Quadruple hot-wire probes in a simulated wall flow

A method for calibration and measurement with a fourwire probe is described. The method does not require any assumption about the response of the wires and it is not necessary to know the exact probe geometry. Measurements in a two-dimensional turbulent boundary layer showed large errors in the shear stress, although the probe had a wire arrangement practically insensitive to mean velocity gradients normal to the wall. The problem seems to be caused by the strong instantaneous spanwise velocity gradients, as suggested by the computed response of a simple probe model inserted into a numerical flow obtained by direct simulation.     

Spatially averaged time-resolved particle-tracking velocimetry in microspace considering Brownian motion of submicron fluorescent particles

A time-series measurement method is proposed to detect velocity fields in a microchannel taking into account Brownian motion of submicron tracer particles. The present study proposes spatially averaged time-resolved particle-tracking velocimetry (SAT–PTV), which can detect temporal variations of fluid flow and eliminate errors associated with Brownian motion without losing temporal resolution. Velocity vectors of tracer particles obtained by PTV are spatially averaged in each interrogation window of particle-image velocimetry, yielding full velocity field information with temporal resolution. Synthetic particle images, which include Brownian motion of submicron fluorescent particles in flow fields with linear velocity gradients, are generated to validate the ability of SAT–PTV to track particles. SAT–PTV correctly captures the velocity gradient profiles. The spatial resolution based on the size of the first interrogation window and the measurement depth of the microscope system is 6.7 m×6.7 m×1.9 m, within which several vectors are averaged. SAT–PTV is shown to measure the velocity field of a pulsating flow generated by an electrokinetic pump.An earlier version of this paper appeared in the Fourth International Symposium on Particle Image Velocimetry at Göttingen, Germany, 17–19 September 2001.     

Deformed particle image pattern matching in Particle Image Velocimetry

The deformation of particle image patterns due to velocity gradients causes errors of velocity measurements and false velocity detections in PIV (Particle Image Velocimetry). A novel technique to overcome those limitations inherent in the conventional PIV by correcting the particle image pattern according to the local velocity gradients in two dimensional flows, i.e. u/x, u/y, v/x and v/y, is proposed and successfully applied to a water flow downstream of a backward facing step.     

Investigation of internal pressure gradients generated in electrokinetic flows with axial conductivity gradients

Field amplified sample stacking (FASS) is used to increase sample concentrations in electrokinetic flows. The technique uses conductivity gradients to establish a non-uniform electric field that accumulates ions within a conductivity gradient, and can be readily integrated with capillary electrophoresis. Conductivity gradients also cause gradients in near-wall electroosmotic flow velocities. These velocity gradients generate internal pressure gradients that drive secondary, dispersive flows. This dispersion leads to a significant reduction in the efficiency of sample stacking. This paper presents an experimental investigation of internally generated pressure gradients in FASS using micron-resolution particle image velocimetry (μPIV). We measure velocity fields of particles seeded into an electrokinetic FASS flow field in a glass microchannel with a single buffer–buffer interface. μPIV allows for the direct quantification of local, instantaneous pressure gradients by analyzing the curvature of velocity profiles. Measurements show internally generated pressure-driven velocities on the order of 1mm/s for a typical applied electric field of 100 V/cm and a conductivity ratio of 10. A one-dimensional (1D) analytical model for the temporal development of the internal pressure gradient generation is proposed which is useful in estimating general trends in flow dynamics.

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Detonation propagation in hydrogen–air mixtures with transverse concentration gradients

The influence of transverse concentration gradients on detonation propagation in \(\hbox {H}_2\)–air mixtures is investigated experimentally in a wide parameter range. Detonation fronts are characterized by means of high-speed shadowgraphy, OH* imaging, pressure measurements, and soot foils. Steep concentration gradients at low average \(\hbox {H}_2\) concentrations lead to single-headed detonations. A maximum velocity deficit compared to the Chapman–Jouguet velocity of 9 % is observed. Significant amounts of mixture seem to be consumed by turbulent deflagration behind the leading detonation. Wall pressure measurements show high local pressure peaks due to strong transverse waves caused by the concentration gradients. Higher average \(\hbox {H}_2\) concentrations or weaker gradients allow for multi-headed detonation propagation.     

In vivo blood flow and wall shear stress measurements in the vitelline network

The wall shear stress plays a key role in the interaction between blood flow and the surrounding tissue. To obtain quantitative information about this parameter, velocity measurements are required with sufficient spatial (and temporal) resolution. We present a methodology for the determination of the wall shear stress in vivo in the vitelline network of a chick embryo. Velocity data is obtained by microscopic particle image velocimetry using correlation ensemble averaging; the latter is used to increase the signal-to-noise ratio of the measurements. The temporal evolution of the pulsatile flow is reconstructed by sorting the image pairs based on a phase estimate. From these flow measurements, the wall shear stress can be derived either directly from the magnitude of the gradients or from fits to velocity profiles. Both methods give results that are in good agreement with each other, while the former method is significantly easier to implement. For more accurate studies, the full three-dimensional velocity field may be required. It is demonstrated how this velocity field can be obtained by scanning the measurement volume.

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Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.     

Dual-plane stereo particle image velocimetry (DSPIV) for measuring velocity gradient fields at intermediate and small scales of turbulent flows

A two-frequency dual-plane stereo particle image velocimetry (DSPIV) technique is described for highly resolved measurements of the complete nine-component velocity gradient tensor field u_i/x_j on the quasi-universal intermediate and small scales of turbulent flows. The method is based on two simultaneous, independent stereo particle image velocimetry (PIV) measurements in two differentially spaced light sheet planes, with light sheet characterization measurements demonstrating the required sheet thicknesses, separation, and two-axis parallelism that determine the measurement resolution and accuracy. The present approach uses an asymmetric forward–forward scatter configuration with two different laser frequencies in conjunction with filters to separate the scattered light onto the individual stereo camera pairs, allowing solid metal oxide particles to be used as seed particles to permit measurements in nonreacting as well as exothermic reacting turbulent flows.     

Measurement of turbulent wall velocity gradients using cylindrical waves of laser light

A new optical instrument has been developed for direct measurement of instantaneous velocity gradients at the bounding wall. Light emerging from two tiny optical slits in the surface is used to form a fan of fringes in the region very near the wall. Doppler frequency of the light scattered by the seed particles is directly proportional to the velocity gradient. The system has been used to measure the statistics of the streamwise and spanwise velocity gradients in a turbulent boundary layer. The streamwise and spanwise rms fluctuations were found to be 38% and 11% of the mean streamwise value respectively. The latter result is subject to a large uncertainty.List of symbols a slit width - B transfer function of the instrument - B ^* normalized transfer function - path-averaged value of the normalized transfer function - c constant in logarithmic velocity profile - C _f skin friction coefficient - d _f fringe spacing - f ₁,f₂ frequencies at the downstream and upstream slits resp. - f _d heterodyne Doppler frequency of the signal - g(t) instantaneous wall velocity gradient - G Clauser shape factor - mean wall velocity gradient - g rms value of the wall velocity gradient - H boundary layer shape factor - i, j, k unit vectors along x, y, z axes - wavenumber of laser light - L major axis of the elliptic cross-section of the laser sheet at the slit - l length of each slit - N number of cycles in a signal - N ₀ number of cycles without frequency-shifting - n difference of the unit vectors u ₁and u ₂ - P power transmitted through a slit - P _o power incident on a slit - Re ₁ Reynolds number based on displacement thickness and free-stream velocity - Re ₂ Reynolds number based on momentum thickness and free-stream velocity - S spacing between the slits - S ^* normalized spacing between the slits - u streamwise velocity - u ₁,u₂ unit vectors along the local directions of propagation of the two cylindrical waves - u _l linear term in the streamwise velocity profile - u _nl nonlinear terms in the streamwise velocity - u _nl ^* normalized value of nonlinear streamwise velocity - u _nl ^* mean streamwise velocity - u friction velocity - u⁺ mean velocity normalized with friction velocity - v velocity component normal to the wall - v ^* normal velocity normalized with streamwise velocity - V velocity vector - w spanwise component of velocity - W minor axis of the elliptic cross-section of the laser sheet at the slit - x streamwise distance - ± x _m limiting values of streamwise distance for a signal - x ^* normalized streamwise distance - x ^* normalized value of x _m - y normal distance - y ⁺ normal distance normalized with friction length scale - z spanwise distance - z ⁺ spanwise distance normalized with friction length scale - half-spreading angle of the cylindrical waves - boundary layer thickness in Coles' profile - ₁ displacement thickness of the boundary layer - ₂ momentum thickness of the boundary layer - ₃ energy thickness of the boundary layer - constant in logarithmic velocity profile - wavelength of laser light - kinematic viscosity - coefficient of wake function in Coles' profile Currently at LSTM, Universitat Erlangen-Nürnberg, Cauerstraße 4, W-8520 Erlangen, BRD     

Measurement of the viscous sublayer in near-separated flows

This paper investigates experimentally the development of the viscous sublayer in a two-dimensional incompressible turbulent wall boundary layer under severe pressure gradients. The wall was also moderately heated and the influence of heat transfer on the development of the viscous sublayer was included. A semi-empirical equation for the thickness of the viscous sublayer: $$\delta _s = 11.5\frac{\nu }{{U_\tau }}(0.61\frac{{T_\omega }}{{T_s }})^{1/2}$$ was derived, which holds everywhere except closely near the separation point of the boundary layer. The measurements were made on a flat plate in a test section 1.7 m long and 0.8 m wide. The height and shape of the top surface of the test section could be varied, and thus it was possible to imposed different pressure gradients on the flow. Specially designed fine probes facilitated the measurement of the velocity distribution very close to the wall.     

Reducing time interval between successive exposures in video PIV

Video PIV (VPIV) is an inexpensive and simple technique for measuring instantaneous velocity fields. Because of the low video framing rate its application is, however, limited to flows with small velocity gradients. In this note a method to reduce the time interval t between successive exposures by means of an external hardware synchronized with the video camera is described. These exposures with shorter time interval are recorded in separate video fields. The cross-correlation technique can be used therefore, eliminating directional ambiguity and enabling the application of PID (Particle Image Distortion), which improves the accuracy of velocity detections.This work was supported by the Deutsche Forschungsgemeinschaft (DFG). The authors would like to thank Minami Yoda and Olaf Uhlig for the help in setting up the laser-scanner system.     

Local Mass Transfer Correlations for Nonaqueous Phase Liquid Pool Dissolution in Saturated Porous Media

Local mass transfer correlations are developed to describe the rate of interface mass transfer of single component nonaqueous phase liquid (NAPL) pools in saturated subsurface formations. A threedimensional solute transport model is employed to compute local mass transfer coefficients from concentration gradients at the NAPL–water interface, assuming that the aqueous phase concentration along the NAPL–water interface is constant and equal to the solubility concentration. Furthermore, it is assumed that the porous medium is homogeneous, the interstitial fluid velocity steady and the dissolved solute may undergo firstorder decay or may sorb under local equilibrium conditions. Powerlaw expressions relating the local Sherwood number to appropriate local Peclet numbers are developed for both rectangular and elliptic/circular source geometries. The proposed power law correlations are fitted to numerically generated data and the correlation coefficients are determined using nonlinear least squares regression. The estimated correlation coefficients are found to be direct functions of the interstitial fluid velocity, pool dimensions, and pool geometry.     

Distribution of the electron concentration and wave processes in a pulsed discharge

A quantitative Schlieren method for measuring the electron-density gradient using a laser source in the infrared range is described, which guarantees measurement of densities above 10¹⁴ cm^–2; a detailed observation of the profile of the gas ionization in a pulsed discharge is likewise described. Certain results are presented of a study of the distribution of the electron concentration over the cross section of the discharge tube in a straight argon discharge during the flow of discharge current and also during the subsequent stages of the process. In order to perform time measurement of the electron-density gradients and to construct an overall picture of the plasma distribution, the Schlieren method with a CO₂ laser (10.6 ) as a light source was used. The measurements that were carried out revealed a complex picture involving the formation of a series of successive radial compression waves that exist during a fairly long period after completion of the discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 15–20, March–April, 1971.     

Intensity broadening of internally reflected laser beam from a meniscus formed in a capillary pore—applied for automated liquid column height measurements

An automated liquid column height measurement technique using the total internal reflection of a collimated laser beam from the convex meniscus surface is proposed. This new technique can alleviate the shortcomings of the traditional cathetometer that tends to introduce user bias. Experimental measurements and theoretical predictions have been conducted to examine the detected signal broadening and measurement uncertainties of the proposed technique, resulting from (1) the finite laser-beam diameter, (2) the capillary pore diameter, (3) the beam steering by thermal gradients, and (4) the beam steering by density variations of the liquid inside a capillary pore. For the collimated 52.6-m diameter laser beam, for three different tested pores of 0.5, 1.0, and 2.0 mm diameter, the overall uncertainty of the wicking height measurement is estimated to be ±12 m in the case of on-axis detection, and ±24 m in the case of off-axis detection.     

Solution of the linearized couette-flow problem in a rarefied gas by the integral-diffusion method

In ordinary diffusion theory the transfer of properties is determined by the local gradients of the corresponding fields. As the mean free path increases, the flux density becomes an integral quantity and is determined by a neighborhood of the point under consideration of the order of a few mean free paths. In a previous article [1], the author proposed a model for a one-dimensional transfer process in linear rarefield-gas problems based on the analogy with radiative transfer. The same approach, though without directional averaging, is used in the present paper to analyze the linearized Couette flow problem. The solution obtained here has the properties of the solution obtained by more exact methods based on the solution of the Boltzmann equation [3-4].Nomenclature p_xy shear stress - c mean thermal velocity of molecules - 2/3 A mean free path - d half-width of channel - ±w₀ plate velocity - c nonequilibriumvalue of momentum flux density - y transverse coordinate - ratio of specific heats - W dimensionless velocity - P_xy shear stress scaled with respect to the shear stress in free-molecule flow - Y dimensionless coordinate - W₁(y) velocity distribution according to Millikan's solution - coefficient of viscosity - R Reynolds number - K Knudsen number     

Example of an exact solution of the stationary problem of two-layer flows with evaporation at the interface

Stationary two-layer liquid and gas flows with fluid evaporation at the interface are studied. On the solid impermeable boundaries of the channel, no-slip conditions are satisfied and a linear temperature distribution along the longitudinal coordinate and a condition for the vapor concentration at the upper boundary are specified. On the thermocapillary interface, remaining undeformed, the following conditions are specified: kinematic and dynamic conditions, a condition for thermal flows with mass transfer, continuity conditions for the velocity, temperature, and mass balance, and a relation for the saturated vapor concentration. An exact solution of the stationary problem for a given gas flow rate is obtained. Examples of velocity profiles are given for stationary flows of the ethanol-nitrogen system under normal and reduced gravity are given. The effect of longitudinal temperature gradients specified at the boundaries of the channel on the flow pattern is investigated.     

Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer

Simultaneous dual-plane PIV experiments, which utilized three cameras to measure velocity components in two differentially separated planes, were performed in streamwise-spanwise planes in the log region of a turbulent boundary layer at a moderate Reynolds number (Re 1100). Stereoscopic data were obtained in one plane with two cameras, and standard PIV data were obtained in the other with a single camera. The scattered light from the two planes was separated onto respective cameras by using orthogonal polarizations. The acquired datasets were used in tandem with continuity to compute all 9 velocity gradients, the complete vorticity vector and other invariant quantities. These derived quantities were employed to analyze and interpret the structural characteristics and features of the boundary layer. Sample results of the vorticity vector are consistent with the presence of hairpin-shaped vortices inclined downstream along the streamwise direction. These vortices envelop low speed zones and generate Reynolds shear stress that enhances turbulence production. Computation of inclination angles of individual eddy cores using the vorticity vector suggests that the most probable inclination angle is 35° to the streamwise-spanwise plane with a resulting projected eddy inclination of 43° in the streamwise-wall-normal plane.

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Heat transfer process in turbulent flows

A system of differential equations is proposed to describe turbulent flows of incompressible fluid boundary layer type with constant thermophysical characteristics A turbulent temperature conductivity is introduced which is expressed in terms of the energy and scale of turbulence, the dimensionless gradients of the mean velocity and turbulence energy, and the dimensionless distance, to the surface being streamlined. This system is integrated on an electronc computer by the mesh method for the flow in a flat-plate boundary layer with different Prandtl numbers (0.2P100) For air (P=0.71) the system is integrated for nonzero values of the transverse mean velocity component on the streamlined surface (0v_W/U0.0045).Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 18–24, July–August, 1972.     

The accuracy of turbulent velocity component measurements by multi-sensor hot-wire probes: a new approach to an old problem

The measurement accuracy of different hot-wire probes possessing between two and 12 sensors is analyzed. Experimental data were sampled in a round free jet and in a zero-pressure-gradient turbulent boundary layer by a 12-sensor hot-wire probe. Testing of the various hot-wire configurations is enabled by selectively considering different combinations of the 12 available anemometer output voltages. The influence on the measurement accuracy of neglecting the velocity gradients as well as neglecting one velocity component is analyzed. Two approaches were applied. One is based on expressions that relate the instantaneous velocity components and velocity gradients, and the other is based on a simple least-squares regression method. It is found that neglecting the instantaneous fluctuations of the velocity gradients for the measurement of the cross-stream velocity component, V, has a crucial influence and results in large errors. It is also shown that this influence is less significant or even negligible for the measurement accuracy of the other two velocity components, U and W.