Direct numerical simulation of rarefied turbulent microchannel flow

Direct numerical simulation (DNS) has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in microchannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64 × 128 × 64. Fractional time-step method is employed for the unsteady Navier–Stokes equations, and the governing equations are discretized with finite difference method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near-wall-region rarefaction can increase the turbulent intensities and temperature variance. The effects of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.     

On the realizability of reynolds stress turbulence closures

The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure model formulated using the strong realizability constraints of Schumann (1977) and Lumley (1978) is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes-a flaw that becomes apparent when the nonanalytic terms in the model are made single-valued as required on physical grounds. More importantly, arguments are advanced which suggest that it is impossible to identically satisfy the strong from of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability—wherein states of one or two component turbulence are made inaccessible in finite time via the imposition of a positive first derivative condition—are found to be realizable. However, unlike the simpler and more commonly used second-order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flow are presented to demonstrate these points which can have important implications for turbulence modeling.     

Effects of Curvature and Stenosis-Like Narrowing on Wall Shear Stress in a Coronary Artery Model with Phasic Flow

To gain insight into the details of intracoronary flow we have used computational fluid dynamic techniques to determine the velocity and wall shear stress distributions in both steady- and phasic-flow models of a curved coronary artery with several degrees of stenosis. The steady-flow Reynolds number was 500 and the peak phasic flow Reynolds number was 700. Without stenosis and at 25% (area) stenosis wall shear stress and velocities are higher at the outer wall than the inner wall but retain the same direction as the superimposed flow. At higher stenoses laminar flow separation occurs and the inner wall is exposed to shear stresses that vary widely, both temporally and spatially.     

Identification of near-wall flow structures producing large wall transfer rates in turbulent mixed convection channel flow

In this paper, we analyze the influence of aiding and opposing buoyancy on the statistics of the wall transfer rates in a mixed convection turbulent flow at low Reynolds numbers in a vertical plane channel. The analysis is carried out using a database obtained from direct numerical simulations performed with a second-order finite volume code. The aiding/opposing buoyancy produces an overall decrease/increase of the intensities of the fluctuations of the wall shear stresses in comparison with the forced convection flow. The near wall structures responsible for the positive extreme values of the fluctuations of the wall shear stress, educed by a conditional sampling technique, consist in two quasi-parallel counterrotating streamwise vortices that convect high momentum fluid towards the wall in the region between them. Buoyancy produces an overall increase of the Reynolds stresses near the cold wall in comparison with the hot wall. This affects the streamwise length, the orientation, the velocity and the intensity of these flow structures near the two walls of the channel. It is found that the flow structures near the cold wall are shorter and produce more intense fluctuations than those near the hot wall.     

Stratified smooth two-phase flow using the immersed interface method

The immersed interface method is used to derive a numerical method for solving fully developed, stratified smooth two-phase flow in pipes. This sharp interface technique makes the representation of the interface independent of the grid structure, and it allows for using an arbitrary shaped interface. The two-dimensional steady-state axial momentum equation is discretized and solved using a finite difference scheme on a composite, overlapping grid with local grid refinement near the interface and near the pipe wall. A low Reynolds number k-ε turbulence model is adopted to account for the effect of turbulence. A level set function is used to represent the interface. Numerical results are presented for laminar and turbulent flows. The numerical method compares well with analytical solution for laminar flow, and it shows acceptable agreement with experimental data for turbulent flow. A few examples are given to demonstrate the capability of the method to solve flow problems with a complex shaped interface.     

Mathematical modelling for pulsatile flow of Casson fluid along with magnetic nanoparticles in a stenosed artery under external magnetic field and body acceleration

In the present paper, the magnetohydrodynamics effects on flow parameters of blood carrying magnetic nanoparticles flowing through a stenosed artery under the influence of periodic body acceleration are investigated. Blood is assumed to behave as a Casson fluid. The governing equations are nonlinear and solved numerically using finite difference schemes. The effects of stenotic height, yield stress, magnetic field, particle concentration and mass parameters on wall shear stress, flow resistance and velocity distribution are analysed. It is found that wall shear stress and flow resistance values are considerably enhanced when an external magnetic field is applied. The velocity values of fluid and particles are appreciably reduced when a magnetic field is applied on the model. It is significant to note that the presence of nanoparticles, magnetic field and yield stress tend to increase the plug core radius. Increased wall shear stress and flow resistance affects the circulation of blood in the human cardiovascular system. The results obtained from the study can be used in normalizing the values of the model parameters and hence can be used for medical applications. The presence of magnetic field helps to slow down the flow of fluid and magnetic particles associated with it. The magnetic particles of nanosize developed in recent days are biodegradable and used in biomedical applications. Biomagnetic principles and biomagnetic particles as drug carriers are used in cancer treatments.

     

Turbulence modeling for two-dimensional water hammer simulations in the low Reynolds number range

Modeling turbulence in two-dimensional water hammer simulations is considered in the present study. The Baldwin–Lomax turbulence model is implemented, both in quasi-steady and frozen forms. Numerical simulations using both forms agree well with experimental data for lower Reynolds numbers (Re = 5600) and the attenuation of the transient is adequately captured. However, for higher Reynolds numbers (Re = 15,800), the frozen form overpredicts the attenuation of the transient. Moreover, it is shown that switching the turbulence model off altogether and applying a quasi-laminar approximation results in good agreement with experimental data for the lower Reynolds number case (Re = 5600) while underpredicting the attenuation of the transient for the higher Reynolds number case (Re = 15,800).     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

A new second-order closure model for rough-wall turbulent flows using the Brinkman equation

A second-order turbulence closure is developed for the new rough-wall layer modeling approach using the Brinkman equation for turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. Interface stress jump conditions including the Reynolds stress components are also considered. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The rough-wall second-order closure is developed by adopting an existing smooth-wall model. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented and compared with those obtained by using a previously developed two-equation turbulence closure. The results show that the new rough-wall layer modeling approach with the second-order turbulence closure model satisfactorily predicted the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress. However, the results for the Reynolds normal stresses are different from the measured data in the inner 20-60% of the boundary layer due to the interface stress jump conditions employed in the present rough-wall layer modeling approach.     

Wall modeling for LES of high Reynolds number channel flows: What turbulence information is retained?

A novel near-wall eddy-viscosity formulation for Large-eddy simulation (LES) has been used to compute high Reynolds number channel flows up to Re_τ = 1,000,000. These computations allow an insight into what turbulence information is retained when LES with a wall model is applied to such high Reynolds numbers. Detailed results are presented for the mean and rms velocities, as well as energy spectra. It is observed that, when an appropriate scaling is used, the rms velocities, energy spectra and the production of turbulence kinetic energy are weakly Reynolds number dependent at these high Reynolds numbers.     

Numerical solution of incompressible flow through branched channels

The work deals with numerical solution of 3D turbulent flow in straight channel and branched channels with two outlets. The mathematical model of the flow is based on Reynolds-averaged Navier–Stokes equations for incompressible flow in 3D with explicit algebraic Reynolds stress turbulence model (EARSM). The mathematical model is solved by artificial compressibility method with implicit finite volume discretization. The channels have constant square or circular cross-section, where the hydraulic diameter is same in order to enable comparison between these numerical simulations. First, developed flow in a straight channel of square cross-section is presented in order to show the ability of the used EARSM turbulence model to capture secondary corner vortices, which are not predicted by eddy viscosity models. Next the flow through channels with perpendicular branch is simulated. Methods of setting the flow rate are discussed. The numerical results are presented for two flow rates in the branch.     

Blood flow dynamics and arterial wall interaction in a saccular aneurysm model of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture and surgical treatment of intracranial aneurysms. This paper describes the flow dynamics and arterial wall interaction in a representative model of a terminal aneurysm of the basilar artery, and compares its wall shear stress, pressure, effective stress and wall deformation with those of a healthy basilar artery. The arterial wall was assumed to be elastic or hyperelastic, isotropic, incompressible and homogeneous. The flow was assumed to be laminar, Newtonian, and incompressible. The fully coupled fluid and structure models were solved with the finite elements package ADINA. The intra-aneurysmal pulsatile flow shows single recirculation region during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations. The wall thickness, the Young’s modulus in the elastic wall model and the hyperelastic Mooney-Rivlin wall model affect the aneurysm deformation and effective stress in the wall especially at systole.     

Turbulence effects of wall-pressure fluctuations for reattached flow

A methodology is presented to predict the frequency spectrum of fluctuating wall-pressures based on a steady Reynolds Averaged Navier Stokes (RANS) solution. The spectral modeling scheme solves a Poisson equation with a linear source term (LST) for the mean-velocity-turbulence interaction (MT) and non-linear source terms (NST) for the turbulence-turbulence interaction (TT). An anisotropic factor is used to account for the anisotropic features of the turbulence field. The prediction method was originally developed based on the equilibrium flow, i.e. turbulent flow with homogeneous and stationary characteristics, with the LST only. In this paper, the model is further applied to a non-equilibrium flow, i.e. flow over a backward facing step (BFS), to explore its predictability for the wall-pressure fluctuations. With the help of DNS results and experimental data for the BFSs, the model is investigated with the inclusion of NST. Prediction results demonstrate the impact of turbulence features of the wall shear layers to the predicted wall-pressure spectrum.     

Statistical and structural similarities between micro- and macroscale wall turbulence

Microscopic particle-image velocimetry (micro-PIV) measurements are made in the streamwise–wall-normal plane of a 536 μm capillary at Re = 4,500 to study the statistical and structural features of wall turbulence at the microscale. Single-point velocity statistics, including the mean velocity profile, the root-mean-square streamwise and wall-normal velocities, and the Reynolds shear stress profile, agree well with established direct numerical simulations of turbulence in the same geometry at Re = 5,300. This consistency validates the efficacy of micro-PIV as an experimental tool for studying instantaneous, and even turbulent, flow behavior at the microscale. The instantaneous micro-PIV velocity fields reveal spanwise vortices that streamwise-align to form larger-scale interfaces that are inclined slightly away from the wall. These observations are entirely consistent with the signatures of hairpin vortices and hairpin vortex packets that are often noted in instantaneous PIV realizations of macroscale wall turbulence. Further, two-point velocity correlations and estimates of the conditionally averaged velocity field given the presence of a spanwise vortex indicate that hairpin structures and their organization into larger-scale vortex packets are statistically significant features of wall turbulence at the microscale.     

Implementation of synthetic turbulence inlet for turbomachinery LES

Large eddy simulation (LES) has the potential to model complex separated flows, where Reynolds Averaged Navier–Stokes (RANS) based methods often fail. An important aspect of LES is specifying correlated turbulent fluctuations at the inlet boundary. This is particularly important in turbomachines, where turbulence length scale and intensity play a key role in the correct prediction of component performance.In this work, a method is implemented into an unstructured Computational Fluid Dynamics (CFD) solver to impose correlated turbulent fluctuations in a compressible form. It is shown that compressibility effects are particularly important in turbomachinery and must be taken into account. The method uses a pre-processing method to generate a cube of isotropic, homogeneous turbulence. The velocity fluctuations so obtained are used to determine a fluctuating Mach number in order to evaluate the instantaneous total pressure and temperature fluctuations at domain inlet. In the authors knowledge this is one of the first attempts to define correlated fluctuations in a compressible form.The method is successfully applied to two turbomachinery related flows. Firstly, the jet flow from a propelling nozzle is investigated. Following this, the flow over a low pressure (LP) turbine blade is predicted. Results from the LES simulations show that modifications to the inlet conditions can significantly affect flow development. For the jet, changes in the shear layer and peak shear stress are shown, important in the context of high frequency sideline noise generated by the jet. Despite what is suggested in the literature the differences in shear stresses are important also in a non-swirling jet.For the LP turbine, incoming turbulent fluctuations modify the onset of transition and the extent of separation bubble. Without imposed turbulence fluctuations, loss is overpredicted by up to 50%. Moreover it is important to use a compressible solver. Despite the fact that the majority of the results proposed in literature on LP turbine is using incompressible solvers, the difference in terms of pressure coefficient, Cp, is comparable to turbulence contribution.     

Non-Newtonian effects of blood flow in complete coronary and femoral bypasses

A numerical investigation of non-Newtonian steady blood flow in a complete idealized 3D bypass model with occluded native artery is presented in order to study the non-Newtonian effects for two different sets of physiological parameters (artery diameter and inlet Reynolds number), which correspond to average coronary and femoral native arteries. Considering the blood to be a generalized Newtonian fluid, the shear-dependent viscosity is evaluated using the Carreau–Yasuda model. All numerical simulations are performed by an incompressible Navier–Stokes solver developed by the authors, which is based on the pseudo-compressibility approach and the cell-centred finite volume method defined on unstructured hexahedral computational grid. For the time integration, the fourth-stage Runge–Kutta algorithm is used. The analysis of numerical results obtained for the non-Newtonian and Newtonian flows through the coronary and femoral bypasses is focused on the distribution of velocity and wall shear stress in the entire length of the computational model, which consists of the proximal and distal native artery and the connected end-to-side bypass graft.     

Unsteady viscous jet flow into stationary surroundings

The unsteady constant-property uniform pressure flow of a viscous laminar axisymmetric jet into stationary surroundings is analyzed with the aid of the boundary layer approximations and an integral method. Numerical solutions of the resulting non-linear system of equations are presented for the response of an initially steady jet to monotonic mass flow variations which are imposed at the initial axial station of the jet. Significant departures from quasi-steady behaviour arise for sufficiently large streamwise distances and/or rates of change of the boundary conditions. Among these effects are overshoots in mass and momentum flux, a dynamic effect on flow entrainment, and a tendency toward discontinous behavior. The influence of the kinematic viscosity on the transient flow is examined, and an estimate is made of the applicability of quasi-steady approximations in this problem.     

Zonal k-l based large eddy simulations

Zonal k-l based large eddy simulation (LES) approaches are presented. To reduce computational demands, near walls, Reynolds averaged Navier-Stokes (RANS) like modelling is used. The interface location for the differing models is either explicitly specified, or, based on length scale compatibility, allowed to naturally locate. With the latter approach the location is strongly grid controlled. When explicitly specified (based on turbulence physics grounds), to enhance results length scale smoothing is implemented. Using standard established LES and RANS model constants the zonal methods are shown to reproduce a satisfactory law of the wall. The approaches are implemented in both cell-vertex and cell-centred codes with similar results being found. Various other sensitivity studies are performed. These show that, as with standard LES, predictions are most sensitive to filter definition, first off wall grid node normal positions and temporal scheme order. For a non-isothermal periodic ribbed channel, the new zonal LES predictions are found to be significantly more accurate than those for an established RANS model and also LES.     

High-throughput,single-stream microparticle focusing using a microchannel with asymmetric sharp corners

A new microfluidic device for fast and high-throughput particle focusing is reported. The particle focusing is based on the combination of inertial lift force effect and centrifugal force effect generated in a microchannel with a series of repeated asymmetric sharp corners on one side of the channel wall. The inertial lift force induces two focused particle streams in the microchannel, and the centrifugal force generated at the sharp corner structures tends to drive the particles laterally away from the corner. With the use of a series of repeated asymmetric sharp corner structures, a single and highly focused particle stream was achieved near the straight channel wall at a wide range of flow rate. In comparison with other hydrodynamic particle focusing methods, this method is less sensitive to the flow rate and can work at a higher flow rate (up to 700 μL/min) and Reynolds number (Re = 129.5). With its simple structure and operation, and high throughput, this method can be potentially used in particle focusing processes in a variety of lab-on-a-chip applications.