected with a strong recirculating flow at the exit of the computation domain, the local mass conservation method be adopted to treat the outflow boundary condition.     

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)     

Influence of vent positions on smoke clearance from a room

Results of solutions to the equations governing the clearance of smoke in laminar and in turbulent flow from a single rectilinear room are presented fof five different vent arrangements. These results show that the average smoke concentration in the room decreases in an approximately exponential manner with time at a rate that depdends much more on room geometry (vent positions in the present case) than on whether the flow is laminar or turbulent. The benefit of this observation is that, provided the clearance air jet is disrupted by impingement on a solid surface within the room, the analysis of smoke movement can for many practical purposes be limited to consideration of laminar flow only. An exceptional case is when the jet is allowed to take a straight line path between the inlet and outlet vents. Here in the absence of the large scale eddies caused by jet impingement, the smaller scale eddies of turbulent flow become relatively important as a mixing mechanism and give higher clearance rates than in laminar flow. Even so, this type of geometry is best avoided. The appearance of the jet is shown in a graphic presentation of the numerical results for laminar flow.     

Der Einfluß von Druck und Temperatur auf die effektive Viskosität in geschmierten kontra-formen Kontakten

Zusammenfassung Die Viskosität von flüssigen Schmierstoffen wird von verschiedenen Parametern, z. B. von der Temperatur, dem Schergefälle und dem herrschenden Druck, beeinflußt. Für die Anwendung der elastohydrodynamischen Schmierungstheorie auf hochbelastete Kontakte, etwa auf Zahnradgetriebe, kommt neben der Viskositäts-Temperaturabhängigkeit der Viskosität-Druckabhängigkeit des Schmierstoffes besondere Bedeutung zu.Derzeitige Möglichkeiten, das Viskositäts-Druckverhalten von flüssigen Schmierstoffen darzustellen und zu messen, wurden aufgezeigt. Insbesondere die Messung des Viskositäts-Druckverhaltens ist bei flüssigen Schmierstoffen nur begrenzt bis ca. 2000 bar möglich.Bei Untersuchungen eines elastohydrodynamischen Linienkontaktes wurden die Verläufe des Druckes, der Temperatur und der Schmierspalthöhe gemessen. Dabei zeigten sich deutliche Einflüsse des Viskositäts-Druckverhaltens auf die untersuchten Parameter. Sowohl das zweite Druckmaximum des Druckverlaufes als auch die Einschnürung im Verlauf der Schmierspalthöhe erwiesen sich als deutlich vom Viskositäts-Druckverhalten des eingesetzten Versuchsöles — bei gleicher Eintrittsviskosität — beeinflußt. Daraus ergibt sich die Möglichkeit, aus solchen Meßergebnissen eines elastohydrodynamischen Kontaktes eine Bestimmung des Viskositäts-Druckverhaltens bis hin zu praxisnahen Drücken vorzunehmen.

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Summary The viscosity of fluid lubricants is influenced by different parameters. For example, viscosity depends on temperature, shear rate and pressure. Applicating the elastohydrodynamic theory of lubrication to high loaded contacts as e.g. realized in gear drives the viscosity pressure dependency also has to be taken into account. Actual possibilities to describe and to measure the viscosity-pressure behaviour of fluid lubricants are offered. In particular, the viscosity-pressure behaviour can be measured up to about 2000 bar.Our investigations of an elastohydrodynamic contact in a two-disk-apparatus with pressure, temperature and gap measurements for several standard oils show new possibilities to estimate the viscosity-pressure behaviour of fluid lubricants.

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Mit 10 Abbildungen und 1 Tabelle     

Single specimen determination of Young's and bulk moduli of polymers

Summary A new method is presented for the rapid and consecutive determination of theYoung's and bulk moduli of polymeric solids in compression loading. Usually these properties are determined by separate measurements. However, by using an undersized specimen in a standard bulk compressibility tester, it is possible to determine both moduli on the same specimen in a single test procedure. Initial loading of the undersized specimen results in a decrease in length and an increase in diameter. From these changes,Young's modulus may be calculated. Once the bore of the tester is filled, the application of additional pressure results in a decrease in the volume of the polymer from which the bulk modulus may be calculated. Both determinations may be made within minutes. The moduli values are in general agreement with published values and the calculated values for Poisson's ratio fall into the expected range.

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Zusammenfassung Es wird eine neue Methode vorgestellt für die schnelle und fortlaufende Bestimmung des Elastizitäts- und Kompressions-Modul us polymerer Festkörper bei einer Druckbelastung. Normalerweise werden diese Eigenschaften durch unterschiedliche Methoden bestimmt. Durch Benutzung einer unterdimensionierten Probe in einem Standard-Kompressionsprüfgerät ist es möglich, beide Moduln an der gleichen Probe in einem einzigen Versuch zu ermitteln. Die Anfangsbelastung einer unterdimensionierten Probe führt zu einer Längenabnahme und einer Zunahme des Durchmessers. Aus diesen Änderungen läßt sich der Elastizitätsmodul berechnen. Sobald die Bohrung des Gerätes gefüllt ist, führt die Erhöhung des Druckes zu einer Volumen-Abnahme des Polymers, aus dem sich der Kompressionsmodul berechnen läßt. Beide Bestimmungen können in wenigen Minuten durchgeführt werden. Die Modulwerte stimmen im allgemeinen mit veröffentlichten Werten überein, und die für dasPoisson-Verhältnis ermittelten Werte liegen in dem erwarteten Bereich.

     

The swirling radial free jet

Summary A general similarity solution suggested by Watson for the problem of the laminar, radial, free-jet with swirl has been previously discussed by Riley who also calculated the order to which the solution was valid. That problem is considered in more detail here and higher order terms are given. It is shown that a perturbation scheme for the stream function consisting of a series of inverse powers of and which uses the asymptotic similarity solution as the basic solution is inadequate, and a modification to the series so as to include terms like ⁿ (ln ) ^m must be adopted in order to satisfy the boundary conditions. It is also shown that the general similarity solution may be obtained from the asymptotic series representing the general case with swirl for certain special values of the free constants and also for the no-swirl or free-jet problem. The asymptotic series is given to order ^–13 for the case of swirl and to order ^–29 when there is no swirl.