Pressure wave speeds from the characteristics of two fluids, two-phase hyperbolic equation system

A three-dimensional transient two-phase flow analysis with a density pertubation finite volume method

“…We refer to [4] and [1][11] [12] for the details of the closure modelings. These modelings concern the source terms (the interphase drag force − → F i k , the interfacial heat transfert Q i k and the mass transfert Γ k ) and the pressure fluctuation p i k .…”

A united model for predicting pressure wave speeds in oil and gas two-phase pipeflows

“…Meanwhile, the results calculated by the Lee et al (1998) model are the same as those of the Nguyen (1976) and Nguyen et al (1981) models. However, we find that the Lee et al (1998) model does not agree with the slug experimental data of Martin and Padamanabhan (1979), with there exists a great difference.…”

“…The Humongous (Bubble) flow Wallis (1969) Martin and Padamanabhan (1979) Nguyen et al (1981) c ¼ Nguyen et al (1981) Lee et al (1998) (continued on next page) (continued on next page) Because of the compressibility of the gas phase, the changes of interface between the gas and liquid, the momentum and energy transfer between the two-phase and the single-phase to the wall, it is extremely complicated to predict the wave speeds for gas-liquid two-phase flow in the long-distance oil-gas transmission pipelines.…”

“…It should be noted that, using the two-fluid model and introducing the gas and liquid bulk module, Lee et al (1998) developed the pressure wave model, which could be applied to the homogenous bubble flow, the separated flow and the slug flow. Meanwhile, the results calculated by the Lee et al (1998) model are the same as those of the Nguyen (1976) and Nguyen et al (1981) models.…”

Extension of a high‐resolution scheme to 1D liquid–gas flow

“…Pioneer works are [4,5]. Among the most recent contributions stand out the volumes ÿnis  a ux caractà eristiques (VFFC) scheme [6], Toumi's approximate Riemann solver [7], St adtke's ux vector splitting scheme [8,9], Masella's Godunov method [10,11], Bedjaoui and Sainsaulieu's models for stratiÿed two-phase ow [12,13], the application of Godunov-type schemes by Berger and Colombeau [14], the non-conservative models of Tiselj and Petelin [15], the Hwang's one [16], the Sung-Jae Lee's ux vector splitting scheme [17,18] and the extension of the AUSM schemes to two-uid ows [19].…”