NSF/GOALI: Validation of a New Algebraic Reynolds Stress Model for Statistically Stationary Flows

NSF/GOALI：统计平稳流的新代数雷诺应力模型的验证

• 批准号: 0083229
• 负责人: Charles Petty
• 金额: $ 6万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2003-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0083229&HistoricalAwards=false
• 关键词: NSF; GOALI; Validation; New; Algebraic

AbstractCTS-0083229C. Petty, Michigan State UniversityThe ability to predict the low-order statistical properties of turbulent flows is an important aspect of modern engineering design. The exact equations governing the instantaneous pressure and velocity fields of constant density, Newtonian fluids are known. However, the Reynolds averaged Navier-Stokes (RANS-) equation for the mean velocity is statistically unclosed. This closure problem has been an intense area of research for more that fifty years.Current commercial CFD codes offer closure models of varying complexity. Although the Boussinesq approximation for the Reynolds stress limits the utility of the k-e theory, engineers attempting to understand the flow behavior within complex spatial domains nevertheless apply this theory. Unfortunately, for many practical flows with streamline curvature, the use of a linear gradient type model for the Reynolds stress may produce qualitatively results. Significant efforts has been expended to address the short comings of the k-e theory by developing closure models for statistical correlation's that appear in the unclosed second-order moment equation for the Reynolds stress. The approach is less appealing for design in astute as six additional non-linear partial differential equations must be solved in addition to the vector-valued RANS equation, the scalar-valued e-equation, and the continuity equation. LES and DNS methods are limited to benchmark flows for model calibration. Unfortunately, computational demands associated with LES and DNS prohibit the use of these methods for routine engineering design calculations in complex geometries.With this research a spatial smoothing approximation is used to derive an algebraic preclosure representation for the Reynolds stress in terns of a prestress correlation. This novel theoretical approach stems directly from the exact dynamical equation governing velocity fluctuations. The prestress, which is a self-correlation of an effective fluctuating force per unit mass of fluid, stems from the divergence of fluctuations in the instantaneous Reynolds stress and pressure fluctuations. The working hypothesis for the research is that the prestress correlation, which depends explicitly on fourth order statistical quantities, is more amenable to a universal phenomenological closure that the Reynolds stresses itself.The resulting new algebraic Reynolds stress model will open up new opportunities for engineering design. An isotropic prestress (IPS-) model and algebraic prestress (AAPS-) model will be validated for flows with strong streamline curvature and integrated into a commercial software code, Fluent. The new closure model will be tested and optimized for a class of statistically stationary benchmark flows with streamline curvature. The IPS- and AAPS- models will be used to describe the internal flow structures encountered in hydrocyclone separators, industrial scale mixers, and swirl combustors.

摘要CTS-0083229C。佩蒂，密歇根州立大学预测湍流低阶统计特性的能力是现代工程设计的一个重要方面。 控制恒密度牛顿流体的瞬时压力和速度场的精确方程是已知的。然而，平均速度的雷诺平均纳维-斯托克斯 (RANS-) 方程在统计上是未闭合的。 五十多年来，这个闭合问题一直是一个热门的研究领域。当前的商业 CFD 代码提供了不同复杂度的闭合模型。 尽管雷诺应力的 Boussinesq 近似限制了 k-e 理论的实用性，但试图了解复杂空间域内的流动行为的工程师仍然应用了该理论。 不幸的是，对于许多具有流线曲率的实际流动，使用线性梯度型雷诺应力模型可能会产生定性结果。 为了解决 k-e 理论的缺点，人们付出了巨大的努力，通过开发出现在雷诺应力的未闭合二阶矩方程中的统计相关性的闭合模型。 该方法对于精明设计的吸引力较小，因为除了矢量值 RANS 方程、标量值方程和连续性方程之外，还必须求解六个附加非线性偏微分方程。 LES 和 DNS 方法仅限于模型校准的基准流程。 不幸的是，与 LES 和 DNS 相关的计算需求禁止使用这些方法进行复杂几何形状的常规工程设计计算。在这项研究中，使用空间平滑近似来推导预应力相关性中雷诺应力的代数预闭合表示。 这种新颖的理论方法直接源于控制速度波动的精确动力学方程。 预应力是每单位质量流体的有效脉动力的自相关性，源于瞬时雷诺应力和压力脉动的波动的发散。 该研究的工作假设是，预应力相关性明确依赖于四阶统计量，更适合雷诺应力本身的普遍唯象闭包。 由此产生的新代数雷诺应力模型将为工程设计开辟新的机会。 各向同性预应力 (IPS-) 模型和代数预应力 (AAPS-) 模型将针对具有强流线曲率的流动进行验证，并集成到商业软件代码 Fluent 中。 新的闭合模型将针对一类具有流线曲率的统计平稳基准流进行测试和优化。 IPS 和 AAPS 模型将用于描述水力旋流分离器、工业规模混合器和旋流燃烧器中遇到的内部流动结构。