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Large-eddy simulations (LES) of a hypersonic boundary layer on a $7^\circ$-half-angle cone are performed to investigate the effects of highly cooled walls (wall-to-recovery temperature ratio of $T_w / T_r \sim 0.1$) on fully developed turbulence and to validate a newly developed rescaling method based on volumetric flow extraction. Two Reynolds numbers are considered, $Re_m = 4.1 \times 10^6\ \text {m}^{-1}$ and $6.4 \times 10^6\ \text {m}^{-1}$, at free-stream Mach numbers of $M_\infty = 7.4$. A comparison with a reference laminar-to-turbulent simulation, capturing the full history of the transitional flow dynamics, reveals that the volumetric rescaling method can generate a synthetic turbulent inflow that preserves the structure of the fluctuations. Equilibrium conditions are recovered after approximately 40 inlet boundary layer thicknesses. Numerical trials show that a longer streamwise extent of the rescaling box increases numerical stability. Analyses of turbulent statistics and flow visualizations reveal strong pressure oscillations, up to $50\,\%$ of local mean pressure near the wall, and two-dimensional longitudinal wave structures resembling second-mode waves, with wavelengths up to 50 % of the boundary layer thickness, and convective Mach numbers of $M_c \simeq 4.5$. It is shown that their quasi-periodic recurrence in the flow is not an artefact of the rescaling method. Strong and localized temperature fluctuations and spikes in the wall-heat flux are associated with such waves. Very high values of temperature variance near the wall result in oscillations of the wall-heat flux exceeding its average. Instances of near-wall temperature falling below the imposed wall temperature of $T_w=300$ K result in pockets of instantaneous heat flux oriented against the statistical mean direction.
The dynamics of evolving fluid films in the viscous Stokes limit is relevant to various applications, such as the modelling of lipid bilayers in cells. While the governing equations were formulated by Scriven (1960), solving for the flow of a deformable viscous surface with arbitrary shape and topology has remained a challenge. In this study, we present a straightforward discrete model based on variational principles to address this long-standing problem. We replace the classical equations, which are expressed with tensor calculus in local coordinates, with a simple coordinate-free, differential-geometric formulation. The formulation provides a fundamental understanding of the underlying mechanics and translates directly to discretization. We construct a discrete analogue of the system using Onsager's variational principle, which, in a smooth context, governs the flow of a viscous medium. In the discrete setting, instead of term-wise discretizing the coordinate-based Stokes equations, we construct a discrete Rayleighian for the system and derive the discrete Stokes equations via the variational principle. This approach results in a stable, structure-preserving variational integrator that solves the system on general manifolds.
In this contribution, we develop a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes as introduced by Loison et al. (Intl J. Multiphase Flow, vol. 177, 2024, 104857). It relies on the stationary action principle and interface geometric variables. This contribution provides a novel method to derive small-scale models for the dynamics of the interface geometry. They are introduced here on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the geometric method of moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model allows the coupling of the two-scale flow with an inter-scale transfer. It is shown, in particular, that the resulting dynamics provides partial closures for the interface area density equation obtained from the averaging approach.
Ciliated microorganisms near the base of the aquatic food chain either swim to encounter prey or attach at a substrate and generate feeding currents to capture passing particles. Here, we represent attached and swimming ciliates using a popular spherical model in viscous fluid with slip surface velocity that affords analytical expressions of ciliary flows. We solve an advection–diffusion equation for the concentration of dissolved nutrients, where the Péclet number ($Pe$) reflects the ratio of diffusive to advective time scales. For a fixed hydrodynamic power expenditure, we ask what ciliary surface velocities maximize nutrient flux at the microorganism's surface. We find that surface motions that optimize feeding depend on $Pe$. For freely swimming microorganisms at finite $Pe$, it is optimal to swim by employing a ‘treadmill’ surface motion, but in the limit of large $Pe$, there is no difference between this treadmill solution and a symmetric dipolar surface velocity that keeps the organism stationary. For attached microorganisms, the treadmill solution is optimal for feeding at $Pe$ below a critical value, but at larger $Pe$ values, the dipolar surface motion is optimal. We verified these results in open-loop numerical simulations and asymptotic analysis, and using an adjoint-based optimization method. Our findings challenge existing claims that optimal feeding is optimal swimming across all Péclet numbers, and provide new insights into the prevalence of both attached and swimming solutions in oceanic microorganisms.
Vibration-based structural health monitoring (SHM) of (large) infrastructure through operational modal analysis (OMA) is a commonly adopted strategy. This is typically a four-step process, comprising estimation, tracking, data normalization, and decision-making. These steps are essential to ensure structural modes are correctly identified, and results are normalized for environmental and operational variability (EOV). Other challenges, such as nonstructural modes in the OMA, for example, rotor harmonics in (offshore) wind turbines (OWTs), further complicate the process. Typically, these four steps are considered independently, making the method simple and robust, but rather limited in challenging applications, such as OWTs. Therefore, this study aims to combine tracking, data normalization, and decision-making through a single machine learning (ML) model. The presented SHM framework starts by identifying a “healthy” training dataset, representative of all relevant EOV, for all structural modes. Subsequently, operational and weather data are used for feature selection and a comparative analysis of ML models, leading to the selection of tree-based learners for natural frequency prediction. Uncertainty quantification (UQ) is introduced to identify out-of-distribution instances, crucial to guarantee low modeling error and ensure only high-fidelity structural modes are tracked. This study uses virtual ensembles for UQ through the variance between multiple truncated submodel predictions. Practical application to monopile-supported OWT data demonstrates the tracking abilities, separating structural modes from rotor dynamics. Control charts show improved decision-making compared to traditional reference-based methods. A synthetic dataset further confirms the approach’s robustness in identifying relevant natural frequency shifts. This study presents a comprehensive data-driven approach for vibration-based SHM.
Typically, the fuselage of a modern military aircraft is designed in such a way that the propulsion system is integrated into it. The main reasons are reduction of installation space and minimisation of radar signature. Those requirements can be achieved by using highly bent engine intakes, which are occluding a direct line of sight to the compressor system. Depending on their design, secondary flows and flow separation can be expected due to the strong curvature of the intake system. In this study, a serpentine intake in front of the Larzac 04 test engine is investigated experimentally and its performance compared with and without flow stabilising measures. In detail, a configuration with vortex generators was compared experimentally with a configuration of active flow control by injected air. In order to analyse and compare the efficiency of both systems, the dimensionless total pressure coefficient, the distortion coefficient (DC60) and detailed surface pressure distributions as well as the aerodynamic interface plane are evaluated. In addition, different throttle lines were recorded for surge line evaluation of the low pressure compressor of the Larzac engine and compared for each flow-stabilising measure investigated. It was found that the application of injecting air showed a larger improvement in surge margin and reduction in distortion coefficients compared to the passive flow control.
In this paper, we designa robust Successive Generalised Dynamic Inversion (SGDI) flight control system for high-performance trajectory tracking of target sun-synchronous orbit Satellite Launch Vehicles (SLVs). The robust SGDI control system is designed to track an optimal reference trajectory such that the desired orbital terminal conditions of the ascent flight phase are achieved. The proposed SGDI is composed of two loops. The attitude control loop employs Dynamically Scaled Generalised Inversion (DSGI) of Servo Constraint Dynamics (SVD) in the deviations of Euler attitude angles from their desired optimal trajectories. The inner-dynamics control loop employs DSGI of an SVD in the SLV angular velocity components. Robustification control elements are augmented within the two loops of the baseline SGDI control system to overcome control performance degradation due to dynamic scaling of the Moore-Penrose generalised inverse, modeling and parametric uncertainties, and exogenous disturbances. The robust SGDI control system works to enforce global convergence of the SLV attitude trajectories to the reference trajectories. The high-performance attributes of the robust SGDI control system are verified via comparisons with a classical sliding mode control system, and by performing numerous runs of Monte Carlo simulations under various types of uncertainties and external wind disturbances.
Aiming at the problems of poor coordination effect and low positioning accuracy of unmanned aerial vehicle (UAV) formation cooperative navigation in complex environments, an adaptive time-varying factor graph framework UAV formation cooperative navigation algorithm is proposed. The proposed algorithm uses the factor graph to describe the relationship between the navigation state of the UAV fleet and its own measurement information as well as the relative navigation information, and detects the relative navigation information at each moment by the double-threshold detection method to update the factor graph model at the current moment. And the robust estimation is combined with the factor graph, and the weight function measurements are used in the construction of the factor nodes for adaptive adjustment to make the system highly robust. The simulation results show that the proposed method realises the effective fusion of airborne multi-source sensing information and relative navigation information, which effectively improves the UAV formation cooperative navigation accuracy.
An advanced deformable Kirkpatrick–Baez (K-B) mirror system was developed, equipped with high-speed piezoelectric actuators, and designed to induce beam decoherence and significantly enhance the quality of X-ray imaging by minimizing undesirable speckles in synchrotron radiation or free-electron laser facilities. Each individual mirror is engineered with 36 independent piezoelectric actuators that operate in a randomized manner, orchestrating the mirror surface to oscillate at a high frequency up to 100 kHz. Through in situ imaging single-slit diffraction measurement, it has been demonstrated that this high-frequency-vibration mirror system is pivotal in disrupting the coherent nature, thereby diminishing speckle formation. The impact of the K-B mirror system is profound, with the capability to reduce the image contrast to as low as 0.04, signifying a substantial reduction in speckle visibility. Moreover, the coherence of the X-ray beam is significantly lowered from an initial value exceeding 80% to 13%.
This study investigates the influence of release timing on the trajectory of internal store separation through numerical solutions of continuity, momentum, energy equations and six degrees of freedom equations in a coupled manner. The internal store separation process in advanced fighter aircraft is analysed using computational fluid dynamics (CFD) and six degrees of freedom equations of motion. Initially, the equations of motion are validated by reenacting the Eglin Air Force Base study, an external store separation example with documented experimental results. Subsequently, validation is extended to the M219 cavity problem. In the internal store separation analysis, a cavity with an L/D ratio of 5, a freestream velocity of 0.85 Mach, and a generic store are utilised. Detached eddy simulation (DES) is applied using both static and dynamic mesh techniques in all numerical solutions. The generic store, positioned within a clean cavity with a 90-degree flap angle, was released at two distinct times, corresponding to the points of maximum and minimum gravitational forces. Interestingly, the results show that releasing the store when the normal force acting on it is at its maximum does not necessarily provide an optimal separation. Specifically, when the force coefficient was at its maximum (0.14), the store collided with the cavity door flap after 0.171465 seconds. In contrast, when the force coefficient was at its minimum (-0.04), the store contacted the cavity door after 0.170295 seconds at the same location. Despite the differences in force magnitudes, the trajectories were nearly identical, suggesting that the timing of the release may not have a significant effect on preventing collision. This further emphasises the need for flow control methods to ensure safe and effective store separation.
Molnupiravir Form I crystallizes in space group C2 (#5) with a = 6.48110(17), b = 8.71848(19), c = 27.0607(19) Å, β = 91.920(4)°, V = 1528.22(12) Å3, and Z = 4 at 295 K. The crystal structure consists of supramolecular double layers of molecules parallel to the ab-plane. The layer centers consist of hydrogen-bonded rings forming a 2D network and the outer surfaces of isopropyl groups, with van der Waals interactions between the layers. Each O atom acts as an acceptor in at least one hydrogen bond. A strong O–H⋯O hydrogen bond forms between the hydroxyl group of the oxolane ring and the carbonyl group of the oxopyrimidine ring. The other oxolane hydroxyl group forms bifurcated intra- and intermolecular hydrogen bonds. The hydroxylamino group forms an intramolecular O–H⋯N hydrogen bond with an N atom of the oxopyrimidine ring. The amino group forms an intermolecular N–H⋯N hydrogen bond to the same N atom of the ring. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).
Mathematical optimization models are mathematical means to find the best possible solutions to real-life optimization problems. They consist of three parts: decision variables that describe possible solutions, constraints that define conditions that these solutions need to satisfy, and an objective function that assigns a value to each solution, expressing how “good” it is.
In all the optimization problems discussed so far, we treated the quantities in the problem description as exact, but, in reality, they cannot always be trusted or assumed to be what we think. Uncertainty might negatively affect solutions to an optimization problem in the following forms:
Estimation/forecast errors (increasingly important in an ML-driven world):
– in a production planning problem, future customer demand is a forecast;
– in a vehicle routing problem, travel times along various roads are real-time updated forecasts;
– in a wind farm layout problem, power production levels are based on wind forecasts.
Measurement errors:
– a warehouse manager might have errors in the data records regarding current stock levels;
– the concentration level of a given chemical substance is different from expected.
Implementation errors:
– a given quantity of an ingredient is sent to production in a chemical company, but due to device errors, a slightly smaller amount is actually received;
– electrical power sent to an antenna is subject to the generator’s errors.
Poiseuille flow is a fundamental flow in fluid mechanics and is driven by a pressure gradient in a channel. Although the rheology of active particle suspensions has been investigated extensively, knowledge of the Poiseuille flow of such suspensions is lacking. In this study, dynamic simulations of a suspension of active particles in Poiseuille flow, situated between two parallel walls, were conducted by Stokesian dynamics assuming negligible inertia. Active particles were modelled as spherical squirmers. In the case of inert spheres in Poiseuille flow, the distribution of spheres between the walls was layered. In the case of non-bottom-heavy squirmers, on the other hand, the layers collapsed and the distribution became more uniform. This led to a much larger pressure drop for the squirmers than for the inert spheres. The effects of volume fraction, swimming mode, swimming speed and the wall separation on the pressure drop were investigated. When the squirmers were bottom heavy, they accumulated at the channel centre in downflow, whereas they accumulated near the walls in upflow, as observed in former experiments. The difference in squirmer configuration alters the hydrodynamic force on the wall and hence the pressure drop and effective viscosity. In upflow, pusher squirmers induced a considerably larger pressure drop, while neutral and puller squirmers could even generate negative pressure drops, i.e. spontaneous flow could occur. While previous studies have reported negative viscosity of pusher suspensions, this study shows that the effective viscosity of bottom-heavy puller suspensions can be negative for Poiseuille upflow, which is a new finding. The knowledge obtained is important for understanding channel flow of active suspensions.
In this chapter, compared to Chapter 8 we assume that data or expert knowledge can tell us not only something about the possible values of the problem’s parameters but also about their relative likelihood, that is, the probability distribution.