arXiv subjects

Wilfried Coenen

Publications and source records attributed to Wilfried Coenen.

5 recordsLinked to original sources

arXiv2024

Non-Boussinesq stability analysis of natural-convection gaseous flow on inclined hot plates

The buoyancy-driven boundary-layer flow that develops over a semi-infinite inclined hot plate is known to become unstable at a finite distance from the leading edge, characterized by a critical value of the Grashof number Gr based on the local boundary-layer thickness. The nature of the resulting instability depends on the inclination angle $ϕ$, measured from the vertical direction. For values of $ϕ$ below a critical value $ϕ_c$ the instability is characterized by the appearance of spanwise traveling waves, whereas for $ϕ>ϕ_c$ the bifurcated flow displays Görtler-like streamwise vortices. The Boussinesq approximation, employed in previous linear stability analyses, ceases to be valid for gaseous flow when the wall-to-ambient temperature ratio $Θ_w$ is not close to unity. The corresponding non-Boussinesq analysis is presented here, accounting also for the variation with temperature of the different transport properties. A temporal stability analysis including nonparallel effects of the base flow is used to determine curves of neutral stability, which are then employed to delineate the dependences of the critical Grashof number and of its associated wave length on the inclination angle $ϕ$ and on the temperature ratio $Θ_w$ for the two instability modes, giving quantitative information of interest for configurations with $Θ_w-1\sim 1$. The analysis provides in particular the predicted dependence of the crossover inclination angle $ϕ_c$ on $Θ_w$, indicating that for gaseous flow with $Θ_w-1\sim 1$ spanwise traveling waves are predominant over a range of inclination angles $0 \le ϕ\le ϕ_c$ that is significantly wider than that predicted in the Boussinesq approximation.

physics.flu-dyn↗

arXiv2024

Influences of stoichiometry on steadily propagating triple flames in counterflows

Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is $1/2$. There then exist lean and rich premixed flames of roughly equal strengths, with a diffusion flame trailing behind from the stoichiometric point at which they meet. In the majority of realistic situations, however, the stoichiometric mixture fraction departs appreciably from unity, typically being quite small. With the objective of clarifying the influences of stoichiometry, attention is focused on one of the simplest possible models, addressed here mainly by numerical integration. When the stoichiometric mixture fraction departs appreciably from $1/2$, one of the premixed wings is found to be dominant to such an extent that the diffusion flame and the other premixed flame are very weak by comparison. These curved, partially premixed flames are expected to be relevant in realistic configurations. In addition, a simple kinematic balance is shown to predict the shape of the front and the propagation velocity reasonably well in the limit of low stretch and low curvature.

physics.flu-dyn↗

arXiv2024

A model for the constant-density boundary layer surrounding fire whirls

This paper investigates the steady axisymmetric structure of the cold boundary-layer flow surrounding fire whirls developing over localized fuel sources lying on a horizontal surface. The inviscid swirling motion found outside the boundary layer, driven by the entrainment of the buoyant turbulent plume of hot combustion products that develops above the fire, is described by an irrotational solution, obtained by combining Taylor's self-similar solution for the motion in the axial plane with the azimuthal motion induced by a line vortex of circulation $2 πΓ$. The development of the boundary layer from a prescribed radial location is determined by numerical integration for different swirl levels, measured by the value of the radial-to-azimuthal velocity ratio $σ$ at the initial radial location. As in the case $σ=0$, treated in the seminal boundary-layer analysis of Burggraf et al. (Phys. Fluids, 1971), the pressure gradient associated with the centripetal acceleration of the inviscid flow is seen to generate a pronounced radial inflow. Specific attention is given to the terminal shape of the boundary-layer velocity near the axis, which displays a three-layered structure that is described by matched asymptotic expansions. The resulting composite expansion, dependent on the level of ambient swirl through the parameter $σ$, is employed as boundary condition to describe the deflection of the boundary-layer flow near the axis to form a vertical swirl jet. Numerical solutions of the resulting non-slender collision region for different values of $σ$ are presented both for inviscid flow and for viscous flow with moderately large values of the controlling Reynolds number $Γ/ν$. The velocity description provided is useful in mathematical formulations of localized fire-whirl flows, providing consistent boundary conditions accounting for the ambient swirl level.

physics.flu-dyn↗

arXiv2024

Oscillating flow around a circular cylindrical post confined between two parallel plates

This work is motivated by the interest in determining the effect of the micro-anatomy of the spinal subarachnoid space on the cerebrospinal fluid flow and on the associated transport of solutes. To that aim, we focus on a canonical model problem in which a circular post of radius $a$, confined between two parallel plates separated by a distance $2h$, is subjected to an oscillatory flow. In particular, we are concerned with the steady, viscous, time-averaged flow that persists in the vicinity on the cylinder, when the stroke length of the oscillating flow, $U_{\infty}/ω$ is smaller or comparable to the radius of the post, $a$, where $U_{\infty}$ and $ω$ are the mean velocity amplitude and the corresponding angular frequency, respectively. First, we analyze the asymptotic limit of small values of the stroke length varying the aspect ratio of the post $λ$ and the Womersley number $M$. First-order steady-streaming corrections at leading order have been computed, together with associated Stokes-drift component, the sum of both yielding the mean Lagrangian velocity field. The confinement effect is seen to induce the three-dimensionality of flow. Moreover, in the mid plane the time-averaged steady flow exhibits a recirculating vortex attached to the wall of the post that decreases as $M$ increases for low values of $M$. However, for values of $M$ larger than a critical one, $M_{cr}(λ)$, a second, outer vortex is also formed. The dependence $M_{cr}(λ)$ has been quantified. The analysis has been corroborated experimentally for a fixed aspect ratio. Consideration of an anharmonic oscillating flow shows the fort-and-aft symmetry of the steady flow is broken. Finally, the analysis is experimentally extended to consider an array of equally spaced posts.

physics.flu-dyn↗

arXiv2023

Floquet stability analysis of a two-layer oscillatory flow near a flexible wall

We investigate the linear Floquet stability of two fluid layers undergoing oscillations in the direction parallel to the flexible wall that separates them. This canonical configuration is inspired by the cerebrospinal fluid flow in the spinal canal of subjects with hydro-/syringomyelia.The analysis focuses on the marginal conditions for the onset of instability, and how these depend on the spatial wavelength of the perturbation, and on the values of the control parameters, which are the two channel widths, the Reynolds number, and the wall stiffness. Unstable perturbations are found to oscillate synchronous with the base flow. The wavelength of the most unstable perturbation, of the order of the stroke length of the basic oscillatory motion, depends strongly on the wall stiffness, but is only weakly influenced by the channel widths and the Reynolds number. In general, around criticality, it was found that increasing the Reynolds number has a destabilizing effect, and that decreasing the canal widths stabilizes the instability. The wall stiffness on the other hand has a non-monotonic effect, exhibiting an intermediate value for which the instability is maximally amplified. The present analysis is a first step towards a better understanding of the physical mechanisms that govern many (bio)fluid mechanical problems that involve oscillatory flows near compliant walls.

physics.flu-dyn↗