Two-dimensional Navier-Stokes Research Articles

Parametric study of a fluidic oscillator for heat transfer enhancement of a hot plate impinged by a sweeping jet

• CFD and experimental studies are conducted on the heat transfer of fluidic oscillators. • Effect on the heat transfer rate due to new geometrical changes is studied. • Experimental study was conducted to verify the numerical results for the fluidic oscillator. • Heat transfer rate was increased by 140% when removing the external diffuser. • Heat transfer was decreased when increasing the distance ratio and divergence angle. Many studies have looked at the effects of various geometrical parameters of fluidic oscillators on the heat transfer rate of a hot plate impinged by a sweeping jet. In this research, Ansys-Fluent software was used to solve two-dimensional Unsteady Reynolds-Averaged Navier-Stokes ( URANS ) equations with a k-ω (SST) turbulence model to study the effect on the heat transfer rate of a hot plate due to some new geometrical changes, such as removing the external diffuser, changing the divergence angle of the external diffuser, and changing the distance from the outlet throat to the hot plate. An experimental setup was provided to verify the numerical results for the fluidic oscillator with an external diffuser. To measure the temperature inside and near the surface, 22 thermocouples were used inside a thick hot plate, which was impinged by a sweeping jet. Three distance ratios ( X/D = 4.5, 5.5 and 7.5) and four divergence angles ( θ = 180°, 50°, 70°, and 90°) were numerically analyzed as the geometrical parameters at Reynolds number of 30,000, 60,000, and 120,000. The results revealed that the heat transfer rate increased by 140% when removing the external diffuser at X/D = 4.5 and Re = 60,000, while it decreased when increasing the distance ratio and divergence angle.

Quantifying particle adhesion to the ureteral walls during peristaltic flow.

In this paper, we investigate the motion of particle(s) under the action of peristaltic flow. The particle trajectories are simulated by considering sinusoidal peristaltic waves. The fluid flow is governed by a two-dimensional Navier-Stokes equation, whereas for the particle dynamics we use the Basset-Boussinesq-Oseen (BBO) equation. The particle trajectories computed for different characteristic peristaltic flows, that is, trapping flow, augmented flow, and backward flow, show that the net horizontal particle displacement is largest for the augmented flow case. In general, the particle motion depends on its location in the peristaltic channel because of the wall curvature, which directly affects the flow velocities. The reported results for a cluster of particles show that whilst a fraction of particles form a group and propagate along the wave, some particles are left behind that deposit on the channel wall. In many biological processes it is desirable to know the number of particles that accumulate on the channel walls. In the present work, we propose empirical relations which can be used to calculate particle adhesion as a function of time.

Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for random dynamical systems via the approach of global random attractors. Then we consider the two-dimensional incompressible Navier-Stokes equations with additive white noise as an example to show how to check the sufficient conditions for concrete stochastic partial differential equations. Our results generalize the Liouville type theorem to the random case and reveal that the invariance of the sample measures is a particular situation of the random Liouville type theorem.

The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows

In this paper, we mainly concern with the order reduction for the unknown solution coefficient vectors about the classical continuous space-time finite element (CCSTFE) method of the two-dimensional (2D) non-stationary incompressible Navier-Stokes equations. Therefore, we first build the CCSTFE scheme for the 2D non-stationary Navier-Stokes equations with respect to stream–vorticity functions, give the existence and stability together with convergence to the CCSTFE solutions, and rewrite the CCSTFE scheme as a matrix form. And then, we use a proper orthogonal decomposition (POD) technique to build a reduced-order extrapolated continuous space-time finite element (ROECSTFE) scheme in the matrix form including very few unknowns but possessing high enough accuracy, employ matrix analysis to demonstrate the existence and stability together with convergence of the ROECSTFE solutions such that the theoretical analysis becomes very concise and convenient, and summarize the flowchart for solving the ROECSTFE scheme. Finally, we take advantage of the numerical simulations for the back-step flow and the flow around airfoil problem to verify the correctness of theoretical results.

Stabilization of exact coherent structures in two-dimensional turbulence using time-delayed feedback

Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form $\dot{\mathbf{x}}(t)=f(\mathbf{x})$ has an additional term $G(\mathbf{x}(t)-\mathbf{x}(t-T))$ introduced where $G$ is some `gain matrix' and $T$ a time delay. The form of the delay term is such that it will vanish for any orbit of period $T,$ therefore making it also an orbit of the uncontrolled system. This non-invasive feature makes the method attractive for stabilising exact coherent structures in fluid turbulence. Here we begin by validating the method for the basic flow in Kolmogorov flow; a two-dimensional incompressible Navier-Stokes flow with a sinusoidal body force. The linear predictions for stabilisation are well captured by direct numerical simulation. By applying an adaptive method to adjust the streamwise translation of the delay, a known travelling wave solution is able to be stabilised up to relatively high Reynolds number. We discover that the famous `odd-number' limitation of this time-delayed feedback method can be overcome in the fluid problem by using the symmetries of the system. This leads to the discovery of 8 additional exact coherent structures which can be stabilised with this approach. This means that certain unstable exact coherent structures can be obtained by simply time-stepping a modified set of equations, thus circumventing the usual convergence algorithms.

Numerical investigation of local scour around a vibration pipeline under free surface wave condition

A two-dimensional finite element numerical model was developed to predict local scour around a vibration submarine pipeline under free surface wave condition. The flow governing equations are the two-dimensional Navier-Stokes equations which were closed by using the Shear-Stress Transport (SST) k-ω turbulence model. Both suspended load and bed load sediment transportations are considered in the scour model. The Arbitrary Lagrangian-Eulerian (ALE) method was used to track the moving boundaries induced by the vibration pipeline, the free wave surface, and the evolution of the seabed due to local scour. Satisfactory results were obtained after validations carried out. The numerical model is then used to investigate local scour around a vibration pipeline under free surface wave conditions. Present numerical results show that vibration makes the scour depth below the pipeline deeper, scour scope around the pipeline wider.

Efficient semi-implicit coupling fluid-structure interaction analysis via model-order reduction of dynamic grids

In this paper, a fluid-structure interaction (FSI) using the model-order reduction (MOR) of dynamic grids is proposed. Within the interface problem between the fluid and the structure, the grid deformation is based on the spring analogy, and it is further extended in order for the efficient computation. In this procedure, the projection-based MOR technique is employed. The relevant MOR technique is realized by using the proper orthogonal decomposition and the discrete empirical interpolation method (POD/DEIM). The resulting FSI framework is based on a semi-implicit coupling approach. In order to achieve this, a characteristic-based split (CBS) scheme is used for an arbitrary Lagrangian–Eulerian (ALE) formulation of the two-dimensional Navier-Stokes equation. Also, a structural analysis is based on the co-rotational (CR) formulation in order to simulate the geometrically nonlinear behavior. Both the fluid and structural analyses are combined with the semi-implicit coupling approach, and the relevant algorithm is embedded in the ALE/CBS scheme. Then, the present FSI analysis is verified using three examples, and the computational efficiency is evaluated. The resulting numerical data demonstrated the validity of the present analysis, and it is found that a significant reduction in the computational cost is possibly achieved with the proposed approach.

Boundedness and asymptotic behavior in a Keller-Segel(-Navier)-Stokes system with indirect signal production

This paper deals with the Keller-Segel(-Navier)-Stokes system with indirect signal production(⋆){nt+u⋅∇n=Δn−∇⋅(n∇v)+rn−μn2,vt+u⋅∇v=Δv−v+w,wt+u⋅∇w=Δw−w+n,ut+κ(u⋅∇)u=Δu−∇P+n∇Φ,∇⋅u=0 in a bounded and smooth domain Ω⊂RN(N=2,3) with no-flux boundary for n, v, w and no-slip boundary for u, where r∈R, μ≥0, κ∈{0,1} and Φ∈W2,∞(Ω). In the case without logistic source (r=μ=0), it is proved that for all suitably regular initial data, the associated initial-boundary value problem for the spatially two-dimensional Navier-Stokes system (⋆) admits a globally bounded classical solution. This result improves and extends the previously known ones. We point out that the same result to the corresponding two-dimensional Navier-Stokes system with direct signal production holds necessarily imposing some saturated chemotactic sensitivity, logistic damping or small total initial population mass. In the case coupled with logistic source (r∈R, μ>0), it is shown that for any reasonably regular initial data, the corresponding initial-boundary value problem for the spatially three-dimensional Stokes system (⋆) possesses a globally bounded classical solution, and that this solution stabilizes toward the corresponding spatially homogeneous equilibrium with the explicit convergence rates for the cases r<0, r=0 and r>0. We underline that the global boundedness of classical solution to the corresponding three-dimensional Stokes system with direct signal production was obtained only for μ≥23 (or sublinear signal production), and that the convergence result to the corresponding system with direct signal production was established only for r=0 and μ≥23. Our results rigorously confirm that the indirect signal production mechanism genuinely contributes to the global boundedness of classical solution to the Keller-Segel(-Navier)-Stokes system.

Convective instability in multicomponent mixtures with Soret effect

We study the two-dimensional modes of gravity-dependent convective instability arising in a ternary mixture in a plane horizontal layer. The gravity force is oriented perpendicular to the layer heated from below. It is assumed that the system is in the state of mechanical equilibrium of a mixture considered as the base state of the system, which can become unstable under certain conditions. The mathematical model uses two-dimensional Navier-Stokes equations, transfer equations for describing mixture components with the Soret effect, and a heat transfer equation. Under the influence of a concentration gradient, the heat transfer symmetric to the Soret effect is neglected because it is usually small in water-based mixtures. The possible concentration-dependent diffusion and cross-diffusion of dissolved components are also neglected. We investigate a convective stability using linear approximation and under finite-amplitude convection regimes. The stability analysis of the base state after linearization of the governing equations with respect to the state of mechanical equilibrium predicts various convection modes. For each case, a neutral curve and the dependences of the disturbance growth decrements on both the Rayleigh number and the wave number are plotted. We show that in the case of the layer being heated from below, there are ranges of governing parameters where both long-wave and short-wave modes of oscillatory instability occur. The numerical analysis of a nonlinear coupling between these modes has revealed that such instabilities develop in the ternary mixtures whose components are arranged (due to the Soret effect) in different directions with respect to the temperature gradient. The effect of the Rayleigh number on the flow structure and heat mass transfer is demonstrated.

On the crest factor and its relevance in detecting turbulent behaviour in solutions of partial differential equations.

In this work we investigate the connection between two fundamental features of solutions of partial differential equations (PDEs), namely the crest factor and the length scale associated to each solution. We illustrate how the crest factor of solutions of some linear and non-linear PDEs, including the incompressible two-dimensional Navier-Stokes equations, has the capability for detecting turbulent and non-turbulent behaviour.

A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations

We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan [1] to compressible Navier-Stokes equations. The new DDGIC framework is based on the observation that the nonlinear diffusion can be represented as a sum of multiple individual diffusion processes corresponding to each conserved variable. A set of direction vectors corresponding to each individual diffusion process is defined as a function of the exact solution and approximated using the average value of the numerical solution at the cell interfaces. The new framework only requires the computation of conserved variables' gradient, which is linear and approximated by the original direct DG numerical flux formula. The proposed method greatly simplifies the implementation, and thus, can be easily extended to general equations and turbulence models. Numerical experiments with P1, P2, P3 and P4 polynomial approximations are performed to verify the optimal (k+1)th high-order accuracy of the method. The new DDGIC method is shown to be able to accurately calculate physical quantities such as lift, drag, and friction coefficients as well as separation angle and Strouhal number.

On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.

CFD investigation on scour beneath different configurations of piggyback pipelines under steady current flow

Scour beneath piggyback pipelines laid on a sandy seabed is numerically investigated by solving two-dimensional (2D) Unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The fluid flow and the sediment transport are resolved using a two-phase flow Eulerian-Eulerian numerical solver SedFoam based on the open-source code OpenFOAM. A parametric study is performed for different Shields parameters defined as θ=Uf2/(s−1)gd50 of 0.068, 0.18 and 0.33 where Uf denotes the shear friction velocity on the seabed, the specific density of the sediment grains is s=ρs/ρf where ρs and ρf are the density of the solid and fluid phases, respectively, g is the gravitational acceleration and d50 is the median grain diameter. Scour processes beneath piggyback pipelines under steady current flow condition are studied for different gap ratios of G/D=0,0.15,0.25 and 0.35 between the main cylinder and the additional ones with a diameter ratio of d/D=0.3 between them. Mesh convergence studies based on the scour depth and the sediment profile are performed to obtain an appropriate grid resolution. A validation study is performed by comparing the scour depth of the single cylinder cases with the published experimental results obtained by Mao (1986). The effects of different θ and geometry configurations on the scour depth and the sediment profile are obtained and discussed.

Wetting and non-wetting liquid flow in nanopores: Wettability, non-Poiseuille profile and intermolecular fundamentals

Wetting and non-wetting liquid flow in nanoscale pores or channels is of great interest in many science and technology fields, such as biotechnology, energy storage/conversion and micro-devices. It is also of considerable significance in geosciences and geoengineering. For instance, for the geological disposal of contaminated waste understanding flow and transport in nanoporous rocks is critical for accurately evaluating potential environmental hazards. Similarly, for oil recovery from tight reservoirs, understanding flow mechanisms in nanopores may improve production forecasts and enable the development of strategies to enhance production.This paper presents a comprehensive study on wetting and non-wetting liquid flow in nanopores, including the development of a new nanoflow model and its demonstration using published findings from molecular dynamics simulations and laboratory tests. The new nanoflow model is formulated based on the general two-dimensional Navier-Stokes equations. The novel aspects include: 1) the model incorporates the parameters relating to the intermolecular interactions between the fluid and the solid wall in a nanopore, which are lacking in traditional continuum models; 2) the model contains the effects of wettability and the nanochannel’s dimension on flowrate, which are unique to nanoflows and not considered in traditional continuum models; and 3) the model is based on a two-dimensional non-Poiseuille flow model described by a set of coupled ordinary differential equations. Therefore, the numerical solutions are much easier to obtain than the partial differential equations of non-Poiseuille flow models. The classic Poiseuille flow is its limiting case.Three examples are presented to demonstrate the model’s capability. The first is the determination of the contact angle of water in hydrophobic carbon nanochannels or nanotubes using published results from MD simulations and laboratory tests. The second example uses the new nanoflow model to simulate non-wetting water flow in hydrophobic nanochannels or nanotubes, including flow in a nanoscale graphene slit representative of those present in graphene batteries for energy storage. The results obtained are compared with those obtained from MD simulations. The last example discusses the wetting or partially wetting liquid flow profiles in nanoscale pores. The three examples provide new insights into wetting and non-wetting liquid flow behaviour in nanopores.

Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas

Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations

In this paper, linearly implicit backward differentiation formulas with variable step-sizes are proposed to solve numerically the two-dimensional incompressible Navier-Stokes equations (formulated in vorticity-stream function). With Fourier pseudospectral methods for spatial discretization, the diffusion term is discretized implicitly and the nonlinear convection term is treated by a combination of implicit and explicit discretizations. As a result, only linear solvers are needed at each time step to achieve the desired temporal accuracy. With the help of a priori assumption and aliasing error control techniques, the error estimates for one-step and two-step backward differentiation formulas are established in several norms under appropriate step-size constraints. Compared with the numerical results of implicit-explicit (the nonlinear convection term is treated explicitly) BDF2 method and fully implicit Crank-Nicolson method, it demonstrates that the proposed linearly implicit variable step-size BDF2 method is effective and robust.

Computer Simulation of Water Flow Animation Based on Two-Dimensional Navier-Stokes Equations

Simulation of water flow animation is a significant and challenging subject in computer graphics. With the continuous development of computational fluid dynamics and computer graphics, many more effective simulation methods have been developed, and fluid animation simulation has developed rapidly. In order to obtain realistic flow animation, one of the key aspects is to simulate flow motion. Based on the two-dimensional Navier-Stokes equations, a mathematical model is established to solve the boundary conditions required by the physical flow field of water. The coordinate transformation formula is introduced to transform the irregular physical area into a regular square calculation area, and then, the specific expressions of the liberalized Navier-Stokes equation, continuity equation, pressure Poisson equation, and dimensionless boundary conditions are given. Using animation software to sequence graphics and images of all kinds of control and direct operation of the relevant instructions, through the computer technology to simulate the flow of animation, based on the stability of fluid simulation method and simulation efficiency, so as to make realistic flow animation. The results show that FluidsNet has considerable performance in accelerating large scene animation simulation on the basis of ensuring the rationality of prediction, and the motion of water wave is realistic. The application of computer successfully simulates water flow.

Characterisation and comparison of unsteady actuators: a fluidic oscillator and a sweeping jet

PurposeThe purpose of this study is to compare two unsteady actuators: an oscillator and a sweeping jet. Both actuators can produce an oscillating jet of different amplitudes and frequencies without any moving parts, making them an attractive actuator concept. The Coanda effect phenomenon can explain the operating principles of these two unsteady actuators.Design/methodology/approachA numerical study was conducted to compare the amplitudes and frequencies of fluidic and sweeping jet (SJ) oscillators to obtain an efficient actuator to control separated flows at high Reynolds numbers. For this goal, two-dimensional unsteady Reynolds-averaged Navier-Stokes simulations were carried out using computational fluid dynamics (CFD) fluent code to evaluate the actuator performances. The discrete fast Fourier transform method determined the oscillation frequencies.FindingsThe oscillation frequencies gradually increase as the inlet pressure increases. The characteristics and dimensions of the vortices produced in the mixing chamber and feedback loops vary overtime when the injected fluid is swept sideways. The frequencies supplied by the SJ are stronger than those obtained by the fluidic oscillator, which may contribute to improving the aerodynamic performance at a lower power supply cost.Originality/valueThe existence of the splitter in the fluidic oscillator led to the production of separate pulses, which would be useful in various industrial applications, including active control of combustion and mixing processes while other applications such as flow separation control require SJs. With the latter actuator higher and interesting frequencies can be obtained, leading to efficient flow control.

Well-posedness and large deviations for 2D stochastic constrained Navier-Stokes equations driven by Lévy noise in the Marcus canonical form

We consider stochastic two-dimensional constrained Navier-Stokes equations driven by Lévy noise in the Marcus canonical form. The aim of this work is two-fold. At first, we prove the existence of a martingale solution based on the construction relying on classical Faedo-Galerkin approximations, compactness method and the Jakubowski's version of Skorokhod representation theorem for non-metric spaces. We further prove that the martingale solution is pathwise unique and deduces the existence of a strong solution. In the second part of the paper, we establish a Wentzell-Freidlin type large deviations principle for the small noise asymptotic of solutions using weak convergence method.

Influence of turbulence intensity on vortex pattern for a rigid cylinder with turbulence stimulation in flow induced oscillations

The effect of ambient turbulence intensity on the flow induced oscillations of rigid circular cylinders with symmetric and asymmetric local turbulence stimulation is studied. Cylinders oscillate in one degree of freedom transversely to a steady uniform flow. Two-dimensional unsteady Reynolds-Average Navier-Stokes equations with the Spalart-Allmaras turbulence model are used to solve the problem numerically. Three freestream turbulence intensity values (0.2%, 1%, 5%) are used to study the influence of turbulence intensity on vortex pattern. Simulation results are compared with experimental data measured in the Marine Renewable Energy Laboratory of the University of Michigan in the range of 30,000 ≤ Re ≤ 110,000. The amplitude ratio, lift coefficient, vortex modes, and the interactions between vortices and cylinders are observed and discussed. Major conclusions are: (a) Vortex patterns strongly depend on the freestream ambient turbulence intensity. (b) Low turbulence intensity can generate multi-vortex patterns at high Re. (c) High turbulence intensity results in fewer separations of a shed vortex into multiple vortices inducing emergence of elongated vortex patterns.