K. Hanjalić

Modeling Rotating and Swirling Turbulent Flows: A Perpetual Challenge

Severaltypesofrotatingandswirlinge owsfora rangeofReynoldsnumbersandrotationratesorswirlintensities have been studied computationally, aimed at identifying specie c features that require special consideration in turbulence modeling. The e ows considered include turbulent channel e ows subjected to streamwise and spanwise rotation,withstationaryandmovingboundaries;developingandfullydevelopede owsinaxiallyrotatingpipes;and swirling e owsin combustorgeometriesand long pipes.Computationsperformed with threeversionsof thesecondmoment closure and two eddy-viscosity models show that the second-moment models are superior, especially when the equations are integrated up to the wall. Such models reproduced the main e ow parameters for all e ows considered in acceptable agreement with the available experimental data and direct numerical simulations. However,challengesstillremaininpredictingaccuratelysomespecie ce owfeatures,suchascapturingthetransition from a freevortex to solid-body rotation in a long straight pipewith a weak swirl, or reproducing the normal stress components in the core region. Also, the so-called uw anomaly in fully developed e ows with streamwise rotation remains questionable. For rotating e ows, the low-Reynolds-number models yield a somewhat premature e ow relaminarization at high rotation speeds.

Vortex structure and heat transfer in turbulent flow over a wall-mounted matrix of cubes

Abstract The paper reports on the turbulent flow structure and the distribution of the local surface heat transfer coefficient of a cube placed in a spatially periodic in-line matrix of cubes mounted on one of the walls of a plane channel. Infrared thermography was applied to measure the surface temperature at the cube walls, from which the distribution of the local heat transfer coefficient was determined. The velocity field and its structure were evaluated from Laser Doppler Anemometry (LDA) measurements and flow visualizations. The spatial periodicity was confirmed from flow field and heat transfer measurements across the entire matrix. The results showed that the flow has a marked vortex structure only in the immediate proximity of the cube, while the flow above the cube and in the streamwise corridors was only mildly distorted, except for a high level of turbulence intensity. Flow separation at the sharp leading top and side edges led to flow recirculations with subsequent flow reattachment at these faces. Reattachment of the top shear layer at the channel floor downstream of the cube produced a two-cell structure in the inter-obstacle space: an arc-type vortex in the wake of the upstream cube and a horseshoe-type vortex in front of the downstream cube. Flow instabilities caused vortex shedding at the side faces of the cube which led to periodic motions in its wake. The measured Strouhal number showed a constant value of St=0.109 over the range of Reynolds numbers considered. The observed local flow structure, in particular flow separation and reattachment, caused marked variation in the distribution of the local heat transfer coefficient, with large gradients detected particularly at the top and side faces of the cube.

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.

Local Convective Heat Transfer from an Array of Wall-Mounted Cubes

Abstract The paper presents some results of the experimental investigation of the local convective heat transfer from a wall-mounted single array of cubical protrusions along a wall of a wind tunnel. The local convective heat transfer was determined from the surface temperature distribution of the internally heated cubical elements, measured with infrared and liquid crystal thermography, and from the local surface heat flux. In addition, smoke and surface oil-film visualizations were performed to characterize the macroscopic flow-field which provided a basis for a qualitative interpretation of the heat transfer coefficient distributions. The results showed a high non-uniformity of the local convective heat transfer over the surfaces of the individual elements.

Turbulent heat transfer from a multi-layered wall-mounted cube matrix: a large eddy simulation

Abstract The dynamics of flow and heat transfer on internally heated multi-layered matrix of cubes mounted on one of the walls of a plane channel is investigated by numerical simulation using a finite-volume unstructured solver. The fluid flow and convective heat transfer were solved by large eddy simulation (LES). The temperature field in the cube mantle and on its outer surface – providing the boundary conditions for the convection – was obtained by solving the conduction equation simultaneously with the velocity field. The simulations were performed on the parallel CrayT3E computer at TU Delft using about 425.000 cells clustered around the cube surface and the base wall. The standard Smagorinsky subgrid-scale model was used for LES, with Spalarts adjustment of the filter width in the near-wall region. Comparisons with experiments and with LES on structured orthogonal meshes reported in the literature show good agreement. The temperature distribution on the cube surface was found to be very nonuniform reflecting complex vortex and turbulence structure around the cube. Numerical flow visualisation and animation are used to provide a better insight into the flow pattern and vortex structure and their relation with the local heat transfer and temperature distribution. The configuration considered is relevant to cooling of electronic components on circuit boards or cooling of gas-turbine blades through internal passages equipped with ribs or pins.

Computational study of turbulent natural convection in a side-heated near-cubic enclosure at a high Rayleigh number

Abstract A computational study of turbulent natural convection in a side-heated near-cubic enclosure at a high Rayleigh number (Ra=4.9×1010) is performed, aimed at gaining a better insight into the flow pattern, particularly in the corner regions. Two types of thermal boundary conditions are applied at the horizontal walls: adiabatic and isothermal. Also, two kinds of lateral vertical walls are studied, corresponding to different experimental approximations of adiabatic conditions: the first by insulation and the second by imposing a stratified wall heating. The latter conditions ensure better flow two-dimensionality, with the temperature stratification on the vertical walls close to that expected in the parallel mid-plane. Computations are performed with both a two-dimensional (2D) and three-dimensional (3D) code using a low-Reynolds-number differential second-moment stress/flux closure and the related k–e model (KEM) simplification. The numerical computations show that the second-moment closure (SMC) is better in capturing thermal three-dimensionality effects and strong streamline curvature in the corners. The KEM, however, still provides reasonable predictions of the first moments away from the corners.

Experimental study of the convective heat transfer from in-line and staggered configurations of two wall-mounted cubes

Abstract The paper reports on the experimental investigation of the effects of the relative obstacle position on the convective heat transfer from a configuration of two wall-mounted cubes located in a fully developed turbulent channel flow. Both in-line and staggered arrangements were studied for various streamwise (Sx/H) and spanwise (Sz/H) distances. Distributions of the local heat transfer coefficient (h) were obtained from infrared thermography and local convective heat flux analyses. Laser Doppler anemometry measurements and flow visualisations were performed to document the flow and turbulence fields around the cubes. The results showed a large variation in the distribution of the local convective heat transfer for the various in-line and staggered configurations studied. While the in-line arrangements were featured by symmetric flow pattern and heat transfer distributions, the staggered arrangements showed distinct asymmetric pattern for certain combinations of Sx/H and Sz/H. Flow reattachment caused typically a monotonic decay of the convective heat transfer. On the other hand, flow separation caused distinct heat transfer extrema at the cube faces. In addition, the effect of vortex shedding on the convective heat transfer of the downstream cube was studied with a fast-responding heat flux sensor. Despite distinct variation in the distribution of the time-averaged heat transfer coefficient, the cube-averaged heat transfer coefficients appeared to be independent of the relative placement of the two cubes.

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 .

Large-eddy simulation and deduced scaling analysis of Rayleigh-Benard convection up to Ra=10^9

Large-eddy simulation of turbulent Rayleigh–Bénard (RB) convection has been performed for a 6:1:6 open-ended domain for Rayleigh numbers ranging from 6.3 × 105 to 109 at Prandtl number of Pr = 0.71. The scaling analysis based on the LES data shows that the heat transfer follows a single relation of Nu = 0.162 Ra 0.286, which is consistent with the scaling law for the hard turbulence regime reported in several earlier experimental and DNS studies. The present LES also supports some earlier experimental and DNS findings that most of characteristic parameters can be scaled reasonably well with Ra number in the considered Ra number range using a single relation. Nonetheless, it is found that the scaling of several quantities shows a sensible offset from a single relation, and could be fitted better with the separate scaling relations for the soft and hard convective turbulence transitioned at about Ra = 4 × 107. It has been argued that the transition, reflected in the scaling relation, may be attributed to the increasing ‘containing effect’ of the plume leaving the horizontal wall on the plume approaching the wall at large Ra numbers in the near-wall region. **This paper is a modified version from the paper presented at the Forth International Symposium of Turbulence and Shear Flow Phenomena (Williamsburg, Virginia, 27–29 June 2005).

A-PRIORI STUDIES OF A NEAR-WALL RANS MODEL WITHIN A HYBRID LES/RANS SCHEME

ABSTRACT Achieving an acceptably accurate representation of the near-wall layer in LES for high-Re flows that are sensitive to viscous near-wall processes is one of the major challenges facing LES. Based on the premise that this can be addressed, in principle, by coupling a RANS near-wall model to the LES domain, the behaviour of a one-equation, turbulence-energy-transport model is examined in fully-developed channel flow. Initially, the response of the model is considered when this is subjected to the LES solution at a prescribed distance from the wall (y+=65). Coupling criteria are then discussed, given the desirability of freedom of choice of the subgrid-scale model in the LES domain and in locating the interface. Initial efforts towards a fully-coupled hybrid solution are also presented.