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%.

     

Comparative characteristics of strong shock and detonation waves in bubble media by an electrical wire explosion

Strong shock and detonation waves in inert and chemically active bubble media, which are generated by a wire explosion initiated by a capacitor with a stored energy $W_0 =12.3$ –1,600 J, is experimentally studied. The measurements are performed near the wire and far from the wire in a vertical shock tube 4.5 m long with a volume fraction of the gas in the medium $\beta _0 =1$ –4 %. It is shown that in inert bubble medium, a short intensely decaying shock wave (SW) with intense pressure oscillations is formed in the vicinity of wire explosion point; near the explosion point at $\beta _0 \le 2$  % the SW propagates with the velocity of sound in a liquid. In chemically active bubble medium, an unsteady detonation wave generated by a wire explosion is formed. The pressure amplitude and the velocity of this wave are greater and the length is smaller than those of SW in an inert bubble medium in the same range of explosion energy. It is found that in the interval of low energy explosion from ${\sim }12$ to 64 J, the formation of the bubble detonation wave occurs faster than that at high energies ( $3\times 10^{2}$ – $10^{3}$  J).     

Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

In this paper, we study the transonic shock problem for the full compressible Euler system in a general two-dimensional de Laval nozzle as proposed in Courant and Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948): given the appropriately large exit pressure p _e(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle, a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes p _e(x). We solve this problem completely for a general class of de Laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible Euler system. The problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic–elliptic system. One of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted Hölder space with low regularities for a second order quasilinear elliptic equation with a free parameter (the position of the shock curve at one wall of the nozzle) and non-local terms involving the trace on the shock of the first order derivatives of the unknown function.     

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.     

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.     

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.

     

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.

     

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.

     

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.     

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.     

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.     

The approach of solutions of nonlinear diffusion equations to travelling front solutions

The paper is concerned with the asymptotic behavior as t → ∞ of solutions u(x, t) of the equation u_t—u_xx—∞;(u)=O, x∈(—∞, ∞) , in the case ∞(0)=∞(1)=0, ∞′(0)<0, ∞′(1)<0. Commonly, a travelling front solution u=U(x-ct), U(-∞)=0, U(∞)=1, exists. The following types of global stability results for fronts and various combinations of them will be given.

1. Let u(x, 0)=u ₀(x) satisfy 0≦u ₀≦1. Let \(a\_ = \mathop {\lim \sup u0}\limits_{x \to - \infty } {\text{(}}x{\text{), }}\mathop {\lim \inf u0}\limits_{x \to \infty } {\text{(}}x{\text{)}}\) . Then u approaches a translate of U uniformly in x and exponentially in time, if a_? is not too far from 0, and a₊ not too far from 1.
2. Suppose \(\int\limits_{\text{0}}^{\text{1}} {f{\text{(}}u{\text{)}}du} > {\text{0}}\) . If a _? and a ₊ are not too far from 0, but u₀ exceeds a certain threshold level for a sufficiently large x-interval, then u approaches a pair of diverging travelling fronts.
3. Under certain circumstances, u approaches a “stacked” combination of wave fronts, with differing ranges.

     

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.     

Shock wave emission during the collapse of cavitation bubbles

Shock wave emission induced by intense laser pulses is investigated experimentally. The present work focuses on the conditions of shock wave emission in glycerine and distilled water during the first bubble collapse. Experimental investigations are carried out in liquids as a function of temperature and viscosity. Comparison is made with the theoretical work of Poritsky (Proc 1st US Natl Congress Appl Mech 813–821, 1952) and Brennen (Cavitation and bubble dynamics, Oxford University Press 1995). To the best knowledge of the authors, this is the first experimental verification of those theories.     

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.

     

C 1 Solutions for Semi-Implicit Systems of Differential Equations

The present note is a continuation of the author??s effort to study the existence of continuously differentiable solutions to the semi-implicit system of differential equations (1) $$f(x^{\prime}(t)) = g(t, x(t))$$ (2) $$\quad x(0) = x_0,$$ where

${\quad\Omega_g \subseteq \mathbb{R} \times\mathbb{R}^n}$ is an open set containing (0, x ₀) and ${g:\Omega_g \rightarrow\mathbb{R}^n}$ is a continuous function,

${\quad\Omega_f \subseteq \mathbb{R}^n}$ is an open set and ${f:\Omega_f\rightarrow\mathbb{R}^n}$ is a continuous function.

The transformation of (1)?C(2) into a solvable explicit system of differential equations is trivial if f is locally injective around an element ${\gamma\in \Omega_f\cap f^{-1}(g(0,x_0))}$ . In this paper, we study (1)?C(2) when such a translation is not possible because of the inherent multivalued nature of f ^?1.     

The interaction of creep and fatigue for a rotor steel

Twenty tests were performed on a 1 Cr?1 Mo?1/4 V rotor steel at 1000° F (538°C) to determine the interaction of creep and low-cycle fatigue. These tests involved five different types of strain-controlled cycling: creep at constant tensile stress; linearly varying strain at different frequencies; and hold periods at maximum compressive strain, maximum tensile strain, or both. The experimental data were then used to characterize the interaction of creep and fatigue by the:

1. Frequency-modified strain-range approach of Coffin;
2. Total time to fracture vs. the time of one cycle relation as proposed by Conway and Berling;
3. Total time to fracture vs. the number of cycles to fracture characterization of Ellis and Esztergar;
4. Summation of damage fractions obtained from tests using interspersed creep and fatigue as proposed by the Metal Properties Council;
5. Strain-range-partitioning method of Manson, Halford, and Hirschberg.

In order to properly assess the strain-range-partitioning approach, seven additional tests were performed at the NASA Lewis Research Center. Visual, ultrasonic, and acoustic-emission methods of crackinitiation determination were unsuccessful. An approximate indication of crack initiation was obtained by finding the cycle N_o where the stress-cycle curve first deviated from a constant slope. Predictive methods (based on monotonic tests) for determining the fatigue life in the creep range were examined and found deficient, though they may still be useful for preliminary comparison of materials and temperatures. The extension of the frequency-modified strain-range approach to notched members was developed and the results of notched-bar tests were shown to corroborate this approach, when crack initiation for the plain and notched bars was campared.