A systematic study of the grid requirements for a spectral element method solver

Direct numerical simulations are performed to study temporal variations of the wall shear stresses and flow dynamics in the turbulent pulsatile pipe flow. The mechanisms, responsible for the paradoxical phenomenon for which the amplitude of the oscillating wall shear stress in the turbulent flow is smaller than that in the laminar flow for the same pulsation conditions, are investigated. It is shown that the delayed response of turbulence in the buffer layer generates a large magnitude of the radial gradient of the Reynolds shear stress near the wall, which counteracts the effect of the oscillating pressure gradient on the change of the streamwise velocity and hence reduces the amplitude of the wall shear stress. Such a delayed response consists of two processes: the delayed development of near-wall streaks and the subsequent energy redistribution from the streamwise velocity fluctuation to the other two co-existing components. This is a dynamical manifestation of the viscoelasticity of turbulent eddies. As the frequency is reduced, the variation of the friction Reynolds number results in a phase-wise variation of the time scale and intensity of the turbulence response, causing the hysteresis of the wall shear stress. Such a phase asymmetry is amplified by the increase of the pulsation amplitude. An examination of the energy spectra reveals that the near-wall streaks are stretched in the streamwise direction during the acceleration phase, and then break up into small-scale structures in the deceleration phase, accompanied by the enhanced dissipation that transforms the turbulent kinetic energy into heat.

Section: Computational Set-upsupporting

confidence: 86%

Time-delayed characteristics of turbulence in pulsatile pipe flow

Liu,

Zhu,

Bao

et al. 2024

“…The grid spacing to Kolmogorov scale ratio, l/η (where l = ( x y z) 1/3 and η is the local dissipation) is calculated at different instantaneous time and is always less than 10. This is more conservative than the l/η ≈ 16 recommended by Lu et al (2023) and Zahtila et al (2023), who studied the grid convergence characteristics of spectral element solvers. Therefore, we have ensured that our grid resolution is sufficient to resolve all of the turbulent length scales and also meet the requirement of x = y ≈ (ReSc) −1/2 , where Sc = 1 (Härtel et al 2000;Birman, Martin & Meiburg 2005;Dai 2015).…”

Section: Computational Set-upmentioning

confidence: 95%

“…(2023) and Zahtila et al. (2023), who studied the grid convergence characteristics of spectral element solvers. Therefore, we have ensured that our grid resolution is sufficient to resolve all of the turbulent length scales and also meet the requirement of , where (Härtel et al.…”

Section: Computational Set-upmentioning

confidence: 99%

Effect of stratification on the propagation of a cylindrical gravity current

Lam,

Chan,

Sutherland

et al. 2024

Direct numerical simulations (DNSs) of three-dimensional cylindrical release gravity currents in a linearly stratified ambient are presented. The simulations cover a range of stratification strengths $0< S\leq 0.8$ (where $S=(\rho _b^*-\rho _0^*)/(\rho _c^*-\rho _0^*), \rho _b^*, \rho _0^*$ and $\rho _c^*$ are the dimensional density at the bottom of the domain, top of the domain and the dense fluid, respectively) at two different Reynolds numbers. A comparison between the stratified and unstratified cases illustrates the influence of stratification strength on the dynamics of cylindrical gravity currents. Specifically, the front velocity in the slumping phase decreases with increasing stratification strength whereas the duration of the slumping phase increases with increments of $S$ . The Froude number calculated in this phase shows a good agreement with models proposed by Ungarish & Huppert (J. Fluid Mech., vol. 458, 2002, pp. 283–301) and Ungarish (J. Fluid Mech., vol. 548, 2006, pp. 49–68), originally developed for planar gravity currents in a stratified ambient. In the inertial phase, the front velocity across cases with different stratification strengths adheres to a power-law scaling with an exponent of $-$ 1/2. Higher Reynolds numbers led to more frequent lobe splitting and merging, with lobe size diminishing as stratification strength increased. Strong interactions among inner vortex rings occurred during the slumping phase, leading to the early formation of hairpin vortices in weakly stratified cases, while strongly stratified cases exhibited delayed vortex formation and less turbulence.

“…It is of note S5 is based on the same two-dimensional mesh as used by Ooi et al (2022) for the same Re, where it was found sufficient for DNS. To also ensure that the near-wall dynamics are well resolved, it is typical in wall-bounded flows to compare the height of the first grid point y 1 with the viscous length scale ν/u τ , where u τ = √ τ w /ρ is the friction velocity, with τ w being the shear stress at the wall, and ρ the fluid density (Zahtila et al 2023). We therefore plot in figure 4 the distribution of y + = y 1 u τ /ν values along the cylinder surface along with the channel walls for different Reynolds numbers.…”

Section: Problem Set-upmentioning

confidence: 99%

Asymmetric wakes in flows past circular cylinders confined in channels

Aljubaili

Zahtila

et al. 2023

Self Cite

In this paper, we investigate the flow past a circular cylinder confined in a channel at a blockage ratio of $\beta =0.7$ (the ratio of the cylinder diameter and the channel height) for Reynolds numbers between ${\textit {Re}}=300$ and $3900$ using direct numerical simulation (DNS). We show for varying Reynolds numbers a wide range of wake dynamics occur as the spanwise domain length is changed. At a lower Reynolds number of ${\textit {Re}}=300$ , a reverse von Kármán wake alongside either a top- or bottom-biased asymmetry was observed at different spanwise locations. The asymmetry was structurally similar the two-dimensional asymmetry studied by prior investigators, and was found to be a result of the confinement effect. Further, wake-jumping between the two intermittent states was present. For larger Reynolds numbers, ${\textit {Re}}=1000$ and $3900$ , these asymmetric structures were found to become dominant. We also examine the dependence of the asymmetries on the spanwise domain. For small spanwise domains the asymmetries were uniformly orientated across the span. In contrast, for sufficiently large spanwise domains, the asymmetry flips its orientation at different spanwise locations. Comparisons of flow statistics demonstrate good agreement between the different spanwise domains, which suggests the same mechanism maintains the asymmetry in both cases. Further analysis at ${\textit {Re}}=1000$ found the number of times the wake flips is dependent on the initial conditions, with a wake that flips zero (purely asymmetric), two and four times being observed. These structures were also determined to remain stable over time scales of $1000D/U$ .