The actuator line method (ALM) is used extensively in wind turbine and rotor simulations. However, its original uncorrected formulation overestimates the forces near the tip of the blades and does not reproduce well forces on translating wings. The recently proposed vortex-based smearing correction for the ALM is a correction based on physical and mathematical properties of the simulation that allows for a more accurate and general ALM. So far, to correct the forces on the blades, the smearing correction depended on an iterative process at every time step, which is usually slower, less stable and less deterministic than direct methods. In this work, a non-iterative process is proposed and validated. First, we propose a formulation of the nonlinear lifting line that is equivalent to the ALM with smearing correction, showing that the results are practically identical for a translating wing. Then, by linearizing the lifting line method, the iterative process of the correction is substituted by the direct solution of a small linear system. No significant difference is observed in the results of the iterative and non-iterative corrections, in both wing and rotor simulations. Additional contributions of the present work include the use of a more accurate approximation for the velocity induced by a smeared vortex segment and the implementation of a free-vortex wake model to define the vortex sheet, which contribute to the accuracy and generality of the method. The results presented here may motivate the adoption of the ALM by other communities, for example, in fixed-wing applications.

Nowadays, firms are constantly looking for methodological approaches that help them to decrease the time needed for the innovation process. Among these approaches, it is worth mentioning the TRIZ-based frameworks such as the Inventive Design Methodology (IDM), where the Problem Graph method is used to formulate a problem. However, the application of IDM is time-consuming due to the construction of a complete map to clarify a problem situation. Therefore, the Inverse Problem Graph (IPG) method has been introduced within the IDM framework to enhance its agility. Nevertheless, the manual gathering of essential information, including parameters and concepts, requires effort and time. This paper integrates the neural network doc2vec and machine learning algorithms as Artificial Intelligence methods into a graphical method inspired by the IPG process. This integration can facilitate and accelerate the development of inventive solutions by extracting parameters and concepts in the inventive design process. The method has been applied to develop a new lattice structure solution in the material field.

Spectral degeneracies where eigenvalues and eigenvectors simultaneously coalesce, also known as exceptional points, are a natural consequence of the strong non-normality of the Orr–Sommerfeld operator describing the evolution of infinitesimal disturbances in parallel shear flows. While the resonances associated with these points give rise to algebraic growth, the development of non-modal stability theory exploiting specific perturbation structures with much larger potential for transient energy growth has led to waning interest in spectral degeneracies. The appearance of subharmonic eigenvalue orbits, recently discovered in the periodic spectrum of pulsating Poiseuille flow, can be traced back to the coalescence of eigenvalues at exceptional points. We present a thorough analysis of the spectral properties of the linear operator to identify exceptional points and accurately map the prevalence of subharmonic eigenvalue orbits for a large range of pulsation amplitudes and frequencies. This information is then combined with solutions of the linear initial value problem to analyse the impact of the appearance of these orbits on the temporal evolution of linear disturbances in pulsating Poiseuille flow. The periodic amplification phases are shown to be heralded by repeated non-normal growth bursts that are intensified by the formation of subharmonic orbits involving the leading eigenvalues. These bursts are associated with the change of alignment of the perturbation from the decaying towards the amplified branch of the subharmonic eigenvalue orbits in a so-called branch transition process.

The stability of an incompressible boundary layer flow over a wing in the presence of free stream turbulence (FST) has been investigated by means of direct numerical simulations and compared with the linearised boundary layer equations. Four different FST conditions have been considered, which are characterised by their turbulence intensity levels and length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free stream vorticity. The breakdown of these streaks into turbulent spots from local secondary instabilities is also observed, presenting the same development as the ones reported in flat plate experiments. The disturbance growth, characterised by its root mean squares value, is found to depend not only on the turbulence level, but also on the FST length scales. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth. We study this boundary layer preference by projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer.

Afghanistan assumed its modern cartographic form in piecemeal fashion between the late 1860s and early 1890s in the context of British imperial boundary-making projects in South Asia and the Middle East. The bordering of Afghanistan was contextualized by the global British empire and multiple boundary conflicts and frontier anxieties involving the British and the French, German, Russian, and other imperial powers as well as local rulers. The fundamental point here is that the map of Afghanistan is a product of imperial and interimperial concerns, and it has not benefited the Afghan people. The map of Afghanistan may or may not have served the imperial purposes for which it was created, but more importantly, by uncritically accepting it and its imperial heritage, we Afghans have become victims of an imperial map of ourselves. Afghans and non-Afghans will benefit from directly confronting the coercive impact of imperial mapping agendas on the largely invisible people “on the map” of Afghanistan. This essay historicizes the production of maps of modern Afghanistan, exposing imperial and crypto-colonial influences upon our national cartography. In so doing, it critically reimagines our spatial politics and reconfigures our intellectual infrastructure. It is an exercise in historical recentering designed to instill Afghan humanity and agency onto the map of Afghanistan.

In the present work, the laminar–turbulent transition of the flow evolving around a low-pressure turbine blade has been investigated. Direct numerical simulations have been carried out for two different free stream turbulence intensity (FSTI) levels to investigate the role of free stream oscillations on the evolution of the blade boundary layer. Emphasis is placed on identifying the mechanisms driving the formation and breakup of coherent structures in the high FSTI case and how these processes are affected by the leading-edge receptivity and/or by the continuous forcing in the blade passage. Proper orthogonal decomposition (POD) has been adopted to provide a clear statistical representation of the shape of the structures. Extended POD projections provided temporal and spanwise correlations that allowed us to identify dominant temporal structures and spanwise wavelengths in the transition process. The extended POD analysis shows that the structures on the pressure side are not related to what happens at the leading edge. The results on the suction side show that the modes defining the leading edge and the passage bases correlate with coherent structures responsible for the transition. The most energetic mode of the passage basis is strongly related to the most amplified wavelength in the boundary layer and breakup events leading to transition. Modes with a smaller spanwise wavelength belong to the band predicted by optimal disturbance theory, they amplify with a smaller gain in the rear suction side, and they show the highest degree of correlation between the passage region and the rear suction side.

Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with an aspect ratio of two at zero angle of attack, completing earlier modal instability analysis of flow around the same geometry. The theoretical framework to perform transient growth analysis of compressible flows on a generalized two-dimensional frame of reference is developed for the first time and is then applied to solve the initial-value problem governing non-modal linear instability on planes perpendicular to the cone axis, taken at successive streamwise locations along the elliptic cone. Parameter ranges examined here are chosen so as to model flight of the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) test geometry at altitudes of 21 km and 33 km, corresponding to Mach numbers 7.45 and 8.05 and unit Reynolds numbers $Re' = 1.07\times 10^7$ and $1.89\times 10^6$, respectively. Results obtained indicate that the significance of the non-modal growth for laminar–turbulent transition increases with increasing flight altitude (decreasing Reynolds number). At a given set of flow parameters, transient growth is stronger in the vicinity of the tip of the cone and in azimuthal locations away from both of the minor (centreline) and major (attachment line) axes of the cone. Linear optimal disturbances calculated at conditions of maximal transient growth are found to peak in the crossflow region of the elliptic cone. These structures are elongated along the streamwise spatial direction, while being periodic along the spanwise direction with periodicity lengths of the same order of magnitude as the well-known structures identified as crossflow vortices in both experiments and simulations.

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$, in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$, a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.

Convective Heat Transfer Coefficient (CHTC) is a determining factor in building energy simulation (BES) tools for building thermal calculations. The accuracy of CHTC calculation has a direct effect on building energy analysis.This study aims to assess the impact of multiple parameters, namely temperature difference, wind speed, and wind direction on CHTC of building exterior surfaces. Then the overall high accuracy correlation based on these parameters for CHTC is provided. According to the specified values for temperature and velocity, Richardson’s number range from 0.1 to 10, representing a mixed heat transfer. The simulated results are compared with a wind tunnel experiment for validation. The standard k-epsilon model is used for turbulence simulation. Several cases are numerically simulated, considering various velocities, wind directions, and temperature differences. Results indicate that the studied parameters could be ranked as velocity, building orientation, and temperature difference in the order of effectiveness. All of the correlations used in EnergyPlus software for the exterior surface of the building are compared with the presented correlation and simulated data. The comparison shows that the proposed expression could predict CHTC for various angles, velocities, and temperature differences with an error of below 3%.

A rigorous derivation and validation for linear fluid–structure-interaction (FSI) equations for a rigid-body motion problem is performed in an Eulerian framework. We show that the ‘added stiffness’ terms arising in the formulation of Fanion et al. (Revue Européenne des Éléments Finis, vol. 9, issue 6–7, 2000, pp. 681–708) vanish at the FSI interface in a first-order approximation and can be neglected when considering the growth of infinitesimal disturbances. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and nonlinear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within $0.1\,\%$ accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero frequency linearly unstable mode of the coupled FSI system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.

The stability of the jet in cross-flow is investigated using a complete set-up including the flow inside the pipe. First, direct simulations were performed to find the critical velocity ratio as a function of the Reynolds number, keeping the boundary-layer displacement thickness fixed. At all Reynolds numbers investigated, there exists a steady regime at low velocity ratios. As the velocity ratio is increased, a bifurcation to a limit cycle composed of hairpin vortices is observed. The critical bulk velocity ratio is found at approximately $R=0.37$ for the Reynolds number $Re_{D}=495$, above which a global mode of the system becomes unstable. An impulse response analysis was performed and characteristics of the generated wave packets were analysed, which confirmed results of our global mode analysis. In order to study the sensitivity of this flow, we performed transient growth computations and also computed the optimal periodic forcing and its response. Even well below this stability limit, at $R=0.3$, large transient growth ($10^{9}$ in energy amplification) is possible and the resolvent norm of the linearized Navier–Stokes operator peaks above $2\times 10^{6}$. This is accompanied with an extreme sensitivity of the spectrum to numerical details, making the computation of a few tens of eigenvalues close to the limit of what can be achieved with double precision arithmetic. We demonstrate that including the meshing of the jet pipe in the simulations does not change qualitatively the dynamics of the flow when compared to the simple Dirichlet boundary condition representing the jet velocity profile. This is in agreement with the recent experimental results of Klotz et al. (J. Fluid Mech., vol. 863, 2019, pp. 386–406) and in contrast to previous studies of Cambonie & Aider (Phys. Fluids, vol. 26, 2014, 084101). Our simulations also show that a small amount of noise at subcritical velocity ratios may trigger the shedding of hairpin vortices.

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST), at the levels of 3.0 % and 3.5 %, in a zero-pressure-gradient transitional boundary layer, by means of localized sensors and actuators. A linear quadratic Gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator that aims to induce the exact structures that are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the FST levels. Integrated total drag reductions observed were up to 21 % and 19 % for turbulence intensity levels of 3.0 % and 3.5 %, respectively, depending on the considered actuator. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered along the wall-normal direction. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer.

The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence by means of active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer by means of a high level of free-stream turbulence. The occurring disturbances are measured by means of localized wall-shear-stress sensors and damped out using near-wall actuators, which resemble ring plasma actuators. Each actuator is powered by a time-varying signal whose amplitude is computed by processing signals from the sensors. The processed signal is the result of two control laws: the linear quadratic Gaussian regulator (LQG) and the inverse feed-forward control technique (IFFC). The use of the first control method, LQG, requires a state-space representation of the system dynamics, so the flow is described by means of a linear time-invariant operator that captures only the most relevant information of the dynamics and results in a reduced-order model (ROM). The ROM is computed by means of the eigensystem realization algorithm (ERA), which is based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering free-stream turbulence because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, based on additional shear-stress measurements in an upstream location. Transfer functions between such measurements and other downstream sensors are obtained and allow the derivation of the ERA system, in a data-driven approach that would be realizable in experiments. Finally, in order to discuss the advantages of the LQG based on the ROM and analyse its performance, the implemented LQG is compared to the IFFC, which consists of wave cancellation. The work (i) presents a systematic and straightforward way to deal with high-dimensional disturbances in order to build ROMs for a feasible control technique, and (ii) shows that even when considering practical constraints, such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in the literature.

In this study the origins of premature transition due to oversuction in boundary layers are studied. An infinite row of circular suction pipes that are mounted at right angles to a flat plate subject to a Blasius boundary layer is considered. The interaction between the flow originating from neighbouring holes is weak and for the parameters investigated, the pipe is always found to be unsteady regardless of the state of the flow in the boundary layer. A stability analysis reveals that the appearance of boundary layer transition can be associated with a linear instability in the form of two unstable eigenmodes inside the pipe that have weak tails, which extend into the boundary layer. Through an energy budget and a structural sensitivity analysis, the origin of this flow instability is traced to the structures developing inside the pipe near the pipe junction. Although the amplitudes of the modes in the boundary layer are orders of magnitude smaller than the corresponding amplitudes inside the pipe, a Koopman analysis of the data gathered from a nonlinear direct numerical simulation confirms that it is precisely these disturbances that are responsible for transition to turbulence in the boundary layer due to oversuction.

Application of ring-type plasma actuators for control of laminar–turbulent transition in a swept-wing boundary layer is investigated thorough direct numerical simulations. These actuators induce a wall-normal jet in the boundary layer and can act as virtual roughness elements. The flow configuration resembles experiments by Kim et al. (2016 Technical Report. BUTERFLI Project TR D3.19, http://eprints.nottingham.ac.uk/id/eprint/46529). The actuators are modelled by the volume forces computed from the experimentally measured induced velocity field at the quiescent air condition. Stationary and travelling cross-flow vortices are triggered in the simulations by means of surface roughness and random unsteady perturbations. Interaction of vortices generated by actuators with these perturbations is investigated in detail. It is found that, for successful transition control, the power of the actuators should be increased to generate jet velocities that are one order of magnitude higher than those used in the experiments by Kim et al. (2016) mentioned above.

With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner–Skan–Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the $\unicode[STIX]{x1D700}$-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.

We present results of numerical simulations of leading-edge acoustic receptivity for acoustic waves impinging on the leading edge of a finite-thickness flat plate. We use both compressible and incompressible flow solvers fitted with high-order high-accuracy numerical methods and independent methods of estimating the receptivity coefficient. The results show that the level of acoustic receptivity in the existing literature appears to be one order of magnitude too high. Our review of previous numerical simulations and experiments clearly identifies some contradictory trends. In the limit of an infinitely thin flat plate, our results are consistent with asymptotic theory and numerical simulations.