Vortex Shedding Regime Research Articles

Energy harvesting from wake-induced vibration of flexible flapper behind a bluff body

Piezoelectric energy harvesting from ambient vibrations offers a promising small-scale energy generation strategy, with wake-induced vibration of flexible structures being an ideal candidate. This study examines a bluff body followed by a fully flexible piezoelectric flapper in a viscous free-stream flow using an in-house discrete forcing immersed boundary method-based fluid-structure-electric energy solver for parametric investigation. Different vortex shedding regimes are identified based on vortex formation around the flexible flapper. The complex and interdependent spatiotemporal dynamics of the wake and flexible body dictated by parameters such as bending rigidity and the gap space between the flapper and bluff body result in various deformation profiles, influencing the strain rate and output power. The study also investigates the independent variation of flapper length and its impact on vortical arrangements and flexibility, introducing different oscillation modes. The present study takes a nuanced view of the overall dynamics and their mutual effect on the power output, unlike most existing studies where enhancing the amplitude and frequency of oscillations for an optimal output was the main concern. Factors such as flapper curvature, its asymmetry, and periodicity have been especially highlighted in the context of the output and the corresponding parametric spaces investigated. Interestingly, the increase in piezo-flapper length has seen a reduction in output, though it was instrumental in bringing symmetry back. The study offers comprehensive insights into ideal harvesting regimes and the underlying dynamical mechanisms and can contribute toward the design of future energy harvesting devices.

High-fidelity numerical simulation of longitudinal thermoacoustic instability in a high-pressure subscale rocket combustor

A detailed analysis of thermoacoustic combustion instability in a subscale rocket combustor at high pressure is reported in this paper using the high-fidelity large-eddy simulation (LES). Self-sustained longitudinal combustion instability is observed in the experiments for this combustor configuration. The computational setup follows the past experimental study of a rig called the Continuously Variable Resonance Combustor (CVRC). In this combustor, both stable combustion and unstable combustion dynamics have been observed by varying the oxidizer injector length. A combustor configuration with an oxidizer injector length of 12 cm is chosen for this study based on the experimental evidence of longitudinal combustion instability. An autonomous meshing using the modified cut-cell Cartesian grid generation approach, coupled with on-the-fly Adaptive Mesh Refinement (AMR) is employed in this study. Chemical reactions during turbulent combustion in this configuration are modeled by solving the species transport equations with a detailed chemistry solver using a kinetic mechanism with 21 species and 84 steps. Similar to the findings of the experiments, we observe a self-sustained combustion instability in the present study, which is characterized by a limit cycle behavior of the acoustic fluctuations. The spectral analysis of these acoustic fluctuations shows good agreement with experimental data for the frequency of the three dominant modes. We further analyze the features of time-averaged and instantaneous reacting flow to study the effects of combustion instability on the flame holding dynamics, vortex shedding, mixing, and combustion regime due to flame movement along the longitudinal direction of the combustor during a limit cycle. These phenomena are effectively captured through the integration of AMR with complex chemistry in the present study. A particular focus of the study is on understanding the role of minor species (OH, HO2, and CH2O) in the physical and state-space in sustaining the flame during the combustion instability. Additionally, the physical mechanisms responsible for the production and dissipation of enstrophy are examined to demonstrate that their contribution can create significant fluctuations in the reacting flow field, which can assist in sustaining the combustion instability.

Arbitrary-order sensitivities of the incompressible base flow and its eigenproblem

First-order sensitivities and adjoint analysis are used widely to control the linear stability of unstable flows. Second-order sensitivities have recently helped to increase accuracy. In this paper, a method is presented to calculate arbitrary high-order sensitivities based on Taylor expansions of the incompressible base flow and its eigenproblem around a scalar parameter. For the incompressible Navier–Stokes equations, general expressions for the sensitivities are derived, into which parameter-specific information can be inserted. The computational costs are low since, for all orders, a linear equation system has to be solved, of which the left-hand-side matrix stays constant and thus its preconditioning can be exploited. Two flow scenarios are examined. First, the cylinder flow equations are expanded around the inverse of the Reynolds number, enabling the prediction of the two-dimensional cylinder base flow and its leading eigenvalue as a function of the Reynolds number. This approach computes accurately the base flow and eigenvalue even in the unstable regime, providing, when executed subsequently, a mean to calculate unstable base flows. This case gives a clear introduction into the method and allows us to discuss its constraints regarding convergence behaviour. Second, a small control cylinder is introduced into the domain of the cylinder flow for stabilization. Higher-order sensitivity maps are calculated by modelling the small cylinder with a steady forcing. These maps help to identify stabilizing areas of the flow field for Reynolds numbers within the laminar vortex shedding regime, with the required number of orders increasing as the Reynolds number rises. The results obtained through the proposed method align well with numerically calculated eigenvalues that incorporate the cylinder directly into the grid.

A strategy of mixed tube bundle to improve anti-deposition performance and heat transfer

Ash deposition is a key issue that limits the energy utilization and safety operation of high-energy-consuming equipment in industrial applications, and the clarification of the heat and mass transfer process under ash deposition is vital. To improve the anti-deposition performance of tube bundles and mitigate heat transfer deterioration, a mixed strategy with attached small cylinders arranged behind the tube has been proposed, which overcomes the difficulties faced by irregular and extended surface tube bundles in manufacturing, cleaning, maintenance, and energy consumption. A CFD model incorporating multiple deposition mechanisms is established to investigate the dynamic deposition behavior, heat transfer characteristics, and comprehensive performance of the tube bundles. In particular, the dynamic growth process of the deposition layer on heat transfer surface in this work is achieved through a dynamic mesh smoothing method based on inverse distance weighting interpolation. Parametric studies are conducted on different arrangements and angles (α = 15° - 65°) of the attached cylinders to obtain the optimal comprehensive performance design. The results show that the attached cylinders suppress the formation and development of the wake vortex caused by the primary tube bundle, significantly enhancing the anti-deposition performance of the tube bundles. The length of vortex evolution increases and the separation point of the boundary layer extends with the angles, leading to a transition of the vortex shedding regime between tube bundles. Compared to the benchmark case, Case 1 exhibits a higher anti-deposition and heat transfer performance, where the deposition mass decreases by 43.98% and the PEC reaches the maximum value of 1.11 at α = 45°, which delivers the best comprehensive performance. The results can provide more realistic predictions for the practical design, operation, and maintenance of thermal equipment.

Effect of topographical pattern on vortex shedding and heat transfer phenomena in power-law fluid flow around a rotating cylinder

The present numerical investigation studies the momentum and heat transfer phenomena from a heated rotating patterned cylinder in the vortex shedding regime. In particular, the effect of surface patterns ( ω , δ ), fluid behavior ( 0.4 ≤ n ≤ 1.6 ), cylinder rotation speed ( 0.5 ≤ α ≤ 2 ), and Prandtl number ( 1 ≤ Pr ≤ 100 ) at Reynolds number 100 on the force coefficients and Nusselt number are studied. Vorticity and isotherm profiles demonstrate the flow dynamics and heat transfer characteristics. According to the findings of this study, the formation of the vortex (including its size, shape, and number of vortices) and the time period during which the vortex shedding pattern repeats itself demonstrates a dependency on the shape of the cylinder, fluid behavior, and rotating speed. It has been noted that a significant decrease in the frequency of vortex shedding occurs on adding topographical patterns. Additionally, it has been noticed that on increasing rotational speed, vortex shedding can be suppressed for all fluid behaviors. Numerical simulation results reveal that the average drag coefficient ( C ¯ D ) for a rotating patterned cylinder decreases with increasing rotational speed ( α ), and it further reduces on increase in pattern frequency ( ω ) and amplitude ( δ ) compared to a smooth circular cylinder. The shear-thinning fluid behavior helps to dissipate the heat from the cylinder to the surrounding fluid. Conversely, shear-thickening fluid behavior exhibits the opposite trend.

Large Eddy Simulation of Flow Characteristics around Cylinders with Crosswise and Streamwise Arrangements in Ocean Energy

The flow around cylinders is one of the most fundamental phenomena in extracting wave energy from ocean waves. Compared with flows around a single cylinder, the investigation of flows around multiple cylinders is still limited and requires further studies to reveal flow characteristics. To this end, large eddy simulations are conducted to investigate the flow around double cylinders with crosswise and streamwise arrangements. Systematic studies on the influence of the number of mesh cells, the first near-wall mesh size, and the transient time step are carried out to achieve accurate and efficient simulations. The drag coefficient, flow separation, and flow pattern for different arrangements under various cylinder spacings are analyzed according to simulation results. For the crosswise arrangement, the flow pattern switches from the single-body regime to the synchronized vortex-shedding regime as the spacing increases. For the streamwise arrangement, the flow pattern develops from the reattachment regime to the vortex-shedding regime as the spacing increases.

Significant influence of fluid viscoelasticity on flow dynamics past an oscillating cylinder

This study focuses on numerically investigating the impact of fluid viscoelasticity on the flow dynamics around a transversely forced oscillating cylinder operating in the laminar vortex shedding regime at a fixed Reynolds number of $Re = 100$ . Specifically, we explore how fluid viscoelasticity affects the boundary between the lock-in and no lock-in regions and the corresponding wake characteristics compared with a simple Newtonian fluid. Our findings reveal that fluid viscoelasticity enables the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than those required for a Newtonian fluid. Consequently, the lock-in region boundary for a viscoelastic fluid differs from that of a Newtonian fluid and expands in the non-dimensional cylinder oscillation amplitude and frequency parameter space. In the primary synchronization region, the wake of a Newtonian fluid exhibits ‘2S’ (two single vortices) and ‘P+S’ (a pair of vortices and a single vortex) shedding modes. In contrast, a ‘2P’ (two pairs of vortices) vortex mode is observed for a viscoelastic fluid within the same region. To gain a deeper understanding of the differences in the coherent flow structures and their associated frequencies between the two fluids, we employ the data-driven reduced-order modelling technique, known as the dynamic mode decomposition (DMD) technique. Utilizing this technique, we successfully extract and visualize the two competing fundamental frequencies (cylinder oscillation and natural vortex shedding frequencies) and their associated flow structures in the case of the no lock-in state, whereas only the dominant cylinder oscillation frequency and associated flow structure in the case of the lock-in state. Furthermore, we propose that the presence of excess strain resulting from the stretching of polymer molecules in viscoelastic fluids leads to a distinct difference in the wake structure compared with Newtonian fluids. This observation aligns with the findings obtained from the $Q$ -criterion and vorticity transport analysis of the wake.

Flow regime identification and flow instability analysis of oscillatory flows over twin circular cylinders

Oscillatory flows past two identical circular cylinders are investigated by two-dimensional direct numerical simulations in the parameter space of gap ratio (0.5 ≤ G ≤ 4.0), angle of flow incidence (0° ≤ α ≤ 90°) and Keulegan–Carpenter number (4 ≤ KC ≤ 12) with a constant Reynolds number Re = 150, where G = L/D, KC = UmT/D and Re = UmD/υ with D being the dimeter of the identical cylinders, L the shortest surface-to-surface distance between the two cylinders, Um and T being the velocity amplitude and period of the sinusoidal oscillatory flow, respectively, and α is defined as the angle between the flow direction to the line connecting the centers of the two cylinders. Comparing with the tandem or side-by-side arrangements of twin circular cylinders in oscillatory flows, the staggered twin cylinders (0° < α < 90°) involve more diverse flow regimes, including the periodic, quasi-periodic and chaotic flow states, due to the inherent asymmetric flow interference around the cylinder pair. In addition to introducing four flow regimes for the tandem and side-by-side arrangements, this study newly identifies 11 flow regimes for the staggered twin cylinders. The newly reported flow regimes in this work are collaboratively identified through the flow visualizations, steady streaming, frequency spectra of fluid forces and Lissajous phase diagrams, as well as the temporal-spatial symmetry features of the wake flows. Connecting with the previous work by Zhao and Cheng [“Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers,” J. Fluid Mech. 751, 1–37 (2014)], this study presents overall regime maps in the KC-α plane for varied gap ratios. It is found that the flow regimes previously and presently identified for the tandem and side-by-side arrangements may also appear for the staggered twin cylinders. The present numerical results suggest the sensitive dependence of the flow regimes on the parameters of KC, α, and G. It is also found that a specific flow regime with narrow parameter bands may appear within another flow regime, forming the abnormal regime hole in the regime map. To understand the profound influence of the control parameters on the flow regime transition, and the relevant temporal-spatial symmetry breaking, the linear Floquet stability analysis is conducted in this work. It was confirmed that the variation of the KC number may result in the Ky symmetry breaking over several periodic flow regimes, while the change of the angle of flow incidence may account for the H2 symmetry covering various periodic and quasi-periodic flow regimes. The stability analysis also explains the temporal flow transition and the abnormal occurrence of the regime holes within either quasi-periodic or chaotic flow regimes.

Suppression of vortex shedding in the wake of a circular cylinder through high-frequency in-line oscillation

This paper presents a new flow control approach to suppress the vortex shedding in the wake of a circular cylinder through high-frequency oscillation. The circular cylinder is forced to oscillate in the streamwise direction at high-frequency and low amplitude, corresponding to a high Stokes number (β = 100–1000) and low Keulegan–Carpenter number (KC = 0.001–4). Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations of an oscillating circular cylinder in steady current have been carried out in the parameter space of KC, Rec, and β. Our numerical results show that when the flow remains in the two-dimensional vortex shedding regime, the cylinder wake sequentially experiences transitions from the vortex shedding regime to the suppression of the vortex shedding regime and finally to the symmetry breaking regime, with increasing KC. Corresponding wake characteristics and variations of hydrodynamic forces over the three wake regimes are explored. Three quantities that represent shear-layer characteristics, including the length of separating shear layers, the circulation of shear layers and wake recirculation length, reach maxima at the onset of suppression. The physical mechanisms for the suppression of vortex shedding and occurrence of symmetry breaking are also explained. Once the flow becomes 3-D, vortex shedding from the cylinder cannot be suppressed, primarily because the outer shear layers induced by the steady approaching flow are enhanced in 3-D flows. The cylinder oscillation over the frequency range investigated in the present study delays wake transition to 3-D. The cylinder oscillation alters the 3-D vortical structure and its spanwise wavelength significantly.

Integrated Numerical Investigation on the Aerodynamics Characteristic and Vortex Development of Airfoil using Spalart-Allmaras Model

In this paper, the numerical simulation successfully obtained good results in analyzing fluid flow over the airfoil. Detailed explanations of simulation steps were also presented. The flow characteristics over three airfoil models were numerically simulated in this work: NACA0021, NACA2409, NACA2409+Fowler flap. The reliable Spalart-Allmaras (S-A) turbulent model was used and validated using reported data from experimental in terms of lift and drag coefficients. In this regard, the discrepancies of less than 10% were obtained for both coefficients, respectively. The boundary layer separation, vortex development, and air separation were clearly captured. The results of symmetric airfoil showed that the vortex shedding regimes occurred at α = 8o, and the stall critical-angle was about 14o. The value was higher for the NACA2409, where the airflow exhibited a relatively more stable behavior. Moreover, it is evident that flap addition altered lift-drag characteristics. The value of the lift-to-drag ratio increased due to the increase of Cl and the reduction of Cd. The parametric study was done on the α and flap deflection angle to attain the desirable airfoil configuration. The maximum result of airfoil configuration was obtained on the NACA2409 at α = 12o with 100 flap deflection angle while it enhanced the lift coefficient by about 54%. This result strengthens the robustness of the S-A turbulence model and projects the use of the S-A model for dealing with the aerodynamics analysis. This study is beneficial for initial aircraft design on the aerodynamics aspect of a wing.

Flow structures around a circular cylinder with bilateral splitter plates and their dynamic characteristics

Flow structures around a circular cylinder with bilateral splitter plates and their dynamic characteristics are numerically investigated at a low Reynolds number of 100. The two splitter plates with the same length as the half of cylinder diameter are symmetrically placed beside the cylinder. In this work, three gap ratios of G/D = 0, 0.5 and 1.0 (G is the gap distance between the cylinder surface and the near end of plate, D is the diameter of circular cylinder) and inclination angle (α, between splitter plate and wake centerline) ranging from 0° to 90° are examined. According to flow characteristics, five vortex shedding regimes are identified, including "2S" (two vortices are alternatively shed per cycle) regime, single-sided regime, wake-flapping regime, steady regime and irregular regime. Apart from the main vortices, some special vortices such as subordinate vortices, tip vortices and persisted vortices are recognized. Additionally, local "2S″ and "4S" (four vortices are shed per cycle) regimes are observed behind the cylinder and the plates, respectively. The dynamic mode decomposition (DMD) results show that the first mode possesses the majority of energy of the flow field. As α increases, the splitter plates contribute to the lift reduction, especially when a gap is introduced. By contrast, the bilateral plates lead to a significant growth in the drag coefficient when α ≥ 15°.

Vortex-induced vibration of a circular cylinder with nonlinear restoring forces at low-Reynolds number

The numerical simulation of two-dimensional flows around an elastically-mounted circular cylinder on a linear/quadratic spring configuration at low-Reynolds number (Re) is conducted in order to study the vortex-induced vibration (VIV) of the system. The extent of Re used in this study range from 50 to 150 inclusive. The data obtained from the numerical simulations are used to investigate the impact of the nonlinearity in the spring configuration on the VIV response of the dynamical system. The equivalent natural frequency for a circular cylinder supported elastically on a linear/quadratic spring is derived and found to depend on the square root of the maximum amplitude of the transverse displacement. The range of Re associated with the initial branch of the response is increased (extended) and the upper and lower branches are suppressed (almost disappearing when the hardening nonlinearity is sufficiently strong) for an elastically-mounted cylinder on a linear/quadratic spring configuration compared to that for the same cylinder supported elastically on a linear spring. The detailed characteristics (e.g., vortex shedding modes, amplitude and oscillation frequency of the transverse displacement, etc.) of the lock-in range and the transition out of this range for the VIV system as a function of increasing Re is studied using power spectrum, phase portrait and dynamical mode decomposition analysis. The information obtained from the analysis is synthesized in order to investigate the different physical mechanisms and phenomena appearing in the VIV system and how these are linked to the underlying vortex shedding and amplitude response regimes (initial branch, upper branch, desynchronization branch) of the dynamics of the fixed (stationary) and elastically-mounted cylinder.

Dynamic mode decomposition analysis and fluid-mechanical aspects of viscoelastic fluid flows past a cylinder in laminar vortex shedding regime

This study presents an extensive numerical investigation to understand the effect of fluid viscoelasticity on the flow dynamics past a stationary cylinder in the laminar vortex shedding regime. The governing equations, namely, mass, momentum, and Oldroyd-B viscoelastic constitutive equations, have been solved at a fixed value of the Reynolds number of 100 and over a range of values of the Weissenberg number as 0≤Wi≤2 and polymer viscosity ratio as 0.5≤β≤0.85. In particular, for the first time, this study presents a detailed analysis of how the fluid viscoelasticity influences the coherent flow structures in this benchmark problem using the dynamic mode decomposition (DMD) technique, which is considered to be one of the widely used reduced order modeling techniques in the domain of fluid mechanics. We show that this technique can successfully identify the low-rank fluid structures in terms of the spatiotemporal modes from the time-resolved vorticity field snapshots and capture the essential flow features by very few modes. Furthermore, we observe a significant difference in the amplitude and frequency associated with these modes for Newtonian and viscoelastic fluids otherwise under the same conditions. This, in turn, explains the differences seen in the flow dynamics between the two types of fluids in an unambiguous way, such as why the fluid viscoelasticity suppresses the vortex shedding phenomenon and decreases the energy associated with the velocity fluctuations in viscoelastic fluids than that in Newtonian fluids. However, before performing the DMD analysis, we also present a detailed discussion on the various fluid-mechanical aspects of this flow system, such as streamline patterns, vorticity fields, drag and lift forces acting on the cylinder, etc. This will ultimately set a reference platform for delineating the importance of the DMD analysis to get further insight into flow physics.

Spatiotemporal dynamics of a vortex induced vibration system in the presence of stochastic inflow fluctuations

In this study, influence of stochastic parametric inflow on the spatiotemporal dynamics of a vortex induced vibration system has been examined. The study has been carried out using an incompressible Navier–Stokes based flow solver at a Reynolds number of 100, and it highlights the role of stochastic fluctuations/noise in triggering complex spatiotemporal dynamics in the laminar vortex shedding regime. Wavelets and space–time plots were used to analyse the spatiotemporal data. Noise has been seen to advance the instability regime and alter the frequency characteristics of the response by exciting additional system frequencies, which in turn affects the phase dynamics as well. The study has also revealed that the time scale of the input is an important factor in deciding the dynamics. A short time-scaled noise can trigger aperiodic dynamics, whereas, a long time-scaled input invokes switch states or intermittent states. Noise affects the separation behaviour of the near-field vortices by delaying or advancing it, depending on the regime of operation. For the long time-scaled case, the flow-field becomes a combination of strong or weak von Kárman streets and transitionally disordered wakes. With the short time-scaled noise, the flow-field is predominantly disordered and characterised by phenomena such as vortex pairing and deflected wakes.

Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.

Characteristics of vortex shedding from a sinusoidally pitching hydrofoil at high Reynolds number

This experimental study characterizes vortex shedding from a sinusoidally pitching hydrofoil at high Reynolds number, reveals the effects of pitching amplitude, reduced frequency, and Reynolds number on the dynamic force responses beyond the linear inviscid theory, and sheds light on the correlation between vortex shedding regimes and dynamic force responses for a high Reynolds number pitching hydrofoil.

Numerical investigation of the effect of triangular cavity on the unsteady aerodynamics of NACA 0012 at a low Reynolds number

Time accurate numerical simulations were conducted to investigate the effect of triangular cavities on the unsteady aerodynamic characteristics of NACA 0012 airfoil at a Reynolds number of 50,000. Right-angled triangular cavities are placed at 10%, 25% and 50% chord location on the suction and have depths of 0.025c and 0.05c, measured normal to the surface of the airfoil. The second-order accurate solution to the RANS equations is obtained using a pressure-based finite volume solver with a four-equation transition turbulence model, γ–Re θt, to model the effect of turbulence. The two-dimensional results suggest that the cavity of depth 0.025c at 10% chord improves the aerodynamic efficiency ( l/d ratio) by 52%, at an angle of attack of α = 8°, wherein the flow is steady. The shallower triangular cavity when placed at 25%c and 50%c enhances the l/d ratio by only 10% and 17%, respectively, in the steady-state regime of angles of attack between α = 6° and 10°. The deeper cavity also enhances the l/d ratio by up to 13%, 22% and 14% at angles of attack between α = 6° and 10°. Even in the unsteady vortex shedding regime, at α =12° and higher, significant improvements in the time-averaged l/d ratios are observed for both cavity depths. The improvements in l/d ratio in the steady-state, pre-stall regime are primarily because of drag reduction while in the post-stall, unsteady regime, the improvements are because of enhancements in time-averaged C l values. The current finding can thus be used to enhance the aerodynamic performance of MAVs and UAVs that fly at low Reynolds numbers.

Computational fluid dynamics simulations of unsteady mixing in spacer-filled direct contact membrane distillation channels

Direct contact membrane distillation (DCMD) is a promising means of concentrating brines to their saturation limit. During that process, membrane spacers play a key role in temperature polarization, concentration polarization, and mineral scaling. These interactions are not well understood, because they are difficult to study experimentally and numerically, and the flow regimes are not fully charted. We consequently develop a tailored in-house CFD code that simulates unsteady two-dimensional heat and mass transport in plate-and-frame DCMD systems with cylindrical spacers. The code uses a combination of finite-volume methods in space, projection methods in time, and recent advances in immersed boundary methods for the spacer surfaces. Using the code, we explore how the transition to unsteady laminar vortex shedding affects polarization and permeate production of DCMD systems. We show that the impact of spacers can be explained by examining the various steady and unsteady vortical flow structures generated in the bulk and near the membranes. Overall, we show that though unsteady vortex structures tend to mix temperature polarization layers with the bulk, they are not similarly able to mix the concentration layers. Rather, vortical structures tend to create regions of preferential salt accumulation. In the vortex shedding regime, the net result is that spacers often increase vapor production at the expense of increasing the risk of mineral scaling.

Transition to turbulence as a result of chaotic distortion of vortex shedding

Abstract The equations of multimoment hydrodynamics supplemented with stochastic terms are used for numerical simulation of chaotic distortion of regular regimes in the problem on flow around a solid sphere. The influence of disordered perturbations arising in the medium due to external influences is investigated. The loss of stability is accompanied by a qualitative change in the behavior of flow. Each perturbation forces the unstable flow to behave purely individually. The possibility of interpreting each of the unstable flows in terms of some average hydrodynamic values passes away. This behavior is called the butterfly effect. Independence in the behavior of disordered perturbations disappears. Conservation laws force disordered perturbations to adapt their behavior in time and space to the behavior of hydrodynamic values. A change in the behavior of disordered perturbations leads to chaotic distortion of both the regular flow in the recirculating zone and the regular regime of vortex shedding. Distortion of regular regimes creates a turbulent flow pattern in the wake behind the sphere. Vortex shedding is called the regular component of turbulence. Disordered perturbations are called the chaotic component of turbulence. The loss of stability is responsible for the growth and accumulation of disordered perturbations in the wake behind the sphere.

Lagrangian interpolation algorithm for PIV data

A new Lagrangian based interpolation scheme is proposed for recovering velocity field data from within masked regions in particle image velocimetry (PIV) experiments. As a first step, the mean field within the masked region is filled through an iterative convolution operation using an optimized kernel. Next, the Lagrangian interpolation scheme estimates velocity field data within the masked region using a weighted average of past and future snapshot data along a mean field streamline from outside of the masked region. The Lagrangian interpolation scheme is compared directly with a traditional bilinear interpolation approach for two datasets: the flow development over a circular cylinder within the laminar vortex shedding regime (ReD=150) and turbulent vortex shedding regime (ReD=3000). The results show that for both Reynolds numbers investigated, the Lagrangian approach provides up to a 5× improvement in average velocity reconstruction error. Application of the proposed interpolation scheme to the estimation of body forces was assessed. For both the momentum and impulse control volume approaches to estimate instantaneous forces, the Lagrangian interpolation scheme provides up to 10× improvement in the estimation of volume integral contributions to instantaneous drag and lift.