The topic of this article is a review of the approach to extract pressure fields from flow velocity field data, typically obtained with particle image velocimetry (PIV), by combining the experimental data with the governing equations. Although the basic working principles on which this procedure relies have been known for quite some time, the recent expansion of PIV capabilities has greatly increased its practical potential, up to the extent that nowadays a time-resolved volumetric pressure determination has become feasible. This has led to a novel diagnostic methodology for determining the instantaneous flow field pressure in a non-intrusive way, which is rapidly finding acceptance in an increasing variety of application areas. The current review describes the operating principles, illustrating how the flow-governing equations, in particular the equation of momentum, are employed to compute the pressure from the material acceleration of the flow. Accuracy aspects are discussed in relation to the most dominating experimental influences, notably the accuracy of the velocity source data, the temporal and spatial resolution and the method invoked to estimate the material derivative. In view of its nature of an emerging technique, recently published dedicated validation studies will be given specific attention. Different application areas are addressed, including turbulent flows, aeroacoustics, unsteady wing aerodynamics and other aeronautical applications.

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PIV-based pressure measurement

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

A review of cavitation in hydraulic machinery

Partial cavitation in the separated region forming from the apex of a wedge is examined to reveal the flow mechanism responsible for the transition from stable sheet cavity to periodically shedding cloud cavitation. High-speed visualization and time-resolved X-ray densitometry measurements are used to examine the cavity dynamics, including the time-resolved void-fraction fields within the cavity. The experimentally observed time-averaged void-fraction profiles are compared to an analytical model employing free-streamline theory. From the instantaneous void-fraction flow fields, two distinct shedding mechanisms are identified. The classically described re-entrant flow in the cavity closure is confirmed as a mechanism for vapour entrainment and detachment that leads to intermittent shedding of smaller-scale cavities. But, with a sufficient reduction in cavitation number, large-scale periodic cloud shedding is associated with the formation and propagation of a bubbly shock within the high void-fraction bubbly mixture in the separated cavity flow. When the shock front impinges on flow at the wedge apex, a large cloud is pinched off. For periodic shedding, the speed of the front in the laboratory frame is of the order of half the free-stream speed. The features of the observed condensation shocks are related to the average and dynamic pressure and void fraction using classical one-dimensional jump conditions. The sound speed of the bubbly mixture is estimated to determine the Mach number of the cavity flow. The transition from intermittent to transitional to strongly periodic shedding occurs when the average Mach number of the cavity flow exceeds that required for the generation of strong shocks.

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Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities

Large eddy simulation and Euler–Lagrangian coupling investigation of the transient cavitating turbulent flow around a twisted hydrofoil

Elements of Gas Dynamics

Tip Vortex Cavitation Suppression by Active Mass Injection

Vortex cavitation forming in the leading-edge vortices of a delta wing was examined to determine how the individual cavitation bubbles incepted, grew, interacted with the underlying vortical flow and produced acoustic tones. The non-cavitating vortical flow over the delta wing was chosen to be similar to those previously reported in the literature. It was found that vortex breakdown was unaffected by the presence of incipient and developed vortex cavitation bubbles in the vortex core. While some cavitation bubbles incepted, grew, and collapsed relatively quickly, others reached an equilibrium position wherein the bubble tip was stationary in the laboratory frame at a particular location along the vortex axis. For a given attack angle, the equilibrium location moved upstream with a reduction in free stream cavitation number. It is shown that the existence of these stationary vortex bubbles is possible when there is a balance between the axial growth of the bubble along the vortex axis and the opposite motion of the axial jetting flow in the vortex core, and only a single equilibrium position is possible along the axially evolving vortex for a given free stream cavitation number. These transient and stationary vortex bubbles emit significant cavitation noise upon inception, growth, and collapse. The spectral content of the noise produced was expected to be related to the interaction of the bubble with the surrounding vortical flow in a manner similar to that reported in previous studies, where sustained tones were similar to the underlying vortex frequency. However, in the present study, the dominant frequency and higher harmonics of the tones occur at a higher frequency than that of the underlying vortex. Hence, it is likely that the highly elongated stationary bubbles have higher-order volume oscillations compared to the two-dimensional radial mode of the vortex cores of vortex cavitation bubbles with much smaller diameter-to-length ratios.

Stationary cavitation bubbles forming on a delta wing vortex

In the present study, the experimental set-up of Ganesh et al. (J. Fluid Mech., vol. 802, 2016, pp. 37–78) is used to examine the dynamics of a shedding cavity by examining the vapour production rate of the natural cavity and determining how minimal injection of non-condensable gas can substantially alter the vapour production rate, the resulting cavity flow and the cavity shedding process. The influence of the dissolved gas content on the shedding natural cavity flow is also examined. High-speed visual imaging and cinemagraphic X-ray densitometry were used to observe the void fraction dynamics of the cavity flow. Non-condensable gas is injected across the span of the cavity flow at two locations: immediately downstream of the cavity detachment location at the apex of the wedge or further downstream into mid-cavity. The gas injected near the apex is found to increase the pressure near the suction peak, which resulted in the suppression of vapour formation. Hence, the injection of gas could result in a substantial net reduction in the overall cavity void fraction. Injection at the mid-cavity did less to suppress the vapour production and resulted in less significant modification of both the mean cavity pressure and net volume fraction. Changes in the cavity void fraction, in turn, altered the dynamics of the bubbly shock formation. Variation of the dissolved gas content alone (i.e. without injection) did not significantly change the cavity dynamics.

The dynamics of partial cavity formation, shedding and the influence of dissolved and injected non-condensable gas

The shedding dynamics of partial cavitation forming on a NACA0015 hydrofoil is known from the previous studies to be multimodal, exhibiting abrupt changes in Strouhal number as the cavitation number is reduced (Arndt et al. in Instability of partial cavitation: a numerical/experimental approach. National Academies Press, Washington, D.C., Retrieved from the University of Minnesota Digital Conservancy. http://hdl.handle.net/11299/49781
 , 2000). The present study aims to understand the underlying shedding mechanisms responsible for this abrupt change in dynamics. As was observed in Ganesh et al. (J Fluid Mech 802:37–78, 2016), the shedding process can result from both re-entrant liquid flow and the formation of propagating bubbly shock waves within the cavity. Time-resolved X-ray densitometry and high-speed videography are combined with time synchronous measurements of acoustic noise produced by the cavity to examine the formation and shedding of the partial cavitation on a NACA0015 hydrofoil. From the experiments on the hydrofoil, it was observed that the mean cavity length increased with decreasing cavitation number, as expected. At higher pressures, stable partial cavities formed that shed smaller vapor clouds mainly due to the re-entrant liquid flow in the cavity closure. With a reduction in cavitation number, the partial cavity grew in length, and shedding often occurred when the cavity was pinched-off from its leading edge. Once a large region of vapor was shed, the pressure pulse caused by its subsequent collapse could suppress the growth of the newly forming partial cavity. This feedback led to complex, multistep cavity shedding dynamics. At still lower cavitation numbers, bubbly shocks were found to be responsible for the strongest periodic shedding of vapor clouds. Spectral analysis of the acoustic signal revealed a multimodal nature, which was more pronounced at lower cavitation numbers, and similar dynamic behavior was also found for the time varying local void fraction measurements in the vicinity of cavity closure. The occurrence of strongest multimodal behavior was also characterized by the presence of bubbly shock waves as the dominant mechanism of shedding. From the measurements and analysis, it is concluded that at least four different types of shedding modes occurred over a range of cavitation numbers at a fixed attack angle (10°).

Harish Ganesh

Papers

Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities

Tip Vortex Cavitation Suppression by Active Mass Injection

Stationary cavitation bubbles forming on a delta wing vortex

The dynamics of partial cavity formation, shedding and the influence of dissolved and injected non-condensable gas

Multimodal partial cavity shedding on a two-dimensional hydrofoil and its relation to the presence of bubbly shocks