J. Y. Kazakia

Air flow in cavities of labyrinth seals

The leakage flow rate through a sequence of labyrinth seal cavities, and the associated pressure and the circumferential velocity distributions are calculated for seals used in turbomachinery. Computational Fluid Dynamics is used to justify the use of bulk cavity variables, and to analyze the details of the flow in a single cavity under steady state, axisymmetric conditions. Periodic, analytic solutions of the continuity and circumferential momentum equations are obtained for the case of time dependent flow generated by a non-axisymmetric rotation of the shaft. The dynamic stiffness and damping coefficients necessary for the lateral stability analysis of the rotor are then calculated. The results compare reasonably well to experimentally obtained values.

The influence of vibration on Poiseuille flow of a non-Newtonian fluid, I.

SummaryThe effect is calculated of a superposed sinusoidal vibration on the rate of discharge of an incompressible, isotropic, non-Newtonian fluid, which is in plane Poiseuille flow, under a constant pressure gradient, between two parallel plates. The calculations are made both when the vibration is longitudinal and when it is transverse. Calculations are also made in the case of Poiseuille flow through a straight pipe of circular cross-section, when a sinusoidal vibration, either longitudinal ar rotational, about the axis of the pipe is superposed.ZusammenfassungEs wird die Wirkung einer überlagerten Sinusschwingung auf den Durchsatz einer inkompressiblen, isotropen, nicht-newtonschen Flüssigkeit berechnet, die in einer ebenen Poiseuille-Strömung zwischen zwei parallelen Platten unter der Wirkung eines konstanten Druckgefälles ausfließt. Dabei werden sowohl Longitudinal- als auch Transversal-Schwingungen betrachtet. Anschließend werden analoge Rechnungen für eine Poiseuille-Strömung in einem geraden zylindrischen Rohr durchgeführt, wobei eine in bezug auf die Rohrachse entweder longitudinale oder rotatorische Sinusschwingung überlagert wird.

Propagation of electromagnetic waves in a nonlinear dielectric slab

The early phases of propagation of a large amplitude electromagnetic disturbance in a nonlinear dielectric slab embedded between two linear media are investigated by the method of characteristics. This disturbance is triggered by the arrival of an electromagnetic shock wave at one of the interfaces. Reflection and transmission of an arbitrary signal when it arrives at one of the slab boundaries is characterized in terms of nonlinear reflection and transmission coefficients for the interface. No restrictions are placed on the form of the constitutive laws of the material comprising the slab.By introducing, for the nonlinear dielectric, a class of model equations, an exact solution to the characteristic equations which describes the interaction of a centered wave with anarbitrary oncoming signal is obtained. Solutions for the electromagnetic fields are derived for the special case in which the incident disturbance interacts with the reflected signal from the slab interface. A particular case of the disturbance propagating across a nonmagnetic slab is also examined.ZusammenfassungDie Anfangsphasen der Fortpflanzung einer elektromagnetischen Störung mit grosser Amplitude in einer nichtlinearen dielektrischen Platte zwischen zwei linearen Materialien werden mit der Methode der Charakteristiken untersucht. Durch Einführung einer Klasse von Modellgleichungen für das nichtlineare Dielektrikum wird eine genaue Lösung erzielt, die die Wechselwirkung zwischen einer zentrierten Schwingung und dem von der Plattengrenzschicht reflektierten Signal beschreibt.

Pressure measurements in highly viscous and elastic fluids

Pressure measurements in flows of highly viscous and elastic fluids are of practical importance in polymer processing and rheology systems. Special problems arise during such pressure measurements. High fluid viscosity results in excessive dynamic response time (rise time) of the pressure measuring systems. This is true for systems that consist of manometers as well as pressure transducers attached to the base of a small hole at the wall. We model the dynamic response and examine related disturbing effects. These systematic errors in pressure measurements include hole-pressure effects, instabilities in cavity flow, and the time lag of the disturbance wave

An asymptotic two-layer model for supersonic turbulent boundary layers

An asymptotic analysis of the compressible turbulent boundary-layer equations is carried out for large Reynolds numbers and mainstream Mach numbers of O(1). A self-consistent two-layer asymptotic structure is described wherein the time-mean velocity and total enthalpy are logarithmic within the overlap zone but in terms of the Howarth-Dorodnitsyn variable ; the proposed structure leads to a compressible law of the wall for high-speed turbulent flows with surface heat transfer. Simple outer-region algebraic turbulence models are formulated to reflect the effects of compressibility. To test the proposed asymptotic structure and turbulence models, a set of self-similar outer-region profiles for velocity and total enthalpy is obtained for constant-pressure flow and for constant wall temperature ; these are combined with wall-layer profiles to form a set of composite profiles valid across the entire boundary layer. A direct comparison with experimental data shows good agreement over a wide range of conditions for flows with and without surface heat transfer.

The Effect of Longitudinal Vibration on Poiseuille Flow in a Non-Circular Pipe

Abstract The effect is discussed of a superposed longitudinal sinusoidal vibration on the flow, under a constant pressure gradient, of a slightly non-Newtonian fluid in a straight pipe of non-circular cross-section. It is found that a flow in transverse planes is produced. This is the superposition of steady and sinusoidal flows. The stream-function corresponding to the steady flow is obtained in the case when the pipe has a rectangular cross-section. The discussion is based on a Rivlin-Ericksen constitutive equation in which only“second-order” non-Newtonian terms are present.

A study of active attenuation of broadband noise

The use of controlled sound, generated by unidirectional secondary sources, in cancelling primary noise of low frequency in long ducts is investigated. It is shown that for broadband primary noise, say four octaves, the simple arrangement of two secondary speakers used in many experimental studies is not efficient. This inefficiency manifests itself by a very low available output for part of the frequency band (0·16 times that of a single speaker) and by an unacceptably slow decay of the cross modes which may confuse the sensing device. The plane waves and the cross modes generated by rectangular or circular loud-speakers which are mounted on a duct wall are investigated. It is seen that an increase of the size of the loudspeaker reduces its efficiency and at the same time slows down the decay of the cross modes. Consequently, the inefficiency of a particular unidirectional arrangement cannot be corrected by the use of larger speakers. The plane wave generated by a secondary source consisting of four speakers is calculated. It is shown that such an arrangement generates unidirectional sound of amplitude at least 1·3 times that of a single speaker over a frequency range of 51/3 octaves.

The evolution of small rotational perturbations to a uniform rotation of a viscoelastic fluid contained between parallel plates

Abstract The transfer mechanism of momentum from the boundaries into the interior of a viscoelastic fluid is examined in the case when the boundary consists of two parallel plates. Special emphasis is given to the case of a Maxwellian fluid. It is seen that an increase in the azimuthal angular velocity at the boundaries progresses into the interior of the liquid in the form of a velocity discontinuity wave. Simultaneously, an axial circulatory flow pumps liquid from the low rotation region near the middle plane into the high rotation region near the boundaries. Detailed calculations are given for the intial stage of evolution.

Some superposition theorems for second-order fluids

Abstract Theorems are derived, within the framework of the second-order Rivlin-Ericksen theory, relating to the superposition of longitudinal flows on plane flows in an incompressible isotropic viscoelastic fluid. Also, some theorems are obtained concerning the effects of inertia on the solution of plane flow problems in such viscoelastic fluids.

Embedded function methods for supersonic turbulent boundary layers

The development of embedded functions to represent the mean velocity and total enthalpy distributions in the wall layer of a supersonic turbulent boundary layer is considered. The asymptotic scaling laws (in the limit of large Reynolds number) for high speed compressible flows are obtained to facilitate eventual implementation of the embedded functions in a general prediction method. A self-consistent asymptotic structure is derived, as well as a compressible law of the wall in which the velocity and total enthalpy are logarithmic within the overlap zone, but in the Howarth-Dorodnitsyn variable. Simple outer region turbulence models are proposed (some of which are modifications of existing incompressible models) to reflect the effects of compressibility. As a test of the methodology and the new turbulence models, a set of self-similar outer region profiles is obtained for constant pressure flow; these are then coupled with embedded functions in the wall layer. The composite profiles thus obtained are compared directly with experimental data and good agreement is obtained for flows with Mach numbers up to 10.