15 research outputs found

    A priori tests of eddy viscosity models in square duct flow

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    We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number Re τ= 1055. We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components aij responsible for turbulent secondary flows, namely the normal stress a22 and the secondary shear stress a23. A priori tests on constitutive relations for aij are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of aij. We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data C~ ij, which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress a12 (C~ 12> 0.99), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress (C~ 22= 0.911 , C~ 23= 0.743). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k–ε and v2–f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the v2–f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.Aerodynamic

    Direct numerical simulation of one-sided forced thermal convection in plane channels

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    We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to are considered, and Prandtl numbers from to, the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be. Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately at unit Prandtl number; however, it can become much more significant at low Prandtl number. Aerodynamic

    Direct numerical simulation of forced thermal convection in square ducts up to

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    We carry out direct numerical simulations (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case of unit Prandtl number. Reynolds numbers up to are considered that are much higher than in previous studies, and that yield clear scale separation between inner- and outer-layer dynamics. Close similarity between the behaviour of the temperature and the streamwise velocity fields is confirmed as in previous studies related to plane channels and pipes. Just like the mean velocity, the mean temperature is found to exhibit logarithmic layers as a function of the nearest wall, but with a different slope. The most important practical implication is the validity of the traditional hydraulic diameter as the correct reference length for reporting heat transfer data, as we show rigorously here. Temperature and velocity fluctuations also have similar behaviour, but apparently logarithmic growth of their inner-scaled peak variances is not observed here, unlike in canonical wall-bounded flows. Analysis of the split contributions to the heat transfer coefficient shows that mean cross-stream convection associated with secondary motions is responsible for about of the total. Finally, we use the DNS database to highlight shortcomings of traditional linear closures for the turbulent heat flux, and show that substantial modelling improvement in principle may be obtained by retaining at least the three terms in the vector polynomial integrity basis expansion. Aerodynamic

    Direct numerical simulation of forced thermal convection in square ducts

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    We carry out direct numerical simulation (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case of unit Prandtl number. Reynolds numbers up to Reτ ≈ 2000 are considered which are much higher than in previous studies, and which yield clear scale separation between inner- and outer-layer dynamics. Close similarity between the behavior of the temperature and the streamwise velocity fields is confirmed as in previous studies related to plane channels and pipes. We find good agreement between the Nusselt number of square duct and circular pipe flow when the Reynolds number based on the hydraulic diameter is used, thus corroborating the common engineering practice. Popular engineering correlations for the heat transfer reveal deviations up to 5% with respect to DNS data, which are nicely fitted by a power law.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Aerodynamic

    Permeability and Turbulence Over Perforated Plates

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    We perform direct numerical simulations of turbulent flow at friction Reynolds number Reτ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter d+≈ 40 - 160 and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.In this article the author name Stefan Hickel was incorrectly written as Hickel Stefan. The original article has been corrected.Aerodynamic

    Direct Numerical Simulation of a Turbulent Boundary Layer over Acoustic Liners

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    The nacelle of aircraft engines is coated with acoustic liners to reduce engine noise. An undesirable effect of these liners is that they increase aerodynamic drag. We study this drag penalty by performing Direct Numerical Simulations of a turbulent boundary layer over an acoustic liner array at friction Reynolds number, Re τ ≈ 850–2500. We use this simulation to confirm several findings that we recently brought forward using a simpler channel flow setup. We show that acoustic liners lead to high wall-normal velocity fluctuations that can be directly correlated with a modulation of the classical near-wall cycle and to an increase in drag. We also confirm that the acoustic liners act as permeable surface roughness and the non-linear Forchheimer coefficient is the relevant permeability parameter for scaling the drag increase.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Aerodynamic

    Acoustic liners and their induced drag

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    In order to reduce the noise emitted by aircraft engines, the nacelle is coated with acoustic liners. An undesirable effect of these surfaces is that they increase the aerodynamic drag. In the present work, we characterize this type of surface roughness by performing Direct Numerical Simulations of fully resolved acoustic liner geometries. We find evidence of a fully rough regime, whose onset is determined by the value of the viscous-scaled Forchheimer coefficient. Moreover, the intensity of the wall-normal velocity fluctuations at the wall also scales with the viscous-scaled wall-normal permeability, leading to a relation between fluctuations and added drag.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Aerodynamic

    Direct numerical simulation of flow in open rectangular ducts

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    We study turbulent flow in open channels with a free surface and rectangular cross-section, for various Reynolds numbers and duct aspect ratios. Direct numerical simulations are used to obtain accurate characterization of the secondary motions, which are found to be more intense than in closed ducts, and to scale with the bulk, rather than with the friction velocity. A notable feature of open-duct flows is the presence of a velocity dip, namely the peak velocity is achieved at some depth underneath the free surface. We find that the depth of the velocity peak increases with the Reynolds number, and correspondingly the flow becomes more symmetric with respect to the horizontal midplane. This is also confirmed from the change of the topology of the secondary motions, which exhibit a strong corner circulation at the free-surface/wall corners at low Reynolds number, which, however, weakens at higher. The structure of the mean velocity field is such that the log law applies with good approximation in the direction normal to the nearest wall, which allows us to explain why predictive friction formulae based on the hydraulic diameter concept are successful. Additional analysis shows that the secondary motions account for a large fraction of the frictional drag (up to %).Aerodynamic

    Dispersive stresses in turbulent flow over riblets

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    We carry out direct numerical simulations of turbulent flow over riblets, streamwise- aligned grooves that are designed to reduce drag by modifying the near-wall flow. Twenty riblet geometries and sizes are considered, namely symmetric triangular with tip angle, and, asymmetric triangular, blade and trapezoidal. To save on computational cost, simulations are performed using the minimal-channel flow configuration. With this unprecedented breadth of high-fidelity flow data near the wall, we are able to obtain more general insights into the flow physics of riblets. As observed by García-Mayoral & Jiménez (J. Fluid Mech., vol. 678, 2011, pp. 317-347), we confirm that the drag-change curves of all the present groove geometries better collapse when reported with the viscous-scaled square root of the groove area, rather than the riblet spacing. Using a two-dimensional generalization of the Fukagata-Iwamoto-Kasagi identity in difference form we isolate the different drag-change contributions. We show that the drag increase associated with dispersive stresses carried by secondary flows can be as important as the one associated with the turbulent stresses and the pre-eminence of dispersive stresses can be estimated by the groove width at the riblet mean height.Aerodynamic

    Direct numerical simulation of supersonic turbulent flows over rough surfaces

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    We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers -, both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature-velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating. Aerodynamic
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