Flow Solution Research Articles

Self-similar solution for laminar bubbly flow evolving from a vertical plate

The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees–Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas specific volume instead of the gas fraction.

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Modelling the Flow in the Utah FORGE Wells Disrete Fracture Network

The focus of this paper is the efficient numerical solution of the fluid flow in the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) reservoir. In this study, the public data available for Discrete Fracture Networks (DFN) around well 58-32 is used to represent the DFN. In this research, a novel computationally efficient method called Hele-Shaw (HS) approximation is used for modeling fluid flow in FORGE well. An analysis of the influence of fracture intensity in a network is carried out using the HS method. The HS method was validated by solving the full Navier–Stokes equations (NSE) for a network of eight fractures. A good agreement was observed between the evaluated results (average deviation of 0.76%).

Purification of a reactive dyes mixture solution by means of pre-hydrolysed coagulants in the standard tests and coagulating flow system

Reactive dyes, widely used in textiles, often leach into sewage due to incomplete bonding with fibers. Coagulation offers an effective solution, yet standard lab tests for coagulation efficiency lack realism and are significantly labour and time-consuming. To address this, a novel approach is proposed: optimizing coagulation through a prototype lab flow. This system automates solution flow, reagent dosing, coagulation, and sludge separation via sedimentation and filtration. Tests reveal effective coagulation of various reactive dyes with pre-polymerized Al coagulants, but limited efficacy with Fe(III) coagulant. The flow system demonstrates mostly better purification results than jar tests, achieving around 95% colour removal with Al coagulants. This study highlights the efficacy of coagulation and filtration in jar tests, offering a simplified yet efficient method for assessing coagulation performance.

Transient flow of electrolyte solution in porous media with membranes fitted at the upper wall surface and lower charged surface

Transient flow of electrolyte solution in porous media with membranes fitted at the upper wall surface and lower charged surface

High‐Throughput Production of Gelatin‐Based Touch‐Spun Nanofiber for Biomedical Applications

Nanofiber production techniques have become increasingly important due to their wide range of applications. However, the complex design of the setup and difficulty in scaling up to high production rate have limited the industrial applicability of some of the conventional fiber generation techniques such as electrospinning. Herein, the touch spinning method is scaled up for nanofiber production using a simple rotating drawing setup with polymers that are relevant for biomedical applications such as polyethylene oxide and gelatin. The process is amenable to use of benign solvent such as water and production of a wide variety of submicron‐scale gelatin‐based nanofibers at a high throughput (≈2.45 g hr−1 with the single channel flow), which is an order of magnitude higher than those produced by other fiber generation methods is shown. The parametric study indicates that the fiber production process can be tuned at a desired rate without sacrificing the fiber quality by simply altering the number of drawing rods, the size of the rotating disk, and the number of solution flow supply channels. The utility of this technique for different biomedical applications such as cell culture and air filtration applications is also demonstrated.

Irrotational Flow over Ogee Spillway Crest: New Solution Method and Flow Geometry Analysis

A spillway is a hydraulic structure of major importance in dam safety, and its current analysis usually involves a hybrid approach combining CFD modeling with experimental research, either using well-known WES design charts or conducting new model experiments in the laboratory. Flow over spillway crests involves fluid accelerations, making irrotationality an adequate simplification of the Navier–Stokes (NS) equations. However, an efficient tool using this method is currently lacking for spillway flow, particularly for ogee spillway flow. This work focuses on this aspect of the problem, and a new method for computing irrotational flow solutions over ogee spillways is proposed by developing flow net computational solutions. The proposed method entails a new iterative procedure in the complex potential plane where free surface pressures are exactly set to zero, contrary to other methods, and an automatic determination of the critical point, the unknown energy head, and the free surface profile. The model generates solutions efficiently in only a few seconds on a personal workstation, permitting a fast estimate of spillway flow operation, and is thus an effective complement to experimental and NS-CFD modeling. The solutions produced are compared with observations of a high operational head equal to five times the design head of the ogee crest, resulting in reasonable agreement. The application of the new model to investigate the limitations of analytical equations used in spillway flow, like Jaeger’s theory, establishes limits for its use by relating its curvature parameter to the spillway chute slope.

Cash Flow Dynamics: Amplifying Swing Models in a Volatile Economic Climate for Financial Resilience and Outcomes

In a volatile economic climate, understanding cash flow dynamics is crucial for companies to improve financial resilience and outcomes. This research focuses on amplifying swing models such as Cash Flow Management (CFM), Solutions (CFS), Dynamics (CFD), Boosters (CFB), Innovations (CFI), and Strategic (CFS) - on cash flow dynamics in a volatile economic climate. By examining the relationship between these models and determinant variables, the study aims to provide insights that can assist companies in achieving financial resilience and outcomes. The data were collected from finance and accounting representatives of 200 companies ((manufacturing (107), services (56), and trade (37)) in Kosovo in 2023 (quarters 1, 2, 3, and the first two months of quarter 4), while processing was done through exploratory factorial, reliability, and multiple regression analyses conducted using SPSS and AMOS software. The results of the study reveal a significant relationship between each cash flow model and the determinant variables. This highlights the importance of these models in comprehending cash flow dynamics within a volatile economic climate. Factors such as optimization strategy clarity, continuous monitoring, effective working capital management, accurate financial decision-making, and technological improvements contribute to positive cash flow. Additionally, precise management of fluctuations, financial advantage, cooperative departmental approaches, and effective communication also play a role in cash flow dynamics. By extending swings models, the study provides valuable insights that can assist firms in achieving financial resilience and overcoming the challenges of a volatile economic environment.

Physically consistent immersed boundary method: A framework for predicting hydrodynamic forces on particles with coarse meshes

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary conditions in the volume-filtered flow solution, thereby allowing to solve the governing flow equations on non-body conforming meshes. The resulting methodology possesses similarities with a continuous forcing immersed boundary method (IBM) and is, therefore, termed physically consistent IBM (PC-IBM). Based on the recent findings of Hausmann et al. [1], the closures arising in the volume-filtered NSE are closed by suitable models or even expressed analytically. The PC-IBM is fully compatible with the large eddy simulation framework, as the volume-filtered NSE converge to the filtered NSE away from solid boundaries. The potential of the PC-IBM is demonstrated by means of different particle-laden flow applications, including a dense packing of fixed particles and periodic settling of 500 particles. The new methodology turns out to be capable of accurately predicting the fluid forces on particles with relatively coarse mesh resolutions. For the flow around isolated spheres, a spatial resolution of six fluid mesh cells per diameter is sufficient to predict the drag force with less than 10% deviation from highly resolved simulation for the investigated particle Reynolds numbers ranging from 10 to 250.

Swirling electrolyte. Part 2. Secondary circulation and its stability

The asymptotic analysis of steady azimuthally invariant electromagnetically driven flows occurring in a shallow annular layer of electrolyte undertaken in Part 1 of this study (McCloughan & Suslov, J. Fluid Mech., vol. 980, 2024, A59) predicted the existence of a two-tori flow state that has not been detected previously. In Part 2 of the study we confirm its existence by numerical time integration of the governing equations. We observe a hysteresis, where the type of solution obtained for the same set of governing parameters depends on the choice of the initial conditions and the way the governing parameters change, which is fully consistent with the analytic results of Part 1. Subsequently, we perform a linear stability analysis of the newly obtained steady state and deduce that the experimentally observed anti-cyclonic free-surface vortices appear on its background as a result of a centrifugal (Rayleigh-type) instability of the interface separating two counter-rotating toroidal structures that form the newly found flow solution. The quantitative characteristics of such instability structures are determined. It is shown that such structures can only exist in sufficiently thin layers with the depth not exceeding a certain critical value.

A qualitative analysis of the artificial neural network model and numerical solution for the nanofluid flow through an exponentially stretched surface

This article aims to analyze the two-dimensional (2D) nanofluid (Ag/C2H6O2) flow past an exponentially stretched sheet. The magnetic field impact, heat source/sink, and convection in the thermal profile are taken into account. The complexity of the problem is reduced by introducing a dimensionless group of functions. The reduced model is transformed into a system of first-order ordinary differential equations (ODEs). This system is further analyzed with the artificial neural network (ANN), which is trained using the Levenberg–Marquardt algorithm. The whole dataset is sub divided into three parts: training (70%), validation (15%), and testing (15%). The impact of nonlinear heat source/sink parameter, magnetic parameter, volume fraction of nanoparticles, and Prandtl number is displayed through graphs. The heat source, volume fraction, and the Prandtl number cause an increase in the thermal profile with its larger values. The magnetic parameter causes a decline in both the thermal and momentum boundary layers with its higher values. The analysis shows that the thermal energy profile is enhanced with the larger values of the volume fraction of silver nanoparticles and heat source. For each case study, the residual error (RE), regression line, and validation of the results are presented. The performance of the proposed methodology is numerically tabulated for the nanoparticle volume fraction shown in Table 3, where the minimum absolute error (AE) is 5.3373e−11 at ϕ=0.05. Based on this, we recommend ϕ=0.05 for better performance. The AEs for the ANN and bvp4c are computed for the state variables in Tables for the magnetic parameter M=5,10, and 15. These tables show the overall performance of the ANN and further validate the present study. We have also validated the results of the ANN through the mean squared error graphically, where the accuracy of the proposed methodology is proven.

Nash–Cournot Equilibrium and Its Impact on Network Transmission Congestion

This paper evaluates the impact of congestion on transmission lines when the operation cost is minimized using economic dispatch (ED), comparing the results obtained with the Nash–Cournot Equilibrium (NCE). A methodology is developed for the optimal power flow solution through the NCE, considering the network topology (upper and lower generation limits, upper and lower limits of the transmission lines, and power balance) for a nine-node system without and considering two bilateral power transactions. The results show that the operation cost is higher when the NCE is implemented than ED. However, the problem of congestion in the transmission lines is reduced due to the equilibrium obtained in the power dispatch against minimizing the operation cost in the dispatch; the transmission lines with the most significant participation tend to become congested when additional bilateral transactions occur. Finally, the above is verified by obtaining the mean and median of the transmission line percentages used in the two simulations.

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

Large global solutions to the three dimensional compressible flow of liquid crystals

The purpose of this paper is to provide a class of large initial data which generates global solutions of the compressible flow of liquid crystals in R3. This class of data relax the smallness restriction imposed on the initial incompressible velocity. Moreover, the result improve considerably the work by Hu and Wu [SIAM J. Math. Anal., 45 (2013), 2678-2699].

Revisiting the natural convection effects at ultra-low redox concentration solutions: The influence of viscosity and diameter of wire electrode

Natural convection could arise even at ultra-low redox concentration solutions (1–10 mM). Models such as convection–diffusion layer model and spontaneous convection model have been established to describe this phenomenon. However, the driving forces as well as the parameters that influence this natural convection effects are still not clear. Herein we investigated the effects of viscosity on natural convection by introducing sodium alginate (SA), which enhanced viscosity without changing the diffusion coefficient of the redox couple. Resultantly, it allowed us to obtain the relationship between microscopic flow of solutions and the thickness of natural convection layer. Moreover, wire electrodes with various diameters were also tested to reveal the natural convection effects on mass transfer. An empirical equation was established to describing the influences of solution viscosity and diameter of wire electrode on the thickness of natural convection layer in ultra-low redox concentration solutions.

Sub-core permeability estimation from coreflooding experiments: Numerical analysis for evaluating accuracy and improving methods

Coreflooding experiments are one of the primary methods for reservoir rock characterization and have been developing in recent years, providing increasing detail. An advanced analysis of coreflooding experiments consists of constructing three dimensional permeability (k) maps of the core sample with sub-core resolution. Such detailed characterizations provide important information on the core heterogeneity and enable the construction of accurate numerical flow models that can reproduce experimental results. This work presents a method for estimating k, combining data from multiple coreflooding experiments, and studies the estimation accuracy considering a large number of test cases consisting of synthetic data obtained by numerical experiments. Cases include varying parameters, such as: fluid injection flow rates and types, relative permeability curves, capillary pressure functions and core heterogeneity. The new method is shown to significantly improve the estimation accuracy in comparison to methods that incorporate data only from a single experiment. Furthermore, a method for improving k estimations in regions where water is trapped is presented and its implementation is shown to increase the overall accuracy of k estimation. An additional method is considered, that requires only single-phase flow solutions, thus increasing the computational efficiency. However, it is shown to be applicable only for a small subset of cases.

Study of inhalation micropowders obtained by spray drying

Objectives. To study the influence of the type of matrix-forming material and excipients concentration, spray drying parameters on the characteristics of the powder for inhalation, as well as to investigate the inhalation compositions for stability under stressful conditions.Methods. Spray drying was used to obtain powder compositions with the required characteristics for inhalation therapy. Microscopic and analytical studies of powders were carried out. Statistical analysis made it possible to estimate the influence of factors on the powder characteristics and rank them by importance. The stability of spray dried powders was studied.Results. The optimal parameters for obtaining powders for inhalation were found by means of mathematical statistics: air flow rate was 37 m3/h; compressed air flow rate — 601 L/h; inlet air temperature — 150°C; solution flow rate — 45% of the power of the peristaltic pump (16.3 g/min for this composition); L-leucine concentration — 10 wt %; ratio of components of the matrix polyvinylpyrrolidone K-30/D-mannitol = 1 : 3. Under these conditions, as well as by means of 2 experiments additionally selected from the research design, a composition with isoniazid as an active substance was spray dried. The resulting powders were analyzed, in order to confirm the correctness of the recommended parameters.Conclusions. The selection of compositions and spray drying conditions involves multiple criteria. The characteristics of the powder for inhalation may deteriorate significantly during long-term storage. The optimal parameters were determined using statistical analysis and confirmed by experimental data.

Effect of the flow-force relationships used in two parameter modelling of freezing and vitrification protocols for bovine embryos

Cells may become damaged by strong volume changes and related intracellular changes during slow freezing or vitrification. These osmotic events can be modelled mathematically, using descriptions of transmembrane flow of solute and water. We compared different variants of an often used 2-parameter (2P) formalism in fitting of an empirical shrink-swell curve of a bovine embryo in 5 vol% glycerol, and in simulations of CPA loading and removal in a vitrification protocol. In its original form, the 2P model uses a flow-force relationship for the flux of CPA that is not analogous to that for water (asymmetrical), but in the other variants used, the flow-force relationships for water and CPA are analogous to each other (symmetrical). The effect of used model on estimated values for Lp and Ps in 5 vol% glycerol was small. Also the effect on shrinking and swelling in vitrification media was small, but the original 2P model predicted stronger swelling of embryos during one-step CPA removal. One variant that we compared simply assumes Raoult’s law, i.e. M = m, even in very concentrated solutions We conclude that this simple model is easy and appropriate for simulating osmotic events of embryo’s. But if a method for correcting for the deviation from Raoult’s law is used, a symmetrical model seems more appropriate than the original (asymmetrical) 2P model.

Unified, Integral Approach to Modeling and Design of High-Pressure Pipelines: Assessment of Various Flow and Temperature Models for Supercritical Fluids

Abstract A unified one-dimensional, steady-state flow and heat transfer model is presented for the pipeline transport of fluids at high pressures, including the supercritical conditions. The model includes a generalized temperature equation, presented here for the first time, and accounts for all of the important effects, including the property variation, viscous dissipation, Joule-Thomson (J-T) cooling, and heat exchange with the surrounding. With appropriate approximations, this model can yield all isothermal and non-isothermal pipe flow solutions reported thus far. A generalized multi-zone integral method is developed which solves the two resulting algebraic equations for pressure and temperature in conjunction with a property database, such as the National Institute of Standard and Technology (NIST) Reference Fluid Thermodynamic and Transport Properties (REFPROP). With appropriately selected number and size of the zones and using property values at the mean temperature and pressure within each zone, this integral method can accurately predict the complex effects of the governing parameters, such as the pipe diameter and length, inlet and exit pressures, mass flow rate, J-T cooling, and inlet and surrounding temperatures. Its accuracy for small-to-large diameter pipes has been ascertained by a comparison with the numerical solutions of the differential form of governing equations that requires a large number of small grids along the pipe and the values of mean properties within each grid. Indeed, this integral model can be used for the pipeline transport at both subcritical and supercritical pressures as long as the fluid does not encounter its anomalous states and the phase-change.

A numerical study of volcanic ash ingestion and erosion of the front components of a high bypass turbofan engine

Abstract Airborne particles, such as dust and volcanic ash, pose a serious hazard to aircraft in flight due to their potential to cause erosion damage to engine components. It is crucial to anticipate and address the impact of erosion wear on engine performance and safety. This study aims to enhance our understanding of how volcanic ash particles behave when ingested through a high bypass turbofan engine (HBTFE) and assess the development of erosion wear in the front components. The effects of four different ash samples are assessed in various scenarios of encountering volcanic ash during cruise flight conditions. First, the flow solution is obtained for all front components, including the Pitot intake, spinner, fan, inlet guide vanes (IGVs), outlet guide vanes (OGVs), and connecting ducts. Based on the flow data, the particle motion equations are solved step by step using an in-house trajectory and erosion code. This latter adopts the Lagrangian approach, which incorporates a particle-eddy interaction model and includes probabilistic descriptions for the release positions of particles, sizes, and restitution factors. The finite element method (FEM) is used to track particles through the computational cells and determine impact positions and conditions. As a result, the Pitot intake design seems to prevent many ash particles from reaching the fan blade beyond 80% of the span. The fan blade leading edge (LE) exhibits extreme erosion on both sides. The blade’s pressure side (PS) displays erosion spreading practically on the entirety of the surface, especially near the trailing edge (TE). In contrast, the suction side (SS) has scattered erosion at lower rates. Furthermore, the rotor’s hub presents almost uniform erosion patterns, whereas the shroud depicts scattered erosion. This large fan appears to function as a separator, expelling a significant amount of ash particles through the secondary duct, thereby reducing the engine core’s susceptibility to erosion. Out of the four volcanic ash samples, those from the Kelud and Etna volcanoes appear to cause the highest hourly eroded mass, about twice as much as the samples from the Chaiten and Eyjafjallajokull volcanoes.