Three-dimensional Incompressible Fluid Research Articles

Numerical investigation of three-dimensional incompressible fluid flow in curved elastic tube

Numerical investigation of three-dimensional incompressible fluid flow in curved elastic tube

One-level and two-level operator splitting methods for the unsteady incompressible micropolar fluid equations with double diffusion convection

In this paper, a one-level operator splitting method (OOSM) and a two-level operator splitting method (TOSM) for the two-dimensional or three-dimensional (2D/3D) unsteady incompressible micropolar fluid equations with double diffusion convection (IMFDDC) are proposed and analyzed. Firstly, a OOSM is constructed, which consists of five steps. The projection strategy is adopted to get the values of linear velocity and pressure in the first two steps, then the three elliptic subproblems about the angular velocity, the temperature, and the concentration variables are solved in the last three steps. The original variables with the predefined boundary conditions need to be solved separately in each step. Next, in order to solve the problem efficiently, a TOSM is presented, which only solves the nonlinear equations in the coarse level subspaces and the Oseen type linearized equations in the fine level. The numerical analysis of stability and error estimates of the fully discrete methods show that TOSM can reach the same accuracy as the OOSM with H∼O(h2/3). Numerical examples are provided to confirm the effectiveness and reliability of the proposed methods.

Hydrodynamic instabilities in a two-dimensional sheet of microswimmers embedded in a three-dimensional fluid

A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated ‘pusher’ swimmers such as bacteria exhibit a collective motion state often referred to as ‘bacterial turbulence’, characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk two and three dimensions, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the three-dimensional bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse the stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: first, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. Given these qualitative differences with respect to the standard bulk setting, we conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.

Modeling of a Three-Dimensional Incompressible Fluid Flow in a Turbulent Boundary Layer in a Diffuser

Modeling of a Three-Dimensional Incompressible Fluid Flow in a Turbulent Boundary Layer in a Diffuser

Large-scale parallel topology optimization of three-dimensional incompressible fluid flows in a level set, anisotropic mesh adaptation framework

This papers considers the topology optimization of duct flows governed by the three-dimensional steady state Navier–Stokes equations, using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The numerical framework combines an immersed volume method solving stabilized, linear equal-order finite element formulations cast in the Variational Multiscale (VMS) framework, and level set representations of the interface, used as a posteriori anisotropic error estimator to minimize the interpolation error under the constraint of a prescribed number of nodes in the mesh. Both the resolution and remeshing steps are performed in a massively parallel framework allowing for the optimization of large-scale systems. In particular, an original parallelization strategy is used for mesh adaptation, that combines local remeshing performed sequentially and independently on each subdomain with blocked interfaces, and constrained repartitioning to optimally move the interfaces between subdomains in an optimal way, both iterated until a satisfying mesh and partition are obtained. The proposed approach reduces the computational burden related to the call of the finite element solver, compared to classical optimization schemes working on uniform grids with similar mesh refinement. For a given number of nodes, it improves the accuracy in the geometric description of all layouts. Finally, it has the potential to alleviates the end user from most of the post-processing step aiming at extracting the final layout, due to ability of anisotropic adapted meshes to generate intrinsically smooth designs. Numerical results are provided for several three-dimensional problems of power dissipation minimization involving several dozen million state degrees of freedom, for which the optimal designs agree well with reference results from the literature, while providing superior accuracy over prior studies solved on isotropic meshes (in the sense that the flow is better resolved, especially in the near-wall regions, and the layouts are more smooth). The potential of the method for engineering problems of practical interest is eventually exposed by optimizing the distributor section conveying the cold fluid within the plates of a plate fin heat exchanger.

Forest density is more effective than tree rigidity at reducing the onshore energy flux of tsunamis

Communities around the world are increasingly interested in nature-based solutions to the mitigation of coastal risks by coastal forests, but it remains unclear how much protective benefits vegetation provides, particularly in the limit of highly energetic flows after tsunami impact. The current study, using a three-dimensional incompressible computational fluid dynamics model with a fluid–structure interaction approach, aims to quantify how energy reflection and dissipation vary with different degrees of rigidity and vegetation density of a coastal forest. We represent tree trunks as cylinders and use the elastic modulus of hardwood trees such as pine or oak to characterize the rigidity of these cylinders. The numerical results show that energy reflection increases with rigidity only for a single cylinder. In the presence of multiple cylinders, the difference in energy reflection created by varying rigidity diminishes as the number of cylinders increases. Instead of rigidity, we find that the blockage area created by the presence of multiple tree trunks dominates energy reflection. As tree trunks are deformed by the hydrodynamic forces, they alter the flow field around them, causing turbulent kinetic energy generation in the wake region. As a consequence, trees dissipate flow energy, highlighting coastal forests reducing the onshore energy flux of tsunamis by means of both reflection and dissipation.

An Evaluation of Accuracy and Efficiency of a 3D Adaptive Mesh Refinement Method with Analytical Velocity Fields

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

Hydrodynamic Characteristics of an Electric Eel-Like Undulating Fin

Taking the electric eel as a bionic object, a long undulatory fin is designed. The turbulent model standard k-ε is used to solve the N‒S equation of a three-dimensional unsteady incompressible fluid. The hydrodynamic characteristics of the undulatory fin are studied, and the influence of the swing angle, wave frequency and ground effects on the propulsion performance of the undulatory fin are discussed. The mathematical models of the average thrust and average lateral force of the undulatory fin are established by using multiple linear regression. The results show that the thrust and lateral force of the undulatory fin increase with increasing swing angle and swing frequency, but in a motion period, the number of fluctuations of the thrust is approximately twice that of the lateral force. The relationship between the average thrust force and the average lateral force of the undulatory fin and the wave frequency and the maximum swing angle satisfies a specific exponential law. When the undulating fin moves near the wall (d ≤0.2 W), due to the coupling between the vortex at the lower edge and the tail vortex where part of the vortex is transferred to the two sides, the total thrust decreases, and the lateral force increases.

Numerical Simulation of Unsteady Hydrodynamic Characteristics of Bionic Fin

A long uncompressed fin driven by fin rays is designed in this paper, and its kinematic model is established. The SST K-ω turbulence model is used to solve the N-S equation of three-dimensional unsteady incompressible fluid, and the hydrodynamic characteristics of the uncompressed fin are studied. The results show that when the undulating fin is started, the velocity of the surrounding fluid gradually increases with the movement of the fin surface, and the fluid moves from the leading edge of the undulating fin to the back edge along the fin surface. A relatively obvious anti-Karman vortex street is formed on both sides of the fin, and a jet is formed at the tail of the fin to generate forward thrust.

Random vortex dynamics via functional stochastic differential equations

In this paper, we present a novel, closed, three-dimensional random vortex dynamics system, which is equivalent to the Navier–Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a stochastic differential equation which is, in contrast with the two-dimensional random vortex dynamics equations, coupled to a finite-dimensional ordinary functional differential equation. This new random vortex system paves the way for devising new numerical schemes (random vortex methods) for solving three-dimensional incompressible fluid flow equations by Monte Carlo simulations. In order to derive the three-dimensional random vortex dynamics equations, we have developed two powerful tools: the first is the duality of the conditional distributions of a couple of Taylor diffusions, which provides a path space version of integration by parts; the second is a forward type Feynman–Kac formula representing solutions to nonlinear parabolic equations in terms of functional integration. These technical tools and the underlying ideas are likely to be useful in treating other nonlinear problems.

Time-Periodic Weak Solutions for an Incompressible Newtonian Fluid Interacting with an Elastic Plate

Under the action of a time-periodic external force we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier--Stokes equation and a two-dimensional elastic plate. The challenge is that the Eulerian domain for the fluid changes in time and is a part of the solution. We introduce a two fixed-point methodology: First we construct a time-periodic solutions for a given variable time-periodic geometry. Then in a second step a (set-valued) fixed point is performed w.r.t. the geometry of the domain. The existence relies on newly developed a priori estimates applicable for both coupled and uncoupled variable geometries. Due to the expected weak regularity of the solutions such Eulerian estimates are unavoidable. Note in particular that only the fluid is assumed to be dissipative; the here-produced a priori estimates show that its possible to exploit the dissipative effects of the fluid also for the solid deformation. The existence of time-periodic solutions for a given geometry is valid for arbitrary large data. The existence of periodic coupled solutions to the fluid-structure interaction is valid for all data that exclude a self-intersection a priori.

An MHD Flow of Non-Newtonian Fluid Due to a Porous Stretching/Shrinking Sheet with Mass Transfer

An examination is carried out for three-dimensional incompressible viscoelastic fluid flow over a porous stretching/shrinking sheet with hybrid nanoparticles copper-alumina (Cu−Al2O3) in base fluid water (H2O). The uniform magnetic field of strength B0 is applied perpendicular to the fluid flow and considered the Navier slip. The mass transfer is considered with the chemical reaction rate. The governing equation for the defined flow forms the system of partial differential equations, which are then transformed into a system of ordinary differential equations via similarity transformations. The goal is to find the exact analytical solution, and the unique solution is determined by considering the boundary layer theory. Furthermore, the obtained system is solved to get the exact analytical solution for velocity and concentration fields in exponential form and in hypergeometric form, respectively. The exact solutions are obtained for velocity and temperature profiles, Skin friction, and Nusselt number. These findings are beneficial for future research in the present area. The parameters magnetic field, Inverse Darcy number, slip parameter, chemical reaction parameter, stretching/shrinking parameter, and viscoelastic parameter, influence the flow. The effect of these parameters on fluid velocity and concentration field will be analyzed through graphs. Skin friction and Nusselt number are also analyzed. This work found many applications in machining and manufacturing, solar energy, MHD flow meters and pumps, power generators, geothermal recovery, flow via filtering devices, chemical catalytic reactors, etc.

Characteristic-Based Fluid Flow Modeling between Two Eccentric Cylinders in Laminar and Turbulent Regimes

Determining the flow between eccentric cylinders is crucial in a wide range of industries. The governing equations for the flow between eccentric cylinders cannot be solved analytically. Therefore, three-dimensional incompressible viscous fluid flow between eccentric and concentric cylinders has numerically been simulated in this paper to investigate them using a characteristic-based approach. The first-order characteristic-based scheme is used to calculate convective terms, whereas the second-order averaging technique is used to calculate viscous fluxes. The Taylor number, eccentricity distance, Reynolds number, and radius ratio are considered the controlling parameters of fluid flow between the cylinders. The influence of flow between cylinders on flow patterns is presented in terms of velocity, pressure, and flow contours. It is found that at a constant Taylor number, the asymmetric centrifugal forces produce the Taylor vortices on the right of the internal rotating cylinder as the eccentric distance increases. When the eccentric distance increases, the magnitude of shear stress and its fluctuation on the cylinder wall, as well as the pressure on the cylinder wall, rise. The numerical results obtained were validated by comparing them to previously published experimental results, which showed a high level of agreement.

Numerical and Experimental Investigation of Internal Flow Characteristics and Pressure Fluctuation in Inlet Passage of Axial Flow Pump under Deflection Flow Conditions

The deflection flow of inlet passage seriously affects the performance of axial flow pump devices, and reduces the operation efficiency and stability of pumping station systems. In this paper, the influence of different deflection angles on the internal flow characteristics and outlet pulsation characteristics of the inlet passage of the vertical axial flow pump are studied. Based on the Reynolds time-averaged N-S equation of the three-dimensional incompressible fluid and the standard k-ε turbulence model, the model axial flow pump device was numerically simulated. Under optimal working conditions (Qbep = 31.04 L/s), the internal flow field of the axial flow pump was analyzed to study the change law of the axial flow pump performance under different deflection angles. Under the flow conditions of 0.6 Qbep, 1.0 Qbep and 1.2 Qbep, the pulsation characteristics of the outlet of inlet passage in axial flow pump at different deflection angles were analyzed. The result shows that with the increase of the deflection angle, the flow pattern of the inlet passage becomes turbulent, forming vortices of different sizes, the hydraulic loss of the inlet passage increases continuously, and the uniformity of the outlet flow velocity of the inlet passage increases first and then decreases. The time-domain waveform of outlet of the inlet passage at the pressure pulsation monitoring point has obvious periodicity, and the dominant frequency of the monitoring point is four times the rotation frequency, which corresponds to the number of impeller blades. It shows that the numerical calculation is in good agreement with the experimental results, which proves the reliability and validity of the numerical simulation calculation.

Spatio-temporal correlations in three-dimensional homogeneous and isotropic turbulence

We use direct numerical simulations (DNSs) of the forced Navier–Stokes equation for a three-dimensional incompressible fluid in order to test recent theoretical predictions. We study the two- and three-point spatiotemporal correlation functions of the velocity field in stationary, isotropic, and homogeneous turbulence. We compare our numerical results to the predictions from the Functional Renormalization Group (FRG) which were obtained in the large wavenumber limit. DNSs are performed at various Reynolds numbers and the correlations are analyzed in different time regimes focusing on the large wavenumbers. At small time delays, we find that the two-point correlation function decays as a Gaussian in the variable kt, where k is the wavenumber and t the time delay. We compute a triple correlation from the time-dependent advection-velocity correlations, and find that it also follows a Gaussian decay at small t with the same prefactor as the one of the two-point functions. These behaviors are in precise agreement with the FRG results, and can be simply understood as a consequence of sweeping. At large time delays, the FRG predicts a crossover to an exponential in k2t, which we were not able to resolve in our simulations. However, we analyze the two-point spatiotemporal correlations of the modulus of the velocity and show that they exhibit this crossover from a Gaussian to an exponential decay, although we lack of a theoretical understanding in this case. This intriguing phenomenon calls for further theoretical investigation.

Global Regularity of Three-Dimensional Incompressible Magneto-Micropolar Fluid Equations with Damping

We deal with the Cauchy problem of three-dimensional incompressible magneto-micropolar fluid equations with a nonlinear damping term $$\alpha |{\mathbf {u}}|^{\beta -1}{\mathbf {u}}\ (\alpha >0\ \text {and}\ \beta \ge 1)$$ in the momentum equations. By cancelation properties of the system under study, we show that there exists a unique global strong solution for any $$\beta \ge 4$$ . Our work extends previous results.

Variable thickness flow over a rotating disk under the influence of variable magnetic field: An application to parametric continuation method

The present work explores the behavior of three-dimensional incompressible viscous fluid flow and heat transfer over the surface of a non-flat stretchable rotating disk. A variable thickness fluid is subjected under the influence of an external variable magnetic field and heat transfer. Navier–Stokes equation is coupled with Maxwell equations to examine the hydrothermal properties of fluid. The basic governing equations of motion are diminished to a system of nonlinear ordinary differential equations using appropriate similarity framework, which are further treated with numerical scheme known as parametric continuation method. The parametric continuation method has combined interesting characteristics of both shooting and implicit finite difference methods. For validity of the present numerical scheme, a comparison with the published work is performed and it is found that the results are in excellent agreement with each other. Numerical and graphical results for the velocity, temperature, and magnetic strength profiles as well as skin fractions and Nusselt number are presented and discussed in detail for various physical parameters. The heat transfer process is reduced with positive increment of no-flatness parameter [Formula: see text], while Prandtl number increases the heat transfer rate at the surface of the disk.

Non-modal stability analysis in viscous fluid flows with slippery walls

A study of optimal temporal and spatial disturbance growths is carried out for three-dimensional viscous incompressible fluid flows with slippery walls. The non-modal temporal stability analysis is performed under the framework of normal velocity and normal vorticity formulations. A Chebyshev spectral collocation method is used to solve the governing equations numerically. For a free surface flow over a slippery inclined plane, the maximum temporal energy amplification intensifies with the effect of wall slip for the spanwise perturbation, but it attenuates with the wall slip when perturbation considers both streamwise and spanwise wavenumbers. It is found that the boundary for the regime of transient growth appears far ahead of the boundary for the regime of exponential growth, which raises a question on the critical Reynolds number for the shear mode predicted from the eigenvalue analysis. Furthermore, the eigenvalue analysis or the modal stability analysis reveals that the unstable region for the shear mode decays rapidly in the presence of wall slip, which is followed by the successive amplification of the critical Reynolds number for the shear mode and ensures the stabilizing effect of slip length on the shear mode. On the other hand, for a channel flow with slippery bounding walls, the maximum spatial energy amplification intensifies with the effect of wall slip in the absence of angular frequency, but it reduces with the wall slip if the angular frequency is present in the disturbance. Furthermore, the maximum spatial energy disturbance growth can be achieved if the disturbance excludes the angular frequency. Furthermore, it is observed that the angular frequency plays an essential role in the pattern formation of optimal response. In addition, the pseudo-resonance phenomenon occurs due to external temporal and spatially harmonic forcings, where the pseudo-resonance peak is much higher than the resonance peak.

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Purpose The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

A single domain velocity - vorticity Fast Multipole Boundary Domain Element Method for three dimensional incompressible fluid flow problems, part II

In the present work, the Fast Multipole Boundary Element Method (FMM / BEM) for solving three-dimensional incompressible fluid flow problems governed by the Navier–Stokes equations is proposed. With the velocity-vorticity formulation the pressure gradient is eliminated from the equations. The kinematics equation, related to the velocity field satisfies continuity and provides a direct boundary condition for the vorticity equation. The single-domain approach is used for the discretization of the entire computational volume. The system of equations is compressed into two vectors and a preconditioner matrix, which is negligible in size. The involved unknowns are velocities, vorticities, and boundary vorticity fluxes. The two governing equations are coupled together in a convergent Newton–Raphson iteration scheme, successfully used for the solution of 3D fluid flow problems on a 32 GB memory computer. The degrees of freedom of the benchmark problems are above to 300000, which is an unreachable limit for the conventional single-domain BEM.