• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.5
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• pp.1383-1393
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• 2014

Recently, with rapid improvement in computer hardware and theoretical development in the field of computational fluid dynamics, high-order accurate schemes also have been applied in the realm of computational hydraulics. In this study, numerical solutions of 1D shallow water equations are presented with TVD Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The transcritical flows such as dam-break flows due to instant dam failure and transcritical flow with bottom elevation change were studied. As a formulation of approximate Riemann solver, the local Lax-Friedrichs (LLF), Roe, HLL flux schemes were employed and MUSCL slope limiter was used to eliminate unnecessary numerical oscillations. The developed model was applied to 1D dam break and transcritical flow. The results were compared to the exact solutions and experimental data.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.15 no.6
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• pp.461-470
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• 2003

The purpose of this study is to investigate the performance of a transcritical cycle for hot water heating using $CO_2$ as a working fluid. Some of the main parameters that affect the practical performance of the $CO_2$ system are discussed; the performance on the variation of refrigerant charge, changes in flow conditions of secondary fluids, and that with or without internal heat exchanger, The experimental results show that the optimum charge is approximately the same for various mass flow rates of the secondary fluid at gas cooler. The experimental results on the effect of secondary fluids are in general agreement with the experimental results of transcritical cycle in the open literature and show similar trend for conventional subcritical vapor compression cycles. The heat exchanger effectiveness increases with an increase of the heat exchange area of the internal heat exchanger regardless of the mass flow rate at the gas cooler.

• Journal of Korea Water Resources Association
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• v.36 no.4
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• pp.597-608
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• 2003

A transcritical flow occurs when the width and slope of a channel are varying abruptly. In this study, the transcritical flow in a two-dimensional open channel is analyzed by using the shallow-water equations. A weighted average flux scheme that has flux limiter with a total variation diminishing condition is introduced for a second-order accuracy in time and space, and non- spurious oscillations at discontinuous points. A HLLC method with three wane speeds is employed to calculate the Riemann problem. To overcome difficulties resulting from variation of channel sections in a two-dimensional analysis of transcritical flow, the numerical model is developed based on a generalized grid system.

• Journal of Korea Water Resources Association
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• v.34 no.1
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• pp.45-55
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• 2001

Transcritical flow is a term intended to denote the existence of both supercritical and subcritical flows within a computational domain. The major problems that need to be addressed while modeling transcritical flows include handling the differing features of signal propagation in subcritical and supercritical flow regions and maintaining conservation. The present study proposes the implicit ENO method as a high-resolution scheme for transcritical flow. This implicit ENO scheme is based on the ENO method, a new class of uniformly high-order-accurate essentially non-oscillatory implicit scheme, which has the advantage of unconditional stability. The implicit ENO scheme has not been used for the transcritical flow in open channel until now. As a result of application to the hypothetical dam-break flow, the implicit ENO scheme was ploved to produce accurate results with good robustness even though in the case of verb strong shock wave.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.320-329
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• 2008

The influence of thermodynamic transition associated with transcritical nitrogen injection upon the flow structure was investigated to explore numerical simulation of the injectant dynamics of oxygen/hydrogen coaxial jet in liquid rocket engines. Single and coaxial nitrogen jets were treated by comparing the transcritical and perfect-gaseous conditions, wherein the numerical model was accommodative to the real-fluid thermodynamics and transport properties at supercritical pressures. The model was in the first place validated by comparing the results of transcritical nitrogen injection between calculations and available experiments. For a single jet under the transcritical condition, the nitrogen kept a relatively high density up to its pseudo-critical temperature inside the mixing layer, since it remains less expanding until heated up to its pseudo-critical temperature. Numerical analysis revealed that cryogenic jets exhibit strong dependence of specific enthalpy profile upon the associated density profile that are both dominated by turbulent thermal diffusion. In the numerical model, therefore, exact evaluation of turbulent heat fluxes becomes very important for simulating turbulent cryogenic jets under supercritical pressures. Concerning the coaxial jets due to transcritical/gaseous nitrogen injections, the density profile inside the mixing layer was again affected by the thermodynamic transition of nitrogen. However, hydrodynamic instability modes of the inner jet did not show significant differences by this thermodynamic transition, so that further study is needed for the mixing process downstream of the near injection position.

• Journal of Korea Water Resources Association
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• v.34 no.1
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• pp.57-65
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• 2001

A numerical model for analyzing transcritical flow in open channel is tested to various cases of channel shape. As the numerical models developed for transcritical flow until now mainly focused on the application to only prismatic or hypothetical channels, there are some restrictions to apply the nonprismatic channels. In this study, to verify the accuracy and stability of second-order implicit ENO scheme, the numerical model was applied to the channels which haute the varying channel bed and width. Also the numerical model was applied to unsteady flow as well as steady flow. The study shows that the numerical model provides good accuracy in the calculation of stage and velocity with no numerical oscillation, particularly in the calculation of hydraulic jump and discontinous flow Then the implicit ENO scheme demonstrated good accuracy as a high-resolution scheme and stability as an implicit scheme.

• Journal of Korea Water Resources Association
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• v.47 no.11
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• pp.1061-1066
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• 2014

A stable second-order finite volume method was proposed to predict sediment transport under rapidly varied flow conditions such as transcritical flow. For the use under unsteady flow conditions, a sediment transport model was coupled with shallow water equations. HLLC approximate Riemann solver based on a monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction was used for the computation of the flux terms. From the comparisons of dam break flow experiments on erodible beds in one- and two-dimensional channels, good agreements were obtained when proper parameters were provided. Lastly, dam surface erosion problem by overtopped water was simulated. Overall, the numerical solutions showed reasonable results, which demonstrated that the proposed numerical scheme could provide stable and physical results in the cases of subcritical and supercritical flow conditions.

• The Journal of the Korea Contents Association
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• v.13 no.3
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• pp.428-434
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• 2013

With the increase of the frequency in large-scale floods and natural disasters, the demands for highly accurate numerical river models are also rapidly growing. Generally, flows in rivers are modeled with previously developed and well-established numerical models based on shallow water equations. However, the so-far-developed models reveal a lot of limitations in the analysis of discontinuous flow or flow which needs accurate modeling. In this study, the numerical shallow water model based on the discontinuous Galerkin method was applied to the simulation of one-dimensional transcritical flow, including dam break flows and a flow over a hump. The favorable agreement was observed between numerical solutions and analytical solutions.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09a
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• pp.193-195
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• 2005

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09a
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• pp.639-640
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• 2005