Effects of slowly varying meniscus curvature on internal flows in the Cassie state

2019 ◽  
Vol 872 ◽  
pp. 272-307 ◽  
Author(s):  
Simon E. Game ◽  
Marc Hodes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Liquid Metal ◽  
Small Parameter ◽  
Cross Section ◽  
Flow Rate ◽  
Pressure Difference ◽  
Liquid Metals ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Local Conditions ◽  
Cassie State

The flow rate of a pressure-driven liquid through a microchannel may be enhanced by texturing its no-slip boundaries with grooves aligned with the flow. In such cases, the grooves may contain vapour and/or an inert gas and the liquid is trapped in the Cassie state, resulting in (apparent) slip. The flow-rate enhancement is of benefit to different applications including the increase of throughput of a liquid in a lab-on-a-chip, and the reduction of thermal resistance associated with liquid metal cooling of microelectronics. At any given cross-section, the meniscus takes the approximate shape of a circular arc whose curvature is determined by the pressure difference across it. Hence, it typically protrudes into the grooves near the inlet of a microchannel and is gradually drawn into the microchannel as it is traversed and the liquid pressure decreases. For sufficiently large Reynolds numbers, the variation of the meniscus shape and hence the flow geometry necessitates the inclusion of inertial (non-parallel) flow effects. We capture them for a slender microchannel, where our small parameter is the ratio of ridge pitch-to-microchannel height, and order-one Reynolds numbers. This is done by using a hybrid analytical–numerical method to resolve the nonlinear three-dimensional (3-D) problem as a sequence of two-dimensional (2-D) linear ones in the microchannel cross-section, allied with non-local conditions that determine the slowly varying pressure distribution at leading and first orders. When the pressure difference across the microchannel is constrained by the advancing contact angle of the liquid on the ridges and its surface tension (which is high for liquid metals), inertial effects can significantly reduce the flow rate for realistic parameter values. For example, when the solid fraction of the ridges is 0.1, the microchannel height-to-(half) ridge pitch ratio is 6, the Reynolds number of the flow is 1 and the small parameter is 0.1, they reduce the flow rate of a liquid metal (Galinstan) by approximately 50 %. Conversely, for sufficiently large microchannel heights, they enhance it. Physical explanations of both of these phenomena are given.

The Effect of Boundary Layer Separation on Accuracy of Flow Measurement Using the Gibson Method

2007 ◽  
Author(s):  
F. Z. Sierra ◽  
A. Adamkowski ◽  
G. Urquiza ◽  
J. Kubiak ◽  
H. Lara ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Cross Section ◽  
Flow Rate ◽  
Pressure Difference ◽  
Proper Time ◽  
Effective Cross Section ◽  
Boundary Layer Separation ◽  
Water Hammer ◽  
Time Interval ◽  
Geometry Factor

The Gibson method utilizes the effect of water hammer phenomenon (hydraulic transients) in a pipeline for flow rate determination. The method consists in measuring a static pressure difference, which occurs between two cross-sections of the pipeline as a result of a temporal change of momentum from t0 to t1. This condition is induced when the water flow in the pipeline is stopped suddenly using a cut-off device. The flow rate is determined by integrating, within a proper time interval, the measured pressure difference change caused by the water hammer (inertia effect). However, several observations demonstrate that changes of pipeline geometry like diameter change, bifurcations, or direction shift by elbows may produce an effect on the computation of the flow rate. The paper focuses on this effect. Computational simulations have shown that the boundary layer separates when the flow faces sudden changes like these mentioned to above. The separation may reduce the effective cross section area of flow modifying a geometry factor involved into the computation of the flow rate. The remainder is directed to quantify the magnitude of such a factor under the influence of pipeline geometry changes. Results of numerical computations are discussed on the basis of how cross section reductions impact on the geometry factor magnitude and consequently on the mass flow rate.

scholarly journals Calculation of acoustic flow-rate measurements error with the help of Fermat’s principle

2018 ◽  
Vol 211 ◽  
pp. 04007
Author(s):  
Alexander Petrov ◽  
Semyon Shkundin
Keyword(s):  
Control Systems ◽  
Cross Section ◽  
Flow Rate ◽  
Three Dimensional ◽  
Air Flow Rate ◽  
Velocity Measurements ◽  
Three Dimensional Flow ◽  
Automatic Control Systems ◽  
A Value ◽  
Flow Changes

The establishment of dispatching and automatic control systems for mine ventilation is impossible without the availability of perfect air flow rate sensors. Existing anemometers (tachometer, heat) do not meet these requirements. The error of average in cross section velocity measurements with such sensors reaches 15-20, sometimes 30%. The reason - the speed measured at one point is interpreted as the average over the cross section. The reliability of the sensors is small, because they are exposed to the damaging effect of a dusty atmosphere. Stationary installed anemometers clutter cross section, which is not always allowed. Fermat’s variational principle is used for derivation of the formula for the time of propagation of a sonic signal between two set points A and B in a steady three-dimensional flow of a fluid or gas. It is shown that the fluid flow changes the time of signal reception by a value proportional to the flow rate independently of the velocity profile. The time difference in the reception of the signals from point B to point A and vice versa is proportional with a high accuracy to the flow rate. It is shown that the relative error of the formula does not exceed the square of the largest Mach number. This makes it possible to measure the flow rate of a fluid or gas with an arbitrary steady subsonic velocity field

The Numerical Simulation Research of Gas Entrainment Based on Three-Dimensional Model

2017 ◽  
Author(s):  
Yilin Zhang ◽  
Shanfang Huang
Keyword(s):  
Experimental Data ◽  
Mass Flow Rate ◽  
Cross Section ◽  
Flow Rate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gas Entrainment ◽  
Simulation Results

Two kinds of three-dimensional model are built to simulate the gas entrainment process through a small break in the horizontal coolant pipe at the bottom of the stratified flow. The results were compared with the two-dimensional simulation results and the experimental data. In terms of the two-phase distribution, the simulation results agree well with the experimental data and show much superiority compared with the two-dimensional model. The results verify the reliability of model building, condition setting and calculating method qualitatively and quantitatively. In general, after gas entrainment, the average velocity over cross section increases obviously, but the mass flow rate decreases contrarily. This is because that void fraction meanwhile reduces the fluid density. In addition, it is found that the larger the void fraction of vapor is, the higher the average discharge velocity of the fracture cross-section fluid is. Besides, with the larger internal and external pressure difference, the gas volume fraction and the flow velocity in the break increase, resulting in the mass flow rate increasing along with them. However, since the critical height increases as well, the total loss amount of liquid in the stable effluent stage decreases, and the time before entrainment becomes shorter.

Nozzle Passage Endwall Effectiveness Values with Various Combustor Coolant Flow Rates - Part 1: Flowfield Velocity and Coolant Concentration Measurements

2021 ◽  
pp. 1-53
Author(s):  
Kedar P. Nawathe ◽  
Rui Zhu ◽  
Enci Lin ◽  
Yong Kim ◽  
Terrence Simon
Keyword(s):  
Flow Rate ◽  
Large Scale ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Coolant Flow ◽  
Surface Cooling ◽  
Cooling Effectiveness ◽  
Flow Rates ◽  
Flow Physics ◽  
High Level

Abstract The stators of the first stage of a gas turbine are exposed to severe temperatures. The coolant streams introduced to prevent the stators from thermal damage further complicate the highly three-dimensional vane passage flow. Recent results have shown that the coolant streams injected for cooling the combustor also influence the flow physics and the cooling effectiveness in the first-stage stator vanes passage. However, the effects of changing the mass flow rate of these combustor coolant streams on the passage flowfield have not been studied. As understanding the coolant transport is necessary for analyzing changes in cooling effectiveness in the vane passage, detailed aerodynamic and thermal measurements along the whole vane passage are required. This two-part paper presents such measurements taken for a variety of combustor coolant and endwall film coolant flow rates. The experiments were conducted in a low-Mach-number facility with engine-representative Reynolds numbers and large-scale high-level turbulence. The objective of the first part is to describe the flow that influences endwall and vane surface cooling effectiveness distributions, which are presented in the second part. The measurements show changes in the passage flowfield due to changes in both combustor coolant and endwall film coolant flow rates. Overall, the flow-physics remains largely unaffected by changes in coolant flow rates except in the endwall-vane surfaces region where the combustor coolant flow rate dominates changes in coolant transport. This is shown to have a high impact on endwall and vane surface cooling.

Influence of Courtyard Size on Stack Effect During Building Fires

2021 ◽  
Vol 13 (6) ◽  
Author(s):  
Yanqiu Chen ◽  
Qianhang Feng ◽  
Xiankun Wang ◽  
Junmin Chen
Keyword(s):  
Numerical Simulations ◽  
Cross Section ◽  
Fire Protection ◽  
Pressure Difference ◽  
Three Dimensional ◽  
Building Fires ◽  
Stack Effect ◽  
Fire Smoke ◽  
The Cross

Abstract This paper studied the stack effect in courtyards in buildings through the pressure difference between the top and the bottom in the courtyard through three-dimensional (3D) numerical simulations, which would provide engineering guidance for the fire protection design of courtyards in buildings. During the fire, the stronger the stack effect was, the pressure difference between the top and the bottom was more significant, the fire smoke reached the top of the courtyard more quickly, and the temperature and the smoke concentration at the top were influenced in a shorter time. The influence of the size of the courtyard in the stack effect was investigated. It was found that the stack effect was linearly negatively related to the width of the cross section W and the length of the cross section L, exponentially negatively related with the area of the cross section A, while it was exponentially positively related to the height of the courtyard H. The change in the walls without windows (W) affected ΔPmax and the stack effect more significantly compared with the change in walls with windows (L). When L/W ≤ 1, the stack effect was strengthened as L/W increased; when L/W > 1, the stack effect was weakened as L/W increased. The stack effect was the most significant when L/W = 1.

Computation of Ingestion Through Gas Turbine Rim Seals

2011 ◽  
Author(s):  
Kunyuan Zhou ◽  
Mike Wilson ◽  
J. Michael Owen ◽  
Gary Lock
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Pressure Difference ◽  
Computational Models ◽  
Three Dimensional ◽  
Rotor Blades ◽  
Driving Mechanism ◽  
Computational Domain ◽  
Complex Flow ◽  
Rotating Blade

Three-dimensional unsteady computational fluid dynamics (CFD) is applied to the ingestion of fluid from a non-uniform mainstream annulus flow via a rim-seal into a rotor-stator wheel-space. The results provide understanding of the complex flow and information for the development of more efficient computational models and analytical ‘orifice models’. The commercial CFD code CFX has been used to carry out unsteady RANS computations with an SST turbulence model. A scalar equation is employed to represent the seeded tracer gas that can be used in experiments to determine sealing effectiveness, and the variation of effectiveness with sealing flow rate is determined for a simple axial clearance seal and one combination of axial and rotational Reynolds numbers. The computational domain comprises one pitch in a row of stator vanes and rotor blades The rotating blade is accounted for by a sliding interface between the stationary and rotating sections of the model, located downstream of the seal clearance. The unsteady computations confirm that the magnitude of the peak-to-trough pressure difference in the annulus is the principal driving mechanism for ingestion (or ingress) into the wheel-space. This pressure difference is used in orifice models to predict sealing effectiveness; its magnitude however depends on the locations in the annulus and the wheel-space that are chosen for its evaluation as well as the sealing flow rate. The CFD is used to investigate the appropriateness of the locations that are often used to determine the pressure difference. It is shown that maximum ingestion occurs when the static pressure peak produced by the vane combines with that produced by the blade, and that highly swirled ingrested flow could contact both the stator and rotor disk when little sealing flow is provided. The relationships between the unsteady simulations and simplified, more computationally efficient steady computations are also investigated. For the system considered here, ingress is found to be dictated principally by the pressure distribution caused by the vane. The effect of the rotating blade on the pressure distribution in the annulus is investigated by comparing the unsteady results with those for steady models that do not involve a blade. It is found that the presence of the blade increases the pressure asymmetry in the annulus. Although the pressure asymmetry predicted by unsteady and steady models have a similar magnitude, the sealing effectiveness is over-predicted considerably for the corresponding steady model. If a “thin seal” geometric approximation is used in the steady model, however, similar effectiveness results compared with the unsteady model may be obtained much more economically.

Three-dimensional features in low-Reynolds-number confined corner flows

2010 ◽  
Vol 668 ◽  
pp. 33-57 ◽  
Author(s):  
LAURA GUGLIELMINI ◽  
R. RUSCONI ◽  
S. LECUYER ◽  
H. A. STONE
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Channel Cross Section ◽  
Radius Of Curvature ◽  
Matched Asymptotic Expansion ◽  
Low Reynolds

In recent microfluidic experiments with solutions of bacteria we observed the formation of biofilms in the form of thread-like structures, called ‘streamers’, which float in the middle plane of the channel and are connected to the side walls at the inner corners. Motivated by this observation, we discuss here the pressure-driven low-Reynolds-number flow around a corner bounded by the walls of a channel with rectangular cross-section. We numerically solve the flow field in a channel of constant cross-section, which exhibits 90° sharp corners, or turns with constant curvature, or portions with slowly changing curvature along the flow direction, for finite, but small, values of the Reynolds numbers and including the limit of vanishingly small Reynolds numbers. In addition, we develop a matched asymptotic expansion solution for the flow around two boundaries intersecting at an angle α and spanning the small gap h between two horizontal plates. We illustrate the basic features of the flow in these channel geometries by describing the three-dimensional velocity field and the distribution of streamwise vorticity and helicity, and comparing the numerical solutions with predictions based on the asymptotic approach. We demonstrate that near a corner or a change in the curvature of the side wall the flow is three-dimensional and pairs of counter-rotating vortical structures are present, as identified by Balsa (J. Fluid Mech., vol. 372, 1998, p. 25). Finally, we discuss how this secondary flow depends on the significant geometric parameters, the aspect ratio of the channel cross-section, the radius of curvature of the turn and, more generally, the variation of the curvature of the channel side boundary. We believe that these three-dimensional secondary flow structures are relevant to transport problems where accumulation of material at the boundary is possible.

Equilibrium magnetohydrodynamic flows of liquid metals in magnetorotational instability experiments

2010 ◽  
Vol 644 ◽  
pp. 257-280 ◽  
Author(s):  
I. V. KHALZOV ◽  
A. I. SMOLYAKOV ◽  
V. I. ILGISONIS
Keyword(s):  
Liquid Metal ◽  
Theoretical Analysis ◽  
Liquid Metals ◽  
Annular Channel ◽  
Reynolds Numbers ◽  
Unified Approach ◽  
Magnetorotational Instability ◽  
Annular Channels ◽  
Magnetohydrodynamic Flows ◽  
Different Types

A theoretical analysis of equilibrium magnetohydrodynamic flows in annular channels is performed from the perspective of establishing required conditions for liquid metal magnetorotational instability (MRI) experiments. Two different types of fluid rotation are considered: electrically driven flow in an annular channel and Taylor–Couette flow between rotating cylinders. The structure of these flows is studied within a unified approach as a function of the Hartmann and Reynolds numbers. The parameters appropriate for realization of MRI experiments are determined.

scholarly journals CPS Based Liquid Metal Divertor Target for EU-DEMO

2020 ◽  
Author(s):  
S. Roccella ◽  
G. Dose ◽  
R. de Luca ◽  
M. Iafrati ◽  
A. Mancini ◽  
...  
Keyword(s):  
Liquid Metal ◽  
Surface Temperature ◽  
Flow Rate ◽  
Fusion Reactor ◽  
Liquid Metals ◽  
Concept Design ◽  
Water Coolant ◽  
Gas Heating ◽  
Plasma Facing Materials ◽  
Facing Material

Abstract Power exhaust is a key mission in the roadmap to the realization of a future fusion reactor. Among the different solutions, the use of liquid metals as plasma facing materials are of interest due to their potential increased lifetime. Several liquid metal limiters have been successfully tested in the Frascati Tokamak Upgrade over the last 10 years. Liquid materials such as lithium and tin have been investigated using capillary porous systems (CPSs), and their impact on plasma performance has been explored. From such experience, a liquid metal divertor (LMD) concept design, CPS-based, is here proposed. Tin has been preferred as plasma facing material. The proposed LMD would operate, in low evaporative regime, with matching heat exhausting capabilities to those of the baseline ITER-like divertor. Continuous refilling of the CPS is guaranteed with a reservoir at the back of the unit, where the metal is kept liquid through a gas heating circuit. The study has been carried out using ANSYS and the thermal results will be shown. All the design choices are compatible with the current materials and the constraints adopted for the DEMO W divertor. Using such configuration, thermal loads up to 20 MW/m2 are exhausted while keeping the surface temperature below 1250 °C. The design foresees values of pressure, temperature and flow rate of the water coolant in the same range expected for the W DEMO divertor, thus facilitating the integration of such solution in the current cassette design. Technological and practical aspects are addressed, i.e. tin corrosion and CPS wettability. Possible solutions to prevent tin corrosion, and its compatibility with structural materials, will be outlined.

scholarly journals A Gravity-Triggered Liquid Metal Patch Antenna with Reconfigurable Frequency

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 701
Author(s):  
Peng Qin ◽  
Guan-Long Huang ◽  
Jia-Jun Liang ◽  
Qian-Yu Wang ◽  
Jun-Heng Fu ◽  
...  
Keyword(s):  
Liquid Metal ◽  
Mobile Networks ◽  
Patch Antenna ◽  
Liquid Metals ◽  
Three Dimensional ◽  
Microstrip Patch ◽  
Naoh Solution ◽  
Operating Bandwidth ◽  
Wide Operating ◽  
5G Mobile Networks

In this paper, a gravity-triggered liquid metal microstrip patch antenna with reconfigurable frequency is proposed with experimental verification. In this work, the substrate of the antenna is quickly obtained through three-dimensional (3D) printing technology. Non-toxic EGaIn alloy is filled into the resin substrate as a radiation patch, and the NaOH solution is used to remove the oxide film of EGaIn. In this configuration, the liquid metal inside the antenna can be flexibly flowed and deformed with different rotation angles due to the gravity to realize different working states. To validate the conception, the reflection coefficients and radiation patterns of the prototyped antenna are then measured, from which it can be observed that the measured results closely follow the simulations. The antenna can obtain a wide operating bandwidth of 3.69–4.95 GHz, which coverage over a range of frequencies suitable for various channels of the 5th generation (5G) mobile networks. The principle of gravitational driving can be applied to the design of reconfigurable antennas for other types of liquid metals.

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