Side Boundary Research Articles

Particle-scale observation of seepage flow in granular soils using PIV and CFD

Seepage-induced instabilities pose a challenge in many geotechnical applications. Particle-scale mechanisms govern the initiation of instability. However, current understanding is based on a macro-scale perspective that draws on continuum mechanics. Recent developments in imaging and numerical analysis can provide the particle-scale fundamental perspective needed to develop a comprehensive insight. This contribution demonstrates the value of combining particle-scale experimental and numerical studies. The experiments consider transparent soil samples created using refractive image matching and monitored by particle image velocimetry (PIV). Three-dimensional pore topology is extracted from a series of two-dimensional images and imported into computational fluid dynamics (CFD) simulations. Permeability is estimated by three distinct approaches: using flow rate, PIV- and CFD-generated data. The flow fields obtained from PIV and CFD are in good agreement considering both flow rate contour plots and flow rate distributions; this demonstrates the successful reconstruction of three-dimensional pore structure and flow-field analysis. The comparison also reveals that the side boundary effects in CFD simulations are constrained within a limited region. The multi-plane results characterise the variance of flow velocity with the three-dimensional pore topology. Finally, the fluid–particle interactions obtained from CFD results show a larger variance in the angular particle packings.

Holographic boundary states and dimensionally reduced braneworld spacetimes

Recently it was proposed that microscopic models of braneworld cosmology could be realized in the context of anti--de Sitter/conformal field theory ($\mathrm{AdS}/\mathrm{CFT}$) correspondence using black hole microstates containing an end-of-the-world brane. Motivated by a desire to establish the microscopic existence of such microstates, which so far have been discussed primarily in bottom-up models, we have studied similar microstates in a simpler version of $\mathrm{AdS}/\mathrm{CFT}$. On one side, we define and study boundary states in the charged Sachdev-Ye-Kitaev model and show that these states typically look thermal with a certain pattern of symmetry breaking. On the other side, we study the dimensional reduction of microstates in Einstein-Maxwell theory featuring an end-of-the-world brane and show that they have an equivalent description in terms of 2D Jackiw-Teitelboim gravity coupled to an end-of-the-world particle. In particular, the same pattern of symmetry breaking is realized in both sides of the proposed duality. These results give significant evidence that such black hole microstates have a sensible microscopic realization.

Pore-Scale Dynamics of Liquid CO2–Water Displacement in 2D Axisymmetric Porous Micromodels Under Strong Drainage and Weak Imbibition Conditions: High-Speed μPIV Measurements

Resolving pore-scale transient flow dynamics is crucial to understanding the physics underlying multiphase flow in porous media and informing large-scale predictive models. Surface properties of the porous matrix play an important role in controlling such physics, yet interfacial mechanisms remain poorly understood, in part due to a lack of direct observations. This study reports on an experimental investigation of the pore-scale flow dynamics of liquid CO2 and water in two-dimensional (2D) circular porous micromodels with different surface characteristics employing high-speed microscopic particle image velocimetry (μPIV). The design of the micromodel minimized side boundary effects due to the limited size of the domain. The high-speed μPIV technique resolved the spatial and temporal dynamics of multiphase flow of CO2 and water under reservoir-relevant conditions, for both drainage and imbibition scenarios. When CO2 displaced water in a hydrophilic micromodel (i.e., drainage), unstable capillary fingering occurred and the pore flow was dominated by successive pore-scale burst events (i.e., Haines jumps). When the same experiment was repeated in a nearly neutral wetting micromodel (i.e., weak imbibition), flow instability and fluctuations were virtually eliminated, leading to a more compact displacement pattern. Energy balance analysis indicates that the conversion efficiency between surface energy and external work is less than 30%, and that kinetic energy is a disproportionately smaller contributor to the energy budget. This is true even during a Haines jump event, which induces velocities typically two orders of magnitude higher than the bulk velocity. These novel measurements further enabled direct observations of the meniscus displacement, revealing a significant alteration of the pore filling mechanisms during drainage and imbibition. While the former typically featured burst events, which often occur only at one of the several throats connecting a pore, the latter is typically dominated by a cooperative filling mechanism involving simultaneous invasion of a pore from multiple throats. This cooperative filling mechanism leads to merging of two interfaces and releases surface energy, causing instantaneous high-speed events that are similar, yet fundamentally different from, burst events. Finally, pore-scale velocity fields were statistically analyzed to provide a quantitative measure of the role of capillary effects in these pore flows.

Flow Coefficient and Reduced Frequency Effects on Wake-Boundary Layer Interaction in Highly Accelerated LPT Cascade

The paper presents a detailed analysis of particle image velocimetry (PIV) measurements performed in a turbine cascade representative of highly accelerated low-pressure turbine (LPT) blades. Two cameras have been simultaneously used to observe a great portion of the suction side boundary layer with the highest possible spatial resolution, thus allowing us to solve the interaction process between impinging upstream wakes and the blade boundary layer. Four unsteady inflow conditions, characterized by different incoming wake reduced frequencies and flow coefficients, have been examined at fixed Reynolds number. The highly resolved flow fields have been processed to explore reduced frequency and flow coefficient effects on the boundary layer unsteady transition process and, consequently, on loss production. For a deep physical insight on the mechanisms responsible for loss generation, proper orthogonal decomposition (POD) has been applied at different phases of the wake passing period. This has provided the dominant structures affecting the cascade aerodynamics during the wake period. Moreover, the examination of POD modes has allowed us to show the effects induced by the parameter variation on the turbulent kinetic energy production and thus to the unsteady loss production mechanisms.

Output tracking for a radiative density optical communication system with unknown disturbance

This paper deals with boundary tracking problem for a radiative density parabolic equation (RDE) coming from an optical communication system. First, the radiative intensity is modeled by a radiative transfer equation (RTE). The idea of this work is to use the fact that the signal sent by the laser beam is collimated in consideration of the radiative density flux. Therefore, the control problem of the RTE model is transformed into a boundary control for an RDE based on the time-dependent SPN approximation. Then, we investigate a boundary output tracking problem of one dimensional parabolic density equation where the unknown disturbance enters the system from one part of the boundary. By utilizing one side boundary measurement, we construct an extended state observer to estimate the system state and the external disturbance. An output feedback boundary control is then designed using the states of the servo system and observer. It is shown that the closed-loop system and the control are uniformly bounded with output being tracking the reference and the closed-loop is internally exponentially stable. The numerical simulations are presented to illustrate the effectiveness of the proposed output feedback method.

Convective heat transfer mechanisms of molten phase change material in a vertical slender rectangular cavity: A numerical case study

In this paper, the convective heat transfer pattern of molten phase change material (mPCM) in a slender rectangular cavity with constant heat flux boundary condition at one side and flow boundary condition at opposite side is numerically investigated. The influences of the Rayleigh number (constant heat flux boundary condition, Ra = 104, 105 and 106), the Reynolds number (flow boundary condition, Re = 1×104, 2×104, 3×104, 4×104 and 5×104) and aspect ratio (AR = 5, 7.5 and 10) on the convective heat transfer mechanisms of the mPCM are analyzed. Several dimensionless parameters are used as quantitative indexes to describe and evaluate the convection and heat transfer process in the cavity. The results show that the convective heat transfer efficiency can be improved by increasing the Ra or Re. With longer length of the cavity in the direction of buoyancy, the internal natural convection heat transfer of mPCM is more intense. Especially, due to different boundary conditions, the heat transfer intensity at two vertical walls of the cavity is different. In addition, the mixing degree of cold and hot fluid in the cavity will also affect the local heat transfer effect at the wall.

Flow Continuity of Isothermal Elastohydrodynamic Point-Contact Lubrication Under Different Numerical Iteration Configurations

Abstract Elastohydrodynamic lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined, and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow-continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid-relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes, and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.

Loss assessment of a counter rotating open rotor using URANS/LES with phase-lagged assumption (draft)

This paper presents the study of the losses generated in a Counter Rotating Open Rotor (CROR) configuration at three different operating conditions (approach, cutback and sideline). Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large-Eddy Simulation (LES) approaches are used and compared to describe the flow field and the mechanisms of loss. Since no common circumferential periodicity occurs in the two blade rows of the configuration (11 blades for the front rotor and 9 for the rear rotor), a full 360∘ simulation would be required. In order to reduce the related computational cost, a phase-lagged assumption approach is used. This method enables to perform unsteady simulations on multi-stage propulsive configurations including multiple frequency flows with a computational domain reduced to one single blade passage for each row. The phase-lagged approach requires a large data storage reduced in the study by a data compression method. The data compression method is based on a Proper Orthogonal Decomposition (POD) replacing the traditional Fourier Series Decomposition (FSD). The inherent limitation of the phase-shifted periodicity assumption remains with the POD data storage but this compression method alleviates some issues associated with the FSD, especially spectrum content issues. The analysis of the losses generated in the configuration is based on an entropy formulation. In particular, the losses are split between boundary layer contributions and the remaining domain where wakes and secondary flows occur. The study shows the influence of the leading edge vortex on the suction side boundary layer transition of the front and rear rotor blades at high rotational speed (cutback and sideline). The main source of losses is associated with the suction side boundary layer over the front and rear rotor blades with a main peak of loss production at around 75% of the blade chord.

Numerical Analysis of Stray Grain Formation during Laser Welding Nickel-Based Single-Crystal Superalloy Part III: Crystallography-Dependent Solidification Behavior

The solidification temperature range was numerically analyzed to optimize nonequilibrium solidification behavior during ternary Ni-Cr-Al nickel-based single-crystal superalloy weld pool solidification with variation of laser welding conditions (either heat input or welding configuration). The distribution of solidification temperature range along the fusion boundary is beneficially symmetrical about the weld pool centerline in the (001)/[100] welding configuration. The distribution of solidification temperature range along the fusion boundary is detrimentally asymmetrical about the weld pool centerline in the (001)/[110] welding configuration. The stray grain formation and solidification cracking are preferentially confined to [100] dendrite growth region. [001] epitaxial growth region with columnar dendrite morphology is favored at the expense of undesirable [100] growth region with equiaxed dendrite morphology to facilitate essential single-crystal solidification with considerable reduction of heat input. The smaller heat input is used, the narrower solidification temperature range is thermodynamically promoted to reduce nucleation and growth of stray grain formation with decrease of constitutional undercooling ahead of dendrite tip and mitigate thermo-metallurgical factors for morphology instability and microstructure anomalies. Potential low heat input(both decreasing laser power and increasing welding speed) with (001)/[100] welding configuration decreases solidification temperature range to significantly minimize columnar/equiaxed transition (CET) and stray grain formation, and improve resistance to solidification cracking through microstructure control. On both sides of weld pool are imposed by the same heat input, while the solidification temperature range along the fusion boundary inside of [100] dendrite growth region on the right part of the weld pool is spontaneously wider than that of [010] dendrite growth region on the left part to increase solidification cracking susceptibility in the (001)/[110] welding configuration. Furthermore, another mechanism of solidification cracking as consequence of severe solidification behavior and anomalous microstructure with asymmetrical crystallographic orientation is therefore proposed. The theoretical predictions are well verified by experiment results. The useful and satisfactory numerical modeling is also available for other single-crystal superalloys during successful laser repair process without stray grain formation.

Optimization of axial water injection to mitigate the Rotating Vortex Rope in a Francis turbine

Rotating Vortex Rope (RVR) resulting from flow instabilities inside draft tube affects the hydraulic turbine's efficiency and wear. Among the passive and active RVR mitigation methods, the water injection method has been widely investigated lately. The present research focuses on the dynamics of RVR mitigation using the water injection method and the optimization of exergy loss during the water injection. The numerical simulations are performed using a reduced turbine geometry consisting of one stay vane, two guide vanes, one runner passage by applying periodic boundary conditions at side boundaries, and a complete draft tube. The pressure fluctuations, velocity field, and the RVR structure are well captured using the Shear Stress Transport - Scale Adaptive Simulation (SST-SAS) turbulence model. The results of the local swirl number during the load variation show that the onset of flow instabilities and RVR formation are created due to a decrease of the axial momentum below the runner cone. The required axial momentum flux of water injection is calculated for a stable swirl number and the local minimum ratio of dimensionless loss to the pressure recovery factor. The numerical results show that the rotating and plunging components of the pressure fluctuations inside the draft tube reduce during the water injection. The pressure recovery of the draft tube improves. The dynamics of RVR mitigation are visualized using λ2 criterion and the spectrogram of pressure probes on the draft tube wall. An optimum water flow rate and jet velocity for a fixed axial momentum are proposed. The results show that a water jet with a large radius and low velocity is more effective to mitigate the RVR and minimizing the draft tube losses.

Application of free side edges to thickness shear bulk acoustic resonator on lithium niobate for suppression of transverse resonances

This paper discusses the applicability of free side edges to a thickness shear bulk acoustic resonators (TSBARs) on a rotated Y-cut lithium niobate plate for suppression of lateral energy leakage and the transverse mode resonances. It is shown both theoretically and experimentally that free edges are effective to suppress lateral leakage and transverse mode resonances in free-standing TSBARs. Although this technique is applicable only to the X side boundaries, it is shown that the Y′ side perpendicular to the X side can be designed for the piston mode operation independently by the simple two-dimensional analysis ignoring wave propagation toward the X direction. Then the discussion is extended to the solidly-mounted TSBAR. It is shown that this technique works well also for this case, and removal of the first few Bragg layers is enough for the transverse mode suppression.

Aerodynamic investigation of a linear cascade with tip gap using large-eddy simulation

The flow in a linear compressor cascade with tip gap is simulated using a wall-resolved compressible Large-Eddy Simulation. The cascade is based on the Virginia Tech Low Speed Cascade Wind Tunnel. The Reynolds number based on the chord is 3.88 x 10⁵ and the Mach number is 0.07. The gap considered in this study is 4.0 mm (2.9% of axial chord). An aerodynamic analysis of the tip-leakage flow allow us identifying the main mechanisms responsible for the development and the convection of the tip-leakage vortex downstream of the cascade. A region of high turbulence and vorticity levels is located along an ellipse that borders the top of the tip-leakage vortex. The influence of the airfoil suction side boundary layer development on the tip-leakage vortex is highlighted by tripping the flow. A tripped boundary layer induces a stronger and larger tip-leakage vortex that tends to move further away from the airfoil suction side and from the endwall compared with an untripped flow. The boundary layer turbulent state influences the tip-leakage flow development.

The classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom of the boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at a point. The smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved, and the conditions under which a piecewise-smooth solution exists are established. The problem with conjugate conditions is considered

Steady compressible radially symmetric flows with nonzero angular velocity in an annulus

In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular velocity in the structure of steady inviscid compressible flows. We give a complete classification of flow patterns in terms of boundary conditions at the inner and outer circle. Due to the nonzero angular velocity, many new flow patterns will appear. There exists accelerating or decelerating smooth transonic flows in an annulus satisfying one side boundary conditions at the inner or outer circle with all sonic points being nonexceptional and noncharacteristically degenerate. More importantly, it is found that besides the well-known supersonic-subsonic shock in a divergent nozzle as in the case without angular velocity, there exists a supersonic-supersonic shock solution, where the downstream state may change smoothly from supersonic to subsonic. Furthermore, there exists a supersonic-sonic shock solution where the shock circle and the sonic circle coincide, which is new and interesting.

On the Importance of Transition Control at Transonic Compressor Blades

AbstractThe flow through a transonic compressor cascade is characterized by high unsteadiness and a high loss level. This results from the shock waves in the blade cascade and their interaction with the blade suction side boundary layer. In the case of a laminar shock wave boundary layer interaction, the loss level is higher due to the occurrence of a laminar separation bubble below the shock wave compared to the shock wave interaction with a turbulent boundary layer. In addition, the oscillation of the shock position in both cases influences the working range concerning the point of stall onset as well as leading to an unsteady interaction with the blade called buffeting. The reduction of losses and of unsteadiness in the shock wave oscillation, connected to a decrease of the blade buffeting effect, is the aim of the current investigation. Therefore, experimental investigations using a roughness patch as well as air jet vortex generators in order to control the transition in a transonic compressor cascade have been conducted at the transonic cascade wind tunnel of the German Aerospace Center (DLR) at Cologne. At an inflow Mach number of 1.21, a loss reduction for both transition control cases is achieved. In spite of a nearly uninfluenced fluctuation range of the passage shock wave compared to the reference cascade, the oscillation spectra of the transition control cases show a reduction of the shock movement amplitude at a frequency below 500 Hz and above 1 kHz. In the closing section of the paper, a detailed discussion on the reasons for the resulting flow behavior based on particle image velocimetry and high-speed shadowgraphy data is given. The resulting conclusion of the study is that the consideration of transition control at transonic compressor blades is very important in order to reduce losses and flow unsteadiness that directly influences blade buffeting and the numerical prediction quality of the stall onset.

Wind-Driven Oscillations in Meridional Overturning Circulations near the Equator. Part II: Idealized Simulations

AbstractLarge-amplitude [±100 Sv (1 Sv ≡ 106 m3 s−1)], high-frequency oscillations in the Pacific Ocean’s meridional overturning circulation within 10° of the equator have been found in integrations of the NEMO ocean general circulation model. Part I of this paper showed that these oscillations are dominated by two bands of frequencies with periods close to 4 and 10 days and that they are driven by the winds within about 10° of the equator. This part shows that the oscillations can be well simulated by small-amplitude, wind-driven motions on a horizontally uniform, stably stratified state of rest. Its main novelty is that, by focusing on the zonally integrated linearized equations, it presents solutions for the motions in a basin with sloping side boundaries. The solutions are found using vertical normal modes and equatorial meridional modes representing Yanai and inertia–gravity waves. Simulations of 16-day-long segments of the time series for the Pacific of each of the first three meridional and vertical modes (nine modes in all) capture between 85% and 95% of the variance of matching time series segments diagnosed from the NEMO integrations. The best agreement is obtained by driving the solutions with the full wind forcing and the full pressure forces on the bathymetry. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Slower variations in the same meridional and vertical modes of the MOC are also shown to be well simulated by a quasi-stationary solution driven by zonal wind and pressure forces.

Hemp-Based Microfluidics.

Hemp is a sustainable, recyclable, and high-yield annual crop that can be used to produce textiles, plastics, composites, concrete, fibers, biofuels, bionutrients, and paper. The integration of microfluidic paper-based analytical devices (µPADs) with hemp paper can improve the environmental friendliness and high-throughputness of µPADs. However, there is a lack of sufficient scientific studies exploring the functionality, pros, and cons of hemp as a substrate for µPADs. Herein, we used a desktop pen plotter and commercial markers to pattern hydrophobic barriers on hemp paper, in a single step, in order to characterize the ability of markers to form water-resistant patterns on hemp. In addition, since a higher resolution results in densely packed, cost-effective devices with a minimized need for costly reagents, we examined the smallest and thinnest water-resistant patterns plottable on hemp-based papers. Furthermore, the wicking speed and distance of fluids with different viscosities on Whatman No. 1 and hemp papers were compared. Additionally, the wettability of hemp and Whatman grade 1 paper was compared by measuring their contact angles. Besides, the effects of various channel sizes, as well as the number of branches, on the wicking distance of the channeled hemp paper was studied. The governing equations for the wicking distance on channels with laser-cut and hydrophobic side boundaries are presented and were evaluated with our experimental data, elucidating the applicability of the modified Washburn equation for modeling the wicking distance of fluids on hemp paper-based microfluidic devices. Finally, we validated hemp paper as a substrate for the detection and analysis of the potassium concentration in artificial urine.

Laboratory and numerical investigation of saline intrusion in fractured coastal aquifers

Laboratory scale experiments and numerical modelling were employed in this study to investigate saltwater intrusion in fractured aquifers. Saline intrusion was initiated in one homogeneous and six fractured experimental aquifers containing individual discontinuities of varying length and orientation. Automated image processing enabled high precision quantification of three intrusion variables, the toe length of the saline wedge, the width of the mixing zone and the aquifer fraction occupied by saltwater. A discrete fracture matrix model was successfully utilized to recreate the experimental data and expand the study's findings through rigorous sensitivity analysis. The presence of fractures significantly impacted all three intrusion variables under consideration. The length of intrusion was negatively correlated to the horizontal fracture's distance from the systems’ seaward boundary. It was demonstrated that for the same fractured aquifer, the presence of a discontinuity can either limit or augment saline intrusion, depending on the applied hydraulic gradient. For gradients steeper than a critical head difference, at which the toe length was the same for both the fractured and the equivalent homogeneous aquifer, intrusion was suppressed further seaward, while for milder ones it intensified. The distance of horizontal fracture from the aquifer's base determined the extend of intrusion in the vertical direction. In general, the longer the discontinuities were, the more significant their impact on groundwater dynamics. In the case of vertical factures, whenever the saline wedges reached their position, the discontinuities contributed significantly in the widening of the mixing zone, while having limited effect on the other two intrusion characteristics. In aquifers with discontinuities adjacent to their side boundaries, a distinct distribution of saltwater concentration was identified, distinguishing them from the rest of the aquifers.

DIRECT AND INVERSE PROBLEMS FOR THERMAL GROOVING BY SURFACE DIFFUSION WITH TIME DEPENDENT MULLINS COEFFICIENT

We consider the Mullins’ equation of a single surface grooving when the surface diffusion is not considered as very slow. This problem can be formed by a surface grooving of profiles in a finite space region. The finiteness of the space region allows to apply the Fourier series analysis for one groove and also to consider the Mullins coefficient as well as slope of the groove root to be time-dependent. We also solve the inverse problem of finding time-dependent Mullins coefficient from total mass measurement. For both of these problems, the grooving side boundary conditions are identical to those of Mullins, and the opposite boundary is accompanied by a zero position and zero curvature which both together arrive at self adjoint boundary conditions.

Boundary layer description of directional polymer crystallisation.

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger-Gryte ansatz.