Steady Flow Regime Research Articles

Predicting the passive control of fluid forces over circular cylinder in a time dependent flow using neuro-computing

The objective of this research is to combine Artificial Neural Networks (ANNs) and Computational Fluid Dynamics (CFD) approaches to leverage the advantages of both methods. To achieve this goal, we introduce a new artificial neural network architecture designed specifically for predicting fluid forces within the CFD framework, aiming to reduce computational costs. Initially, time-dependent simulations around a rigid cylinder and a passive device (attached and detached) were conducted, followed by a thorough analysis of the hydrodynamic drag and lift forces encountered by the cylinder and passive device with various length L=0.1,0.2,0.3 and gap spacing Gi=0.1,0.2,0.3. The inhibition of vortex shedding is noted for gap separations of 0.1 and 0.2. However, a splitter plate of insufficient length or placed at an unsuitable distance from an obstacle yields no significant benefits. The finite element method is employed as a computational technique to address complex nonlinear governing equations. The nonlinear partial differential equations are spatially discretized with the finite element method, while temporal derivatives are addressed using a backward implicit Euler scheme. Velocity and pressure plots are provided to illustrate the physical aspects of the problem. The results indicate that the introduction of a splitter plate has reduced vortex shedding, leading to a steady flow regime, as evidenced by the stable drag and lift coefficients. The data obtained from simulations were utilized to train a neural network architecture based on the feed-forward backpropagation algorithm of Levenberg–Marquardt. Following training and validation stages, predictions for drag and lift coefficients were made without the need for additional CFD simulations. These results show that the mean square error values are very close to zero, indicating a strong correlation between the fluid force coefficients obtained from CFD and those predicted by the ANN. Additionally, a significant reduction in computational time was achieved without sacrificing the accuracy of the drag and lift coefficient predictions.

Effects of offset jet width on periodic flow in a dual jet

The primary aim of this work is to investigate the impact of the offset jet width on the unsteady flow characteristics of a turbulent dual jet, which consists of a wall jet and an offset jet. A computational fluid dynamics code is developed to solve the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. The width of the offset jet is varied while keeping the width of the wall jet constant at the separation distance between the two jets. When the ratio of the offset jet width (w) to the separation distance (d) is w/d=0.5, the flow field exhibits a periodic vortex shedding phenomenon. Conversely, when w/d=0.4, the flow field remains steady. The shedding phenomenon is discernible even when w/d=2. The instantaneous velocity components display sinusoidal oscillations at 0.5≤w/d≤2. Applying the fast Fourier transform to these sinusoidal signals yields a distinct frequency peak at the vortex shedding frequency. Within the range of 0.5≤w/d≤2, the shedding frequency decreases as the width of the offset jet increases. This trend continues until it reaches a constant value at w/d=1.4. This indicates that the width of the offset jet has a notable influence on the shedding phenomenon within the range of 0.5≤w/d≤1.4. For 1.4<w/d≤2, the shedding frequency remains unaffected by the offset jet width variation. Depending on the value of w/d, the shedding phenomenon is characterized by three flow regimes: a steady flow regime (forw/d≤0.4), an outer share layer-influenced shedding regime (for w/d=0.5−1.4), and an outer shear layer-free shedding regime (for w/d>1.4).

Effect of the Womersley number on transition to turbulence in pipe flow: An experimental study

The mechanisms driving the transition to turbulence in pulsatile flows are not well understood. Prior studies in this domain have noted the dynamics of this flow regime to depend on the mean Reynolds number, pulsation frequency (i.e., Womersley number), and inflow pulsatile waveform shape. Conflicting findings, particularly regarding the role of the Womersley number on the critical Reynolds number and the development of turbulence, have been reported. The discord has primarily been observed for flows, with Womersley numbers ranging from 4 to 12. Hence, in this work, we use particle image velocimetry to explore the effects of the Womersley number within this 4–12 range on the dynamics of the pulsatile transition. Eighteen test cases were captured using six mean Reynolds numbers (range 800–4200) and five Womersley numbers. Turbulent kinetic energy, turbulence intensity (TI), and phase lag were computed. Our results indicated that the critical Reynolds number was roughly independent of the Womersley number. At high Womersley numbers, the TI trend maintained lower pulsatility, and the flow was observed to mimic a steady transitional flow regime. A plateau of the TI-velocity and TI-acceleration phase lag was observed at a Womersley number of 8, highlighting that this may be the critical value where further increases to the Womersley number do not alter the transition dynamics. Furthermore, this suggests that the phase lag may provide a universal indicator of the specific influence of the Womersley number on transition for a given flow. Overall, these findings elucidate critical details regarding the role of the Womersley number in the transition to turbulence.

Effect of a fixed downstream cylinder on the flow-induced vibration of an elastically supported primary cylinder

This paper numerically investigates the influence of a fixed downstream control cylinder on the flow-induced vibration of an elastically supported primary cylinder. These two cylinders are situated in a tandem arrangement with small dimensionless center-to-center spacing (L/D, L is the intermediate spacing and D is the cylinder diameter). The present two-dimensional (2D) simulations are carried out in the low Reynolds number (Re) regime. The primary focus of this study is to reveal the underlying flow physics behind the transition from vortex-induced vibration to galloping in the response of the primary cylinder due to the presence of another fixed downstream cylinder. Two distinct flow field regimes, namely, steady flow and alternate attachment regimes, are observed for different L/D and Re values. Depending on the evolution of the near-field flow structures, four different wake patterns, “2S,” “2P,” “2C,” and “aperiodic,” are observed. The corresponding vibration response of the upstream cylinder is characterized as interference galloping and extended vortex-induced vibration. As the L/D ratio increases, the lift enhancement due to flow-induced vibration is seen to be weakened. The detailed correlation between the force generation and the near-wake interactions is investigated. The present findings will augment our understanding of vibration reduction or flow-induced energy harvesting of tandem cylindrical structures.

Identifying steady and pulsatile two-phase flow regimes with pressure drop signals and acoustic emissions

Identifying two-phase flow regimes is vital for understanding phase-change heat and mass transfer processes. Traditionally, flow regime identification has relied on subjective flow visualization studies, which are then converted to flow regime maps applicable to specific operating conditions. However, these conventional, largely subjective, maps fall short in predicting abrupt changes in flow patterns that often occur during regular operation of vapor compression and absorption heat pumps and other thermal systems. Conventional flow regime maps are also inadequate for addressing the transient, intermittent, or periodic flow regimes that occur in boiling and condensation enhanced using acoustic and other emerging techniques. Therefore, there is a pressing need for alternative flow regime identification techniques that can adapt and reliably track rapid and local changes in two-phase hydrodynamics. Promising candidates for dynamic flow pattern classification include high-resolution pressure drop signals and acoustic emission spectra, which can provide insights into the local hydrodynamics within a flow channel. To assess the feasibility of these measurement techniques, differential pressure and condenser microphone measurements are recorded alongside high-speed videos of a two-phase flow of saturated R134a. The total mass flux and vapor quality are varied to understand the effects of phase velocity and liquid inventory on wave propagation in the channel. Additionally, forced oscillations are introduced to a steady two-phase flow to analyze their impact on flow patterns and their corresponding pressure drop and acoustic signals. Statistical analyses, including Gaussian mixture modeling, are employed to reveal characteristic pressure drop probability associated with each flow pattern, which form the basis for developing a model capable of predicting flow regimes in both steady and oscillating flows. The resulting framework introduces a new flow regime identification technique that can adapt to dynamic operating conditions, benefiting a wide range of thermal systems and phase-change processes.

Fluid structure interaction problem for flow past three unequal sized square cylinders at different Reynolds numbers

The flow past three square cylinders of unequal size placed in an inline arrangement is studied using the lattice Boltzmann method at different Reynolds numbers [Re = (u∞ d)/ν] within the range of Re = 120, 150, 160, 175, and 200 for various gap spacings (g = s/d), ranging from 1 to 6. This study focused on the symmetric examination of flow behavior for various gap spacing within the three unequal-sized square cylinders. The main objective of this study was to investigate the effects of Reynolds numbers and gap spacing for flow structure mechanism and vortex shedding suppression in between the gap and down-stream position of all three cylinders. Results are obtained in terms of vorticity contours visualization, drag and lift coefficients, Strouhal number, and physical parameters. In vorticity contour visualization, different flow behaviors are observed, known as flow regimes, and are named according to their characteristics, and they are (i) steady flow regime, (ii) shear layer reattachment flow regime (SLR), (iii) fully developed vortex shedding flow regime, (iv) two-row fully developed vortex shedding flow regime, and (v) fully developed irregular vortex shedding flow regime. The present study also includes a discussion on aerodynamic forces, namely the mean drag coefficient (Cdmean), root mean square of the lift coefficient (Clrms), and Strouhal numbers (St) for three cylinders with sizes d = 20, d1 = 15, and d2 = 10, respectively. The maximum value of Cdmean for the first cylinder (C1) is obtained at (Re, g) = (200, 3) that is, 1.5156, where the existing flow regime is the SLR flow regime, while for C2 and C3, the maximum Cdmean values are examined at critical flow behaviors, where the existing flow regime is a fully developed irregular vortex shedding flow regime. Negative values of Cdmean are also examined for cylinders C2 and C3 at some combinations of (Re, g), attributed to the effect of thrust. Furthermore, it is noticed that the values of Strouhal number are increased with an increment in values of gap spacing. The highest value of the Strouhal number for all three cylinders is observed for C1 at (Re, g) = (120, 5), reaching 0.1556 along with a two-row fully developed flow regime. Furthermore, it is investigated from the present problem that the position of unequal sized square cylinders strongly influenced the flow structure mechanism. The information found and discussed in this study could be effective for structure designing arrangement in the case of three square cylinders of unequal size placed in a horizontal arrangement.

On the laminar wake of curved plates

Numerical simulations are performed to investigate the effect of the Reynolds number (Re) on flow over curved plates. Concave and convex plates, obtained by introducing curvature on a flat plate, are analyzed in the Reynolds number range 0.1 ≤Re≤ 120. It is observed that for a concave plate, the separation point is dependent on Re, while for a convex plate, the flow separates from the outermost tips for all Reynolds numbers. The analysis of time-averaged quantities reveals that concave and convex plates behave differently for the same Reynolds number. In the steady flow regime, visualization of streamlines reveals the presence of a recirculation bubble on the front side of the concave plate, even for the lowest Reynolds number (Re = 0.1). However, at higher Reynolds numbers (Re = 110, 120), the near wake of concave plate witnesses secondary and tertiary recirculating entities. The present simulations also report the unique phenomenon of vortex realignment and divergence of vortex street in the wake of a concave plate. For a convex plate, the vortex realignment is followed by the movement of upper and lower vortices as two parallel vortex streets. The existence of multiple instabilities is another highlight in the near and far wakes of the concave plate, some of which arise due to the secondary vortex interactions. A comprehensive analysis further reveals a handful of novel phenomenal occurrences in the wake of concave surfaces.

The wake characteristics and hydrodynamic forces of a near-wall circular cylinder with the splitter plate

Flow around a near-wall circular cylinder with the splitter plate is numerically performed at Reynolds number of 500, with the objective of investigating the wake characteristics and hydrodynamic forces. Five gap ratios [Formula: see text] and [Formula: see text] (G is the gap between the lower surface of the cylinder and the wall, D is the diameter of the cylinder) are selected, and the splitter plate length [Formula: see text] ranges from 0 to [Formula: see text]. The flow characteristics of an isolated cylinder with the splitter plate are investigated first for comparison, and four wake flow modes are observed, which include 2S mode ([Formula: see text]), P+S mode ([Formula: see text]), 2S+S mode ([Formula: see text]) and 2P mode ([Formula: see text]). As [Formula: see text] increases from 0 to [Formula: see text], the mean drag coefficient ([Formula: see text]) is decreased, and there is a slight increase of [Formula: see text] for [Formula: see text]. In addition, the cases of [Formula: see text] and [Formula: see text] produce a very significant reduction of drag, and the [Formula: see text] is reduced by as much as [Formula: see text] and [Formula: see text], respectively. The wake characteristics and hydrodynamic forces of a near-wall cylinder with the splitter plate are investigated in detail, and five wake regimes are observed, which include the wake vortex merging regime I, merged vortex attaching regime II, steady flow regime III, wall shear layer elongation regime IV and upper shear layer attaching regime V. For [Formula: see text], the wake vortex shedding is suppressed. For [Formula: see text], the Strouhal number (St) is decreased as [Formula: see text] increases from 0 to 1.0, and there is an increase of St at [Formula: see text]. At [Formula: see text], the St of the near-wall cylinder is larger than that of the isolated cylinder, and the increase in St is affected by the deflected gap flow. What is more, the hydrodynamic characteristics are affected by the wall. For [Formula: see text], the variations of [Formula: see text] with [Formula: see text] are similar to that of the isolated cylinder. It is found that the cases of [Formula: see text] and [Formula: see text] still produce a significant reduction of drag for [Formula: see text], and the [Formula: see text] is increased for all cases of [Formula: see text] as [Formula: see text] increases.

Modeling liquid rate through wellhead chokes using machine learning techniques

Precise measurement and prediction of the fluid flow rates in production wells are crucial for anticipating the production volume and hydrocarbon recovery and creating a steady and controllable flow regime in such wells. This study suggests two approaches to predict the flow rate through wellhead chokes. The first is a data-driven approach using different methods, namely: Adaptive boosting support vector regression (Adaboost-SVR), multivariate adaptive regression spline (MARS), radial basis function (RBF), and multilayer perceptron (MLP) with three algorithms: Levenberg–Marquardt (LM), bayesian-regularization (BR), and scaled conjugate gradient (SCG). The second is a developed correlation that depends on wellhead pressure (Pwh), gas-to-liquid ratio (GLR), and choke size (Dc). A dataset of 565 data points is available for model development. The performance of the two suggested approaches is compared with earlier correlations. Results revealed that the proposed models outperform the existing ones, with the Adaboost-SVR model showing the best performance with an average absolute percent relative error (AAPRE) of 5.15% and a correlation coefficient of 0.9784. Additionally, the results indicated that the developed correlation resulted in better predictions compared to the earlier ones. Furthermore, a sensitivity analysis of the input variable was also investigated in this study and revealed that the choke size variable had the most significant effect, while the Pwh and GLR showed a slight effect on the liquid rate. Eventually, the leverage approach showed that only 2.1% of the data points were in the suspicious range.

Inflow Conditions and the Flow Behavior of Submerged Annular Viscoplastic Non-Newtonian Jets

Abstract Submerged annular viscoplastic jet flows were studied numerically within the steady laminar flow regime. The impacts of inner-to-outer annular nozzle diameter ratio, and yield number, for uniform and fully-developed inflow conditions, were investigated. The extent of the outer recirculation region and recirculation intensities of both the central and outer regions were found to substantially diminish with the yield number, resulting in the elimination of recirculation throughout the whole flow field at high yield numbers. The axial penetration of the jet decreases with both the yield number and the annular diameter ratio. The impact of inflow conditions on the flow structure and decay characteristics of the jet are more pronounced at low yield numbers.

An Investigation on the Steady and Unsteady Wake Flow Regimes and Aerodynamic Characteristics of the Trapezoidal Cylinders Using Immersed Boundary-Lattice Boltzmann Method

Abstract In this study, the flow physics of the forward-facing (FF) and backward-facing (BF) trapezoidal cylinders (TC) subjected to two-dimensional, incompressible, and laminar flow is investigated using an in-house developed flexible forcing immersed boundary-lattice Boltzmann solver. The Reynolds number (Re) is defined based on the cylinder's characteristic length D. For the steady and unsteady flow regimes, Re is varied in the ranges of 10–40 and 75–125, respectively. The TCs shape is varied by modifying its nondimensional axial H/D and transverse Y/D length scales, between 0.5 to 2 and 0 to 1, respectively. Here, TCs horizontal central axis is always aligned along the incoming flow direction. It is observed that the flow separation points on the FF-TC and BF-TC are strongly influenced by the geometric (H/D and Y/D) and flow parameters (Re). Based on the boundary layer separation point, we have categorized the wake flow regimes behind the FF-TC and BF-TC into four types. In addition, the effect of the geometric and flow parameters on the drag coefficient (Cd), vortex shedding frequency, and steady and unsteady wake characteristics are thoroughly investigated here. Furthermore, by performing nonlinear regression analysis, we have proposed a set of correlation equations for the Cd and Strouhal number (St), using which the aerodynamic characteristics of differently shaped TC can be derived in the considered Re range without performing rigorous numerical simulations or experiments.

Effect of fluid elasticity and shear thinning on heat transfer from a heated sphere at moderate Reynolds numbers

The drag and heat transfer characteristics of an isothermal sphere in a FENE-P-type viscoelastic fluid have been studied in the steady axisymmetric flow regime. The governing equations, namely, mass, momentum, and energy equations, together with FENE-P type viscoelastic constitutive equations, have been solved using the finite volume method based opensource CFD code OpenFOAM over the following ranges of conditions: Reynolds number, 1 ≤ Re ≤ 100 ; Prandtl number, 1 ≤ Pr ≤ 50 ; Weissenberg number, 0 ​ ≤ Wi ≤ 10 and polymer extensibility parameter, 10 ≤ L 2 ≤ 500 for a fixed value of the polymer viscosity ratio of β = 0.5 . At low Reynolds numbers, fluid viscoelasticity causes an upward and downward shifting in the axial velocity profiles with reference to that in a Newtonian fluid along the upstream and downstream axis of the sphere, respectively. However, such a shift progressively diminishes with the increasing Reynolds number. Furthermore, a “velocity overshoot” and/or a “negative wake” is also observed in a viscoelastic polymer solution at low Reynolds numbers, and this is accentuated with the increasing Weissenberg number. The separation of boundary layers is seen to be suppressed with the increasing Weissenberg number. The drag coefficient decreases with the Reynolds number irrespective of the fluid type and the corresponding dependence on the Weissenberg number is found to be non-monotonic depending upon the values of Re and L 2. The average Nusselt number always increases with the increasing values of Re, Pr, and Wi and with the decreasing value of L 2. A limited number of simulations have also been carried out to show the effect of the temperature-dependent viscosity of the fluid on the flow dynamics and heat transfer characteristics. Finally, simple correlations for the drag coefficient and average Nusselt number are presented which not only capture the functional dependence but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.

Storm-driven sedimentation and dynamics of a sediment slug in an ephemeral stream: Influence on sediment-routing systems within source areas

Abstract Stream-terrace morphostratigraphy and optically stimulated luminescence (OSL) geochronology indicate that storm-driven sedimentation has caused down-system decoupling of the uppermost reaches of McMillan Creek (southern California, USA) from the lower reaches of McMillan Creek since 1960 ± 190 yr B.P. This is significant because source-to-sink studies report high degrees of sediment transport connectivity over millennial time scales during periods of high fluvial discharge in sediment routing systems. The most recent relatively large-magnitude episode of sedimentation emplaced a sediment slug in the ephemeral channel of McMillan Creek. The sediment slug is correlated to the “California Storm of January 1862” via OSL dating. In this paper, a conceptual model of sediment slug dynamics in an ephemeral stream over 16 decades is developed based on fluvial sedimentation events that in most instances included reworking slug-derived sediment. Due to the episodic nature of streamflow in ephemeral streams and the dearth of sediment transport between streamflow events, sediment slug coherency is sustained over longer periods of time in ephemeral streams than in perennial streams having steady or variable flow regimes. The longevity of sediment-slug coherency in ephemeral streams leads to more prolonged down-system decoupling in sediment routing systems than down-system decoupling caused by ordinary fluvial sedimentation. In McMillan Creek, it is possible that up-system decoupling driven by sedimentation has been contemporaneous with down-system decoupling, but factors other than sedimentation may have a more significant role in up-system decoupling. Source-to-sink studies completed in areas having a Mediterranean climate cannot assume that sediment flux out of upland source areas includes the total amount of sediment available for transport.

Improved Vanadium Redox Flow Battery Performance through a Pulsating Electrolyte Flow Regime

The increase in emissions of greenhouse gases and their environmental impact lead to a transition from primarily fossil fuel-based energy sources to renewable and eco-friendly ones, such as solar panels and wind turbines. However, these sources are intermittent, resulting in fluctuating energy production levels that require buffering, which poses significant challenges in matching production-consumption profiles. [1,2] In order to stabilise the grid and reduce dependency on fossil fuels, integrating electrical energy carriers into a smart grid to store excess energy produced during peak periods and employ it during periods of low production is a potential solution. Redox flow batteries hold promise in this regard, as the storage capacity can be decoupled from the battery size, enabling capacity to be scaled independently of power output by increasing the volume of the electrolyte. [3] In contrast to conventional secondary battery types, such as lead-acid or lithium-ion batteries, the electrolyte in a redox flow battery is non-stationary, inducing convective mass transport effects that are critical for achieving a high power output.In this work we introduced pulsations to the electrolyte flow of an all-vanadium redox flow battery, leading to a reduced stagnant boundary layer attributed to shear forces. Previously, Pérez-Gallent et al. demonstrated that the conversion can be increased by a factor of two while selectivity gains of 15-20% can be made in a electrolyser by introducing a pulsating flow. [4] Furthermore, Vranckaert et al. studied a pulsating flow combined with pillar field electrodes, using the well-known ferri-ferrocyanide redox couple, and concluded that the average limiting current density can be increased fourfold compared to working with a conventional steady state flow regime. [5] Overall, a pulsating flow behaviour yields an enhanced mass transfer of electroactive species by increasing the local velocity through pulsations. The net residence time of the reactants remains unchanged since the pulsating flow has no influence on the overall flow velocity. However, the resulting improvement of mass transfer leads to an increase in conversion. As it is clear that mass transfer enhancement strategies open the door for more efficient systems, our work will for the first time focus on the influence of a pulsating electrolyte flow on the redox flow battery performance. The results show a significant improvement: the discharge capacity at 100 mA/cm2 increased by 38.7% when applying a pulse with pulse amplitude (PA) 0.4ml and pulse frequency (PF) 2.4 Hz at a flow rate of 5 ml/min (Figure 1 A). Furthermore, this 38.7% increase in discharge capacity surpassed the performance achieved at a constant steady-state flow of 25 ml/min. Therefore, a fivefold reduction of the net flow rate is possible without performance losses, decreasing necessary pumping costs. When regarding the stability of an all-vanadium redox flow battery operated with a pulsating electrolyte flow initial fluctuations of the current efficiency (CE), voltage efficiency (VE) and energy efficiency (EE) were recorded. However, the efficiencies became stable at 98.4%, 70.5% and 69.4% respectively, showing no decline over time (Figure 1 B). This novel and improved redox flow battery system allows to take the next step towards integrating electrical energy carriers into a smart grid suitable for renewable and green energy sources.[1] P. D. Lund, J. Lindgren, J. Mikkola, J. Salpakari, Renew. Sustain. Energy Rev. 2015, 45, 785–807.[2] H. Kondziella, T. Bruckner, Renew. Sustain. Energy Rev. 2016, 53, 10–22.[3] E. Sánchez-Díez, E. Ventosa, M. Guarnieri, A. Trovò, C. Flox, R. Marcilla, F. Soavi, P. Mazur, E. Aranzabe, R. Ferret, J. Power Sources 2021, 481, 228804.[4] E. Pérez-Gallent, C. Sánchez-Martínez, L. F. G. Geers, S. Turk, R. Latsuzbaia, E. L. V. Goetheer, Ind. Eng. Chem. Res. 2020, 59, 5648–5656.[5] M. Vranckaert, H. P. L. Gemoets, R. Dangreau, K. Van Aken, T. Breugelmans, J. Hereijgers, Electrochim. Acta 2022, 436, 141435. Figure 1

Improved Vanadium Flow Battery Performance through a Pulsating Electrolyte Flow Regime

AbstractThe interest in flow batteries as energy storage devices is growing due to the rising share of intermittent renewable energy sources. In this work, the performance of a vanadium flow battery is improved, without altering the electrochemical cell, by applying a pulsating flow. This novel flow battery flow regime aims to enhance performance by improving its mass transfer properties. Both the pulse volume and frequency have an influence on the battery performance, and lead to a 38.7 % increase in accessible discharge capacity compared to the conventional steady flow regime at values of 0.40 cm3 and 2.4 Hz in this cell, respectively. Furthermore, at these parameter settings a reduction of the mass transfer resistance by 71.4 % is achieved at 0.2 cm3/min ⋅ cm2. These results show that a pulsating flow can be beneficial in certain conditions, opening new possibilities for boosting performance in flow batteries.

Analysis of Discrete Velocity Models for Lattice Boltzmann Simulations of Compressible Flows at Arbitrary Specific Heat Ratio

This paper is devoted to the comparison of discrete velocity models used for simulation of compressible flows with arbitrary specific heat ratios in the lattice Boltzmann method. The stability of the governing equations is analyzed for the steady flow regime. A technique for the construction of stability domains in parametric space based on the analysis of eigenvalues is proposed. A comparison of stability domains for different models is performed. It is demonstrated that the maximum value of macrovelocity, which defines instability initiation, is dependent on the values of relaxation time, and plots of this dependence are constructed. For double-distribution-function models, it is demonstrated that the value of the Prantdl number does not seriously affect stability. The off-lattice parametric finite-difference scheme is proposed for the practical realization of the considered kinetic models. The Riemann problems and the problem of Kelvin–Helmholtz instability simulation are numerically solved. It is demonstrated that different models lead to close numerical results. The proposed technique of stability investigation can be used as an effective tool for the theoretical comparison of different kinetic models used in applications of the lattice Boltzmann method.

Aspect ratio effect on flow past an elliptical cylinder near a moving wall

In this paper, flow over an elliptical cylinder located near a moving wall is investigated numerically to ascertain the effect of aspect ratio (AR) on flow characteristics in terms of wake pattern, separation and stagnation points, and hydrodynamic forces. The two-dimensional simulations span both steady and unsteady flow regimes, where the effect of AR is analyzed in conjunction with other important parameters, such as gap ratio (GR∈ [0.6, 1.2]), Reynolds number (Re ∈ [5, 150]), and angle of attack (AOA∈ [−45°, 45°]). At a low AR = 0.1, significant differences in the wake pattern and critical Re for steady to unsteady wake transition are observed in GR-Re space in comparison with previous results for high AR cylinders. This results from an influence of AR on vorticity convection into the wake. Additionally, the effect of variation in AR from a flat plate (AR = 0) to a circular cylinder (AR = 1) on the wake pattern is discussed and presented in AR-Re space at a low GR. The locations of separation and stagnation points are shown to result from an interplay of AR and wall suppression depicting a low sensitivity to Re with low AR or high wall suppression effect. Subsequently, the effect of AR in conjunction with AOA is analyzed where counterclockwise inclination is observed to reduce wall suppression, while a competing effect arising from the contrasting movements of cylinder bottom and rear side governs the wake pattern for clockwise inclination that is explicit at a certain AR. Eventually, the variations in drag and lift forces with AR for different AOA are characterized.

Reaction performance in T-, X- and arrow-shaped microdevices

Microreactors are widely used for continuous flow operations. The assessment of their performance has a crucial role in determining the optimal geometries and working conditions. Among the most common geometries, we compare T-, X- and arrow-shaped devices to highlight how flow features, mixing degree and residence time affect the reaction yield and productivity. We focus on the steady flow regimes occurring in the three devices fed with reactive streams for varying Reynolds numbers. The Reynolds number, Rei, is herein based on the bulk velocity and the inlet-channel hydraulic diameter. The flow regimes presenting a central vortex in the mixing channel, found in X- and arrow-microreactors, lead to the best mixing and reaction yield. For Rei≤ 120 the maximum productivity is obtained with the X-microreactor, whereas above Rei = 120, with the arrow-reactor. Conversely, lower reaction yields and productivities are found in the T-microreactor, which exhibits an engulfment regime with two co-rotating vortices in the mixing channel. It is thus evident that the spiral pattern induced by a single central vortex extends the contact area between the reactants and leads to better performance. In terms of reaction cost, for the lower productivity values, the associated pressure drops are similar for all three geometries. For higher productivities, the best performance, i.e., the lowest pressure drops, is reached in the arrow-microreactor, followed by the T- and, then, by the X-device.

Flow division under a steady flow mode

Many scientists have been involved in the division of open streams. Existing methods for calculating fission nodes do not allow choosing their optimal designs that create a favorable regime for dividing flows. Most of the available results of studies of fission nodes are scattered, non-systematic, and in some cases, contain data that do not coincide with each other. The conducted studies of division nodes were carried out mainly for the steady flow regime; the flow turbulence issues in the flow division section have been little studied. However, in practice, an unsteady flow regime and an increase in flow turbulence are often observed, which leads to complex channel processes in the water intake area. The aim of the work is to develop a refined method for the hydraulic calculation of flow division nodes with a calm flow regime. This goal is achieved by an analytical solution to the problem of determining the water depth in the nodes of flow division under a steady flow regime. The paper uses theoretical studies using the equation for changing the momentum, laboratory studies on a hydraulic model, field surveys of existing water intake units, and an analysis of the experimental data available in the literature on this issue. According to the theoretical studies, calculated dependencies were obtained to determine the depth of the main flow in front of the fission node. The equation is a cubic equation concerning the OX axis and a quadratic equation concerning the OY axis. These two equations are solved independently of each other and are intended to determine the flow depth h1, which is established before the fission node. Taking into account the simplicity of the solution for practical calculations, we recommend the first dependence, and the second dependence is proposed for performing control calculations.

Flow past a sphere: Numerical predictions of thixo-viscoelastoplastic wormlike micellar solutions

In this work, we present numerical solutions to the benchmark flow past a sphere problem considering the rheology of semi-diluted and concentrated wormlike micellar viscoelastic solutions using the most recent model-variant of the Bautista–Manero–Puig (BMP) family of fluids, i.e. the BMP+ _ τ p model (López-Aguilar et al., [1] ). This study is performed using our in-house finite volume/element algorithm, stabilised to attain highly-elastic non-linear solutions with two novel constitutive and boundary-condition implementations, i.e. the ABS- f (ABSolute f -functional) and the VGR (Velocity GRadient) corrections (López-Aguilar et al., [2] ). The structuring level of various wormlike micellar fluids with different solute concentrations (from semi-diluted to extremely concentrated solutions) and degrees of strain-hardening is studied with a dynamic dimensionless fluidity that connects the internal structure construction-destruction dynamics with viscoelasticity. In complex flow, a viscoelastic flow-regime unveils the prediction of a flow transition from a stable steady flow (related to a steady sphere settling) to an unsteady quasi-periodic flow regime, in which transient cycles of vortex formation-disappearance behind the sphere are present, resembling experimental findings on negative-wake instabilities and oscillations in the settling velocity for the descend of particles in wormlike micellar solutions. This instability is predicted here for semi-diluted to concentrated wormlike micellar solutions and it is located in flow-rate ranges corresponding to extensional Deborah numbers in the interval of around 26 . 7 ≤ D e e x t ≤ 40 . 3 , as reported experimentally. This behaviour is correlated with a chaotic flow-structure behind the obstacle, for which strong fluctuation in the fluid’s internal-structure is recorded. In the steady viscoelastic flow regime, correlation between the BMP+ _ τ p fluidity structure-variable and its normal-stress response around and downstream of the sphere (in the form of localised extrema) is detected, where interaction between the rheological response of the material and mixed shear-to-extensional deformation provide insights into the forces the fluid elements experiment in the sphere wake. Here, a monotonic decline in the drag-correction factor is observed, this being one of the main experimental manifestations of the steady sphere-settling phase in these materials. These findings may serve to further understand flow transitions and instabilities related to negative wakes in this kind of shear-thinning extensional-hardening fluids (Rothstein and Mohammadigoushki, [3] ). In a plastic regime, complex thixo-viscoelastoplastic BMP+ _ τ p features manifest through the prediction of fore-aft asymmetries promoted by the thixotropic structure construction-destruction and viscoelastic properties of the model under extremely low solute-concentrations. Predicted yield-fronts resemble those reported experimentally by Holenberg et al. [4] for carbopol solutions. • Negative-wake instability predictions in the De -range recorded experimentally. • Correlation between extensional viscosity and normal stresses in the sphere wake. • Localised N 1 and internal-structure f -functional in the sphere wake. • First normal-stress activity in the sphere wake follows extensional viscosity response. • Asymmetric yield-fronts under highly-concentrated gel-like wormlike micellar solutions.