# Scale interactions in wall turbulence: Old challenges tackled with new perspectives

Lead Research Organisation:
University of Southampton

Department Name: Faculty of Engineering & the Environment

### Abstract

The need to improve the efficiency of fluid-based systems is now of paramount importance. In experimental aerodynamics, one of the most difficult measurements is an accurate determination of surface friction. Our need to predict it accurately is fundamentally important to the design of efficient systems. Reynolds number similarity is an essential concept in describing the fundamental properties of turbulent wall-bounded flow. Unlike the drag coefficient for bluff bodies, that for a turbulent boundary layer continues to decrease indefinitely with increasing Reynolds number because the small-scale motion near the surface is directly affected by viscosity at any Reynolds number. Therefore Reynolds number similarity is very important in design and is a vital tool for the engineer, who, plied with information from either direct numerical simulations or wind-tunnel tests (or both), may well have to extrapolate over several orders of magnitude in order to estimate quantities such as drag at engineering or even meteorological Reynolds numbers. Perhaps the most well-known example of Reynolds number similarity is the region of log velocity variation (the log law) found in wall-bounded flows which, at sufficiently high Reynolds numbers, exists regardless of the nature of the surface boundary condition or the form of the outer imposed length scale.

In wall-bounded flows relevant to practical applications, where the flow is turbulent and the Reynolds number is high, the transport and loss of fluid momentum and energy is not well understood. Consequently, most predictive and modelling methods rely on a variety of assumptions. The two most critical ones are the Law of the Wall (the log law) and Townsend's local-equilibrium hypothesis. Both assumptions implicitly assume that large scales in the flow are weak and that they function independently of the small scales. However, this is clearly not true, especially in flows of engineering importance, such as when the surface is rough or when the flow is not in equilibrium. In fact, there is a multiscale interaction, referred to here as an inner-outer interaction (IOI), where the large scales influence the dynamics of the small scales and vice-versa. These interactions are not well understood and therefore any corrections to the predictive models to include these interactions are essentially achieved through ad-hoc means.

A better understanding of IOI will help explain the apparent non-universality of the constants in the log law and will certainly influence the development of models for both Reynolds-Averaged Navier-Stokes (RANS) calculation methods, Large-Eddy Simulations (LES) and hybrid RANS-LES. It will also be useful in the development of models for the control of wall turbulence, complementing knowledge from Direct Numerical Simulations which, we believe, are inherently incomplete owing to the restriction to low Reynolds numbers. Accurate models for prediction and control at realistic Reynolds numbers typical of practical applications will have to address IOI. Researchers working in specific areas of internal rough-wall flows, rough-wall boundary layers and freestream turbulence effects on boundary layers will also benefit from this fundamental work. All these aspects are abundantly present in a variety of practical applications and natural systems. For example, researchers exploring modelling strategies for practical applications such as oil and natural-gas pipelines, ship hulls and the natural and urban terrains will find the the data obtained from the roughness experiments to be very useful for validation exercises. Similarly, researchers in the area of turbomachinery will find the data from the roughness and freestream turbulence experiments extremely useful.

In wall-bounded flows relevant to practical applications, where the flow is turbulent and the Reynolds number is high, the transport and loss of fluid momentum and energy is not well understood. Consequently, most predictive and modelling methods rely on a variety of assumptions. The two most critical ones are the Law of the Wall (the log law) and Townsend's local-equilibrium hypothesis. Both assumptions implicitly assume that large scales in the flow are weak and that they function independently of the small scales. However, this is clearly not true, especially in flows of engineering importance, such as when the surface is rough or when the flow is not in equilibrium. In fact, there is a multiscale interaction, referred to here as an inner-outer interaction (IOI), where the large scales influence the dynamics of the small scales and vice-versa. These interactions are not well understood and therefore any corrections to the predictive models to include these interactions are essentially achieved through ad-hoc means.

A better understanding of IOI will help explain the apparent non-universality of the constants in the log law and will certainly influence the development of models for both Reynolds-Averaged Navier-Stokes (RANS) calculation methods, Large-Eddy Simulations (LES) and hybrid RANS-LES. It will also be useful in the development of models for the control of wall turbulence, complementing knowledge from Direct Numerical Simulations which, we believe, are inherently incomplete owing to the restriction to low Reynolds numbers. Accurate models for prediction and control at realistic Reynolds numbers typical of practical applications will have to address IOI. Researchers working in specific areas of internal rough-wall flows, rough-wall boundary layers and freestream turbulence effects on boundary layers will also benefit from this fundamental work. All these aspects are abundantly present in a variety of practical applications and natural systems. For example, researchers exploring modelling strategies for practical applications such as oil and natural-gas pipelines, ship hulls and the natural and urban terrains will find the the data obtained from the roughness experiments to be very useful for validation exercises. Similarly, researchers in the area of turbomachinery will find the data from the roughness and freestream turbulence experiments extremely useful.

### Publications

Dogan E
(2017)

*Modelling high Reynolds number wall-turbulence interactions in laboratory experiments using large-scale free-stream turbulence.*in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Elsinga G
(2013)

*Advances in 3D velocimetry*in Measurement Science and Technology
Ganapathisubramani B
(2012)

*Amplitude and frequency modulation in wall turbulence*in Journal of Fluid Mechanics
Hanson R
(2016)

*Development of turbulent boundary layers past a step change in wall roughness*in Journal of Fluid Mechanics
Placidi M
(2015)

*Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers*in Journal of Fluid Mechanics
Taddei S
(2016)

*Characterisation of drag and wake properties of canopy patches immersed in turbulent boundary layers*in Journal of Fluid Mechanics
Vanderwel C
(2015)

*Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers*in Journal of Fluid MechanicsDescription | In this project, we attempted to understand the impact of changes in boundary conditions on the nature of turbulent flows. This will enable us to develop new ways to control flows and improve the efficiency of flow systems. We developed a new way of examining the flow where the the surface of the flow goes from rough to smooth. This has a wide variety of practical applications where regions of wing surfaces or pipes have areas that are rough and those that are smooth. Understanding how the flow over these areas interact with each other will allow us to predict the power consumption in these systems. |

Exploitation Route | We have carried out extensive measurements of turbulent flows that flow from a rough surface on to a smooth surface. We analysed the data and we have an extensive database for this type of flow. This database (which is now published) will allows modellers and computational experts to use the data to develop new models to predict drag and power consumption of such flows and also for validation of their methods. In fact, this has already started happening with researchers from around the world are downloading this data (It has been downloaded from our website 8 times). A new worldwide special interest group was setup under the auspices of NATO to examine scale interactions and its effect of non-equilibrium flows. I could not participate in this because I am not a citizen of a NATO country. |

Sectors | Aerospace, Defence and Marine,Energy,Transport |

Description | The findings from this project will be used to develop new models to predict the behaviour of flows over surfaces that some regions that are smooth and other regions that are rough. These type of surfaces are abundant in nature as well as in engineering applications. |

First Year Of Impact | 2014 |

Sector | Aerospace, Defence and Marine,Energy,Transport |

Description | Collaboration with Melbourne |

Organisation | University of Melbourne |

Country | Australia |

Sector | Academic/University |

PI Contribution | We carried out collaborative experiments at Southampton of flows over smooth and rough surfaces. The rough surfaces were manufactured in Melbourne and shipped to Southampton for the measurements. |

Collaborator Contribution | The collaborators allowed access to their unique wind tunnel facility as well as provided the rough surfaces for measurements in Southampton. |

Impact | We have published 2 papers as a result of the collaboration with Melbourne. We are currently working on further publications. |

Start Year | 2009 |

Description | Collaboration with Princeton |

Organisation | Princeton University |

Country | United States |

Sector | Academic/University |

PI Contribution | I spent 6 months on a sabbatical at Princeton working with students to develop a new experiment as well as in data analysis. The fact that I got access to the utilise the superpipe facility (A unique facility) at Princeton is critical. |

Collaborator Contribution | The partners at Princeton provided a host institution for my sabbatical as well as provided the human and infrastructure resources to carry out state-of-the-art research in the area of turbulent flows. |

Impact | We are currently working on publications that is came out of the work that was carried out when I was in Princeton. |

Start Year | 2013 |