Abstract 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.

中文翻译：

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一维热力水力系统分析代码交错网格系统下内能方程的数值推导

摘要 本文介绍了在交错网格系统的各种流动条件下为多相流推导的修正内能方程。目前正在开发的内部能量守恒方程中的压降和散热项基于假设标量和动量变量，分别源自总能量和机械能方程，都位于控制单元的中心体积被重新定义，以便存储在单元中心和面的两种不同的压力和速度用于内部能量守恒。为了实现这一点，首先，通过从总能量方程中减去机械能方程，推导出交错网格的修正内部能量守恒方程。然后将方程离散化，按每个项的原点分类；源自总能量方程的变量在单元中心定义，而来自机械能方程的项在面处确定。由于所提出方程的离散形式分别包含散热和压降项的面速度和单元压力，因此隐式计算了这两项，从而提高了数值稳定性。评估了修正的内部能量方程在预测系统压力、流体温度和各种流动通道的热平衡方面的准确性。通过对饱和液体降压、氢气绝热膨胀、螺旋蒸汽发生器中的热传递，以及会聚管中的能量传递。改进后的方程得到了改进的结果，数值计算结果与解析解吻合较好，大多数情况下相对偏差小于0.1%，而常规内能方程得到的解与解析解有较大偏差。解决方案。