Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

The thermal convection of a Jeffreys fluid subjected to a plane Poiseuille flow in a fluid-porous system composed of a fluid layer and a porous layer is studied in the paper.A linear stability analysis and a Chebyshevτ-QZ algorithm are employed to solve the thermal mixed convection.Unlike the case in a single layer,the neutral curves of the two-layer system may be bi-modal in the proper depth ratio of the two layers.We find that the longitudinal rolls(LRs)only depend on the depth ratio.With the existence of the shear flow,the effects of the depth ratio,the Reynolds number,the Prandtl number,the stress relaxation,and strain retardation times on the transverse rolls(TRs)are also studied.Additionally,the thermal instability of the viscoelastic fluid is found to be more unstable than that of the Newtonian fluid in a two-layer system.In contrast to the case for Newtonian fluids,the TRs rather than the LRs may be the preferred mode for the viscoelastic fluids in some cases.

Algorithm for transient growth of perturbations in channel Poiseuille flow

This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.

THE LINEAR STABILITY OF PLANE POISEUILLE FLOW UNDER UNSTEADY DISTORTION

This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show that in the initial period of disturbance development, the distortion profiles presented by paper [1] will make the disturbances grow up, thus augmenting the possibility of instability.

ON THE RECEPTIVITY OF PIPE POISEUILLE FLOW WITH A BUMP ON THE WALL UNDER THE PERIODICAL PRESSURE

Asymptotic method was adopted to obtain a receptivity model for a pipe Poiseuille flow under periodical pressure,the wall of the pipe with a bump.Bi_orthogonal eigen_function systems and Chebyshev collocation method were used to resolve the problem.Various spatial modes and the receptivity coefficients were obtained.The results show that different modes dominate the flow in different stages,which is comparable with the phenomena observed in experiments.

Design of Poiseuille Flow Controllers Using the Method of Inequalities

This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.

Receptivity of plane Poiseuille flow to local micro-vibration disturbance on wall

The receptivity of plane Poiseuille flow to local single-period micro-vibration disturbances with different phases at the top and bottom walls was investigated through direct numerical simulation of three-dimensional incompressible Navier-Stokes equations. Results show that the disturbance presents a symmetrical distribution in the spanwise direction when the micro-vibration on the wall ends, and the initial disturbance velocities and spatial distribution of the disturbance structure are different at the top and bottom walls. The disturbance＇s velocity, amplitude, and high- and low-speed streaks increase with time, and the amplitude of streamwise disturbance velocity is larger than those of spanwise and vertical disturbance velocities. However, no significant Tollmien-Schlichting wave was found in the flow field. The number of disturbance vortex cores gradually increases with the disturbance area. High-speed disturbance fluid concentrates near the wall and its normal velocity largely points to the wall, while low-speed disturbance fluid largely deviates from the wall. Furthermore, the streamwise velocity profiles near the top and bottom walls both become plump because of the existence of the disturbances, and the streamwise velocity profiles show a trend of evolving into turbulent velocity profiles. The shear stress near the wall increases significantly. The local micro-vibration disturbance on the wall in plane Poiseuille flow can induce the development of a structure similar to turbulent spots.

NUMERICAL SIMULATION OF NANOPARTICLE COAGULATION IN A POISEUILLE FLOW VIA A MOMENT METHOD

Numerical simulations of coagulating nano-scale aerosols in a two dimensional Poiseuille flow between fixed plates are performed. Evolution of the particle field is obtained by utilizing a moment method to approximate the aerosol general dynamic equation. A moment method is used, which assumes a lognormal function for the particle size distribution and requires knowledge of the first three moments. A Damk？hler number is defined to represent the ratio of the convection time scale to the coagulation time scale. Simulations are performed based on three Reynolds numbers, 100, 500 and 1000, and on three initial particle volume fractions corresponding to Damk？hler numbers 0.1, 0.2 and 1.0. Spatio-temporal evolution of the first three moments along with the geometric mean volume and standard deviation are discussed.

INVESTIGATION OF INFLUENCE OF WETTABILITY ON POISEUILLE FLOW VIA MOLECULAR DYNAMICS SIMULATION

In this article,the influence of wettability on a liquid flow between two parallel plane walls were studied by using Non-Equilibrium Molecular Dynamics（NEMD） simulation.The wettability of the solid surfaces can be described as the contact angle.The liquid flow rate,the slip velocity and the slip length which are affected by the contact angle were investigated.The results show that the boundary condition at a microscopic level is different from a ＂no-slip＂ condition at a macroscopic level.There exits a slippage of a liquid flow for the hydrophobic boundary and an external force is needed to overcome threshold pressure for the hydrophilic boundary.And the orderly layered distributions of the liquid particles near the hydrophilic surface vary from a place near the hydrophobic surface.The study indicates that the surface wettability plays a significant role on possibilities of forming a viscous layer and the direct slip at the solid surface.The resistance of liquid flow can be decreased by changing the wettability of boundary surface.

Experimental study of an ellipsoidal particle in tube Poiseuille flow

Behaviors of a prolate ellipsoid inside circular tube Poiseuille flow are studied experimentally. In the study, Reynolds number Re ∈ (100,700) and the confinement ratio D/A ∈ (1.2,2.8) are considered, where D is the diameter of the tube and A is the length of the major axis of the ellipsoid. Two typical stable motion modes are identified, namely, the horizontal, and inclined modes. Then another inclined mode (inclined mode II) is found at high Reynolds number (Re ∈ (1000,3200)) and small D/A, and the inclined angle of ellipsoid increases with the increase of Re. The possible mechanism is explained. Our experiment shows that the lagging velocity U increases as Re increases. Further numerical analysis using FLUENT shows that due to the increase of U, the moment acting on the particle would make the inclined angle of the particle increase.

ANOMALOUS DIFFUSION IN FINITE LENGTH FINGERS COMB FRAME WITH THE EFFECTS OF TIME AND SPACE RIESZ FRACTIONAL CATTANEO-CHRISTOV FLUX AND POISEUILLE FLOW

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds＇ upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the Ll-scheme and shifted Griinwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

Unsteady Dynamics of Vesicles in a Confined Poiseuille Flow

The dynamic behaviors of a single vesicle bounded by the cylindrical wall in a Poiseuille flow were investigated by considering different confinements and dimensionless shear rates. By observing the evolution of two adjacent particles attached to the internal and external surfaces of the spherical vesicles, we found they had the same frequency. The vorticity trajectories formed by the time-tracing of the particles on the membrane are parallel, which can be identified as the unsteady rolling motion of the membranes due to the unfixed axis. The dynamic behaviors of vesicles are associated with the confinement degree and the dimensionless shear rate. The smaller dimensionless shear rate will result in the slower frequency of the rolling by examining the velocity of the rolling. The weakened rolling motion under stronger confinements is observed by measuring the evolution of the orientation angles. The changes of revolution axes over time can be interpreted by the lateral excursion of the center of mass on the orthogonal plane of the flow.

Role of Hydrodynamic Interactions in the Deformation of Star Polymers in Poiseuille Flow

Stretching polymer in fluid flow is a vital process for studying and utilizing the physical properties of these molecules,such as DNA linearization in nanofluidic channels.We studied the role of hydrodynamic interactions(His)in stretching a free star polymer in Poiseuille flow through a tube using mesoscale hydrodynamic simulations.As increasing the flow strength,star polymers migrate toward the centerline of tube due to His,whereas toward the tube wall in the absence of His.By analyzing the end monomer distribution and the perturbed flow around the star polymer,we found that the polymer acts like a shield against the flow,leading to additional hydrodynamic drag forces that compress the arm chains in the front of the star center toward the tube axis and lift the arm chai ns at the back toward the tube wall.The balanced hydrodynamic forces freeze the polymer into a trumpet structure,where the arm chains maintain a steady strongly stretched state at high flow strength.In contrast,the polymer displays remarkably large conformational change when switching off His.Our simulation results explained the coupling between His and the structure of star polymers in Poiseuille flow.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Numerical Simulation of Interaction Between Red Blood Cell with Surrounding Fluid in Poiseuille Flow

In this research,motion and deformation of a red blood cell(RBC)in a microchannel with stenosis is investigated by combined Lattice Boltzmann-Immersed Boundary method.The fluid flow occurs due to the pressure difference between the inlet and the outlet of the microchannel.The immersed boundary algorithm guaranteed that there is no relative velocity between the RBC and fluid.Therefore,mass transfer along the immersed border does not occur.It can be seen that the healthy RBC has more deformation and passes the stenosis easier while the sick one passes the stenosis with less deformation and returns to its initial state faster.Increasing the pressure gradient(i.e.,increasing Reynolds number)would cause more deformation of the RBC.It is found that a healthy RBC moves faster than a sick one along the microchannel.Blood pressure increases due to the presence of stenosis and low deformable RBCs.It is the reason of many serious diseases including cardiovascular diseases.The results of this paper were compared to the previous valid results and good agreements were observed.

Numerical Validation of Brenner’s Hydrodynamic Model by Force Driven Poiseuille Flow

Recently Brenner[Physica A 349,60(2005)]proposed a modified NavierStokes set of equations.Based on some theoretical arguments and some limited experiments,the model is expected to be able to describe flows with a finite Knudsen number.In this work,we apply this model to the plane Poiseuille flow driven by a force,and compare the results with the Direct Simulation Monte Carlo(DSMC)measurements.It is found that Brenner’s model is inadequate for flows with a finite Knudsen number.

Linear Stability of Taylor-Couette Flows with Axial Heat Buoyancy

The linear stability is studied of flows confined between two concentric cylinders, in which the radial temperature gradient and axial gravity are considered for an incompressible Newtonian fluid. Numerical method based on the Petrov-Galerkin scheme is developed to deal with the buoyancy term in momentum equations and an additional temperature perturbation equation. Computations of the neutral stability curves are performed for different rotation cases. It is found that the flow instability is influenced by both centrifugal and axial shear instabilities, and the two instability mechanisms interact with each other. The outer cylinder rotation plays dual roles of stabilizer and destabilizer under different rotating stages with the inner cylinder at rest. For the heat buoyancyinduced axial flow, spiral structures are found in the instability modes.

Linear stability of a fluid channel with a porous layer in the center

We perform a Poiseuille flow in a channel linear stability analysis of a inserted with one porous layer in the centre, and focus mainly on the effect of porous filling ratio. The spectral collocation technique is adopted to solve the coupled linear stability problem. We investigate the effect of permeability, σ, with fixed porous filling ratio ψ = 1/3 and then the effect of change in porous filling ratio. As shown in the paper, with increasing σ, almost each eigenvalue on the upper left branch has two subbranches at ψ = 1/3. The channel flow with one porous layer inserted at its middle （ψ = 1/3） is more stable than the structure of two porous layers at upper and bottom walls with the same parameters. By decreasing the filling ratio ψ, the modes on the upper left branch are almost in pairs and move in opposite directions, especially one of the two unstable modes moves back to a stable mode, while the other becomes more instable. It is concluded that there are at most two unstable modes with decreasing filling ratio ψ. By analyzing the relation between ψ and the maximum imaginary part of the streamwise phase speed, Cimax, we find that increasing Re has a destabilizing effect and the effect is more obvious for small Re, where ψ a remarkable drop in Cimax can be observed. The most unstable mode is more sensitive at small filling ratio ψ, and decreasing ψ can not always increase the linear stability. There is a maximum value of Cimax which appears at a small porous filling ratio when Re is larger than 2 000. And the value of filling ratio 0 corresponding to the maximum value of Cimax in the most unstable state is increased with in- creasing Re. There is a critical value of porous filling ratio （= 0.24） for Re = 500; the structure will become stable as ψ grows to surpass the threshold of 0.24; When porous filling ratio ψ increases from 0.4 to 0.6, there is hardly any changes in the values of Cimax. We have also observed that the critical Reynolds number is especially sensitive for small ψ where the fastest drop is observed, and there may be a wide range in which the porous filling ratio has less effect on the stability （ψ ranges from 0.2 to 0.6 at σ = 0.002）. At larger permeability, σ, the critical Reynolds number tends to converge no matter what the value of porous filling ratio is.

Numerical investigation of Reynolds number and scaling effects in microchannels flows

Compared with conventional channels, experiments of microchannel often exhibit some controversial findings and sometimes even opposite trends, most notably the effects of the Reynolds number and the scaled channel height on the Poiseuille number. The experimental method has still been constrained by two key facts, firstly the current ability to machine microstructures and secondly the limitation of measurement of parameters related to the Poiseuille number. As a consequence, numerical method was adopted in this study in order to analyze a flow in two-dimensional rectangular microchannels using water as working fluid. Results are obtained by the solution of the steady laminar incompressible Navier-Stokes equations using control volume finite element method（CVFEM） without pressure correction. The computation was made for channel height ranging from 50 ？m to 4.58 ？m and Reynolds number varying from 0.4 to 1 600. The effect of Reynolds number and channel heights on flow characteristics was investigated. The results showed that the Poiseuille numbers agree fairly well with the experimental measurements proving that there is no scale effect at small channel height. This scaling effect has been confirmed by two additional simulations being carried out at channel heights of 2.5 ？m and 0.5 ？m, respectively and the range of Reynolds number was extended from 0.01 up to 1 600. This study confirm that the conventional analysis approach can be employed with confidence for predicting flow behavior in microchannels when coupled with carefully matched entrance and boundary conditions in the dimensional range considered here.

AN IMPLICIT SCHEME FOR INCOMPRESSIBLE LBGK MODEL

In this paper, an implicit scheme (also called the θ method) was proposed for the Lattice Bhatager-Gross-Krook (LBGK) model simulating incompressible flows. The new parameter θ made the model more flexible. Through the Chapman-Enskog procedure the impressible Navie-Stokes equations could be recovered with the coupled kinetic viscosity. Boundary conditions were treated briefly and it kept the numerical accuracy of the Lattice Boltzmann Method (LBM). The two-dimensional Poiseuille flow was simulated with different values of the parameters. It is found that the numerical accuracy and stability of the implicit scheme can be improved if some adaptable parameters are chosen.

Improving the Stability of theMultiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.