A numerical derivation of internal energy equation under a staggered mesh system for 1-D thermal hydraulic system analysis codes
| Autor: | Kwi-Seok Ha, Kyung Doo Kim, Jaeseok Heo |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Pressure drop Nuclear and High Energy Physics Internal energy 020209 energy Mechanical Engineering Multiphase flow 02 engineering and technology Mechanics 01 natural sciences Control volume 010305 fluids & plasmas Nuclear Energy and Engineering 0103 physical sciences Heat transfer 0202 electrical engineering electronic engineering information engineering General Materials Science Safety Risk Reliability and Quality Adiabatic process Waste Management and Disposal Mechanical energy Numerical stability |
| Zdroj: | Nuclear Engineering and Design. 371:110935 |
| ISSN: | 0029-5493 |
| Popis: | This paper introduces a modified internal energy equation derived for multiphase flow in various flow conditions for a staggered mesh system. The pressure drop and heat dissipation terms in the internal energy conservation equation currently being developed based on the assumption that the scalar and momentum variables, which originate from the total energy and mechanical energy equations, respectively, are all located in the cell center of the control volume were redefined such that two different pressures and velocities stored in both cell centers and faces were imposed for the internal energy conservation. To achieve this, first, a modified internal energy conservation equation for a staggered mesh was derived by subtracting the mechanical energy equation from the total energy equation. The equation was then discretized classifying each term by its origin; variables that originated from the total energy equation were defined in the cell center, whereas terms that came from the mechanical energy equation were identified at faces. Since the discretized form of the proposed equation contained face velocity and cell pressure for the heat dissipation and pressure drop terms, respectively, these two terms were calculated implicitly leading to enhanced numerical stability. The accuracy of the modified internal energy equation in predicting the system pressure, fluid temperature, and heat balance for various flow channels was assessed. The verification of the proposed equation was completed through simulations of multiple theoretical problems including saturated liquid depressurization, adiabatic expansion of hydrogen, heat transfer in a helical steam generator, and energy transfer in a converging pipe. An improved result was obtained with the modified equation as the numerical calculation results agreed well with the analytic solutions with relative deviations less than 0.1% for most cases, while the solution obtained by the conventional internal energy equation showed a significant amount of deviation from the analytic solution. |
| Databáze: | OpenAIRE |
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