PIV measurements of the flow field inside an enclosed cubical cavity in natural convection

The natural convective velocity field in an enclosed air-filled cubical cavity with two opposing isothermal faces and the remaining four sides having a well-defined linear temperature rise from the cold to the hot face has been measured at different physical orientations and Rayleigh (Ra) numbers. In particular, two components of the velocity at the mid-plane have been measured by using particle image velocimetry (PIV) at Ra = 10⁶ and 6 × 10⁶ at each of two different physical orientations: heating-from-the-side (HFS), and heating-from-below (HFB). The 95% confidence limit uncertainties in the measured velocity vectors are about 2% for laminar flow. The accuracy and integrity of the experiments were validated by the comparison to some well-established CFD results at the HFS orientation at Ra = 10⁶. It was concluded that the experimental method is sound and so findings at other orientations and at other values of Ra should have an accuracy consistent with the findings of the uncertainty analysis. Therefore, the other results can be confidently used as benchmark data for testing CFD codes. The turbulence intensities at the mid-plane are also presented.     

Stereoscopic PIV: validation and application to an isotropic turbulent flow

 A new stereoscopic PIV system to measure the three velocity components is developed and applied to grid turbulence flows. This system uses two CCD cameras coupled with an accurate cross-correlation calculation method. An experimental test (based upon three-dimensional displacements) has been carried out to demonstrate the capability of this process to locate the maximum of correlation, and to detect accurately the 3D displacements. Experiments in a well-established turbulent flow have validated the method for quantitative measurements and a comparison with LDV results showed a good agreement in terms of mean and fluctuating velocities. Combined PIV and stereoscopic PIV measurements on a turbulent flow revealed the need to the stereoscopic systems to measure accurate 2D velocity fields. It has been shown that an error of up to 10% in the velocity fluctuation measured by conventional PIV could be attained due to 3D effects in highly turbulent cases. Finally, the digital cross-correlation technique adapted to the determination of small displacements seems to be the most suitable technique for stereoscopic PIV. Received: 22 July 1997/Accepted: 27 January 1998     

Wall pressure fluctuations of a turbulent separated and reattaching flow affected by an unsteady wake

The spatio-temporal characteristics of the wall-pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated through pressure-velocity joint measurements carried out using multiple-arrayed microphones and split-film probes. A spoke-wheel-type wake generator was installed upstream of the backward-facing step. The flow structure at the effective forcing frequency (St _f=0.2) was found to be well organized in terms of wall pressure spectrum, cross-correlation, wavenumber-frequency spectrum, and wavelet auto-correlation. Introduction of the unsteady wake (St _f=0.2) reduced the reattachment length by 10%. In addition, the unsteady wake enhanced the turbulence intensity near the separation edge and, as a consequence, enhanced the quadrupole sound sources; however, the turbulence intensity near the reattachment region was weakened and the overall flow noise was attenuated. The greater organization of the flow structure induced by the unsteady wake led to a weakening of the dipole sound sources, which are the dominant sound sources in this system. The dipole sound sources generated by wall pressure fluctuations were calculated using Curles integral formula.Abbreviations AR Aspect ratio - SBF Spatial box filtering Roman symbols C _p Wall pressure fluctuation coefficient, p/0.5U ² - H Step height of backward-facing step (mm) - H _s Shape factor (H _s = ^*/) - R _s Distance from acoustic source point to observation point (m) - Re _H Reynolds number, U H/ - St The reduced frequency, fH/U - St _f Normalized forcing frequency by unsteady wake, f _p H/U - T Vortex shedding period (s) - U Free-stream velocity (m/s) - a Speed of sound (m/s) - f Frequency (Hz) - f _p Wake passing frequency (Hz) - k Turbulent kinetic energy (m²/s²) - k _x Streamwise wave number (1/m) - k _z Spanwise wave number (1/m) - l _j Cosine of angle - p Instantaneous wall pressure (Pa) - p _rms Root-mean-square of wall pressure (Pa) - p _SBF Spatial box filtered wall pressure (Pa) - p _d Dipole sound source (Pa) - p _w Conditionally-averaged wall pressure (Pa) - q Dynamic pressure, 0.5U ² (Pa) - r Distance from origin to observation point (mm) - u _c Convection velocity (m/s) - u_max Root-mean-square of streamwise velocity (m/s) - x _R Time-mean reattachment length (mm) Greek symbols _p Forward-flow time fraction - Auto-correlation of pressure at x ₀ - Two-dimensional cross-correlation of pressure with streamwise separation interval , spanwise separation interval , and time delay , at (x ₀, z ₀) - Boundary layer thickness (mm, _99%) - ^* Displacement thickness (mm, ) - _ij Kroneckers delta function - Phase angle (°) - Wavelength (mm) - Momentum thickness (mm, ) - Angle between vertical axis and observation point (°) - Density (kg/m³) - Time delay (s) - Streamwise separation interval (m) - Spanwise separation interval (m) - _p (f; x ₀) Autospectrum of pressure measured at x ₀ (Pa² s) - _pp (, ; x ₀) Streamwise cross spectrum of pressure at x ₀ (Pa² s) - _pp (, , ; x ₀, z ₀) Streamwise and spanwise cross spectrum of pressure at (x ₀, z ₀) (Pa² s) - _pp (kx, ; x ₀) Streamwise wavenumber-frequency spectrum of pressure at x ₀ (Pa² s) - _pp (kx, kz, ; x ₀, z ₀) Two-dimensional wavenumber-frequency spectrum of pressure at (x ₀, z ₀) (Pa² s)     

Improvement of a pressure gradient method and its application to an unsteady flow problem

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.     

3-D scanning-particle-image-velocimetry: Technique and application to a spherical cap wake flow

A 3-D time-resolving and whole-volume Digital-Particle-Image-Velocimetry (DPIV) technique based on the concept of a scanning light-sheet is presented and applied here to the 3-D transient wake phenomena in the spherical cap wake flow. The technique uses a scanning light-sheet for rapid sampling of the flow in depth and a two-camera recording system for stereoscopic 3-D DPIV. Application of a correlation technique in combination with a calibration yields, aside from the correct in-plane displacement, also the out of plane component and thus the total velocity vectors within the planes of the scanning light-sheet. With a high scanning rate in comparison to the characteristic time scales the method provides the 3-D velocity field in space and time. Through the use of conventional video-techniques the temporal evolution of the complete velocity and vorticity field can be obtained quantitatively from experiments. This is demonstrated for the 3-D starting flow around a spherical cap at Re=300. During the starting process, the flow in the wake evolves into a spherical vortex ring where the velocity distribution is very close to the theoretical solution of the Hill-type vortex. Later on, the Hill-type vortex ring deforms and the flow changes from a rotational symmetric stage to a planar symmetric flow with a double-threaded vortical structure which consists of two counter-rotating streamwise vortices similar to the ones observed in sphere wake flow.Presented at the EUROMECH Coll. 335, Image Techniques and Analysis in Fluid Dynamics, 5–7 June 1995, Roma, Italy. A version of this paper has been published in Proc. 7th Int. Symp. Flow Visualization (ed. J.P. Crowder), Begell House Inc., New York, 1995, pp. 715–720.     

The two-dimensional velocity shift caused by the use of a rotating mirror in PIV flow field measurements

A theoretical analysis of the two-dimensional velocity shift by the use of a rotating mirror in PIV flow field measurements has been carried out by the application of ray optics. The velocity shift has been calculated directly in the flow field co-ordinates. In dimensionless form the results are also available in the image plane. It is shown that the distribution of the velocity shift over the entire observation field may not usually be assumed to be uniform (and may vary by up to 20%). The effect of the layout and arrangement of the rotating mirror on the velocity shift and its distribution has been analysed. In addition, the sensitivity of the velocity shift to the design tolerances and imperfections of the rotating mirror is given.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.     

A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.     

Comparison of velocity and temperature measurements with simulations in a hypersonic wake flow

A hypersonic shock-tunnel flow around an axisymmetric model of a planetary entry probe is analyzed. Planar laser-induced fluorescence is applied to measure both the velocity and the rotational temperature everywhere in the central plane of the flow field. The experimental test case is compared to simulations using the direct simulation Monte Carlo (DSMC) method. While the Mach 9.7 flow at a freestream Reynolds number based on the model diameter of 35,000 is chemically frozen, effects of thermal non-equilibrium and localized rarefaction cannot be neglected. DSMC and measurements agree well within the outer wake, but disagree close to the centerline, where in particular the measured velocity is higher than values predicted by the simulations. The experimental results indicated a shorter recirculation region and increased local fluctuations in the free shear layer upstream of the wake recompression shock when compared to the simulation. These effects are attributed to incipient transition, which is not observed in the simulations, as the simulations did not model the effects of freestream fluctuations. Furthermore, measured and simulated vorticities are compared with theoretical predictions.     

The application of stereoscopic PIV to measure the flow of air into an enclosure containing a fire

Flow fields encountered in full-scale enclosure fires are highly three-dimensional and span a large spatial extent. Stereoscopic particle image velocimetry (SPIV) was applied to provide a large-scale planar interrogation of the flow of air available to a series of fires burning inside an enclosure. Time-averaged velocity fields across the doorway of the enclosure are presented. These flows are bi-directional and SPIV reveals that the time-averaged height of the region of flow reversal depends on location within the doorway. The volume flow rate of available air computed from the classical one-dimensional flow approach agrees well with the numerical integration using the velocity field provided by SPIV. Good agreement between the measured velocities for SPIV configurations optimized for seed particle displacements along the laser sheet axis and optimized for displacements perpendicular to the laser sheet demonstrate that large-scale SPIV measurements can be conducted with very good precision.     

Multilevel methods for temporal and spatial flow transition simulation in a rough channel

We investigate the instability of 2D incompressible flows in a rough planar channel by tracking the growth of the unstable mode in its early stage. We develop both second- and fourth-order finite difference methods on a staggered grid, together with a fully implicit time-marching scheme, using grid generation to accommodate fairly general geometries. A multigrid full approximation scheme based on the line-distributive relaxation method is used for fast convergence. For a 2D smooth channel, numerical results show good agreement with the analytic solution obtained from linear theory for small disturbances. Numerical results for a 2D channel with one and two roughness elements are analysed by Fourier analysis. They show how the roughness elements affect the growth of the perturbation.     

A novel PIV technique for measurements in multiphase flows and its application to two-phase bubbly flows

A new experimental procedure for performing simultaneous, phase-separated velocity measurements in two-phase flows is introduced. Basically, the novel particle image velocimetry (PIV) technique is a combination of the three most often used PIV techniques in multiphase flows: PIV with fluorescent tracer particles, shadowgraphy, and the digital phase separation with a masking technique. The combination of these three independent measurement techniques is achieved by shifting the background intensity of a PIV recording to a higher, but uniform gray value level. In order to combine the advantages of these multiphase-PIV methods, a new PIV set-up was developed. With this set-up the velocity distributions of the two phases are measured simultaneously with only one b/w camera. This experimental set-up is aimed at providing a means for characterizing the modification of turbulence in the liquid phase by bubbles. This phenomenon is often called "pseudo-turbulence".     

Simultaneous PIV and thermography measurements of partially blocked flow in a differentially heated rotating annulus

A radial barrier has been mounted in a differentially heated rotating annulus that partially blocks the azimuthal flow component. The experiment can be seen as an analog to geophysical flows with constrictions, e.g., the Antarctic Circumpolar Current. However, the experiment has been carried out without a particular natural flow in mind. The main interest was to observe a baroclinic annulus flow that does not become saturated. Hence, in contrast to the annulus flow without a barrier, the partially blocked flow remains transient and surface heat fluxes associated with baroclinic life cycles can be studied. The annulus can be subdivided into the upstream half of the barrier, where waves amplify, and the downstream half of the barrier, where waves decay. In the upstream half, the azimuthal mean flow is moderate but with a significant positive eddy radial heat flux. In the downstream half, we find a strong jet in the mean azimuthal flow and furthermore an increased radial mean temperature gradient. The latter points to a weakened or even reversed radial eddy heat flux in the lee side of the barrier. Temperature anomalies appear as large bulges in the outer part of the annulus. Moreover, an outward shift of vortex centers can be observed with respect to centers of temperature anomalies. This phase shift between pressure and temperature anomalies differs from that of classical Eady modes of baroclinic instability.     

Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder

PIV technique is applied for measurements of instant velocity distributions in a liquid film flowing down an inclined tube in the form of a wavy rivulet. An application of special optical calibration is applied to correct distortion effects caused by the curvature of the interface. A vortex flow of liquid is observed inside a wave hump in the reference system moving with wave phase velocity. Conditionally averaged profiles of longitudinal and transverse components of liquid velocity are obtained for different cross-sections of developed non-linear waves. It is shown that the increase in wave amplitude slightly changes the location of the vortex center. The analysis of modification of vortex motion character due to wavy flow conditions, such as tube inclination angle, film Reynolds number, wave excitation frequency, is fulfilled.     

PIV, 2D-LIF and 1D-Raman measurements of flow field,composition and temperature in premixed gas turbine flames

Several laser diagnostic measurement techniques have been applied to study the lean premixed natural gas/air flames of an industrial swirl burner. This was made possible by equipping the burner with an optical combustion chamber that was installed in the high-pressure test rig facility at the DLR Institute of Combustion Technology in Stuttgart. The burner was operated with preheated air at various operating conditions with pressures up to p = 6 bar and a maximum thermal power of P = 1 MW.The instantaneous planar flow field inside the combustor was studied with particle image velocimetry (PIV). Planar laser induced fluorescence (PLIF) of OH radicals on a single-shot basis was used to determine the shape and the location of the flame front as well as the spatial distribution of reaction products. 1D laser Raman spectroscopy was successfully applied for the measurement of the temperature and the concentration of major species under realistic gas turbine conditions.Results of the flow field analysis show the shape and the size of the main flow regimes: the inflow region, the inner and the outer recirculation zone. The highly turbulent flow field of the inner shear layer is found to be dominated by small and medium sized vortices. High RMS fluctuations of the flow velocity in the exhaust gas indicate the existence of a rotating exhaust gas swirl. From the PLIF images it is seen that the primary reactions happened in the shear layers between inflow and the recirculation zones and that the appearance of the reaction zones changed with flame parameters. The results of the multiscalar Raman measurements show a strong variation of the local mixture fraction allowing conclusions to be drawn about the premix quality. Furthermore, mixing effects of unburnt fuel and air with fully reacted combustion products are studied giving insights into the processes of the turbulence–chemistry interaction.     

A calibration technique for multiple-sensor hot-wire probes and its application to vorticity measurements in the wake of a circular cylinder

A calibration technique for multiple-sensor hot-wire probes is presented. The technique, which requires minimal information about the probe geometry, is tested using a four-sensor and a twelve-sensor probe. Two data reduction algorithms are introduced. The first one assumes a uniform velocity over the probe sensing-volume and is applied to the four-sensor probe measurements. The second one assumes a uniform velocity gradient over the sensing volume of the probe. The procedure, when applied to the twelve-sensor probe, is shown to measure the velocity gradient components successfully. In both algorithms, the unknowns (velocity and velocity gradient components) are obtained by solving the resulting systems of nonlinear algebraic equations in a least-squares sense. The performances of the probes and the algorithms are tested with measurements in the wake of a circular cylinder. The statistics and spectra show that the twelve-sensor probe is successful in the simultaneous measurement of all three components of the velocity and all three components of the vorticity vectors.     

Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution

As testified by a previous article (Astarita and Cardone in Exp Fluids 38:233–243, 2005), a critical point that can influence significantly the accuracy of image deformation methods (IDM) for particle image velocimetry (PIV) is the interpolation scheme (IS) used in the reconstruction of deformed images. In the cited paper the effect of noise has been neglected and for this reason in this follow-up paper the influence of the IS, in the presence of noise, on both accuracy and spatial resolution is studied. Performance assessment is conducted using synthetic images with particles of Gaussian shape and with constant and sinusoidal displacement fields. Both the local and the top hat moving average approaches are investigated and the modulation transfer function, the total and bias errors have been used to evaluate the performances of IDMs for PIV applications. The results show that, when a high noise level is present in the images, the influence of the IS is less relevant than what was shown by Astarita and Cardone (Exp Fluids 38:233–243, 2005).     

Synchronized analysis of an unsteady laminar flow downstream of a circular cylinder centred between two parallel walls using PIV and mass transfer probes

Experiments are carried out in the wake of a cylinder of d _c  = 10 mm diameter placed symmetrically between two parallel walls with a blockage ratio r = 1/3 and a Reynolds number varying between 75 ≤ Re ≤ 277. Particle image velocimetry is exerted to obtain the instantaneous velocity components in the cylinder wake. A snapshot proper orthogonal decomposition (POD) is also applied to these PIV results in order to extract the dominant modes through the implementation of an inhomogeneous filtering of these different snapshots, apart from an interpolation to estimate the wall shear rate at the lower wall downstream the cylinder. Mass transfer circular probes are placed at the lower wall downstream this obstacle so as to further determine the time evolution of the wall shear rate, by bringing the inverse method to bear on the convective-diffusion equation. Comparisons between the two synchronized techniques demonstrate that electrochemical method can give more accurate information about the coherent structures present in the flow and about the interaction of the von Kármán vortices with the walls of the tunnel as well. The comparison between the two measurement techniques in the flow regions concerns the spatiotemporal evolutions of the wall shear rate obtained from PIV measurements and the wall shear rate using mass transfer probes. Discrepancy between the PIV measurements and the electrochemical ones near the wall, where the secondary vortices P ₁′ are generated at wall, are caused by a PIV bias and a limitations of the singular mass transfer probes.     

Time and spatial correlation measurements in the turbulent wake of a circular cylinder using Laser Doppler Anemometry

The present paper reports Laser Doppler Anemometry (LDA) measurements in the turbulent (R _d =1300) wake of a circular cylinder (d=2 mm). On several typical locations in the wake, at cross-section x/d=125, temporal and lateral space velocity correlations have been measured. Temporal autocorrelation functions were determined from the randomly sampled LDA data by means of the Slotting Technique. The autocorrelation functions which were obtained were too low, the discrepancy giving an indication of the influence of noise in the measurements. The influence of noise generated by the photomultiplier tubes, which appeared to be the most important noise source, could be reduced by a cross-correlation technique. A partly new LDA system for two-point velocity correlation measurements was developed, consisting of an elongated measuring volume and a two-point detection system including a semireflecting mirror to divide the scattered light. The results of this investigation clearly demonstrate that LDA is a powerful tool for measuring time and spatial correlations and related properties of turbulence.