Small-scale Flow Features Research Articles

Positivity-preserving discontinuous spectral element methods for compressible multi-species flows

We introduce a novel positivity-preserving numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the adaptive entropy filtering approach (Dzanic and Witherden, J. Comput. Phys., 468, 2022), which is extended to the conservative formulation of the multi-species flow equations. We show that the straightforward enforcement of entropy constraints in the filter yields poor results around species interfaces and propose an adaptive switch for the entropy bounds based on the convergence properties of the pressure field which drastically improves its performance for multi-species flows. The proposed approach is shown in a variety of numerical experiments applied to the multi-species Euler and Navier–Stokes equations computed on unstructured grids, ranging from shock-fluid interaction problems to three-dimensional viscous flow instabilities. We demonstrate that the approach can retain the high-order accuracy of the underlying numerical scheme even at smooth extrema, ensure the positivity of the species density and pressure in the vicinity of shocks and contact discontinuities, and accurately predict small-scale flow features with minimal numerical dissipation.

Analysis of the interaction of a shock with two square bubbles containing different gases

The shock–bubble interaction problem remains of interest to researchers to study shock accelerated in-homogeneous flows and the Richtmyer–Meshkov instability. In the present work, simulations have been performed using the high-order Direct Flux Reconstruction scheme to study such interactions when a Mach 1.22 shock is incident on two configurations: one in which a helium bubble is in front of SF6, and, the other in which SF6 is in front of helium; in both cases, the ambient gas is nitrogen. High-order schemes are often preferred for such cases since these interactions usually involve small-scale flow features that are better resolved using high-order methods. When helium is in front of SF6, the helium bubble traverses along the initial horizontal surface of the SF6 and nitrogen, and with time, moves ahead of SF6. There are no regions of pure helium for this case at later stages. When SF6 is placed in front of helium, a separation of helium takes place in two parts, one of which mixes with SF6 while the other remains mostly pure even at later stages. A jet of nitrogen can also be seen moving at very high speeds, penetrating the region of pure helium.

Prediction of Mean Heat Transfer Characteristics of Multiple Impinging Jets with Steady RANS Simulation Using a Coarse Mesh

The capability of the standard SST k-ω turbulence model for the prediction of jet impingement cooling characteristics using a coarse mesh is investigated. The discussion is based on a sensitivity study with five computational grids, differing from each other in topology and resolution. The analysis considers a hexagonal configuration of turbulent jets at the inlet Reynolds number equal to 20,000, with the distance between the nozzle and target plates equal to four nozzle diameters. The results of steady RANS simulations are validated against the time-averaged LES results and data from experiments. The mean heat transfer characteristics of turbulent impinging jets have been successfully reproduced with all tested grids, which indicates that for a rather accurate mean heat transfer prediction, it is not necessary to resolve all the small-scale flow features of impinging jets above the target plate.

Pore-scale modeling of two-phase flow: A comparison of the generalized network model to direct numerical simulation.

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted.

Comparing LES and URANS results with a reference DNS of the transitional airflow in a patient-specific larynx geometry during exhalation

Air exhalation in the laryngeal area produces a complex transitional flow. A detailed investigation of the resulting flow features is very interesting from a fundamental point of view and useful to support medical researchers regarding treatment options. In the current study, the highly complex, unsteady, transitional flow in a patient-specific geometry has been described by three different numerical approaches, (1) using the unsteady Reynolds-averaged Navier–Stokes (URANS) equations with the k−ω shear stress transport (SST) turbulence model, (2) by large-eddy simulation (LES) with the WALE subgrid-scale model, and finally (3) using direct numerical simulation (DNS) – without any model needed. These three approaches deliver different pictures of the resulting flow, obviously with noticeable differences in terms of accuracy, but also regarding the associated computational efforts. The present article is devoted to the detailed comparison of these three approaches, using the DNS results as a reference. It has been found that even though URANS is able to predict with a fair accuracy the large-scale features of velocity and pressure in an average sense, it fails to predict correctly most relevant turbulent features; large differences are found concerning fluctuations, power spectral density, or spectral entropy. On the other hand, LES is able to reproduce both small-scale and large-scale flow features in a good agreement compared to DNS; additionally, LES delivers an appropriate description of the evolution of spectral entropy and can thus be used to predict flow transition. Obviously, DNS delivers an even more detailed and accurate view of the flow properties, but this comes with a tremendous increase in computing effort. For this configuration, a high-quality LES appears as best compromise between accuracy and computational requirements and, therefore, best suitable for medical studies of transitional airflows. All data-sets are publicly available under Abdelsamie et al. [1].

Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom.

Aortic valve dysfunction and stroke have recently been reported in transcatheter aortic valve implantation (TAVI) patients. Thrombus in the aortic sinus and neo-sinus due to hemodynamic changes has been suspected. In vitro experiments help investigate the hemodynamic characteristics in the cases where an in vivo assessment proves to be limited. In vitro experiments are also more robust, and the variable parameters are controlled readily. Particle image velocimetry (PIV) is a popular velocimetry method for in vitro studies. It provides a high-resolution velocity field such that even small-scale flow features are observed. The purpose of this study is to show how PIV is used to investigate the flow field in the aortic sinus after TAVI. The in vitro setup of the aortic phantom, TAVI for PIV, and the data acquisition process and post-processing flow analysis are described. The hemodynamic parameters are derived, including the velocity, flow stasis, vortex, vorticity, and particle residence. The results confirm that in vitro experiments and PIV help investigate the hemodynamic features in the aortic sinus.

A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations: Dynamical system reconstruction

Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the resolved large scales. For this purpose, most of current research is focused on development of parameterizations directly accounting for the small scales. In this work we propose an alternative to the mainstream ideas by showing how to reconstruct a dynamical system from the available reference solution data (our proxy for observations) and, then, how to use this system for modelling not only large-scale but also nominally-resolved flow patterns at low resolutions. This approach is advocated as a part of the novel framework for data-driven hyper-parameterization of mesoscale oceanic eddies in non-eddy-resolving models. The main characteristic of this framework is that it does not require to know the physics behind large–small scale interactions to reproduce both large and small scales in low-resolution ocean simulations. We tested it in the context of a three-layer, statistically equilibrated, steadily forced quasigeostrophic model for the beta-plane configuration and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark. The proposed methodology robustly allows to retrieve a system of equations governing reduced dynamics of the observed data, while the additional adaptive nudging counteracts numerical instabilities by keeping solutions in the region of phase space occupied by the reference fields. Remarkably, its solutions simulate not only large-scale but also small-scale flow features, which can be nominally resolved by the low-resolution grid. In addition, the proposed method reproduces realistic vortex trajectories. One of the important and general conclusions that can be drawn from our results is that not only mesoscale eddy parameterization is possible in principle but also it can be highly accurate (up to reproducing individual vortices) for significantly reduced dynamics (down to 30 degrees of freedom). This conclusion provides great optimism for the ongoing parameterization studies, which are still far away from being completed.

Transitions of turbulent superstructures in generalized Kolmogorov flow

Self-organized large-scale flow structures occur in a wide range of turbulent flows. Yet, their emergence, dynamics, and interplay with small-scale turbulence are not well understood. Here, we investigate such self-organized turbulent superstructures in three-dimensional turbulent Kolmogorov flow with large-scale drag. Through extensive simulations, we uncover their low-dimensional dynamics featuring transitions between several stable and meta-stable large-scale structures as a function of the damping parameter. The main dissipation mechanism for the turbulent superstructures is the generation of small-scale turbulence, whose local structure depends strongly on the large-scale flow. Our results elucidate the generic emergence and low-dimensional dynamics of large-scale flow structures in fully developed turbulence and reveal a strong coupling of large- and small-scale flow features.

High-order central-upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) algorithm

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.

Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm

Based on the fifth-order scheme in our previous work (Deng et. al (2019) [28]), a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called PnTm−BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm), are designed by employing high-order upwind-biased interpolations and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. We devise the new schemes up to eleventh order in an efficient way by directly increasing the order of the underlying upwind scheme using high order polynomials. The analysis of the spectral property and accuracy tests show that the new reconstruction strategy well preserves the low-dissipation property of the underlying upwind schemes with high-order polynomials for smooth solution over all wave numbers and realizes n+1 order convergence rate. The performance of new schemes is examined through widely used benchmark tests, which demonstrate that the proposed schemes are capable of simultaneously resolving small-scale flow features with high resolution and capturing discontinuities with low dissipation. With outperforming results and simplicity in algorithm, the new reconstruction strategy shows great potential as an alternative numerical framework for computing nonlinear hyperbolic conservation laws that have discontinuous and smooth solutions of different scales.

On data-driven augmentation of low-resolution ocean model dynamics

The problem of augmenting low-resolution ocean circulation models with the information extracted from the data relevant to the unresolved subgrid processes is addressed. A highly nonlinear model of eddy-resolving oceanic circulation – quasigeostrophic wind-driven double gyres – is considered. The model solutions are characterized by a vigorous dynamic coupling between the resolved large-scale and small-scale (eddy) flow features. This solution provides the data for augmenting the low-resolution model with the same configuration. The eddy forcing field, which contains the essential information about coupling between the large and eddy scales, is obtained, modified, coarse-grained and added to augment the low-resolution model. The implemented modification involves novel data-adaptive harmonic decomposition analysis and dynamical constraining based on the low-resolution nonlinear advection operator. The resulting augmentation of the low-resolution model significantly improves the solution, including its time-mean circulation and low-frequency variability. This result also paves the way for a systematic data-driven emulation of unresolved and under-resolved scales of motion.

Numerical simulation study on the opening process of the atmospheric relief valve

The opening characteristics of a 3-D power operated pressure relief valve were studied experimentally and numerically. The experimental results were used to study the mechanism controlling the valve opening time. The CFD simulations used the trimmed volume mesh deformation technique to study the full transient opening dynamic characteristics of the valve. The pressure and velocity fields were obtained including the small scale flow features. The CFD results were used to analyze the upper surface average pressure, surface velocity, resultant force and displacement of the disc during opening. The inlet and outlet mass flow of the valve was in a stable state when the valve opening time was 1.43 s. Moreover, the influence of the size structural parameters on the valve opening time was studied. The simulation results compare well with test data including the shock wave during the valve opening. The results show that the geometric factors affecting the valve opening time can be modified to reduce the valve opening time. It shows that the area of the region between the relief hole (orifice D) connected to the solenoid valve and the vertical tube has the greatest influence on the valve opening time. Due to the upward movement and misalignment of the disc, the valve opening time is delayed during the operation of pressure relief valves. The conclusions of this paper provide guidance for the optimal design of safety valves.

Numerical simulation of wind-driven circulation and pollutant transport in Taihu Lake based on a quadtree grid

In this study, a two-dimensional flow-pollutant coupled model was developed based on a quadtree grid. This model was established to allow the accurate simulation of wind-driven flow in a large-scale shallow lake with irregular natural boundaries when focusing on important small-scale localized flow features. The quadtree grid was created by domain decomposition. The governing equations were solved using the finite volume method, and the normal fluxes of mass, momentum, and pollutants across the interface between cells were computed by means of a Godunov-type Osher scheme. The model was employed to simulate wind-driven flow in a circular basin with non-uniform depth. The computed values were in agreement with analytical data. The results indicate that the quadtree grid has fine local resolution and high efficiency, and is convenient for local refinement. It is clear that the quadtree grid model is effective when applied to complex flow domains. Finally, the model was used to calculate the flow field and concentration field of Taihu Lake, demonstrating its ability to predict the flow and concentration fields in an actual water area with complex geometry.

Tidal eddies at a narrow channel inlet in operational oil spill models

In operational oil spill modeling, hydrodynamic models often employ a coarse-resolution grid for computational efficiency. However, this practical grid resolution poorly resolves small-scale flow features, such as starting jet vortices (tidal eddies) that are common at the inlet of bar-built estuaries with narrow inlet channels, particularly where channel dredging and jetties have been employed to aid ship traffic. These eddies influence Lagrangian transport paths and hence the fate of an oil spill potentially entering or leaving an estuary. This research quantifies the effect of tidal eddies on the mixing process and effects at model scales relevant to the operational prediction of oil spills, using the Galveston Bay entrance channel as a study site. Model grid sensitivity was analyzed, yielding an adequate eddy solution at the horizontal grid size of ∼140 m. It is demonstrated that the SUNTANS model at a practical operational grid resolution (∼400 m) captures neither the eddies nor their effects on particle movement, despite showing a satisfactory prediction of net transport through the inlet. The need for subgrid eddy modeling is discussed, and an empirical approach is proposed that can improve oil spill predictions at operational grid resolution scales when results from a high-resolution model are available.

Scaling Up Highly Permeable Thin Layers Into Flow Simulation

Summary Giant reservoirs such as Lula (Santos Oil Basin, Brazil) and Ghawar (Saudi Arabia) have high-permeability intervals, known as super-k zones, associated with thin layers. Modeling these small-scale flow features in large-scale simulation models is difficult. Current methods are limited by high computational costs or simplifications that mismatch the representation of these features in simulation gridblocks. This work has two purposes: present an upscaling work flow to integrate highly laminated or interbedded reservoirs with thin, highly permeable layers in reservoir simulations through a combination of an explicit modeling of super-k layers using the Parsons (1966) formula and dual-medium flow models, and compare this method with two conventional upscaling approaches that are available in commercial software. We use the benchmark model UNISIM-II-R (Correia et al. 2015a), a fine single-porosity grid dependent on field information from the Brazilian presalt and Ghawar oil fields, as the reference solution to compare the upscaling matching between the three methods. We compare oil recovery factor (ORF), water cut (WC), average reservoir pressure (RP), water front, and the time consumption for simulation. Our proposed Parson's dual-medium (PDP) methodology achieved better upscaling matches with the reference model and had minimal time consumption compared with the representation of super-k layers through an implicit matrix modeling by single-porosity flow models (IMP) and through the explicit representation of super-k zones in the fracture system of dual-medium flow models (DFNDP).

On viscoelastic cavitating flows: A numerical study

The effect of viscoelasticity on turbulent cavitating flow inside a nozzle is simulated for Phan-Thien-Tanner (PTT) fluids. Two different flow configurations are used to show the effect of viscoelasticity on different cavitation mechanisms, namely, cloud cavitation inside a step nozzle and string cavitation in an injector nozzle. In incipient cavitation condition in the step nozzle, small-scale flow features including cavitating microvortices in the shear layer are suppressed by viscoelasticity. Flow turbulence and mixing are weaker compared to the Newtonian fluid, resulting in suppression of microcavities shedding from the cavitation cloud. Moreover, mass flow rate fluctuations and cavity shedding frequency are reduced by the stabilizing effect of viscoelasticity. Time averaged values of the liquid volume fraction show that cavitation formation is strongly suppressed in the PTT viscoelastic fluid, and the cavity cloud is pushed away from the nozzle wall. In the injector nozzle, a developed cloud cavity covers the nozzle top surface, while a vortex-induced string cavity emerges from the turbulent flow inside the sac volume. Similar to the step nozzle case, viscoelasticity reduces the vapor volume fraction in the cloud region. However, formation of the streamwise string cavity is stimulated as turbulence is suppressed inside the sac volume and the nozzle orifice. Vortical perturbations in the vicinity of the vortex are damped, allowing more vapor to develop in the string cavity region. The results indicate that the effect of viscoelasticity on cavitation depends on the alignment of the cavitating vortices with respect to the main flow direction.

A phase-field lattice Boltzmann model for simulating multiphase flows in porous media: Application and comparison to experiments of CO2 sequestration at pore scale

Abstract We implement a phase-field based lattice-Boltzmann (LB) method for numerical simulation of multiphase flows in heterogeneous porous media at pore scales with wettability effects. The present method can handle large density and viscosity ratios, pertinent to many practical problems. As a practical application, we study multiphase flow in a micromodel representative of CO2 invading a water-saturated porous medium at reservoir conditions, both numerically and experimentally. We focus on two flow cases with (i) a crossover from capillary fingering to viscous fingering at a relatively small capillary number, and (ii) viscous fingering at a relatively moderate capillary number. Qualitative and quantitative comparisons are made between numerical results and experimental data for temporal and spatial CO2 saturation profiles, and good agreement is found. In particular, a correlation analysis shows that any differences between simulations and results are comparable to intra-experimental differences from replicate experiments. A key conclusion of this work is that system behavior is highly sensitive to boundary conditions, particularly inlet and outlet ones. We finish with a discussion on small-scale flow features, such as the emergence of strong recirculation zones as well as flow in which the residual phase is trapped, including a close look at the detailed formation of a water cone. Overall, the proposed model yields useful information, such as the spatiotemporal evolution of the CO2 front and instantaneous velocity fields, which are valuable for understanding the mechanisms of CO2 infiltration at the pore scale.

Uncertainty in counting ice nucleating particles with continuous flow diffusion chambers

Abstract. This study investigates the measurement of ice nucleating particle (INP) concentrations and sizing of crystals using continuous flow diffusion chambers (CFDCs). CFDCs have been deployed for decades to measure the formation of INPs under controlled humidity and temperature conditions in laboratory studies and by ambient aerosol populations. These measurements have, in turn, been used to construct parameterizations for use in models by relating the formation of ice crystals to state variables such as temperature and humidity as well as aerosol particle properties such as composition and number. We show here that assumptions of ideal instrument behavior are not supported by measurements made with a commercially available CFDC, the SPectrometer for Ice Nucleation (SPIN), and the instrument on which it is based, the Zurich Ice Nucleation Chamber (ZINC). Non-ideal instrument behavior, which is likely inherent to varying degrees in all CFDCs, is caused by exposure of particles to different humidities and/or temperatures than predicated from instrument theory of operation. This can result in a systematic, and variable, underestimation of reported INP concentrations. We find here variable correction factors from 1.5 to 9.5, consistent with previous literature values. We use a machine learning approach to show that non-ideality is most likely due to small-scale flow features where the aerosols are combined with sheath flows. Machine learning is also used to minimize the uncertainty in measured INP concentrations. We suggest that detailed measurement, on an instrument-by-instrument basis, be performed to characterize this uncertainty.

Uncertainty quantification of three-dimensional velocimetry techniques for small measurement depths

In this paper, the multi-camera techniques tomographic PTV and 3D-PTV as well as the single-camera defocusing PTV approach are assessed for flow measurements with a small measurement depth in conjunction with a high resolution along the optical axis. This includes the measurement of flows with strong velocity gradients in z direction and flow features, which have smaller scales than the actual light sheet thickness. Furthermore, in fields like turbomachinery, the measurement of flows in domains with small depth dimensions is of great interest. Typically, these domains have dimensions on the order of 100 mm in z direction and of 101 mm in x and y direction. For small domain depths, employing a 3D flow velocimetry technique is inevitable, since the measurement depths lie in the range of the light sheet thickness. To resolve strong velocity gradients and small-scale flow features along the z axis, the accuracy and spatial resolution of the 3D technique are very important. For the comparison of the different measurement methods, a planar Poiseuille flow is investigated. Quantitative uncertainty analyses reveal the excellent suitability of all three methods for the measurement of flows in domains with small measurement depths. Naturally, the multi-camera approaches tomographic PTV and 3D-PTV yield lower uncertainties, since they image the measurement volume from different angles. Other criteria, such as optical access requirements, hardware costs, and setup complexity, clearly favor defocusing PTV over the more complex multi-camera techniques.

English

doi: http://dx.doi.org/10.15447/sfews.2014v12iss4art1 In branching channel networks, such as in the Sacramento–San Joaquin River Delta, junction flow dynamics contribute to dispersion of ecologically important entities such as fish, pollutants, nutrients, salt, sediment, and phytoplankton. Flow transport through a junction largely arises from velocity phasing in the form of divergent flow between junction channels for a portion of the tidal cycle. Field observations in the Georgiana Slough junction, which is composed of the North and South Mokelumne rivers, Georgiana Slough, and the Mokelumne River, show that flow phasing differences between these rivers arise from operational, riverine, and tidal forcing. A combination of Acoustic Doppler Current Profile (ADCP) boat transecting and moored ADCPs over a spring–neap tidal cycle (May to June 2012) monitored the variability of spatial and temporal velocity, respectively. Two complementary drifter studies enabled assessment of local transport through the junction to identify small-scale intrajunction dynamics. We supplemented field results with numerical simulations using the SUNTANS model to demonstrate the importance of phasing offsets for junction transport and dispersion. Different phasing of inflows to the junction resulted in scalar patchiness that is characteristic of MacVean and Stacey’s (2011) advective tidal trapping. Furthermore, we observed small-scale junction flow features including a recirculation zone and shear layer, which play an important role in intra-junction mixing over time scales shorter than the tidal cycle (i.e., super-tidal time scales). The study period spanned open- and closed-gate operations at the Delta Cross Channel. Synthesis of field observations and modeling efforts suggest that management operations related to the Delta Cross Channel can strongly affect transport in the Delta by modifying the relative contributions of tidal and riverine flows, thereby changing the junction flow phasing.