## Publications

59 results found

Ruban AI, Keshari SK, Kravtsova MA, 2021, On boundary-layer receptivity to entropy waves, *Journal of Fluid Mechanics*, Vol: 929, Pages: 1-33, ISSN: 0022-1120

<jats:p>In this paper, we consider the generation of the Tollmien–Schlichting waves in the boundary layer on the surface of a wing exposed to entropy waves. It is well known that the free-stream turbulence is composed of two perturbation modes: the vorticity waves and the entropy waves. The receptivity of the boundary layer to the vorticity waves has been studied extensively by various authors. The entropy waves have not attracted such attention. We show that, in high speed subsonic flows, the entropy waves are as important for the receptivity as the vorticity waves. Methodologically, our work relies on the asymptotic analysis of the Navier–Stokes equations at large values of the Reynolds number, which results in the formulation of a suitably modified triple-deck theory. The entropy waves produce oscillations of the gas temperature and density, but the velocity and the pressure remain unperturbed to the leading order. This precludes the entropy waves from penetrating the boundary layer, as happens, for example, with the acoustic waves. Our analysis reveals that the entropy waves decay rapidly in the transition layer that forms near the outer edge of the boundary layer. We find that an entropy wave alone cannot generate the Tollmien–Schlichting waves. However, when the boundary layer encounters a wall roughness, the flow near the roughness appears to be perturbed not only inside the boundary layer but also in the inviscid region outside the boundary layer. The latter comes into the interaction with the density perturbations in the entropy wave. As a result, a localised ‘forcing’ is created that produces the Tollmien–Schlichting waves. In this paper we present the results of a linear and nonlinear receptivity analysis. We find that the nonlinearity enhances the receptivity significantly, especially when a local separation region forms on the roughness.</jats:p>

Ruban AI, Broadley H, 2021, The generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow, *Journal of Engineering Mathematics*, Vol: 129, Pages: 1-26, ISSN: 0022-0833

This paper studies the generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow over a half-infinite flat plate with a roughness element using an asymptotic approach. It is assumed that the Reynolds number (denoted Re) is large, and that the free-stream turbulence is uniform so it can be modelled as vorticity waves. Close to the plate, a Blasius boundary layer forms at a thickness of O(Re−1/2), and a vorticity deformation layer is also present with thickness O(Re−1/4). The report shows that there is no mechanism by which the vorticity waves can penetrate from the vorticity deformation layer into the classical boundary layer; therefore, a transitional layer is introduced between them in order to prevent a discontinuity in vorticity. The flow in the interaction region in the vicinity of the roughness element is then analysed using the triple-deck model for transonic flow. A novel asymptotic expansion is used to analyse the upper deck, which enables a viscous–inviscid interaction problem to be derived. In order to make analytical progress, the height of the roughness element is assumed to be small, and from this, we find an explicit formula for the receptivity coefficient of the Tollmien–Schlichting wave far downstream of the roughness.

Djehizian A, Ruban AI, 2021, Discontinuous solutions of the unsteady boundary-layer equations for a rotating disk of finite radius, *Journal of Fluid Mechanics*, Vol: 915, Pages: 1-30, ISSN: 0022-1120

We consider the motion at large Reynolds number of an incompressible fluid around a thin circular disk of finite radius rotating in its plane. The disk is placed in a large tank filled with an initially stagnant fluid. Then it is brought into rotation about its centre with constant angular velocity. Due to viscosity, a layer of fluid adjacent to the disk gets involved in the circumferential motion. This activates centrifugal forces; the fluid particles start to deviate in the radial direction. When they cross the edge of the disk, a thin jet is formed. Firstly, we solve the classical boundary-layer equations for the flow in the boundary layer in the direct neighbourhood of the disk surface and in the jet. The solution is found to develop a discontinuity at the ‘head’ of the jet where the radial and circumferential velocity components experience a jump. This type of discontinuity, called a pseudo-shock, was previously observed by Ruban & Vonatsos (J. Fluid Mech., vol. 614, 2008, pp. 407–424). Then, we investigate the internal structure of the pseudo-shock. We find that the fluid motion is described by the Euler equations in the leading-order approximation. Their solution shows that, as the jet penetrates the stagnant fluid, it ejects the fluid from the boundary layer into the surrounding area. Analysis of the inviscid region outside the boundary layer reveals that the ejected fluid returns back to the boundary layer through the ‘entrainment process’. Finally, we conclude this paper with the study of the wake in the vicinity of the disk rim.

Jain K, Ruban AI, Braun S, 2021, On receptivity of marginally separated flows, *Journal of Fluid Mechanics*, Vol: 907, ISSN: 0022-1120

In this paper we study the receptivity of the boundary layer to suction/blowing in marginally separated flows, like the one on the leading edge of a thin aerofoil. We assume that the unperturbed laminar flow is two-dimensional, and investigate the response of the boundary layer to two-dimensional as well as to three-dimensional perturbations. In both cases, the perturbations are assumed to be weak and periodic in time. Unlike conventional boundary layers, the marginally separated boundary layers cannot be treated using the quasi-parallel approximation. This precludes the normal-mode representation of the perturbations. Instead, we had to solve the linearised integro-differential equation of the marginal separation theory, which was done numerically. For two-dimensional perturbations, the results of the calculations show that the perturbations first grow in the inside of the separation region, but then start to decay downstream. For three-dimensional perturbations, instead of dealing with the integro-differential equation of marginal separation, we found it convenient to work with the Fourier transforms of the fluid-dynamic functions. The equations for the Fourier transforms are also solved numerically. Our calculations show that a three-dimensional wave packet forms downstream of the source of perturbations in the boundary layer.

Ruban A, Djehizian A, Kirsten J,
et al., 2020, On quasi-steady boundary-layer separation in supersonic flow. Part 2. Downstream moving separation point, *Journal of Fluid Mechanics*, Vol: 900, ISSN: 0022-1120

In this paper we study the perturbations produced in the boundary layer by an impinging oblique shock wave or Prandtl–Meyer expansion fan. The flow outside the boundary layer is assumed supersonic, and we also assume that the point, where the shock wave/expansion fan impinges on the boundary layer, moves downstream. To study the flow, it is convenient to use the coordinate frame moving with the shock; in this frame, the body surface moves upstream. We first study numerically the case when the shock velocity Vsh=O(Re−1/8) . In this case the interaction of the boundary layer with the shock can be described by the classical equations of the triple-deck theory. We find that, as Vsh increases, the boundary layer proves to be more prone to separation when exposed to the expansion fan, not the compression shock. Then we assume Vsh to be in the range 1≫Vsh≫Re−1/8 . Under these conditions, the process of the interaction between the boundary layer and the shock/expansion fan can be treated as inviscid and quasi-steady if considered in the reference frame moving with the shock/expansion fan. The inviscid analysis allows us to determine the pressure distribution in the interaction region. We then turn our attention to a thin viscous sublayer that lies closer to the body surface. In this sublayer the flow is described by classical Prandtl's equations. The solution to these equations develops a singularity provided that the expansion fan is strong enough. The flow analysis in a small vicinity of the singular point shows an accelerated ‘expansion’ of the flow similar to the one reported by Neiland (Izv. Akad. Nauk SSSR, Mech. Zhidk. Gaza, vol. 5, 1969a, pp. 53–60) in his analysis of supersonic flow separation from a convex corner.

De Grazia D, Moxey D, Sherwin SJ,
et al., 2018, Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime, *Physical Review Fluids*, Vol: 3, ISSN: 2469-990X

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

Ruban AI, 2017, Fluid Dynamics Part 3 Boundary Layers, Publisher: Oxford University Press, ISBN: 9780199681754

"This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then ...

Ruban AI, Bernots T, Kravtsova MA, 2016, Linear and nonlinear receptivity of the boundary layer in transonic flows, *Journal of Fluid Mechanics*, Vol: 786, Pages: 154-189, ISSN: 1469-7645

In this paper we analyse the process of the generation of Tollmien–Schlichting waves in a laminar boundary layer on an aircraft wing in the transonic flow regime. We assume that the boundary layer is exposed to a weak acoustic noise. As it penetrates the boundary layer, the Stokes layer forms on the wing surface. We further assume that the boundary layer encounters a local roughness on the wing surface in the form of a gap, step or hump. The interaction of the unsteady perturbations in the Stokes layer with steady perturbations produced by the wall roughness is shown to lead to the formation of the Tollmien–Schlichting wave behind the roughness. The ability of the flow in the boundary layer to convert ‘external perturbations’ into instability modes is termed the receptivity of the boundary layer. In this paper we first develop the linear receptivity theory. Assuming the Reynolds number to be large, we use the transonic version of the viscous–inviscid interaction theory that is known to describe the stability of the boundary layer on the lower branch of the neutral curve. The linear receptivity theory holds when the acoustic noise level is weak, and the roughness height is small. In this case we were able to deduce an analytic formula for the amplitude of the generated Tollmien–Schlichting wave. In the second part of the paper we lift the restriction on the roughness height, which allows us to study the flows with local separation regions. A new ‘direct’ numerical method has been developed for this purpose. We performed the calculations for different values of the Kármán–Guderley parameter, and found that the flow separation leads to a significant enhancement of the receptivity process.

Ruban A, Cimpeanu R, Papageorgiou DT, et al., 2015, How to make a splash: droplet impact and liquid film applications in aerodynamics, 68th Annual Meeting of the APS Division of Fluid Dynamics doi: 10.1103/APS.DFD.2015.GFM.P0032

Mengaldo G, Kravtsova M, Ruban A,
et al., 2015, Triple-deck and direct numerical simulation analyses high-speed subsonic flows past a roughness element, *Journal of Fluid Mechanics*, Vol: 774, Pages: 311-323, ISSN: 1469-7645

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number ( ) is large, we performed the Navier–Stokes calculations at Re = 4 x 10^5 based on the distance of the roughness element from the leading edge of the flat plate. This Re is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number Ma_∞ = 0.5 and Ma_∞ = 0.87 . We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.

De Tullio N, Ruban AI, 2015, A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers, *Journal of Fluid Mechanics*, Vol: 771, Pages: 520-546, ISSN: 1469-7645

Ruban AI, 2015, Fluid Dynamics Asymptotic Problems of Fluid Dynamics, Publisher: Oxford University Press, USA, ISBN: 9780199681747

"This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then ...

Logue RP, Gajjar JSB, Ruban AI, 2014, Instability of supersonic compression ramp flow, *Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, Vol: 372, Pages: 20130342-20130342, ISSN: 1364-503X

<jats:p> The instability of supersonic compression ramp flow is investigated. It is assumed that the Reynolds number is large and that the governing equations are the unsteady triple-deck equations. The mean flow is first calculated by solving the steady equations for various scaled ramp angles <jats:italic>α</jats:italic> , and the numerical results suggest that there is no singularity for increasing ramp angles. The stability of the flow is investigated using two approaches, first by solving the linearized unsteady equations and looking for global modes proportional to <jats:italic>e</jats:italic> <jats:sup> λ <jats:italic>t</jats:italic> </jats:sup> . In the second approach, the linearized unsteady equations are solved numerically with various initial conditions. Whereas no globally unsteady modes could be found for the range of ramp angles studied, the numerical simulations show the formation of wavepacket type disturbances which grow and convect and reach large amplitudes. However, the numerical results show large variations with grid size even on very fine grids. </jats:p>

Ruban AI, Kravtsova MA, 2013, Generation of Steady Longitudinal Vortices in Hypersonic Boundary Layer, *Journal of Fluid Machanics*, Vol: 729, Pages: 702-731, ISSN: 0022-1120

AI Ruban, JSB Gajjar, 2013, Fluid Dynamics. Part 1. Classical Fluid Dynamics, Publisher: Oxford University Press

Ruban AI, Bernots T, Pryce D, 2013, Receptivity of the boundary layer to vibrations of the wing surface, *Journal of Fluid Mechanics*, Vol: 723, Pages: 480-528, ISSN: 0022-1120

Ruban AI, Araki D, Yapalparvi R,
et al., 2011, On unsteady boundary-layer separation in supersonic flow. Part 1. Upstream moving separation point, *JOURNAL OF FLUID MECHANICS*, Vol: 678, Pages: 124-155, ISSN: 0022-1120

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- Citations: 10

Logue RP, Gajjar JSB, Ruban AI, 2011, Global stability of separated flows: subsonic flow past corners, *THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS*, Vol: 25, Pages: 119-128, ISSN: 0935-4964

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- Citations: 2

AI Ruban, 2010, Asymptotic Theory of Separated Flows, Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances, Editors: H Steinruck, Publisher: Springer

RUBAN AI, VONATSOS KN, 2008, Discontinuous solutions of the boundary-layer equations, *Journal of Fluid Mechanics*, Vol: 614, Pages: 407-424, ISSN: 0022-1120

Ruban AI, Wu X, Pereira RMS, 2006, Viscous-inviscid interaction in transonic Prandtl-Meyer flow, *JOURNAL OF FLUID MECHANICS*, Vol: 568, Pages: 387-424, ISSN: 0022-1120

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- Citations: 8

Kravtsova MA, Zametaev VB, Ruban AI, 2005, An effective numerical method for solving viscous-inviscid interaction problems, *PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 363, Pages: 1157-1167, ISSN: 1364-503X

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- Citations: 11

Kerimbekov RM, Ruban AI, 2005, Receptivity of boundary layers to distributed wall vibrations, *Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, Vol: 363, Pages: 1145-1155, ISSN: 1364-503X

<jats:p> Linear three-dimensional receptivity of boundary layers to distributed wall vibrations in the large Reynolds number limit ( <jats:italic>Re</jats:italic> →∞) is studied in this paper. The fluid motion is analysed by means of the multiscale asymptotic technique combined with the method of matched asymptotic expansions. The body surface is assumed to be perturbed by small-amplitude oscillations being tuned in resonance with the neutral Tollmien–Schlichting wave at a certain point on the wall. The characteristic length of the resonance region is found to be O( <jats:italic>Re</jats:italic> <jats:sup>−3/16</jats:sup> ), which follows from the condition that the boundary-layer non-parallelism and the wave amplitude growth have the same order of magnitude. The amplitude equation is derived as a solvability condition for the inhomogeneous boundary-value problem. Investigating detuning effects, we consider perturbations in the form of a wave packet with a narrow O( <jats:italic>Re</jats:italic> <jats:sup>−3/16</jats:sup> ) discrete or continuous spectrum concentrated near the resonant wavenumber and frequency. The boundary-layer laminarization based on neutralizing the oncoming Tollmien–Schlichting waves (or wave packets) is also discussed. </jats:p>

FLETCHER AJP, RUBAN AI, WALKER JDA, 2004, Instabilities in supersonic compression ramp flow, *Journal of Fluid Mechanics*, Vol: 517, Pages: 309-330, ISSN: 0022-1120

BATTAM NW, GOROUNOV DG, KOROLEV GL,
et al., 2004, Shock wave interaction with a viscous wake in supersonic flow, *Journal of Fluid Mechanics*, Vol: 504, Pages: 301-341, ISSN: 0022-1120

BULDAKOV EV, RUBAN AI, 2002, On transonic viscous–inviscid interaction, *Journal of Fluid Mechanics*, Vol: 470, Pages: 291-317, ISSN: 0022-1120

<jats:p>The paper is concerned with the interaction between the boundary layer on a smooth body surface and the outer inviscid compressible flow in the vicinity of a sonic point. First, a family of local self-similar solutions of the Kármán–Guderley equation describing the inviscid flow behaviour immediately outside the interaction region is analysed; one of them was found to be suitable for describing the boundary-layer separation. In this solution the pressure has a singularity at the sonic point with the pressure gradient on the body surface being inversely proportional to the cubic root d<jats:italic>p</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub>/d<jats:italic>x</jats:italic> ∼ (−<jats:italic>x</jats:italic>)<jats:sup>−1/3</jats:sup> of the distance (−<jats:italic>x</jats:italic>) from the sonic point. This pressure gradient causes the boundary layer to interact with the inviscid part of the flow. It is interesting that the skin friction in the boundary layer upstream of the interaction region shows a characteristic logarithmic decay which determines an unusual behaviour of the flow inside the interaction region. This region has a conventional triple-deck structure. To study the interactive flow one has to solve simultaneously the Prandtl boundary-layer equations in the lower deck which occupies a thin viscous sublayer near the body surface and the Kármán–Guderley equations for the upper deck situated in the inviscid flow outside the boundary layer. In this paper a numerical solution of the interaction problem is constructed for the case when the separation region is entirely contained within the viscous sublayer and the inviscid part of the flow remains marginally supersonic. The solution proves to be non-unique, revealing a hysteresis character of the flow in the interaction region.</jats:p

KOROLEV GL, GAJJAR JSB, RUBAN AI, 2002, Once again on the supersonic flow separation near a corner, *Journal of Fluid Mechanics*, Vol: 463, Pages: 173-199, ISSN: 0022-1120

<jats:p>Laminar boundary-layer separation in the supersonic flow past a corner point on a rigid body contour, also termed the compression ramp, is considered based on the viscous–inviscid interaction concept. The ‘triple-deck model’ is used to describe the interaction process. The governing equations of the interaction may be formally derived from the Navier–Stokes equations if the ramp angle θ is represented as θ = θ<jats:sub>0</jats:sub>Re<jats:sup>−1/4</jats:sup>, where θ<jats:sub>0</jats:sub> is an order-one quantity and <jats:italic>Re</jats:italic> is the Reynolds number, assumed large. To solve the interaction problem two numerical methods have been used. The first method employs a finite-difference approximation of the governing equations with respect to both the streamwise and wall-normal coordinates. The resulting algebraic equations are linearized using a Newton–Raphson strategy and then solved with the Thomas-matrix technique. The second method uses finite differences in the streamwise direction in combination with Chebychev collocation in the normal direction and Newton–Raphson linearization.</jats:p><jats:p>Our main concern is with the flow behaviour at large values of θ<jats:sub>0</jats:sub>. The calculations show that as the ramp angle θ<jats:sub>0</jats:sub> increases, additional eddies form near the corner point inside the separation region. The behaviour of the solution does not give any indication that there exists a critical value θ<jats:sup>*</jats:sup><jats:sub>0</jats:sub> of the ramp angle θ<jats:sub>0</jats:sub>, as suggested by Smith & Khorrami (1991) who claimed that as θ<jats:sub>0</jats:sub> approaches θ<jats:sup>*</jats:sup><jats:sub>0</jats:sub>, a singularity develop

Ackroyd JAD, Axcell BP, Ruban AI, 2001, Early Developments of Modern Aerodynamics

This text presents these papers, in English translation, together with an accompanying commentary putting them into the context of their period and showing their relevance to modern aerodynamics.

Bos SH, Ruban AI, 2000, A semi–direct method for calculating flows with viscous–inviscid interaction, *Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences*, Vol: 358, Pages: 3063-3073, ISSN: 1364-503X

RUBAN AI, TURKYILMAZ I, 2000, On laminar separation at a corner point in transonic flow, *Journal of Fluid Mechanics*, Vol: 423, Pages: 345-380, ISSN: 0022-1120

<jats:p>The separation of the laminar boundary layer from a convex corner on a rigid body contour in transonic flow is studied based on the asymptotic analysis of the Navier–Stokes equations at large values of the Reynolds number. It is shown that the flow in a small vicinity of the separation point is governed, as usual, by strong interaction between the boundary layer and the inviscid part of the flow. Outside the interaction region the Kármán–Guderley equation describing transonic inviscid flow admits a self-similar solution with the pressure on the body surface being proportional to the cubic root of the distance from the separation point. Analysis of the boundary layer driven by this pressure shows that as the interaction region is approached the boundary layer splits into two parts: the near-wall viscous sublayer and the main body of the boundary layer where the flow is locally inviscid. It is interesting that contrary to what happens in subsonic and supersonic flows, the displacement effect of the boundary layer is primarily due to the inviscid part. The contribution of the viscous sublayer proves to be negligible to the leading order. Consequently, the flow in the interaction region is governed by the <jats:italic>inviscid</jats:italic>–<jats:italic>inviscid interaction</jats:italic>. To describe this flow one needs to solve the Kármán–Guderley equation for the potential flow region outside the boundary layer; the solution in the main part of the boundary layer was found in an analytical form, thanks to which the interaction between the boundary layer and external flow can be expressed via the corresponding boundary condition for the Kármán–Guderley equation. Formulation of the interaction problem involves one similarity parameter which in essence is the Kármán–Guderley parameter suitably modified for the flow at hand. The solution of the

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