# Academic

Fluid dynamics is the study of how liquids and gases move, and how objects move through them. Perhaps fittingly, given the metaphor of the lake that started everything off, I gradually drifted towards this field of applied mathematics.

My PhD, under the guidance of Professor Frank Smith at University College London, had applications in aerodynamics, looking at the flow of air over an aeroplane’s wings and a possible technique to reduce drag and delay or avoid the separation of the boundary layer. It was a blast!

You can find a copy of my thesis below, along with some papers that came from it. There’s a theme of exploration woven throughout the thesis, in an honest and heartfelt attempt to make the reading of it enjoyable, in some way. The first chapter aims to be as accessible as possible to the general reader, while the second contains an introduction to boundary layer theory that might be of use to a student of the topic. Or maybe that’s thinking too much of myself. In any case, Sir Ernest Shackleton and Sir Douglas Mawson (both Antarctic explorers); Henry David Thoreau and Edward Abbey (US naturalists, among other things); Edgar Lawrence Doctorow (author); Sir Samuel White Baker, Sir Richard Burton, Dr David Livingstone, Florence von Sass, John Hanning Speke and Sir Henry Morton Stanley and their search for the source of the White Nile; and Ryszard Kapuściński (journalist and traveller) all make an appearance.

### Thesis

Roughing up wings: boundary layer separation over static and dynamic roughness elements, Servini, *PhD thesis*, 2018

The separation of a boundary layer from an aeroplane wing can have severe effects on aeroplane safety and efficiency, as its occurrence directly results in decreases in lift and increases in drag. Similar considerations apply to other technologies that rely on airfoils, such as drones, helicopters, propellers and wind turbines. Hence recent experimental and numerical work on dynamic roughness elements—small bumps that are made to oscillate up and down at a given frequency—is exciting, as it suggests that these elements are able to delay separation or increase the angle of attack at which it occurs, provided that the Reynolds number is such that the flow remains laminar.

Our aims are to gain further insight into whether this is indeed the case; to determine the possible impact of the roughness parameters on the separation of a boundary layer from a surface; and to attempt to understand the physical mechanisms that may be involved, with our focus very much on the pressure gradient. To this end, we will make use of a mathematical approach and exploit asymptotic methods throughout.

Three scenarios will be considered, and we will study both dynamic and static roughnesses. The first consists of small roughness elements, which are able to modify the mean flow pressure gradient, on a flat plate. The second will revolve around flow over a hump within a condensed boundary layer, first described by Smith & Daniels (1981), but with the addition of roughness elements on its lee side, in the region in which local separation occurs and the advent of full breakaway separation is seen. The final scenario is set near the leading edge of an airfoil, inclined to the oncoming flow at or near the critical angle of attack, where marginally separated flow exists and a small separation bubble is possible.

### Papers

The impact of dynamic roughness elements on marginally separated boundary layers, Servini, Smith & Rothmayer, *Journal of Fluid Mechanics*, 855 (2018), 351–370

It has been shown experimentally that dynamic roughness elements—small bumps embedded within a boundary layer, oscillating at a fixed frequency—are able to increase the angle of attack at which a laminar boundary layer will separate from the leading edge of an airfoil (Grager et al. 2012). In this paper, we attempt to verify that such an increase is possible by considering a two dimensional dynamic roughness element in the context of marginal separation theory, and suggest the mechanisms through which any increase may come about. We will show that a dynamic roughness element can increase the value of Γ_{c} as compared to the clean airfoil case; Γ_{c} representing, mathematically, the critical value of the parameter Γ below which a solution exists in the governing equations and, physically, the maximum angle of attack possible below which a laminar boundary layer will remain predominantly attached to the surface. Furthermore, we find that the dynamic roughness element impacts on the perturbation pressure gradient in two possible ways: either by decreasing the magnitude of the adverse pressure peak or increasing the streamwise extent in which favourable pressure perturbations exist. Finally, we discover that the marginal separation bubble does not necessarily have to exist at Γ = Γ_{c} in the time-averaged flow and that full breakaway separation can therefore occur as a result of the bursting of transient bubbles existing within the length scale of marginal separation theory.

The impact of static and dynamic roughness elements on flow separation, Servini, Smith & Rothmayer, *Journal of Fluid Mechanics*, 830 (2017), 35–62

The use of static or dynamic roughness elements has been shown in the past to delay the separation of a laminar boundary layer from a solid surface. Here, we examine analytically the effect of such elements on the local and breakaway separation points, corresponding respectively to the position of zero skin friction and presence of a singularity in the roughness region, for flow over a hump embedded within the boundary layer. Two types of roughness elements are studied: the first is small and placed near the point of vanishing skin friction; the second is larger and extends downstream. The forced flow solution is found as a sum of Fourier modes, reflecting the fixed frequency forcing of the dynamic roughness. Solutions for both the static and dynamic roughness show that the presence of the roughness element is able to move the separation points downstream, given an appropriate choice of roughness frequency, height, position and width. This choice is found to be qualitatively similar to that observed for leading-edge separation. Furthermore, for a negative static roughness a small region of separated flow forms at high roughness depth, although there is a critical depth above which boundary-layer breakaway moves suddenly upstream.