One-Dimensional Two-Equation Two-Fluid Model Stability

Lopez-de-Bertodano, Martin; Fullmer, William D.; Vaidheeswaran, Avinash

doi:10.1615/multscientechn.v25.i2-4.60

Cited by 12 publications

(7 citation statements)

References 12 publications

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“…The incompressible fixed-flux TFM of Lopez de Bertodano et al (2013) obtained from the full TFM of Fullmer et al (2014b) and validated with the experiment of Thorpe (1969) …”

Section: Fixed-flux Two-equation Modelmentioning

confidence: 85%

“…Recently Lopez de Bertodano et al (2013) derived the twoequation fixed-flux model from the TFM that reduces exactly to SWT for flow conditions below the KH instability, thus rendering the TFM amenable to Whitham's analyses. The fixed-flux model is based on the fixed flux assumption, which allows local instabilities like SWT and KH, but precludes global instabilities like flow excursion and density waves.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

Bertodano

Fullmer

Clausse

2016

Nuclear Engineering and Design

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“…The incompressible fixed-flux TFM of Lopez de Bertodano et al (2013) obtained from the full TFM of Fullmer et al (2014b) and validated with the experiment of Thorpe (1969) …”

Section: Fixed-flux Two-equation Modelmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

Bertodano

Fullmer

Clausse

2016

Nuclear Engineering and Design

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“…This enabled us to perform numerical experiments over long periods of time in order to collect adequate statistics. The domain was initialized using a slightly perturbed liquid volume fraction field given by, 12) where, δ = 0.02, α 1,0 = 0.542, σ 01 = σ 02 = 0.02 m, x 01 = 0.45 m, and x 02 = 0.55 m. A constant velocity field is specified, u 1 = -0.1 m/s, calculated from the kinematic (quasi-static) condition, i.e., by solving F = 0 in Equation 8. The resulting FFT spectra in Figure 4 shows that the long-wavelength (low frequency) energy generated from the linear KHI is transferred to higher frequencies through nonlinear dissipation, resulting in a continuous distribution of Fourier modes.…”

Section: B Numerical Simulationsmentioning

confidence: 99%

“…LSA can also help identify terms which stabilize the model and prevent immediate numerical divergence, i.e., terms that make the model well-posed. For instance, higher-order terms present in the TFM have been proven to influence the stability of the system of equations [9][10][11][12][13][14] without completely hyperbolizing the model, i.e., no growth at all wavelengths. However, based on LSA of a well-posed TFM, there persists exponential growth at finite wavelengths, which is bounded by the inherent nonlinearity 15 .…”

Section: Introductionmentioning

confidence: 99%

Chaos in wavy-stratified fluid-fluid flow

Vaidheeswaran

Clausse

Fullmer

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We perform a non-linear analysis of a fluid-fluid wavy-stratified flow using a simplified twofluid model, i.e., the fixed-flux model (FFM) which is an adaptation of shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the short-wave physics leading to the Kelvin-Helmholtz instability (KHI). The interface dynamics are chaotic and analysis beyond the onset of instability is required to understand the non-linear evolution of waves. The two-equation FFM solver based on a higher-order spatiotemporal finite difference discretization scheme is used in the current simulations. The solution methodology is verified and the results are compared with the measurements from a laboratory-scale experiment. The Finite-Time Lyapunov Exponent (FTLE) based on simulations is comparable and slightly higher than the Autocorrelation function (ACF) decay rate, consistent with findings from previous studies. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square (RMS) of the interface height exhibits a square-root dependence. It is demonstrated that this simple 1-D FFM captures the essential chaotic features of the interfacial behavior. arXiv:1809.10599v1 [physics.flu-dyn]

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“…Similarly, in [33] and, more recently, in [34,35] and in [36], an analogous formulation of the two-equation two-fluid model is considered, which reduces the model from four to two equations.…”

Section: The Modelmentioning

confidence: 99%

Simplified 1D Incompressible Two-Fluid Model with Artificial Diffusion for Slug Flow Capturing in Horizontal and Nearly Horizontal Pipes

2017

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This article proposes a numerical resolution of a one-dimensional (1D), transient, simplified two-fluid model regularized with an artificial diffusion term for modeling stratified, wavy and slug flow in horizontal and nearly horizontal pipes. Artificial diffusion is introduced to prevent the unbounded growth of instabilities where the 1D two-fluid model is ill-posed. We propose a method to set the artificial diffusion case by case to obtain the desired cut-off at short wavelengths by combining the choice of the spatial discretisation and the amplification factors obtained by the linear stability analysis of the model. A proper criterion to simulate two-phase to single-phase flow transition, which occurs during slug formation, is also developed. Flow pattern transitions have been numerically computed and compared against theoretical transition boundaries and experimental observations. Moreover, we showed that the developed code computes slug initiation and slug characteristics, in a reasonably accurate way considering the simplicity of the model, comparing numerical results with well-known empirical correlations and experimental data. Furthermore, the model simplicity leads to a computationally-inexpensive numerical resolution; this can be useful in engineering applications where obtaining fast numerical results is fundamental, such as applications involving automated control for two-phase flows.

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One-Dimensional Two-Equation Two-Fluid Model Stability

Cited by 12 publications

References 12 publications

One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

Chaos in wavy-stratified fluid-fluid flow

Simplified 1D Incompressible Two-Fluid Model with Artificial Diffusion for Slug Flow Capturing in Horizontal and Nearly Horizontal Pipes

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