Stationary Form Research Articles

Heat Transfer and Effectiveness on Film Cooled Turbine Blade Tip Models

In unshrouded axial turbine stages, a small but generally unavoidable clearance between the blade tips and the stationary outer seal allows a clearance gap leakage flow to be driven across the blade tip by the pressure-to-suction side pressure difference. In modern high-temperature machines, the turbine blade tips are often a region prone to early failure because of the presence of hot gases in the gap and the resultant added convection heating that must be counteracted by active blade cooling. The blade tip region, particularly near the trailing edge, is often very difficult to cool adequately with blade internal coolant flow, and film cooling injection directly onto the blade tip region can be used in an attempt to reduce the heat transfer rates directly from the hot clearance flow to the blade tip. An experimental program has been designed and conducted to model and measure the effects of film coolant injection on convection heat transfer to turbine blade tips. The modeling approach follows earlier work that found the leakage flow to be mainly a pressure-driven flow related strongly to the airfoil pressure loading distribution and only weakly, if at all, to the relative motion between blade tip and shroud. In the present work the clearance gap and blade tip region is thus modeled in stationary form with primary flow supplied to a narrow channel simulating the clearance gap above a plane blade tip. Secondary film flow is supplied to the tip surface through a line array of discrete normal injection holes near the upstream or pressure side. Both heat transfer and effectiveness are determined locally over the test surface downstream of injection through the use of thin liquid crystal coatings and a computer vision system over an extensive test matrix of clearance heights, clearance flow Reynolds numbers, and film flow rates. The results of the study indicate that film injection near the pressure-side corner on plane turbine blade tips can provide significant protection from convection heat transfer to the tip from the hot clearance gap leakage flow.

Microwave noncontact examination of disbond and thickness variation in stratified composite media

Numerical and experimental results of a microwave noncontact, nondestructive detection and evaluation of disbonds and thickness variations in stratified composite media are presented. The aperture admittance characteristics of a flange mounted rectangular waveguide radiating into a layered, generally lossy dielectric media backed or unbacked by a conducting sheet is modeled. The theoretical implementation is based on a Fourier transform boundary matching technique to construct the field components in each medium, coupled with a stationary form of the terminating aperture admittance of the waveguide. The model can serve as a reliable test bed for real-time examination of layered composite media. Experimental results for several cases are presented which show good agreement with the theoretical findings. This is a versatile technique for near-field in situ interrogation of stratified composite media which provides for high resolution measurements. >

Hyperviscous shock layers and diffusion zones: Monotonicity, spectral viscosity, and pseudospectral methods for very high order differential equations

We solve two problems ofx∈[−∞, ∞] for arbitrary orderj. The first is to compute shock-like solutions to the hyperdiffusion equation,u1=(−1) j+1 u 2j,x. The second is to compute similar solutions to the stationary form of the hyper-Burgers equation, (−1) j u 2j.x+uu x=0; these tanh-like solutions are asymptotic approximations to the shocks of the corresponding time dependent equation. We solve the hyperdiffusion equation with a Fourier integral and the method of steepest descents. The hyper Burgers equation is solved by a Fourier pseudospectral method with a polynomial subtraction. Except for the special case of ordinary diffusion (j=1), the jump across the shock zone is described bynonmonotonic, oscillatory functions. By smearing the front over the width of a grid spacing, it is possible to numerically resolve the shock with a weaker and weaker viscosity coefficient asj, the order of the damping, increases. This makes such “hyperviscous” dampings very attractive for coping with fronts since, outside the frontal zone, the impact of the artificial hyperviscosity is much smaller than with ordinary viscosity. Unfortunately, both the intensity of the oscillations and the slowness of their exponential decay from the center of the shock zone decrease asj increases so that the shock zone is muchwider than for ordinary diffusion. We also examined generalizations of Burgers equation with “spectral viscosity”, that is, damping which is tailored to yield exponentially small errors outside the frontal zone when combined with spectral methods. We find behavior similar to high order hyperviscosity. We conclude that high order damping, as a tool for shock-capturing, offers both advantages and drawbacks. Monotonicity, which has been the holy grail of so much recent algorithm development, is a reasonable goal only for ordinary viscosity. Hyperviscous fronts and shock zones in flows with “spectral viscosity” aresupposed to oscillate.

Single P100 visual evoked potential analyses in man.

Standards evoked potential averaging leads to a loss of information inherent in the moment to moment variability of the amplitude and latency of single evoked potentials. In order to extract this information, attempts were made to develop procedures which would allow recording of single visual evoked potentials in at least a selected group of subjects. In 11 out of 25 non-selected subjects, 43% to 86% of all stimuli (reversal checkerboard pattern elicited single visual evoked potentials (VEP) which were recognized as such by a group of independent observers. The mean amplitude and latency obtained by directly measuring the peak to peak amplitudes and peak latencies of these single VEPs (arithmetic averaging) were compared to those obtained following conventional time-locked averaging of the same data. During long-term continuous stimulation, the arithmetic averaged VEPs increased in amplitude to a steady state while the time-locked averages of the same sets of responses decreased in amplitude. This reduction was found to be closely related to the latency jitter. It may provide a better understanding of the phenomenon of habituation. This finding was confirmed in model single VEPs obtained by summing on-going pre-stimulus EEG activity with a time-locked average VEP stationary wave form. The variability of the true single VEPs was found to be less than the variability of the model single VEPs. The latency and amplitude parameters of the true single VEPs were strongly correlated with each other while those of the model single VEPs were not. These findings show that single VEPs have an inherent variability which may reflect brain processing.

Perceptual integration of motion and form information: is the movement filter involved in form discrimination?

Seven experiments reinvestigated J. Driver and P. McLeod's (1992) report of a "visual search asymmetry reversal" in a task that required the integration of motion and form information. They found that, when the form discrimination was easy, search was more efficient for a moving rather than a stationary conjunction target; the reverse was true when form discrimination was difficult. J. Driver and P. McLeod proposed that 2 mechanisms are involved: a "stationary form system," which supports accurate form discrimination but is relatively insensitive to movement, and a "movement filter," which segregates the moving from the stationary items but is relatively insensitive to aspects of form. The present experiments failed to find the asymmetry reversal. The results agree with the (more parsimonious) proposal that the function of the movement filter is limited to separating moving from stationary items, whereas form discrimination is accomplished within a unitary form system.

Calculation of the stationary cross-section form of nonaxisymmetrical crystals growing from the melt

A numerical analysis of the geometrical model has been carried out for a shaping of crystals growing from the melt. The evolution of cross-section crystal form has been studied as a function of the anisotropy of the growth angle and shape of the crystallization front. The melting meniscus surface has been determined by a numerical solution of the 2D nonlinear capillary equation. The influence of the cross section crystal contour curvature and negative effective pressure on the angle inclination of the meniscus close to tri-junction line has been investigated. Numerical results agree well with experimental data.

Multiple, two-dimensional solutions to the Dean problem in curved triangular ducts

The two-dimensional, stationary form of the equations of motion governing the flow in loosely coiled ducts of equilateral, triangular cross section are solved using a finite volume discretization procedure. The primary solution branch consists of a flow with two large, symmetrical streamwise vortices which are generated by the centrifugal force. Earlier works have investigated the formation of additional Moffat vortices near the corner of such ducts, driven by the secondary flow. Such corner vortices tend to be extremely weak in strength. When the outer wall is flat and one corner of the triangle points inwards, centrifugal instability gives rise to the formation of an additional pair of vortices near the center of the outer wall. Such four-cell solutions appear as dual solutions at the same Dean number, Dn, and the additional vortices are much stronger than the Moffat vortices. This phenomenon is very similar to those observed in the Dean problem for square and circular cross section. The four-cell solutions are found to be unstable to asymmetric perturbations. When the orientation of the triangular duct is changed such that the inner wall is flat such additional vortices do not form near the outer region of the duct and a unique two-cell solution that remains stable is obtained for Dean numbers as high as 350.

RAPID MICROPROPAGATION OF COCOYAM (XANTHOSOMA SAGITTIFOLIUM SCHOTT)

Shoot tips, approximately 3-5mm, were isolated from corms of young greenhouse-grown plants of cocoyam, cultivar South Dade White. After preliminary evaluations, the initiation media evaluated were B5 basal salts supplemented with 0.05 μM NAA with 5μM BAP, 20μM BAP or 2μM TDZ. The above media were in the form of liquid medium in flasks on a rotary shaker, liquid medium with filter paper bridges, stationary liquid medium without filter paper and solidified medium with 0.4% agar. TDZ stimulated greater growth with multiple shoot formation. Liquid media either in the shaker or stationary form were more effective in terms of growth. Shoots were subsequently evaluated for multiplication with 1μM TDZ and 5μM BAP with 0.05μM NAA producing greater shoot numbers. Over 30 plants have subsequently been rooted and acclimatized under mist or humidity tent.

Stationary likelihood ratios and smoothed perturbation analysis gradient estimates for the routing problem

We present stationary and regenerative form estimates for the gradients of the cycle variables with respect to a thinning parameter in the arrival process of G/G/1 queueing systems. Our estimates belong to the category of the likelihood ratio method (LRM) and smoothed perturbation analysis (SPA) estimates. The results are useful in adaptive routing design.

Exact solutions of coupled scalar field equations

Exact analytical solutions of a generic system of coupled ordinary differential equations for a pair of real scalar fields have been explicitly obtained. The equations may be considered to be the stationary form of the coupled time-dependent Schrodinger-Boussinesq (or Korteweg-de Vries) equations. The generic equations have six free parameters whereas it has been possible to obtain exact solutions valid on a five-dimensional hypersurface in six-dimensional parameter space using a technique developed by Varma and Rao (1980). While the solution for the variable of the Boussinesq (or Korteweg-de Vries) equation always has a symmetric structure, both symmetric and antisymmetric solutions are possible for the variable of the Schrodinger equation. The results are applied to an example dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in magnetised plasmas.

Level repulsion in the spectrum of two-dimensional harmonic oscillators

The asymptotic-energy limit of the density P(S) of spacings between adjacent levels of the two-dimensional harmonic oscillator (TDHO) spectrum is studied. It is shown that in any integer segment (M, M+1), containing approximately M/α levels, of the TDHO spectrum m + αn, P(S) has the form Σ wi δ(S - Si) where i takes on at most three values. For large M, P(S) displays strong level repulsion for irrational α, but it does not settle on a stationary form nor does its average over M. This is in marked contrast with the behaviour of generic integrable systems for which the Poisson statistics, P(S)= exp(-S), is known to apply.

Application of the principle of detailed balance to the random vibration of non-linear oscillators

The principle of detailed balance, which was developed in the field of statistical physics, relates to the microscopic reversibility of a stochastic process. It has recently been suggested that this principle may be used to expedite the solution of the Fokker-Planck equation which arises when the response of a non-linear system to white noise excitation is considered. To investigate this, the most general externally excited non-linear oscillator which satisfies detailed balance is derived, and it is found that the result coincides with a class of system for which there is an existing solution to the stationary form of the Fokker-Planck equation. In deriving this result, the stationary response statistics of a slightly more general class of oscillator (which does not satisfy detailed balance) are found, and a number of results regarding the probability current of the response are obtained.

Calculation of the self-diffusion coefficient of interacting Brownian particles based on the time-independent Smoluchowski equation

A method of calculating the first-order concentration dependence of the self-diffusion coefficient of spherical Brownian particles interacting with one another is derived on the basis of the time-independent (i.e., stationary) form of the two-particle Smoluchowski equation. The method is applied to the cases of hard spheres with and without hydrodynamic interactions. The hydrodynamic interactions are taken into account by use of Oseen’s and Felderhof ’s approximations for the diffusion tensors. Explicit expressions for the self-diffusion coefficient are obtained which are in agreement with previous ones based on the time-dependent (i.e., nonstationary) form of the Smoluchowski equation.

A finite element method for the statistics of non-linear random vibration

The transitional probability density function for the random response of a certain class of non-linear system satisfies the Fokker-Planck-Kolmogorov equation. This paper concerns the numerical solution of the stationary form of this equation, yielding the stationary probability density function of response. The weighted residual statement for the problem is integrated by parts to yield the weak form of the equations, which are then solved by the finite element method. The method is applied to a Duffing oscillator and good agreement is found with the exact result, and the method is compared favourably with a Galerkin solution method given by Bhandari and Sherrer [1]. Also, the method is applied to the ship rolling problem and good agreement is found with an approximate analytical result due to Roberts [2].

Some Schwarzschild solutions and their singularities

A number of different forms of the Schwarzschild solution are considered. The static forms all have a singularity at the Schwarzschild radius. This Schwarzschild singularity can be eliminated if one goes over to a stationary or time-dependent form of solution. However, the coordinate transformations needed for this have singularities. It is stressed that coordinate systems connected by singular transformations are not equivalent and the corresponding metrics may describe different physical situations.

THE ANISOTROPY OF THE SURFACE ENERGY OF NICKEL MEASURED BY T.E.M. OF FIELD EMITTERS

The stationary form of a clean nickel tip is produced in a field electron microscope (FEM) under ultra-high vacuum. The shape of the tip is then visualized in a transmission electron microscope (TEM). It is shown that the cap around the apex of a bulbous tip closely approximates the equilibrium shape of an isolated nickel crystal. The anisotropy of the surface energy (γ) of nickel is measured as a function of the crystallographic orientation.

A measurement of the surface energy anisotropy of nickel by transmission electron microscopy of field emitter crystals

A combination of field emission (FEM) and transmission electron microscopy (TEM) is used to measure the anisotropy of the surface tension (γ) of a metal (nickel). The stationary form of a clean nickel tip is produced and controlled in a field electron microscope, under ultrahigh vacuum. The shape of the tip is visualized in a TEM and then analysed. It is shown that the cap around the apex of a bulbous tip closely approximates the equilibrium shape of a nickel crystal. By using the inverse Wulff construction, the anisotropy of γ can be measured as a function of crystallographic orientation. Values of γ normalized to (111) have been obtained for the 〈200〉 and the 〈2̄20〉 zones. The maximum anisotropy is found at [026] along the 〈200〉 zone ( γ 026 γ 111 = 1.05 ). The results agree with the available experimental or theoretical data reasonably well.

Human ovarian surface epithelium in primary culture.

The ovarian surface epithelium (OSE) represents a minute fraction of the cell mass of the ovary but gives rise to over 80% of human ovarian carcinomas. No experimental models for the study of human OSE exist. To characterize OSE cells in culture, explants of ovarian surface from normal ovary of premenopausal women were grown on plastic, glass, and collagen gel in 25% fetal bovine serum/Waymouth's medium 752/1. About 25% of explants produced epithelial outgrowths. Morphologically, these outgrowths resembled OSE in vivo and endothelial and mesothelial cells in culture, but they differed from cultured ovarian stromal, granulosa, and luteal cells. Only OSE among ovarian cell types were intensely keratin positive by immunofluorescence. Keratin also distinguished OSE cells from the keratin-negative endothelial cells. Most but not all OSE colonies tested showed 17 beta-hydroxysteroid dehydrogenase (HSD) activity, which was absent in peritoneal mesothelial cells. Colonies from most patients were limited to a few millimetres and became stationary within a few weeks. Changes that accompanied cessation of growth included senescence, increased keratin content, or the formation of multicellular papillary aggregates. With time, OSE cells tended to assume a fibroblast-like morphology but remained keratin positive and continued to resemble OSE by scanning electron microscopy (SEM). Subcultured OSE cells persisted in a stationary keratin-positive form for many weeks. Throughout this study, all pavementlike epithelial outgrowths that were contiguous with an explant stained for keratin; thus, such colonies can be assumed to be OSE. Conversely, fibroblast-shaped cells may represent OSE as indicated by keratin content and SEM appearance. The methods presented here permit culture of normal human OSE under conditions in which the cells exhibit morphologic plasticity, variable 17 beta-HSD activity, and presence of keratin.

Incremental Launching of Structures

The incremental launching method for concrete structures was first developed in the early 1960'S. Since then it has spread all over the world. Bridges constructed by this method are cast in segments behind an abutment in a stationary form against a previously cast segment of the bridge girder. The whole superstructure is then longitudinally jacked forward incrementally to make room for the next segment in the stationary form. This method combines the advantages of precasting with those of cast‐in‐place methods, resulting in a high concrete quality and low costs. Remarkable achievements of incrementally launched bridges the to data are: Longest continuous superstructure [3,809 ft (1,161 m)]; longest span in final stage [551 ft (168 m)]; longest span during launching with auxiliary stays on top [436 ft (133 m)]; and a strongly curved bridge superstructure in plan with a radius of 492 ft (150 m). The incremental launching method has also been applied to buildings; e.g. across railway tracks. A new potential application is the construction of underwater tunnels. The main savings are achieved by the reduced labor and equipment expenditure.

Gödel‐type universe with a perfect fluid and a scalar field

The paper contains, along with a brief review of solutions of general relativistic field equations when the metric is of a particular cylindrically symmetric stationary form, a new solution of the same general category when the energy‐momentum tensor is due to a perfect fluid plus a scalar field. It turns out that under these constraints, the space‐time is completely homogeneous and contains closed timelike lines. There is, however, a nonuniqueness in the interpretation as one can introduce a Maxwellian electromagnetic field of arbitrary strength along with the perfect fluid and the scalar field.