Phase-resolved PIV measurements in a transitional plane wall jet: a numerical comparison

The transitional process of a forced plane wall jet is studied both experimentally and numerically. Experimentally, Particle Image Velocimetry (PIV) and laser-sheet/smoke flow-visualization techniques are implemented to provide an overall understanding of the flow features. Numerically, time-accurate computational results are obtained by solving the two-dimensional, unsteady Navier–Stokes equations. Comparison of PIV data and two-dimensional computed results shows excellent agreement in the early stages of transition, demonstrating that the numerical study can be used to complement the experimental one. The results show that, under the influence of external excitation, linear-instability growth is bypassed and a discrete shear-layer vortex is formed in the immediate vicinity of the nozzle exit. This vortex interacts with the boundary-layer vorticity, leading to the formation of another vortex in the inner layer. These two vortices form a vortex couple that for high forcing convects downstream in a stable manner. By adoption of either a no-slip or a slip boundary condition in the numerical computation, it is determined that the flow development is relatively insensitive to the imposed wall-boundary condition. This seems to suggest that the physical mechanism leading to the formation of the boundary-layer vortex is an inviscid rotational one. Received: 14 February 1998/Accepted: 11 August 1998     

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

Rayleigh scattering temperature measurements in a plane turbulent air jet at moderate Reynolds numbers

Rayleigh scattering temperature measurements were made in a slightly heated plane jet at various Reynolds numbers and the effect of this parameter on the temperature field was determined. The axial and lateral distributions of the mean and rms temperature as well as the temperature spectra along the jet axis were determined. Results indicated that increasing Reynolds numbers led to lower levels of rms temperature and jet dilution in the moderate Reynolds number regime (between 700 and 2500). It was also found that slower spread rates of the thermal jet occured with larger Reynolds numbers in this regime.List of symbols b _T temperature half-width of the jet - C calibration constant for Rayleigh scattering optics - C _T, C _T,0 constants defining the temperature decay rate - D nozzle width - E _T power spectrum of temperature fluctuations - f frequency - I _L laser light intensity - I _R Rayleigh signal intensity - K _T, K _T,0 constants defining the jet spread rate - k wavenumber (2f/ U) - N total molecular number density - Re Reynolds number (U ₀D/) - T mean excess temperature - T _m mean excess temperature on the jet axis - T ₀ mean excess temperature at jet exit - T fluctuating temperature - U local mean velocity - U ₀ mean velocity at the jet exit - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - Rayleigh scattering cross section - density - kinematic viscosity A version of this paper was presented as paper no 86-WA/ HT-98 at the 1986 ASME Winter Annual Meeting.     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.     

Free and confined jets at low Reynolds numbers

Free jets, and jets with tubular confinements, are investigated in the jet Reynolds number regime 80 Re_j 1000 being of interest for micro-jet pumps, among other applications. For issuing the jets, conventional (single-hole) nozzles as well as dual-hole nozzles of a particular design are used. Both flow visualization and LDA measurement indicate that, in agreement with previous findings, the jets issuing from conventional nozzles remain laminar up to large distances from the orifice. Thus there is but little entrainment of ambient fluid, and the performance of conventional nozzles in micro-jet pumps is rather poor. The dual-hole nozzles, on the other hand, are found to enforce transition to turbulent flow near the orifices. As a result, the entrainment rate is considerably increased, and the performance of jet pumps is improved when the dual-hole nozzles are applied. The experimental data are found to be in fair agreement with predictions based on mass and momentum balances.     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Turbulence characterisation of a confined jet using PIV

The turbulence in the bulk free region of a confined jet is investigated using a simple video-based particle image velocimetry technique. The latter, which relies on the interlacing properties of video filming and simple particle tracking concepts, is suitable for less dense seeding levels and lower flow velocities. The results obtained for the turbulence intensity variation in the jet agree with known data from literature. Spatially resolved integral length scales are calculated, and a relation for Eulerian-type length scales is proposed.     

The effect of slot jet size on the confined transverse slot jet

The current study explored the flowfield characteristics of an induced recirculation zone resulting from a transverse slot jet issuing in a cross flow. The slot jet spanned 95% of the full channel spanwise dimension which resulted in a highly three-dimensional mean flowfield. Experimental investigations were carried out at various jet momentums for two different transverse slot jet thicknesses. Velocity field data were gathered using digital particle image velocimetry and hot-wire anemometry. The momentum ratio of the jet to the channel was found to be the leading parameter for scaling the dimensions of the mean recirculation zone. The jet thickness demonstrated an influence on the level of three-dimensionality, turbulence levels, and integral length scales.     

The development of a plane laminar flow at low Reynolds numbers

Summary The development of a plane Poiseuille flow at low Reynolds numbers is studied; given any velocity distribution in the section x=0, it is possible to evaluate its evolution along the direction of motion, by means of quite simple calculation. A numerical example is also given.

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Sommario Si esamina l'evoluzione del profilo di velocità in moto piano laminare a bassi numeri di Reynolds. Assegnata una qualsiasi distribuzione di velocità nella sezione x=0, è possibile calcolare come questa si modifichi lungo il percorso. Si fornisce un esempio numerico.

     

Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes

We present a comparative analysis of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) computed from experimental data of a turbulent, quasi 2-D, confined jet with co-flow (Re?=?11,500, co-flow ratio inner-to-outer flow ≈2:1). The experimental data come from high-speed 2-D particle image velocimetry. The flow is fully turbulent, and it contains geometry-dependent large-scale coherent structures; thus, it provides an interesting benchmark case for the comparison between POD and DMD. In this work, we address issues related to snapshot selections (1), convergence (2) and the physical interpretation (3) of both POD and DMD modes. We found that the convergence of POD modes follows the criteria of statistical convergence of the autocovariance matrix. For the computation of DMD modes, we suggest a methodology based on two criteria: the analysis of the residuals to optimize the sampling parameters of the snapshots, and a time-shifting procedure that allows us to identify the spurious modes and retain the modes that consistently appear in the spectrum. These modes are found to be the ones with nearly null growth rate. We then present the selected modes, and we discuss the way POD and DMD rank them. POD analysis reveals that the most energetic spatial structures are related to the large-scale oscillation of the inner jet (flapping); from the temporal analysis emerges that these modes are associated with a low-frequency peak at St?=?0.02. At this frequency, DMD identifies a similar mode, where oblique structures from the walls appear together with the flapping mode. The second most energetic group of modes identified is associated with shear-layer oscillations, and to a recirculation zone near the inner jet. Temporal analysis of these modes shows that the flapping of the inner jet might be sustained by the recirculation. In the DMD, the shear-layer modes are separated from the recirculation modes. These have large amplitudes in the DMD. In conclusion, the DMD modes with eigenvalues on the unit circle are found to be similar to the most energetic POD modes, although differences appear due to the fact that DMD isolates structures associated with one frequency only.     

PIV measurements of flow past a confined cylinder

This study investigates the flow past a confined circular cylinder built into a narrow rectangular duct with a Reynolds number range of 1,500 ≤ Re _d ≤ 6,150, by employing the particle image velocimetry technique. In order to better explain the 3-D flow behaviour in the juncture regions of the lower and upper plates and the cylinder, respectively, as well as the dynamics of the horseshoe vortex system, both time-averaged and instantaneous flow data are presented for regions upstream and downstream of the cylinder. The size, intensity and interaction of the vortex systems vary substantially with the Reynolds number. Although the narrow rectangular duct with a single built-in cylinder is a geometrically symmetrical arrrangement, instantaneous flow data have revealed that the flow structures in both the lower and upper plate–cylinder junction regions are not symmetrical with respect to the centreline of the flow passage. The vortical flow structures obtained in side-view planes become dominant sometimes in the lower juncture region and sometimes in the upper juncture region in unsteady mode.     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.     

Tomographic PIV measurements in a turbulent lifted jet flame

Measurements of instantaneous volumetric flow fields are required for an improved understanding of turbulent flames. In non-reacting flows, tomographic particle image velocimetry (TPIV) is an established method for three-dimensional (3D) flow measurements. In flames, the reconstruction of the particles location becomes challenging due to a locally varying index of refraction causing beam-steering. This work presents TPIV measurements within a turbulent lifted non-premixed methane jet flame. Solid seeding particles were used to provide the 3D flow field in the vicinity of the flame base, including unburned and burned regions. Four cameras were arranged in a horizontal plane around the jet flame. Following an iterative volumetric self-calibration procedure, the remaining disparity caused by the flame was less than 0.2 pixels. Comparisons with conventional two-component PIV in terms of mean and rms values provided additional confidence in the TPIV measurements.     

Spherical particle sedimentation along an inclined plane at high Reynolds numbers

At high Reynolds numbers (10²Re _p <10⁵), the gravity-driven motion of a solid spherical particle along an inclined surface in a Newtonian liquid at rest was studied experimentally. The parameters which determine the particle drag coefficient and its relation with the hydrodynamic force component normal to the wall were obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1996.     

Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers

The phenomenon of low amplitude self-sustained pitch oscillations in the transitional Reynolds number regime is studied numerically through unsteady, two-dimensional aeroelastic simulations. Based on the experimental data, simulations have been limited in the Reynolds number range 5.0×10⁴<Re_c<1.5×10⁵. Both laminar and URANS calculations (using the SST k–ω model with a low-Reynolds-number correction) have been performed and found to produce reasonably accurate limit cycle pitching oscillations (LCO). This investigation confirms that the laminar separation of the boundary layer near the trailing edge plays a critical role in initiating and sustaining the pitching oscillations. For this reason, the phenomenon is being labelled as laminar separation flutter. As a corollary, it is also shown that turbulence tends to inhibit their existence. Furthermore, two regimes of LCO are observed, one where the flow is laminar and separated without re-attachment, and the second for which transition has occurred followed by turbulent re-attachment. Finally, it is established that the high-frequency, shear instabilities present in the flow which lead to von Kármán vortex shedding are not crucial, nor necessary, to the maintaining mechanism of the self-sustained oscillations.