Numerical Study of Heat Transfer by Natural Convection in Concentric Hexagonal Cylinders Charged with a Nanofluid

In this document, a numerical study of the natural convection of steady-state laminar heat transfer in a horizontal ring between a heated hexagonal inner cylinder and a cold hexagonal outer cylinder. A Cu - water nanofluid traverses this annular space. The system of equations governing the problem was solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. The interior and exterior sides from the two cylinders are maintained at a fixed temperature. We investigated the impacts of various thermal Rayleigh numbers (103≤ Rat ≤2.5x105), and the volume fraction from the nanoparticles (0≤ Ø ≤0.12) on fluid flow and heat transfer performance. It is found that in high thermal Rayleigh numbers, a thin thermal boundary layer is illustrated at the flow that heavily strikes the ceiling and lower from the outer cylinder. In addition, the local and mean Nusselt number from a nanofluid are enhanced by enhancing the volume fraction of the nanoparticles.The results are shown within the figure of isocurrents, isotherms, and mean and local Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.

A numerical investigation of the influence of land-sea breeze on the atmospheric effluents released at a coastal site

ABSTRACT. Mesoscale features of a coastal atmospheric boundary layer such as the land-sea circulation and the thermal internal boundary layer (TIBL) structure have been simulated using a two-dimensional numerical boundary layer model. Using Boussinesq approximation for horizontal momentum equations and hydrostatic approximation for vertical momentum equation the model solves the 'shallow water' equations year over a grid domain 80 km length on either side of the coastline and 2 km height. The influence of the land-sea breezes on the dispersion of pollutants released from a continuous point source located at the roast has been studied. The fumigation of pollutants from an offshore source into TIBL over the land has also been illustrated. The limitations associated with the model are also discussed.

Numerical modeling of the formation of D-T mixture spherical layer in micro-targets of LTS

The article presents a two-dimensional economical computational model of the formation of D-T mixture cryogenic layer in a spherical shell. The model is based on the description of the motion of the gas phase in the Boussinesq approximation. The thermal problem is a Stefan problem with a gas-solid phase transition. The technique is based on the finite volume method, the use of a structured mobile grid, whose movement is associated with the separation of the phase front, implicit approximations and the method of splitting two-dimensional equations in directions into one-dimensional equations. It is numerically shown that, due to natural radioactivity, the target is symmetrized. A calculated estimation of the symmetrization time for one geometry of the target with different filling coefficients is carried out.

Vortex Flow on the Surface Generated by the Onset of a Buoyancy-Induced Non-Boussinesq Convection in the Bulk of a Normal Liquid Helium

The onset of the Rayleigh–Benard convection (RBC) in a heated from above normal He-I layer in a cylindrical vessel in the temperature range Tλ < T ≤ Tm (RBC in non-Oberbeck–Boussinesq approximation) is attended by the emergence of a number of vortices on the free liquid surface. Here, Tλ = 2.1768 K is the temperature of the superfluid He-II–normal He-I phase transition, and the liquid density passes through a well-pronounced maximum at Tm ≈ Tλ + 6 mK. The inner vessel diameter was D = 12.4 cm, and the helium layer thickness was h ≈ 2.5 cm. The mutual interaction of the vortices between each other and their interaction with turbulent structures appeared in the layer volume during the RBC development gave rise to the formation of a vortex dipole (two large-scale vortices) on the surface. Characteristic sizes of the vortices were limited by the vessel diameter. The formation of large-scale vortices with characteristic sizes twice larger than the layer thickness can be attributed to the arising an inverse vortex cascade on the two-dimensional layer surface. Moreover, when the layer temperature exceeds Tm, convective flows in the volume decay. In the absence of the energy pumping from the bulk, the total energy of the vortex system on the surface decreases with time according to a power law.

Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

Some aspects in Kelvin-Helmholtz instability with and without Boussinesq approximation

The topic of this paper is the Kelvin-Helmholtz instability, a phenomenon which occurs on the interface of a stratified fluid, in the presence of a parallel shear flow, when there is a velocity and density difference across the interface of two adjacent layers. This paper focuses on a numerical simulation modelled by the Taylor-Goldstein equation, which represents a more realistic case compared to the basic Kelvin-Helmholtz shear flow. The Euler system is solved with new modelled smooth velocity and density profiles at the interface. The flux at cell boundaries is reconstructed by implementing a third order WENO (Weighted Essentially Non-Oscillatory) method. Next, a Riemann solver builds the fluxes at cell interfaces. The use of both Rusanov and HLLC solvers is investigated. Temporal discretization is done by applying the second order TVD (total variation diminishing) Runge-Kutta method on a uniform grid. Numerical simulations are performed comparatively for both Kelvin-Helmholtz and Taylor-Goldstein instabilities, on the same simulation domains. We find that increasing the number of grid points leads to a better accuracy in shear layer vortices visualization. Thus, we can conclude that applying the Taylor-Goldstein equation improves the realism in the general fluid instability modelling.

Laboratory-scale investigation of a periodically forced stratified basin with inclined endwalls

We present results of numerical simulations of a stratified reservoir with a three-layer stratification, subject to an oscillating surface shear stress. We investigate the effect of sloped endwalls on mixing and internal wave adjustment to forcing within the basin, for three different periods of forcing. The simulations are carried out at a laboratory scale, using large-eddy simulation. We solve the three-dimensional Navier–Stokes equations under the Boussinesq approximation using a second-order-accurate finite-volume solver. The model was validated by reproducing experimental results for the response of a reservoir to surface shear stress and resonant frequencies of internal waves. We find interesting combinations of wave modes and mixing under variation of the forcing frequencies and of the inclination of the endwalls. When the frequency of the forcing is close to the fundamental mode-one wave frequency, a resonant internal seiche occurs and the response is characterized by the first vertical mode. For forcing periods twice and three times the fundamental period, the dominant response is in terms of the second vertical mode. Adjustment to forcing via the second vertical mode is accompanied by the cancellation of the fundamental wave and energy transfer to higher-frequency waves. The study shows that the slope of the endwalls dramatically affects the location of mixing, which has a feedback on the wave field by promoting the generation of higher vertical modes.

Mathematical modeling of three-layer flows with evaporation based on exact solutions

The stationary flow in the “liquid-liquid-gas” system in a horizontal channel with solid impermeable upper and lower walls is investigated. Mathematical modeling in each of the layers of the system is based on exact solutions of a special type of Navier-Stokes equations in the Boussinesq approximation. The processes of vapor evaporation or condensation at the liquid-gas interface are modeled using the boundary conditions of the problem. In the upper layer the thermal diffusion effect and the effect of diffusional thermal conductivity are taken into account. Examples of three-layer flows for the “silicone oil - water - air” system are given. The influence of the thermal regime at the boundaries of the system and the thickness of the upper layer on the longitudinal velocity and temperature distribution is considered.

On the performance of RANS turbulence models in predicting static stall over airfoils at high Reynolds numbers

Purpose This paper aims to conduct, a detailed investigation of various Reynolds averaged Navier–Stokes (RANS) models to study their performance in attached and separated flows. The turbulent flow over two airfoils, namely, National Advisory Committee for Aeronautics (NACA)-0012 and National Aeronautics and Space Administration (NASA) MS(1)-0317 with a static stall setup at a Reynolds number of 6 million, is chosen to investigate these models. The pre-stall and post-stall regions, which are in the range of angles of attack 0°–20°, are simulated. Design/methodology/approach RANS turbulence models with the Boussinesq approximation are the most commonly used cost-effective models for engineering flows. Four RANS models are considered to predict the static stall of two airfoils: Spalart–Allmaras (SA), Menter’s k – ω shear stress transport (SST), k – kL and SA-Bas Cakmakcioglu modified (BCM) transition model. All the simulations are performed on an in-house unstructured-grid compressible flow solver. Findings All the turbulence models considered predicted the lift and drag coefficients in good agreement with experimental data for both airfoils in the attached pre-stall region. For the NACA-0012 airfoil, all models except the SA-BCM over-predicted the stall angle by 2°, whereas SA-BCM failed to predict stall. For the NASA MS(1)-0317 airfoil, all models predicted the lift and drag coefficients accurately for attached flow. But the first three models showed even further delayed stall, whereas SA-BCM again did not predict stall. Originality/value The numerical results at high Re obtained from this work, especially that of the NASA MS(1)-0317, are new to the literature in the knowledge of the authors. This paper highlights the inability of RANS models to predict the stall phenomenon and suggests a need for improvement in modeling flow physics in near- and post-stall flows.