Nonlinear aspects of high Reynolds number channel flows

This paper considers the flow in a two-dimensional channel at high Reynolds number, with wall deformations which can lead to flow separation. An asymptotic model is proposed by using the successive complementary expansion method with generalized asymptotic expansions. In particular, the model emphasizes the asymmetry of the channel geometry by introducing a change of variables. It is shown that the model is more general than the models developed with the method of matched asymptotic expansions. Comparisons with Navier–Stokes solutions show that the model is well founded and enables us to treat original problems

High Reynolds Channel Flows: Variable curvature

Two-dimensional laminar flow, at high Reynolds number Re, of an incompressible Newtonian fluid in a curved channel connected to 2 fitting tangent straight channels at its upstream and downstream extremities is considered. The Successive Complementary Expansion Method (SCEM) is adopted. This method leads to an asymptotic reduced model called Global Interactive Boundary Layer (GIBL) which gives a uniformly valid approximate solution of the flow field in the whole domain. To explore the effect of the variable curvature on the flow field, the bend has an elliptical median line. The validity of the proposed GIBL model is confronted to the numerical solution of complete Navier- Stokes equations. This comparison includes the wall shear stress which is a very sensitive measure of the flow field. The GIBL results match very well the complete Navier-stokes results for curvatures $K_{max}$ up to 0.4, curvature variations $\vert K'_{max}\vert$ up to 0.7 and eccentricities $e$ up to $\simeq 0.943$ in the whole geometrical domain. The upstream and downstream effects as well as the impact of the curvature discontinuities and the behaviour in the entire bend are well captured by the GIBL model

Uniformly Valid Asymptotic Flow Analysis in Curved Channels

The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method (SCEM) which is based on generalized asymptotic expansions leading to a uniformly valid approximation. The GIBL model is valid when the non dimensional number μ = δmath is O(1) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers Re ranging from 1 to 10 puissance 4 and for constant curvatures δ = math ranging from 0.1 to 1, where H is the channel width and Rc the curvature radius. The asymptotic analysis shows that μ, which is the ratio between the curvature and the thickness of the boundary layer of any perturbation to the Poiseuille flow, is a key parameter upon which depends the accuracy of the GIBL model. The upstream influence length is found asymptotically and numerically to be O(math)

Curved channel flow with stenoses and aneurysms

Curvature is everywhere, in man or nature made devices. Its implication on physiological flows may be as important as other inertial or viscous effects. Relatively to an otherwise straight vessel, the so called centrifugal forces induce secondary flow that modify the whole flow structure and give rise to Dean vortices. Since the pioneering work of Dean many fundamental and applied investigations were performed. More specifically, in the blood dynamics studies, experimental and numerical simulations were also achieved. On the other hand many studies dealt with stenoses or aneurysms mainly situated in otherwise straight vessels. Thus the coupling between the global curvature effects and local section variations due to stenoses or aneurysms is not enough investigated. In the present work we will quantify how the impact of a stenosis or an aneurysm is modified when it occurs in a curved vessel compared to when it is located in a straight environment

High Reynolds Channel Flows: Upstream interaction of various wall deformations

The flow at high Reynolds number in the entrance of distorted channel is considered. We analyse the anticipated fluid responds to a downstream wall distortion, and we find that the non linear upstream length \Delta={\mbox{O}}(R_e^{1/7}), using either a new asymptotic approach called Successive Complementary Expansions Method (SCEM) with generalized asymptotic expansions and a modal analysis of the perturbed flow. Comparisons with Navier-Stokes solutions show that the mathematical model is well founded

The flow structure behind vortex generators embedded in a decelerating turbulent boundary layer

The objective of the present work is to analyse the behaviour of a turbulent decelerating boundary layer under the effect of both passive and active jets vortex generators (VGs). The stereo PIV database of Godard and Stanislas [1, 2] obtained in an adverse pressure gradient boundary layer is used for this study. After presenting the effect on the mean velocity field and the turbulent kinetic energy, the line of analysis is extended with two points spatial correlations and vortex detection in instantaneous velocity fields. It is shown that the actuators concentrate the boundary layer turbulence in the region of upward motion of the flow, and segregate the near-wall streamwise vortices of the boundary layer based on their vorticity sign

Wave propagation into the spinal cavity: a 1d model with coaxial compliant tubes

One–Dimensional models have been used to simulate pulse waves propagation in the spinal cavity and the interactions between CSF, blood and the spinal cord. Some adopted compliant coaxial configurations but neglected the fluid's viscosity [1, 2] while others took into account CSF viscosity but simplified the cavity as one equivalent distensible tube [3]. Previous studies in the inviscid coaxial configuration have shown that the confinement reduces the wave propagation speed of the compliant part by a factor equal to the square root of the area parameter, i.e. the ratio of the tubes cross-sectional areas, when the dura is considered rigid

A coaxial coupled model of cerebral flows: blood and cerebrospinal fluid

International audienceThis study aimed to develop a one dimensional (1D) model to simulate the Cerebrospinal Fluid (CSF) flows in the cerebral sub-arachnoid spaces, and its coupling with the entire cerebral blood flow vascular network. The model consist in a network of coaxial tubes: the interior network represents the cerebral vasculature from the carotid and vertebral arteries to the sinuses and jugular veins (Zagzoule, 1986), and the coaxial exterior tubes the sub arachnoid spaces where the CSF flows. By integrating the mass and momentum flow conservation equations over the tubes cross-sections, we obtain a 1D coupled coaxial model of the blood and CSF flows. Our model takes into account the viscosity of the fluids (Cathalifaud, 2015), and assumes compliant boundary conditions for the coaxial compartment. Given the input pressure signal at the carotid and vertebral arteries, we therefore obtained an induced CSF flow, as shown in Figure 1. Results depends on the confinement of the coaxial compartment and the compliances of the boundary conditions, and well compared to measured CSF flows of the literature (between 2 and 5 cm3/s). We also investigate the coupling effect of the CSF on the blood flows, especially on the cerebral autoregulation characteristic time. We show that it strongly depends on the confinement of the coaxial compartment

A one-dimensional model of wave propagation within the co-axial viscous fluid filled spinal cavity

One–Dimensional models have been used to simulate pulse waves propagation in the spinal cavity and the interactions between CSF, blood and the spinal cord

Validation of an adjoint method for compressible channel flow sensitivities

Adjoint methods are used in fluid dynamics to perform sensitivity analysis, to find optimal perturbations and optimal control. In this study the adjoint of the 2D unsteady compressible Navier-Stokes equations are applied to wall bounded flows. Suitable wall boundary conditions for the adjoint equations are derived and the whole direct-adjoint system is  validated for a plane channel flow. This academic test case is the first step to perform adjoint analysis of more complex flows