Numerical Simulations Of Stratified Flow Research Articles

Numerical investigation of internal wave and free surface wave induced by the DARPA Suboff moving in a strongly stratified fluid

ABSTRACT Numerical methods for simulating a strongly stratified flow were proposed based on a two-layer model. The VOF method was employed to trace the free surface and interface, and the SST model was used as the turbulence model. To verify the methods, numerical simulations of stratified flow around a cylinder were performed. Results were compared with relevant experiments. The near field around a 1:20 of the DARPA Suboff moving in a strongly stratified flow was simulated. The effects of pycnocline, submarine depth, and speed on the free surface wave and internal wave were analysed. The results demonstrate that the presence of pycnocline can increase the intensity of divergence and convergence at the free surface. Increasing the depth leads to a decrease of the free surface wave and shrinkage of the internal wave’s scope. As the speed increases, the free surface wave shows a significant increase in wavelength and a decrease in Kelvin angle.

Direct numerical simulation of stratified flow past a sphere at a subcritical Reynolds number of 3700 and moderate Froude number

Direct numerical simulation of flow past a sphere in a stratified fluid is carried out at a subcritical Reynolds number of 3700 and $Fr=U_{\infty }/ND=1,2$ and 3 to understand the dynamics of moderately stratified flows with $Fr=O(1)$. Here, $U_{\infty }$ is the free stream velocity, $N$ is the background buoyancy frequency and $D$ is the sphere diameter. The unstratified flow past the sphere consists of a separated shear layer that transitions to turbulence, a recirculation zone and a wake with a mean centreline deficit velocity, $U_{0}$, that decreases with downstream distance as a power law. With increasing stratification, the separated shear layer plunges inward vertically and its roll up is inhibited, the recirculation zone is shortened and the mean wake decays at a slower rate of $U_{0}\propto (x_{1}/D)^{-0.25}$ in the non-equilibrium (NEQ) region. The transition from the near wake where $U_{0}$ has a decay rate similar to the unstratified case to the NEQ regime occurs as an oscillatory modulation by a steady lee wave pattern with a period of $t=2\unicode[STIX]{x03C0}/N$ that leads to accelerated $U_{0}$ between $Nt=\unicode[STIX]{x03C0}$ and approximately $Nt=2\unicode[STIX]{x03C0}$. Far downstream, the wake is dominated by coherent horizontal motions. The acceleration of $U_{0}$ by the lee wave and the lower turbulence production in the NEQ regime, thereby less loss to turbulence, prolongs the lifetime of the wake relative to its unstratified counterpart. The intensity, temporal spectra and structure of turbulent fluctuations in the wake are assessed. Buoyancy induces significant anisotropy among the velocity components and between their vertical and horizontal profiles. Consequently, the near wake ($x_{1}/D<10$) exhibits significant differences in turbulence profiles relative to its unstratified counterpart. Spectra of vertical velocity show a discrete peak in the near wake that is maintained further downstream. The turbulent kinetic energy (TKE) balance is computed and contributions from pressure transport and buoyancy are found to become increasingly important as stratification increases. The findings of this investigation will be helpful in designing accurate initial conditions for the temporally evolving model of stratified wakes.

Numerical simulation of stratified flow around a tall building of a complex shape

Results of large-eddy simulations of stably stratified atmospheric flow around an isolated, complex-shaped tall building are presented. The study focuses on the identification of flow structures in the building wake in high and low Froude number regimes. A qualitative comparison of results with available literature data and existing theories is presented. In addition to flow structures identified in earlier studies such as the horseshoe and recirculation eddy vortices, we analyze a stationary disturbance akin to mountain gravity wave, and a complex vortex structure associated with this wave, consisting of multiple symmetric pairs of vortices. The Froude number appears to be the principal parameter controlling the structure of the wake, waves and vortex pattern.

Sensitivity of stratified turbulence to the buoyancy Reynolds number

AbstractIn this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

Enclosure Fires, Gravity Waves, and the Backdraft Problem

The air flow to an underventilated compartment fire often depends on the flow velocities in the gravity wave of cold air that feeds the fire with oxygen. This problem has been studied in laboratory experiments and by CFD simulations. The main problem seems to be whether mixing and entrainment between the two layers of hot and cold air has a profound effect on the flow velocities. In this article, an analytical gravity wave model that can calculate the velocities in a simple gravity wave is presented. This model uses the equations of stratified flow hydraulics and the translatory wave solution of the flow equations. It is found that the velocities of the model compare very well to the velocities reported from laboratory tests and numerical simulations. Numerical simulations of stratified flow in a CFD model are discussed with respect to model construction. It is concluded that the densimetric Froude number is the main parameter for the velocity calculations and the length/height ratio is important for the friction forces.

The effect of small‐scale hills on orographic drag

AbstractThe purpose of this study is to investigate the extent to which the presence of hills with relatively short horizontal scales can influence the drag, due to mountain waves and flow blocking, exerted on the flow by larger‐scale mountains. Numerical simulations of stratified flow over mountains are presented for flow over orography described by the linear superposition of broad mountains, whose length scales are large enough to generate mountain waves, and narrow corrugations, whose wavelengths fall below the minimum horizontal wavelength for stationary gravity waves. Results are presented for both two‐ and three‐dimensional mountain shapes, and for a range of corrugation heights. It is shown that the corrugations can significantly reduce the amplitude of the mountain waves generated by the broader mountain, or they can suppress the unsteadiness of the wake. When these mechanisms make an important contribution to the total drag, this implies a significant drop in the total drag, compared to the sum of the contributions from the two scales of orography. From the point of view of drag parametrization, the extent to which the effect of the small‐scale hills can be represented via an effective roughness length is investigated. © Crown Copyright 2007. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd

Flow past a sphere in density-stratified fluid

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The effects of stratification is implemented by density transport without diffusion. The computed results include the characteristics of the near wake as well as the effects of stratification on the separation angle. Under increased stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder. With further increase in stratification, the wake becomes unsteady, and consists of planar vortex shedding similar to von Karman vortex streets.

구 후류에 미치는 유동장 밀도 성층화 영향 전산 해석

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of<br/> geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier-Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The computed results include the characteristics of the near wake and the unsteady vortex shedding. With a strong stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder.<br/>

On breaking internal waves over the sill in Knight Inlet

This paper describes a new series of numerical simulations of stratified flow over localized topography which has been designed to address issues arising from a recently published sequence of detai...