Showing papers on "Hele-Shaw flow published in 2022"

A data assimilation model for wall pressure-driven mean flow reconstruction

Abstract: This study establishes a continuous adjoint data assimilation model (CADA) for the reproduction of global turbulent mean flow from a limited number of wall pressure measurements. The model-form error induced by the Boussinesq assumption is corrected by a body force vector, which reinforces the eddy viscosity-based Reynolds force vector. The Stokes–Helmholtz decomposition is applied to this Reynolds force vector to isolate the crucial information contained with the Reynolds stress, and the primary-adjoint system is solved only for the anisotropic components. The CADA model is theoretically derived to minimize discrepancies between the wall pressure measurements and the numerical predictions of the primary-adjoint system. This minimization reveals the optimal anisotropic contribution of the Reynolds force vector. Four test cases are used for the assessment and validation of our CADA model. First, simulation of the wake in a flow over a cylinder demonstrates the ability of our CADA model to accurately recover the global fields from different regions of local synthetic wall measurements. Second, simulation of the flow over a backward-facing step illustrates that our CADA model can reconstruct a detached flow with a high Reynolds number. Third, simulation of the flow in a converging–diverging channel shows that our CADA model can reconstruct a strong adverse pressure-gradient flow. Fourth, simulation of the periodic hill flow further showcases the ability of our CADA model to predict complex flows. The method demonstrated here opens up possibilities for assimilating realistic observations, serving as a complement to our anisotropic DA scheme for future DA work.

Anisotropic Approach to Control Viscous Fingering Pattern Generated in Lifting Plate Hele-Shaw Cell

Abstract: Stability is one of the important aspects of life, our everyday systems — the permanence of things. When this stability gets disturbed, instability is produced. Sometimes this instability is desirable, and sometimes not. In the crude oil extraction process, fluid instability is observed. Saffman and Taylor explored the concept of the Hele-Shaw cell to study these instabilities. The Hele-Shaw cell involves a high viscous fluid sandwiched between two parallel plates, and the low viscosity fluid enters from the periphery. Insertion of low viscous fluid into a high viscous fluid generates a pattern that is a resemblance to a finger. This phenomenon is called viscous fingering. In this paper, the authors control the instabilities and mimic patterns available in nature. These instabilities can be controlled by controlling one of the fluids in the cell. Here authors control the low viscous fluid (air) by providing anisotropies. Anisotropy means providing holes and slots on any plate of the cell. This anisotropy guides air to interact with high viscous fluid at some desired location. The authors further studied the effect of size, position, the orientation of these holes and slots on the viscous fingering exhaustively.

Stability of a laminar pipe flow subjected to a step-like increase in the flow rate

Abstract: We perform the linear modal stability analysis of a pipe flow subjected to a step-like increment in the flow rate from a steady initial flow with flow rate, $Q_i$, to a final flow with flow rate, $Q_f$, at the time, $t_c$. A step-like increment in the flow rate induces a non-periodic unsteady flow for a definite time interval. The ratio, $\Gamma_a={Q}_i/{Q}_f$, parameterizes the increase in the flow rate, and it ranges between $0$ to $1$. The stability analysis for a pipe flow subjected to a step-like increment in the flow rate from the steady laminar flow ($\Gamma_a>0$) is not reported in the literature. The present work investigates the effect of varying $\Gamma_a$ on the stability characteristics of an unsteady pipe flow. The step-like increment in the flow rate for $0\leq\Gamma_a\leq0.72$ induces a viscous type instability for a definite duration and the flow is modally unstable. The non-axisymmetric disturbance with azimuthal wavenumber, $m=1$ is the most unstable mode. The flow is highly-unstable for $\Gamma_a=0$ and the flow becomes less unstable with an increase in $\Gamma_a$. The flow becomes stable before it attains the steady-state condition for all $\Gamma_a$.

Laminar flow and pressure loss in planar Tee joints: Numerical simulations and flow analysis

Abstract: This paper presents a numerical investigation of the laminar flow and pressure drop characteristics of planar Tee joints, a canonical flow of interest for the thermal-hydraulic design of oil-immersed power transformer windings. After formulating the problem in nondimensional form, the steady, constant property flow in planar 90∘ Tee joints is computed numerically by integrating the Navier–Stokes equations with fully developed upstream and downstream boundary conditions. The analysis assumes a straight-through configuration in which the straight duct holds flow in the same direction before and after the junction, whereas the flow in the side branch can either divide from the incoming flow or combine with it. The analysis starts with the description of the flow patterns that emerge in the dividing and combining flow cases for all mass split ratios, 0≤ṁ1≤1, and a wide range of straight duct to side branch width ratios, 1≤α≤3, and Reynolds numbers of the common branch, 0 ¡ Re3 ≤ 200, representative of the cooling oil flow in oil-immersed transformer winding. Flow maps for planar Tee joints are then presented, showing the existence of different regions in the (Re3, ṁ1)-plane that exhibit different number and location of recirculation zones. Pressure distributions and secondary loss coefficients are then computed and analyzed, providing a numerical database that is used to develop new local pressure loss correlations for planar Tee joints in an accompanying paper.

Characterizing purely elastic turbulent flow of a semi-dilute entangled polymer solution in a serpentine channel

Abstract: Polymer solutions in the semi-dilute regime are of considerable industrial importance. The complex rheological properties of such highly viscoelastic fluids and the complexity of their flow characteristics, especially in curved geometries, necessitate a thorough experimental characterization of the dynamics of such fluid flows. We apply statistical, spectral, and structural analyses to the experimentally obtained velocity fields of a semi-dilute entangled polymer solution in a serpentine channel to fully characterize the corresponding flow. Our results show that at high Weissenberg numbers, yet vanishing Reynolds numbers, the flow resistance is significantly increased, which indicates the emergence of a purely elastic turbulent flow. Spatial flow observations, and statistical analysis of temporal flow features show that this purely elastic turbulent flow is non-homogeneous, non-Gaussian, and anisotropic at all scales. Moreover, spectral analysis indicates that compared to elastic turbulence in the dilute regime, the range of present scales of the excited fluctuations is narrower. This is partly due to the entanglement of the polymers in this concentration regime, which restricts their movement, and partly due to the mixed flow type inherent in the serpentine geometry, which can reduce the extent of polymer stretching and thus reduce the intensity of the fluctuations in the flow. Furthermore, proper orthogonal decomposition analysis is applied to directly extract the turbulent flow structure and reveals the activity of the counter-rotating vortices associated with secondary flow, which significantly contribute to the total kinetic energy of the flow.

Viscous Fingering Dynamics and Flow Regimes of Miscible Displacements in a Sealed Hele-Shaw Cell

Abstract: Miscible viscous fingering occurs when a less viscous fluid displaces a more viscous one in porous media or a Hele–Shaw cell. Such flow instabilities are of particular interest in a variety of applications in flows and displacements in subsurface energy and environment systems. In this study, we investigate the miscible viscous fingering dynamics experimentally using water to displace glycerol in a sealed Hele–Shaw cell with two wells located in it instead of at the boundary or corners. We comprehensively examine the spatial and temporal variations of fingering dynamics, different flow regimes, and how they are affected by the water injection rate and control of pressure or rate at the outlet. Alongside the widely recognized diffusion-dominated and convection-dominated flow regimes, we identify three new regimes: a slow expansion regime prior to breakthrough, a rapid shrinkage regime immediately after breakthrough, and a uniform, slow expansion regime without fingering instability. Each regime is characterized by interesting flow dynamics, which has not been reported previously. The duration of each regime depends on the water injection rate and whether constant pressure or a constant production rate is applied at the outlet. The variations of swept area, interfacial length, and count of fingers are also quantitatively examined. This study provides new insights into the fundamental mechanisms for miscible fluid displacements in a variety of applications such as CO2 sequestration, hydrogen storage, enhanced oil recovery, and groundwater contaminate remediation.

A computational fluid dynamics study on rimming flow in a rotating cylinder

Abstract: Extensive computational fluid dynamics (CFD) simulations were conducted to study rimming flow in a partially-filled horizontally rotating cylinder. These flows are encountered in aero-engine bearing chambers which often exhibit complex two-phase flow scenarios as well as in multiple other engineering applications. A robust numerical scheme to model two-phase rimming flow has been adopted and validated against analytical expression and experimental data obtained from the literature. We used the volume of fluid method to solve the system of multi-phase flow governing equations and track the interface of rimming flow. The gas-liquid interface was resolved and the liquid-film thickness was determined. First, we performed our simulations within small to moderate ranges of Reynolds and Bond numbers and compared our results with previously reported analytical and experimental investigations. The present CFD results were found to be in very good agreement with previously reported data, both in identifying different rimming flow regimes and liquid-film thickness predictions. We also performed several additional simulations at much larger and practical ranges of Reynolds and Bond numbers, beyond the limitations imposed in previous analytical and experimental investigations on thin-film flows. We showed that the three different flow regimes of shear-dominated, transitional and gravitational-dominated are attainable for the rimming flow for different combinations of Reynolds, Bond, and gravitational numbers. The present numerical results led us to propose a new map of rimming flow regimes by introducing functions of Froude number and Capillary number, which successfully identify and separate these regimes for a significant number of flow conditions.

Gas‐liquid flow patterns in a rectangular milli‐structured channel with static mixing elements

Abstract: The gas-liquid flow behavior through a milli-scaled channel provided with a staggered herringbone-like static mixer was investigated using high-speed recordings. For three different substance systems consisting of water, 5 wt % acetic acid in aqueous solution, and propylene glycol as liquid phase and nitrogen as gas phase, flow patterns and their transitions were determined by analyzing image sequences of the flow and summarized in flow pattern maps. Surge flow, slug flow, and bubbly flow were observed at different flow rates. The flow distribution and transitions between flow patterns mainly depend on the viscosity and surface tension of the liquid phase. By just reducing the surface tension, slug flow is not observed, and thus an early transition into a bubbly flow regime takes place. An increase in viscosity counteracts this effect.

Polymer-turbulence interactions in a complex flow and implications for the drag reduction phenomenon

Abstract: We present direct numerical simulation data for turbulent duct flow of a finite-extensibility non-linear elastic dumbbell model with the Peterlin approximation (FENE-P) fluid in the high drag reduction regime. While the secondary flow pattern is qualitatively similar to that in a Newtonian fluid, its magnitude is significantly reduced, resulting in a less uniformly distributed velocity profile and hence smaller gradients at the wall. The Reynolds stress tensor in the polymer-laden flow was found to be increasingly anisotropic with most of the turbulent kinetic energy retained in the streamwise component, [Formula: see text]. We introduce a novel approach for investigating polymer stretching using the anisotropy invariant map of the polymer stress tensor and observe the persistence of both uniaxial and biaxial extension. Analysis of the transport equation for the mean kinetic energy indicates that polymer stretching and relaxation is a highly dissipative process; hence, the introduction of an additional channel for dissipation in a flow is key to drag reduction.

Flow non-uniformity and secondary flow characteristics within a serpentine cooling channel of a realistic gas turbine blade

Abstract: Unlike the ideal conditions considered in most previous studies, the actual cooling flow passage inside gas turbine blades is extremely complex. This complexity is due to the geometrical restrictions resulting from the external cooling holes and blade shape, which change the secondary flow and flow non-uniformity of the internal cooling flow. This study conducted experimental and numerical analysis to characterize the secondary flow and flow non-uniformity in a realistic internal cooling serpentine passage. Magnetic resonance velocimetry was utilized to measure the average three-dimensional–three-components of the mean velocity. By integrating the flow field, parameters indicating the flow non-uniformity and secondary flow strength were obtained. Reynolds averaged Navier-Stokes simulations were also conducted, and the Reynolds stress transport model showed relatively good performance when predicting the separation bubble in the U-bend. The secondary flow intensity exponentially decreases after the U-bend, but the rib turbulators maintain the secondary flow at a certain level. Additionally, the high-velocity regions in the inlet zone and beyond the separation bubble creates significant flow non-uniformity and inherent shear. At the same time, the turbulence intensity becomes strong at the low-velocity region, which is key for heat transfer enhancement. Therefore, high flow non-uniformity has the potential to enhance heat transfer.

Effect of Hele–Shaw cell gap on radial viscous fingering

Abstract: The flow through a Hele-Shaw cell is an experimental prototype to study the flow through a porous medium as well as the flow in microfluidic devices. In context with porous medium flows, it is used to visualize and understand hydrodynamic instabilities like viscous fingering (VF). The gap between the plates of the cell is an important parameter affecting the flow dynamics. However, the effect of the gap on the Hele-Shaw cell flows has been minimally explored. We perform experiments to understand the effect of the gap on VF dynamics. It is observed that a minimum gap is required to observe rigorous fingering instability. The onset time of instability, as well as the width of the fingers, increases with an increment in the gap due to a decrease in the convection. The instability increases with an increase in Péclet number, but the effect of gap width on fingering patterns is evident with broader fingers observed for larger b. The results are validated by performing numerical simulations. It is further shown that the gap-averaged three-dimensional simulations using the Stokes law approach and the two-dimensional Darcy's law result in a small gap Hele-Shaw cell.

Flow features of shallow cylindrical cavities subject to grazing flow

Abstract: The flow behavior within shallow cavities of circular planform, subject to grazing flows, exhibits a strong dependence on the cavity depth ( h)-to-diameter ( d) ratio. In the present experimental study, the internal flow patterns within shallow circular cavities having a depth-to-diameter ratio of 0.15 ≤ h/d ≤ 1 have been extracted from mean static and unsteady surface pressure measurements collected on the cavity surfaces. In the literature, no comprehensive experimental study spanning this entire h/d range is available characterizing the flow behavior in shallow cylindrical cavities; only certain aspects of flow at select h/d are present in the current literature, and the present paper addresses this shortcoming. In agreement with the previous research on shallow cylindrical cavities, the mean flow orientation and the amplitude of large-scale pressure fluctuations within the cavity are observed to follow a non-monotonic function as the depth-to-diameter ratio is varied, with h/d = 0.5 exhibiting the greatest asymmetry in flow orientation. The division of the internal cavity flow into stable, switching, and flapping regimes established by previous related studies has been reevaluated, and utilizing a simple filtering technique, a modification to the classification of these flow regimes has been proposed for the present conditions. Furthermore, the observation of two high-frequency pressure oscillations, measured within the cavity for the flapping regime, has been linked to shear layer instabilities.

Flow instability and heat transfer enhancement of unsteady convection in a step channel

Abstract: The formation of flow instability and heat transfer enhancement of unsteady convection is studied for backward-facing step flow, forward-facing step flow and combined step flow. The governing equations are solved by a program of FORTRAN code. The numerical method is validated by PIV and heat transfer experiments. The effects and the affecting factors of flow instability are investigated. The results show that the flow instability caused by the reattachment flow has a positive effect on heat transfer. In combined step flow, the formation of this flow instability is mainly affected by the bottom wall length and the critical Reynolds number. The minimum critical Reynolds number of the transition from steady to unsteady case is between 200 and 250. The fundamental flow pattern results show that 7 typical flow characters appear in different step channel. A new concept named the vortex length ratio (LRv) is proposed to distinguish the vortex shape. The vortex with the smaller LRv is more effective in heat transfer enhancement mainly because of the increase of vortex attack angle and vortex rotating speed.

Hele-Shaw flow for parity odd three-dimensional fluids

Abstract: A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by a small gap. The governing equation of flow within a Hele-Shaw cell is Darcy's law, which also describes flow through a porous medium. In this work, we derive a generalization to Darcy's law starting from a three-dimensional fluid with a parity-broken viscosity tensor with no isotropy. We discuss the observable effects of parity-odd fluids in various physical setups relevant to Hele-Shaw experiments, such as channel flow, flow past an obstacle, bubble dynamics, and the Saffman-Taylor instability. In particular, we show that when such a fluid is pushed through a channel, a transverse force is exerted on the walls, and when a bubble of air expands into a region of such fluid, a circulation develops in the far field, with both effects proportional to the parity-odd viscosity coefficients. The Saffman-Taylor stability condition is also modified, with these terms tending to stabilize the two-fluid interface. Such experiments can in principle facilitate the measurement of parity-odd coefficients in both synthetic and natural active matter systems.

Study of flow through and around a pair of porous cylinders covering steady and unsteady regimes

Abstract: The present article focuses on the incompressible flow around two identical porous cylinders for a side-by-side configuration in a closed channel. The formation of various flow patterns behind permeable cylinders is more intriguing and further compelling to assimilate the underlying flow physics. The effects of three critical parameters, gap ratio (s/d), Reynolds number ( Re), and the Darcy number ( Da), on the flow behavior are investigated for the ranges of s/d=1.5-6, Re=5-100, and Da=10-6-10-2. Both attached standing and detached vortices are observed in a steady flow regime. One secondary wake structure is also observed for s/d=1.5, whose size gradually reduces with increased permeability. In an unsteady flow regime, jet-like flow in the gap section mainly governs the unsteady wake patterns. In the low range of Darcy numbers (10-6-10-3), asymmetric flip-flopping patterns are observed for s/d=1.5 and 2; and synchronized wake patterns either in anti-phase or in-phase mode are observed for higher gap ratios. The velocity profiles in the gap and free sides of the cylinders and pressure distribution along the porous surface are also discussed to facilitate the understanding of different wake patterns. Surprisingly, a case of pattern shifting from anti-phase to in-phase mode is observed when permeability is altered for the same flow-time. A symmetric and clustered strands of vorticity near the centerline is observed for all cases of s/d at Da=10-2. The effects of Re, s/d and Da on the drag co-efficient are also examined.

Stability of laminar viscoplastic flows down an inclined open channel

Abstract: In this paper we study the two-dimensional linear stability of a Papanastasiou fluid flowing down an inclined plane. The Papanastasiou constitutive law is a regularization of the Bingham law in which the singularity at zero strain rate is smoothed by an exponential function. The stability eigenvalue problem is solved by a spectral collocation method based on Chebyshev polynomials. We prove that, while the Bingham flow is unconditionally stable for every Reynolds number, the Papanastasiou flow becomes unstable at a critical Reynolds that depends on the material parameters, on the angle of inclination of the plane and on the prescribed inlet discharge. In particular, we show that the critical Reynolds is a decreasing function of the yield stress, showing the destabilizing effect of the yield stress. The results obtained her e show that the stability characteristics of a regularized flow can be extremely different from that of the exact Bingham fluid even if the two flows are “practically indistinguishable”.

Gas-liquid flow in small channels: Artificial neural network classifiers for flow regime prediction

Abstract: To design and operate multiphase apparatus with mini- and microchannels, it is important to know how the fluids stream inside. Most literature reports the occurrence of flow regimes in dependence on gas and liquid superficial velocities in flow maps that are valid for fluids with similar properties and channels with similar geometry. Attempts to develop universally applicable flow maps show limitations in the number and variation of considered model parameters or in the number of considered flow regimes. This paper presents artificial neural network classifiers able to predict all relevant flow regimes: (a) Taylor flow, (b) bubbly flow, (c) Taylor-annular flow, (d) churn flow, (e) dispersed flow, (f) annular flow, (g) rivulet flow, and h) parallel flow in dependence on geometric and operational parameters as well as fluid properties with a high precision (R=0.92...0.95 and classification rates were generally above 80%). The classifiers were developed and validated by using more than 13,000 experimental data on gas-liquid flows extracted from 97 flow maps and are based on 7 significant dimensionless groups, namely, ReG, ReL, WeG, WeL,CaL, Θ*, and the channel form factor FC.