Horizontal Symmetry Plane Research Articles

Reflection coefficients in attenuative anisotropic media

Such reservoir rocks as tar sands are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here we study the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on transversely isotropic models with a vertical symmetry axis (VTI). Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation must be strong, with the quality factor [Formula: see text] not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-styleattenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost “isotropic” dependence on attenuation. Our formalism also helps evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes conventional amplitude-variation-with-offset (AVO) analysis inadequate for strongly attenuative media. For instance, an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PS-wave at normal incidence, even if both half-spaces have a horizontal symmetry plane. The developed linearized solutions can be used in AVO inversion for highly attenuative (e.g., gas-sand and heavy-oil) reservoirs.

Semiconductor laser with the subhertz linewidth

A semiconductor laser emitting at 972 nm is stabilised with respect to a vibrationally and thermally compensated reference Fabry—Perot resonator with the vertical axis. The supporting points lie in the horizontal symmetry plane of the resonator, the influence of vibrations in the vertical direction being substantially suppressed in this case. This configuration provides a low sensitivity of the laser emission frequency to vertical accelerations of the reference resonator. To reduce the influence of temperature fluctuations, the resonator is made of an ULE (ultra-low-expansion) glass and is kept at temperature at which the expansion coefficient of this glass is close to zero. The laser linewidth is smaller than 0.5 Hz and the frequency drift is ≈0.1 Hz s-1. The minimum of the Allan deviation achieved for 3 s is 2×10-15. The laser was used to record the spectra of the 1S—2S transition in atomic hydrogen.

Flow structures around a three-dimensional rectangular body with ground effect

An experimental investigation of the flow over the rectangular body located in close proximity to a ground board was reported using the particle image velocimetry (PIV) technique. The present experiments were conducted in a closed-loop open surface water channel with the Reynolds number, <TEX>$Re_H=1.2{\times}10^4$</TEX> based on the model height. In addition to the PIV measurements, flow visualization studies were also carried out. The PIV technique provided instantaneous and time-averaged velocity vectors map, vorticity contours, streamline topology and turbulent quantities at various locations in the near wake. In the vertical symmetry plane, the upperbody flow is separated from the sharp top leading edge of the model and formed a large reverse flow region on the upper surface of the model. The flow structure downstream of the model has asymmetric double vortices. In the horizontal symmetry plane, identical separated flow regions occur on both vertical side walls and a pair of primary recirculatory bubbles dominates the wake region.

Moveout-based geometrical-spreading correction for PS-waves in layered anisotropic media

This paper is devoted to pre-stack amplitude analysis of reflection seismic data from anisotropic (e.g., fractured) media. Geometrical-spreading correction is an important component of amplitude-variation-with-offset (AVO) analysis, which provides high-resolution information for anisotropic parameter estimation and fracture characterization. Here, we extend the algorithm of moveout-based anisotropic spreading correction (MASC) to mode-converted PSV-waves in VTI (transversely isotropic with a vertical symmetry axis) media and symmetry planes of orthorhombic media. While the geometrical-spreading equation in terms of reflection traveltime has the same form for all wave modes in laterally homogeneous media, reflection moveout of PS-waves is more complicated than that of P-waves (e.g., it can become asymmetric in common-midpoint geometry). Still, for models with a horizontal symmetry plane, long-spread reflection traveltimes of PS waves can be well approximated by the Tsvankin–Thomsen and Alkhalifah–Tsvankin moveout equations, which are widely used for P-waves. Although the accuracy of the Alkhalifah–Tsvankin equation is somewhat lower, it includes fewer moveout parameters and helps to maintain the uniformity of the MASC algorithm for P- and PS-waves. The parameters of both moveout equations are obtained by least-squares traveltime fitting or semblance analysis and are different from those for P-waves. Testing on full-waveform synthetic data generated by the reflectivity method for layered VTI media confirms that MASC accurately reconstructs the plane-wave conversion coefficient from conventional-spread PS data. Errors in the estimated conversion coefficient, which become noticeable at moderate and large offsets, are mostly caused by the offset-dependent transmission loss of PS-waves.

Small-angle AVO response of PS-waves in tilted transversely isotropic media

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

Velocity-independent layer stripping of PP and PS reflection traveltimes

Building accurate interval velocity models is critically important for seismic imaging and AVO (amplitude variation with offset) analysis. Here, we adapt the [Formula: see text] method to develop an exact technique for constructing the interval traveltime-offset function in a target zone beneath a horizontally layered overburden. All layers in the model can be anisotropic, with an essential assumption that the overburden has a horizontal symmetry plane (i.e., up-down symmetry). Our layer-stripping algorithm is entirely data-driven and, in contrast to the generalized Dix equations, does not require knowledge of the velocity field anywhere in the medium. Important advantages of our approach compared to the Dix-style formalism also include the ability to handle mode-converted waves, long-offset data, and laterally heterogeneous target layers with multiple, curved reflectors. Numerical tests confirm the high accuracy of the algorithm in computing the interval traveltimes of both PP- and PS-waves in a dipping, transversely isotropic layer with a tilted symmetry axis (TTI medium) beneath an anisotropic overburden. In combination with the inversion techniques developed for homogeneous TTI models, the proposed layer stripping of PP and PS data can be used to estimate the interval parameters of TTI formations in such important exploration areas as the Canadian Foothills. Potential applications of this methodology also include the dip-moveout inversion for the P-wave time-processing parameter [Formula: see text] and stable computation of the interval long-spread (nonhyperbolic) moveout for purposes of anisotropic velocity analysis.

Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser

We report a novel mounting of the reference cavity used for stabilization of the clock laser in an optical frequency standard. The cavity axis is oriented horizontally and the cavity is supported in its horizontal symmetry plane on four support points. The positions of the points were optimized by finite-element analysis. A sensitivity to accelerations of 1.5 kHz/(m/s2) in the vertical and 14 kHz/(m/s2) in the horizontal direction was measured, which is a reduction in the vertical sensitivity by two orders of magnitude compared to the usual support from below.

Parameter estimation in orthorhombic media using multicomponent wide-azimuth reflection data

Orthorhombic models with a horizontal symmetry plane adequately describe seismic signatures recorded over many naturally fractured reservoirs. The inversion of wide-azimuth traveltimes of PP and SS (the fast [Formula: see text] and slow [Formula: see text]) reflections are discussed for Tsvankin's anisotropic parameters and the azimuths of the vertical symmetry planes of orthorhombic media. If shear waves are not excited, SS traveltimes can be found from PP and PS (converted-wave) data, which makes the method applicable to offshore surveys. The feasibility of parameter estimation is strongly dependent on reflector dip and orientation. For a horizontal reflector beneath a single orthorhombic layer, the vertical velocities and reflector depth cannot be found from conventional-spread reflection traveltimes alone. If the reflector is dipping, the inversion is ambiguous when the dip plane is close to one of the vertical symmetry planes of the orthorhombic layer above it. The parameter estimation becomes possible if the dip direction deviates by more than 10° from the nearest symmetry plane. We apply multicomponent stacking velocity tomography to perform velocity analysis for stratified orthorhombic models composed of homogeneous layers separated by plane or curved interfaces. The tomographic algorithm, which operates with the normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of PP- and SS-waves, is designed to build the orthorhombic velocity model in the depth domain by estimating the anisotropic parameters and the shapes of the reflecting interfaces. Numerical tests show that for layered orthorhombic media, it is necessary to put constraints on the vertical velocities to avoid instability in the inversion of noise-contaminated reflection data.

General formalism for plane guided waves in transversely inhomogeneous anisotropic plates

The sextic approach to plane waves in infinite (visco)elastic plates of arbitrary anisotropy and transverse inhomogeneity is outlined. A particular thrust is set on continuous inhomogeneity when the propagator is defined by the Peano expansion. Despite underlying explicit intricacy, the basic framework of the pursued formalism is little affected by a through-plate variation of material. To make it evident, the principal algebraic symmetry of the propagator for unattenuated waves and the ensuing arrangement of the impedance as a Hermitian matrix with specific traits are inferred directly from energy considerations. Staying the same as for homogeneous plates, those features yield useful developments in the broader context of inhomogeneity. The formalism may be expressed in either pair picked among velocity, frequency and wavenumber, but different choices of a dispersion variable are shown to entail analytical dissimilarities. In addition, the impact of the profile symmetry and of the horizontal plane of crystallographic symmetry is examined. The surface-impedance method and some other aspects of the numerical treatment are discussed.

Dipole formation by two interacting shielded monopoles in a stratified fluid

The interaction between two shielded monopolar vortices has been investigated experimentally in a nonrotating linearly stratified fluid and by full three-dimensional (3D) numerical simulations. The characteristic Reynolds and Froude numbers in the experiments are approximately Re≈500–1000 and F≈0.2–0.4. In a first set of numerical simulations the flow is initialized with the experimentally obtained two-dimensional horizontal velocity field, which is measured in the horizontal symmetry plane of the vortices, and the lacking initial data such as the density perturbation and the full 3D vorticity field are provided by the so-called diffusion model [Beckers et al., J. Fluid Mech. 433, 1 (2001)]. A comparison of the experimental and numerical data shows that using the diffusion model to supply the full 3D initial data is reliable for the Reynolds and Froude numbers considered in present experiments. Conjecturing a wider range of applicability, a second set of numerical simulations has been performed using initial conditions for the flow field and the density perturbation entirely based on the diffusion model. These numerical simulations enable an investigation of the role of Reynolds numbers (up to Re=10 000) and Froude numbers (F=0.30, 0.65, and 1.0) which are outside the experimentally accessible range. These simulations provide a better understanding of the dipole formation process, the influence of the vortex shields and the density perturbation in this process, and of the 3D structure of the dipoles. Compactness of the dipole, entrainment of irrotational fluid from the rear, and tail formation behind the dipole have been discussed. Additionally, experimental and numerical results are reported on the interaction between two shielded monopoles of the same sign in a linearly stratified fluid. It is found that for the full range of Reynolds and Froude numbers mentioned above the presence of the vortex shields prevents the merging of these monopoles.

Azimuth‐dependent AVO in reservoirs containing non‐orthogonal fracture sets

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. The symmetry of a rock with horizontal bedding that contains two or more non‐orthogonal sets of vertical fractures may be approximated as monoclinic with a horizontal plane of mirror symmetry. For offsets that are small compared with the depth of the reflector, the azimuthal variation in P‐wave AVO gradient for such a medium varies with azimuth as where φ is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. φ2 depends on both the normal compliance BN and the shear compliance BT of the fractures and may differ from zero if BNBT varies significantly between fracture sets. If BNBT is the same for all fractures, and the principal axes of the azimuthal variation in P‐wave AVO for fixed offset are determined by the polarization directions of a vertically propagating shear wave. At larger offsets, terms in and are required to describe the azimuthal variation in AVO accurately. φ4 and φ6 also depend on BNBT. For gas‐filled open fractures but a lower value of BNBT may result from the presence of a fluid with non‐zero bulk modulus.

Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry

Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between the anisotropic parameters defined in the vertical symmetry planes. Subsequently, the fracture weaknesses, which carry information about the density and content of the fracture network, can be estimated in the same way as for fracture‐induced transverse isotropy with a horizontal symmetry axis (HTI media) examined in our previous paper (part I). The parameter estimation procedure can be based on the azimuthally dependent reflection traveltimes and prestack amplitudes of P-waves alone if an estimate of the ratio of the P- and S-wave vertical velocities is available. It is beneficial, however, to combine P-wave data with the vertical traveltimes, NMO velocities, or AVO gradients of mode‐converted (PS) waves. In each vertical symmetry plane of the model with two orthogonal fracture sets, the anisotropic parameters are largely governed by the weaknesses of the fractures orthogonal to this plane. For weak anisotropy, the fracture sets are essentially decoupled, and their parameters can be estimated by means of two independently performed HTI inversions. The input data for this model must include the vertical velocities (or reflector depth) to resolve the anisotropic coefficients in each vertical symmetry plane rather than just their differences. We also discuss several criteria that can be used to distinguish between the models with one and two fracture sets. For example, the semimajor axis of the P-wave NMO ellipse and the polarization direction of the vertically traveling fast shear wave are always parallel to each other for a single system of fractures, but they may become orthogonal in the medium with two fracture sets.

Explicit analytic expression for normal moveout from horizontal and dipping reflectors in weakly anisotropic media of arbitrary symmetry type

When processing and inverting seismic reflection data, the NMO velocity must be correctly described, taking into account realistic situations such as the presence of anisotropy and dipping reflectors. Some dip‐moveout (DMO) algorithms have been developed, such as Tsvankin’s analytic formula. It describes the anisotropy‐induced distortions in the classical isotropic cosine of dip dependence of the NMO velocity. However, it is restricted to the vertical symmetry planes of anisotropic media, so the technique is unsuitable for the azimuthal inspection of sedimentary rocks, either with horizontal bedding and vertical fractures or with dipping bedding but no fractures. However, under the weak anisotropy approximation the deviations of the rays from a vertical plane can be neglected for the traveltimes computation, and the equation can still be applicable. Based on this approach, an explicit analytic expression for the P-wave NMO velocity in the presence of horizontal or dipping reflectors in media exhibiting the most general symmetry type (triclinic) is obtained in this work. If the medium exhibits a horizontal symmetry plane, the concise DMO equations are formally identical to Tsvankin’s except that the parameters δ and ε are not constant but depend on the azimuth ψ Physically, δ(ψ) is the deviation from the vertical P-wave velocity of the P-wave NMO velocity for a horizontal reflector normalized by the vertical P-wave velocity for the azimuth ψ. The function ε(ψ) has the same definition as δ(ψ) except that the P-wave NMO velocity is replaced by the horizontal P-wave velocity. Both depend linearly on (1) new dimensionless anisotropy parameters and (2) generalizing to arbitrary symmetry the transversely isotropic parameters δ and ε. In the most general symmetry case (triclinic), an additional term to the DMO formula is necessary. The numerical examples, based on experimental data in rocks, show two things. First, the magnitude of the DMO errors induced by anisotropy depends primarily on the absolute value of ε(ψ) − δ(ψ) and not on the individual values of ε(ψ) and δ(ψ), which is a direct consequence of the similarity between Tsvankin’s equation and the equation presented here. Second, the anisotropy‐induced DMO correction can be significant even in the presence of moderate anisotropy and can exhibit complex azimuthal dependence.

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide‐azimuth reflection data (combined with known vertical velocity or reflector depth) or multi‐azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media.In order to facilitate the inversion procedure, we introduce a Thomsen‐style parametrization for monoclinic media that includes the vertical velocities of the P‐wave and one of the split S‐waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal‐moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε(1,2), δ(1,2,3) and γ(1,2)) analogous to those defined by Tsvankin for the higher‐symmetry orthorhombic model. The parameters ε(1,2), δ(1,2) and γ(1,2) are primarily responsible for the pure‐mode NMO velocities along the coordinate axes x1 and x2 (i.e. in the shear‐wave polarization directions). The remaining coefficient δ(3) is not constrained by conventional‐spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ(1,2,3) which control the rotation of the P‐, S1‐ and S2‐wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P‐wave NMO ellipse and shear‐wave polarization directions was recently observed on field data by Pérez et al.Our parameter‐estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P‐, S1‐ and S2‐waves. A Dix‐type representation of the NMO velocity of mode‐converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS1‐ and PS2‐waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.

Joint inversion ofP- andPS-waves in orthorhombic media: Theory and a physical modeling study

Reflection traveltimes recorded over azimuthally anisotropic fractured media can provide valuable information for reservoir characterization. As recently shown by Grechka and Tsvankin, normal moveout (NMO) velocity of any pure (unconverted) mode depends on only three medium parameters and usually has an elliptical shape in the horizontal plane. Because of the limited information contained in the NMO ellipse of P-waves, it is advantageous to use moveout velocities of shear or converted modes in attempts to resolve the coefficients of realistic orthorhombic or lower‐symmetry fractured models. Joint inversion of P and PS traveltimes is especially attractive because it does not require shear‐wave excitation. Here, we show that for models composed of horizontal layers with a horizontal symmetry plane, the traveltime of converted waves is reciprocal with respect to the source and receiver positions (i.e., it remains the same if we interchange the source and receiver) and can be adequately described by NMO velocity on conventional‐length spreads. The azimuthal dependence of converted‐wave NMO velocity has the same form as for pure modes but requires the spatial derivatives of two-way traveltime for its determination. Using the generalized Dix equation of Grechka, Tsvankin, and Cohen, we derive a simple relationship between the NMO ellipses of pure and converted waves that provides a basis for obtaining shear‐wave information from P and PS data. For orthorhombic models, the combination of the reflection traveltimes of the P-wave and two split PS-waves makes it possible to reconstruct the azimuthally dependent NMO velocities of the pure shear modes and to find the anisotropic parameters that cannot be determined from P-wave data alone. The method is applied to a physical modeling data set acquired over a block of orthorhombic material—Phenolite XX-324. The inversion of conventional‐spread P and PS moveout data allowed us to obtain the orientation of the vertical symmetry planes and eight (out of nine) elastic parameters of the medium (the reflector depth was known). The remaining coefficient (c12or δ(3)in Tsvankin’s notation) is found from the direct P-wave arrival in the horizontal plane. The inversion results accurately predict moveout curves of the pure S-waves and are in excellent agreement with direct measurements of the horizontal velocities.

Misalignment of the orientation of fractures and the principal axes forPandSwaves in rocks containing multiple non-orthogonal fracture sets

SUMMARY Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. A shear wave propagating in an azimuthally anisotropic medium splits into two components with diVerent polarizations if the source polarization is not aligned with the principal axes of the medium. In the presence of two or more non-orthogonal sets of vertical fractures, the symmetry of the medium may be approximated as monoclinic with a horizontal plane of mirror symmetry if, in the absence of fractures, the rock is transversely isotropic (TI) with the symmetry axis perpendicular to the bedding plane. For such a medium, the fast and slow polarization directions for vertically propagating shear waves are not parallel or perpendicular to any of the fracture planes but lie in directions given by the principal axes of a second-rank fracture compliance tensor. This tensor is independent of the normal compliance of the fractures. It follows that for vertical propagation of shear waves in a vertically fractured TI medium, any number of arbitrarily oriented vertical fracture sets is equivalent to two mutually perpendicular fracture sets, provided that the seismic wavelength is large compared to the size of the fractures. For oVsets typical of surface seismic acquisition, the P-wave velocity at fixed oVset varies with azimuth as cos 2(w’w 0 ), where w is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave; w 0 depends on both the normal and the shear compliance of the fractures and may diVer from zero if the ratio of the normal to shear compliance of the fractures varies significantly between fracture sets. If this ratio is similar for all fractures, w 0 #0 and the principal axes of the variation in P-wave velocity with azimuth for fixed oVset are determined by the principal axes of the second-rank fracture compliance tensor.

Experimental study of turbulent flow in the near wakes of single and tandem prisms

An experimental study was performed for the flow of air normal to a prism of square cross section (side dimension D and length H) spanning a duct of square cross section (side dimension H). Two prism arrangements were investigated corresponding to: (1) the prism of side D on its own, at different distances α ( = a H ) from the bottom duct wall; and, (2) the prism of side D with a second, smaller prism of side δ (= d/ D) placed upstream, parallel to and in line with it. In both arrangements, the top and bottom surfaces of the prisms were aligned parallel to the top and bottom walls of the duct. In the second arrangement, the longitudinal axes of the prisms were always contained in the horizontal symmetry plane of the duct (α=0.50) and the center-to-center interprism distance λ ( = L D ) was varied. Laser-Doppler velocimetry (LDV) was used to measure the mean and rms streamwise velocity components at various streamwise locations along traverses contained in the vertical symmetry plane of the duct normal to the axes of the prisms. These data were obtained for a value of the Reynolds number Re D= 1.0 × 10 4 (Re D = U iD v , where U i is the average velocity of the air at the duct inlet, and v its kinematic viscosity). Lift and drag coefficients, as well as the Strouhal number ( St D = fD U i , where f is the vortex-shedding frequency in Hz), were also determined for the prism of side D for values of the Reynolds number equal to 1.0 × 10 4, 2.0 × 10 4 and 2.75 × 10 4. The measurements of the above quantities reveal a significant dependence of the flow on all the parameters investigated, with large differences arising between the single and tandem prism arrangements. For the tandem arrangements with δ < 1.0, the downstream prism experiences a decrease in drag and an increase in vortex-shedding frequency (relative to the single-prism case) that varies with λ. For the single-prism arrangement, decreasing the wall distance α to values α < 0.20 significantly decreases the drag coefficient while increasing the lift coefficient and the Strouhal number. In addition to their intrinsic value, the measurements provide modest but challenging targets for testing numerical calculations of single and interacting near-wake turbulent flows.

Expected displacements and stresses in the encasing concrete of a francis turbine scroll case

The finite element stress analysis is used to determine the expected displacements and stresses in the encasing concrete of the scroll case of a Francis turbine. The minimum principal stress in all cases examined is compressive and has higher concentrations close to the stay ring supports. The maximum principal stress indicates tensile stress areas at the inside concave faces of the cross sections, which are extended into most of the central area of the cross section, around the horizontal plane of symmetry of the turbine. The displacements are within the allowed width of the asphalt cork liner of the scroll case.

La perte de température à travers la charge: intérêt pour le pilotage d'un séchoir à bois à haute température

This paper aims to analyse the temperature drop (temperature loss of the superheated steam across a stack of boards) during convective drying of wood at high temperature. The study is based on measurements made in an adapted test section of an aerodynamic wind tunnel for simulating a stack of five (27 mm x 150 mm x 1000 mm) boards located parallel to the horizontal plane of symmetry of the test section and separated from one other by a 20 mm gap. The results are compared to those obtained from a global enthalpic balance (from the derivation of the kinetic drying curve) and to those resulting from the integration of a local enthalpic balance which needs the characteristic drying curve (van Meel model). The good agreement leads us to suppose that control of the drying by the temperature drop evolutions could be used. Nevertheless, two factors are sources of error: the heat loss inherent in the kiln and, in the case of wood, the variability of the characteristic drying curve. The effects of both parameters are quantified. It emerges from the study that, taking great precautions, the preciseness can be improved in such a way that kiln control by the temperature drop becomes possible. Taking account of the simplicity of implementing the temperature probes and of the global information it gives, the system can also be used as a complement of other existing devices.

Analytic representation of cyclotron magnetic field

A model has been developed for the rapid but accurate calculation of the static magnetic field in the Chalk River cyclotron. The field is expressed in terms of elementary functions which can be handled efficiently in differential-algebra trajectory integrations. Maxwell's equations are satisfied exactly. Each of seven subdivisions of the superconducting coils is treated by a moment expansion about a central circle. Each pole is modeled as a uniformly magnetized semi-infinite prism. Monopoles and dipoles at the vertices of the polygonal pole faces correct for departures from the true pole shape. Uniform distributions of dipole strength along the edges of the pole-face polygons correct for the local inappropriateness of the assumption of uniform magnetization. The contributions of the yoke and of other relatively distant parts of the structure to the held in the region of particle acceleration are represented by low-order polynomials. Some of the source parameters are obtained by fitting to the measured values of B/sub z/ in the horizontal plane of symmetry.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>