1、RANS（Reynolds

不同的 RANS 模型采用不同的方式来描述湍流的封闭方程和湍流应力（雷诺应力），每种模型都有其适用范围和优缺点。 以下是几种常见的 RANS 湍流模型：

2、雷诺平均方程_百度百科

所谓湍流模型，就是以雷诺平均NS (RANS)方程与脉动方程为基础，依靠理论与经验的结合，引进一系列模型假设，建立一组描写湍流平均量的封闭方程组的理论计算方法。

3、Reynolds

RANS, or Reynolds-Averaged Navier-Stokes, refers to a time-averaged equation used to describe fluid flow motion, particularly in turbulent flows. It approximates the time-averaged solutions of the Navier-Stokes equations by incorporating knowledge of flow turbulence properties.

孙博华院士：对湍流雷诺平均方程 (RANS)的重新考察

针对湍流研究一百多年来没有多少本质进展的困境，作者敢于把目光越过所有先代学者的伟大成就，直接回到130年前Reynolds研究湍流的起点，重温 Reynolds 的湍流原点思想，以期获得对湍流RANS方程的深刻理解。

The Reynolds

The Reynolds-averaged Navier-Stokes (RANS) equations are a reduced form of the general Navier-Stokes equations. In the RANS equations, the steady-state solution is decoupled from the time-varying fluctuations in the system, the latter of which will account for turbulence in different flow regimes.

CFD理论

虽然瞬时的Navier-Stokes方程可以描述湍流，但是方程的非线性使得求解精确解极端困难，在工程应用上应用很少。 而均化的Navier-Stokes方程（《CFD理论|湍流流动方程》）可以将瞬态的脉动量通过时均化方程体现。

4.1.1. Reynolds (Ensemble) Averaging

In Reynolds averaging, the solution variables in the instantaneous (exact) Navier-Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged) and fluctuating components.

雷诺平均方程

湍流运动是随空间和时间随机变化的复杂流动，但其平均运动往往为时空缓变的，因而首先受到关注，特别是在实际应用中。 为研究湍流的平均运动，O.雷诺提出对描述流体运动的纳维-斯托克斯方程进行平均运算（见 湍流平均方法），根据平均运算法则，得到如下平均化后的纳维-斯托克斯方程组（以均质不可压缩流动为例），在直角坐标系中可表示为： 式中， 分别为平均速度和脉动速度；， 分别为平均压强和脉动压强； 为流体密度； 为平均体积力； 为运动学黏性系数。 该方程组称为雷诺平均方程。 可压缩流也有类似的雷诺平均方程。 雷诺平均方程由于出现了不封闭项（动量方程右边最后一项），需要在引入适当的模型后才能求得湍流平均流动的解。 由于湍流的普遍存 …

B2.4 雷诺平均纳维·Stokes

RANS (Reynolds-Averaged Navier-Stokes) 模型被广泛用于风工程领域，以及各种长度尺度的湍流模型建模。 基本方法是将速度分解为平均波动速度和湍流波动速度。

Reynolds

The Reynolds-averaged Navier-Stokes (RANS) equations are time-averaged [1] equations of motion for fluid flow. They are primarily used while dealing with turbulent flows.

Reynolds Averaged Navier-Stokes (RANS) is a computational fluid dynamics (CFD) method used to simulate the flow behavior of incompressible fluids in fluid fields. This approach is primarily applied in engineering fields such as aerospace, automotive industry, and energy systems. The core of the RANS method involves solving the Navier-Stokes equations using finite volume and finite element methods. These equations describe the relationships between fluid momentum, energy, and turbulence characteristics.

The main categories of RANS elements include:

1. Governing Equations: The foundation of RANS is the Navier-Stokes equations, which describe the relationships between fluid momentum, energy, and turbulence. In practical applications, these equations are typically solved through discretization and numerical methods.

2. Discretization Methods: To transform continuous partial differential equations into discrete forms, appropriate discretization methods are required. Common methods include finite difference, finite element, and finite volume methods. The choice depends on the geometric shape of the problem, boundary conditions, and precision requirements.

3. Numerical Solving: The discretized equations must be solved numerically. Popular methods include finite difference, finite element, and finite volume approaches. The selection depends on the physical properties of the problem, mesh generation techniques, and computational performance.

4. Boundary Conditions: RANS models require appropriate boundary conditions to describe interactions between fluids and solid walls. These may include no-slip boundaries, adiabatic boundaries, or non-heat-exchange boundaries.

5. Initial Conditions: RANS models also need initial conditions to define the fluid's starting state, such as velocity distribution, pressure distribution, and temperature distribution.

6. Iterative Solving: Numerical solutions involve iterative processes to gradually approach the true solution. Methods like Newton's method, Gaussian elimination, or conjugate gradient algorithms are commonly used. The choice depends on geometric complexity, precision requirements, and computational resources.

7. Post-Processing Analysis: Output results from RANS models require post-processing to extract useful information. Common techniques include visualization, data interpolation, and statistical analysis, which help engineers better understand and optimize fluid system performance.

8. Validation and Optimization: To ensure accuracy and reliability, RANS models must be validated against experimental data. Model performance can also be improved by adjusting parameters or refining mesh techniques.

9. Parallel Computing: With advancements in computing technology, large-scale problems often necessitate parallel computing to enhance efficiency. Techniques like distributed computing or GPU acceleration are frequently employed.

10. Multi-Scale Simulation: Fluid systems in engineering often span multiple scales. Multi-scale simulation decomposes large-scale problems into smaller subproblems, solves them independently, and integrates the results for comprehensive analysis.

RANS is a widely used CFD method in engineering. By discretizing and numerically solving the Navier-Stokes equations, it effectively simulates incompressible fluid flow. As computing technology advances, RANS continues to evolve, providing engineers with increasingly precise and reliable tools for design and analysis.