Piezo-electric control of stiffened panels subject to interactive buckling

The paper examines the feasibility of piezo-electric control of stiffened plates carrying axial compression and subject to interaction of local and overall buckling. A simple control strategy involving piezo-electric patches along the tips of the stiffeners carrying equal and opposite electric fields to resist bending of the stiffeners was found to effectively counteract the adverse effects of mode interaction and imperfection-sensitivity. For the dynamic problem, this strategy needed to be supplemented with patches attached to the surfaces of the plate in the middle of the panel to damp out local buckling oscillations. Two panels were considered, these being scaled replicas of each other. This enabled an examination of the scaling laws of response with practical applications in view. The results demonstrate that the structural performance of optimally designed stiffened structures can be enhanced with minimal energy consumption by appropriately designed piezo-electric patch configuration.     

Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability

Boundary layer approximation is applied for mixed convection about a horizontal flat plate in a saturated porous medium with aiding external flows. Similarity solutions are obtained, incorporating the variation of permeabilty, for 1) horizontal flat plate at zero angle of attack with constant heat flux; 2) stagnation point flows about horizontal flat plates with wall temperature varying asT _w ∝x ². The temperature and velocity profiles for different values of Ra/(RePr)^3/2 and the parameters governing the flow are obtained. The heat transfer rate is calculated and its implications in a geothermal application is discussed. Further, the criteria for pure mixed convection about horizontal flat plates in a porous media are established.     

POD-based surrogate modeling of transitional flows using an adaptive sampling in Gaussian process

A surrogate model, based on proper orthogonal decomposition (POD) with the adaptive sampling method, was proposed to predict the transitional flow past rough flat plates simulated by a four-equation k-ω-γ-A_r transition model. Gaussian process regression was used to map the input parameters to the POD expansion coefficients. The variance and gradient of Gaussian process were taken as the criteria for the adaptive sampling. The proposed methodology was applied to a one-dimensional heat conduction problem and two-dimensional transitional flow past rough flat plates. At the same time, the results were compared with those of Halton sequences. With the same sample size, the adaptive method achieved a higher accuracy on the test set, and the proposed adaptive criterion could serve as an indicator for the model discrepancies.     

Scaling impacted structures when the prototype and the model are made of different materials

By properly applying scaling laws, it is possible to infer the behaviour of a structure from the response of a similar model whose dimensions are scaled by a factor β. In some cases, however, e.g. in the case of strain rate sensitive structures under severe dynamic loads, these laws become distorted, severely limiting this approach. In this article, a methodology for the correction of this distortion is explored for the case when the structure and the model are made of different materials. It is shown that the behaviour of a structure, say, made of mild steel, can be forecast from the response of a model, say, made of aluminium. The technique here detailed is shown to be valid for simple structures subject to axial and transverse impact loads.     

Formation of a jet of gas outflowing into evacuated space

Unsteady outflow from a sonic nozzle with off-design factor 4 · 10⁸ at an ambient pressure of 2 · 10^?5 mm Hg is studied by means of the absorption of an electron beam. The motion laws of the front of the outflowing gas and other characteristic regions of the outflow are studied. A comparison to the results of other works clarifies the features of outflow with high offdesign factors. An equation is obtained describing the motion of the front of outflowing gas along the flow axis. Results are presented in generalized similitude parameters.     

Flow development upstream of a fence

The effect of Reynolds number on the flow development upstream of a rigid, non-porous, static fence is investigated experimentally. The flow field is measured using time-resolved, two-component particle image velocimetry at Reynolds numbers based on fence height of 18000, 36000, and 54000. The results show that a laminar separation bubble forms upstream of the junction vortex at the base of the fence. The mean extent of the bubble decreases with increasing Reynolds number, with mean separation moving downstream and mean reattachment moving upstream. In the aft portion of the bubble, shear layer vortices form and are shed at scaled frequencies and wavelengths that are comparable to laminar separation bubble shedding in low Reynolds number airfoils and flat plates with an imposed adverse pressure gradient. The strong periodicity of the associated coherent structures and the proximity of shear layer roll-up relative to the fence should be taken into consideration in the relevant designs due to potential implications to structural loading. A simple flow separation prediction model combining inviscid fence flow solution with Thwaites’ method is introduced and shows good agreement with the experimental results for the Reynolds number range considered.     

Squeeze flow of a power-law fluid between non-parallel plates

Squeeze flow in the gap between non-parallel circular plates of radius R is discussed. The test material is assumed to be a power-law fluid, with a no-slip boundary condition at the plates. If the mean separation between the plates is h, and the angle of inclination between the plates is ? ? h/R, the force on the plates is perturbed only at O(?²) and is increased by less than 10% if ? < 0.35h/R. A torque O(?) tends to return the plates to a parallel configuration.     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.     

The Absolute Instability of Thin Wakes in an Incompressible/Compressible Fluid

RID="ID=" Communicated by P. HallAbstract:The absolute/convective instability of two-dimensional wakes forming behind a flat plate and near the trailing-edge of a thin wedge-shaped aerofoil in an incompressible/compressible fluid is investigated. The mean velocity profiles are obtained by solving numerically the classical compressible boundary-layer equations with a negative pressure gradient for the flat plate case, and the incompressible triple-deck equations for a thin wedge-shaped trailing-edge. In addition for a Joukowski aerofoil the incompressible mean boundary-layer flow in the vicinity of the trailing-edge is also calculated by solving the interactive boundary-layer equations. A linear stability analysis of the boundary-layer profiles shows that a pocket of absolute instability occurs downstream of the trailing-edge with the extent of the instability region increasing with more adverse pressure gradients. The region of absolute instability persists along the near-wake axis, while the majority of the wake is convectively unstable. For a thin wedge-shaped trailing-edge in an incompressible fluid, a similar stability analysis of the velocity profiles obtained via a composite expansion, also shows the occurrence of absolute instability behind the trailing-edge for a wedge angle greater than a critical value. For increasing values of the wedge angle and for thicker aerofoils, separation takes place near the trailing-edge and the extent of absolute instability increases. Calculations also show that for insulated plates compressibility has a stabilizing effect but cooling the wall destabilizes the flow unlike wall heating.} Received 11 May 1998 and accepted 25 February 1999     

Methodical investigation of free convection from vertical and horizontal plates

This paper attempts of review the literature on free convection from flat surfaces transferring heat in an unlimited space. Data from the references have been presented as final criterial relations both in tabular form and in graphic system, separately for the vertical plates and the horizontal ones. About 45 results of investigations on free convection have been examined and the following mean criterial relations have been calculated:Nu=0.550·(Ra)^0.250 for vertical plates,Nu=0.310·(Ra)^0.290 for horizontal plates. It has been observed for the vertical plates that divergence of these results relatively to the mean values is constant within the whole variability range of the Rayleigh number and amounts to about ± 15%. In the case of horizontal plates the divergencies are more considerable and vary within ± 50% for the laminar, and within ± 25% for the turbulent range. In the next step the attempt was made to determine the causes of these divergencies and errors. The work was performed because of two main reasons: imperfection of measuring methods and a lack of uniformity in the choice of the characteristic linear dimension.     

Effect of the use of the balance and gradient methods as a result of experimental investigations of natural convection action with regard to the conception and construction of measuring apparatus

Measurement apparatus designed and constructed according to conceptions of the authors, enabled a more precise calculation of the heat transfer coefficient with the balance and gradient methods. Construction and use of the apparatus and devices are described below, results of experimental investigations for horizontal and vertical, isothermal, flat plates obtained independently with the balance and gradient methods, are also presented. The following equations were found:Nu=0.612 · (Ra)^1/4 10⁴ ≦Ra ≦ 10⁸ for vertical platesNu=0.766 · (Ra)^1/5 10⁴ ≦Ra ≦ 10⁷ Nu=0.173 · (Ra)^1/3 10⁵ ≦Ra≦ 10⁸ for horizontal plates. On the basis of the results obtained from both these methods, differences of natural convection acting from vertical and horizontal plates are discussed. The usefulness of the balance and gradient methods have been considered for qualitative and quantitative investigations of heat transfer by natural convection.     

Numerical analysis of natural convection around a vertical channel in a rectangular enclosure

Numerical computations were performed for the heat transfer and fluid flow characteristics of an internal vertical channel composed by a pair of parallel plates situated in a rectangular enclosure, with the inner plates and the bounding wall of the enclosure maintained at uniform but different temperatures. Natural convection occurred in the air which occupied the enclosure space. The plates were symmetrically arranged. The dimensionless channel widthS was varied parametrically. The Rayleigh numbers ranged from 10² to 10⁷. Static bifurcation was found in this configuration. The bifurcation is related to the flow pattern transition from single-vortex structure to double-vortex structure or vice versa. Comparison with the empirical correlations obtained for a vertical plate and a channel in an infinite space showed that the heat transfer process of the plates and the channel was deteriorated by the existence of the enclosure.     

On Rayleigh scattering by a grating

The acoustic diffraction of a plane wave by a periodic row of identical cylinders of arbitrary cross section and characteristic dimension a is calculated for ka ? kd < π, where k is the wave number and d is the wavelength of the array. The reflection and transmission coefficients depend only on d, k, the angle of incidence, and the area and virtual mass of the cross section. The general results are applied to a grating of inclined flat plates.     

Experimental study of the aerodynamic characteristics of a low-aspect-ratio flat plate array in a configuration of interest for a tidal energy converter

Wind tunnel experiments were conducted for the flow around a single flat plate and through an array of three parallel flat plates at different angles of incidence to compare their lift and drag coefficients for several values of the Reynolds number around 10⁵ and for three aspect ratio values. The selected cascade configuration is of interest for a particular type of tidal hydrokinetic energy converter. The main differences in the lift and drag forces are discussed, finding that for a plate in a cascade the maximum lift coefficient takes place at a quite different angle of attack, depending on the aspect ratio. The optimal conditions for extracting power from a tidal current are analyzed.     

Higher-order effects in natural convection flow over uniform flux inclined flat plates in porous media

Higher-order boundary-layer effects for natural convection flow along inclined flat plates (of both positive and negative inclinations) with a uniform heat flux surface condition in a saturated porous medium are studied. Using the method of matched asymptotic expansions the three terms in inner and outer expansions have been obtained. It is shown that the first eigenfunction for this considered problem coincides with 0(? ²)-term in the inner expansion.     

End effects of nominally two-dimensional thin flat plates

Differences in the structure and dynamics of nominally two-dimensional turbulent wakes are investigated experimentally for a thin flat plate, normal to a uniform flow, with two different end conditions: with and without end plates. Both cases are characterized by Karman-like vortex shedding with broadband low frequency unsteadiness. Both wakes evidence a low frequency flapping motion in addition to the slowly drifting base flow common to cylinder wakes. For the case without end plates, an interaction between the drift motion and the vortex formation process is associated with a much stronger modulation of the quasiperiodic vortex shedding amplitude when compared to the case with end plates where a flapping motion is more strongly expressed. These dynamics underlie structural differences in the mean wake and Reynolds stress fields.     

Low Reynolds number airfoil aerodynamic loads determination via line integral of velocity obtained with particle image velocimetry

The small magnitude lift forces generated by both a NACA 0012 airfoil and a thin flat plate at Re?=?29,000 and 54,000 were determined through the line integral of velocity, obtained with particle image velocimetry, via the application of the Kutta–Joukowsky theorem. Surface pressure measurements of the NACA0012 airfoil were also obtained to validate the lift coefficient C _l. The bound circulation was found to be insensitive to the size and aspect ratio of the rectangular integration loop for pre-stall angles. The present C _l data were also found to agree very well with the surface pressure-determined lift coefficient for pre-stall conditions. A large variation in C _l with the loop size and aspect ratio for post-stall conditions was, however, observed. Nevertheless, the present flat-plate C _l data were also found to collectively agree with the published force-balance measurements at small angles of attack, despite the large disparity exhibited among the various published data at high angles. Finally, the ensemble-averaged wake velocity profiles were also used to compute the drag coefficient and, subsequently, the lift-to-drag ratio.     

A thin-plate analysis and experimental evaluation of couple-stress effects

Couple-stress effects in materials have received much theoretical consideration recently but little or no experimental verification. The first part of this paper deals with a simplified elastic analysis for thin plates with couple stress which should provide a simple experimental approach to the determination of the order of magnitude of these effects. Classical concepts were utilized where applicable and many existing solutions can be modified by the present analysis to include couple stress. In the second part, experiments approximating cylindrical bending were carried out on plates of commercial-grade low-carbon steel and high-purity aluminum in the annealed and wrought conditions in order to establish the order of magnitude of the couple stress constantl as found in a simple couple-stress theory. Results were compared with classical theory and other experimental data correlated by the Neuber method to determine whether or not the couple-stress effect as predicted by a simple couple-stress theory could account for the reduction in the stress concentration found for small-radius notches and holes. It was found that the order of magnitude ofl was not greater than 0.002 in. rather than 0.02 in. as would be required to explain the above-mentioned reduction in stress concentration. Since the grain size of those materials was also ?0.002 in., it was concluded that:

1. (a)
   Couple-stress effects predicted by a simple theory were not significant enough to account for the reduction of stress concentration noted above for the material tested.     
   
   

A nth-order shear deformation theory for the free vibration analysis on the isotropic plates

In the present paper, a nth-order shear deformation theory is used to perform the free vibration analysis of the isotropic plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy??s third order theory can be considered as a special case of present nth-order theory (n=3). The governing equations and boundary conditions are derived by the principle of virtual work. The governing differential equations of the isotropic plates are solved by the meshless radial point collocation method based on the thin plate spline radial basis function. The effectiveness of the present theory is demonstrated by applying it to free vibration problem of the square and circular isotropic plate.