Imperial College London

Dr Shahid Mughal

Faculty of Natural SciencesDepartment of Mathematics

Lecturer in Applied Mathematics



+44 (0)20 7594 2648s.mughal Website




734Huxley BuildingSouth Kensington Campus





Publication Type

40 results found

Thomas C, Mughal S, 2022, Optimising control of stationary cross-flow vortices excited by surface roughness, Physics of Fluids, Vol: 34, Pages: 1-15, ISSN: 1070-6631

Stationary cross-flow vortices are excited within the swept Hiemenz boundary layer via surface roughness and actively controlled using an optimally configured control device. Control is modelled using localised wall motion, but in practice the optimisation strategy could be applied to other laminar flow control technologies. A sensor-control iterative procedure, based on solutions of the forward and adjoint linearised Navier--Stokes equations, is applied to both feedforward and feedback loop systems. The former strategy only allows the control settings to be configured once, while the latter approach permits the repeated reoptimisation of the control device. Surface roughness establishes a stationary cross-flow disturbance with a pre-defined set of flow conditions, but an unknown amplitude and phase. A sensor measures the local amplitude of the perturbation and relays the information to the control mechanism. Solutions of the adjoint linearised Navier--Stokes equations are coupled with the sensor measurements to configure and optimise the control mechanism, and establish an anti-phase wave that brings about destructive wave interference. The amplitude of the stationary cross-flow instability is reduced by an order $10^3$ for the feedforward system, while amplitude reductions of the order $10^3$ per iteration and $10^8$ overall are realisable for the feedback modelling approach. Similar levels of flow control are realisable for a multiple controller configuration. However, stationary cross-flow disturbances could not be eliminated indefinitely. Inevitably, the cross-flow instability started to grow again, albeit at a considerably lower magnitude. The analysis is extended to include the effects of systematic error in the sensors measuring capability.

Journal article

Lyu G, Chen C, Du X, Mughal M, Sherwin Set al., 2022, Open-source Framework for Transonic Boundary Layer Natural Transition Analysis over Complex Geometries in Nektar++, AIAA Aviation 2022 Forum

Conference paper

Raposo H, Mughal M, Bensalah A, Ashworth Ret al., 2021, Acoustic-roughness receptivity in subsonic boundary-layer flows over aerofoils, Journal of Fluid Mechanics, Vol: 925, ISSN: 0022-1120

The generation of a viscous–inviscid instability through scattering of an acoustic wave by localised and distributed roughness on the upper surface of a NACA 0012 aerofoil is studied with a time-harmonic compressible adjoint linearised Navier–Stokes approach. This extends previous work by the authors dedicated to flat plate geometries. The key advancement lies in the modelling of the inviscid acoustic field external to the aerofoil boundary layer, requiring a numerical solution of the convected Helmholtz equation in a non-uniform inviscid field to determine the unsteady pressure field on the curved aerofoil surface. This externally imposed acoustic pressure field subsequently drives the acoustic boundary layer, which fundamentally determines the amplitudes of acoustic-roughness receptivity. A study of receptivity in the presence of Gaussian-shaped roughness and sinusoidally distributed roughness at Mach number M∞ = 0.4 and Strouhal numbers S ≈ {46, 69, 115} shows the effects of various parameters, most notably angle of attack, angle of incidence of the externally imposed plane acoustic wave and geometry of surface roughness; the latter is varied from viewpoint of its placement on the aerofoil surface and its wavelength. The parametric study suggests that non-parallel effects are quite substantial and that considerable differences arise when using parallel flow theory to estimate the optimal width of Gaussian-shaped roughness elements to provoke the greatest response. Furthermore, receptivity amplitudes for distributed roughness are observed to be generally higher for lower angles of attack, i.e. for less adverse pressure gradients. It is also shown that the boundary layer is more receptive to upstream-travelling acoustic waves.

Journal article

Raposo H, Mughal MS, Ashworth R, 2021, On the effects of sound in subsonic boundary layer flows, IUTAM Laminar-Turbulent Transition, Vol: 38, Pages: 1-1

The study of acoustic receptivity in quiet disturbance environments can bedecomposed into several sub-problems. One such problem consists of determining the response of the unsteady boundary layer to acoustic forcing in the freestream. In this paper, we describe two methods to characterize the acoustic boundary layer response based on the linear stability equations. In their inviscid form, we first show how to determine the reflection coefficient. The sum of the incident and reflected waves then drives the unsteady Stokes motion within the boundary layer, for which a double-layer high Strouhal number asymptotic solution is obtained. The outer layer solution is calculated numerically whereas the inner layer solution, introduced to satisfy the no-slip condition, is determined analytically. The full linear stability equations can also be integrated numerically to directly obtain a complete disturbance profile accounting for the effects of viscosity. A comparison between these models and the linearised unsteady boundary layer equation (LUBLE) model shows good agreement at high Strouhal number, low Mach number and for downstream-travelling waves. However, for near sonic Mach numbers and for upstream-travelling waves, the LUBLE are shown to be not valid because the assumption that the acoustic wavelength is long compared to the boundary layer thickness no longer holds.

Journal article

Appel T, Cooke E, Mughal MS, Ashworth Ret al., 2021, BiGlobal stability analysis of swept-wing boundary layers with forward and backward facing steps, IUTAM Laminar-Turbulent Transition, Vol: 38, Pages: 1-1, ISSN: 1875-3507

The temporal stability characteristics of generic, swept-wing boundary-layer flows of practical engineering significance with a smooth, isolated backward facing step or a forward-facing step are investigated. A streamwise BiGlobal analysis is undertaken on previously computed steady-state, Mach 0.3 Navier-Stokes solutions that had been obtained for four spanwise invariant step heights and at two chordwise locations on an infinite swept-wing geometry. Temporal instability is detected for heights exceeding 25% of the undisturbed boundary-layer thickness, or one unit of the undisturbed displacement thickness at the step chordwise location. Forward-facing steps with the greatest height are not found to be temporally unstable in contrast to backward-facing steps. Unstable modes feature localised regions of large streamwise and spanwise perturbation velocity magnitude near the lower corner of the backward-facing step or just downstream of the forward-facing step. Wave-like modes are found to arise from the deepest backward-facing step.

Journal article

Cooke EE, Mughal MS, Sherwin S, Ashworth R, Rolston Set al., 2021, Destabilisation of stationary and travelling crossflow disturbances due to forward and backward facing steps over a swept wing, IUTAM Laminar-Turbulent Transition, Vol: 38, Pages: 713-723

The destabilisation effects of forward and backward facing steps on cross-flow (CF) disturbances on an infinite swept wing is investigated. Stationary and travelling CF-wave instability modulations, as they convect over the abrupt surface features, are investigated computationally with step heights ranging from 18% to 53% of the boundary layer thickness at chordwise locations of 10% and 20%. An embedded mesh approach is used to compute boundary layer base flow profiles over the swept wing with the high order spectral / hp element solver, Nektar++. Linear Stability Theory (LST), Parabolised Stability Equations (PSE) and Linearised Harmonic Navier-Stokes (LHNS) models are used to investigate the development of the convecting CF disturbances. LST is used to understand the instability parameter space and map out neutral curves. PSE equations fail to correctly capture the effects of the steps due to the strong short scale variations introduced whereas, the LHNS provide a rapid and more physics correct technique to ascertain flow destabilisation effects.

Journal article

Gowree ER, Mughal MS, Xu H, Atkin CJet al., 2020, Linear and non-linear instability of Tollmien-Schlichting waves over a localised three-dimensional surface indentation, Publisher: Journal Fluid Mechanics

The stability of a Tollmien-Schlichting (T-S) wave undergoing rapid three dimensional (3D) distortion and destabilisation by a localised surface depression was studied experimentally and numerically. All the depression heights (h) and wavelengths (λ) considered appeared to modulate an artificially excited T-S wave. The severest destabilisation arises with increasing strength of the 3D laminar separation bubble which arises within the surface indentation. The 3D modulation of the T-S disturbance was investigated with the fully 3D parabolised stability equations (PSE3D) model and nonlinear behaviour with a novel nonlinear harmonic Navier-Stokes formulation. The 3D effect during the recovery phase of the T-S wave in the downstream part of the depression, where the boundary layer flow accelerates, was significant and was confirmed by differences arising between the PSE3D and two-dimensional modelling. For the severest of indentations, the recirculation bubble was found to amplify the growth of the convecting wave significantly. Within the 3D depression, the initially 2D disturbance was distorted and during the secondary growth stage the energy of the T-S wave tended to become more focussed and concentrated along the symmetry plane. The frequency spectra showed that the initial non-linear development was dominated by the harmonic modes. The hot-wire measurements also showed some evidence of oscillation of the laminar separation bubble, but the instability process and flow destabilisation was found to be through convective processes as opposed to resonator dynamics.

Working paper

Xu J, Liu J, Mughal MS, Yu P, Bai Jet al., 2020, Secondary instability of Mack mode disturbances in hypersonic boundary layers over micro-porous surface, Physics of Fluids, Vol: 32, ISSN: 1070-6631

In laminar hypersonic boundary layers, it is known that secondary instability plays a crucial role in transition to turbulence. The secondary instability usually includes the fundamental mode, the subharmonic mode, and the detuned mode. Considerable research exists on the secondary instability mechanism in hypersonic boundary layers with the smooth wall condition. The topic of using micro-porous surfaces for disturbance stabilization has recently drawn interest. The stabilization and, thus, a possible delay in the transition arise due to a reduction in the growth rate of the primary Mack mode by the porous surface. This paper focuses on investigating whether the secondary instability mechanism of Mack modes can also be affected by a surface porosity condition. It is known that the primary Mack mode linear disturbances are changed significantly on the porous surface, and how it subsequently influences the secondary instability of the modified time varying basic flow is our concern. The analysis demonstrates that on the porous surface, as the amplitude of the primary Mack mode increases, the fundamental mode is not stable. Instead, the fundamental mode amplifies rapidly with increasing primary amplitudes. At larger secondary instability spanwise wavenumbers, when the primary amplitude exceeds a certain threshold value, the fundamental modes surpass the subharmonic modes and dominate the secondary instability. However, when the spanwise wavenumber is relatively small, especially at the spanwise wavenumber corresponding to the maximum growth rate of the subharmonic mode, the fundamental modes are weakened and lose their dominant position. We find that corresponding to different amplitudes of primary Mack mode disturbances affected by the porosity parameters, there are no strongly preferred interaction modes that dominate the secondary instability; this contrasts with smooth wall findings. We further find that the larger the pore size or porosity, the more severe the sup

Journal article

Kang KL, Ashworth R, Mughal S, 2020, Stabilization of crossflow instability with plasma actuators: Linearized Navier–Stokes simulations, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol: 234, Pages: 68-78, ISSN: 0954-4100

<jats:p> This paper describes work carried out within the European Union (EU)-Russia Buterfli project to look at the control of transition-causing “target” stationary cross flow vortices, by the use of distributed plasma actuation to generate sub-dominant “killer” modes. The objective is to use the “killer” modes to control the “target” modes through a non-linear stabilizing mechanism. The numerical modelling and results are compared to experimental studies performed at the TsAGI T124 tunnel for a swept plate subject to a favorable pressure gradient flow. A mathematical model for the actuator developed at TsAGI was implemented in a linearized Navier–Stokes (LNS) solver and used to model and hence predict “killer” mode amplitudes at a measurement plane in the experiment. The LNS analysis shows good agreement with experiment, and the results are used as input for non-linear parabolized stability equation (PSE) analysis to predict the effect of these modes on crossflow transition. Whilst the numerical model indicates a delay in transition, experimental results indicated an advance in transition rather than delay. This was determined to be due to actuator-induced unsteadiness arising in the experiment, resulting in the generation of travelling crossflow disturbances which tended to obscure and thus dominate the plasma stabilized stationary disturbances. </jats:p>

Journal article

Raposo H, Mughal M, Ashworth R, 2019, An adjoint compressible linearised Navier-Stokes approach to model generation of Tollmien-Schlichting waves by sound, Journal of Fluid Mechanics, Vol: 877, Pages: 105-129, ISSN: 0022-1120

The generation of the first-mode instability through scattering of an acoustic wave by localised surface roughness, suction or heating is studied with a time-harmonic compressible adjoint linearised Navier-Stokes (AHLNS) approach for subsonic flow conditions. High-Strouhal number analytical solutions to the compressible Stokes layer problem are deduced and shown to be in better agreement with numerical solutions compared to previous works. The adjoint methodology of Hill in the context of acoustic receptivity is extended to the compressible flow regime and an alternative formulation to predict sensitivity to the angle of incidence of an acoustic wave is proposed. Good agreement of the acoustic AHLNS receptivity model is found with published direct numerical simulations and the simpler finite-Reynolds number approach. Parametric investigations of the influence of the acoustic wave angle on receptivity amplitudes reveal that the linearised unsteady boundary layer equations are a valid model of the acoustic signature for a large range of acoustic wave obliqueness values, failing only where the wave is highly oblique and travels upstream. An extensive parametric study of the influence of frequency, spanwise wavenumber, local Reynolds number and free-stream Mach number over the efficiency function for the different types of wall perturbation mechanisms is undertaken.

Journal article

Cooke EE, Mughal MS, Sherwin S, Ashworth R, Rolston Set al., 2019, Destabilisation of Stationary and Travelling Crossflow Disturbances Due to Steps over a Swept Wing, AIAA Aviation 2019 Forum, Publisher: American Institute of Aeronautics and Astronautics

Destabilization effects of forward facing steps, backward facing steps and bumps on stationary and travelling crossflow disturbances are investigated computationally for a 40° infinite swept wing. Step and bump heights range from 24% to 53% of the boundary layer thickness and are located at 10% chord. The spectral/hp element solver, Nektar++, is used to compute base flow profiles with an embedded swept wing geometry. Parabolized Stability Equations (PSE) and Linearized Harmonic Navier-Stokes (LHNS) models are used to evaluate growth of convecting instabilities. The paper describes derivations of the PSE and LHNS models which accurately solve for the perturbed field over the very localized and rapid variations imposed by the surface step-features. Unlike the PSE, which suffer from a stream-wise numerical step size restriction, the LHNS are a fully elliptic set of equations which may use arbitrarily fine grid resolution. Unsurprisingly, the PSE codes fail to capture the effect of abrupt changes in surface geometry introduced by the steps features. Results for the LHNS and roughness incorporating LHNS are given for the varying step types. Comparisons are made between the LHNS model and direct numerical simulations involving the time-stepping linearized Navier-Stokes solver in the Nektar++ software suite. Most previous work in the topic area has focused on Tollmien-Schlichting perturbations over two-dimensional flat plate flows or airfoils, the novelty of this work lies with analyzing crossflow instability over a swept wing boundary-layer flow with step features.

Conference paper

Ciarella A, Lawson S, Wong P, Mughal MSet al., 2019, Aerodynamic and Transition Analysis of the Hybrid Laminar Flow Control Wing Experiment at the ARA Wind Tunnel, AIAA Aviation 2019 Forum, Publisher: American Institute of Aeronautics and Astronautics

This paper presents the work undertaken to evaluate the result of the Hybrid Laminar Flow Control (HLFC) test campaign performed in the Aircraft Research Association (ARA) transonic wind tunnel. The transition location was extracted from Infra-Red images at a range of angles of attack and Mach number. Experimentally measured pressure data were also acquired and interpolated to provide input to the laminar boundary layer code, the output of which was used for the stability calculations. The first aim of this paper is to assess the use of stability analysis in conjunction with wind tunnel data and to analyse these results. During the analysis, it was noticed that there exist critical cases in which stability analysis provides an unexpected very low N-factor. It is suggested that the gradients of the pressure distribution determines these critical cases. The calculated N-factor distribution demonstrates that it is not possible to use a single critical N-factor for transition prediction in wind tunnel environment. The second aim of this paper is to assess the effect of suction on transition location and the differences between constant and variable porosity. It is shown that variable porosity has an advantage over constant porosity in terms of required suction pressure and mass-flow.

Conference paper

Appel T, Mughal MS, Ashworth R, 2019, Global stability analysis of a boundary layer with surface indentations, AIAA Aviation 2019 Forum, Publisher: American Institute of Aeronautics and Astronautics

In the quest for laminar flow control on aircraft wings, quantifying the impact of structural deformation on laminar-turbulent transition remains a challenge. The purpose of this work is to numerically investigate the stability of two-dimensional incompressible boundary layers developing on a flat-plate geometry with indented surfaces of different depths. These surface indentations generate laminar separation bubbles, known to have strong destabilizing effects on Tollmien-Schlichting disturbances. The parallel efficiency of the developed computational tool based on state-of-the-art numerical libraries allows rapid parametric studies within the usually expensive global stability analysis framework. Using an incompressible linearized Navier-Stokes formulation, we use the perfectly matched layer method to absorb waves at the inflow and outflow boundaries. Forced receptivity analysis is performed in order to investigate the effect of the indentation region on the convecting Tollmien-Schlichting waves. Furthermore, the likelihood of global temporal mechanisms arising is investigated through BiGlobal stability analysis. The deepest surface indentation, which features a peak-reversed flow velocity of 9 % in the laminar separation bubble, leads to significant levels of Tollmien-Schlichting amplification. It is also characterized by two temporally unstable modes, namely a dominant, localized stationary mode as well as a traveling Kelvin-Helmholtz mode.

Conference paper

Raposo H, Mughal M, Ashworth R, 2019, Uncertainty Quantification of Acoustic Receptivity with an Adjoint Linear Navier-Stokes Approach, ERCOFTAC Bulletin 118, Editors: Marek, Publisher:, Pages: 25-30

Receptivity remains one of the key challenges towards holistic models of boundary layer transition and amplitude-based transition criteria. In this paper we briefly describe a high-fidelity acoustic receptivity model built upon the compressible time-harmonic linearised Navier-Stokes equations which is believed to be generalizable to complex geometries and could potentially be used in industrial applications. We demonstrate how the adjoint methodology is essential to rapidly quantify the effects of uncertainty in distributed random roughness over the amplitude of Tollmien-Schlichting waves. Three models of the acoustic boundary layer signature (BLAS) based on the linearised unsteady boundary layer equations (LUBLE) and the linear stability equations (LSE) are indirectly compared against each other and against finite-Reynolds number theory (FRNT) through quantification of the efficiency function. The LUBLE are shown to be an adequate choice of model through a large range of incidence angles at M∞ = 0.9 (θ < 140⁰) but they fail to model a weakening of the BLAS at larger incidences, i.e. for near-upstream propagating waves. In turn, the inviscid-LSE model is qualitatively correct but over-predicts receptivity at finite-Strouhal numbers. Lastly, the viscous-LSE model is in remarkable agreement with FRNT, thus showing that non-parallel flow effects for two-dimensional disturbances convecting over a flat plate geometry remain weak up to near-sonic flow conditions.

Book chapter

Raposo H, Mughal MS, Ashworth R, 2018, Acoustic receptivity of compressible Tollmien-Schlichting waves with an efficient time-harmonic linearized Navier-Stokes method, 2018 Fluid Dynamics Conference, Publisher: AIAA

The compressible formulation of the time-harmonic linearized Navier-Stokes (LNS) methodfor acoustic receptivity prediction is described. The efficiency of the proposed approachis rooted in the assumption that the problems of interest only require the time-asymptoticsolution of a few select frequencies. We explore the parabolic nature of the basic flow and of theStokes layer, and we implement an efficient LU decomposition method to obtain the roughness-induced steady perturbation and Tollmien-Schlichting wave. Before attempting to predictreceptivity amplitudes, the compressible Stokes layer solution based on the linearized unsteadyboundary layer equations is validated in the subsonic regime against an Orr-Sommerfeld-typeequation. Further testing of the model is conducted by reproducing the experiments of King&Breuer in near incompressible conditions. The results are consistent with the analogueincompressible receptivity model, and reveal excellent agreement with finite-Reynolds numbertheory for two-dimensional instabilities. Qualitative agreement with the experimental resultsfor oblique waves is observed. Differences can be partially explained by the choice of physicalmodel used to determine the N-factors, which in turn are used to extrapolate amplitudes tothe first-branch of stability. Ultimately, a comprehensive comparison with direct-numerical-simulation-based subsonic receptivity amplitudes is conducted, demonstrating the correctnessof the mathematical model and numerical implementation described herein.

Conference paper

Thomas C, Mughal MS, Roland H, Ashworth R, Martinex-Cava Aet al., 2018, Effect of small surface deformations on the stability of Tollmien–Schlichting disturbances, AIAA Journal, Vol: 56, Pages: 2157-2165, ISSN: 0001-1452

The effect of a small Gaussian shaped deformation on the development and growth of Tollmien–Schlichting disturbances on an unswept airfoil is investigated. A broad range of gap depths and widths is modeled that can be sufficient to generate localized pockets of reverse flow. Boundary-layer profiles are computed using a Navier–Stokes solver, permitting a thorough investigation of all configurations considered. The linear stability of Tollmien–Schlichting waves is then examined using parabolized stability equations and linearized Navier–Stokes formulations, with the former method giving excellent agreement with the latter for all disturbances studied, including within separated boundary layers. Tollmien–Schlichting disturbances are amplified by deeper and wider gaps, with a correlation derived by relating the increase in the N factor with the gap dimensions and freestream Reynolds number.

Journal article

Raposo H, Mughal MS, Ashworth R, 2018, Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness, Physics of Fluids, Vol: 30, ISSN: 1070-6631

Acoustic receptivity to Tollmien-Schlichting waves in the presence of surface roughness is investigated for a flat plate boundary layer using the time-harmonic incompressible linearized Navier-Stokes equations. It is shown to be an accurate and efficient means of predicting receptivity amplitudes, and therefore to be more suitable for parametric investigations than other approaches with DNS-like accuracy. Comparison with literature provides strong evidence of the correctness of the approach, including the ability to quantify non-parallel flow effects. These effects are found to be small for the efficiency function over a wide range of frequencies and local Reynolds numbers. In the presence of a two-dimensional wavy-wall, non-parallel flow effects are quite significant, producing both wavenumber detuning and an increase in maximum amplitude. However, a smaller influence is observed when considering an oblique Tollmien-Schlichting wave. This is explained by considering the non-parallel effects on receptivity and on linear growth which may, under certain conditions, cancel each other out. Ultimately, we undertake a Monte-Carlo type uncertainty quantification analysis with two-dimensional distributed random roughness. Its power spectral density (PSD) is assumed to follow a power law with an associated uncertainty following a probabilistic Gaussian distribution. The effects of the acoustic frequency over the mean amplitude of the generated two-dimensional Tollmien-Schlichting waves are studied. A strong dependence on the mean PSD shape is observed and discussed according to the basic resonance mechanisms leading to receptivity. The growth of Tollmien-Schlichting waves is predicted with non-linear parabolized stability equations computations to assess the effects of stochasticity in transition location.

Journal article

Kang KL, Ashworth R, Mughal MS, 2017, Stabilization of Crossflow Instability with Plasma Actuators: Linearized Navier Stokes Simulations, EUCASS 2017

This paper describes work carried out within the Buterfli project to look at the control of transition causing “target” cross flow vortices through the generation of subdominant “killer” modes with distributed plasma actuation leading to non-linear interaction and damping of the “target” modes. Experimental studies performed at the TsAGI T124 tunnel for a swept plate subject to favourable pressure gradient flow have been compared with numerical modelling. A mathematical model for the actuator developed at TsAGI has been implemented in a linearised Navier Stokes solver and used to predict “killer” mode amplitudes at a measurement plane in the experiment. This shows good agreement with experiment and is used as input for non-linear PSE analysis to predict the effect of these modes on transition. Whilst the numerical model indicates a delay in transition in the experiment actuator induced unsteadiness results in the generation of travelling cross flow modes and an advance rather than delay in transition

Conference paper

Xu H, Mughal SM, Gowree E, Atkin CJ, Sherwin Set al., 2017, Destabilisation and modification of Tollmien-Schlichting disturbances by athree dimensional surface indentation, Journal of Fluid Mechanics, Vol: 819, Pages: 592-620, ISSN: 1469-7645

We consider the influence of a smooth three-dimensional (3-D) indentation on the instability of an incompressible boundary layer by linear and nonlinear analyses. The numerical work was complemented by an experimental study to investigate indentations of approximately 11δ99 and 22δ99 width at depths of 45 %, 52 % and 60 % of δ99 , where δ99 indicates 99% boundary layer thickness. For these indentations a separation bubble confined within the indentation arises. Upstream of the indentation, spanwise-uniform Tollmien–Schlichting (TS) waves are assumed to exist, with the objective to investigate how the 3-D surface indentation modifies the 2-D TS disturbance. Numerical corroboration against experimental data reveals good quantitative agreement. Comparing the structure of the 3-D separation bubble to that created by a purely 2-D indentation, there are a number of topological changes particularly in the case of the widest indentation; more rapid amplification and modification of the upstream TS waves along the symmetry plane of the indentation is observed. For the shortest indentations, beyond a certain depth there are then no distinct topological changes of the separation bubbles and hence on flow instability. The destabilising mechanism is found to be due to the confined separation bubble and is attributed to the inflectional instability of the separated shear layer. Finally for the widest width indentation investigated ( 22δ99 ), results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using N -factors to assess instability of properly 3-D disturbances reveals that a general indication of flow destabilisation and development of strongly nonlinear behaviour is indicated as N=6 values are attained. However N -factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdown to turbu

Journal article

Thomas C, Mughal M, Ashworth R, 2017, Development of Tollmien-Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing, Physical Review Fluids, Vol: 2, ISSN: 2469-990X

The effect of long-wavelength sinusoidal surface waviness on the development of Tollmien-Schlichting (TS) wave instabilities is investigated. The analysis is based on the compressible flow that forms over an unswept infinite wavy wing with surface variations of variable amplitude, wavelength, and phase. Boundary layer profiles are extracted directly from solutions of a Navier-Stokes solver, which allows a thorough parametric analysis to be undertaken. Many wavy surface configurations are examined that can be sufficient to establish localized pockets of separated flow. Linear stability analysis is undertaken using parabolized stability equations (PSE) and linearized Navier-Stokes (LNS) methods, and surface waviness is generally found to enhance unstable behavior. Results of the two schemes are compared and criteria for PSE to establish accurate solutions in separated flows are determined, which are based on the number of TS waves per wavelength of the surface deformation. Relationships are formulated, relating the instability variations to the surface parameters, which are consistent with previous observations regarding the growth of TS waves on a flat plate. Additionally, some long-wavelength surface deformations are found to stabilize TS disturbances.

Journal article

Moore MR, Mughal MS, Papageorgiou DT, 2017, Ice formation within a thin film flowing over a flat plate, Journal of Fluid Mechanics, Vol: 817, Pages: 455-489, ISSN: 0022-1120

We present a model for ice formation in a thin, viscous liquid film driven by aBlasius boundary layer after heating is switched off along part of the flat plate. Theflow is assumed to initially be in the Nelson et al. (J. Fluid Mech., vol. 284, 1995,pp. 159–169) steady-state configuration with a constant flux of liquid supplied atthe tip of the plate, so that the film thickness grows like x1/4in distance alongthe plate. Plate cooling is applied downstream of a point, Lx0, an O(L)-distancefrom the tip of the plate, where L is much larger than the film thickness. Thecooling is assumed to be slow enough that the flow is quasi-steady. We present athorough asymptotic derivation of the governing equations from the incompressibleNavier–Stokes equations in each fluid and the corresponding Stefan problem for icegrowth. The problem breaks down into two temporal regimes corresponding to therelative size of the temperature difference across the ice, which are analysed in detailasymptotically and numerically. In each regime, two distinct spatial regions arise, anouter region of the length scale of the plate, and an inner region close to x0 in whichthe film and air are driven over the growing ice layer. Moreover, in the early timeregime, there is an additional intermediate region in which the air–water interfacepropagates a slope discontinuity downstream due to the sudden onset of the ice atthe switch-off point. For each regime, we present ice profiles and growth rates, andshow that for large times, the film is predicted to rupture in the outer region whenthe slope discontinuity becomes sufficiently enhanced.

Journal article

Thomas C, Mughal, Ashworth R, 2017, On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer, Physics of Fluids, Vol: 29, ISSN: 1089-7666

The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers, and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

Journal article

Thomas C, Mughal MS, Gipon M, Ashworth Ret al., 2016, Stability of an infinite swept wing boundary layer with surface waviness, AIAA Journal, Vol: 54, Pages: 3024-3038, ISSN: 1533-385X

A scheme for generating boundary layers is described and applied to an infinite sweptwing model with wavy surface deformations. Steady laminar mean flow is extracteddirectly from solutions of the Navier-Stokes system of equations, which is validatedagainst computations of a compressible boundary layer method. Furthermore, theroutines capture separated boundary layer profiles, overcoming the constraints of theconventional methods. The stability of crossflow disturbances is investigated using bothPSE and LNS methods and the effect of chordwise waviness of variable wavelength,amplitude and phase is considered. Wavy surfaces are found to influence the growthof crossflow disturbances, suggesting that the onset of transition may also be affectedby the variations in the surface geometry.

Journal article

Xu H, Mughal MS, Gowree ER, Sherwin Set al., 2016, Effect of a 3d indentation on boundary layer instability, ICAS 2016, 30th Congress of the International Council of the Aeronautical Sciences, Publisher: ICAS

Conference paper

Xu H, Mughal MS, Gowree ER, Sherwin Set al., 2016, Effect of a 3d surface indentation on boundary layer stability, 24th International Congress of Theoretical and Applied Mechanics ICTAM 2016, Publisher: ICAS

We are concerned about effect of a 3D surfaceindentation on instability and laminar-turbulenttransition in a boundary layer. For naturaltransition in a boundary layer, the transitiononset is dominated by growth of the Tollmien-Schlichting (TS) wave and its subsequentsecondary instability. In the paper, both linearanalysis and nonlinear calculations are carriedout to address the 3D surface indentation effecton amplifying TS waves’ amplitudes andprompting transition onset. By the linearanalysis, we address sudden amplification of theTS modes by a separation bubble in a surfaceindentation region. The nonlinear calculationsare implemented to validate the traditionaltransition criteria predicted by the linear theorywhen a 3D indentation is present. Finally,applicability of the traditional transitioncriteria is assessed.

Conference paper

Ashworth R, Lawson S, Lowry S, Martinez-Cava A, Mughal M, Thomas Cet al., 2016, Numerical and experimental study of the tolerance of natural laminar flow on a wing to TS destabilisation at the leading edge /wing-box junction, Royal Aeronautical Society Applied Aerodynamics Conference

The junction between the leading edge and wing box components of natural laminar flow wings presents a feature to the flow that can potentially enhance the growth of transition causing Tollmein Schlichting (TS) instabilities leading to a significant forward movement of transition. Even when a filler is applied to the gap between the components, subsequent curing will lead to a shallow cavity formed by the filler surface. This paper describes a detailed experimental and numerical study of flow over realistic filler shapes under conditions representative of a natural laminar flow wing. Wind tunnel results show that for the width of gap examined there is an initial forward movement of transition by a quite significant amount for very shallow filled gaps but essentially no further movement as the depth is increased. PSE based stability analysis reveals that there is a destabilisation of modes near the gap. The degree of destabilisation appears to plateau with increasing depth due to recirculation of flow inside the gap which maintains an almost constant effective depth. Compensating stabilisation soon after the gap means however that there is very little lasting effect of the gap on the magnitude of the transition causing modes further downstream and stability analysis suggests there is little movement in transition as seen beyond a certain depth. The initial movement observed in the tunnel tests may be due to enhanced receptivity to TS waves at the site of the gap which is not captured by the stability analysis.

Conference paper

Saeed TI, Mughal MS, Morrison JF, 2016, The Interaction of a Swept-Wing Boundary Layer with Surface Excrescences, 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, Publisher: American Institute of Aeronautics and Astronautics

The influence of steps and gaps on swept-wing crossflow development is an emergingarea of interest. An experiment is performed on a 40◦swept-wing model in a facility witha turbulence level of 0.10%. Periodic discrete roughness elements are spaced at the criticalcrossflow wavelength and used to excite the crossflow disturbance. The subsequent interactionwith a two-dimensional roughness strip of various height and chordwise location isinvestigated. Naphthalene flow visualisation is used to help understand the global transitionfeatures, whilst detailed boundary layer measurements are conducted using hot-wireanemometry. Excrescences located closest to the neutral point are seen to have the biggestinfluence on stationary-crossflow disturbance amplitude. There appears to be a thresholdheight below which the excrescence has no significant influence on the boundary layer development.Excrescences located further downstream appear to generate greater unsteadinessin the boundary layer for a given excrescence height, leading to earlier transition.

Conference paper

Xu H, Mughal MS, Sherwin S, 2015, Effect of a 3D surface depression on boundary layer transition, 68th Annual Meeting of the APS Division of Fluid Dynamics

The influence of a three-dimensional surface depression on the transitional boundary layer is investigated numerically. In the boundary layer transition, the primary mode is a Tollmien-Schlichting (TS) wave which is a viscous instability. These modes are receptive to surface roughness interacting with free stream disturbances and/or surface vibrations. In this paper, numerical calculations are carried out to investigate the effect of the depression on instability of the boundary layer. In order to implement linear analysis, two/three (2D/3D)-dimensional nonlinear Navier-Stokes equations are solved by spectral element method to generate base flows in a sufficient large domain. The linear analyses are done by the parabolic stability equations (PSE). Finally, a DNS calculation is done to simulate the boundary layer transition.

Conference paper

Thomas C, Mughal MS, Ashworth R, 2015, The Effect of Surface Waviness on the Growth and Development of TS Waves, 68th Annual Meeting of the APS Division of Fluid Dynamic

The growth and development of TS wave disturbances on an infinitely swept wing are investigated, where surface waviness is imposed along the chordwise direction. Boundary layers are extracted directly from Reynolds Averaged Navier-Stokes solutions, which allows a stability analysis to be undertaken for many flow systems that may include regions of boundary layer separation. Stability analysis is then carried out using both PSE and LNS methods. The effects of varying the wavelength, amplitude and phase of the waviness are considered and the impact on the development of the boundary layer and TS wave disturbances are investigated. It is found that wavy surfaces can significantly affect the amplification rates of the TS wave disturbances, causing large variations in both the onset of the instability and transition.

Conference paper

Ashworth R, Mughal MS, 2015, Modeling Three Dimensional Effects on Cross Flow Instability from Leading Edge Dimples, Procedia IUTAM, Vol: 14, Pages: 201-210, ISSN: 2210-9838

The formation of shallow dimples near the leading edge of natural laminar flow wings can occur during operation due to impact by hail, potentially changing the stability characteristics and causing an early transition to turbulence downstream of the dimple. Changes in the base flow will be strongly three-dimensional in character putting this problem beyond the capability of the standard strip based approaches founded on conical flow assumptions that are routinely used in the aerospace industry. This paper describes the application of a fully 3d method to a dimple on a wing for flow resembling that on a natural laminar flow wing. Solving the three-dimensional compressible boundary layer equations for the base flow and using a point to point marching scheme for solving the 3d PSE equations, it is shown that high wave-number stationary cross-flow modes can become unstable and grow rapidly in the dimple wake in a region well beyond the leading edge where stationary cross-flow modes would normally be decaying.

Journal article

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