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Maximum Entropy Method for Solving the Turbulent Channel Flow Problem.

T-W Lee1

  • 1Mechanical and Aerospace Engineering, SEMTE, Arizona State University, Tempe, AZ 85287, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study presents a new method for solving turbulent channel flow using Galilean-transformed Navier-Stokes equations and the maximum entropy principle. The approach accurately predicts turbulent kinetic energy and Reynolds stress, validating with direct numerical simulation data.

Keywords:
energy distributionmaximum entropy principleturbulence

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Area of Science:

  • Fluid Dynamics
  • Turbulence Modeling
  • Computational Fluid Dynamics

Background:

  • Turbulent channel flow is a fundamental problem in fluid dynamics.
  • Accurate modeling of Reynolds stress and turbulent kinetic energy is crucial for predicting flow behavior.
  • Existing methods often rely on empirical models or computationally expensive simulations.

Purpose of the Study:

  • To develop a novel theoretical framework for solving turbulent channel flow problems.
  • To derive expressions for Reynolds stress and turbulent kinetic energy using fundamental principles.
  • To validate the proposed method against high-fidelity simulation data.

Main Methods:

  • Utilizing Galilean-transformed Navier-Stokes equations to derive a theoretical expression for Reynolds stress (u'v').
  • Applying the maximum entropy principle to determine the spatial distribution of turbulent kinetic energy.
  • Integrating derived quantities to compute velocity profiles in channel flows.

Main Results:

  • The study successfully derived theoretical expressions for Reynolds stress and turbulent kinetic energy.
  • The computed velocity profiles showed excellent agreement with direct numerical simulation (DNS) data at Reynolds numbers Reτ = 400 and 1000.
  • The Reynolds stress gradient budget confirmed the alternative interpretation of turbulence momentum balance.

Conclusions:

  • The combined approach of Galilean-transformed Navier-Stokes equations and maximum entropy principle offers a robust method for turbulent channel flow analysis.
  • This work provides a theoretically grounded alternative to traditional turbulence modeling approaches.
  • The findings have implications for improving the accuracy and efficiency of computational fluid dynamics simulations.