The mixing-enhancement effect of turbulence is widely applied to various fluid-related machinery in mechanical engineering.
Therefore, in addition to the fundamental knowledge of fluid mechanics, a basic understanding of statistical analysis methods
for turbulence and knowledge of numerical simulation techniques for turbulent flows are essential for the development and
research of such fluid-related technologies.
The objective of this course is to provide students with a fundamental understanding of turbulence engineering.
The objective of this course is to provide students with a fundamental understanding of turbulence engineering.
In turbulent flows, countless vortices of various sizes are generated within the flow and interact with one another in a complex
manner. The interactions among these vortical structures across different scales enhance mixing in the flow, which leads to
significant increases in frictional drag and heat transfer experienced by objects in the flow, thereby affecting the energy
efficiency of fluid-related machinery.
As a foundation for analytical approaches to turbulence, this course first introduces the derivation of the Reynolds-averaged Navier–Stokes equations and explains the concept of Reynolds stresses, followed by a discussion of the Reynolds stress transport equations. It then examines what kinds of vortical structures arise and how turbulence is sustained in a fundamental turbulent flow field, namely wall-bounded turbulence along a flat plate.
In the latter half of the course, after covering the multiscale nature of turbulence and spectral analysis, various turbulence prediction methods are introduced, including direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged modeling. Students will conduct simulations and present their results in a final presentation to deepen their understanding.
As a foundation for analytical approaches to turbulence, this course first introduces the derivation of the Reynolds-averaged Navier–Stokes equations and explains the concept of Reynolds stresses, followed by a discussion of the Reynolds stress transport equations. It then examines what kinds of vortical structures arise and how turbulence is sustained in a fundamental turbulent flow field, namely wall-bounded turbulence along a flat plate.
In the latter half of the course, after covering the multiscale nature of turbulence and spectral analysis, various turbulence prediction methods are introduced, including direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged modeling. Students will conduct simulations and present their results in a final presentation to deepen their understanding.
- Students are able to explain the derivation of the Reynolds-averaged Navier–Stokes (RANS) equations and the physical meaning of Reynolds stresses. They will also be able to derive the Reynolds stress transport equations and explain, with mathematical justification, the physical significance of the production, dissipation, diffusion, and other terms appearing in these equations. Furthermore, based on these fundamental analytical methods, students will be able to critically analyze and interpret data obtained from turbulence experiments and numerical simulations.
- Students are able to describe the characteristics of wall-bounded turbulence, including the mean velocity profile and the
distribution of velocity fluctuation intensities near the wall, with reference to wall units and the law of the wall.
They are also able to explain why these mean velocity and turbulence intensity distributions take such forms, relating them to the coherent vortex structures that arise in the near-wall region. - Students are able to explain the multi-scale nature of turbulence and how it depends on the Reynolds number. They will understand the physical meaning of the energy spectrum and its relationship to turbulent kinetic energy, and be able to apply this understanding to the analysis of turbulent flows.
- Students are able to understand the differences among the major numerical simulation methods for turbulence and select an appropriate approach depending on the problem at hand. They will also be able to assess and discuss the validity of the simulation results obtained.
| Reports | Final Presentation | Final Report | Total. | |
|---|---|---|---|---|
| 1. | 10% | 5% | 5% | 20% |
| 2. | 10% | 10% | 10% | 30% |
| 3. | 5% | 10% | 10% | 25% |
| 4. | 5% | 10% | 10% | 25% |
| Total. | 30% | 35% | 35% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Introduction and Overview of the Course | Review of Applied Mathematics | 190minutes |
| 2． | The Fundamental Flow Equations (Continuity Equation and Navier–Stokes Equations) | Review of Fundamentals of Fluid Mechanics | 190minutes |
| 3． | Introduction of Turbulence | Assignments | 190minutes |
| 4． | Scales of Turbulent Fluid motions and Numerical Simulations of Turbulent Flows | Assignments | 190minutes |
| 5． | Numerical simulations of Turbulent Flows based on the Reynolds-Averaged Navier-Stokes (RANS) Equation (1): Introduction of Eddy Viscosity and Transport Equation of Turbulent Kinetic Energy |
Assignments | 190minutes |
| 6． | Numerical simulations of Turbulent Flows based on the Reynolds-Averaged Navier-Stokes (RANS) Equation (2): k-ε Closure model |
Assignments | 190minutes |
| 7． | Numerical simulations of Turbulent Flows based on the Reynolds-Averaged Navier-Stokes (RANS) Equation (3): Closure based on the Reynolds-Stress Transport Equations (RSM) |
Assignments | 190minutes |
| 8． | Large-Eddy Simulation | CFD Practice | 190minutes |
| 9． | Wall Turbulence | CFD Practice | 190minutes |
| 10． | Midterm Presentation on the CFD Project | CFD Practice | 190minutes |
| Preparation for the Presentation | 100minutes | ||
| 11． | Applications of Turbulence Modeling Simulations to Various Flow Fields | CFD Practice | 190minutes |
| 12． | CFD Practice | CFD Practice | 190minutes |
| 13． | CFD Practice | CFD Practice | 190minutes |
| 14． | Final Presentation | Preparation of Presentation | 190minutes |
| Preparation of Final Report | 240minutes | ||
| Total. | - | - | 3000minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback outside of the class (ScombZ, mail, etc.) |
Course materials will be distributed via Scombz.
Recommended Additional Textbooks to read：
H.Tennekes, J.L.Lumley, ”First couse in Turbulence”, MIT Press
Peter S. Bernard, James M. Wallace, ”Turbulent Flow: Analysis, Measurement, and Prediction”, Wiley
Recommended Additional Textbooks to read：
H.Tennekes, J.L.Lumley, ”First couse in Turbulence”, MIT Press
Peter S. Bernard, James M. Wallace, ”Turbulent Flow: Analysis, Measurement, and Prediction”, Wiley
Students should review linear algebra, partial differential equations, ordinary differential equations, and fluid mechanics-related
subjects.
- If you have any questions, please contact me by email : kawata@shibaura-it.ac.jp
If you would like to discuss something in person, please make an appointment via email.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
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Last modified : Sat Mar 14 14:15:19 JST 2026