•Proposed a multi-scale physics-informed neural networks scheme for solving high Reynolds number boundary layer flows.•Applied the matched asymptotic expansions to ensure the continuity of the whole ...domain solutions after dividing.•Demonstrated the effectiveness of multi-scale physics-informed neural networks capturing flow details in different scales.
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Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The evolution of water-entry cavities gives rise to interesting dynamic phenomena that occur in nature and engineering fields. The evolution and seal types of the cavities remain unsettled at
Bo
less ...than 10
−2
since it is difficult to propel a small sphere to impact a water surface at high speed. In the present study, an experiment based on the laserdriven principle is conducted to accelerate a small sphere to hundreds m/s. The types of cavity seal are classified as quasi-static, shallow seal, deep seal, and surface seal within a
Bo
range of 1–7.57×10
−2
. The transition mechanism from a shallow seal to a deep seal is investigated by analyzing the cross-sectional characteristics of cavity necks. With a further decrease in
Bo
(5.69×10
−2
–8.41×10
−3
), the shallow seal is changed directly to a surface seal since the pinch-off time of the cross section at the cavity neck decreases with Bo, and hence, the deep seal disappears. Finally, a parameter study is conducted by varying
We
and
Bo
in the air cavity. Two boundaries are obtained:
We
≈ 64 for the transition between quasi-static and shallow seals and
We
≈ 326 for the transition between shallow seals and surface seals.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A two-bubble model with radiate (
α
bubble)-receive (
β
bubble) structure is constructed to study the energy transfer from one bubble to another. The influence of the non-dimensional distance
d
and ...the initial energy ratio
ψ
on the energy transfer rate is investigated via numerical simulation. The relative received energy
ε
, relative jet energy
J
, and energy transfer rates
η
are defined to quantify energy transfer. Results show that the energy transfer rate decreases with the increase of
d
and
ψ
when the two bubbles’ initial radius is identical. With the increase of d, the interactions between two bubbles are weakened, and the relative received energy satisfies the law of
ε
∝ 1/
d
2
. With the increase of
ψ
, the maximum inner pressure of the
β
bubble increase first and then decreases, while the jet energy of bubble
β
changes with the law of
J
∝
ψ
. It is found that the energy storage capacity increases with the bubble radius by simulating different bubble radius ratios.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
•Dynamic mode decomposition (DMD) is applied in unsteady cavitating flow.•The frequencies of cavitating flow are extracted to analyze the characteristic of cavitating flow.•The velocity field of ...cavitating flow is reconstructed with high accuracy using less information.
The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion. Based on the ranking dominant modes, frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform. Furthermore, the cavitating flow field is reconstructed by the first four modes, and the dominant flow features are well captured with the reconstructed error below 12% when compared to the simulated flow field. This paper offers a reference for observing and reconstructing the flow fields, and gives a novel insight into the transient cavitating flow features.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Experimental study on the surface-piercing hydrofoil at high speed.•The coupling of the ventilated cavity and vaporous cavity.•A prediction model of the maximum depression depth of the water ...surface.•A criterion of cavitation-induced ventilation.
In this study, the cavitating flow and cavitation-induced ventilation flow around a surface-piercing hydrofoil were investigated to gain in-depth understanding of the interaction mechanism between the vaporous cavity and free surface at low cavitation numbers. Experiments were conducted in a constrained-launching water tank to visualize the cavity using a high-speed camera. Unsteady cloud cavitation and cavitation-induced ventilation at atmospheric pressure were observed and analyzed while piercing the free surface. The flow regime map was summarized at a fixed aspect ratio of ARh = 1.5. Subsequently, a physical model was proposed to predict the maximum depression depth of the water surface (H) at the trailing edge of the hydrofoil. Both the physical model and experimental results reveal that the non-dimensional depth H/c has a linear relation to Fn2 c × Rec × sin2α. Finally, a criterion for cavitation-induced ventilation based on the improved lifting-line theory and a physical model were proposed. A new relation H/Lc ∼ α0.5 was obtained, where Lc is the maximum cavity length. The results of this study can guide the design and application of hydrofoils for ventilation and cavitation processes.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This research aims to extend our understanding of propeller wake dynamics under a light loading condition, thereby laying a foundation for design optimization and flow control of the propeller. ...Dynamic mode decomposition (DMD) and reconstruction are used to analyze the transient vortical wake structures obtained by large eddy simulation. The propeller wake includes stable tip and hub vortices without interacting evolution at the light loading condition, and elliptical instabilities are observed downstream of the tip vortices. DMD describes the most energetic modes and the corresponding dominant frequencies are the blade passing frequency and its multiples. The coherent structures identified via DMD are primarily associated with the ordered convection of the tip vortices and have little correlation with the hub vortices. Additionally, the propeller wake flow is reconstructed using the first four DMD modes, and the primary wake features are well restored with a maximum reconstructed error of 7.98%. This demonstrates that the flow-field reconstruction based on the DMD reduced-order model is promising for predicting the propeller wake and controlling the propeller operation.
•The propeller wake is simulated using the LES method under a light loading condition.•DMD identifies the most energetic modes and the associated dominant frequencies.•DMD analyzes contribution of tip and hub vortices to the wake coherent structures.•The propeller wake flow is well reconstructed by a DMD reduced-order model.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The objective of this paper is to investigate the space-time frequency spectra for cavitating flows in a mixed-flow pump by using both fast Fourier transform and wavelet transform. Unsteady ...cavitating flows in a mixed-flow pump are numerically investigated by using the Reynolds-averaged Navier-Stokes method, which is closured with SST k-ω turbulence model and Zwart cavitation model. The cavitation performance is fairly predicted when compared with available experimental data. There are two stages for unsteady cavitation evolution during one impeller rotating cycle, including the cavity growth stage and diminution stage. The cavitation in the impeller is characterized by the spatial non-uniform distribution since a high-pressure region presents at the impeller inlet plane. The pressure amplitude decreases when the cavitation becomes severer at a smaller operating velocity. Besides, the dominant frequency in the impeller is the impeller rotating frequency (fn), i.e. the cavity evolution frequency. Due to the rotor-stator interaction from the six-blade impeller, there is a dominant long-term frequency of 6fn in the intake duct and the diffuser inlet. Furthermore, a broadband low-frequency around 1.5fn exhibits near the diffuser exit, and the 1.5fn amplitude varies over time corresponding to different corner-vortex dynamics. Therefore, wavelet analysis is a more favorable and practical method to obtain time-dependent frequency information for unsteady cavitating flows.
•Spatial non-uniform cavity distribution due to a high-pressure region at the inlet.•The amplitude of pressure fluctuations decreases when the cavitation becomes severer.•The 1.5fn amplitude varies over time with different corner-vortex dynamics.•Wavelet transform can obtain time-varying frequency information for cavitating flows.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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