Reynolds Averaged Navier-Stokes (RANS) equations are a set of equations used to model turbulent flows by averaging the effects of turbulence, making them computationally feasible for engineering applications. They introduce additional terms known as Reynolds stresses, which require modeling through turbulence models to close the system of equations.

Reynolds Averaged Navier-Stokes Equations

Reynolds Averaged Navier-Stokes

Turbulent Flows

Effects of turbulence

Computationally feasible

Engineering applications involve the practical implementation of engineering principles and techniques to solve real-world problems across various industries. These applications span multiple fields such as civil, mechanical, electrical, and software engineering, each utilizing specialized knowledge to innovate and improve systems, structures, and technologies.

Engineering Applications

Reynolds stresses are apparent stresses in turbulent flow that arise from the averaging of the nonlinear convective terms in the Navier-Stokes equations, representing the momentum transfer due to velocity fluctuations. They are crucial in the closure problem of turbulence modeling, where they need to be modeled to solve the Reynolds-averaged Navier-Stokes equations (RANS).

Reynolds Stresses

Turbulence models

A system of equations is a collection of two or more equations with a common set of variables, where the goal is to find values for the variables that satisfy all the equations simultaneously. Solving systems of equations is fundamental in various fields, including mathematics, engineering, and economics, as it allows for the modeling and solving of complex problems with multiple constraints.

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