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.

     

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.     

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.     

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.

     

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.     

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.     

Die Berechnung des Blasenwachstums beim Verdampfen von Flüssigkeiten an Heizflächen als numerische Lösung der Erhaltungsgleichungen

A numerical procedure on the basis of the Marker and Cell-method [1] was developed in order to solve the conservation equations for mass, momentum and energy for the case of bubble growth on a heating surface. This procedure was used to calculate steam bubble growth on a horizontal stainless steel heating surface under saturated pool boiling conditions at a system pressure of 1 bar and different superheatings. The essential results obtained are:

-Good agreement was found between calculations and experiments concerning bubble growth rates, bubble shape and temperature field in the liquid surrounding the bubble.

-During its growth the bubble penetrates the temperature boundary layer formed in the liquid on the heating surface, simultaneously liquid is displaced aside.

-The microlayer evaporation fraction of the total bubble growth increases with growth time from 20 % to 50%.

     

Experiments on tension measurement in manufacturing processes

Today's demand to preserve energy, to optimally utilize limited resources and to still increase quality calls for more-precise measurements in virtually all manufacturing processes. One such field is the measurement of tension in, for instance, paper machines, printing presses, machines for the manufacturing of rubber, plastics, fabrics, etc. Newspaper-printing presses produce today an impressive number of paper breaks. Measurement of the web tension at critical positions could give an early warning when the tension in the paper is growing to dangerous values. In a paper macnine, it is necessary to introduce webtension measurements at many positions to optimize quality, to prevent paper breaks and to reduce wear. Measurements have been carried out with a particular force transducer that can be easily built into an existing, as well as a new machine. Several installations, mainly in paper machines and newspaper-printing presses, show that

- the number of paper breaks are drastically reduced

- a more-uniform quality of the paper can be achieved

- the lifetime of machine parts, such as wires and felts, can be increased.

     

Pressure drop in alternating curved tubes

Pressure drop measurements in the laminar and turbulent regions for water flowing through an alternating curved circular tube (x=h sin 2πz/λ) are presented. Using the minimum radius of curvature of this curved tube in place of that of the toroidally curved one in calculating the Dean number (ND=Re(D/2R _c )², it is found that the resulting Dean number can help in characterizing this flow. Also, the ratio between the height and length of the tube waves which represents the degree of waveness affects significantly the pressure drop and the transition Dean number. The following correlations have been found:

1. For laminar flow: $$F_w \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} = F_s \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 0.03,\operatorname{Re}< 2000.$$
2. For turbulent flow: $$F_w \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} = F_s \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 0.005,2000< \operatorname{Re}< 15000.$$
3. The transition Dean number: $$ND_{crit} = 5.012 \times 10^3 \left( {\frac{D}{{2R}}} \right)^{2.1} ,0.0111< {D \mathord{\left/ {\vphantom {D {2R_c }}} \right. \kern-\nulldelimiterspace} {2R_c }}< 0.71.$$

     

The initial-value problem for elastodynamics of incompressible bodies

We prove short-time well-posedness of the Cauchy problem for incompressible strongly elliptic hyperelastic materials. Our method consists in:

1. Reformulating the classical equations in order to solve for the pressure gradient (The pressure is the Lagrange multiplier corresponding to the constraint of incompressibility.) This formulation uses both spatial and material variables.
2. Solving the reformulated equations by using techniques which are common for symmetric hyperbolic systems. These are:

1. Using energy estimates to bound the growth of various Sobolev norms of solutions.
2. Finding the solution as the limit of a sequence of solutions of linearized problems.

Our equations differ from hyperbolic systems, however, in that the pressure gradient is a spatially non-local function of the position and velocity variables.     

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.     

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.     

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.

     

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.     

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.

     

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.

     

Some characteristics of supersonic flow of an electrically conductive gas in an MHD-channel

We study supersonic flows of an electrically conductive gas in crossed electric and magnetic fields [1] in the presence of shock waves. It is shown that three steady flow regimes can exist, and that these are defined by the electrical conductivity of the gas as a function of temperature and density.

1. The normal regime is characterized by a tendency for the shock to move toward the channel entrance on increase of the static pressure at the channel exit. The steady regime of this type exists and is stable.
2. The anomalous regime (formally constructed) is characterized by a tendency for the shock to move toward the exit on increase of the static pressure at the channel exit. This regime is unstable and the flow in the MHD-channel may be either entirely supersonic or entirely subsonic.
3. The limiting (boundary) regime is intermediate between the normal and anomalous regimes and is characterized by the fact that the stationary position of the shock wave and its amplitude are not uniquely defined. Steady flow in this case is not unique.

This study involves formal construction both of the solution to the steady-state problem and the corresponding nonsteady-state problem [4]. The establishment of a steady regime in the solution of the unsteady problem, is at the same time, a verification of its stability.