Flow Control using Convergent-Divergent Riblets, a Type of Bio-Inspired Micro-Scale Surface Patterns

**Principal Investigator:**

Jian Fang

**Affiliation:**

Scientific Computing Department, STFC Daresbury Laboratory, UK

**Local Project ID:**

FlowCDR

**HPC Platform used:**

Hawk of HLRS

**Date published:**

**Introduction**

It has recently been discovered that micro-scale directional grooves with spanwise heterogeneity can induce large-scale vortices across the boundary layer. This phenomenon is of great importance to both theoretical research and industrial applications, because of its influence on near-wall turbulence dynamics and its potential in reducing surface friction drag and suppressing flow separation. The fact that such grooves are small is especially attractive in aerospace engineering because shock-waves might be triggered by large devices mounted on the surface (vortex generators, for instance). Surface friction drag and flow separation are common flow phenomena in practical engineering applications, such as the ones including aircrafts, road vehicles, ships, turbine blades, for instance. Surface friction drag has a large impact on fuel consumption, cruising range and endurance, while flow separation can result in a drag increase and degradation of the aerodynamic performance.

Many experiments and numerical simulations have been devoted to such a passive control method. Most of the studies involve experimental methods, and due to the limitation of measurement methods in their experiments, the flow field data near the wall and the surface skin friction are not available. Although the large-scale roll motion is observed, the micro-scale secondary flow near the wall is not captured. The latter plays an important role in momentum transfer near the wall and surface skin friction modification. Prior experimental investigation based on fully developed turbulent pipe flows have shown a total drag reduction up to 20%, which is much higher than for longitudinal riblets. However no convincing explanation has been given. why this occurs.

**Methods**

In the present project, we have used the direct numerical simulation (DNS) approach to explore flow structure and control mechanism of convergent-divergent (C-D) riblets, as well as the impact of the riblet dimensions. DNS is the most accurate computational fluid dynamics (CFD) approach to simulate turbulent flows, as it resolves turbulence down to the smallest scale without using any empirical models. It provides the most accurate and detailed data about turbulence, especially for the study of wall turbulence under the influence of small-scale control devices.

The CFD solver used for this project is the in-house code called ASTR, which is developed by Dr Jian Fang. It is a high-order finite-difference solver for compressible Navier-Stokes equations, and has been applied in a series of DNS of turbulent flows. The code is written in FORTRAN 90, and uses MPI to handle parallelisation. In the present project, the study is limited to the incompressible regime, and a 6^{th}-order compact central scheme with 10^{th}-order compact filter is used to solve the Navier-Stokes equations. The compact scheme has the advantage of resolving small-scale flow structures, but does not parallelise well. An interface decoupling method was developed to improve its parallel performance, while retaining accuracy [1].

The computational domain is sketched in Fig. 1. The C-D riblets are mounted on both the bottom and top walls, and the domain is symmetrical with regard to the channel centre plane. As displayed in Fig. 1(a), adjacent left-tilted and right-tilted grooves intersect at a diverging line (DL) and converging line (CL). The yaw angle *γ* denotes the angle between the riblet grooves and the *x*-axis direction, and the wavelength *Λ* is the width of two adjacent riblet strips. Riblets with trapezoidal grooves are used and the riblet geometry is described by the height (*h*), spacing (*s*) and ridge angle (*α*). A structured grid with hexahedral cells is generated to mesh the computational domain, where stretching is controlled by an analytical formulation that adapts the grid to the highly distorted surface of the riblets, which ensures smoothness and resolution in the near-wall region.

**Results **

The instantaneous flow field is shown in Fig. 2. The turbulence structures are modulated by the alternatively distributed C-D riblets. More dense and intensive vortical structures are seen around DL, and the turbulence is somewhat less energetic around CL. The instantaneous velocity is clearly heterogeneous due the addition of the C-D riblets, showing large-scale alternatively distributed high and low speed fluids. This can be regarded as an effect of the transport of the large-scale streamwise vortices (LSSVs) induced by the riblets. The swirling motion of the LSSVs enhances the mixing process in the various fluid layers and therefore enhances the momentum exchange across the boundary layer (sketched with white arrow lines in Fig. 2). This shows its potential in suppressing flow separation in engineering applications. By focusing on the streamline near the riblet surface in Fig. 3, it is possible to understand how the C-D riblets work. The riblets direct the flow into grooves and lower the velocity of the fluids. The highly swirling fluids move along the grooves, meet the fluid on the other side of the converging line, eject to the outer part of the boundary layer, and lower the friction along the converging line. The opposite process happens along the diverging line.

By conducting a series of simulations, we have conducted a parametric characterisation of the C-D riblets. The circulation of the flow, which is regarded as an indication of LSSV induced by riblets, changes with the spacing (s) and wavelength (*L*) of the riblets and the wavelength of the C-D. In this project we have identified that at *s*=4 and *L* =1, the LSSVs can be the strongest (as shown in Fig. 4), which provides a guideline for further application of the C-D riblets in engineering.

For the present studied cases, both the friction drag and pressure drag were largely increased, as the result of the enhanced momentum exchange due to LSSV. The reduction of the drag reported in the experiment of Chen et al. [2] was not found, probably due to the lower Reynolds number used in the present DNS. More simulations are therefore needed to further explore the performance of C-D riblets at higher Reynolds numbers.

In this project we have also started a preliminary study of C-D riblets control for a supersonic flow including shock-wave induced flow separation (as shown in Fig. 5). The higher flow velocity downstream DL indicates the ability of the C-D riblets in supressing flow separation in high-speed flow, and more important, no extra shock-wave is induced by the C-R riblet, meaning the control device can minimise its interruption to the flow field while supressing flow separation.

**References and Links**

[1] Fang, J., Gao, F., Moulinec, C., Emerson, D. R. 2019 An improved parallel compact scheme for domain‐decoupled simulation of turbulence. INT J NUMER METH FL. 90,479-500.

[2] Chen, H., Rao, F., Shang, X., Zhang, D., Hagiwara, I. 2014 Flow over bio-inspired 3D herringbone wall riblets. EXP FLUIDS. 55.

**Research Team**

Dr Jian Fang^{1}(PI), Tongbiao Guo^{2}, Dr Charles Moulinec^{1}, Prof Shan Zhong^{2 1} Scientific Computing Department, Science and Technology Facilities Council (STFC) Daresbury Laboratory, UK^{2} Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, UK

**Scientific Contact**

Dr Jian Fang

Senior Computational Scientist

Scientific Computing Department,

Science and Technology Facilities Council, Daresbury Laboratory

Keckwick Lane, Daresbury, Warrington, WA4 4AD, UK

e-mail: jian.fang [@] sttfc.ac.uk

**NOTE: **This simulation project was made possible by PRACE (Partnership for Advanced Computing in Europe) allocating a computing time grant on GCS HPC system Hawk of the High-Performance Computing Center Stuttgart (HLRS). GCS is a hosting member of PRACE.

*Local project ID: flowCDR*

*December 2021*