Flow of a dipolar fluid between parallel plates

The flow of a dipolar fluid between two parallel plates with and without heat transfer is studied. The following cases are discussed:

1. Isothermal flow due to the relative motion of the plates,
2. Isothermal flow due to a constant pressure gradient with the plates at rest,
3. Nonisothermal flow with linearly varying plate temperatures.

Case (ii) is of particular interest to the experimentalists as it shows the effect of the material constants even when there are no externally applied dipolar tractions on the plates.     

Marangoni convection at alcohol aqueous solutions-air interfaces

For aqueousn-heptanol solutions and in a nearly two-dimensional flow, two strikingfeatures have been detected:

1. a shift of the minimum of the surface tension
2. a discrepancy between the observed Marangoni flow velocities and the expected ones from static surface tension values.

A qualitative explanation is given.     

Hamilton principle for an inviscid compressible fluid model in Eulerian coordinates

It is shown that the well-known variational principles for the ideal compressible fluid model in Eulerian coordinates have the following deficiencies:

1. They are not related to the corresponding variational principles in Lagrangian coordinates;
2. The variation procedure in these variational problems does not lead to the equations of motion themselves in the Euler form; rather it leads to relations which correspond to definite classes of solutions of the Euler equations. Here allowance for the equations of the constraints imposed by the adiabaticity and continuity conditions limits the region of application of these variational principles to only potential flows;
3. More general results, involving flows other than potential, are achieved by artificial selection of certain additional constraint conditions imposed on the quantities being varied, and in this case additional clarification is required to ascertain whether any inviscid compressible fluid flow is the extremum of the corresponding variational problem.

A new formulation of the Hamilton principle for the inviscid compressible fluid in Eulerian coordinates is suggested which is free from these deficiencies.     

Flow past a suddenly cooled horizontal plate

The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet<0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely

1. an analytical solution which is valid for small time,
2. an asymptotic analytical solution which is valid for large time, and
3. a numerical solution which matches these two limiting analytical solutions.

It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed.     

Oscillation modes of laval nozzle flow

Experimental investigations of Laval nozzle flow show for relatively low supply to exit pressure ratios, which correspond to shock wave positions close to the nozzle throat, three different, oscillatory instabilities.

1. Shock pattern oscillations where the root of a λ-like shock front remains nearly in constant position, but where the proportion between the normal part and the oblique part of the shock changes periodically.
2. Shock wave and separation bubble oscillations where the motion of the shock wave is accompanied by displacements of the separation bubble.
3. Flow rate oscillations where the shock waves leave periodically through the nozzle throat in upstream direction.

     

Investigation of a vibrating piezoelectric ceramic disk by synthesis of optical coherent methods

Modes of a vibrating disk, made of piezoelectric ceramic-type PZT-5A, were investigated by two optical coherent methods:

1. Time-average holography (TAH).
2. Speckle-shearing interferometry (SSI). It is shown how synthesis of data from the two methods can give a good picture of the modes of vibration, more exact than the picture one can derive from each method alone.

     

Variable isochromatic/isopachic-fringe visibility in photoholoelasticity

This paper presents a new “hybrid” method whereby the ratio of the isochromatic-fringe visibility/isopachic-fringe visibility may be easily and continuously varied. This simple procedure merely combines a conventional polariscope with a holographic system. A variable beam splitter permits an incoherent superposition of the reconstruction of a doubly exposed hologram with real-time isochromatics, either dark or light field. By varying the ratios of the above two, in the image plane, numerous interesting results may be obtained including:

1. Isochromatics only, without errors in position
2. Isochromatics-isopachic fringes identical to those obtained through classical interferometry
3. Isochromatic-isopachic fringes whereby the amplitude modulation between the two may be minimized
4. Continuously variable isopachic/isochromatic-fringe visibility.

     

Guidance properties of nonlinear planar waveguides

We discuss the propagation of electromagnetic waves through a stratified dielectric. The ability of such a device to support guided waves depends upon the way in which the refractive index varies across the layers. In the present discussion, we show how nonlinear effects and appropriate stratification can be used to obtain any one of the following behaviours:

1. guidance occurs only at low power.
2. guidance occurs only at high power.
3. guidance occurs at all powers.
4. there is no guidance.

The situation (i) is obtained by using materials with a defocusing dielectric response, whereas the situation (ii) is obtained for suitable configurations of self-focusing materials. The situations (iii) and (iv) can be obtained by using either defocusing or self-focusing materials. By seeking solutions of a particular form, we reduce the problem to the study of solutions in the Sobolev space H ¹(?) of a second-order differential equation. The discussion of defocusing nonlinearities is based in the study of the global behaviour of the branch of solutions bifurcating from a simple eigenvalue. For self-focusing nonlinearities we use a variational approach.     

On the steady motion of two immiscible fluids in an undulating porous reservoir

We describe steady two-dimensional flows of two immiscible fluids through an undulating porous medium of constant thickness, with impermeable or slightly permeable boundaries. Flows in the same or opposite directions are called, respectively, direct or counter flows. Three special classes of flow are determined:

1. The pressure dominated case occurs for high direct flows and has the interface approximately a constant vertical distance from the impermeable boundaries.
2. The gravity dominated case occurs for low direct flows and has the interface very close to the lower (upper) boundary for downward (upward) sloping boundaries except at crossovers.
3. Counter flows require the interface to decrease in the direction of flow of the lower fluid.

Numerical examples illustrate the three classifications above. For incompressible flows the interface and pressure equations uncouple. A stability analysis shows that the direction of integration of the differential equation for the interface must be opposite to the flow direction for direct flows; for counter flows the direction of integration depends on whether the interface is above or below a critical height. Direct flows through cyclic geometries are asymptotically cyclic upstream. If the reservoir is ‘leaky’, asymptotically self-similar flows result when the (small) permeability ratio is scaled to the dynamical flow parameters.     

Interferogram processing by spatial filtering

This paper describes a technique of interferogram processing by the use of spatial-frequency filtering. Proper part of Fourier spectrum of the interferogram is blocked out by a matched mask located in the focal plane of the imaging system. Depending on the mask shape and dimensions one can obtain

1. interferogram images with delineating fringes or
2. interferogram images of one component of strain.

     

Rapid interpretation of moiré photographs

The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moiré method. The moiré photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moiré photographs, moiré fringes of second order for the curvature or the twist are obtained. It is shown how charts can be produced which indicate:

1. The distribution of the bending moments
2. The distribution of the bending moments for which the reinforcement should be designed
3. The distribution of the shear forces and the magnitude of the bearing reactions.

     

Some pending problems in polymer melt rheology,as seen from the point of view of Doi's slip-link model

An exposition is given of results, as obtained with the aid of Doi's sliplink model, being considered as the most simple version of the famous “reptation model”. It turns out that this model which exhibits three distinct phases of relaxation (an extremely fast phase, an equilibration phase and a slow disengagement phase) is capable of explaining several peculiar features of polymer melt rheology:

1. The molecular mass dependence of the breadth of the rubber plateau in the storage modulus, of the zero-shear viscosity and of the normal-stress coefficients.
2. The molecular mass independence of the equilibrium (shear and tensile) compliances for monodisperse polymers (semi-quantitative prediction).
3. The seemingly contradictory sensitivity of these compliances for the breadth of the molecular mass distribution.
4. The critical value of the shear stress at which melt fracture occurs in capillary flow.
5. An equilibration phase in tensile experiments on unvolcanized rubber.

In this evaluation optical (flow birefringence) measurements are preferentially used.     

Fracture data and stress-strain behavior of rocks in triaxial compression

Test results are reported for a recently completed experimental research program on rocks subjected to triaxial compression. Sandstone, marble, granite and shale specimens were tested at confining pressures as high as 90,000 psi corresponding to mean stresses of up to 143,000 psi. Recognizing that the largest potential experimental error in such tests results from making strain and load measurements external to the vessel, special load and strain-measuring devices were designed and fabricated for use inside the pressure vessel. The specimens were carefully machined cylinders with length-to-diameter ratios of two and with diameters ranging from 4/16 in. to 1 in. The confining pressure was held constant during each run, but varied from 0 to 90,000 psi over the tests. Results are reported in the form of:

1. Stress-strain curves for individual specimens
2. Maximum shear stress at fracture vs. mean-stress curves for each rock type tested
3. Tabulation of results for 59 specimens

A number of tests were run on granite specimens which had been previously fractured. Results from these tests showed good agreement with tests on intact granite, providing the confining pressure was above 30,000 psi.     

Effects of artificial cracks and poisson's ratio upon photoelastic stress-intensity determination

A series of stress-freezing photoelastic experiments were performed with multiple replications upon edge-cracked strips for three types of “cracks” in current use:

1. Rectangular slots 0.152 mm wide,
2. 1.59-mm-wide slots terminating in a 30-deg vee notch of approximately 0.025-mm root radius, and
3. Natural cracks (approximately 0.0025-mm root radius).

Stress-intensity results were compared with the Gross-Srawley analysis; in addition (1) was compared with Savin's solution. It was concluded that (2) and (3) yield the same results but (1) was slightly higher. Both (2) and (3) were about 12 percent higher than the Gross-Srawley results. This is shown to be related to a Poisson's ratio effect.     

A fast and accurate graphical method for designing an air conditioning cooling coil

The aim of this paper is to develop a fast and simple accurate graphical method for designing the required cooling coil for an air conditioning system in which both the sensible and latent heat are transferred. The method has the following advantages:

1. Direct solution utilizing only Psychrometer charts.
2. Solution of combined heat and mass transfer problems occuring at pressures other than that of atmosphere.
3. Direct determination of boundary temperature at which dehumidification begins for that type of problem where a portion of the surface is in a dry condition.
4. Less effort required than trial and error method in determination of air condition leaving a counterflow coil of a given area.

The calculated values of the method showed a good agreement with the experimental results. The average deviation for the total heat is about + 15 % and for sensible heat is + 9 %, which are of positive nature and on the safe side for practical design purposes. The method is also useful for similar practical application.     

Glass-bonding techniques for semiconductor strain gages

Conventional organic-epoxy adhesives outgas when exposed to ultra-high vacuum and, as operating temperatures are increased, they begin to exhibit plastic behavior causing hysteresis and zero instability in the transducer. The use of an inorganic glass as the bonding material has resulted in a significant advance in transducer-fabrication technology for the following reasons:

1. The outgassing of transducers in high-vacuum applications is minimized.
2. Mechanical properties of the transducer such as hysteresis and repeatability are improved.
3. The electrical isolation of the strain gages from the metallic elements of the transducer is increased at high temperatures over that provided by epoxy. Also, the glass bond can survive and operate in severe radiation environments, wherein the epoxy adhesive will suffer either temporary or permanent loss of its dielectric strength.
4. Glass-bonding techniques are particularly useful for the extension of the temperature range of operation of silicon-strain-gage transducers.

Nispan C and 440-C stainless-steel substrates were successfully used with glass-bonded silicon strain gages to fabricate transducers for evaluation.     

A logrithmic bound on the location of the poles of the scattering matrix

It is shown that the complex poles z of the scattering matrix satisfy the inequality: Im z≧a+b log ¦z¦, b>0, in three instances of classical scattering in three space dimensions described by the wave equation u_{t t}?c²Δu+qu=0.

1. c and q smooth with c=1 and q=0 for ¦x¦>p, all rays going to infinity, and the energy form positive definite.
2. c=1 and q=0 outside of a convex body on which u=0.
3. c=1, q bounded and measurable, q=0 for ¦x¦>p, and the energy form not necessarily positive definite.

     

Stress concentrations around horizontal circular tunnels

The problem of axial variation of stress concentrations at the periphery and normal to the axis of a circular tunnel is solved by means of the three-dimensional photoelasticity technique, under the following conditions:

1. The center lines of two horizontal tunnels of equal diameter (2r) are separated by a distanceK and include an angle α.
2. K and α assume values of 0, 3r, 7/2r, 4r and 30 deg, 60 deg, 90 deg, respectively.
3. The tunnels are located in a uniform, uniaxial stress field normal to the axes of the tunnels.

     

Determination of stress-intensity factors from photoelastic data with applications to surface-flaw problems

ATaylor-series correction to the maximum inplane shear stress was studied as a means of extending the data zone in photoelastic determination of stress-intensity factors beyond the singular region of a two-degree-of-freedom analysis. Convergence properties were obtained by comparing with several complete two-dimensional solutions. Experiments were performed on two kinds of three-dimensional problems, plates containing surface flows in both bending and extension. Results were analyzed by both a two-degree-of-freedom and aTaylor-series correction method (TSCM). Results were compared to theories of F. W. Smith and A. S. Kobayashi and R. C. Shah. It was concluded that:

1. The TSCM program converges rapidly to accurateK _I values and will accommodate the scatter inherent in experimental data if the series is properly truncated.
2. The TSCM program is essentially equivalent to the two-parameter representation when only the crack-surface effects dominate.
3. When effects other than crack surfaces are important, TSCM requires more terms but still predictsK _I with reasonable accuracy.

     

Experimental determination of viscosity of rocks

An important parameter involved in the viscoelastic deformation of structural materials is the coefficient of “solid” viscosity. Determination of this parameter is necessary, if it is to be used in structural design. This paper deals with pertinent analytical considerations concerning solid viscosity and describes the procedures followed in the determination of parameters for structural and true viscosity of a Queenston limestone. The following three techniques were used:

1. Relaxation technique
2. Uniaxial compressive loading
3. Cantilever-beam loading

The results obtained are in close mutual agreement except for (2) above, where experimental conditions were different from those in (1) and (3). A quasi-periodic behavior of strain is indicated. It has been shown that the solid viscous parameter is a transient property and may depend on such factors as applied load, time, grain size, grain-packing in a material, and the direction of testing. It has been concluded that coefficients of true and structural solid viscosity of materials can be determined for a given set of conditions.