quasi-2D Flow Research Articles

An analysis of fluid–structure interaction coupling mechanisms in liquid-filled viscoelastic pipes subject to fast transients

An extension of a recently developed quasi-2D flow model for fluid transients in viscoelastic pipes to handle fluid–structure interaction mechanisms is presented. In a context in which the fluid flow is devised as a structured pseudo-mixture and the pipe’s viscoelasticity is rooted in an internal variable theory, the axial movement of the pipe wall is allowed to occur, giving rise to friction, Poisson, and junction coupling mechanisms. The resulting governing equations of the model form a quasi-linear hyperbolic system of partial differential equations, which approximated solution is achieved by means of the method of characteristics. The proposed approach is validated against pressure traces acquired from a reservoir–pipe–valve experimental setup found in the literature. In the course of the validating process, different pipe anchoring conditions are employed to study the system responses. Focus is given to pipe–fluid interface interactions, energy dissipation, and transfer of energy between both media.

A thermodynamically consistent model for hydraulic transients in metallic pipes undergoing elasto-viscoplastic deformations

This work presents an extension of the fluid transient analysis to include the elasto-viscoplastic behavior of the pipe material. A previously developed quasi-2D flow model is employed as a basic framework, and the pipe’s elasto-viscoplastic behavior is added by considering constitutive equations formulated via an internal variables theory. The resulting governing equations form a non-linear hyperbolic system of partial differential equations whose approximated solutions are obtained by employing the method of characteristics followed by the Newton–Raphson method. The model is thermodynamically consistent, a feature that is consistently detailed in this work to uphold the application of energy-based theoretical analyses of the phenomenon. Taking as reference the transient responses obtained from an experimental installation that simulates an accident, the present approach is found to be fully consistent and valuable for simulating fast hydraulic transients in metallic materials experiencing plastic deformation. By comparing the pressure fluctuations of models with and without elasto-viscoplasticity, more attenuation and dispersion of the pressure responses are found when such behavior is considered. The elasto-viscoplasticity effect on the pressure responses is better understood when the connection between the viscoplastic mechanisms and energy dissipation is exposed. During the fluid transient, the pipe dissipates meaningful amounts of energy that cause a significant alteration in the whole fluid–pipe dynamics. Another numerical example, based on a hypothetical water hammer flow that causes plastic deformation in the pipeline, is also addressed. Such a case puts in evidence that not only the anelastic behavior of the pipe must be taken into account but also that an accurate description of the fluid friction may be significant to portray realistically fluid transient responses. At last, an assessment of the pipe integrity by means of a scalar damage variable theory is carried out to emphasize the application prospects of the present research.

A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described based on nonlinear continuum mechanics allowing for finite deformations and arbitrary constitutive laws. The fluid film is modelled as a quasi-2D flow problem governed by the (thickness-)averaged Reynolds equation. In contrast to existing approaches, the proposed model accounts for the co-existence of frictional contact tractions and hydrodynamic fluid tractions at every local point on the contact surface of the interacting bodies and covers the entire range of lubrication in one unified modelling framework with smooth transition between these different regimes. From a physical point of view, this approach can be considered as a model for the elastic deformation of asperities on the lubricated contact surfaces. The finite element method is applied for spatial discretization of the 3D solid-mechanical problems and the 2D interface effects, consisting of the averaged Reynolds equation governing the fluid film and the non-penetration constraint of the mechanical contact problem. A consistent and accurate model behavior is demonstrated by studying several challenging benchmark test cases.

Fluid transients in viscoelastic pipes via an internal variable constitutive theory

This work presents a fluid transient model capable of handling the viscoelastic behavior of the pipe. A previously developed quasi-2D flow model is employed as a base, and the viscoelastic behavior of the pipe is incorporated by considering constitutive equations formulated in a thermodynamically consistent framework of an internal variable theory. Such an approach straightforwardly provides expressions for computing the rates of energy dissipation in the fluid and pipe accurately and separately. This novel feature discerns the local and overall impacts of the energy dissipation on the pressure oscillations caused by each medium. The governing equations of the model form a hyperbolic system of partial differential equations whose approximated solutions are obtained by the method of characteristics. Taking as reference pressure signals obtained by a classic reservoir-pipe-valve experiment found in the literature, it is shown that the model predictions are fully consistent. A comparison between the pressure responses of viscoelastic and elastic pipes reveals that in addition to delaying the pressure oscillations, the viscoelastic behavior causes a faster attenuation of them. The rates of energy dissipation in the viscoelastic pipe attain significant magnitudes during the first moments of the fluid transient and alters the hydrodynamical behavior of the flow. Such interference is exposed by comparing the responses of the same experimental setup when two different viscoelastic pipe materials are considered. It is also shown that the knowledge of the parcels of energy dissipated in the fluid and pipe individually can improve the comprehension of the phenomenon and be utilized for theoretical and applied research in the field.

Modeling of Dynamic Response of a Radial Turbine to Pulsatile Incoming Flow

Abstract The unsteady response of a turbine exposed to pulsatile incoming flow is studied via the analytical model in this article. First, the response of output torque of the turbine to pulsatile condition is theoretically studied and a correlation of the torque response is deduced. The results confirm that the fluctuations of the torque are proportional to the fluctuations of velocity at the rotor inlet. Next, the unsteady response of turbine system is modeled by the method of transfer matrixes of quasi-2D flow elements connected in sequence. The correlations of swallowing capacity and output torque with the imposed pulsatile inlet pressure are obtained via the models. The results prove that the unsteadiness of turbine performance is proportionally enhanced by the pulse magnitude and the acoustic throttle slope in swallowing capacity curve. In particular, the unsteadiness increases first, but then reduces as the Strouhal number increases. The strongest unsteady performance is achieved when the resonance of the system happens at the Strouhal number as 1. Furthermore, the model proves that the total torque deviation of the turbine is proportional to the mass accumulation in a pulse period. This justifies the validity of the widely used assumption of the mass accumulation as an indicator of turbine performance unsteadiness. Finally, the results of the theoretical model are validated against the 1D gas-dynamic simulation via in-house developed code.

Validation and evaluation of the CPFD modeling of dense particle flow velocity: Taking particle flow around an obstacle as an example

The computational particle fluid dynamic (CPFD) method is a common approach to simulating dense particle flow, but the direct validation of the CPFD model using the particle velocity distribution is lacking. Taking particle flow around an obstacle as an example, the accuracy of the CPFD method in the simulation of the dense particle velocity field was validated and evaluated in the present study. The particle flow field was experimentally visualized using a quasi-2D flow channel and the particle velocity distribution was measured by a newly-proposed stained-particle image velocimetry technique. The simulated particle velocity using the CPFD method was compared with the measured data and the results indicated that the CPFD method was capable of accurately predicting the particle flow velocity distribution as well as the overall parameters such as the apparent mass flux if the CPFD model parameters were properly adopted. The sensitivity analysis of the simulated particle velocity to the key CPFD parameters was conducted and the results showed that the simulated particle velocity distribution was quite sensitive to the particle pack volume fraction, while the particle stress model parameters and particle-to-wall restitution coefficients show less and close sensitivity in the dense particle flow situations. The recommended model parameters were given in the present study. It is also found that multiple choices of the model parameter combinations could all give accurate overall mass flow predictions but might lead to very different flow velocity distributions with a prediction error even higher than 45%. One should directly verify the CPFD simulated flow velocity using the experimental data if the flow field study was desired.

A new model for fluid transients in piping systems taking into account the fluid–structure interaction

The present work extends a recently developed quasi-2D flow model for fluid transients in elastic pipes to accommodate fluid–structure interaction mechanisms. In this context, the primary goal of the proposed approach is to analyze energy transfer and dissipative effects in the fluid–pipe system. The fluid–structure interaction couples the flow dynamics with the axial movement of the tube, giving rise to friction, Poisson, and junction coupling mechanisms to take place. The mechanical model mathematical structure forms a quasi-linear hyperbolic system of partial differential equations for which approximated solutions are sought by employing the method of characteristics. The proposed model reproduces classical benchmark solutions and presents a good agreement with experimental data. In addition, the whole thermomechanical consistent framework in which the model is established allows an accurate description of the flow’s internal structure. This feature allows a better comprehension of the phenomenon when compared to the classic frictionless and quasi-steady-friction-based four-equation models. The present approach allows a better description of the friction coupling mechanism and unveils uneven shear stress distributions in the unsteady flow. As a result, the energy dissipation in the fluid is captured with accuracy. Due to the absence or limited ability to describe these dispersive and dissipative effects, the traditional approaches are proved to lose their accuracy as the fluid transient goes. The coupled and uncoupled models are also analyzed and are proven to respond differently due to localized pipe–fluid interface effects in addition to the bulk mechanisms of transfer of energy that occur differently in both approaches.

Two-Dimensional Investigation of the Fundamentals of OGV Buffeting

The increased demands of compact modern aero engine architectures have highlighted the problem of outlet guide vane (OGV) buffeting in off-design conditions. This structural response to aerodynamic excitations is characterised by increased vibration, risking structural fatigue. Investigations focused on understanding, mitigation and avoidance are therefore of high priority. OGV buffet is a type of transonic buffet caused by unsteady shock movement, but the exact parameters driving it are not fully understood. To try and understand them, this paper examines the buffet of a quasi-2D OGV geometry. Parametric studies of the incidence angle and inlet Mach number were performed. Forcing frequencies for both studies were found to be close to the experimentally detected frequency of vibration in the first bow mode, which demonstrates that buffet is driven by quasi-2D flow features. Increasing the inlet Mach number increased the dominant forcing frequency, whereas increasing the incidence yielded little change. Profiles of unsteady pressure amplitudes were shown to smoothly increase in magnitude with an increasing incidence and inlet Mach number.

Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

Large eddy simulation study of a wave-induced shallow-water monopolar vortex

Detailed flow and turbulence characteristics of a long-wave-induced shallow-water monopolar vortex are investigated using a 3D large eddy simulation. The numerical model is validated with measured data where nearly 2D shallow turbulent coherent structures were generated by sending a single asymmetric wave through a harbour channel in a large 3D wave basin. Model results demonstrate that the vortex centre trajectory is sensitive to small perturbations applied via a surface tension coefficient. Instantaneous model results are averaged over three numerical runs with slightly different surface tension coefficients so that a sufficient number of realisations are obtained for ensemble-averaging. Because of shallow water depth, flow fields are dominated by a horizontally rotating current and vertically suppressed velocities resembling quasi-2D flow conditions. Bed shear stress calculated using the decay of peak azimuthal velocity is qualitatively similar to that obtained using a near-wall modelling method. Although 2D turbulent coherent structures evolve into monopolar vortices at later stages, flow is not completely axisymmetric due to secondary turbulent coherent sub-structures located in the middle of the water column and away from the core. Turbulence production and turbulence dissipation rate demonstrate a local imbalance where turbulence is mainly produced by flow shear correlated with recirculation patterns, while turbulent kinetic energy is predominantly dissipated near the no-slip bottom boundary. While the free surface elevation at the vortex core indicates an upwelling pattern consistent with laboratory experiments, model results show evidence that the recirculation pattern is influenced by a low frequency resonant mode of the wave basin.

Abrupt Transition between Three-Dimensional and Two-Dimensional Quantum Turbulence.

We present numerical evidence of a critical-like transition in an out-of-equilibrium mean-field description of a quantum system. By numerically solving the Gross-Pitaevskii equation we show that quantum turbulence displays an abrupt change between three-dimensional (3D) and two-dimensional (2D) behavior. The transition is observed both in quasi-2D flows in cubic domains (controlled by the amplitude of a 3D perturbation to the flow), as well as in flows in thin domains (controlled by the domain aspect ratio) in a configuration that mimics systems realized in laboratory experiments. In one regime the system displays a transfer of the energy towards smaller scales, while in the other the system displays a transfer of the energy towards larger scales and a coherent self-organization of the quantized vortices.

Using quasi two-dimensional systems to understand large-scale vortical structures and dynamics

An experimental physicist, surveying the research, describes how quasi 2D flows on curved, thin liquid films provide insight into the macroscopic properties of turbulent flows.

Observing Nitrogen Bubbles in Liquid Zinc in a Vertical Hele-Shaw Cell

Observations of gas bubbles in liquid metal are strongly hindered by the opacity of metals. To circumvent this limitation, the authors recently proposed to study such systems under quasi-2D flow conditions in a Hele-Shaw cell. The current paper presents a successful application of this approach for nitrogen bubbles in liquid zinc at 973 K (700 °C) in a fused quartz cell with a thickness of 1.5 mm. At low oxygen levels, the cell walls are not wetted by the liquid zinc, and bubbles can be observed directly through the transparent cell walls. Furthermore, using a moving high-speed camera that travels upwards with the bubbles, their properties are quantified in detail along the entire trajectory. In the range of equivalent diameters between 5.9 and 9.0 mm, this reveals a single periodic flow regime in which bubbles follow a sinusoidal path with a characteristic frequency of 3.31 Hz. In addition, systematic intermediate accelerations are observed of which the origin remains unexplained. Considering the unprecedented resolution of such observations for bubbles in liquid metals, especially at high temperatures, it is expected that this approach will contribute to a better understanding of the mechanisms that govern gas injection in pyrometallurgy.

Numerical investigation of conventional and modified Savonius wind turbines

The performance of a Savonius wind turbine with constant cross-sections is examined by means of quasi 2D flow predictions executed in ANSYS CFX. Simulations were performed in a way that allows comparison with wind tunnel data presented in a related paper, where two designs were simulated: the Classical and so-called Bach-type Savonius rotor. Comparison revealed the importance of applying a laminar–turbulent transition model. Additionally, turbine design with an Elliptical blade shape was modelled. Such a shape has not been examined before with the use of CFD. All mentioned designs were analysed at different values of tip speed ratio. The paper presents a systematic analysis of the obtained coefficients of power, coefficients of torque and torque variation with the angle of incidence. The most characteristic flow structures are identified and compared. Finally, the wake is observed and examined by means of FFT analysis of pressure fluctuations at the point located downstream of the rotor.

TURBULENCE IN THICK LAYERS

Properties of turbulence, such as the direction of the energy cascade depend on the flow dimensionality. Recent experimental results reveal new physics understanding of flows in thick layers. We show that the flow dimensionality can be characterized by the flow damping and that a comparison of the decay rate with that of a quasi-2D flow can be used as a measure of dimensionality of a turbulent flow in a layer. This dimensionality, however can be strongly affected if large scale coherent vortices are present in the flow. These vortices can imposed twodimensionality and reduce the damping rate. Finally we show that even in thick layers with unperturbed free surface, turbulent flow can be viewed as co-existing 2D top sub-layer and the bulk 3D flow.

Spectrally condensed turbulence in thin layers

We present experimental results on the properties of bounded turbulence in thin fluid layers. In contrast with the theory of two-dimensional (2D) turbulence, the effects of the bottom friction and of the spectral condensation of the turbulence energy are important in our experiment. Here we investigate how these two factors affect statistical moments of turbulent fluctuations. The inverse energy cascade in a bounded turbulent quasi-2D flow leads to the formation of a large coherent vortex (condensate) fed by turbulence. This vortex, depending on its strength, can substantially affect the turbulence statistics, even at small scales. Up to the intermediate strength of the condensate, the velocity moments similar to those in isotropic 2D turbulence are recovered by subtracting the coherent component from the velocity fields. A strong condensate leaves a footprint on the underlying turbulence; it generates stronger non-Gaussianity and reduces the efficiency of the inverse energy cascade. Remarkably, the energy flux in the cascade derived from the third-order structure function using the Kolmogorov flux relation gives physically meaningful values in a broad range of experimental parameters regardless of the condensate strength. This result has important implications for the analysis of the atmospheric wind data in upper troposphere and lower stratosphere.

Extraction of coherent structures in a rotating turbulent flow experiment

The discrete wavelet transform (DWT) and discrete wavelet packet transform (DWPT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle image velocimetry measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity field exhibits vortex creation, merger, scattering, and destruction. We separate the flow into a low-entropy "coherent" and a high-entropy "incoherent" component by thresholding the coefficients of the DWT and DWPT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWT and DWPT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWT and DWPT are necessary to represent the coherent component and preserve the vorticity probability distribution function (PDF), transport properties, and spatial and temporal correlations. The remaining small-amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.

Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

We have made velocity time series measurements (using hot film probes) and velocity field measurements (using particle image velocimetry) on turbulent flow in a rotating annulus. For low annulus rotation rates the Rossby number was of order unity and the flow was three-dimensional (3D), but at high rotation rates the Rossby number was only about 0.1, comparable to the value for oceans and the atmosphere on large length scales. The low Rossby number (quasi-geostrophic) flow was nearly two-dimensional (2D), as expected from the Taylor–Proudman theorem. For the 3D flow we found that the probability distribution function (PDF) for velocity differences along the direction of the flow, δv(d)=v(x0+d)−v(x0), was Gaussian for large separations d and non-Gaussian (with exponential tails) for small d, as has been found for nonrotating turbulent flows. However, for low Rossby number flow, the PDF was self-similar (independent of d) and non-Gaussian. The exponents characterizing the structure functions, Sp=〈(δv)p〉∼dζp were obtained by the extended self-similarity method. For 3D flow the exponents departed from p/3 with increasing p, as has been found for turbulence in nonrotating flows, while for the quasi-2D turbulent flow, the exponents increased linearly with p, as expected for a self-similar flow. We applied the β-test of the hierarchical structure model [She and Lévêque, Phys. Rev. Lett. 72, 336 (1994)] and found that β remained constant at β≃0.75 as the rotation was increased from the 3D to the 2D regime; this indicates that both the quasi-2D and 3D flows are highly intermittent. The PIV images provided another indication of the intermittency—both the quasi-2D and 3D flows had coherent vortices which could be distinguished from the background flow. We also applied the γ-test of the hierarchical structure model and found that γ increased from 0.18 for the 3D flow to 0.34 for the quasi-2D flow; the latter value is in accord with expectation for self-similar turbulence. We conclude that our rotating 3D flow is similar to nonrotating turbulent flows, while the rotating quasi-2D turbulence is different from both the 3D rotating turbulence and from nonrotating 2D turbulence studied in other experiments.

Unsteady Flow in Hydraulic Networks with Polymeric Additional Pipe

This paper presents results of an experimental and theoretical study on the use of a high density polyethylene (HDPE) additional pipe inserted downstream of a pump in a hydraulic network as a surge suppressor. The experiments consistently show a reduction of the oscillations with respect to the case without a HDPE device, while in the case of a single pumping pipeline the oscillations can be amplified for small volumes of the additional pipe. Previously calibrated mechanical parameters are considered in the mathematical models whose results are compared with experimental results. Both linear elastic and Kelvin-Voigt viscoelastic behavior of the pipe material and both one-dimensional (1D) and quasi-2D flow models are taken into account. The numerical results show that the viscoelastic model better describes the phenomenon, but the elastic model adequately estimates the maximum and minimum oscillations. Furthermore, the results of the quasi-2D model are in better agreement with the experimental maximum and minimum oscillations than those of the 1D model, but the differences are less important than in the case of networks without a HDPE device.

Quasi-2D flows of 3He - 4He mixtures

Transport in degenerate 3 He- 4 He mixtures in quasi-2D flow channels is discussed. The quasiparticle mean free path combines particle-wall and particle-particle collisions including the interference between them. The temperature, concentration, and polarization dependences of the transport coefficients allow easy extraction of the correlation parameters of random surface roughness from transport data.