An investigation of the flow over a three-dimensional (3-D) double backward-facing step is presented using a combination of both quantitative measurements from a particle image velocimetry (PIV) system and qualitative oil-flow visualizations. The arrangement of the PIV instrument allows for snap-shots of the (x, y) and (y, z) planes at various axial and spanwise positions. The measurements illustrate characteristics that are found in both two-dimensional (2-D) backward-facing steps and 3-D flows around wall mounted cubes. In particular, the development of a horseshoe vortex is found after each step alongside other vortical motions introduced by the geometry of the model. Large turbulence levels are found to be confined to a region in the center of the backstep; their mean square levels being much larger than what has been observed in 2-D backward-facing steps. The large turbulent fluctuations are attributed to a quasi-periodic shedding of the horseshoe vortex as it continuously draws energy from the spiral nodes of separation, which form to create the base of the horseshoe vortex. A combination of effects including the shedding of the first horseshoe vortex, the horizontal entrainment of air and the presence of two counter rotating vortices initiated at reattachment, are shown to cause the steering vector of the flow to jettison away from the surface in the first redeveloping region and along the center at z/h = 0. Oil-flow visualizations confirm these observations.
Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flow’s nearfield regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity–pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthill’s analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D =75. Retarded time topologies of the predicted field at 90" and 30" are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m=0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows.
An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, !)-plane of the jet at discrete streamwise locations between x/D = 3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 at x/D = 3.0, and a gradual shift to azimuthal mode 2 by x/D = 8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 at x/D = 3.0, followed by a gradual decay to azimuthal mode 2 at x/D = 8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.
Results are presented from pressure measurements performed in the irrotational near field of unbounded co-axial jets. Measurements were made for a variety of velocity and temperature ratios, and configurations both with and without serrations on the secondary nozzle lip. The principal objective of the study is to better understand the near pressure field of the jet, what it can tell us regarding the underlying turbulence structure, and in particular how it can be related to the source mechanisms of the flow.
A preliminary analysis of the axial, temporal and azimuthal structure of the pressure field shows it to be highly organized, with axial spatial modes (obtained by proper orthogonal decomposition) which resemble Fourier modes. The effects of serrations on the pressure fluctuations comprise a global reduction in level, a change in the axial energy distribution, and a modification of the evolution of the characteristic time scales.
A further analysis in frequency–wavenumber space is then performed, and a filtering operation is used to separate the convective and propagative footprints of the pressure field. This operation reveals two distinct signatures in the propagating component of the field: a low-frequency component which radiates at small angles to the flow axis and is characterized by extensive axial coherence, and a less-coherent high-frequency component which primarily radiates in sideline directions. The serrations are found to reduce the energy of the axially coherent propagating component, but its structure remains fundamentally unchanged; the high-frequency component is found to be enhanced. A further effect of the serrations involves a relative increase of the mean-square pressure level of the acoustic component – integrated over the measurement domain – with respect to the hydrodynamic component. The effect of increasing the velocity and temperature of the primary jet involves a relative increase in the acoustic component of the near field, while the hydrodynamic component remains relatively unchanged: this shows that the additional acoustic energy is generated by the mixing region which is produced by the interaction of the inner and the outer shear layers, whereas the hydrodynamic component of the near field is primarily driven by the outer shear layer.
A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jet’s turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jet’s modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-dimensional features of the sound source mechanisms are illustrated.
Particle image velocimetry measurements of an unheated Mach 0.85 jet are used to examine its various turbulence properties. The data are presented from two separate experiments; one with the light sheet orientated in the streamwise direction (r–x plane) and one with the light sheet perpendicular to the flow direction (r– plane). The instrument’s characteristics allow for the calculation and subsequent analysis of the two-point spatial correlations which are known to be relevant to the source terms in acoustics analogies where sound production is concerned. An examination of the spatial correlations demonstrates the averaged spatial evolution of the jet’s large-scale turbulent structures throughout the noise producing region. In particular, the (r–x) spatial dependence of the axial and azimuthal normal stresses manifest a oblique structure in the mixing layer regions of the flow, whereas the radial normal stresses evolve more uniformly toward the end of the potential core. Quadrupole source terms relevant to the sound production mechanisms are also calculated from which their spatial distributions are analyzed with zero time delay. The analysis of these source terms at x=D 4 show how the peak energy for the shear-noise component resides on the high-speed side of the shear layer around r=D 0:33, whereas the self-noise terms peak along the lip-line at r=D 0:5, and are most energetic for the streamwise and azimuthal components of the velocity. To fully evaluate the quadrupole sources of noise, the space-time correlations of the full three-dimensional turbulent flowfield are required which are currently not available from experiments.
An extension to classical stochastic estimation techniques is presented, following the formulations of Ewing and Citriniti (1999), whereby spectral based estimation coefficients are derived from the cross spectral relationship between unconditional and conditional events. This is essential where accurate modeling using conditional estimation techniques are considered. The necessity for this approach stems from instances where the conditional estimates are generated from unconditional sources that do not share the same grid subset, or possess different spectral behaviors than the conditional events. In order to filter out incoherent noise from coherent sources, the coherence spectra is employed, and the spectral estimation coefficients are only determined when a threshold value is achieved. A demonstration of the technique is performed using surveys of the dynamic pressure field surrounding a Mach 0.30 and 0.60 axisymmetric jet as the unconditional events, to estimate a combination of turbulent velocity and turbulent pressure signatures as the conditional events. The estimation of the turbulent velocity shows the persistence of compact counter-rotating eddies that grow with quasi-periodic spacing as they convect downstream. These events eventually extend radially past the jet axis where the potential core is known to collapse.
Two rakes of cross-wire probes were used to capture the two-point velocity statistics in a flow through an axisymmetric sudden expansion. The expansion ratio of the facility is 3, and has a constant geometry. Measurements were acquired at a Reynolds number equal to 54 000, based on centreline velocity and inlet pipe diameter. The two-point velocity correlations were obtained along a plane normal to the flow (r, θ), at eleven downstream step-height positions spanning from the recirculating region, through reattachment, and into the redeveloping region of the flow. Measurements were acquired by means of a flying-hot-wire technique to overcome rectification errors near the outer wall of the pipe where flow recirculations were greatest. A mixed application of proper orthogonal (in radius) and Fourier decomposition (in azimuth) was performed at each streamwise location to provide insight into the dynamics of the most energetic modes in all regions of the flow. This multi-point analysis reveals that the flow evolves from the Fourier-azimuthal mode m=2 (containing the largest amount of turbulent kinetic energy) in the recirculating region, to m=1 in the reattachment and redeveloping regions of the flow. An eigenvector reconstruction of the kernel, using the most energetic modes from the decomposition, displays the spatial dependence of the Fourier-azimuthal modes and the characteristics that govern the turbulent shear layer and recirculating regions of the flow.
Flow over a circular cylinder with its axis aligned with the free stream was investigated experimentally. Both upstream and downstream faces of the cylinder are sharply truncated. The fineness ratio (length to diameter ratio) was varied and the behavior of the leading-edge separating shear layer and its effect on the wake were studied in water using both flow visualization and PIV techniques. For the moderately large fineness ratio, the shear layer reattaches with subsequent boundary layer growth, whereas over a shorter cylinder the shear layer remains detached. This causes differences in the wake recirculation region and the immediate wake patterns. The shear layer structure was analyzed using the proper orthogonal decomposition (POD). The model in the water channel was sting-mounted and in some cases the effect of model support was detected in the wake measurements. To avoid such disturbance from the model support, an experiment was initiated in air using a magnetic model support and balance system. The drag variation with fineness ratio is presented and discussed in light of the flowfield measurements.