Viscous Boundary Research Articles

Numerical study of thermo-viscous effects in acoustic materials using linearized Navier-Stokes equations

Acoustic materials, characterized by small-scale structures, require a detailed understanding of dissipation effects within the viscous and thermal boundary layers where most of the dissipation takes place. Despite the prevalent assumption of lossless or isentropic conditions in many applications, a comprehensive study of regions where thermal and viscous losses occur is crucial, particularly in scenarios where wall-induced losses are significant. Bridging this gap, the study aims to investigate these losses in various structures to guide the development of innovative acoustic materials. To achieve this objective, the Linearized Navier-Stokes Equations (LNSE) solver from the finite element software COMSOL is employed to determine the absorption coefficients and to identify predominant regions of thermal and viscous losses. The model is validated using experimental and published data. The study effectively reveals specific regions where these losses significantly dominate, highlighting their critical influence on acoustic material performance. Although the structures are simplified to 2D models to balance physical details with computational feasibility, the ability to identify dominant loss regions marks a significant contribution to the field and paves the way to refine the design of acoustic materials.

Microstructure design of a stack for independent control of thermal and viscous phenomena

\textit{Thermal and viscous energy conversion in a thermoacoustic device occurs inside a particular porous material, named stack/regenerator. Viscous losses and thermal exchanges arise thanks to the interaction of an acoustic field and the solid skeleton of a porous material. Its microstructure strongly influences the amount of energy which can be converted or dissipated due to viscous and thermal boundary layers. Thermal and viscous losses are strictly interconnected, meaning that by altering the pore size (i.e. the hydraulic radius) of the microstructure, both thermal and viscous effects are generally affected. However, there are cases where independent control of thermal or viscous effects could be crucial such as in the thermoacoustics devices. Enhancing heat exchanges while minimizing viscous losses becomes necessary to enhance power conversion. This work paves the way to the design of a microstructure suitable for controlling viscous and thermal effects in a relatively independent way.

Influence of viscous shear boundary layers on the sound performance of acoustic metasurfaces

Acoustic metasurfaces are mostly designed in a static medium, ignoring the influence of flow characteristics. However, in actual aeroacoustic noise reduction, e.g., aircraft engine liner design, the background flow can have effects on the sound performance of acoustic metasurfaces, especially for a viscous shear flow. The effect of a viscous shear flow is often neglected in previous studies on the design and sound field prediction of acoustic metasurfaces. For considering the viscous and thermal dissipation effects, an analytical model is developed to predict the sound field of a periodic metasurface in a viscous shear boundary layer. In this model, the effective impedance based on the high-frequency limits is utilized to consider both the actual impedance of the acoustic metasurface and the effect of a finite-thickness viscous shear boundary layer. An acoustic metasurface designed in the static medium or even redesigned with only the effect of an inviscid shear flow is not suitable for wave manipulation when the Reynolds number (Re) changes significantly, since the viscosity is an important and non-negligible factor affecting the sound performance. For the cases in this work, the sound performance gradually deteriorates with the decrease in Re when Re≥5×106. When Re≤1×106, especially at Re=1×105, the existence of viscous shear flows could result in the destruction of expected anomalous reflection and significant intensity change of the reflected waves. This research provides a method for the design of acoustic metasurfaces under viscous shear flow conditions, which is significant for future aeroacoustic applications.

Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

Effects of time-dependent and radiation on a tri-hybrid nanofluid flowing on stretchable/shrinkable cylinders with irregular heat generation/absorption using Ohmic heating

This work focuses on the non-linear dynamics of unsteady tri-hybrid nanofluids inside a thermally radiative, expandable or contractible cylinder, which has been a consistent subject of interest for contemporary researchers. An advanced model is formulated to address the unsteady external flowing of a conductive 50 %:50 % by volume aqueous solution of ethylene glycol-based ternary hybrid nanofluid (THNF) over a linearly stretched cylindrical structure, considering the significant applications of an anti-freeze agent in industrial, construction, nuclear, and mechanical domains. The proposed tri-hybrid nanomaterials consist of cobalt magnetite, titania, and magnesium oxide nanoparticles. The heat transfer rate is analyzed concerning viscous dissipation, Ohmic heating, and convective boundary conditions. This research examines the effects of magnetic and induced electric fields. The non-dimensional similarity model for the controlling partial differential system is derived using appropriate transformations and solved by the homotopy analysis technique (HAM) to get series solutions. In contrast to porosity and magnetic characteristics, the flow rate increases with increasing unsteadiness and electric factors. Close to the surface, the Nusselt number rises with an increasing unsteadiness parameter, but skin frictions diminishes. THNF has been shown to significantly enhance the cooling of cylindrical conduits and mechanical antifreeze agents.

Dynamically Linearized Time-Domain Approach for Limit-Cycle Oscillation Prediction for an Elastic Panel

A nonlinear aeroelastic model for a flexible panel is extended to consider the Euler equation as the aerodynamic model. A highly efficient method is presented to compute the generalized aerodynamic forces from a CFD simulation, and the results are compared to those results previously obtained using full potential flow aerodynamics and the linear piston theory. The flutter onset condition as well as limit cycle oscillation amplitudes are computed for a range of supersonic Mach numbers. Additionally, the effects of a shock wave and a viscous boundary layer (Reynolds-averaged Navier–Stokes) are considered in the computational fluid dynamics simulation and are implemented in the aeroelastic model via the generalized aerodynamic force obtained by the new approach. Conclusions are made based on the use and application of this more complete aerodynamic theory, including cases with shock impingement and near-transonic Mach numbers.

Study on the seismic wave input method for earth-rock dam on overburden foundation with dynamic nonlinearity based on nonlinear artificial boundary

Accurately obtaining the seismic response of earth-rock dams on overburden foundations is crucial for seismic safety assessment and design, and a reasonable seismic input method is necessary. The seismic wave input method based on artificial boundaries is widely used in elastic foundations. However, the overburden with obvious dynamic nonlinearity is an insurmountable obstacle for the traditional method. In this research, relying on a specific earth-rock dam project, the essence of the seismic wave input method for nonlinear foundations is analyzed in detail from equivalent loads and viscous boundaries, respectively. The mechanism of inapplicability of the traditional seismic wave input method is illustrated, and an effective modified method is validated and presented. The research indicated that equivalent loads for the nonlinear dynamic response of the overburden foundation can be accurately acquired with the shear box model. The dynamic parameters of soil can be captured dynamically by the nonlinear viscous coupling boundary. The states of the lateral boundary of the overburden foundation are consistent with the free field precisely with the modified seismic wave input method by combining the shear box model and the nonlinear viscous coupling boundary. A large error will be caused by neglecting the dynamic nonlinear behavior of the overburden foundation, where the maximum deviation of peak acceleration may be over 55 % or more. A numerical model with a relatively small lateral range of overburden foundation will be obtained when the modified seismic wave input method is engaged. Moreover, the computational accuracy is enhanced remarkably, with a maximum deviation of no more than 5 %. This study provides effective theoretical support for seismic analysis and safety assessment of earth-rock dams on deep overburden foundations.

Pressure feedback system for flow separation mitigation in scramjet intakes

Shock Wave Boundary Layer Interactions (SWBLI) occur due to the convergence of a shock wave and a viscous boundary layer. The resulting separation bubble is a major setback for the performance of high-speed air intakes. This paper presents a numerical investigation into the potential of a Pressure Feedback Technique (PFT) to alleviate shock-induced flow separation within a Scramjet engine intake operating at Mach 4. The PFT is a novel self-sustaining flow control technique that combines simultaneous suction and injection. The two main output parameters used to support the hypothesis of the present study are the size of the separation bubble as well as the total pressure recovery at the isolator outlet. The most prominent observation of this study is that with the installation of the PF tubes, the total pressure recovery at the exit is noted to rise. The effectiveness of the pressure feedback technique in reducing the intensity of the separation bubbles is found to depend on the diameter of the PFT, pitch-to-diameter ratio, and PFT tube design.

Implementation of the non-reflection boundary for the seismic response analysis in the framework of non-local general particle dynamics

A thorough understanding of the seismic response of geotechnical structures has always been an aspiration for all engineers. Recently, the non-local general particle dynamics (NLGPD), which considers the variation of material density, has exhibited excellent promise in modelling extremely large deformation and dynamic problems. To extend the capacity of NLGPD to carry out seismic response analysis, four non-reflection boundaries are newly added in the framework of NLGPD in this paper. The viscous boundary allows wave energy to be absorbed by dashpot, in which a stress input method is proposed to input the seismic motion. The viscous-spring boundary can capture the elasticity recovery ability of the far-field medium. The free-field boundary achieves the free-field motion at lateral boundaries in the process of absorbing wave, and the corresponding relation between the points of the main model and the free-field column is determined. The static-dynamic unified boundary is introduced to model the transformation process from fixed boundary conditions in a static state to free field boundary conditions in dynamic analysis. Several representative numerical examples are solved to validate the feasibility of the proposed method. The numerical results show that the NLGPD method provides robustness and broad applicability for the seismic response analysis.

Multi-scale modeling of fog harvesting using thin-fiber grids – Towards new design rubrics

Fog collectors with fibers thinner than 1 mm harvest fog droplets more effectively at a low airflow velocity around 1 m s-1 than thicker fibers. However, existing models and design rubrics are restricted to thick fibers at higher velocity. This paper reports a multi-scale numerical model for fog harvesting at airflow velocity of 1 m s-1 using thin-fiber grids with different fiber spacing and diameter. The numerical model can simulate fog harvesting at two extreme length scales that are comparable to collector scale at the large end and fiber scale at the small end. The results confirm two new and important effects of fiber grid geometries on water collection efficiency, which are not included in existing theories and design rubrics. First, dense thin-fiber grids negatively influence the collection efficiency because of wall effect caused by viscous boundary layers. Second, the sparse thin-fiber grids can benefit from isolated clogging waterdrops and maintain relatively high efficiency when clogging blocks multiple grid openings. The two identified effects are then included to develop a new performance map for fog collectors, thereby shaping new design rubrics for fog harvesting. This work extends the existing theories of fog harvesting and sheds light on the design of novel fog collectors.

Study on the wettability of Sn/Cu system under ultrasonic vibration

In this study, the wetting behavior of Sn solder on Cu substrate under ultrasonic vibration using the sessile drop method was investigated. The distribution of the vibration field on the substrate surface was analyzed via COMSOL Multiphysics finite element analysis, while the spreading behavior and interfacial reaction products of intermetallic compounds (IMCs) induced by varying ultrasonic amplitudes were explored. ultrasonic vibration demonstrates a significant influence on both wettability and interfacial reaction products. The wetting mechanism under ultrasonic vibration is primarily attributed to physical driving forces generated by ultrasound-induced interfacial viscous boundary layers, along with chemical driving forces facilitated by ultrasonic-accelerated interfacial atomic diffusion and reactions.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

AbstractDesign of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high‐speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem. This paper presents a velocity‐based space–time finite element procedure, v‐ST/finite element method (FEM), to solve dynamic SSI problems. The main goal of this study is to present the computation details of implementing viscous boundary conditions of Lysmer–Kuhlemeyer to truncate the unbounded soil domain. Furthermore, additional time‐dependent boundary conditions, in terms of the free‐field response, are included to facilitate energy flow from the far field to the computation domain at the vertical truncated boundaries. In the FEM, seismic input motion is applied to an effective nodal force vector, which can be obtained explicitly in the numerical simulations. Finally, the response of a concrete gravity dam resting on an elastic half‐space to the horizontal component of earthquake motion is computed and successfully compared with the results of semidiscrete FEM using the Newmark‐ method.

Onset of Nonlinear Instabilities in Monotonic Viscous Boundary Layers

Onset of Nonlinear Instabilities in Monotonic Viscous Boundary Layers

Threshold of Keulegan–Carpenter instability within a 6 × 6 rod bundle

The literature is rich in fluid–structure interaction studies of a single rod in oscillating fluid (or the reciprocate), however, there is a dearth of experimental data for rod bundle oscillation, particularly if the bundle is in a confined environment. The presence of the fluid surrounding the moving solid is modeled with force coefficients such as inertial and drag. In case of small amplitudes oscillating flow, these force coefficients depend non-linearly on the Keulegan–Carpenter number KC. The dependence present different regimes, separated by threshold KC numbers. At different regimes correspond different fluid dynamics, hence different force coefficients. The aim of this paper is to experimentally investigate the fluid dynamic for a rod bundle oscillating in a stagnant fluid. The velocity fields have been measured with Particle Image Velocimetry (PIV). Both the rod bundle and the fluid have the same refractive index, which allow to measure the velocity fields within the rod bundle in an non intrusive manner. The bundle is hosted in a double tank, immersed in a refractive index matched solution and placed on an earthquake shake table. The shake table sets the bundle into motion along a single direction.Data enable the identification of a threshold effect in the fluid response to the oscillating assembly. This threshold effect is due to the formation of vortexes in the fluid. Data show a clear trend on how the development of turbulence occurs firstly inside the rod assembly and then in the bypass between the assembly and the tank wall. The experimental results indicate the presence of a viscous boundary layer developed along the rod, above the threshold KC. The results presented in this paper represent a step forward the comprehension of the damping effect induced by the fluid at different oscillating amplitudes and frequencies, due to different KC regimes.

Singular layer physics informed neural network method for plane parallel flows

We construct in this article the semi-analytic Physics Informed Neural Networks (PINNs), called singular layer PINNs (or sl-PINNs), that are suitable to predict the stiff solutions of plane-parallel flows at a small viscosity. Recalling the boundary layer analysis, we first find the corrector for the problem which describes the singular behavior of the viscous flow inside boundary layers. Then, using the components of the corrector and its curl, we build our new sl-PINN predictions for the velocity and the vorticity by either embedding the explicit expression of the corrector (or its curl) in the structure of PINNs or by training the implicit parts of the corrector (or its curl) together with the PINN predictions. Numerical experiments confirm that our new sl-PINNs produce stable and accurate predicted solutions for the plane-parallel flows at a small viscosity.

Finite-Dimensional Boundary Control of a Wave Equation With Viscous Friction and Boundary Measurements

Finite-Dimensional Boundary Control of a Wave Equation With Viscous Friction and Boundary Measurements

Onset of Plate Motion in the Presence of Chemical Heterogeneities in the Mantle and the Effect of Mantle Temperature

AbstractChemical heterogeneities of various origins have been observed in the Earth's mantle. Their assumed higher density acts on the style of mantle convection and therefore, as tectonic plates form the highly viscous upper boundary layer of mantle convection, the onset of surface motion is also affected by chemical heterogeneities. We perform 2D basally heated thermochemical mantle convection models which initially include layers of dense material at different mantle depths. In comparison to purely thermal convection models, the onset of first plate motion is delayed. This delay is even more pronounced, the deeper the location of dense material, the larger its volume and the higher its density. Additionally, we varied the starting temperature of our models. In an initially hot mantle, a strong temperature‐dependent viscosity contrast between the mantle and cold surface leads to a cold, highly viscous plate (stagnant lid). For an initially cold mantle, rising plumes first need to transport basal heat upwards to create a sufficient viscosity contrast. Consequently, the formation and subsequent breaking of the stagnant lid is delayed. Considering a hotter mantle after Earth's magma ocean phase, we find that plate motion can occur within approximately the first 0.5 Gyr of solid‐state convection if no chemical structures are present or for dense material situated at the surface. Deep chemical heterogeneities delay the onset by at least one order of magnitude. Furthermore, the early surface motion will have been more erratic than todays stable plate motion, probably with a few single subduction events.

Numerical heat and mass transfer in magnetized Williamson liquid motion over a sensor wall engulfed in a micro-cantilever system: An application to thin-film fluidic cells

Central focus of this numerical analysis is to investigate the influence of magnetic body force and thermal radiation on the time-dependent electrically conducting two-dimensional viscous incompressible boundary layer flow of non-Newtonian Williamson fluid over a microcantilever sensor surface suspended in a squeezed regime numerically. A novel heat source/sink and Soret effects are included in the respective governing equations. The constructed time-dependent nonlinear coupled partial differential equations are solved by using a bobust RK-4 technique. Increasing magnetic number increases the velocity distribution and decreases the temperature and concentration profiles in the flow regime.Enhancing Soret number increases the mass diffusion profile. Increasing magnetic number suppress the skin-friction coefficient. Heat transport rate booted with rising radiation number and Sherwood number decreased with enlarged Schmidt number in the channel regime. Finally, the numerical accuracy of the present similarity solutions and used numerical method is validated with existing results and observed a remarkable agreement.

Single Layer Silk and Cotton Woven Fabrics for Acoustic Emission and Active Sound Suppression.

Whether intentionally generating acoustic waves or attempting to mitigate unwanted noise, sound control is an area of challenge and opportunity. This study investigates traditional fabrics as emitters and suppressors of sound. When attached to a single strand of a piezoelectric fiber actuator, a silk fabric emits up to 70dB of sound. Despite the complex fabric structure, vibrometer measurements reveal behavior reminiscent of a classical thin plate. Fabric pore size relative to the viscous boundary layer thickness is found-through comparative fabric analysis-to influence acoustic-emission efficiency. Sound suppression is demonstrated using two distinct mechanisms. In the first, direct acoustic interference is shown to reduce sound by up to 37 dB. The second relies on pacifying the fabric vibrations by the piezoelectric fiber, reducing the amplitude of vibration waves by 95% and attenuating the transmitted sound by up to 75%. Interestingly, this vibration-mediated suppression in principle reduces sound in an unlimited volume. It also allows the acoustic reflectivity of the fabric to be dynamically controlled, increasing by up to 68%. The sound emission and suppression efficiency of a 130 µm silk fabric presents opportunities for sound control in a variety of applications ranging from apparel to transportation to architecture.