Wall shear stress characterization of a 3D bluff-body separated flow

Efficient flow control strategies aimed at reducing the aerodynamic drag of road vehicles require a detailed knowledge of the reference flow. In this work, the flow around the rear slanted window of a generic car model was experimentally studied through wall shear stress measurements using an electrochemical method. The mean and fluctuating wall shear stress within the wall impact regions of the recirculation bubble and the main longitudinal vortex structures which develop above the rear window are presented. Correlations allow a more detailed characterization of the recirculation phenomenon within the separation bubble. In the model symmetry plane the recirculation structure compares well with simpler 2D configurations; specific lengths, flapping motion and shedding of large-scale vortices are observed, these similarities diminish when leaving the middle plane due to the strong three-dimensionality of the flow. A specific attention is paid to the convection processes occurring within the recirculation: a downstream convection velocity is observed, in accordance with 2D recirculations from the literature, and an upstream convection is highlighted along the entire bubble length which has not been underlined in some previous canonical configurations.     

Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies

Cardiovascular diseases are one of the major causes of long‐term morbidity and mortality in human beings. The nearly epidemic increase in prevalence of such diseases poses a serious threat to public health and calls for efficient methods of diagnosis and treatment. Non‐invasive diagnostic procedures such as MRI are often used in this context; however, these are limited in terms of spatial and temporal resolution and do not provide information on time‐dependent pressures and wall shear stresses—key quantities considered to be partially responsible for the formation and development of related pathologies. The present study is concerned with the numerical simulation of oscillatory flow through the abdominal aortic bifurcation. Computational fluid dynamics simulation of oscillatory flow in a branched geometry at high Reynolds numbers poses considerable challenges. The present study reports a detailed comparison of simulations performed with a finite volume and a finite element method, two approaches with significant differences in their discretization strategy, treatment of boundary conditions and other numerical aspects. Both solvers were parallelized, using loop parallelization of the BiCGStab linear solver for the finite volume and domain decomposition based on the Schur complement method for the finite element technique. The experience gained with these two approaches for the solution of flow in a bifurcation forms the focus of this study. Although similar results were obtained for both methods, the computation time required for convergence was found to be significantly smaller for the finite element approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Construction of hybrid 1D-0D networks for efficient and accurate blood flow simulations

The one-dimensional (1D) modeling of blood flow in complex networks of vessels and cardiovascular models can result in computationally expensive simulations. The complexity of such networks has significantly increased in the last years, in terms of both enhanced anatomical detail and modeling of physiological mechanisms and mechanical characteristics. To address such issue, the main goal of this work is to present a novel methodology to construct hybrid networks of coupled 1D and 0D vessels and to perform computationally efficient and accurate blood flow simulations in such networks. Departing from both the 1D and lumped-parameter (0D) nonlinear models for blood flow, we propose high-order numerical coupling strategies to solve the 1D, 0D, and hybrid coupling of vessels at junctions. To effectively construct hybrid networks, we explore different a-priori model selection criteria focusing in obtaining the best possible trade-off between computational cost of the simulations and accuracy of the computed solutions for the hybrid network with respect to the 1D network. The achievement of the expected order of accuracy is verified in several test cases. The novel methodology is applied to two different arterial networks, the 37-artery network and the reduced ADAN56 model, where, in order to identify the best performing a-priori model selection criteria, the quantitative assessment of CPU times and errors and the qualitative comparison between results are carried out and discussed.     

Flow division at a channel crossing with subcritical or supercritical flow

The passage of an extreme storm over an urban area can lead to the flooding of the streets if the rainfall intensity exceeds the design value and/or the drainage system is not functional. The study of flow distribution in street networks thus is important for the design of flood protection measures. The flow distribution is affected by the junction flow characteristics, inflow discharges and downstream water depths. To reduce the degree of empiricism, a 3D Reynolds‐averaged Navier–Stokes equations model has been implemented in this study to investigate the flow phenomena in a cross junction. The Spalart–Allmaras model is used for turbulence closure. The numerical model utilizes the split‐operator approach, in which the advection, diffusion and pressure propagations are solved separately. The numerical model predicts accurately the flow distribution in a channel crossing under different subcritical flow conditions, for which experimental data are available. Recirculation zones exist at both the downstream channels and the associated contraction coefficient varies linearly with the ratio of the discharges at the two inlets. Secondary currents are apparent for the flow with strong asymmetric outlet conditions. Under supercritical inflow conditions, the model reproduces the hydraulic jump and hydraulic drop phenomena and predicts accurately the relationship between the input power ratio and the outflow discharge ratio of the street crossing. Copyright © 2009 John Wiley & Sons, Ltd.     

Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

We present a remeshed particle‐mesh method for the simulation of three‐dimensional compressible turbulent flow. The method is related to the meshfree smoothed particle hydrodynamics method, but the present method introduces a mesh for efficient calculation of the pressure gradient, and laminar and turbulent diffusion. In addition, the mesh is used to remesh (reorganise uniformly) the particles to ensure a regular particle distribution and convergence of the method. The accuracy of the presented methodology is tested for a number of benchmark problems involving two‐ and three‐dimensional Taylor‐Green flow, thin double shear layer, and three‐dimensional isotropic turbulence. Two models were implemented, direct numerical simulations, and Smagorinsky model. Taking advantage of the Lagrangian advection, and the finite difference efficiency, the method is capable of providing quality simulations while maintaining its robustness and versatility.     

An efficient method for discretizing 3D fractured media for subsurface flow and transport simulations

We introduce a new method to discretize inclined non‐planar two‐dimensional (2D) fractures in three‐dimensional (3D) fractured media for subsurface flow and transport simulations. The 2D fractures are represented by ellipsoids. We first discretize the fractures and generate a 2D finite element mesh for each fracture. Then, the mesh of fractures is analyzed by searching and treating critical geometric configurations. Based on that search, the method generates a quality mesh and allows for including finer grids. A solute transport problem in fractured porous media is solved to test the method. The results show that the method (i) adequately represents the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides accurate results for both simple and complex fractured domains, (iii) is insensitive to spatial discretization, and (iv) is computationally very efficient. For inclined and vertical fractures, analytical and numerical solutions are shown to be in good agreement. The method is therefore suitable to discretize fracture networks for flow and transport simulations in fractured porous media. Copyright © 2010 John Wiley & Sons, Ltd.     

Compressible gas-liquid mixture flow at abrupt pipe enlargements

A detailed investigation was made of the flow of compressible gas-liquid mixtures through sudden enlargements in diameter of circular pipes. One-dimensional analysis shows that the dimensionless pressure rise varies with mixture void fraction and mixture momentum, while the establishment of choking conditions at the enlargement is controlled by the length of pipe downstream in which frictional pipe flow occurs. The flows were found to exhibit two characteristic modes, jet flow and submerged flow, with intermediate flows displaying unsteady oscillation between these modes. The distance to the downstream position of maximum pressure increased steadily with mixture void fraction when the upstream pipe outlet was choked, varying from 5 to 50 times the downstream pipe diameter. If the flow was not choked, this distance was much smaller and showed discrete fixed values associated with the mode of flow.

One-dimensional analysis accurately predicted maximum pressure, but when flow was choked at the enlargement the calculation was sensitive to the pressure in the region of separated flow surrounding the central jet in the enlargement. Although analysis of maximum pressure in terms of flow expansion and normal shock gave a general indication of the maximum pressure (which was thus concluded to depend on the general flow processes expected in the enlargement), accurate prediction of maximum pressures will depend on empirical knowledge of the separated flow region pressures. The maximum pressure rise was found to be in the range extending down to 0.3 of the upstream pipe outlet pressure and reduced with void fraction; it was also influenced by the enlargement area ratio. Flows in the approach and outlet pipes were found to be compressible, frictional pipe flows of the Fanno type, with somewhat reduced friction factors occurring in the outlet pipe.     

Multiscale coupling of compliant and rigid walls blood flow models

Numerical methods based on geometrical multiscale models of blood flows solve for averaged flow statistics on a network of vessels while providing more detailed information about fluid dynamics in a specific region of interest. In such an approach, a 3D model based on the Navier–Stokes equations posed in a domain with rigid walls is often used to describe blood flow dynamics in the refined region. While ignoring elasticity effects in 3D models is plausible in certain applications and saves computational time significantly, coupling such models with 1D flow models may result in non‐physiological phenomena in the computed solutions. Thus, the immediate coupling conditions based on continuity of normal stresses, flow rate, pressure, or a combination of thereof do not account for the inconsistency between elasticity effects in the 1D model and the non‐compliance of the 3D model. In this paper, we introduce and study an auxiliary absorbing 0D model, which is placed at the interface between 1D and 3D models. A virtual device mimics the effect of the 3D model compliance and hence reduces pressure wave reflection and instabilities caused by the inconsistency. The absorbing model is developed from basic mechanical principles. As a result, parameters of the 0D model can be designed based on hemodynamic data. We analyze the stability of the geometrical multiscale model and perform several numerical experiments to assess its computational efficiency. Copyright © 2016 John Wiley & Sons, Ltd.     

Turbulent flow through bifurcated nozzles

A finite-element model has been used to study steady-state turbulent flow through bifurcated submerged-entry nozzles with oversized ports typical of those used in the continuous casting of steel. Both 2D and 3D simulations have been performed with the commercial code FIDAP, using the standard K–? turbulence model. Predicted velocities from 3D simulations compare reasonably with experimental measurements using a hot-wire anemometer conducted in a physical water model, where severe turbulent fluctuations are present. Results show that a 2D simulation can also capture the main flow characteristics of the jet existing the nozzle and requires two orders of magnitude less computer time than the 3D simulation. A model combining the nozzle and mould was set up to study the effect of the outlet boundary conditions of the nozzle on the jet characteristics. This modelling technique will assist in the design of submerged-entry nozzles, especially as applied to enhance steel quality in the continuous casting process. Further, the model will provide appropriate inlet boundary conditions for a separate numerical model of the mould.     

Three‐dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model

Turbulent flow in a compound meandering open channel with seminatural cross sections is one of the most complicated turbulent flows as the flow pattern is influenced by the combined action of various forces, such as centrifugal force, pressure, and shear stresses. In this paper, a three‐dimensional (3D) Reynolds stress model (RSM) is adopted to simulate the compound meandering channel flows. Governing equations of the flow are solved numerically with finite‐volume method. The velocity fields, wall shear stresses, and Reynolds stresses are calculated for a range of input conditions. Good agreement between the simulated results and measurements indicates that RSM can successfully predict the complicated flow phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical analysis of developing turbulent flow in a 180° bend tube by an algebraic Reynolds stress model

A numerical analysis has been performed for three‐dimensional developing turbulent flow in a 180° bend tube with straight inlet and outlet section used by an algebraic Reynolds stress model. To our knowledge, numerical investigations, which show the detailed comparison between calculated results and experimental data including distributions of Reynolds stresses, are few and far between. From this point of view, an algebraic Reynolds stress model in conjunction with boundary‐fitted co‐ordinate system is applied to a 180° bend tube in order to predict the anisotropic turbulent structure precisely. Calculated results are compared with the experimental data including distributions of Reynolds stresses. As a result of this analysis, it has been found that the calculated results show a comparatively good agreement with the experimental data of the time‐averaged velocity and the secondary vectors in both the bent tube and straight outlet sections. For example, the location of the maximum streamwise velocity, which appears near the top or bottom wall in the bent tube, is predicted correctly by the present method. As for the comparison of Reynolds stresses, the present method has been found to simulate many characteristic features of streamwise normal stress and shear stresses in the bent tube qualitatively and has a tendency to under‐predict its value quantitatively. Judging from the comparison between the calculated and the experimental results, the algebraic Reynolds stress model is applicable to the developing turbulent flow in a bent tube that is known as a flow with a strong convective effect. Copyright © 2005 John Wiley & Sons, Ltd.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Non‐Newtonian blood flow dynamics in a right internal carotid artery with a saccular aneurysm

Flow dynamics plays an important role in the pathogenesis and treatment of cerebral aneurysms. The temporal and spatial variations of wall shear stress in the aneurysm are hypothesized to be correlated with its growth and rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This work describes the flow dynamics in a patient‐specific model of carotid artery with a saccular aneurysm under Newtonian and non‐Newtonian fluid assumptions. The model was obtained from three‐dimensional rotational angiography image data and blood flow dynamics was studied under physiologically representative waveform of inflow. The three‐dimensional continuity and momentum equations for incompressible and unsteady laminar flow were solved with a commercial software using non‐structured fine grid with 283 115 tetrahedral elements. The intra‐aneurysmal flow shows complex vortex structure that change during one pulsatile cycle. The effect of the non‐Newtonian properties of blood on the wall shear stress was important only in the arterial regions with high velocity gradients, on the aneurysmal wall the predictions with the Newtonian and non‐Newtonian blood models were similar. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

An investigation of random choice method for three‐dimensional steady supersonic flows

In this paper, an unsplit random choice method (RCM) is developed and applied to numerically solve three‐dimensional supersonic steady flow problems. In order to keep the contacts (slip surfaces) crisply resolved, a new Lagrangian formulation is employed. Due to the lack of exact solutions to 3D Riemann problems, approximate Riemann solutions in the weak sense are adopted. The RCM is thus as efficient as the deterministic TVD schemes, and yields almost identical results in the model problems. Copyright © 1999 John Wiley & Sons, Ltd.     

3D numerical simulation of compressible swirling flow induced by means of tangential inlets

The objective of the present work is to predict compressible swirl flow in the nozzle of air‐jet spinning using the realizable k–ε turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free‐vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.     

A non‐linear dynamical system approach to finite amplitude Taylor‐Vortex flow of shear‐thinning fluids

The effect of shear thinning on the stability of the Taylor–Couette flow is explored for a Carreau–Bird fluid in the narrow‐gap limit. The Galerkin projection method is used to derive a low‐order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional non‐linear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the circular Couette flow, becomes lower as the shear‐thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow, which coincides with the onset of a supercritical bifurcation. Comparison with existing measurements of the effect of shear thinning on the critical Taylor and wave numbers show good agreement. The Taylor vortex cellular structure loses its stability in turn, as the Taylor number reaches a critical value. At this point, an inverse Hopf bifurcation emerges. In contrast to Newtonian flow, the bifurcation diagrams exhibit a turning point that sharpens with shear‐thinning effect. Copyright © 2004 John Wiley & Sons, Ltd.     

Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.