Complex Fluid Flow Research Articles

Cattaneo-Christov flow analysis of unsteady couple stress fluid with variable fluid properties: By using Adam’s method

This work investigates the transference of mass and heat rate with the Cattaneo-Christov model for the 2-D magnetohydrodynamic couple stress fluid flowing in a sensory surface. The considered fluid flowing on the microcantilever sensor surface squeezed at free stream which can perceive the motion of fluid and the variance in temperature and concentration rates. The physical nature of fluid in this study is investigated by using the variable fluid properties. The study of couple stress fluid flowing in the context of squeezing surface is important due to their unique rheological properties. The understanding of these types of flow behavior enables engineers and scientists to design efficient processes, improve lubrication, enhance coating techniques, optimize material transport and avoid instabilities associated with complex fluid flow. The governing PDEs equations are attained by adapting the considered assumptions, and then the PDEs are altered into the form of ODEs via similarity transformations. The numerical solutions are achieved by taking Adams-Bashforth (Predictor-Corrector) technique along with RK-4 method. The declining behavior of velocity is inspected for inputs of permeable velocity, couple stress parameter and squeezing flow index. The transport of mass and heat drops due to thermal relaxation coefficients.

A data-driven online prediction method for surface-deformed liquid level in vessels under ocean conditions

Measurement of liquid level in vessels under ocean conditions, such as in the marine nuclear reactor pressure vessel, pressurizer and so on, suffers from the problem of strong free surface distortion. In order to solve such problem, an online prediction method based on reduced order model (ROM) and compressive sensing theory is proposed in this paper. The whole field online prediction of complex fluid flow characteristics can be realized by combining the observation data from the known sparse sensor with the ROM. In this paper, the three-dimensional flow field of sloshing flow in a cavity is numerically simulated to establish abundant numerical database. Taking the liquid level of the flow field as the prediction object, the ROM is established by using the proper orthogonal decomposition (POD) method to predict the liquid level. The results show that POD ROM can accurately predict the unknown case, the smaller the rotating speed is, the better the prediction result is, and increasing the number of measuring points and the number of basis functions can reduce the prediction error to a certain extent. The reduced model constructed by using QR decomposition to obtain measuring points can effectively reduce the error of prediction results.

Numerical Simulation of Three-Dimensional Free Surface Flows Using the K-BKZ-PSM Integral Constitutive Equation.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K-BKZ-PSM (Kaye-Bernstein, Kearsley, Zapas-Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

Development of mechanistic-artificial intelligence model for simulation of numerical data of water flow in porous materials

Fluid dynamics of water flow through porous metallic media is significant for cooling and heating applications. The prediction of the velocity of fluid flowing inside the porous media could provide useful data for pressure drop calculations. This prediction is usually performed by a mathematical modeling approach like computational fluid dynamics (CFD). The computational method is a powerful means of precision calculation, although it could take more time and expenditure for more complex geometries or more complex fluid flow regimes. Artificial intelligence (AI) algorithms could learn and map CFD data under several conditions. AI algorithms could continue the prediction of physical data, saving computing time and performance. The present study focuses on CFD modeling of water flow inside a pipe filled with copper porous media. For the first time, the fuzzy bee algorithm (BAFIS) maps the generated CFD data to inlet velocities of 0.5, 0.7, 1.1, and 1.3 m/s. The BAFIS intelligence assessment for accurate convective flow prediction in porous media is not available in the literature. Additionally, the reliability of this method for missing CFD data prediction has not been considered yet. The results showed that the maximum intelligence (regression=0.97) is for a bee number of 140. Using the most intelligent BAFIS, the outlet velocity can be predicted by the artificial intelligence method for further nodes and inlet velocities without CFD modeling. BAFIS could precisely predict the outlet velocity for missing data with an inlet velocity of 0.91 m/s based on previously mapped data. A comparison was made between BAFIS and the fuzzy neural network (ANFIS) for CFD data predictions. The mean-square error and the root-mean-square error of ANFIS were slightly more than BAFIS (i.e., 0.1% and 3%, respectively).

Reduced order modeling of parametrized pulsatile blood flows: Hematocrit percentage and heart rate

This paper numerically evaluates the accuracy and performance of a stabilized finite element Reduced Order Modelling (ROM) approach that is designed to simulate pulsatile blood flows. The method is able to estimate fluid flow parametric solutions of interest in hemodynamics by considering the hematocrit percentage (Hct%) and the heart rate (fc) as parameters. The method estimates off-trained parametric scenarios which have not been included in the training data set composing the ROM basis and that can adopt arbitrary values from specific patient conditions. The hematocrit percentages modifies the viscous properties of blood, which are incorporated into the problem physics through a power-law model. The hematocrit percentages are 5≤Hct%≤50, ranging from severe anemia to physiological values. The pulsatile flow condition is modeled via a Womersley function, with fcbpm (beats per minute) ranging between 60bpm≤fc≤120bpm. These frequencies comprise physiological conditions of patients at rest and tachycardia or moderate exercise. Two-and-three-dimensional flows are simulated inside a representative geometry of a carotid artery, where the accuracy is tested by studying the effect of the number of components of the ROM approximating basis and the number of sampling points composing the training data set. The parametric calculation verifies that the proposed approach constitutes a valuable computational tool for simulating complex fluid flow hemodynamics and can be applied to clinical decision-making.

Interplay between advective, diffusive and active barriers in (rotating) Rayleigh–Bénard flow

Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract the most influential advective, diffusive and active barriers to transport from data sets in a frame-indifferent fashion. To date, however, there has been very limited investigation into these objectively defined transport barriers in 3-D unsteady flows with complicated spatiotemporal dynamics. Similarly, no systematic comparison of advective, diffusive and active barriers has been carried out in a 3-D flow with both thermally driven and mechanically modified structures. In our study, we utilize simulations of turbulent rotating Rayleigh–Bénard convection to uncover the interplay between advective transport barriers (Lagrangian coherent structures), material barriers to diffusive heat transport, and objective Eulerian barriers to momentum transport. For a range of (inverse) Rossby numbers, we identify each type of barrier and find intriguing relationships between momentum and heat transport that can be related to changes in the relative influence of mechanical and thermal forces. Further connections between bulk behaviours and structure-specific behaviours are also developed.

Heat transfer in the Jeffery-Hamel flow of a yield-stress fluid

Heat transfer in the Jeffery-Hamel flow of a yield-stress fluid that obeys the Bingham-Papanastasiou model is investigated in the present study. Among various rheological models proposed to formulate the flow of yield-stress fluids, the Bingham model is usually used to address the effect of yield-stress. A fluid that obeys the Bingham model does not show any shear-thinning or shear-thickening behaviors; this makes the interpretation of the results much easier. Addressing the unyielded regions (regions at which the yield-stress material behaves like a solid) in a yield-stress fluid flow is not a trivial task, and it could be impossible, especially in complex geometries. Unfortunately, the Bingham model itself cannot be used to formulate complex fluid flow problems due to the mathematical difficulties (i.e., addressing the unyielded regions); hence it is usually regularized to avoid these mathematical challenges. One of these regularized models is the Bingham-Papanastasiou model. Using an exponential term enables the Bingham-Papanastasiou model to address the unyielded regions. However, this exponential term results in highly non-linear equations, which are difficult to be handled mathematically. In the present study, the effect of the yield-stress (Bingham number) on the hydrodynamics and heat transfer in the Jeffery-Hamel flow is investigated by using the Bingham-Papanastasiou model. The momentum transfer in the Jeffery-Hamel flow of a Bingham-Papanastasiou fluid is governed by a highly non-linear ordinary differential equation (ODE) which is a boundary value problem. Assuming that the fluid's properties are independent of the temperature and pressure, this highly non-linear ODE is solved numerically. The heat transfer in the flow, with a constant wall temperature boundary condition, is investigated, assuming the flow to be an equilibrium viscous dissipation flow (the fluid's mixed mean temperature variation is negligible along the channel). The resultant linear energy equation is also solved numerically to obtain the temperature distribution across the channel. The results obtained in this work show that the yield-stress increases the wall shear stress, Nusselt number, and Stanton number. In fact, the effect of the yield-stress on the Nusselt number is comparable to the effects of Prandtl and Eckert numbers. It is also found that the yield-stress can prevent the flow separation in a divergent channel. Considering the advantages of using the yield-stress fluids as the working fluids in the Jeffery-Hamel flow, they can be considered as an alternative to nanoparticles which are usually used to enhance the fluid's thermal conductivity and also the Nusselt number.

Influence of PST and PHF heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid with a rotating cone

Swirl flow heat exchangers are commonly used in industrial processes such as power generation, chemical processing, and refrigeration. They can be used for both heating and cooling applications and can be designed to handle a wide range of fluid flow rates and temperatures. This study investigated the influence of PST (prescribed surface temperature) and PHF (prescribed heat flux) heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol (50/50) based nanofluid with a heated rotating cone. The governing ordinary differential equations were derived from the partial differential equations using the proper similarity transformations. The problem was solved using the Shifted Legendre Collocation Method (SLCM), which is a powerful numerical method. The results showed that the PST heating conditions had a significant impact on the flow and heat transfer characteristics of the ternary hybrid nanofluid. Under PHF heating conditions, the swirl velocity distribution was leading to a noteworthy influence. The use of the Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid resulted in a significant enhancement in the convective heat transfer coefficient. The SLCM method provided accurate and efficient numerical solutions for the problem, demonstrating its suitability for simulating complex fluid flow and heat transfer problems.

A review on the application of bionic underwater robots in different underwater environment

People have the spirit of constantly exploring the unknown areas of the world. The flow of fluid is ever-changing, and it can be simply divided into laminar flow and turbulent flow. In this context, the underwater robot was born. In order to cater to people's exploration of complex fluid flows such as lakes and oceans, bionic underwater robots with innate advantages have given full play to their role and become a certain trend. This paper mainly reviews the bionic underwater robots from three aspects, namely the prediction of the robot's trajectory in complex fluid, the rationality of its structural design, and the strength suitability of materials. Finally, the future of bionic underwater robots is analysed.

Shear flow-driven droplet motion with smoothed dissipative particle dynamics

Droplet motion in shear flow is a typical phenomenon in nature that also plays an important role in the spread of COVID-19 when viruses like SARS-CoV-2 exist in exhalation droplets. In this paper, we adopted smoothed dissipative particle dynamics (SDPD) to simulate the Couette flow and Poiseuille flow. Then, the self-diffusion coefficient and the Schmidt number of the quiescent flow in SDPD are confirmed by comparison with those in DPD. In addition, the SDPD method with pacific coefficients is used to simulate the disintegration of droplets and the collisional aggregation and separation of droplets in shear flow. The applicability of the SDPD method is demonstrated through these simulations, which can be useful in the investigation of many complex fluid flows during the expansion of COVID-19.

Error propagation for quantile estimation via combining Polynomial Chaos expansions and metalog distributions

Introducing parametric uncertainties to models is a quintessential step of simulation-based risk assessment and rare event simulations. A novel quantile estimation method is proposed based on generalized Polynomial Chaos expansions and metalog distribution estimation. We propose to derive the metalog distribution based on the statistical information of an expansion of the random model. The advantage of latter lies in a reduced number of evaluations of the full model, while deriving the metalog distribution avoids sampling-related challenges of quantile estimation. Error estimates and an algorithm to choose the relevant number of statistical moments are developed and analyzed, giving a framework for assessing the method applicability and the accuracy of the quantile estimation. The proposed method and the analysis are demonstrated on numerical examples. The method is applied to a complex fluid flow problem in transpiration cooling.

Tip clearance influence on hydrodynamic performance and pressure fluctuation of a composite ducted propeller using a two-way FSI method

With the development of advanced materials, composite materials have been studied by researchers over the world to make them more applicable to many applications, especially in the marine industry. As an important component of marine vehicles, propellers have been studied over decades to achieve the goals of increasing hydrodynamic performances and structural properties. However, traditional marine propellers manufactured with metallic materials have many limits. Therefore, the use of composite material to improve the performances of the propeller has become a research hotspot since their great structural performances and material damping properties can improve the comprehensive performance of the propellers such as increased hydrodynamic performances and reduced pressure fluctuation characteristics. The ducted propeller is a typical marine propulsor, which has a tip clearance between the blade tip and the inner face of the duct that can cause a complex fluid flow around the blades and influence the performance of the propeller. In this research, the tip clearance influence on hydrodynamic performance and pressure fluctuation of a composite ducted propeller compared with a metallic equivalent is calculated using a two-way fluid-structure interaction (FSI) method. The results indicate that the use of composite materials with a proper stacking sequence on the ducted propeller blade with a smaller tip clearance size corresponding to GSR = 0.417 can achieve good hydrodynamic properties for the propeller, and it has a significant inhibiting effect on pressure fluctuations on the blade surface.

Role of Interfacial Evaporation Process in Thin Vapor Chambers With Variable Pillar Spacing and Nonuniform Heat Flux

This paper reports the results of our numerical studies on the performance of thin film evaporation, mostly seen in the evaporator of a thin vapour chamber, using micropillar arrays of varying pitch and under both uniform and non-uniform heat flux conditions. The dry-out heat flux and evaporator surface temperature have been used as the performance metrics. A numerical model has been formulated to solve the fluid flow and phase change heat transfer considering the capillary pumping action (wicking action). The model is next exercised to study the performance of the evaporator with variable pitch of the micropillar array and with both uniform and non-uniform heat flux at the base. The pitch variations are done either by maintaining the mean pitch to be constant (same number of pillars) or by keeping the limiting pitch (maximum) equal to the uniform pitch scenario. The results show that a linearly decreasing pillar spacing arrangement along the downstream direction, i.e., along the flow direction (+ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> direction), results in significant enhancement of the cooling limit up to 1.5 times along with the reduction in overall evaporator surface temperature when compared to uniform pillar spacing where increase in cooling limit is accompanied with increase in overall evaporator surface temperature. In addition, the interplay of variable spacing and non-uniform heat flux results in design guidelines for pillar arrangements for given power maps while throwing new insights into the complex fluid flow and heat transfer phenomena encountered in this process. A higher concentration of pillars is found to result in lower evaporator surface temperatures, thereby recommending more number of pillars in high heat flux zones.

Machine-learned constitutive relations for multi-scale simulations of well-entangled polymer melts

We investigate the use of a machine-learning-based simulation scheme to predict flows of complex fluids with a non-linear constitutive relation. This scheme, originally proposed by Seryo et al. for general complex fluids [N. Seryo et al., “Learning the constitutive relation of polymeric flows with memory,” Phys. Rev. Res. 2, 033107 (2020)], is used to learn the time derivative of the stress as a function of the stress and velocity gradient. However, previous assessments were limited to fluids with linear constitutive relations. In this study, we employ the dual sliplink model to express the dynamics of well-entangled polymers as a fluid exhibiting a non-linear stress response. We test the simulation scheme by using it to predict the flow of a viscoelastic fluid between two parallel plates with only shear deformations and compare the results with those of a multi-scale simulation using microscopic simulators. Overall, our machine-learning method possesses good predictive capabilities, for both the transient response and the non-linear behavior at steady-state, i.e., the shear-thinning. We are able to accurately track the evolution of the stress, for both the weak and strong elastic cases, although the velocity predictions for the latter show a decreased accuracy in the transient regime. Furthermore, our simulation scheme is more computationally efficient than the conventional multi-scale simulation approach, which uses microscopic simulators, containing a system of coarse-grained polymers, to evaluate the macroscopic stress. We discuss possible extensions and improvements for enhancing the predictive capabilities and generality of the method.

Data-driven reduction and decomposition with time-axis clustering

A new approach for modal decomposition through re-interpretation of unsteady dynamics, termed time-axis clustering, is developed in this work and is demonstrated on an experimental turbulent reacting flow dataset consisting of simultaneously measured planar OH-PLIF and PIV fields in a model combustor. The method executes a K-Means clustering algorithm on an alternative representation of the input snapshot dataset: the dataset is interpreted here as a collection of one-dimensional time series, where each time series represents the time evolution of some flow quantity of interest (QoI) at a fixed point in physical space (i.e. pixel locations). The clustering algorithm in the modal decomposition context produces (a) spatial modes (called time-axis modes) that identify localized regions of dynamical similarity in physical space and (b) temporal coefficients that represent average trajectories of the flow QoI conditioned on the regions in physical space identified by the corresponding spatial mode. Due to the non-overlapping nature of K-Means clusters, visualization of the modes provides a unique pathway for flow feature extraction based on dynamical similarity. Ultimately, this work shows how time-axis clustering provides a promising avenue for domain-localized data-based modelling of complex fluid flows.

Flows inside polymer microfluidic droplets: Role of elasticity

The role of elasticity on the flow topology inside viscoelastic (Boger) droplets moving in a rectangular microchannel is examined experimentally by means of micro Particle Image Velocimetry (μPIV). Polyacrylamide (PAAM) water -glycerol solutions of different concentrations are employed to vary droplet elasticity. Varying the Wi number alters the flow topology inside the Boger microdroplets, progressively reducing the number of vortical structures observed until their complete disappearance. The flow structure resembles that of Newtonian inelastic droplets for low Wi and elasticities. However, when the Wi and elastic number increase above one-i.e. elastic effects become more important- a new flow structure is observed at the front of the droplets characterized by two recirculating regions either side of the droplet centreline. Spatiotemporal maps show that the flow in this new regime fluctuates periodically around the centreline indicating the onset of an elastic instability. This flow transition is attributed to the well documented coupled effects of polymer stretching and curved streamlines and resultant hoop stresses. The findings highlight the importance elasticity can have on the nature of microdroplet flows of complex fluids and the potential of tuning elasticity to engineer flow structures for given microfluidic applications.

Two-Way PBM-Euler Model for Gas and Liquid Flow in the Ladle.

Ladle metallurgy is an important steelmaking technology in high-quality steel production. The blowing of argon at the ladle bottom has been applied in ladle metallurgy for several decades. Until now, the issue of breakage and coalescence among bubbles was still far from being solved. In order to have a deep insight into the complex process of fluid flow in the gas-stirred ladle, the Euler-Euler model and population balance model (PBM) are coupled to investigate the complex fluid flow in the gas-stirred ladle. Here, the Euler-Euler model is applied to predict the two-phase flow, and PBM is applied to predict the bubble and size distribution. The coalescence model, which considers turbulent eddy and bubble wake entrainment, is taken into account to determine the evolution of the bubble size. The numerical results show that if the mathematical model ignores the breakage of bubbles, the mathematical model gives the wrong bubble distribution. For bubble coalescence in the ladle, turbulent eddy coalescence is the main mode, and wake entrainment coalescence is the minor mode. Additionally, the number of the bubble-size group is a key parameter for describing the bubble behavior. The size group number 10 is recommended to predict the bubble-size distribution.

Motion Estimation for Complex Fluid Flows Using Helmholtz Decomposition

In this paper, we proposed a novel motion model with Helmholtz decomposition for complex fluid flows in a filtering-based optical flow framework, where the optimization of the regularization term is treated as a filtering process, and different motion patterns can be captured by finding appropriate filter kernels based on the designed filters. In this framework, we introduce a novel optical flow method with a joint spatial filter, which is based on the Helmholtz decomposition theorem that assumes a local motion field is composed of a curl field and a divergence field. By adjusting the scale of the weights in the filter kernels and combining a curl filter with a divergence filter in a certain ratio, it can simulate different motion patterns. In addition, if the correlation between the horizontal and vertical components of the optical flow field in the filter kernel is eliminated, it will be transformed into a linear motion model. Based on this linear motion model, we also develop a novel optical flow method with an adaptive guided filter. By finding an adaptive filter kernel driven by both the input image and the guided motion field for the designed filter, it can successfully capture different motion patterns, and yield an edge-preserving smoothing optical flow field. Most importantly, the proposed optical flow model provides a new way to design the regularizers for capturing different motion patterns in complex fluid flow. In particular, the designed optical flow method with an adaptive guided filter significantly outperforms the current state-of-the-art optical flow methods in predicting complex fluid flows.

CFD simulation of flow interference between multi-stage fractures along a horizontal wellbore

This paper investigates flow interference between multiple hydraulic fractures along a horizontal wellbore. The flow interference may cause large production rate losses and is a threat to reservoir asset management, but it has not received sufficient attention. Capable of simulating complex fluid flow phenomena with a high degree of accuracy, Computational fluid dynamics (CFD) simulation is employed to investigate the flow interference behavior of individual fracture streams and bulk flow in a horizontal wellbore with different fracture numbers and spacing and to provide insights into the relationship between fracture number, fracture spacing, flow velocity, pressure differential, and flow interference intensity. The results show that flow interference arises from competition for flow space between fracture streams. A longer horizontal wellbore and more hydraulic fractures can lead to higher bulk flow velocity and thus higher interference intensity. The interference intensity is found to be positively dependent on fracture number with a fixed fracture spacing. The velocity behaviors of individual fracture streams driven by declining pressure differential are also studied, showing a decline trend related to flow velocity. The intensity undergoes a mitigatory process before reaching a steady decline, and even flow interference at a lower intensity level still can lead to large production rate losses and profit reduction. The study suggests the need for countermeasures during well design and fracturing design to mitigate flow interference and reduce asset management risk.

A Numerical Method for Conformal Mapping of Closed Box Girder Bridges and Its Application

Conformal mapping has achieved many successes in engineering. It can help to solve some complex fluid flow problems. This study proposed a numerical method for conformal mapping of closed box girder bridges and applied it to flutter performance prediction, which is crucial for ensuring the safety and sustainability of bridge structures. The characteristics of conformal mapping coefficients for the closed box were investigated. Thereafter, a numerical method through searching the conformal mapping coefficients was presented. The results show that the proposed numerical method has a smaller error in the existing research. The conformal mapping of six practical bridges agrees well with the closed box girder shapes, indicating the validity of the proposed method. The flutter prediction results by the proposed method are consistent with the wind tunnel test. The conformal mapping and flutter calculations took no more than ten seconds, showing high computing efficiency. This method is easier to understand and implement without complex mathematical derivation, which is helpful for the extensive application of conformal mapping in bridge engineering.