Roger E. A. Arndt

The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet

It is shown that the pressure signal measured at the outer edge of a jet mixing layer is entirely hydrodynamic in nature and provides a good measure of the large-scale structure of the turbulent flow. Measurement of the pressure signal provides a unique opportunity to utilize proper orthogonal decomposition (POD) to deduce the streamwise structure. Since pressure is a scalar, a significant reduction in the numerical and experimental complexity inherent in the analysis of velocity vector fields results. The POD streamwise eigenfunctions show that the structure associated with any frequency‐azimuthal mode number combination displays the general characteristics of amplification‐saturation‐decay of an instability wave, all within about three wavelengths. High-frequency components saturate early in x and low-frequency components saturate further downstream, indicative of the inhomogeneous character of the flow in the streamwise direction. Application of the POD technique allows the phase velocity to be determined taking into account the inhomogeneity of the flow in the streamwise direction. The phase velocity of each instability wave (POD eigenvector) is constant and equal to 0.58U j , indicating that the jet structure is non-dispersive. Using the shot-noise decomposition, a characteristic event is constructed. This event is found to contain evidence of both pairings and triplings of vortex structures. The tripling results in a rapid increase in the first asymmetric (m fl 1) component. On average, pairing occurs once every four U j }D while tripling occurs once every 13U j }D. This paper deals with the identification of large-scale structures in turbulent jets through an examination of the near-field pressure signal which is an outgrowth of studies going back more than 20 years (Arndt & George 1974). The measurement procedure is based on the proper orthogonal decomposition (POD) originally proposed by Lumley (1967) for the study of spatial structure associated with inhomogeneous flows. The measurements reported herein are based on work initiated in 1980 to study the influence of coherent structures on jet noise radiation using these earlier concepts. At the time no reliable method for deducing coherent structures in high-Reynolds-number flows in an unbiased manner was available. A review of the literature indicated that coherent structures were readily identified in clean jets at low Mach number and Reynolds numbers less than about 10&. However, subsonic jet noise measurements were made at higher Mach numbers and correspondingly higher Reynolds numbers as reviewed by Long & Arndt (1984). Clearly, there was a need to deduce the presence of

Pressure spectra in turbulent free shear flows

Spectral models for turbulent pressure fluctuations are developed by directly Fourier transforming the integral solution to the Poisson equation for a homogeneous constantmean-shear flow. The turbulence-turbulence interaction is seen to possess the well-known k −7/3 inertial subrange and to dominate the high-wavenumber region. The turbulence–mean-shear contribution is seen to be dominant in the energy-containing range and falls off as

Spectral Characteristics of Sheet/Cloud Cavitation

k^{-\frac{11}{3}}

Some observations of tip-vortex cavitation

in the inertial subrange. The subrange constants and the mean-square pressure fluctuation are evaluated using a spectral model for the velocity. A spectral analysis of the velocity contamination of a pressure probe is also presented. Results are compared with spectral measurements with a static-pressure probe in the mixing layer of an axisymmetric jet.

Water Quality Effects on Cavitation Inception in a Trailing Vortex

Cavitation observations were made using a highly instrumented 2D NACA 0015 hydrofoil mounted in a specially designed water tunnel. It was found that the dynamic characteristics of the cavitation vary considerably with various combinations of angle of attack and cavitation number, a. At higher angles of attack, two types of flow unsteadiness are observed. At low σ, a low frequency shedding of cloud cavitation results in a strong oscillation in lift and Ap at a Strouhal number, based on chord length, fc/U, of about 0.15. This frequency is relatively insensitive to changes in a. As a is raised, the harmonic content of the oscillations changes significantly. A spectral peak at much higher frequency is noted that increases in frequency almost linearly with cavitation number. Similar behavior is noted in the lift fluctuations

On the evolution of turbulent scales in the wake of a wind turbine model

Cavitation has been observed in the trailing vortex system of an elliptic planform hydrofoil. A complex dependence on Reynolds number and gas content is noted at inception. Some of the observations can be related to tension effects associated with the lack of sufficiently large-sized nuclei. Inception measurements are compared with estimates of pressure in the vortex obtained from LDV measurements of velocity within the vortex. It is concluded that a complete correlation is not possible without knowledge of the fluctuating levels of pressure in tip-vortex flows. When cavitation is fully developed, the observed tip-vortex trajectory shows a surprising lack of dependence on any of the physical parameters varied, such as angle of attack, Reynolds number, cavitation number, and dissolved gas content.

Two Aspects of Cavitation Damage in the Incubation Zone: Scaling by Energy Considerations and Leading Edge Damage

Tip vortex cavitation studies were made with a hydrofoil that was elliptical in planform, with an aspect ratio of 3, and having a modified NACA 662 -415 profile. LDV measurements of the tangential velocity component in the vortex were used to determine that the minimum pressure in the vortex varies with lift coefficient squared, i.e., that the incipient cavitation number σi should follow a Cl 2 relation (σi ≈ Cl 2 ). This is in contradiction to previous observations (Arndt et al. 1991) that the tip vortex cavitation index varied approximately with lift coefficient to the power 1.4. By carefully monitoring the tensile strength of the water, i.e., its susceptibility to cavitation, the discrepancy was traced to the capability of the test water to sustain a tensile stress. Cavitation in “weak” water (no tensile strength) does follow the Cl 2 relationship, whereas observations in “strong” water (rupture considerably below vapor pressure) more closely followed the previously observed variation, i.e., σi ≈ Cl 1.4 . Since the structure of the vortex cannot be affected by changes in the water quality, the discrepancy can be explained only by the amount of tension that can be sustained by the test water before inception occurs. Apparently a relatively larger value of tension can be sustained in the vortex is the strength of the vortex is increased (i.e., increasing Cl ). This would explain the observed deviation from the expected Cl 2 law for water with measurable tensile strength.

MEASUREMENTS IN HIGH VOID-FRACTION BUBBLY WAKES CREATED BY VENTILATED SUPERCAVITATION

Wind-tunnel experimental data from the wake of a model wind turbine were used to provide a scale-by-scale energetic description of the flow at various locations downwind of the turbine. Pre-multiplied spectra of the streamwise and vertical velocity components were considered for the analysis and compared with those obtained in the base flow (smooth wall condition). Results showed that in the relatively high-frequency range, the turbine induces strong turbulent energy into the wake, which is an indicator of its active character. However, large scales and very large scales were observed to be dampened in the wake close to the wall, implying that the turbine also acts as a high-pass filter. These two distinct processes occurring in the wake suggest to conceptualize and model the turbine as an ‘active filter’. Various terms in the turbulent kinetic energy (TKE) equation were also estimated at different locations to study the physical processes modulating the enhanced levels of turbulence intensity observed in...

Some remarks on hydrofoil cavitation

This study focused on two aspects of the cavitation damage problem, namely an energy approach to the scaling of cavitation damage in the incubation zone and damage near the leading edge of a test model. The damage to the surface of the models was in the form of small indentations in which no material was removed. For a wide range of velocities namely 14.9 to 59.3 m/s the rate of pit formation per unit area in the maximum damage zone increased by the sixth power of velocity. Furthermore it is shown that the damage rate versus velocity data are in good agreement with three other investigations. The volumes of the pits were found to increase by the fifth power of velocity. A relationship between the volume of a pit and the cavitation bubble collapse energy absorbed was developed. The damage to the leading edge was felt to be due to the reentrant jet striking the leading edge of the cavity creating a short term pressure rise causing the collapse of any cavitation bubbles in this area.

Nucleation and Bubble Dynamics In Vortical Flows

A detailed study of ventilated supercavitation in the reentrant jet regime is being carried out in the high-speed water tunnel at St. Anthony Falls Laboratory, as the hydrodynamics part of an interdisciplinary study on stability and control of high-speed cavity-running bodies. It is aimed at understanding the interaction between a ventilated supercavity and its turbulent bubbly wake, with the goal to provide the information needed for the development of control algorithms. Here Particle Image Velocimetry (PIV) measurements in high void fraction bubbly wakes created by the collapse of ventilated supercavities are reported. Bubble velocity fields are obtained, and shown to submit to the same high Reynolds number similarity scaling as the single-phase turbulent axisymmetric wake. A grayscale technique to measure local average void fraction is outlined. Initial results of a timeresolved PIV experiment (2000 Hz) are also presented.