Sasa Kenjeres

Transient analysis of Rayleigh-Bénard convection with a RANS model

Abstract Rayleigh–Benard (RB) convection at high Rayleigh numbers was studied by transient Reynolds-averaged-Navier–Stokes (TRANS) approach. The aim of the study was to assess the RANS method in reproducing the coherent structure and large-scale unsteadiness in buoyancy-driven turbulent flows. The method can be regarded as a very large eddy simulation (VLES) combining the rationale of the LES and of RANS modelling. Following the experimental and DNS evidence that the RB convection is characterised by a coherent cellular motion with scales which are much larger than the scales of the rest of turbulent fluctuations, the instantaneous flow properties are decomposed into time-mean, periodic and random (triple decomposition). A conventional single-point closure (here an algebraic low-Re-number k−e− θ 2 stress/flux model), used for the unresolved motion, was found to reproduce well the near-wall turbulent heat flux and wall heat transfer. The large scale motion, believed to be the major mode of heat and momentum transfer in the bulk central region, is fully resolved by time solutions. In contrast to LES, the contribution of both modes to the turbulent fluctuations are of the same order of magnitude. In the horizontal wall boundary layers the model accounts almost fully for the turbulence statistics, with a marginal contribution of resolved scales. The approach was assessed by comparison with the available direct numerical simulations (DNS) and experimental data using several criteria: visual observation of the large structure morphology, different structure identification techniques, and long-term averaged mean flow and turbulence properties. A visible similarity with large structures in DNS was observed. The mean flow variables, second-moments and wall heat transfer show good agreement with most DNS and experimental results for different flow cases considered.

A comparative assessment of the second-moment differential and algebraic models in turbulent natural convection

Results of direct numerical simulation (DNS) of turbulent natural convection between two differentially heated infinite vertical plates for Ra=5.4 x 10 5 (Versteegh and Nieuwstadt, Boudjemadi et al.) have been used to assess models of various terms in the transport equations for the turbulent heat-flux vector θu i and the temperature variance θ 2 . The hypotheses used to truncate the differential model into algebraic forms have also been examined. We present some results of the computation of natural convection in the tall cavity, obtained with a fully differential and a four-equation (κ-e-θ 2 -e θθ ) algebraic model. Despite the unsatisfactory reproduction of individual terms in the equations, computations yielded acceptable agreement with available experimental and DNS data. Based on new evidence, possible improvements of the model are briefly discussed, aimed at ensuring a better term-by-term modelling of the transport equations for θu i and θ 2 .

Prediction of turbulent thermal convection in concentric and eccentric horizontal annuli

Natural convection in horizontal concentric and eccentric annuli with heated inner cylinder has been studied using several variants of single-point closure models at the eddy-diffusivity and algebraic-flux level. The results showed that the application of the algebraic model for the turbulent heat flux θu i , derived from the differential transport equation and closed with the low-Reynolds number form of transport equations for the kinetic energy k, its dissipation rate e, and temperature variance θ 2 , reproduced well the experimental data for mean and turbulence properties and heat transfer over a range of Rayleigh numbers, for different overheatings and inner-to-outer diameter ratios. The application of the extended algebraic turbulence models proved to be crucial for predicting the flow pattern and wall heat transfer at transitional Rayleigh numbers, where substantial turbulence persists only in a narrow plume above the heated inner cylinder, with laminar flow, or even stagnant fluid, prevailing in the remainder of the annuli.

A direct-numerical-simulation-based second-moment closure for turbulent magnetohydrodynamic flows

A magnetic field, imposed on turbulent flow of an electrically conductive fluid, is known to cause preferential damping of the velocity and its fluctuations in the direction of Lorentz force, thus leading to an increase in stress anisotropy. Based on direct numerical simulations (DNS), we have developed a model of magnetohydrodynamic (MHD) interactions within the framework of the second-moment turbulence closure. The MHD effects are accounted for in the transport equations for the turbulent stress tensor and energy dissipation rate—both incorporating also viscous and wall-vicinity nonviscous modifications. The validation of the model in plane channel flows with different orientation of the imposed magnetic field against the available DNS (Re = 4600,Ha = 6), large eddy simulation (Re = 2.9×104,Ha = 52.5,125) and experimental data (Re = 5.05×104 and Re = 9×104, 0 ? Ha ? 400), show good agreement for all considered situations.

Reorganization of turbulence structure in magnetic Rayleigh-Benard convection: a T-RANS study

Effects of a uniform, vertically oriented, magnetic field on the reorganization of coherent structure in Rayleigh–Benard convection of electrically conductive fluid were studied using a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach. This method can be regarded as a very large eddy simulation (VLES) in which the unresolved random motion is modelled using a low-Re-number k–ϵ–θ2 algebraic stress/flux single-point closure model. The large-scale deterministic motion, which is the major mode of heat and momentum transfer in the bulk central region, is fully resolved by the time solution. In contrast to LESs, the contribution of both modes to the turbulent fluctuations are of the same order of magnitude. The approach was first assessed by comparison with the available direct numerical simulations (DNSs) and experimental data for non-magnetic Rayleigh–Benard convection for Rayleigh (Ra) numbers 6.5 × 105 and 109, as well as with our own LES for Ra = 6.5 × 105, using several criteria: visual obse...

Modelling and simulation of low-density lipoprotein transport through multi- layered wall of an anatomically realistic carotid artery bifurcation

A high concentration of low-density lipoprotein (LDL) is recognized as one of the principal risk factors for development of atherosclerosis. This paper reports on modelling and simulations of the coupled mass (LDL concentration) and momentum transport through the arterial lumen and the multi-layered arterial wall of an anatomically realistic carotid bifurcation. The mathematical model includes equations for conservation of mass, momentum and concentration, which take into account a porous layer structure, the biological membranes and reactive source/sink terms in different layers of the arterial wall, as proposed in Yang & Vafai (2006). A four-layer wall model of an arterial wall with constant thickness is introduced and initially tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with previously published results demonstrated proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the arterial lumen and in the artery wall are obtained. Then, an anatomically realistic carotid artery bifurcation is studied. This is the main novelty of the presented research. We find a strong dependence between underlying blood flow pattern (and consequently the wall shear stress distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reactions within the multi-layered artery wall is crucial for accurate predictions of the LDL concentration in the media. It is shown that a four-layer wall model produced qualitatively good agreement with the experimental results of Meyer et al. (1996) in predicting levels of LDL within the media of a rabbit aorta under identical transmural pressure conditions. Finally, it is demonstrated that the adopted model represents a good initial platform for future numerical investigations of the initial stage of atherosclerosis for patient-specific geometries.

Tackling complex turbulent flows with transient RANS

This article reviews some recent applications of the transient-Reynoldsaveraged Navier–Stokes (T-RANS) approach in simulating complex turbulent flows dominated by externally imposed body forces, primarily by thermal buoyancy and the Lorentz force. The T-RANS aims at numerical resolving unsteady (semi-) deterministic vortical structures in flows with sufficiently strong internal forcing. With a well-tested RANS model to account for the unresolved ‘subscale’ motion, the T-RANS is considered as a tool for solving large-scale high Rayleigh and Reynolds numbers, which are inaccessible to the conventional large-eddy simulation (LES) or any other numerical simulation approach. First, a brief outline of the T-RANS rationale is presented and its potential illustrated in the simulation of Rayleigh–Bernard convection in an infinite domain for over a ten-decade range of Rayleigh numbers (106–2×1016). The accurate prediction of heat transfer over a wide range of Rayleigh numbers provided sufficient credibility in the approach and its application to a variety of real-life flows dominated by body forces. This is illustrated by three examples of complex environmental and multi-physics phenomena: dynamics of a fuel-oil cooling inside a sunken tanker wreck, diurnal variations of air-movement and pollutant spreading over a mesoscale mountain city in a valley capped by a thermal inversion layer, and finally in the generation and self-sustenance of a magnetic field by a highly turbulent helical sodium movement. The simulated results agree well with the experimental data where available.

Effects of wavy surface roughness on the performance of micronozzles

Recent trends in small-scale (~1 dm 3 ) satellites motivate the further development of microscale propulsion subsystems. In the present paper, we focus on flow dynamics simulations of conical convergent-divergent micronozzles and on the increased importance of wall effects due to the decrease in the characteristic length of such small systems. The inefficiency associated with viscous losses due to the developing boundary layer and the effect of sinusoidal surface roughness due to the employed microelectromechanical-system fabrication techniques are studied through computational fluid dynamics simulations for nonturbulent, nonrarefied flow conditions. Depending on the specific nature of the surface roughness, the formation and reflection of several weak shocks and, as a consequence, a decreased performance are observed.

A stereo vision method for tracking particle flow on the weld pool surface

The oscillation of a weld pool surface makes the fluid flow motion quite complex. Two-dimensional results cannot reflect enough information to quantitatively describe the fluid flow in the weld pool; however, there are few direct three-dimensional results available. In this paper, we describe a three-dimensional reconstruction method to measure weld pool surface features based on a single high-speed camera. A stereo adapter was added in front of the high-speed camera lens to obtain two images in the same frame from different view points at the same time. According to machine vision theory, three-dimensional parameters can be reconstructed based on two such images. In this work, three-dimensional velocity fields have been obtained using this method. Based on the calibration technique employed, the associated error is estimated to be less than 11.4%. Quantitative experimental results are useful for understanding the flow pattern, and possibly for controlling the flow of liquid in the weld pool.

Numerical insights into magnetic dynamo action in a turbulent regime

We report on hybrid numerical simulations of a turbulent magnetic dynamo. The simulated set-up mimics the Riga dynamo experiment characterized by Re ≈ 3.5 × 106 and (Gailitis et al 2000 Phys. Rev. Lett. 84 4365–8). The simulations were performed by a simultaneous fully coupled solution of the transient Reynolds-averaged Navier–Stokes (T-RANS) equations for the fluid velocity and turbulence field, and the direct numerical solution (DNS) of the magnetic induction equations. This fully integrated hybrid T-RANS/DNS approach, applied in the finite-volume numerical framework with a multi-block-structured nonorthogonal geometry-fitted computational mesh, reproduced the mechanism of self-generation of a magnetic field in close accordance with the experimental records. In addition to the numerical confirmation of the Riga findings, the numerical simulations provided detailed insights into the temporal and spatial dynamics of flow, turbulence and electromagnetic fields and their reorganization due to mutual interactions, revealing the full four-dimensional picture of a dynamo action in the turbulent regime under realistic working conditions.