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

摘要CTS-0083229 C。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。 恒定密度牛顿流体的瞬时压力场和速度场的精确方程是已知的。然而，雷诺平均Navier-Stokes（RANS-）方程的平均速度是统计不封闭的。 这个封闭问题一直是一个激烈的研究领域超过50年。目前的商业CFD代码提供不同复杂性的封闭模型。 虽然雷诺应力的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流动行为的工程师仍然应用该理论。 不幸的是，对于许多具有流线曲率的实际流动，采用雷诺应力的线性梯度型模型可能会产生定性的结果。 为了解决k-ε理论的短周期性问题，人们进行了大量的努力，为雷诺应力的非闭合二阶矩方程中出现的统计相关性建立了闭合模型。 该方法是不太吸引人的设计精明的六个额外的非线性偏微分方程必须解决除了向量值RANS方程，标量值的e-方程，和连续性方程。 LES和DNS方法仅限于用于模型校准的基准流。 不幸的是，与LES和DNS相关的计算需求禁止使用这些方法在复杂的几何形状的常规工程设计calculations.With这项研究的空间平滑近似推导出一个代数preclosure表示的Reynolds应力的预应力相关的。 这种新的理论方法直接源于控制速度波动的精确动力学方程。 预应力是单位质量流体的有效脉动力的自相关，它源于瞬时雷诺应力和压力脉动的波动发散。 研究的工作假设是，预应力相关性，这显然取决于四阶统计量，更适合于一个普遍的唯象封闭的雷诺应力本身，由此产生的新的代数雷诺应力模型将开辟新的机会，工程设计。 各向同性预应力（IPS-）模型和代数预应力（AAPS-）模型将被验证的流动与强大的流线曲率和集成到一个商业软件代码，Fluent。 新的封闭模型将进行测试和优化的一类统计平稳的基准流与流线曲率。 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。

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.