Plane Channel Research Articles

Numerical investigation of gas separation in the system of filaments with different temperatures

The article presents a numerical investigation of separation effect for the mixture of noble gases in a plane channel with a system of differently heated cylindrical filaments. The separation performance for various geometric configurations and Knudsen numbers is studied through event-driven molecular dynamics method (EDMD). A detailed physical explanation of the separation mechanism in such a device is provided based on the obtained results.

Application of the analytical discrete velocities method for calculating mass and heat fluxes of rarefied gas in the problem of the Poiseuille flow

Analytical version of the discrete ordinates method is used to for calculating the gas macroparameters in a plane channel in the problem of Poiseuille flow. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables is written in a matrix form. Householder algorithm is used for reducing the coefficient matrix to a tridiagonal one. QL algorithm with implicit shifts is applied for searching eigenvalues. The Gauss method with a permutation of the rows is used to determine the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls. The software implementation of the algorithm is developed using the C ++ programming language. The mass velocity profile and the heat flow profile of the gas, the flow rate and heat flow through the cross section of the channel are calculated for a wide range of the Knudsen number. The comparison with similar results presented in the open press is performed.

Numerical investigation of two-phase flow characteristics in multiphase pump with split vane impellers

Multiphase pump is a cost-effective option for subsea oil and gas field development. The ability to handle different inlet gas volume fractions (GVFs) especially high inlet GVF is critical to the development of pump performance. In this study, the two-phase flow characteristics in normal impeller and split vane impeller at different inlet GVFs were investigated by steady numerical simulations. The gas distribution on blade-to-blade plane and meridional flow channel at different inlet GVFs were analyzed and compared. Gas accumulation area and movement characteristics of the gas-liquid flow in impeller flow passage were also pointed out by unsteady simulations. Experimental results of the pump differential pressure were compared with the numerical simulation results, to validate the accuracy of numerical simulation method. The flow characteristics in pump with modified impeller and its performance at different inlet GVFs were both compared with that of the normal impeller. The steady simulation results of normal impeller in different inlet GVFs show that gas concentrating area in the flow passage increases as inlet GVF grows. The unsteady simulation results indicate that gas pocket firstly occurs on the pressure side of impeller, then moves to the suction side in the middle area of blade and finally transfers to outlet of impeller and disappears. The errors between numerical simulation results and experiment data are below 10 %, which validated the feasibility of the numerical simulation method. Simulation results on the split vane impeller demonstrate that the gas accumulation area in flow passage of the modified impeller is dramatically decreased compared to that of the normal impeller. The performance of the modified impeller is generally better than the normal impeller especially in high inlet GVF conditions.

On formation of exotic particles at channeling of low energy antiprotons in LiH crystals

In this work we propose a new method to form both protonium exotic $$ \mathrm{p}\overline{\mathrm{p}} $$ and lithium antiproton $$ \overline{\mathrm{p}}{\mathrm{Li}}^{+} $$ atoms by capturing the hydrogen H− and lithium Li+ ions of the LiH crystal lattice at planar or axial channeling of low-energy antiproton beams. Within sudden-perturbation approximation the probability for protons as well as for ions to be bound into different quantum levels defined by the antiproton Coulomb potential are calculated. It is shown that the probability strongly depends on the parameters of channeled antiprotons revealing various extremes (resonances): the functions of capture probabilities for all excited quantum states of antiproton are characterized by three most intense peaks. Higher probability to form heavier particles, namely antiproton lithium $$ \overline{\mathrm{p}}{\mathrm{Li}}^{+} $$, have been demonstrated.

A lotus leaf based random laser

Abstract Random lasing in a lotus leaf, with a wide tunable spectrum from planar liquid waveguide gain channels is described. The lotus leaf shows multiple scattering from the micro-papilla and nanoscale coralloid tomentum on its surface. The Fraunhofer diffraction pattern demonstrates excellent coherence and directionality for our random laser. The emission spectrum wavelength can be tuned by changing the pump position due to the random distribution of the micro/nano-scale features on the lotus leaf. Potential applications of the random laser include probing micro/nano-scale structural alterations, optical biosensors on chips, and developing a multi-color random laser.

Heat transfer enhancement in flow past triangular turbulence promoters in closed channels

The global competitiveness has led industries to investigate innovative strategies to increase heat transfer. This work is inserted within this context and focuses on heat transfer enhancement in plane channels using triangular turbulence promoters. The SST turbulence model is adopted owing to its improved capacity to simulate flows with adverse pressure gradients. Verification and validation are performed by comparing numerical results against theoretical/experimental/numerical data for a plane channel and backward facing step. The location of the turbulence promoters was investigated and the best performance (minimum pressure drop/maximum heat transfer rate) was achieved when the turbulence promoters are aligned and positioned close to one of the channel walls.

Characteristics of the Instability Developing in the Turbulent Flow in a Plane Channel

Disturbance evolution in developed turbulent flows in a plane channel is numerically investigated at the Reynolds numbers up to Reτ = 586. Steady turbulent flows calculated on the basis of the solution of the incompressible Navier—Stokes equations are then used as the baseline flows in studying the disturbance development process. The values of the highest Lyapunov exponent (HLE) λ1 are found and the instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are determined. Under arbitrary initial conditions the regime of the exponential disturbance growth ~ exp(λ1t) is reached for a time Δt+ < 50. It is found that the HLE value increases with the Reynolds number from λ1+ ≈ 0.021 at Reτ = 180 to λ1+ ≈ 0.026 at Reτ = 586. The LLV exhibits itself in the form of time- and space-localized spots of highly intense pulsations, concentrated in the buffer layer region. The distributions of the r.m.s. intensities of the velocity and vorticity pulsations in the LLV are qualitatively similar with the corresponding distributions in the main flow with near-wall streaks artificially extracted from it. The difference is a large disturbance concentration in the vicinity of the buffer layer, y+ = 10–30, and a relatively high (about 80% higher) vorticity pulsations amplitude. Basing upon the energy spectra of the velocity and vorticity pulsations we determined the integral spatial scales of the structures in the LLV field. It is found that the LLV structures are on average half as wide and long as the corresponding structures in the main flow. The contributions of all the terms included in the expression for the production of the kinetic energy of disturbances are determined. It is shown that the process of disturbance development is essentially controlled by the main flow inhomogeneity and the occurrence of transverse motion in it. Neglecting these factors leads to a considerable underestimation of the disturbance growth rate. Contrariwise, the presence of near-wall streaks in the main flow does not play a considerable role in the LLV disturbance development. The artificial extraction of the streaks from the main flow field does not change the nature of disturbance growth.

Production‐limited delayed detached eddy simulation of turbulent flow and heat transfer

AbstractA hybrid RANS/LES model based on the BSL k‐ω RANS model, termed the production‐limited delayed detached eddy simulation (PL‐DDES) model, was developed for simulating turbulent flow and heat transfer. The PL‐DDES model was obtained by limiting the production of turbulence kinetic energy with the proposed control resolution function. The PL‐DDES model was tested by simulating turbulent flow and heat transfer in a plane and a wavy channel with different thermal boundary conditions and different Reynolds numbers in this paper. The results of the plane channel flow show that the performance of the PL‐DDES model is better than that of the improved delayed detached eddy simulation (IDDES) model for alleviating the log‐law layer mismatch (LLM) issue. With a much coarser grid resolution, although the resolved turbulent scales decrease, the time‐averaged velocity and temperature are successfully predicted. The capability of predicting turbulent flow and heat transfer over a wavy wall manifests, and the PL‐DDES model has considerable potential in industrial and environmental applications.

Direct numerical simulation of developed compressible flow in square ducts

We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers Mb=0.2−3, and up to friction Reynolds number Reτ=500. The effects of flow compressibility on the secondary motions are found to be negligible, with the typical Mach number associated with the cross-stream flow always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars.

Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal

This is a theoretical study of the superfocusing and zero-degree focusing effects appearing in channeling of protons of energy of 2 MeV in the {1 1 0} channel of a thin silicon crystal. We prove that the ultimate origin of these effects is the crystal rainbow effect, which has been discovered and explored in ion transmission through axial crystal channels, nanotubes and graphene. Moreover, the effect is the origin of the shapes of the whole spatial and angular distributions of channeled protons. The incident proton velocity vector is taken to be parallel to the channel midplane. We use the Molière's approximation of the Thomas-Fermi proton-atom interaction potential and the continuum approximation. The effect of thermal vibrations of the crystal's atoms is included. We solve numerically the proton equation of motion and analyze the spatial and angular proton transmission functions. The extrema of these functions are the spatial and angular rainbow points, respectively. When the whole proton beam is taken into account, a spatial rainbow pattern, composed of the lines emerging from the superfocusing points, and an angular rainbow pattern, consisting of the lines emerging from the origin and the zero-degree focusing points, appear along the channel. We consider the region of crystal thickness comprising the first, second and third superfocusing and zero-degree focusing points. When the effect of thermal vibrations is neglected, each of these rainbow lines look like the bifurcation set of the cusp catastrophe, and when the effect is included, the line resembles the bifurcation set of the butterfly catastrophe. We demonstrate that the spatial and angular distributions of transmitted protons are fully determined by the spatial and angular rainbow lines, respectively. The superfocusing and zero-degree focusing effects weaken with the increase of the crystal thickness. This is a consequence of the anharmonicity of the continuum proton-crystal interaction potential, which makes the proton beam propagation through the channel incoherent. We also explore the influence of the effect of proton collisions with the crystal's electrons on the beam dynamics in the channel. This effect additionally contributes to the incoherence of the beam motion along the channel. Our opinion is that the peaks of the spatial and angular distributions of ions transmitted through the planar channels lying off the origin registered before were in fact the rainbow peaks.

Restricted nonlinear model for high- and low-drag events in plane channel flow

A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh &amp; Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi &amp; Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.

The hydraulic resistance of thermoviscous liquid flow in a plane channel with a variable cross-section

The problem of the possibility of adjusting the hydraulic resistance due to local thermal action is considered. The liquid flow with the temperature dependence of the viscosity in a plane channel with sudden contraction is investigated. The velocity profiles of the thermoviscous liquid flow and the dependence of the hydraulic resistance coefficient on various types of local action on the liquid flow with a temperature dependence of the viscosity in a plane channel are numerically obtained.

Software Implementation of the discrete ordinates method in the problem of the Poiseuille flow in a plane channel with infinite parallel walls

The algorithm for calculating the gas macroparameters in a channel using the discrete ordinates method was considered. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables was written in a matrix form. The coefficient matrix in the resulting system of equations was reduced to a symmetric one and then to a tridiagonal matrix using the Householder algorithm. The search for the eigenvalues of the tridiagonal matrix was performed using a QL algorithm with implicit shifts. The determination of the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls was reduced to a system of linear algebraic equations. The Gauss method with a permutation of the rows was used to solve it. The software implementation of the algorithm was carried out using the C++ programming language. The mass velocity profile of the gas and the flow rate through the cross section of the channel in the Poiseuille flow problem were calculated as an application. The comparison with similar results presented in the open press was performed.

Numerical Simulation of the Structure and Mechanical Properties of Silicene Layers on Graphite during the Lithium Ion Motion

The molecular dynamics method is applied to study structural and mechanical effects appearing during the lithium ion motion in a dc electric field along a planar channel formed by perfect silicene sheets and sheets containing vacancy-type defects. Mono-, di-, tri-, and hexavacancies of rather densely and uniformly filled silicene sheets are arranged one above the other on a graphite substrate. The times of Li+ ion passage through silicene channels with various gaps are determined. The construction of Voronoi polyhedra and truncated polyhedrons, whose centers coincide with the moving ion position allowed revealing the structural features inherent to the two-dimensional layered structure. The nature of stresses appearing in silicene sheets most critical to ion motion over the channel is determined.

Flow boiling characteristics in a novel minichannel with a step on each corner

ABSTRACTIn the present study, flow boiling in a single minichannel with a longitudinal step on its each corner is studied experimentally. Bubble/flow dynamics, and thus, underlying physical phenomenon is investigated through high-speed flow visualization experiments. The results are also compared with those of the conventional single rectangular minichannel (plane channel) in terms of heat transfer and total pressure drop. Experiments are performed for different values of the mass flux and wall heat flux at a constant inlet temperature. It is obtained that the stepped channel improves heat transfer performance up to 13.2% compared to the plane channel. During the visualization studies, five flow patterns are observed: bubbly flow, slug flow, churn flow, annular flow, and inverted annular flow.

Prediction of Cleaning by Means of Computational Fluid Dynamics: Implication of the Pre‐wetting of a Swellable Soil

The cleaning behavior of a pre-wetted soil is studied experimentally and modeled numerically for the prototypical case of plane channel flow. One of the channel walls is soiled with a food-based model soil containing luminescent tracer particles to perform space- and time-resolved investigations of the cleaning process. Pre-wetting is applied for a few minutes before the soil removal is started with flow of Reynolds number up to 20,000. Physical model and simulation are based on a transient boundary condition to represent the behavior of the soil. Pre-wetting is taken into account by an initial removal of a certain amount of soil due to cohesive separation and the subsequent cleaning modeled as being limited by a diffusive process. Compared to a conventional multiphase simulation, the computation time is lowered by about three orders of magnitude. The results obtained with this elementary approach match the experiments astonishingly well.

Exponential growth of lifetime of localized turbulence with its extent in channel flow

The transition to turbulence in wall-bounded flows, for example pipe flow, plane Couette flow and channel flow, initially occurs as localized clusters of turbulence. It is well known that these localized structures are transient and decay in a memoryless process. In this paper we investigate the relationship between the extent of a localized structure and its lifetime. By performing numerical simulations of channel flow with small spanwise periodicity we produce streamwise-localized but spanwise-extended turbulence, turbulent ‘puffs’ instead of spots. We vary the spanwise periodzation length as the parameter of its extent to show that the lifetime of turbulent ‘puffs’ increases double-exponentially as a function of the Reynolds number for any spanwise extent. It is also shown that the lifetime increases exponentially as a function of the spanwise size when it is not large.

Spin rotation of the planar channeled muons

In the present paper we obtain exact solution of the BMT equation for the spin rotation of relativistic negatively charged particles passing through a thin crystal in the regime of planar channeling. The derived equations are applied for investigation of spin rotation of relativistic muons channeled in the tungsten crystal.

Exact coherent states of attached eddies in channel flow

A new set of exact coherent states in the form of a travelling wave is reported in plane channel flow. They are continued over a range in $Re$ from approximately $2600$ up to $30\,000$, an order of magnitude higher than those discovered in the transitional regime. This particular type of exact coherent states is found to be gradually more localised in the near-wall region on increasing the Reynolds number. As larger spanwise sizes $L_{z}^{+}$ are considered, these exact coherent states appear via a saddle-node bifurcation with a spanwise size of $L_{z}^{+}\simeq 50$ and their phase speed is found to be $c^{+}\simeq 11$ at all the Reynolds numbers considered. Computation of the eigenspectra shows that the time scale of the exact coherent states is given by $h/U_{cl}$ in channel flow at all Reynolds numbers, and it becomes equivalent to the viscous inner time scale for the exact coherent states in the limit of $Re\rightarrow \infty$. The exact coherent states at several different spanwise sizes are further continued to a higher Reynolds number, $Re=55\,000$, using the eddy-viscosity approach (Hwang &amp; Cossu, Phys. Rev. Lett., vol. 105, 2010, 044505). It is found that the continued exact coherent states at different sizes are self-similar at the given Reynolds number. These observations suggest that, on increasing Reynolds number, new sets of self-sustaining coherent structures are born in the near-wall region. Near this onset, these structures scale in inner units, forming the near-wall self-sustaining structures. With further increase of Reynolds number, the structures that emerged at lower Reynolds numbers subsequently evolve into the self-sustaining structures in the logarithmic region at different length scales, forming a hierarchy of self-similar coherent structures as hypothesised by Townsend (i.e. attached eddy hypothesis). Finally, the energetics of turbulent flow is discussed for a consistent extension of these dynamical systems notions to high Reynolds numbers.

Two-dimensional dynamic model of the interaction of a fluid and a piezoelectric bending actuator in a plane channel

The paper proposes a two-dimensional computer model of the fluid flow in a plane channel under the action of an applied pressure drop with a flat ceramic piezoelectric actuator immersed in it, bending in the transverse direction in proportion to the applied electric voltage. A mathematical model of the coupled liquid-piezodrive system in variational form for numerical simulation by the finite element method is proposed. Since the assignment of the Dirichlet boundary conditions for displacement in this problem, is difficult, an equivalent piezo actuator deformation scheme using the Neumann boundary conditions is constructed. The deformations and equivalent stresses of von Mises on a piezo actuator are calculated. The influence of the geometry of the channel and the hydrodynamic resistance formed by the piezo actuator on the dynamics of the fluid flow is analyzed. An algorithm is proposed for adaptive dynamic remeshing of the channel computational mesh under deformations exceeding the size of finite elements. With a symmetric control signal supplied to the piezoelectric actuator, the asymmetry of the geometry leads to a violation of the symmetry of the fluid flow within the period, both in terms of fluid flow rate and in time. In the absence of a pressure drop at low frequencies of the oscillations of the piezoelectric element (of the order of the inverse relaxation time of the velocity), the period-average liquid flow rate is nonzero and increases with increasing frequency. In the presence of an external pressure drop along the layer, the average liquid flow rate is proportional to the pressure drop; at low frequencies, it is inversely proportional to the frequency; with increasing frequency, it reaches saturation. Based on the results of numerical modeling, various variants of new microfluidic technical devices generating a fluid flow using a piezoelectric bending actuator are proposed: a micropump creating a closed-circuit flow; fluid flow regulator and fluid volume dispenser.