Study on the algorithm for solving two-fluid seven-equation two-pressure model

Chao, Fei; Shan, Jianqiang; Gou, Junli; Wu, Pan; Ge, Li

doi:10.1016/j.anucene.2017.09.021

Cited by 10 publications

(4 citation statements)

References 25 publications

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“…Similar to RELAP5 [3], for dealing with numerical challenges in phase appearance and disappearance in solving the advanced two-pressure model, mass and momentum conservation equations (1)- (4) are rearranged into sum and difference equation forms and the time derivative terms in conservation equations (1)- (6) are expanded in this numerical scheme. Such semi-implicit scheme is achieved by treating implicitly phasic velocities in mass and energy conservation equations, pressure gradient in momentum conservation equations, and all interfacial exchange terms in conservation equations and all the rest terms are treated effectively at the new time [49,50]. The time advancement for all conservation equations (1)- (7) is achieved by the first-order approximation.…”

Section: High-resolution Tvd Scheme Using the Convection Flux (mentioning

confidence: 99%

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

Wu¹,

Chao²,

Wu³

et al. 2017

Science and Technology of Nuclear Installations

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As compared to the two-fluid single-pressure model, the two-fluid seven-equation two-pressure model has been proved to be unconditionally well-posed in all situations, thus existing with a wide range of industrial applications. The classical 1st-order upwind scheme is widely used in existing nuclear system analysis codes such as RELAP5, CATHARE, and TRACE. However, the 1st-order upwind scheme possesses issues of serious numerical diffusion and high truncation error, thus giving rise to the challenge of accurately modeling many nuclear thermal-hydraulics problems such as long term transients. In this paper, a semiimplicit algorithm based on the finite volume method with staggered grids is developed to solve such advanced well-posed twopressure model. To overcome the challenge from 1st-order upwind scheme, eight high-resolution total variation diminishing (TVD) schemes are implemented in such algorithm to improve spatial accuracy. Then the semi-implicit algorithm with high-resolution TVD schemes is validated on the water faucet test. The numerical results show that the high-resolution semi-implicit algorithm is robust in solving the two-pressure two-fluid two-phase flow model; Superbee scheme and Koren scheme give two highest levels of accuracy while Minmod scheme is the worst one among the eight TVD schemes.

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Section: High-resolution Tvd Scheme Using the Convection Flux (mentioning

confidence: 99%

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

Wu¹,

Chao²,

Wu³

et al. 2017

Science and Technology of Nuclear Installations

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“…The pressure relaxation coefficient can be defined as

μ = \frac{1}{τ_{P}} \frac{α_{f} α_{g}}{P_{f} + P_{g}},

where an empirical constant τ P = 1.0 × 10 −6 s is used and the numerical results in this paper show reasonable agreement with the exact solutions or those from the other T‐H codes. The net interfacial mass transfer per unit volume can be calculated by

Γ_{g} = - \frac{H_{ig} ((), T^{s} - T_{g}) + H_{if} ((), T^{s} - T_{f})}{h_{g}^{*} - h_{f}^{*}} .

…”

Section: Two‐fluid Two‐pressure Modelmentioning

confidence: 99%

“…Since the TOU_TVD_CFL scheme lies in the TVD region under the Courant limit, it is a stable TVD scheme without compromising its higher-order accuracy whenever possible. The high-order scheme can be achieved by substituting Equation (32) or Equation (33) into Equation (16) to calculate the donor quantities with an over-dot in the numerically evaluated flux (12).…”

Section: High-order Spatial Discretization Schemementioning

confidence: 99%

Development of temporal and spatial high‐order schemes for two‐fluid seven‐equation two‐pressure model and its applications in two‐phase flow benchmark problems

Chao

Liu

Shan

et al. 2018

Numerical Methods in Fluids

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Summary Current existing main nuclear thermal‐hydraulics (T‐H) system analysis codes, such as RALAP5, TRACE, and CATHARE, play a crucial role in the nuclear engineering field for the design and safety analysis of nuclear reactor systems. However, two‐fluid model used in these T‐H system analysis codes is ill posed, easily leading to numerical oscillations, and the classical first‐order methods for temporal and special discretization are widely employed for numerical simulations, yielding excessive numerical diffusion. Two‐fluid seven‐equation two‐pressure model is of particular interest due to the inherent well‐posed advantage. Moreover, high‐order accuracy schemes have also attracted great attention to overcome the challenge of serious numerical diffusion induced by low‐order time and space schemes for accurately simulating nuclear T‐H problems. In this paper, the semi‐implicit solution algorithm with high‐order accuracy in space and time is developed for this well‐posed two‐fluid model and the robustness and accuracy are verified and assessed against several important two‐phase flow benchmark tests in the nuclear engineering T‐H field, which include two linear advection problems, the oscillation problem of the liquid column, the Ransom water faucet problem, the reversed water faucet problem, and the two‐phase shock tube problem. The following conclusions are achieved. (1) The proposed semi‐implicit solution algorithm is robust in solving two‐phase flows, even for fast transients and discontinuous solutions. (2) High‐order schemes in both time and space could prevent excessive numerical diffusion effectively and the numerical simulation results are more accurate than those of first‐order time and space schemes, which demonstrates the advantage of using high‐order schemes.

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“…Mathematical models for the simulation of two-phase compressible flows based on the Baer–Nunziato (BN) system of equations (Baer and Nunziato, 1986) and its following developments became widespread in the past decade. They are used nowadays in various fields such as simulation of propagation of detonation waves in heterogeneous explosives (Schwendeman et al , 2008), (Schwendeman et al , 2010), the thermal-hydraulic problems with respect to the nuclear reactors safety application (Chao et al , 2018), the motion of droplets and babbles (Nguyen and Dumbser, 2015), volcanic flows (Zeidan, 2016), cavitating flows (Goncalves and Zeidan, 2017) and many others.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of shock wave – dense particles cloud interaction using Godunov solver for Baer–Nunziato equations

Utkin

2019

HFF

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Purpose This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction. Design/methodology/approach The statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method. Findings For the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data. Originality/value Godunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.

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Study on the algorithm for solving two-fluid seven-equation two-pressure model

Cited by 10 publications

References 25 publications

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

Development of temporal and spatial high‐order schemes for two‐fluid seven‐equation two‐pressure model and its applications in two‐phase flow benchmark problems

Numerical simulation of shock wave – dense particles cloud interaction using Godunov solver for Baer–Nunziato equations

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