On the accuracy of velocity and vorticity measurements with PIV

A number of numerical techniques aimed at improving the accuracy of measurements using the correlation approach in Particle Image Velocimetry, PIV, are proposed and investigated. In this approach the velocity (displacement) is found as the location of a peak in the correlation map. Based on an experimental model the best performing peak finding approaches are selected among different strategies. Second, an algorithm is proposed which minimizes errors on the estimates of vorticity using velocity distributions obtained by means of PIV. The proposed methods are experimentally validated against a flow with known properties. Work supported by NASA Ames Research Center     

Transverse velocity and temperature derivative measurements in grid turbulence

The same probe, comprising two parallel wires, is used to measure either velocity or temperature derivatives in shearless grid turbulence at a Taylor microscale Reynolds number of about 40. The aerodynamic interference of the probe affects the mean velocity when the transverse separation jy between the wires is smaller than about 3m, where m (ۂ.4 mm for the present experiments) is the Kolmogorov length scale, but not the mean temperature. Spectra and corresponding moments of transverse velocity and temperature derivatives are significantly but similarly affected when jyh3m, thus suggesting that this effect is more likely to be caused by electronic noise than aerodynamic interference. Indeed, after noise corrections are applied, the resulting derivative variances are brought into alignment with values inferred from two-point correlations with respect to y. Transverse derivative variances and their corresponding spectra satisfy isotropy closely but second-order structure functions satisfy it only when the separation is less than about 10m, i.e. the dissipative range scales.     

A note on wind-tunnel turbulence measurements with DPIV

At moderate Reynolds numbers (10⁴ ≤ Re ≤ 10⁵), the performance of lifting surfaces is strongly affected by the potential for laminar boundary layer separation and subsequent reattachment and the use of high-quality, low-turbulence wind tunnels is essential in characterising flight at comparatively small scales (where the wing chord may be from 1 to 5 cm in length) and low speeds (on the order of 10 m/s). Measurement of the existing turbulence levels in such facilities is hard and has not been achieved using DPIV methods due to the relatively small bandwidth of measurable velocities. A series of experiments is reported here where DPIV sampling parameters are driven beyond their normal range in an attempt to measure turbulence levels in a low turbulence wind tunnel. The results show that DPIV can measure the background turbulence, and therefore its instantaneous structure. The measurements also reveal certain challenges in investigating the aerodynamic performance of small-scale flying devices.     

Volumetric velocity measurements of vortex rings from inclined exits

Vortex rings were generated by driving pistons within circular cylinders of inner diameter D = 72.8 mm at a constant velocity U ₀ over a distance L = D. The Reynolds number, U ₀ L/(2ν), was 2500. The flow downstream of circular and inclined exits was examined using volumetric 3-component velocimetry (V3V). The circular exit yields a standard primary vortex ring that propagates downstream at a constant velocity and a lingering trailing ring of opposite sign associated with the stopping of the piston. By contrast, the inclined nozzle yields a much more complicated structure. The data suggest that a tilted primary vortex ring interacts with two trailing rings; one associated with the stopping of the piston, and the other associated with the asymmetry of the cylinder exit. The two trailing ring structures, which initially have circulation of opposite sign, intertwine and are distorted and drawn through the center of the primary ring. This behavior was observed for two inclination angles. Increased inclination was associated with stronger interactions between the primary and trailing vortices as well as earlier breakdown.     

Skewness factor of turbulent velocity derivative

Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence approaches a constant −0.515 when the Reynolds number is very high, which is in agreement with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991). The project supported by the National Basic Research Program “Non-linear Science”     

Visualization and two-color DPIV measurements of flows in circular and square coaxial nozzles

 High-resolution, reactive Mie scattering laser-sheet visualizations, two-color digital particle image velocimetry (DPIV) and thermal anemometry measurements in flows generated by equivalent coaxial circular and square jets are presented. Visualization results were obtained for three square, coaxial configurations, and a reference circular coaxial nozzle, at two Reynolds numbers of the outer jet (19,000 and 29,000) and for inner-to-outer jet velocity ratios of 0.15, 0.22, and 0.3. These indicated that the internal unmixed region diminished with decreasing velocity ratio. Strong evidence of unsteady recirculation and back-flow was observed at the end of the core of the inner jet, for the low velocity ratios. Comparisons between circular and square jet configurations indicated considerable mixing enhancement when square nozzles were used. Low-coherence, organized large-scale structure was evident from the visualizations and DPIV measurements near the origin of the inner mixing-region shear layers, and more so in the core region of the near field. These observations were confirmed by velocity spectra, which displayed peaks corresponding to a free shear-layer instability mode in the inner mixing-region shear layers, and a wake-type mode in the core region where the mean flow has a wake-like character. Although some large-scale structure was observed in the outer mixing layer during the visualizations, this was found to be incoherent on the basis of the DPIV measurements and the velocity spectra. It is noted that no axis-switching phenomena were observed in the square nozzle flows examined here. This is attributed to the absence of an organized structure in the outer shear layer, which was initially highly turbulent, and the weakly coherent nature of the organized structure observed in the inner mixing-region near field. Received: 2 November 1998/Accepted: 8 September 2000     

Improvements to PIV image analysis by recognizing the velocity gradients

Two iterative PIV image processing methods are introduced, which utilize displacement and deformation of the interrogation areas to maximize the correlation. The velocity gradients used for the window deformation are iteratively estimated directly from the images and no velocity values are required from neighbouring interrogation areas, as with numerical differentiation. The improved accuracy and resolution of the velocity gradient estimation compared to numerical differentiation is shown using synthetic images. The performance in a real application is shown using experimental reference images.     

Use of simultaneous IR temperature measurements and DPIV to investigate thermal plumes in a thick layer cooled from above

 Simultaneous measurements of surface temperature and the underlying velocity field are presented for a thick horizontal layer evaporatively cooled from above. Previous studies have focused on either the temperature field at the cooled surface or, in a small number of cases, on point velocity measurements in the flow. The current investigation is, to the knowledge of the authors, the first to simultaneously and non-intrusively document both the surface temperature and underlying velocity field in this type of flow. An infrared (IR) sensing array was used to capture the instantaneous free surface temperature field while two-dimensional velocity measurements in planes either perpendicular or parallel to the free surface were acquired using digital particle image velocimetry (DPIV). Data from two cases are discussed. Received: 19 January 1998/Accepted: 22 October 1998     

Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data

 A study of the errors in out-of-plane vorticity (ω _z ) calculated using a local χ² fitting of the measured velocity field and analytic differentiation has been carried out. The primary factors of spatial velocity sampling separation and random velocity measurement error have been investigated. In principle the ω _z error can be decomposed into a bias error contribution and a random error contribution. Theoretical expressions for the transmission of the random velocity error into the random vorticity error have been derived. The velocity and vorticity field of the Oseen vortex has been used as a typical vortex structure in this study. Data of different quality, ranging from exact velocity vectors of analytically defined flow fields (Oseen vortex flow) sampled at discrete locations to computer generated digital image frames analysed using cross-correlation DPIV, have been investigated in this study. This data has been used to provide support for the theoretical random error results, to isolate the different sources of error and to determine their effect on ω _z measurements. A method for estimating in-situ the velocity random error is presented. This estimate coupled with the theoretically derived random error transmission results for the χ² vorticity calculation method can be used a priori to estimate the magnitude of the random error in ω _z . This random error is independent of a particular flow field. The velocity sampling separation is found to have a profound effect on the precise determination of ω _z by introducing a bias error. This bias error results in an underestimation of the peak vorticity. Simple equations, which are based on a local model of the Oseen vortex around the peak vorticity region, allowing the prediction of the ω _z bias error for the χ² vorticity calculation method, are presented. An important conclusion of this study is that the random error transmission factor and the bias error cannot be minimised simultaneously. Both depend on the velocity sampling separation, but with opposing effects. The application of the random and bias vorticity error predictions are illustrated by application to experimental velocity data determined using cross-correlation DPIV (CCDPIV) analysis of digital images of a laminar vortex ring. Received: 31 October 1997/Accepted: 6 February 1998     

The effects of air bubbles on ultrasound velocity measurements

We report on experiments on the effects of air bubbles on ultrasound velocity measurements in fluids. We used an acoustic Doppler velocimeter system for measuring the three velocity components in a single point and an acoustic Doppler velocimetry profiler system for measuring axial velocity in several points along the beam. The results suggest that both systems essentially measure the velocity of the bubbles, independent of the low air-volume concentration and of bubble radii in the flow field.     

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.     

Using stereo multigrid DPIV (SMDPIV) measurements to investigate the vortical skeleton behind a finite-span flapping wing

The structure of the flow behind wings with finite span (3D) is significantly more complex than the flow behind infinite span (2D) wings. It has been shown that the presence of wingtip vortices behind finite span wings significantly modifies the geometry of the wake flow. It is felt that this modification alters the dynamics of interaction between leading and trailing edge vorticity in a manner that affects the ability of 2D flapping wings to produce thrust. A model of the mean flow skeleton has been proposed from qualitative flow visualization experiments. An unambiguous quantitative representation of the actual flow is required for comparison to the proposed model. To accomplish this the full 3D 3C velocity is required in the volume behind the 3D flapping wing. It is proposed to use stereoscopic multigrid digital particle image velocimetry (SMDPIV) measurements to investigate this unsteady oscillatory flow. This paper reports preliminary SMDPIV measurements along the plane of a symmetrical NACA-profile wing at a Strouhal number of 0.35. Phase averaged measurements are used to investigate the complex flow topology and the influence of the forcing flow on the evolution of the large scale structure of a jet-flow. This paper focuses on optimizing the SMDPIV experimental methodology applied to liquid flows. By refining the 2D 3C technique, the 3D topology of the flow can be investigated with a high degree of accuracy and repeatability. Preliminary results show that the flow is characterized by two pairs of coherent structures of positive and negative vorticity. The arrangement of these structures in the flow is controlled by the motion of the wing. Vorticity of opposite rotation is shed at the extreme heave and pitch positions of the aerofoil to set up a thrust indicative vortex street in support of the suggested topological model.     

Non-intrusive measurements of bubble size and velocity

A non-intrusive measuring technique based on video-imaging has been developed for the measurement of bubble size, velocity and frequency. Measurements carried out with this method have been compared to those obtained by an optimized phase-Doppler system in standard configuration, for a wide range of bubble sizes produced from single injectors in a quiescent environment. The two measuring techniques have yielded velocities and frequencies that are in very good agreement while the size of spherical bubbles was consistently measured by both methods. The phase-Doppler system was also used to size oblate-spheroidal bubbles moving with their equatorial plane parallel to the scattering plane, yielding measurements reasonably close to the average radius of curvature of the bubbles in the neighborhood of the equatorial plane, as calculated from the video-imaging data. Both methods were used for detailed velocity measurements of the bubble-stream in the neighborhood of the injector tip. The observed bubble-velocity variation with the distance from the injector tip does not always display the usual increasing trend leading into the terminal velocity. When injection conditions are near the transition from discrete to jet injection mode and the bubbles are small, the latter decelerate into a terminal velocity due to direct interaction of successive bubbles at the injector tip. The measured terminal velocities of bubble-chains for a variety of bubble sizes and injection frequencies, are successfully predicted by using a far-field wake approximation to account for the drafting effect which is responsible for bubble-chain velocities higher than those of single bubbles.The authors gratefully acknowledge the support from the Louisiana Board of Reagents through grants LEQSF (1991-1992)-ENH-31 and LEQSF (1990-1992)-RD-A-07, ARCO Chemical Company through it's University Grants Program and the National Science Foundation through its Graduate Fellowship Program.     

Morphology estimation from normal stress measurements for dilute immiscible polymer blends

A method to obtain gross blend morphological information from normal stress measurements is proposed. The blend consists of Newtonian and immiscible constituents in dilute conditions. It is shown that a master curve for the first normal stress difference (N1) can be readily obtained either theoretically or experimentally. The curve is parametric in the viscosity ratio, and relates the actual capillary number to the dimensionless interfacial stress. As a consequence, N1 data determine a capillary number through which a characteristic dimension of the morphology can be estimated. Since globular morphology is typical in dilute conditions, as an example the master curve is here calculated by using a phenomenological model to describe single drop deformation. Morphology predictions are compared with experimental data found in the literature; the comparisons give satisfactory results even up to intermediate concentrations.     

On estimation of entrance boundary parameters from downstream measurements using adjoint approach

An estimation of entrance boundary conditions from the downstream measurements is considered in variational statement form for two‐dimensional supersonic laminar flow. The adjoint problem is used for the calculation of the discrepancy gradient in space of control parameters. The numerical tests presented demonstrate the successful estimation of boundary parameters of spatial distribution by using gradient methods. Copyright © 2001 John Wiley & Sons, Ltd.