## Periodic Reporting for period 1 - NiCoFlow (Nature-inspired control of turbulent flows)

Reporting period: 2016-03-01 to 2018-02-28

Overview:- There are no smooth surfaces in nature. Almost all surfaces present in nature are covered with patterned rough elements or rigid/elastic porous coatings in the form of hairs, feathers, and other filamentous features. A few notable scenarios include dermal denticles of shark skins, seal fur, hierarchical roughness on lotus leaves, scales on butterfly wings, feathers of birds and geometry of arterial walls. The geometry of these coatings are so complex and have gone through several cycles of optimization during the course of million years of evolution. With the help of such controlled geometrical coatings, these living creatures modify the surrounding fluid flows to their favour, and achieve energy efficient locomotion by minimizing skin-friction forces acting on them. The present work is focused on developing the essential mathematical framework to aid the design of such nature-inspired surfaces.

Importance:- Researchers in recent years are interested in designing biomimetic complex surfaces that can be useful in aerospace, automobile and energy sector. An essential prerequisite to design tailor-made surfaces is the quantification of the complex interplay between microscale geometrical details of the coating and the associated transport phenomena. Existing mathematical models and computational schemes are very expensive to provide this knowledge. In this work, we derive an accurate mathematical formulation to simulate the coupled interaction between the fluid flow and the surface coatings. The important implication of this project is that it provides a viable computational tool that can be used to understand how geometrical details of the coating will affect the flow field, and aid the design of novel surfaces.

Overall objectives: A major obstacle to simulate flow over complex surface coatings is the multiscale nature of the problem. This is exemplified in figure 1, which shows geometry of flow through a channel of which one wall is covered with rough features. This renders geometry resolved numerical simulations a prohibitively expensive task even with most powerful supercomputers. Hence, they are ‘intractable’ in practice. The objective of this work is to provide an alternative ‘tractable’ computational framework that enables us to model flow over complex surface coatings. To be precise, we derive physics-motivated equivalent mathematical formulations that does not require us to consider all the complex details of the coating (figure 1).

Importance:- Researchers in recent years are interested in designing biomimetic complex surfaces that can be useful in aerospace, automobile and energy sector. An essential prerequisite to design tailor-made surfaces is the quantification of the complex interplay between microscale geometrical details of the coating and the associated transport phenomena. Existing mathematical models and computational schemes are very expensive to provide this knowledge. In this work, we derive an accurate mathematical formulation to simulate the coupled interaction between the fluid flow and the surface coatings. The important implication of this project is that it provides a viable computational tool that can be used to understand how geometrical details of the coating will affect the flow field, and aid the design of novel surfaces.

Overall objectives: A major obstacle to simulate flow over complex surface coatings is the multiscale nature of the problem. This is exemplified in figure 1, which shows geometry of flow through a channel of which one wall is covered with rough features. This renders geometry resolved numerical simulations a prohibitively expensive task even with most powerful supercomputers. Hence, they are ‘intractable’ in practice. The objective of this work is to provide an alternative ‘tractable’ computational framework that enables us to model flow over complex surface coatings. To be precise, we derive physics-motivated equivalent mathematical formulations that does not require us to consider all the complex details of the coating (figure 1).

Complex surface coatings are ubiquitous in nature. Understanding the underlying fluid dynamic mechanisms and mimicking them to develop nature-inspired complex surfaces will have an impact both on technology and environment. In this regard, the main results achieved in this projects are as follows:

1. We proposed a unified physics-motivated mathematical framework to model the interaction of free-fluid with rough, porous and poroelastic surfaces. A linear constitutive law between velocity and deviatoric stress provided an accurate representation of flow over patterned rough surfaces. In addition to this, stress balance conditions are utilized to model flow over porous media.

2. The formulations that we discussed above are purely based on our understanding of the underlying physics of the problem. We employed first-principles and derived rigorously the same formulations using multiscale homogenization techniques.

3. The formulations developed using physical arguments and multiscale homogenization are utilized to develop a computational framework that can be used to accurately simulate flow over rough, porous and poroelastic surfaces. The computational tool is developed using the open source parallel finite element solver Freefem++, and all these tools are made available as open source software using GitHub repository.

4. The accuracy of the model discussed above are quantified by making a thorough comparison with geometry resolved direct numerical simulations (DNS). Of several test problems studied, we discuss here a lid-driven cavity problem with a rough bottom (figure 1). The comparison of tangential as well as transpiration velocity components at the rough boundary shows that the present model is as accurate as DNS, while DNS is an order of magnitude more expensive than the proposed model.

5. Multiscale direct numerical simulations of turbulent flow over rough patterned surfaces are studied by our effective model. We simulate turbulent flow through a channel with one wall covered by ordered cubic roughness elements. Performing DNS on such configurations is expensive due to the combination of the necessity of resolving geometrical features of the rough elements, and the small scale eddies of turbulent flows. The use of our constitutive model gives us the flexibility that we do not need to resolve geometrical features of the roughness elements. Figure 2 shows the comparison of averaged turbulent velocity profile between geometry resolved simulations and our constitutive model. It is directly evident that the constitutive model developed in this work matches accurately with geometry resolved simulations.

1. We proposed a unified physics-motivated mathematical framework to model the interaction of free-fluid with rough, porous and poroelastic surfaces. A linear constitutive law between velocity and deviatoric stress provided an accurate representation of flow over patterned rough surfaces. In addition to this, stress balance conditions are utilized to model flow over porous media.

2. The formulations that we discussed above are purely based on our understanding of the underlying physics of the problem. We employed first-principles and derived rigorously the same formulations using multiscale homogenization techniques.

3. The formulations developed using physical arguments and multiscale homogenization are utilized to develop a computational framework that can be used to accurately simulate flow over rough, porous and poroelastic surfaces. The computational tool is developed using the open source parallel finite element solver Freefem++, and all these tools are made available as open source software using GitHub repository.

4. The accuracy of the model discussed above are quantified by making a thorough comparison with geometry resolved direct numerical simulations (DNS). Of several test problems studied, we discuss here a lid-driven cavity problem with a rough bottom (figure 1). The comparison of tangential as well as transpiration velocity components at the rough boundary shows that the present model is as accurate as DNS, while DNS is an order of magnitude more expensive than the proposed model.

5. Multiscale direct numerical simulations of turbulent flow over rough patterned surfaces are studied by our effective model. We simulate turbulent flow through a channel with one wall covered by ordered cubic roughness elements. Performing DNS on such configurations is expensive due to the combination of the necessity of resolving geometrical features of the rough elements, and the small scale eddies of turbulent flows. The use of our constitutive model gives us the flexibility that we do not need to resolve geometrical features of the roughness elements. Figure 2 shows the comparison of averaged turbulent velocity profile between geometry resolved simulations and our constitutive model. It is directly evident that the constitutive model developed in this work matches accurately with geometry resolved simulations.

Existing flow control strategies can be classified into active and passive methods. Majority of works employ active control strategies that require external energy input. In contrast, the present project is on nature-inspired passive flow control technique, which requires no energy input. Existing biomimetic flow control strategies include shark-skin inspired riblets to reduce skin-friction drag, boundary layer separation control technique driven by the design of whale flippers’ wavy leading edge appendages, and dolphin skin inspired compliant surface coatings.

One aspect in nature that received least attention of the scientists is the following: the wing surfaces of the flying animals are coated with hairs, feathers and other filamentous structures. These surface coatings strongly influence the flow field characteristics, and preliminary investigations suggest that such coatings can achieve superior fluid dynamic performance than a conventional smooth surface. The present work pushed the boundaries of the state of the art mathematical methods by devising a unified mathematical formulations to analyse nature-inspired rough, porous and poroelastic coating while majority of the existing methods are limited to specific geometry of the surfaces.

Outcomes of the proposed project have a huge potential for designing nature-inspired surface coatings to achieve energy-efficient locomotion in aerospace, automobile and energy sector, of which one example is detailed below.

Growth of aviation industry contributes significantly to the economy as a whole, but it leads to increased carbon footprint by approximately 10% a year. More than 50% of energy spent on flying an aircraft is spent on overcoming the frictional drag experienced by the vehicle. Outcomes of this proposal provide an accurate tool to understand the connection between the topology of surface coatings and its skin-friction drag. Moreover, we also elucidated flow physics behind the observation. These tools and the knowledge gained will be crucial for devising biomimetic surface coatings for reduced drag on airplane wings, and thereby achieving improved fuel efficiency. These prospective impacts will lead to reduced aviation emissions, and help to achieve sustainable growth of aviation industry without harmful environmental effects.

One aspect in nature that received least attention of the scientists is the following: the wing surfaces of the flying animals are coated with hairs, feathers and other filamentous structures. These surface coatings strongly influence the flow field characteristics, and preliminary investigations suggest that such coatings can achieve superior fluid dynamic performance than a conventional smooth surface. The present work pushed the boundaries of the state of the art mathematical methods by devising a unified mathematical formulations to analyse nature-inspired rough, porous and poroelastic coating while majority of the existing methods are limited to specific geometry of the surfaces.

Outcomes of the proposed project have a huge potential for designing nature-inspired surface coatings to achieve energy-efficient locomotion in aerospace, automobile and energy sector, of which one example is detailed below.

Growth of aviation industry contributes significantly to the economy as a whole, but it leads to increased carbon footprint by approximately 10% a year. More than 50% of energy spent on flying an aircraft is spent on overcoming the frictional drag experienced by the vehicle. Outcomes of this proposal provide an accurate tool to understand the connection between the topology of surface coatings and its skin-friction drag. Moreover, we also elucidated flow physics behind the observation. These tools and the knowledge gained will be crucial for devising biomimetic surface coatings for reduced drag on airplane wings, and thereby achieving improved fuel efficiency. These prospective impacts will lead to reduced aviation emissions, and help to achieve sustainable growth of aviation industry without harmful environmental effects.