Recording and evaluation methods of PIV investigations on a helicopter rotor model

Three-component particle image velocimetry measurements at moderate speeds and observation distances can now be accomplished on a routine basis. This article discusses the experiment performed on a 4 m-diameter model rotor in the 6-m×8-m open test section of the Large Low Speed Facility of the German–Dutch Wind Tunnels. More than half a terabyte of raw data were recorded at various positions on the advancing and retreating sides of the rotor in order to obtain detailed measurements of the trailing vortex in the frame of an international project. This paper addresses measuring techniques and possible sources of errors and presents a limited number of cases for the purpose of illustrating the solutions to numerous technical challenges relating to the acquisition and analysis of vortical flows.List of symbols C _T thrust coefficient (T/² R ⁴) - M magnification - r _c radius of vortex core (mm) - R rotor radius (m) - T thrust (N) - u,v,w velocity components in x, y and z coordinates (m/s) - (u,v,w)_wt velocity components in wind tunnel coordinates (m/s) - U _max maximum in-plane velocity component (m/s) - W _max maximum out-of-plane velocity component (m/s) - x,y,z particle image velocimetry (PIV) frame coordinates (m) - (x,y,z)_wt wind tunnel coordinates (m) - t time delay (s) - Z light sheet thickness (mm) - Z light sheet thickness (mm) - rotor rotation frequency (rad/s) - rotor azimuth angle during recording (deg) vortex age - rotor shaft angle (deg) - _x displacement measurement error - advance ratio (V/R) - air density (kg/m³) - circulation (m²/s) - _z vorticity (s^–1) Abbreviations AFDD Aeroflightdynamics Directorate - BVI blade–vortex interaction - DLR Deutches zentrum für Luft- und Raumfahrt - DNW German–Dutch Wind tunnel - HART HHC aeroacoustic rotor test - LLF large low speed facility - NASA National Aeronautics and Space Administration - ONERA Office National dEtudes e de Recherches Aerospatiales - RANS Reynolds-averaged Navier–Stokes - SPR stereo pattern recognition - 3C-PIV three-component particle image velocimetry     

The Reissner–Sagoci Problem for a Non-homogeneous Half-space with a Surface Constraint

This paper deals with the problem of twisting a non-homogeneous, isotropic, half-space by rotating a circular part of its boundary surface (0 r < a, z = 0) through a given angle. A ring (a < r < b, z = 0) outside the circle is stress-free and the remaining part (r > b, z = 0) is rigidly clamped. The shear modulus is assumed to vary with the cylindrical coordinates, r, z by the relation (z) = ₁(c + z), c 0 where ₁, c and are real constants. Expressions for some quantities of physical importance, such as torque applied at the surface of the disk and stress intensity factors, are obtained. The effects of non-homogeneity on torque and stress intensity factor are illustrated graphically.     

Two-color particle-imaging velocimetry using a single argon-ion laser

A swept-beam, two-color particle-imaging velocimetry (PIV) technique has been developed which utilizes a single argon-ion laser for illuminating the seed particles in a flowfield. In previous two-color PIV techniques two pulsed lasers were employed as the different-color light sources. In the present experiment the particles in a two-dimensional shear-layer flow were illuminated using arotating mirror to sweep the 488.0-nm (blue) and 514·5-nm (green) lines of the argon-ion laser through a test section. The blue- and greenparticle positions were recorded on color film with a 35-mm camera. The unique color coding eliminates the directional ambiguities associated with single-color techniques because the order in which the particle images are produced is known. Analysis of these two-color PIV images involved digitizing the exposed film to obtain the blue and green-particle image fields and processing the digitized images with velocity-displacement software. Argon-ion lasers are available in many laboratories; with the addition of a rotating mirror and a few optical components, it is possible to conduct flow-visualization experiments and make quantitative velocity measurements in many flow facilities.List of symbols d length of displacement vector - d _m distance between rotating mirror and concave mirror - n _f number of facets on rotating mirror - R seed-particle radius - v velocity in x, y plane - v _s sweep velocity of laser beams, assumed to be in y direction from top to bottom of field of view - v _x, v _y, v _z x, y, and z components of velocity - x ₁, y ₁ color-1 particle coordinates - x ₂, y ₂ color-2 particle coordinates - y _max y dimension of field of view, assumed to be the long dimension - s spatial separation of beams as they approach rotating mirror - t time separation of laser sheets or of swept beams passing fixed point - t _b time between successive sweeps through test section by same beam - t _s time required for both beams to sweep through test section - angular separation of beams reflecting from rotating mirror - fluid viscosity - v angular velocity of rotating mirror in cycles per second - seed-particle density - seed-particle response time - _v, _d, _t standard deviation of velocity, displacement, and time - vorticity This work was supported, in part, by the Aero Propulsion and Power Directorate of Wright Laboratory under Contract No. F33615-90-C-2033.     

On natural convection from a vertical plate with a prescribed surface heat flux in porous media

This paper presents a theoretical and numerical investigation of the natural convection boundary-layer along a vertical surface, which is embedded in a porous medium, when the surface heat flux varies as (1 +x ²)), where is a constant andx is the distance along the surface. It is shown that for > -1/2 the solution develops from a similarity solution which is valid for small values ofx to one which is valid for large values ofx. However, when -1/2 no similarity solutions exist for large values ofx and it is found that there are two cases to consider, namely < -1/2 and = -1/2. The wall temperature and the velocity at large distances along the plate are determined for a range of values of .Notation g Gravitational acceleration - k Thermal conductivity of the saturated porous medium - K Permeability of the porous medium - l Typical streamwise length - q _w Uniform heat flux on the wall - Ra Rayleigh number, =gK(q _w /k)l/(v) - T Temperature - Too Temperature far from the plate - u, v Components of seepage velocity in the x and y directions - x, y Cartesian coordinates - Thermal diffusivity of the fluid saturated porous medium - The coefficient of thermal expansion - An undetermined constant - Porosity of the porous medium - Similarity variable, =y(1+x ) ^/3/x ^1/3 - A preassigned constant - Kinematic viscosity - Nondimensional temperature, =(T – T )Ra^1/3 k/qw - Similarity variable, = =y(log_e x)^1/3/x ^2/3 - Similarity variable, =y/x ^2/3 - Stream function     

Measurement of the temperature distribution within monodisperse combusting droplets in linear streams using two-color laser-induced fluorescence

Two-color laser-induced fluorescence can be use to perform space-averaged flying droplet temperature measurements. In this paper, the possibility to extend this technique to the measurement of the temperature distribution within a moving combusting droplet is considered and demonstrated. This technique may provide new experimental data related to the heat diffusion in liquid fuel droplets injected in high-temperature gas streams, for example, in combustion chambers. The main principles of the technique and the data reduction process are discussed, and a test on combusting a monodisperse ethanol droplets (200 m in diameter) stream is presented.Nomenclature a _i , b _i temperature sensitivity coefficients for i th spectral band - C molecular concentration of fluorescent tracer - D droplet diameter - I ₀ incident laser beam intensity - I _f fluorescence intensity - K _opt optical constant - K _spec spectroscopic constant - V _c collection volume - R _f fluorescence ratio - T absolute temperature - T _i injection temperature - V _i injection velocity - ( x, y , z) spatial coordinates Greek symbols temperature sensitivity coefficient     

A crossed beam laser shadow technique for spatially resolved measurements in turbulent flow

Optical methods such as the shadowgraph and schlieren techniques do not directly allow three-dimensional spatial resolution because of the inherent integration along the line of sight. For the particular case of the laser shadow technique, it is attempted to circumvent this restriction by employing a pair of crossed laser beams and cross-correlating the optical signals obtained from the beams. The information obtained is supposed to pertain only to the common volume of both beams. It is theoretically shown that this concept will work if the turbulence spectrum does not decay faster than K ^–5 in the range of wave numbers corresponding to the inverse diameter of the laser beam. Experiments on a round jet confirm that local values of the mean flow velocity can be obtained.List of symbols A electromagnetic amplitude at x = 0 - B ₁₂ correlation of light intensity fluctuations - C ₁₂ normalized correlation (Eq. (1)) - I (I) light intensity (fluctuating part) - k wavenumber of light - K wavenumber of turbulent eddies - L ₀ outer scale of turbulence - n refractive index - R ₀ radius of curvature of the wavefront of the laser beam at x = 0 - u (u ₀) (undisturbed) electromagnetic field of the laser beam - drift velocity of the laser shadow pattern - W spatial weighting function (Eq. (11)) - W ₀ diameter of the laser beam at x = 0 - x, y, z spatial coordinates (Figs. 1, 2) - see Eq. (6) - see Eq. (A3) spectrum of turbulent refractive index fluctuations exponent of _n - = (y, z) - ₁ see Eq. (7) - , spatial coordinates (Fig. 2) - , spatial and temporal delay variables in a correlation function     

LDV measurements of a turbulent air-solid two-phase flow in a 90° bend

Simultaneous measurements of the mean streamwise and radial velocities and the associated Reynolds stresses were made in an air-solid two-phase flow in a square sectioned (10×10 cm) 90° vertical to horizontal bend using laser Doppler velocimetry. The gas phase measurements were performed in the absence of solid particles. The radius ratio of the bend was 1.76. The results are presented for two different Reynolds numbers, 2.2×10⁵ and 3.47×10⁵, corresponding to mass ratios of 1.5×10^–4 and 9.5×10^–5, respectively. Glass spheres 50 and 100 m in diameter were employed to represent the solid phase. The measurements of the gas and solid phase were performed separately. The streamwise velocity profiles for the gas and the solids crossed over near the outer wall with the solids having the higher speed near the wall. The solid velocity profiles were quite flat. Higher negative slip velocities are observed for the 100 m particles than those for the 50 gm particles. At angular displacement =0°, the radial velocity is directed towards the inner wall for both the 50 and 100 m particles. At =30° and 45°, particle wall collisions cause a clear change in the radial velocity of the solids in the region close to the outer wall. The 100 m particle trajectories are very close to being straight lines. Most of the particle wall collisions occur between the =30° and 60° stations. The level of turbulence of the solids was higher than that of the air.List of symbols D hydraulic diameter (100 mm) - De Dean number,De = - mass flow rate - number of particles per second (detected by the probe volume) - r radial coordinate direction - r _i radius of curvature of the inner wall - r ₀ radius of curvature of the outer wall - r ^* normalized radial coordinate, - R mean radius of curvature - Re Reynolds number, - R _r radius ratio, - U ,U _z mean streamwise velocity - U _r ,U _y mean radial velocity - U _b bulk velocity - , _z rms fluctuating streamwise velocity - _r , _y rms fluctuating radial velocity - -r shear stress component - z-y shear stress component - x spanwise coordinate direction - x ^* normalized spanwise coordinate, - y radial coordinate direction in straight ducts - y ^* normalized radial coordinate in straight ducts, - z streamwise coordinate direction in straight ducts - z ^* normalized streamwise coordinate in straight ducts, Greek symbols streamwise coordinate direction - kinematic viscosity of air     

Experimental investigations on two-phase flow past a sphere using digital Particle-Image-Velocimetry

Digital Particle-Image-Velocimetry was applied to investigate particle trajectories in a gas flow past a sphere. The particle displacement was determined by autocorrelation analysis of image sections. To enhance the signal/noise ratio a synthetic image with idealized particle pictures was generated from the real image. The autocorrelation function (ACF) was calculated using the Fast Hartley Transformation (FHT). The desired secondary maximum of this function was detected by an algorithm with subpixel resolution. A data validation step testing the plausibility of the velocity vectors completes the image analysis. Particle trajectories are traced with help of the particles' velocity vectors. The particle deposition on a sphere can be deduced from the course of these trajectories.List of symbols Cu Cunningham correction - e double distance between the limiting particle trajectory and the stagnation point axis - f focal length - H Hartley-Transform - M enlargement factor - S interference band spacing - x coordinate - y coordinate - x _p particle diameter - x _T droplet or sphere diameter - V image as grey value function - _.rel face velocity of droplet or sphere - particle image displacement - x particle image displacement in x-direction - y particle image displacement in y-direction - collection efficiency - wavelength of the laser light - _L fluid viscosity - _L fluid density - _p particle density     

The moving, plane heat source in an elastic medium

Summary This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.Nomenclature mass density - diffusivity - thermal conductivity - Q heat emitted by plane heat source per unit time per unit area - speed of propagation of plane heat source - shear modulus - Poisson's ratio - T temperature - _x, _y, _z normal stress components - u _x, u_y, u_z displacement components - c speed of irrotational waves - t time - x, y, z Cartesian coordinates - =x–vt moving coordinate     

Effect of radial and rotational lubricant inertia on the pressure distribution in externally pressurised thrust bearings

Expressions are obtained for the pressure distribution in an externally pressurised thrust bearing for the condition when one bearing surface is rotated. The influence of centripetal acceleration and the combined effect of rotational and radial inertia terms are included in the analysis. Rotation of the bearing causes the lubricant to have a velocity component in an axial direction towards the rotating surface as it spirals radially outwards between the bearing surfaces. This results in an increase in the pumping losses and a decrease in the load capacity of the bearing. A further loss in the performance of the bearing is found when the radial inertia term, in addition to the rotational inertia term is included in the analysis.Nomenclature r, z, cylindrical co-ordinates - V _r, V , V _z velocity components in the r, and z directions respectively - U, X, W representative velocities - coefficient of viscosity - p static pressure at radius r - p mean static pressure at radius r - Q volume flow per unit time - 2h lubricant film thickness - density of the lubricant - r ₂ outside radius of bearing = D/2 - angular velocity of bearing - R dimensionless radius = r/h - P dimensionless pressure = h ³ p/Q - Re channel Reynolds number = Q/h     

Laminar forced convection in elliptic ducts

The problem of laminar forced convection heat transfer in short elliptical ducts with (i) uniform wall temperature and (ii) prescribed wall heat flux is examined in detail with the well known Lévêque theory of linear velocity profile near the wall. Moreover, consideration is given to the variation of the slope of the linear velocity profile with the position on the duct wall. A correction factor for the temperature dependent viscosity is included. Expressions for the local and average Nusselt numbers and wall temperatures are obtained. For the case of constant heat flux the Nusselt numbers are higher than for constant wall temperature.The results corresponding to the classical Graetz and Purday problems are deduced as special cases.Nomenclature a, b semiaxes of ellipse, b Graetz number (average), Re Pr D _e/Z - h _i ^o local heat transfer coefficient - J _n(x) Bessel function of order n - K thermal conductivity of the fluid - [X] Laplace transform of X - N _u ^o local Nusselt number, h _i ^o D _e/K - perimeter average Nusselt number - overall average Nusselt number - Nu _w wall Nusselt number - Nu Nusselt number at large distance from the inlet - p Laplace transform parameter - Pr Prandtl number, C _a/K - Re Reynolds number, D _e / _a - T temperature of the fluid - T ₁, T _W inlet and wall temperatures, respectively - u _z local isothermal velocity along the axis of the duct - average fluid velocity - x, y, z Cartesian coordinates, z-axis parallel to the axis of the duct (z=0 at duct inlet) - Z length of the duct - thermal diffusivity, K/C - * correction factor for the temperature dependent viscosity - (x) gamma function - coordinate measured normal to the wall of the duct - _a, _w viscosity of fluid at average and wall temperatures - , , z elliptic cylindrical coordinates - density of fluid - (z) heat flux     

Reynolds number dependence of the drag coefficient for laminar flow through fine-scale photoetched screens

The laminar steady flow downstream of fine-mesh screens is studied. Instead of woven-wire screens, high-uniformity screens are fabricated by photoetching holes into 50.8 m thick Inconel sheets. The resulting screens have minimum wire widths of 50.8 m and inter-wire separations of 254 m and 318 m for the two screens examined. A flow facility has been constructed for experiments with these screens. Air is passed through the screens at upstream velocities yielding wire width Reynolds numbers from 2 to 35. To determine the drag coefficient, pressure drops across the screens are measured using pressure transducers and manometers. Threedimensional flow simulations are also performed. The computational drag coefficients consistently overpredict the experimental values. However, the computational results exhibit sensitivity to the assumed wire cross section, indicating that detailed knowledge of the wire cross section is essential for unambiguous interpretation of experiments using photoetched screens. Standard semi-empirical drag correlations for woven-wire screens do not predict the present experimental results with consistent accuracy.List of symbols A ₁, A ₂ screen aspect ratios - c _d screen drag coefficient - d woven-wire diameter - D photoetched minimum wire width (spanwise) - f woven-wire screen drag function - M distance between adjacent wires - N spectral-element order - o woven-wire open area fraction - O photoetched open area fraction - _p pressure drop across screen - Re _d woven-wire diameter Reynolds number - Re _D photoetched wire width Reynolds number - U fluid velocity upstream of screen - W photoetched sheet thickness (streamwise) - x, y, z spatial coordinates - fluid density - fluid viscosity     

Entrance flow of a yield-power law fluid

In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Nomenclature

Nomenclature a constant - D diameter - F dimensionless pressure gradient in (4.3) - f _x friction factor in (5.1) - f _app total friction factor in (5.2) - K entrance pressure drop coefficient - n power law exponent - p pressure - r radial co-ordinate - R radius of a tube - Re Reynolds number (5.3) - s rate of shear, u/r - u axial velocity - average velocity - v velocity in radius direction - x axial co-ordinate - y normal co-ordinate - Y yield number in (4.4) - z dimensionless axial distance =(x/D)/Re - z ₁ 1/z Greek Symbols plug flow radius in (4.6) - _eff effective viscosity - density - shear stress - _y yield stress - dimensionless stream function     

The deformation of an interface between two fluids in a porous medium

Summary The interface between two moving fluids in a porous medium will, in general, deform under the influence of gravity and drag forces. An example of some importance is the formation of so-called gravity tongues in oil reservoirs. This paper deals with the displacement of oil by water in a homogeneous non-horizontal oil stratum. The deformation of such an interface can be deduced by numerical procedures based upon exact methods. The use of these methods is limited, however, owing to the fact that in oil reservoirs the dip is usually smaller than 10 to 20 degrees. In such cases, where the interface is initially horizontal, the computation of the form of the interface as a function of time becomes so enormous, even when a fast electronic computer is used, that an approximative method is more useful. In this paper two approximate solutions are presented. The first one is obtained by using a simplified form of the dynamic interface condition, in which the flow velocity component perpendicular to the dip direction of the reservoir is neglected. This simplification has previously been used by Dietz, who gave a first-order approximation with respect to time. More complicated results are obtained by using the second approximation where, in accordance with the dynamic boundary condition, this velocity component is more or less taken into account. In both methods, the form of the interface as a function of time is expressed in a parametric representation. Moreover, the amount of water that has passed a given cross-section and the flow of water at this section are obtained as a function of time and the parameter used. Results of both methods are compared with each other and with those obtained by an exact method. Both approximations are found to be good in those cases where the dip of the reservoir is not too high, but this is precisely when exact methods are impracticable.Nomenclature d thickness of the idealised reservoir (see fig. 1) - f function of y as given by (2.7) - f, f, f first, second and third derivative of f with respect to y - F(y, ) function of y and as given in the appendix - G dimensionless quantity - G* dimensionless quantity {= G cos /(1–G sin )} - H(y, ) function of y and as given in the appendix - M dimensionless quantity _{2 1}/ _{1 2} - p pressure - q _w the flow of water at a given cross-section - Q _w the total amount of water that has already passed a given cross-section at a certain time - S ₀ oil saturation in the oil region - S _w water saturation in the water region - r integration variable - s the co-ordinate along the interface (positive direction as given in fig. 1) - t time - t _w time at which water breaks through at a given cross-section - u ₁ mean velocity component of fluid 1 in x-direction in the pores of the porous medium (water) - u ₂ mean velocity component of fluid 2 in x-direction in the pores of the porous medium (oil) - U _r the relative deformation velocity of the interface {=(x _i –W ₀ t)/t} _y - the mean fluid velocity vector in the pores of the porous medium - v ₁ mean velocity component of fluid 1 in y-direction in the pores of the porous medium (water) - v ₂ mean velocity component of fluid 2 in y-direction in the pores of the porous medium (oil) - v _n mean velocity component of the fluids normal to the interface (positive direction from fluid 1 to fluid 2) - W ₀ mean velocity of fluid 1 (water) when x –, where the velocity component in y-direction is equal to zero - x co-ordinate, parallel to the boundaries of the reservoir (see fig. 1) - x _e value of x for a given cross-section - x _i , y _i values of the x and y co-ordinates corresponding to the points of the interface - x ₀(y) initial value of the x co-ordinate of the points of the interface (at t=0) - y co-ordinate, perpendicular to the boundaries of the reservoir (see fig. 1) - y _e (t) time-dependent value of the y co-ordinate of the interface if the value of the x co-ordinate is equal to x _e - y _i , x _i values of the y and x co-ordinates corresponding to the points of the interface - z vertical co-ordinate (positive direction as given in fig. 1) - the angle between the horizon and the boundaries of the reservoir (see fig. 1) - the angle between the x axis and the normal to the interface (see fig. 1) - _e the angle if the value of x _i is equal to x _e - ₀(y) initial value of the angle (at t=0) - effective permeability of the porous medium divided by the product of the porosity and fluid saturation - ₁ effective permeability of the porous medium to fluid 1 divided by the product of the porosity and the saturation of fluid 1 - ₂ effective permeability of the porous medium to fluid 2 divided by the product of the porosity and the saturation of fluid 2 - fluid viscosity - ₁ viscosity of fluid 1 (water) - ₂ viscosity of fluid 2 (oil) - fluid density - ₁ density of fluid 1 (water) - ₂ density of fluid 2 (oil) - porosity of the porous medium Formerly with Koninklijke/Shell Exploratie en Produktie Laboratorium, Rijswijk, The Netherlands.     

States of classical statistical mechanical systems of infinitely many particles. I

We study a general mathematical model of a classical system of infinitely many point particles. The space X of infinite particle configurations is equipped with a natural topology as well as a measurable structure related to it. It is also connected with a family {X _A } of local spaces of finite configurations indexed by bounded open sets A in the one-particle space E. A theorem analogous to Kolmogoroff's fundamental theorem for stochastic processes is proved, according to which a consistent family { _A } of local probability measures _A defined on the X _A gives rise to a unique probability measure on X. We also study the problem of integral representation for positive linear forms defined over some linear space of real functions on X. We prove that a positive linear form F(f), defined for functions f in the class C+P, admits a uniquely determined integral representation F(f)= f () d, where is a probability measure over X.     

Acetone: a tracer for concentration measurements in gaseous flows by planar laser-induced fluorescence

The structure of fully-developed turbulence in a smooth pipe has been studied via wavenumber spectra for various friction velocities, namely, u ,=0.61 and 1.2 m/s (the corresponding Reynolds numbers based on centerline velocity and pipe radius being respectively 134,000 and 268,000) at various distances from the wall, namely y ⁺ = 70, 200,400 and 1,000. For each distance from the wall, correlations of the longitudinal component of turbulence were obtained simultaneously in seven narrow frequency bands by using an automated data acquisition system which jointly varied the longitudinal (x) and transverse (z) separations of two hot-wire probes. The centre frequencies of the bandpass filters used correspond to a range of nondimensional frequencies ⁺ from 0.005 to 0.21. By taking Fourier transforms of these correlations, three-dimensional power spectral density functions and hence wavenumber spectra have been obtained at each y ⁺ with nondimensional frequency ⁺ and nondimensional longitudinal and transverse wavenumbers k _x ⁺ and k _z ⁺ as the independent variables. The data presented in this form show the distribution of turbulence intensity among waves of different size and inclination. The data reported here cover a wave size range of over 100, spanning a range of wave angles from 2° to 84°. The effects of friction velocity and Reynolds number on the distribution of waves, their lifetimes and convection velocities are also discussed.List of symbols A wave strength function - C _x streamwise phase velocity - C _z circumferential phase velocity - f wave intensity function - k resultant wave number = [k _x ² + k _z ² ]^1/2 - k _x , k _z longitudinal (x) and transverse (z) wavenumber respectively - P(k _x ⁺ , k _z ⁺ , ⁺) power spectral density function in u - R radius of pipe - Re Reynolds number (based on centerline velocity and pipe radius) - R _uu (x ⁺, z⁺, ) normalized correlation function in u - R _unu (x ⁺, z⁺,¦⁺¦) normalized filtered correlation function in u, as defined in equation (1) - t time - U mean velocity in the x-direction - u, v, w turbulent velocities in the cartesian x, y and z directions respectively - û, v, turbulent velocities in the wave coordinate x, and directions respectively - u friction velocity - x, y, z cartesian coordinates in the longitudinal (along the pipe axis), normal (to the pipe wall) and transverse (along the circumference of the pipe) directions respectively, as defined in Fig. 1 - wave angle - difference between two quantities - v kinematic viscosity - time delay - circular frequency (radians/s) - + quantity nondimensionalized using u and v - overbar time average A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 September, 1990     

A focusing aid for the X-ray projection microscope

Summary Part of the electrons reflected by the target of an X-ray microscope pass the demagnifying lens in opposite direction and form a magnified image of the focus in the electron source. This secondary image can be caught on a fluorescent screen and observed. The position, shape and size of the image give information on alignment, focusing conditions and image errors. The brightness is a factor 10³ to 10⁴ higher than that of the X-ray fluorescent image under normal focusing conditions. If a magnetic objective is used, centering can be done very accurately (angle of tilt < 1/600 radians). In practice this method proves to be very satisfactory, even for voltages as low as 6 kV and less. At these voltages the depth of penetration of the electrons in gold is less than 500 Å, so that for a 0.1 resolution there is no need for a thin target.     

Image shifting for PIV using birefringent and ferroelectric liquid crystals

This paper discusses a new implementation of electrooptical image shifting, used to resolve directional ambiguity in particle image velocimetry (PIV) measurements. The setup uses a ferroelectric liquid crystal (FLC) as a polarization rotator and a birefringent calcite plate as a shifter. The system can be used with non-polarized light sources and fluorescent particles. The minimum shifting time (pulse separation) is approximately 100 s. This compact electrooptical device is usually positioned in front of the camera lens, though it has also been mounted inside the lens body. Sample vector maps from a turbulent multidirectional flow are included.This work is supported by ARPA, Gary Jones, Program Manager. Funding is provided under ONR Contract N° N00014-92-1634. The authors would like to thank Shewen Liu for the use of his facility and data.     

Effect of slip on porous-walled squeeze films in the presence of a transverse magnetic field

The present investigation is devoted to study the effect of viscous resistance, arising due to sparse distribution of particles in porous media, on the load capacity and thickness time response of porous-walled squeeze films in the presence of a uniform magnetic field. The results of the analysis obtained by using Beavers and Joseph [1] slip-boundary condition show that the viscous resistance increases the load capacity and thickness time response of squeeze films when compared with the results of Chandrasekhara [2] obtained in the absence of viscous resistance. Hence, for efficient performance of a porous walled squeeze film a suitable porous media in which the material is loosely packed may be used.Nomenclature p pressure in the squeeze film - h thickness of the squeeze film at time t - h ₀ thickness of the film at t=0 - u streamwise velocity component in the squeeze film - v transverse velocity component in the squeeze film - P pressure in the porous material - H thickness of the porous material - U streamwise velocity component in the porous material - V transverse velocity component in the porous material - B B ₀+b - B ₀ impressed uniform magnetic field - b induced magnetic field - E electric field vector (E _x , E _y , E _z ) - m ₀ constant defined in (6), (B ₀ ² / _{m f m})^1/2 - v _h value of v at y=h - h/h ₀, the non-dimensional variable - _n eigen values - _f viscosity - _m magnetic permeability - density - _m magnetic diffusivity, 1/ _{m e} - dimensionless parameter, - _e electrical conductivity - q velocity vector (u, v) - L load capacity - I _n integral defined in (37) - M Hartmann number defined in (7), (m ₀ ² h ²)^1/2 - l length of the strips in x-direction - K permeability of the porous material - J current density vector (J _x , J _y , J _z ) - t time - G _n series coefficient appearing in equation (27)