Sudden Expansion Flow Research Articles

Numerical simulation of sudden-expansion particle-laden flows using the Eulerian lagrangian approach

A Lagrangian-Eulerian model for the dispersion of solid particles in sudden-expansion flows is reported and validated. The fluid was calculated based on the Eulerian approach by solving the Navier-Stokes equations. A Lagrangian model is also applied, using a Runge-Kutta method to obtain the particle trajectories. The effect of fluid turbulence upon particle dispersion is taken into consideration through a statistical model. The predicted axial mean velocity and turbulent kinetic energy of both phases agree well with experimental data reported by Sommerfield.

STREAMWISE DYNAMICS CONTROLLED JET SPREADING, MIXING AND PHYSICAL SOURCE OF THE VORTICES

Within the framework of the present investigation we perform Direct Numerical Simulations to study the role of streamwise dynamics in the jet spreading and mixing, and provide a clear understanding about the source of these important vortices in two-step rectangular sudden expansion flows. The present setup is designed to generate higher mass entrainment, and the system generated passive forcing provided the necessary impetus for the sustained growth/evolution of the streamwise vertices, which played the key role in the mixing enhancement. On the other hand, by suitably placing two tiny rectangular ‘tabs’ on the inlet channel walls, the nature of growth and the dynamics of the streamwise extended threedimensional vortical rollers could be effectively controlled. These vortices through their inflow/outflow type dynamics are found to effectively control the downstream jet spreading; and the associated physical processes either lead to quick axis switching of the jet section, or stop axis switching altogether. In addition, an extensive pressure analysis, as presented here, suggests that the transverse pressure gradient skewing is probably the major source of streamwise vorticity generation for the flow

Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer (PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes (RANS) model and a large-eddy simulation (LES). The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups (30 µm, 50 µm, and 95 µm) and the gas-particle velocity correlation for 30 µm and 50 µm particles. From the measurements, theoretical analysis, and simulation, it is found that the two-phase velocity correlation of sudden-expansion flows, like that of jet flows, is less than the gas and particle Reynolds stresses. What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows. The measurements, theoretical analysis, and numerical simulation all lead to the above-stated conclusions. Quantitatively, the results of the LES are better than those of the RANS model.

Mixed convection flows in a vertical plane duct preceded by a sudden expansion

PurposeThe purpose of this paper is to numerically investigate the effects of different heating and cooling scenarios on the flow structure in a vertically oriented plane sudden expansion. Four different heating and cooling scenarios are considered. The scenarios include symmetric or asymmetric heating or cooling of the downstream channel walls.Design/methodology/approachThe governing equations are formulated using a stream function‐vorticity approach. Second‐order accurate central differencing is used to discretize all terms, including the nonlinear convection terms in the vorticity transport and energy equations. Numerical test cases are simulated for Reynolds number values up to 200 and Grashof number values up to 400.FindingsNumerical simulations show that symmetric heating results in the reduction and ultimately the elimination of flow separation zones near the channel walls while creating a region of reversed flow in the core. On the other hand, symmetric cooling causes the flow to adopt a wavy structure which significantly enhances heat transfer due to jet impingement effects. Finally, it is shown that asymmetric heating causes the flow to preferentially attach to the high‐temperature wall while asymmetric cooling causes the flow to separate completely from the low‐temperature wall.Originality/valueThe behaviour of fluid flow in a plane sudden expansion under symmetric heating is available in the literature. In the present study, the flow structure under alternative heating and cooling scenarios is investigated for the first time.

Numerical analysis of axisymmetric and planar sudden expansion flows for laminar regime

AbstractIn this study, the Navier–Stokes equations are solved numerically for axisymmetric and planar sudden expansion flows. The flow is considered laminar and steady state, and the fluid is incompressible. Finite difference equations are obtained using a control volume method in a non‐staggered grid arrangement, and solved by line‐by‐line TDMA technique using the SIMPLEM (SIMPLEM‐Modified) algorithm. Calculations are performed for higher expansion ratios, β, ranging from 1.5 to 10 and Reynolds numbers from 0.1 to 500. Results are presented in terms of streamlines, relative eddy intensity, location of the eddy center, and the eddy reattachment length depending on Re number and β values for both axisymmetric and planar sudden expansions. It is aimed to provide a picture of the effects of high values of expansion ratio and Reynolds number on the sudden expansion flow. As a result, it is found that the flow characteristics keep their structure for both higher expansion ratios and higher Reynolds numbers. Further, correlations were developed for the nondimensional eddy reattachment length, location of the eddy center and the relative eddy intensity, which have agreeable results to the computed results available from the literature. Copyright © 2010 John Wiley & Sons, Ltd.

Bingham fluid simulation with the incompressible lattice Boltzmann model

The Bingham fluid flow is numerically studied using the lattice Boltzmann method by incorporating the Papanastasiou exponential modification approach. The He–Luo incompressible lattice Boltzmann model is employed to avoid numerical instability usually encountered in non-Newtonian fluid simulations due to a strong non-linear relationship between the shear rate tensor and the rate-of-strain tensor. First, the value of the regularization parameter in Bingham fluid mimicking is analyzed and a method to determine the value is proposed. Then, the model is validated by pressure-driven planar channel flow and planar sudden expansion flow. The velocity profiles for the pressure-driven planar channel flow are in good agreement with analytical solutions. The calculated reattachment lengths for a 2:1 planar sudden expansion flow also agree well with the available data. Finally, the Bingham flow over a cavity is studied, and the streamlines and yielded/unyielded regions are discussed.

The structure of parallel layers in steady two-dimensional magnetohydrodynamic flows in sudden duct expansions and contractions

The structure of non-linear, steady, two-dimensional parallel layers at high values of the Hartmann number, Ha, the Reynolds number, Re, and the interaction parameter, N, for duct expansions and contractions has been investigated. The magnetic field is transverse to the flow. For the flow regime, in which the electromagnetic force balances the inertial force in the layer, a viscous sublayer at the solid wall parallel to the magnetic field has been obtained, in which the flow is driven by the pressure gradient induced in the outer, inviscid layer.

Phase Doppler anemometry measurements and analysis of turbulence modulation in dilute gas–solid two-phase shear flows

Flow velocities of a dilute gas–solid two-phase flow in a vertical sudden expansion were measured using phase Doppler anemometry to study the behaviour of the turbulence modulation for the stronger shear for various particle mass loadings, inlet Reynolds numbers and particle diameters. The measurements show that the particles changed the gas turbulence by elongation of the entire gas flow field in the downstream direction, which displaced the axial profile of the section-averaged fluctuation velocity in comparison with that of the single-phase flow, and by either the particle inertia reducing the local turbulence or the wake eddy effects enhancing the turbulence. Both mechanisms resulted in an apparent turbulence modulation, which has not been referred to in the related literature, and have led to an ambiguous understanding of turbulence modulation. The elongation and inlet effects should be eliminated to estimate whether the gas turbulence was really modified. The linear relationship between the gas mean velocity gradient and the root-mean-square fluctuation velocity, which was found to be similar to that in single-phase flows, gradually disappeared as the flow developed and the shear intensity reduced. The linear relationship also varied with different conditions. Specifically, the turbulence modulation was enhanced by higher particle mass loadings and the linear relationship disappeared with increasing particle mass loading. This linearity can perhaps be regarded as a criterion for determining the effect of stronger turbulence modulation.

Numerical Simulation of Flow Pattern and Liquid-solid Flow in Sudden Pipe Expansion

In order to analyse the diffusion features of solid particles in sudden pipe expansion, the turbulence flow field inside sudden pipe expansion was simulated with some Reynolds Time-average Models and Large Eddy Simulation (LES). The results showed that simulation with LES could respond the vortex dissipation and the flow instability better than the others. And the solid particle diffusion in sudden pipe expansion was simulated with LES and Discrete Phase Models(DPM). The results showed that the diffusance of particles decreased as the number of P St increased, the bigger particles remained their original flow track more and influenced less by coherent vortex and turbulence discrete vortex of the flow field, and the flow field had stronger capability of carrying particles with small diameter of particles.

Bifurcation phenomenon for forced convection of supercritical CO 2 sudden expansion flow and heat transfer in symmetric regime

A computational investigation of laminar forced convection of supercritical CO 2 flow in horizontal duct with plane symmetric sudden expansion and its bifurcation phenomenon are presented in this study. The computations were conducted at various Reynolds numbers for cases of different wall heat fluxes. A parameter named recirculation disturbance intensity is introduced that is aimed to shed some light on the reduction of flow stability when Reynolds number or wall heat flux increases. The Nusselt number distribution in the symmetric flow regime is presented, the variations of peak Nusselt number and its relative location are discussed. Wall friction coefficient and pressure coefficient distributions are presented and discussed.

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

Parallel pseudo-transient Newton–Krylov–Schwarz continuation algorithms for bifurcation analysis of incompressible sudden expansion flows

We propose a parallel pseudo-transient continuation algorithm, in conjunction with a Newton–Krylov–Schwarz (NKS) algorithm, for the detection of the critical points of symmetry-breaking bifurcations in sudden expansion flows. One classical approach for examining the stability of a stationary solution to a system of ordinary differential equations (ODEs) is to apply the so-called a method-of-line approach, beginning with some perturbed stationary solution to a system of ODEs and then to investigate its time-dependent response. While the time accuracy is not our concern, the adaptability of time-step size is a key ingredient for the success of the algorithm in accelerating the time-marching process. To allow large time steps, unconditionally stable time integrators, such as the backward Euler's method, are often employed. As a result, the price paid is that at each time step, a large sparse nonlinear system of equations needs to be solved. The NKS is a good candidate solver for a system. Our numerical results obtained from a parallel machine show that our algorithm is robust and efficient and also verify, qualitatively, the bifurcation prediction with published results. Furthermore, imperfect pitchfork bifurcations are observed, especially for the case with a small expansion ratio, in which the occurrence of bifurcation points is delayed due to the stabilization terms in Galerkin/Least squares finite elements on asymmetric, unstructured meshes.

Computer Experiments on Rapidly Rotating Plane Couette Flow

Turbulent flows in rotating frame-of-reference are of considerable interest in a variety of industrial, geophysical and astrophysical applications. In these flows, the system rotation induces additional body forces, i.e. centrifugal and Coriolis forces, acting on the turbulent flow, so that the momentum mechanism becomes more complicated. The present doctoral thesis concerns the system rotation influence on turbulent shear flows. To this end, direct numerical simulations (DNSs) have been performed in order to investigate the effect of system rotation on different turbulent flow configurations including plane Couette flow, sudden expansion flow and wake behind a flat plate. In addition, the PIV measurements for rotating plane channel and sudden expansion flows have been carried out in order to support the numerical simulations results. A realistic turbulent inflow boundary condition is needed in order to perform direct numerical simulations for spatially developing flows subjected to system rotation such as rotating sudden expansion flows. The cost effective method is introduced based on a separate (precursor) simulation in order to establish fully turbulent inflow including wide ranges of length and time scales needed in the direct numerical simulations. On the other hand, the characteristic features of the rotating turbulent flows were investigated by means of three-dimensional flow visualization, two-point correlations and transport for the individual second-moments of the velocity and vorticity fluctuations.

A Lattice Boltzmann Method Based Numerical Scheme for Microchannel Flows

Conventional lattice Boltzmann method (LBM) is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The LBM has been applied to different types of complex flows with varying degrees of success, and with increased attention focusing on microscale flows now. Due to its small scale, microchannel flows exhibit many interesting phenomena that are not observed in their macroscale counterpart. It is known that the Navier–Stokes equations can still be used to treat microchannel flows if a slip-wall boundary condition is assumed. The setting of boundary conditions in the conventional LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of a finite difference LBM (FDLBM) based numerical scheme suitable for microchannel flows to solve the modeled Boltzmann equation using a splitting technique that allows convenient application of a slip-wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the FDLBM is carried out against microchannel and microtube flows, a driven cavity flow, and a two-dimensional sudden expansion flow. Excellent agreement is obtained between numerical calculations and analytical solutions of these flows.

The effect of expansion ratio for creeping expansion flows of UCM fluids

A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER ≥ 4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER ≤ 3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases.

Three-dimensional polymer melt flow in sudden expansions: Non-isothermal flow topology

Three-dimensional, non-isothermal, polymer melt flow in sudden expansion is numerically investigated. The main goal of the paper is to study the general features of the flow field. The generalized Newtonian formulation is adopted, and the mathematical model corresponds to the laminar, incompressible Navier–Stokes equations. A second order finite difference scheme is used to discretize the governing equations in a collocated mesh. The non-Newtonian flow behaviour is modelled by the Cross constitutive relation, in which temperature effects are accounted for. The simulations show that, despite the high viscosity exhibited by polymer melts, a complex three-dimensional flow structure is found close to the expansion section, characterized by a spiral motion. The results also indicate that viscous dissipation causes limited effect in temperature rise and viscosity variations. The latter was found mostly affected by the shear rate.

Numerical Investigation of the Effect of Ignition Area on the Subsequent Flame Propagation Behavior

In this paper, the effect of ignition area on the propagation of a laminar premixed flame is investigated numerically in a two-dimensional channel. A single-step irreversible overall exothermic chemical reaction is applied to model combustion chemistry. The time-dependent system of governing equations for reacting flows is discretized using the finite volume method (FVM) on the hexahedral structure grid cells. The discretized system of equations is solved by adopting Front Flow Red, a multi-scale and -physics computational fluid dynamics (CFD) solver. The computed results show that the flame oscillates during the propagation owing to the strong roll-up of the vortices generated by the strong shear layer originating from the sudden high gas expansion flow at the large ignition area. The instantaneous acceleration of the vortices increases the flame surface area which gives rise to higher propagation speed; consequently, combustion time is shortened. These results suggest that the rapid increase in flame surface, caused by the large ignition area induced strong vortices, could be one of the potential methods in improving combustion efficiency by reducing the burning time in the internal combustion devices.

Planar sudden symmetric expansion flows and bifurcation phenomena of purely viscous shear-thinning fluids

The goal of a present study is to investigate the effects of the generalized Newtonian fluids on the threshold of the transition from flow symmetry to its asymmetry for the flow through a 1:3 planar sudden expansion. We consider purely viscous shear-thinning fluids covering a range of the index n of Power law model n = 0.6 , 0.8 and compare them with the Newtonian fluid ( n = 1.0 ). Sudden expansion fluid flow is studied numerically by solving the two-dimensional momentum equations along with the continuity equation and the Power law rheological model. We report a systematic results in a range of generalized Reynolds number 10 ≤ R e g e n ≤ 150 with a focus on its critical value. The subsequent effects are investigated by means of a different flow parameters, i.e. generalized Reynolds number ( R e g e n ), modified Reynolds number ( R e m o d ) and the Reynolds number defined in accordance with the inlet wall viscosity ( R e w a l l ). Results indicate that the shear-thinning viscous behaviour increases the onset of bifurcation phenomena and the critical value of Reynolds number.

Numerical study of three recirculation zones in the unilateral sudden expansion flow

Numerical simulations of the two-dimensional laminar flow over a backward-facing step channel using two commercially-available Computational Fluid Dynamics (CFD) code are reported. The subject is to analyze the three recirculation regions of the flow in a unilateral sudden expansion. Results are presented for laminar air flow for Reynolds number lower than 2500. The mathematical model equations (mass conservation and momentum) were solved with finite element (FEM) and finite volume (FVM) methods and a segregated approach. To get the grid independent, intensive refinement studies were carried out. Results obtained are compared to experimental data presenting a good agreement. The numerical results of this work show a non-linear increase of the reattachment length as also shown by the experimental results extracted from literature.

Inlet Conditions for Large Eddy Simulation of Gas-Turbine Swirl Injectors

In this paper, we present a novel technique for generating swirl inlets for large eddy simulation. The velocity a short distance downstream of the inlet to the main domain is sampled and the flow velocity data are reintroduced backintothedomaininlet,creatinganinletsectionintegratedintothemaindomaininwhichturbulencecandevelop. Additionally, variable artificial body forces and velocity corrections are imposed in this inlet section, with feedback control to force the flow toward desired swirl, mean, and turbulent profiles. The method was applied to flow in an axisymmetric sudden expansion, with and without swirl at the inlet, and compared against experimental and literature large eddy simulation data and against similar results in the literature. The method generates excellent results for this case and is elegant and straightforward to implement.