Three-dimensional Disturbances Research Articles

Unravelling the existence of asymmetric bubbles in viscoelastic fluids

We study the motion and deformation of a single bubble rising inside a cylindrical container filled with a viscoelastic material. We solve numerically the mass and momentum balances along with the constitutive equation for the viscoelastic stresses, without assuming axial symmetry to allow the growth of three-dimensional disturbances. Hence, we may predict the emergence of the notorious knife-edge shape of the bubble, which is a result of a purely elastic instability triggered in the locality of the trailing edge. Our results compare well with existing experiments. We visualize, for the first time to the best of our knowledge, the flow kinematics and dynamics that arise downstream of the bubble. We propose two quantities, one kinematical and one geometrical, for the determination of the onset of the instability. We demonstrate that extension-rate thinning in the constitutive law is necessary for the emergence of the instability. Moreover, our results indicate that increasing (a) the deformability of the bubble and (b) the initial extension rate hardening of the viscoelastic material, prior to thinning, triggers the instability earlier. These novel findings help us formulate and propose a mechanism that controls the onset of the instability and explain why the knife-edge shape is not encountered as frequently.

The Performance Analysis of Grouting Repair Effect on the Accuracy of Disturbance Stress Test in Damaged Surrounding Rock Mass.

Disturbance stress assessment is crucial for ensuring the safety of deep engineering projects. Currently, the primary technique for continuously monitoring three-dimensional disturbance stress is the stress relief method, but its accuracy can be compromised by rock damage that occurs after excavation. To mitigate this issue, grouting is employed to repair damaged rock masses and enhance their mechanical properties. However, the impact of grouting techniques on improving the accuracy of disturbance stress testing is challenging to evaluate through laboratory and in situ experiments. To address this problem, numerical simulation technology is employed to investigate disturbance stress testing after the repair of damaged surrounding rock through grouting. The simulation results indicate that grouting repair significantly enhances the accuracy of stress testing. As the depth of damaged rock mass repair increases, the error in stress testing decreases. Achieving complete repair of the initial damage zone during grouting is essential to eliminate errors in stress testing. Expanding on the positive effects of grouting repair on stress testing, a segmented testing method for disturbance stress is proposed. The method involves separately testing the initial stress and stress changes, thereby reducing the stress level within the rock, minimizing rock failure, and enhancing the accuracy of disturbance stress testing. This study provides valuable reference methods, and the outcomes of this research will serve as a foundation for enhancing the accuracy of disturbance stress testing in deep hard rock engineering.

Theoretical study of the influence of gas phase turbulent disturbances on the kinetics of ultrasonic coagulation of PM2.5

A numerical model of ultrasonic coagulation of PM2.5 aerosol particles in three-dimensional vortex and turbulent acoustic flows is proposed in the article. The model is intended to identify the possibility of increasing the efficiency of the process. A numerical analysis of the model using the example of PM2.5 aerosol made it possible to establish that the presence of three-dimensional turbulent disturbances leads to the fact that the coagulation efficiency of PM2.5 reaches almost 100% at a sound pressure level of no more than 165 dB.

Spatiotemporal Evolution of Wind Turbine Wake Characteristics at Different Inflow Velocities

In this paper, the spatiotemporal evolution of wind turbine (WT) wake characteristics is studied based on lattice Boltzmann method-large eddy simulations (LBM-LES) and grid adaptive encryption at different incoming flow velocities. It is clearly captured that secondary flow occurs in the vortex ring under shear force in the incoming flow direction, the S-wave and the Kelvin–Helmholtz instability occur in the major vortex ring mainly due to the unstable vortex ring interface with small disturbance of shear velocity along the direction of flow velocity. The S-wave and Kelvin–Helmholtz instability are increasingly enhanced in the main vortex ring, and three-dimensional disturbances are inevitable along the mainstream direction when it evolves along the flow direction. With increasing incoming flow, the S-wave and Kelvin–Helmholtz instability are gradually enhanced due to the increasing shear force in the flow direction. This is related to the nonlinear growth mechanism of the disturbance. The analysis of the velocity signal, as well as the pressure signal with a fast Fourier transform, indicates that the interaction between the vortices effectively accelerates the turbulence generation. In the near-field region of the wake, the dissipation mainly occurs at the vortex at the blade tip, and the velocity distribution appears asymmetric around the turbine centerline under shear and the mixing of fluids with different velocities in the wake zone also leads to asymmetric distributions.

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

Intermittent disturbance mechanical behavior and fractional deterioration mechanical model of rock under complex true triaxial stress paths

Mechanical excavation, blasting, adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass, leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters. Therefore, a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed. True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro. The effects of intermediate principal stress and amplitude on the strength characteristics, deformation characteristics, failure characteristics, and precursors of monzogabbro are analyzed, intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism. Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance. Based on the experimental result, the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed. A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established, and the model predicted results align well with the experimental results. The sensitivity of stress states and model parameters is further explored, and the intermittent disturbance behaviors at different f are predicted. This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.

Three-dimensional trajectory tracking guidance against near-space maneuvering targets with multiple constraints under wind field

This paper presents a three-dimensional disturbance observer-based adaptive tracking guidance scheme for the trajectory tracking problem of a missile intercepting a hypersonic vehicle with the wind field, autopilot lag dynamics, and input saturation. Unlike most of the existing missile trajectory tracking guidance systems without velocity controllability and external wind field model, the wind field model is added to the dynamic model, and the velocity control channel is introduced into the three-dimensional trajectory tracking guidance problem to prevent impractical scenarios and increase tracking precision. The proposed tracking guidance methodology incorporates the sliding mode and adaptive control techniques, in which the sliding mode motion is finite time stable independently of the tracking guidance system's initial conditions. Also, the super twisting switch control law is added to cope with the chattering problem. In this context, external uncertainty disturbances and unmeasured states are lumped into lump disturbance and estimated using the backpropagation neural network extended state observer. To this end, numerical simulations demonstrate the tracking to reach zero between 3 s and 5 s against various uncertainties in engineering practical, and position tracking errors are within 0.15 m, superior to the existing tracking guidance methods.

Damping of three-dimensional waves on coating films dragged by moving substrates

Paints and coatings often feature interfacial defects due to disturbances during the deposition process, which, if they persist until solidification, worsens the product quality. In this article, we investigate the stability of a thin liquid film dragged by a vertical substrate moving against gravity, a fundamental flow configuration in various coating processes. The receptivity of the liquid film to three-dimensional disturbances is analyzed with Direct Numerical Simulations (DNS) and an in-house Integral Boundary Layer (IBL) film model. The latter was used for linear stability analysis and nonlinear wave propagation analysis. The numerical implementation of the IBL film model combines a finite volume formulation with a pseudo-spectral approach for the capillary terms that allows one to investigate non-periodic surface tension-dominated flows. The numerical model was successfully validated with DNS computations. The combination of these numerical tools allows one to describe the mechanisms of capillary and nonlinear damping and identify the instability threshold of the coating processes. The results show that transverse modulations can be beneficial for damping two-dimensional waves within the range of operational conditions considered in this study, which are relevant to air-knife and slot-die coating.

Research on a Three-Dimensional Fuzzy Active Disturbance Rejection Controller for the Mechanical Arm of an Iron Roughneck

In the position control of the mechanical arm of an iron roughneck (MAIR), a controller with high responsiveness, high accuracy, and high anti-interference capability is necessary. An MAIR consists of two proportional-valve-controlled single-extension (PVCSE) hydraulic cylinders, and a traditional proportional–integral–derivative (PID) controller cannot easily achieve the accuracy and robustness requirements of the hydraulic cylinders. In this paper, a three-dimensional fuzzy active disturbance rejection controller (TF-ADRC) is proposed for an MAIR, which adds a three-dimensional fuzzy module to a classical active disturbance rejection controller (ADRC) to adjust the controller output according to the tracking of differential deviation, deviation change rate, and deviation change acceleration rate. Firstly, the trajectory planning of the MAIR was carried out using the quintic polynomial interpolation method to improve the smoothness of the target trajectory. Then, the reliability of the established model was verified by experiments. Finally, the comprehensive performance of a PID controller, fuzzy PID controller, ADRC, and TF-ADRC were compared based on the AMESim-Simulink model. The system with the TF-ADRC exhibits higher position control accuracy and better anti-interference capability than the system with a PID or Fuzzy PID controller, and accuracy is higher compared with the common ADRC.

An optimized stability framework for three-dimensional Hartman flow via Chebyshev collocation simulations

Hydrodynamics instability is studied for an electrical conducting fluid against small disturbance between the channels by using normal magnetized force. Chebyshev collocation technique is used to determine the stability of three-dimensional Hartmann flow problem. The distinctive case of the perturbations is calculated. It is also considered that perturbations intensity be determined by just on quantified by different parameters. We have considered one of the flow stabilities conditions to analyze our problem. QZ (Qualitat and Zuverlassigkeit) technique is applied to investigate the problem to draw stability curves. αc,βc are critical wave numbers in streamwise and span-wise respectively and for a big range of Hartmann value (Ha), we obtained critical Reynolds number (Rec). It is found that Couette flow is destabilized for a specific value of Magnetize force while with greater or lesser magnitude than the particular one will stabilize the flow. Disturbances with particular oblique angle θ will grow while the others will decay for the three-dimensional disturbance. We observed from over results that for Ha(>2.0) Rec, increases steadily and when Ha more than 3.886, Rec decreases fast to the minimum. It is also established that for drop down from Ha = 3.886 and Rec becomes very large. For distinct Hartmann values, there exist two Rec numbers due to closed contour. The outcomes of current study are utilized in drug-delivery systems and photodynamic therapy.

Superposition of AC-DBD plasma actuator outputs for three-dimensional disturbance production in shear flows

This investigation explores the utility of Alternating Current, Dielectric Barrier Discharge (AC-DBD) plasma actuators for producing three-dimensional disturbances of a desired spanwise wavelength via superposition. The technique utilizes two pairs of exposed and covered electrodes on a single dielectric layer arranged in streamwise succession. Two-dimensional forcing is achieved through operation of the upstream, spanwise uniform electrode pair, while three-dimensional forcing at a prescribed spanwise wavelength is attained by operating both electrode pairs simultaneously, with the downstream actuator spanwise modulating the upstream, two-dimensional output. The ability to produce disturbances of different spanwise wavelengths but with equal streamwise wavelength, frequency and total momentum is established through a combined characterization effort that considers quiescent and in-flow conditions. A demonstration of the technique in an exemplary wall-bounded shear flow, a laminar separation bubble, is provided, revealing spanwise wavelength dependent disturbance growth in the flow that could be exploited for performance gains in future flow control endeavours.Graphical abstract

On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field

The linear stability of a fully developed liquid–metal magnetohydrodynamic pipe flow subject to a transverse magnetic field is studied numerically. Because of the lack of axial symmetry in the mean velocity profile, we need to perform a BiGlobal stability analysis. For that purpose, we develop a two-dimensional complex eigenvalue solver relying on a Chebyshev–Fourier collocation method in physical space. By performing an extensive parametric study, we show that in contrast to the Hagen–Poiseuille flow known to be linearly stable for all Reynolds numbers, the magnetohydrodynamic pipe flow with transverse magnetic field is unstable to three-dimensional disturbances at sufficiently high values of the Hartmann number and wall conductance ratio. The instability observed in this regime is attributed to the presence of velocity overspeed in the so-called Roberts layers and the corresponding inflection points in the mean velocity profile. The nature and characteristics of the most unstable modes are investigated, and we show that they vary significantly depending on the wall conductance ratio. A major result of this paper is that the global critical Reynolds number for the magnetohydrodynamic pipe flow with transverse magnetic field is Re = 45 230, and it occurs for a perfectly conducting pipe wall and the Hartmann number Ha = 19.7.

High-fidelity computational study of roughness effects on high pressure turbine performance and heat transfer

While blade surface roughness arising from in-service wear and/or the manufacturing process greatly affects aero-thermal performance, the detailed underlying physical mechanisms remain far from fully understood. In this study, a series of highly-resolved Large-Eddy Simulations of compressible flow past a high-pressure turbine vane with systematically varied levels of blade surface roughness have been performed, along with a smooth-blade simulation at matched flow conditions for comparison. Three non-dimensional roughness amplitudes have been investigated, namely, ks/c={1.0,2.0,3.0}×10−3, where ks is an equivalent value of Nikuradse’s sandgrain roughness for an irregular, multi-scale near-Gaussian height distribution, and c is the axial blade chord. All simulations have been performed at an axial chord Reynolds number of 0.59 ×106 and a Mach number of 0.9, based on the exit conditions of the reference smooth vane, and with synthetic inflow turbulence to mimic unsteady, three-dimensional disturbances from an upstream combustion chamber. The present investigation highlights the profound impact that blade surface roughness can have upon boundary-layer transition mechanisms, wall shear stress and blade surface heat flux, as well as the levels of turbulence kinetic energy and total pressure losses incurred in the wake. While blade surface roughness leads to major aero-thermal differences between the suction-side of the smooth and rough vanes, the pressure-side surface remains relatively unaffected — even for the largest roughness amplitude investigated here.

On the origin of spanwise vortex deformations during the secondary instability stage in compressible mixing layers

The three-dimensionality of turbulence initiates with spanwise vortex deformations associated with the amplification of three-dimensional disturbance modes. However, the origin of spanwise vortex deformations is still not well understood. In this paper, compressible mixing layers are performed via direct numerical simulation (DNS). Two typical types of secondary instabilities producing spanwise vortex deformations are of consideration: fundamental instability and subharmonic instability. Based on the fast Fourier transform and DNS data, a low-rank velocity model v0 is obtained to demonstrate that spanwise vortex deformations are originated from a linear superposition of fundamental norm mode, a pair of fundamental or subharmonic oblique modes, and the mean mode. Through observing flow structures of the above norm and oblique modes, a striking feature is found that the velocity model v0 containing deformed spanwise vortices can be decomposed into three new velocity models v1, v2, and v3 containing relatively simplified counterparts (spanwise or oblique vortices). Then, the instability mechanism of the latter vortices is explored by analyzing the position relationship between the function of the generalized inflection points and cores of relatively simplified vortices. We find that an inviscid inflectional instability mechanism is responsible for the formation of spanwise and oblique vortices. Based on the above findings, a view is first proposed that spanwise vortex deformations with aligned and staggered patterns are a joint result of the parametric resonant mechanism and the inviscid inflectional instability mechanism.

Three-dimensional vortex dipole solitons in self-gravitating systems.

We derive the nonlinear equationsgoverning the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to the rotation frequency. Analytical solutions of these equations are found in the form of the 3D vortex dipole solitons. The method for obtaining these solutions is based on the well-known Larichev-Reznik procedure for finding two-dimensional nonlinear dipole vortex solutions in the physics of atmospheres of rotating planets. In addition to the basic 3D x-antisymmetric part (carrier), the solution may also contain radially symmetric (monopole) or/and antisymmetric along the rotation axis (z-axis) parts with arbitrary amplitudes, but these superimposed parts cannot exist without the basic part. The 3D vortex soliton without the superimposed parts is extremely stable. It moves without distortion and retains its shape even in the presence of an initial noise disturbance. The solitons with parts that are radially symmetric or/and z antisymmetric turn out to be unstable, although, at sufficiently small amplitudes of these superimposed parts, the soliton retains its shape for a very long time.

Displacement response characteristics of different sand tunnel excavation faces under true triaxial loading

During the construction of subway tunnels, the geotechnical body is affected by excavation to produce three-dimensional spatial deformation. The deformation of geotechnical bodies is an important safety hazard for project advancement, so it is important to understand the excavation disturbance range and deformation mechanism. The current related research is mainly about the theory of land subsidence and the two-dimensional plane displacement of the stratum, and there are few studies on the specific three-dimensional disturbance mode and its mechanism. In order to better understand the three-dimensional displacement characteristics of the tunnel excavation soil, a tunnel excavation model test was established based on a true triaxial stress loading system combined with three-dimensional scanning technology for a superimposed sandy soil. Based on the established model, the vector displacement response range and three-dimensional deformation characteristics of the excavation face were studied in the main displacement affected area around the excavation face. Meanwhile, the deformation characteristics, such as vertical settlement and horizontal displacement of the stratum in the main influence area were analyzed. The results show that the main influence area of tunnel excavation is elliptical and distributed within a range of twice the diameter of the tunnel axis. The main influence range is bell-shaped in the vertical direction and inverted wedge-shaped in the horizontal direction. The three-dimensional space presents a “W” deformation distribution. The three-dimensional deformation theoretical model of the excavation face established in this paper can provide some references for the excavation engineering of superimposed sand-soil tunnels.

Effects of anisotropy on the stability of Giesekus fluid flow

In the present work, the stability of a viscoelastic fluid flow is studied by linear stability theory, and some results are verified by direct numerical simulation. The investigation considers the fluid flow between two parallel plates, modeled by the Giesekus constitutive equation. The results show the influence of the anisotropic tensorial correction parameter αG on this model, showing a stabilizing influence for two-dimensional disturbances for small values of αG. However, as αG increases, a reduction in the critical Reynolds number values is observed, possibly hastening the transition to turbulence. Low values for αG for three-dimensional disturbances cause more significant variations for the critical Reynolds number. This variation decreases as the value of this parameter increases. The results also show that low values of αG increase the instability of three-dimensional disturbances and confirm that Squire's theorem is not valid for this model. As for the two-dimensional disturbances, the anisotropic term on the Giesekus model lowers the critical Reynolds number for higher quantities of polymer viscosity in the mixture and high values for the Weissenberg number.

Development of Disturbances in a Circular Submerged Jet with Two Instability Modes

The stability and nonlinear interaction between the disturbances in a round jet are investigated numerically at Re = 2850. The conditions of the laboratory experiment performed earlier in the Institute of Mechanics of Moscow State University are reproduced. The characteristic feature of the jet considered is the presence of three points of inflection in the inflow velocity profile. This fact determines essentially the properties of flow. Linear stability is investigated using two approaches: quasi-parallel and spatial. Good quantitative agreement between the results of two approaches and adequate agreement with the results of inviscid theory are obtained. Numerical calculations are carried out with the aim to explain and interpret the results of the laboratory experiment in which change in the length of the laminar-turbulent transition zone in the jet under the action of time-periodic axisymmetric perturbations is revealed. It is shown that axisymmetric disturbances of even considerable initial amplitude do not lead to laminar-turbulent transition. The transition observed experimentally is attributable to the presence of non-controlled three-dimensional disturbances that are strengthened against the background of fairly intense artificial disturbances. The investigations carried out in the present study confirm this hypothesis. Thus, the three-dimensional disturbances serve as an initiator of transition, while the axisymmetric disturbances of a fairly high amplitude only accelerate their growth. It is shown that more intense three-dimensional disturbances are able to ensure still more rapid transition even in the absence of axisymmetric component.

On the validity of Squire’s theorem for viscoelastic fluid flows

This work presents a practical methodology to verify the validity of Squire’s theorem for viscoelastic fluid flow stability analysis. Squire’s theorem presents a relationship between two-dimensional and three-dimensional disturbances. The theorem shows that the critical Reynolds number for two-dimensional disturbances is smaller than any value for which unstable three-dimensional disturbances exist. This conclusion simplifies the stability analysis for fluid flows which satisfies this theorem by becoming sufficient for the stability analysis to look only for the two-dimensional disturbances to find the most dangerous condition. In the present investigation, the validity of Squire’s theorem is accessed for viscoelastic fluid flows considering the Upper-Convected Maxwell, Oldroyd-B, Giesekus, LPTT and FENE-type models. The mass, momentum, and viscoelastic constitutive equations are manipulated to arrive at the equivalent two-dimensional equations required for Squire’s Theorem validity. It was verified that Squire’s theorem is valid for the Upper-Convected Maxwell and the Oldroyd-B isotropic models as already known in the literature, showing that the proposed methodology is consistent with previous results. However, for the Giesekus, the LPTT and the FENE-type anisotropic models, the analysis shows that Squire’s theorem is not valid, indicating the relation between the isotropic behavior of the fluids and the validity of Squire’s theorem.

Physical origin of vortex stretching and twisting: Viscous or inertial forces

In this paper, the physical origin of vortex stretching and twisting is theoretically investigated. The effects of inertial and viscous forces are mainly considered and discussed. Two key conditions, i.e., solid walls and three-dimensional (3D) disturbances, are adopted in three typical cases. Among them, the first two cases are straight and curved vortex lines at the initial time without any kind of disturbance. The third case is a straight vortex line at the initial time with introduced 3D natural disturbances. Through experimental observations, numerical simulations, and theoretical analysis in these cases, the first two cases illustrate that the straight or curved vortex lines are still straight or curved at the next time, respectively, regardless of whether solid walls are introduced. However, the third case clearly shows that once natural disturbances are introduced, the straight vortex lines near and at solid walls at the initial time are stretched and twisted mainly by viscous forces, instead of inertial forces, typically demonstrated by the 3D wake transition of a straight circular cylinder and the transition of the laminar boundary layer at a flat plate. Accordingly, based on definitions of generation and enhancement in vortex stretching and twisting, it is confirmed that the viscous forces with two key conditions are the generation mechanism, while the inertial forces alone are the enhancement mechanism.