Time-varying Flow Field Research Articles

Error analysis of asymptotic solution of a heavy particle motion equation in fluid flows

For weakly inertial particles subjected to volumetric forces and Stokes drag force in fluid flows, we can solve the simplified particle motion equation using the perturbation method. This method allows us to obtain a recursive formula for the nth-order correction of the asymptotic solution of particle velocity. We verified the error of the asymptotic solution under two typical flow fields: a time-varying uniform flow field with a volumetric force field and a two-dimensional non-uniform cellular flow field. In the former, the relative error of the asymptotic solution of particle velocity and position increases with the Stokes number, and we provided a quantitative analysis of the results. In the latter, we verify and analyze the asymptotic solution from two perspectives: the behavior of a single particle and the collective behaviors of many particles. For asymptotic solutions with maximum velocity and position errors of less than 5%, we select the solution with the lowest order correction and designate it as the optimal asymptotic solution. The order of the optimal asymptotic solution increases with increasing Stokes numbers and motion durations. However, in most cases, for weakly inertial particles [St ∼ O(10−3)], and the time t* ∼ O(10), the first-order asymptotic solution can achieve accuracy, where both St and t* are defined using the flow field characteristic time, Tf = 4π s. The results validate the rationale behind utilizing first-order asymptotic solutions in the fast Eulerian method for turbulent dispersion of weakly inertial particles.

Simultaneous Reconstruction of Multiple Time-Varying Thermal Properties Based on Translucent Materials.

In the realm of high-tech materials and energy applications, accurately measuring the transient heat flow at media boundaries and the internal thermal conductivity of materials in harsh heat exchange environments poses a significant challenge when using conventional direct measurement methods. Consequently, the study of photothermal parameter reconstruction in translucent media, which relies on indirect measurement techniques, has crucial practical value. Current research on reconstructing photothermal properties within participating media typically focuses on single-objective or time-invariant properties. There is a pressing need to develop effective methods for the simultaneous reconstruction of time-varying thermal flow fields and internal thermal conductivity at the boundaries of participating media. This paper introduces a computational model based on the numerical simulation theory of internal heat transfer systems in participating media, stochastic particle swarm optimization algorithms, and Kalman filter technology. The model aims to enable the simultaneous reconstruction of various thermal parameters within the target medium. Our results demonstrate that under varying levels of measurement noise, the inversion results for different target parameters exhibit slight oscillations around the true values, leading to a reduction in reconstruction accuracy. However, overall, the model demonstrates robustness and accuracy in ideal conditions, validating its effectiveness.

Controlled transport of fluid particles by microrotors in a Stokes flow using linear transfer operators

The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow structures direct Lagrangian transport. We investigate this problem of directing the transport by manipulating the flow, specifically in the Stokes flow context, by controlling the strengths of two rotors fixed in space. We demonstrate a novel dynamical systems approach for this problem and apply this method to several scenarios of Stokes flow in unbounded and bounded domains. Furthermore, we show that the time-varying flow field produced by the optimal control can be understood in terms of dynamical structures such as coherent sets that define Lagrangian transport. We model the time evolution of the fluid particle density using finite-dimensional approximations of the Liouville operators for the microrotor flow fields. Using these operators, the particle transport problem is framed as an optimal control problem, which we solve numerically. This framework is then applied to the problem of transporting a blob of fluid particles in domains with different boundary conditions: free space, near to a plane wall, in a circular confinement, and the transport of two distributions of particles to a common target. These examples demonstrate the effectiveness of the proposed framework and also shed light on the effects of boundaries on the ability to achieve a desired fluid transport using a rotor-driven flow.

Practical finite-time coordinated path following in uncertain time-varying flow field

In this paper, the problem of practical finite-time coordinated path following control of a multi-agent system in an uncertain Euler flow field is studied. The coordinated path following control system is decoupled into a path following sub-system and a coordinated formation sub-system. The uncertain Euler flow field is estimated by constructing an extended state observer. By embedding the extended state observer into the design of the finite-time controllers for both sub-systems, practical finite-time stability of the coordinated path following control system is proved. Simulation results are provided for validating the feasibility and effectiveness of the control method.

Estimation of the point source parameters by the adjoint equation in the time-varying atmospheric environment with unknown turn-on time

Bayesian inference coupled with computational fluid dynamics (CFD) has been widely used in the source term estimation (STE). At present, most scholars have studied the pollution source released in the time-invariant flow field and the turn-on time of the source is often regarded as a known parameter which requires no estimation. Nevertheless, it is of greater practical significance to estimate the source parameters by considering the time-varying characteristics of flow field. Besides, estimating the turn-on time is very important as it provides the critical information for post-disaster rescue and accident cause analysis. In this paper, the predicted concentrations are calculated by the adjoint equation in the time-varying flow field, and the turn-on time, taken as an unknown parameter, is estimated together with the source location and the release rate. Accurate estimated results are thereby obtained. Then, how the sensors’ sampling time intervals and the measured data in different dispersion stages influence the estimated results is investigated. It is found that reducing the sampling time interval can decrease the uncertainties of the estimations. In addition, in order to estimate the turn-on time accurately, the measured information in the developing stage of dispersion is indispensable. However, only using the measured information in the stable stage of dispersion cannot predict the turn-on time. Finally, the earliest time when the source parameters can be estimated with accuracy is also explored. The results show that the method of the STE proposed can obtain accurate source information at the early stage of dispersion.

An Active Perception Framework for Autonomous Underwater Vehicle Navigation Under Sensor Constraints

Inertial navigation for autonomous underwater vehicles (AUVs) is challenging because of the drift error caused by the noise and measurement errors of inertial sensors, typically packaged as an inertial measurement unit (IMU), integrated over time. To mitigate the drift error, recent AUV state estimation approaches incorporate external references or environmental information obtained from exteroceptive sensors, with increased costs and limited operational domains. For improved navigation under sensor constraints, this article proposes an active perception framework that exploits vehicle motion to estimate the flow state together with the vehicle state using IMU and depth sensors only. The proposed framework uses the estimated flow state as external information to improve vehicle state estimation. We construct a linear time-varying system for the flow state, separated from a nonlinear system for the vehicle state. This formulation allows us to analyze uniform complete observability for the flow state, which is found to depend on vehicle motion. Then, along with vehicle and flow state estimators, we design a vehicle controller to enable vehicle motion to maximize an information metric pertaining to estimation performance based on either observability or constructability Gramian for the flow state. The proposed framework is validated through simulations for a case study with a vehicle descending through the water column in a time-varying flow field. The effectiveness of the framework is demonstrated by comparing results obtained from its four implementations with those from baseline approaches without active perception.

Numerical study on free-spinning performance of oscillating water column Wells turbine in reciprocating airflows

The axial-flow Wells turbine is one of the most widely used air turbines in oscillating water column wave energy converters. By Wells turbine, we mean a reaction air turbine developed by A. A. Wells of Queen's University Belfast in the late 1970s. A comprehensive understanding of its free-spinning performance is crucial for determining control strategies for output power enhancement in practical engineering applications. In the present study, a three-dimensional (3D) transient model was established on an ANSYS-Fluent® platform to simulate the time-varying flow field and motion state of the rotor during the free-spinning process. After the model was validated with our experimental data, it was used to investigate the operation patterns in airflows with various profiles. The magnitude and phase features of the pressure difference and turbine torque were examined to identify the mechanism for overcoming the gradually ascending stage and maintaining dynamic equilibrium in the stable state. Additionally, the 3D flow-field details for several instants were demonstrated, including the severe vortex from the suction side in the post-stall region, strong tip leakage vortex downstream of the rotor, downstream helical strip vortex, and cyclic-asymmetric surface pressure distributions over the turbine. Furthermore, the effects of the cyclic volume flux on the free-spinning performance were investigated.

Ray tracing and finite element modeling of sound propagation in a compartment fire

A compartment fire (a fire in a room or building) creates temperature gradients and inhomogeneous time-varying temperature, density, and flow fields. This work compared experimental measurements of the room acoustic impulse/frequency response in a room with a fire to numerically modeled responses. The fire is modeled using a Fire Dynamics Simulator (FDS). Acoustic modeling was performed using the temperature field computed by FDS. Room acoustics were modeled using two-dimensional ray and finite element modeling. A three-dimensional model was used to simulate an open flame. COMSOLTM Multiphysics was used for finite element acoustic modeling and BELLHOPTM for ray trace acoustics modeling. The results show that the fire causes wave-fronts to arrive earlier (due to the higher sound speed) and with more variation in the delay times (due to the sound speed perturbations). The resonance frequencies of low-frequency modes were shifted upwards. Model results are compared with data and show good agreement in observed trends.

Fine scale reconstruction (VIC#) by implementing additional constraints and coarse-grid approximation into VIC+\u2009

This study proposes a method that complements Vortex-In-Cell plus (VIC+) (Schneiders and Scarano, Exp Fluids 57:139, 2016), a data assimilation technique that reconstructs a dense flow field from sparse particle tracks. Here, the focus is on the treatment of boundary conditions. In the VIC+ method, the choice of boundary conditions significantly affects a large part of the inner domain through their role as Dirichlet boundary conditions of the Poisson equations. By nature, there are particle tracks on one side of the boundaries, and often, due to experimental limitations, the track density is low, just close to the boundaries. This lack of data near the boundaries leads to a poor iterative update of the boundary condition for VIC+. Overall, the VIC+ method tends to be sensitive about the specific choice of the initial conditions, including the inner domain and the boundaries. Without prior flow information, a large padded volume has been proposed to achieve stable and reliable convergence, at the cost of a large number of additional unknowns that need to be optimized. The present method pursues the following concepts to resolve the above issues: use of the smallest possible padding size, reconstruction starting with “all zero” initial conditions, and progressive correction of the boundary conditions by considering the continuity law and the Navier–Stokes equation. These physical laws are incorporated as additional terms in the cost function, which so far only contained the disparity between PTV measurements and the VIC+ reconstruction. Here, the Navier–Stokes equation allows an instantaneous pressure field to be optimized simultaneously with the velocity and acceleration fields. Moreover, the scale parameters in VIC+ are redefined to be directly computed from PTV measurement instead of using the initial condition, and new scaling factors for the additional cost function terms are introduced. A coarse-grid approximation is employed in order to both improve reconstruction stability and save computation time. It provides a subsequent finer-grid with its low-resolution result as an initial condition while the interrogation volume slightly shrinks. A numerical assessment is conducted using synthetic PTV data generated from the direct numerical simulation data of forced isotropic turbulence from the Johns Hopkins Turbulence Database. Improved reconstructions, especially near the volume boundary, are achieved while the virtues of VIC+ are preserved. As an experimental assessment, the existing data from a time-resolved water jet is processed. Two reconstruction domains with different sizes are considered to compare the boundary of the smaller domain with the inside of the larger one. Visible enhancements near the boundary of the smaller domain are observed for this new approach in time-varying flow fields despite the limited input from PTV data.Graphical abstract

Head-related transfer function measurements in a compartment fire.

The Personal Alert Safety System (PASS) is an alarm signal device carried by firefighters to help rescuers locate and extricate downed firefighters. A fire creates temperature gradients and inhomogeneous time-varying temperature, density, and flow fields that modify the acoustic properties of a room. To understand the effect of the fire on an alarm signal, experimental measurements of head-related transfer functions (HRTF) in a room with fire are presented in time and frequency domains. The results show that low-frequency (<1000 Hz) modes in the HRTF increase in frequency and higher-frequency modal structure weakens and becomes unstable in time. In the time domain, the time difference of arrival between the ears changes and becomes unstable over time. Both of these effects could impact alarm signal detection and localization. The receive level of narrowband tones is presented that shows that the fire makes the receive level of a source vary by > 10 dB. All of these effects could impact the detection and localization of the PASS alarm and have life safety consequences.

Dynamic Modeling and Simulation of Quick-Setting Slurry with Spatiotemporal Rheological Properties

A major concern in underground infrastructures is how to sufficiently seal the area from water ingress. To achieve this, grout needs to be spread adequately in the surrounding fractures. Cement-based composite grouting is probably the best method for this purpose because of its lower costs and reduced environmental impacts. Chemical reaction accompanied by the flow is a prominent feature of cement-based composites. Rheological properties, especially yield stress and viscosity, are non-uniformly distributed in time and space. In this paper, the rheological properties of quick-setting slurry of cement-based composites were measured over time, and the rheology constitutive equation including time was established based on non-Newtonian fluids. Considering the rheological properties, the Lagrangian method was introduced to track their space–time distribution, and then a dynamic model of quick-setting slurry was established based on continuity equation and momentum equation. The relationship between time-varying rheological characteristics and flow field characteristics was obtained through a numerical simulation of equal pressure injection and equal flux injection. The simulation results were compared with the experimental results in the references, thereby verifying the reliability and accuracy of the model. Results show that the local erosion state and local sealing effect of grouting directly depend on the yield stress of different positions in the flow field. The yield stress of quick-setting slurry increases rapidly with time, which is more likely to affect the flow field, and the viscosity of the slurry has a small effect on the flow field.

Large Two-Stroke Marine Diesel Engine Operation with a High-Pressure SCR System in Heavy Weather Conditions

Abstract The transient performance of a direct-drive large two-stroke marine diesel engine, installed in a vessel operating in a seaway with heavy weather, is investigated via simulation. The main engine of the ship is equipped with a selective catalytic reduction (SCR) aftertreatment system for compliance with the latest International Maritime Organization (IMO) rules for NOx reduction, IMO Tier III. Because of limitations of exhaust gas temperature at the inlet of SCR systems and the low temperature exhaust gases produced by marine diesel engines, in marine applications, the SCR system is installed on the high-pressure side of the turbine. When a ship sails in heavy weather, it experiences a resistance increase, wave-induced motions, and a time-varying flow field in the propeller, induced by ship motions. This results in a fluctuation of the propeller torque demand and, thus, a fluctuation in engine power and exhaust gas temperature, which can affect engine and SCR performance. To investigate this phenomenon and take into account the engine–propeller interaction, the entire propulsion plant was modeled, namely, the slow-speed diesel propulsion engine, the high-pressure SCR system, the directly driven propeller, and the ship’s hull. To simulate the transient propeller torque demand, a propeller model was used, and torque variations due to ship motions were taken into account. Ship motions in waves and wave-added resistance were calculated for regular and irregular waves using a 3D panel code. The coupled model was validated against available measured data from a shipboard propulsion system in good weather conditions. The model was then used to simulate the behavior of a Tier III marine propulsion plant during acceleration from low to medium load, in the presence of regular and irregular waves. The effect of the time-varying propeller demand on the engine and the SCR system was investigated. Introduction The effect of waves on a marine propulsion system is a complex phenomenon involving interactions between different subsystems of the propulsion plant, i.e., the prime mover, the propeller, and the ship’s hull. Ships sailing in heavy weather conditions experience a resistance increase, wave-induced motions, and a time-varying flow field in the propeller. This leads to a fluctuation of the propeller torque demand which results in a fluctuation in engine-produced power and exhaust gas temperature.

Unsteady flow structures behind a shark denticle replica on the wall: Time-resolved particle image velocimetry measurements

Experiments were performed to determine the unsteady flow structures of a shark denticle replica with three longitudinal ridges of different elevations and sharp trailing edges. Time-resolved particle image velocimetry measurements were conducted to capture the time-varying flow fields behind a shark denticle replica and contoured denticle, using the latter as a benchmark configuration for comparison. The flow fields in the streamwise and spanwise planes were obtained experimentally to determine the highly three-dimensional flow behavior. The flow dynamics of the unsteady superimposed flow structures behind the denticle replica are illustrated in terms of the time-averaged flow fields, statistical flow quantities, dominant vortex structures, and their phase-dependent evolution processes. The findings demonstrate that the denticle replica reduces the size and stability of the recirculation zone, suppressing flow separation. The velocity fluctuations and Reynolds shear stresses of the denticle replica are higher than those of the contoured denticle. Proper orthogonal decomposition analysis on the fluctuating velocity fields reveals alternating clockwise and counterclockwise vortices that convect along the streamwise direction, which correspond to decomposed flow structures, such as counter-rotating vortex pairs in the spanwise plane. These aspects are considered to be signatures of a hairpin-shaped vortex based on the phase-averaging analysis of the unsteady three-dimensional behavior. A hairpin-shaped vortex makes a concerted contribution to fluid mixing between the central wake region and surrounding area. As the fluid flows downstream, fast detachment of the hairpin-shaped vortex is recognized away from the wall to the main stream, which in turn attenuates the flow structure signatures in the spanwise plane. A low-frequency swinging motion of the fluid is also identified in the central wake region, which enhances fluid mixing on the two sides of the wake.

Magnetic separation of rare-earth ions: Transport processes and pattern formation

The effective body force associated with the application of a magnetic field to a solution containing rare earth ions produces convection and a time varying flow field that enables separation of the ions from solution.

Formation keeping method of weakly driven multi robot in time-varying flow field

In order to solve the problem that group formation control and optimal path cannot be considered simultaneously for weakly driven multi robot under the influence of environmental flow field, a method combining time-optimal path planning and leader-follower formation control is proposed in this paper. The time-optimal path of the leader is obtained by level set method, and the formation keeping is based on this path. According to the position of the leader and the reachable set of the follower at a certain time, the position of the follower is determined by solving the formation optimization function, and the complete path is completed by solving the formation optimization problem iteratively. While the formation optimization function maintains the group formation, the reachable set generated by the level set method ensures the feasibility of the path obtained in the time-varying strong flow.

Inclined impact of drops

Here we extend the results in Gordillo et al. (J. Fluid Mech., vol. 866, 2019, pp. 298–315), where the spreading of drops impacting perpendicularly a solid wall was analysed, to predict the time-varying flow field and the thickness of the liquid film created when a spherical drop of a low viscosity fluid, like water or ethanol, spreads over a smooth dry surface at arbitrary values of the angle formed between the drop impact direction and the substrate. Our theoretical results accurately predict the time evolving asymmetric shape of the border of the thin liquid film extending over the substrate during the initial instants of the drop spreading process. In addition, the particularization of the ordinary differential equations governing the unsteady flow when the rim velocity vanishes provides an algebraic equation for the asymmetric final shapes of the liquid stains remaining after the impact, valid for low values of the inclination angle. For larger values of the inclination angle, the final shape of the drop can be approximated by an ellipse whose major and minor semiaxes can also be calculated by making use of the present theory. The predicted final shapes agree with the observed remaining stains, excluding the fact that a liquid rivulet develops from the bottom part of the drop. The limitations of the present theory to describe the emergence of the rivulet are also discussed.

Experience in using a synthetic turbulence generator for eddy-resolving simulation of the free convection boundary layer on a vertical plate

The paper presents results of eddy-resolving numerical simulation of the turbulent free convection boundary layer that develops along a vertical isothermally heated plate. The problem of definition of boundary conditions at the computational domain inlet, where a time-varying flow field has to be specified, is considered. Mean characteristics of inflow are defined from results of RANS simulation of a 2D boundary layer, and a synthetic turbulence generator is used to introduce unsteady fluctuations at the inlet. Calculations are performed with an in-house unstructured finite-volume code; results of comparison with known experimental data are presented. The influence of the choice of the turbulence model used for RANS-based calculations of the mean inlet flow profiles is considered.

Observation of lock-in for viscoelastic fluid–structure interactions

Under the right conditions, viscoelastic fluids can exhibit elastic flow instabilities in the absence of inertia. If the fluid is in contact with a flexible or flexibly-mounted structure, these elastic flow instabilities lead to time-dependent forces on the structure, which can cause the structure to oscillate. This constitutes a new class of Viscoelastic Fluid–Structure Interactions (VFSI). Up until now, the VFSI reported in the literature demonstrated a one-way coupling between the fluid and the structure where little feedback from the structure to the flow was observed. Here, we report for the very first time, the presence of a lock-in behavior in VFSI. We have designed and conducted a set of experiments in which the frequency of the elastic flow instabilities and the natural frequency of the flexible structure become equal as the flow velocity is increased, and therefore lock-in is observed. We present amplitude and frequency responses of two sets of flexibly-mounted cylinders over a range of Weissenberg numbers and reduced velocities to show the lock-in range. The time-varying flow fields inside and outside the lock-in range were studied through streak-line imaging and particle image velocimetry. The viscoelastic lock-in range was observed for a Weissenberg number range of 5≤Wi≤15 for one of the cylinders tested and for a range of 20≤Wi≤30 for the other. For both cylinders, the lock-in started at a reduced velocity of Vr≈1.5. In Cylinder 1, the lock-in ended at Vr≈4, while for Cylinder 2 the end of the lock-in was not observed, because the data points did not cover a wide enough range. Similar to the lock-in observed in the typical VIV response in a Newtonian fluid, the frequency of the elastic flow instability was found to increase with increasing flow velocity before plateauing at the natural frequency of the cylinder in the lock-in range. Unlike the VIV response of a Newtonian fluid, where the lock-in range corresponds to the maximum observed amplitude of oscillations, in VFSI the amplitude of oscillations reached a plateau while in lock-in, but increased with Weissenberg number and reduced velocity before and after the lock-in range.

Energetics of Eddy–Mean Flow Interactions along the Western Boundary Currents in the North Pacific

AbstractThe energetics of eddy–mean flow interactions along two western boundary currents of the North Pacific, the Kuroshio and Ryukyu Currents, are systematically investigated using 22 years of numerical data from the Ocean General Circulation Model for the Earth Simulator (OFES). For the time-mean and time-varying flow fields, all the energy components and conversions exhibit inhomogeneous spatial distributions. In the two currents, complex cross-stream and along-stream variations are seen in the eddy–mean flow energy conversions. East of Taiwan, the kinetic energy is mainly transferred from the mean flow to the eddy field through barotropic instability, whereas the baroclinic energy conversions form a meridional dipole structure caused by the topographic constraint. In the northern area, particularly, the eddy field drains 2.25 × 108 W of kinetic energy and releases 2.82 × 108 W of available potential energy when interacting with the mean flow, indicating that mesoscale eddies impinging on the Kuroshio decay with baroclinic inverse energy cascades. In the Ryukyu Current, inverse energy conversions from the eddy field to the mean flow also dominate the power transfer in the subsurface layer. The eddy field transfers 0.16 × 108 W of kinetic energy and 1.89 × 108 W of available potential energy to the mean flow, suggesting that meososcale eddies play an important role in maintaining the velocity and hydrographic structure of the current. In other areas, both barotropic and baroclinic instabilities contribute to the generation of eddy kinetic energy with the latter one providing more than 3 times as much power as the former one.

Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field

In this paper, we address the problem of guiding an aerial or aquatic vehicle to a fixed target point in a partially uncertain flow-field. We assume that the motion of the vehicle is described by a point-mass linear kinematic model. In addition, the velocity of the flow-field, which is taken to be time varying, can be decomposed into two components: one which is known a priori and another one which is uncertain and only a bound on its magnitude is known. We show that the guidance problem can be reformulated as an equivalent pursuit evasion game with time-varying affine dynamics. To solve the latter game, we propose an extension of a specialized solution approach, which transforms the pursuit–evasion game (whose terminal time is free) via a special state transformation into a family of games with fixed terminal time. In addition, we provide a simple method to visualize the level sets of the value function of the game, along with the corresponding reachable sets. Furthermore, we compare our conservative game-theoretic solution with a pure optimal control solution, for the special case in which the flow-field is perfectly known a priori.