A generalized Reynolds analogy for compressible wall-bounded turbulent flows

Zhang, You Sheng; Bi, Wei Tao; Hussain, Fazle; She, Zhen‐Su

doi:10.1017/jfm.2013.620

Cited by 137 publications

(226 citation statements)

References 33 publications

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“…The core part of the pipe is found to have a relatively simple structure, whereby the van Driest transformed velocity follows a universal parabolic law in a wide region, and it is controlled by a single universal constant, here found to be identical to that of incompressible pipe flow. As in other compressible wall-bounded flows, the mean temperature distribution is found to quadratically depend on the mean streamwise velocity, and we find that the generalized Reynolds analogy of Zhang et al [46] yields very good prediction of its variation. Together with TL transformation, use of the temperature/velocity relation yields a closed system of equations, which in prin-ciple lends itself to closed formulas for the prediction of the friction and heat transfer coefficients, which might be the subject of further investigations.…”

Section: Discussionsupporting

confidence: 76%

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Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

Modesti

Pirozzoli

2019

International Journal of Heat and Fluid Flow

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We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson [38] yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Re τ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. [46]. The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear.

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Section: Discussionsupporting

confidence: 76%

“…The classical temperature/velocity relation by Walz [41] has proven its accuracy in the case of adiabatic walls [8], but it is found to fail in the case of isothermal walls [22]. Recently, Zhang et al [46] derived the following generalized temperature/velocity relation,…”

Section: Temperature/velocity Relationshipmentioning

confidence: 99%

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

Modesti

Pirozzoli

2019

International Journal of Heat and Fluid Flow

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“…This conclusion is not surprising, since even the most advanced and refined forms of the Reynolds analogy [40] are all based on the chief assumption/approximation of a quasi-one-dimensional flow, which clearly fails in the presence of mean flow separation as in the present SBLI cases.…”

Section: Wall Properties In Adiabatic and Non-adiabatic Sblimentioning

confidence: 67%

Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions

Bernardini¹,

Asproulias²,

Larsson³

et al. 2016

Phys. Rev. Fluids

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Direct numerical simulations are carried out to investigate the effect of the wall temperature on the behavior of oblique shock-wave/turbulent boundary layer interactions at freestream Mach number 2.28 and shock angle of the wedge generator ϕ = 8• . Five values of the wall-to-recovery-temperature ratio (Tw/Tr) are considered, corresponding to cold, adiabatic and hot wall thermal conditions. We show that the main effect of cooling is to decrease the characteristic scales of the interaction in terms of upstream influence and extent of the separation bubble. The opposite behavior is observed in the case of heating, that produces a marked dilatation of the interaction region. The distribution of the Stanton number shows that a strong amplification of the heat transfer occurs across the interaction, and the maximum values of thermal and dynamic loads are found in the case of cold wall. The analysis reveals that the fluctuating heat flux exhibits a strong intermittent behavior, characterized by scattered spots with extremely high values compared to the mean. Furthermore, the analogy between momentum and heat transfer, typical of compressible, wall-bounded, equilibrium turbulent flows does not apply for most part of the interaction domain. The pre-multiplied spectra of the wall heat flux do not show any evidence of the influence of the low-frequency shock motion, and the primary mechanism for the generation of peak heating is found to be linked with the turbulence amplification in the interaction region. * matteo.bernardini@uniroma1.it arXiv:1606.04305v1 [physics.flu-dyn]

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“…Also, the original SRA seems to fail linking velocity and temperature fluctuations, and the modified SRA relations, better accounting for the isothermal condition, are preferred [14,15,28,18]. In their recent work, Zhang et al [29] introduced a generalized Reynolds analogy for compressible wall bounded flows. In terms of flow organization, near-wall streaks were found to be more coherent when decreasing the wall temperature [17,25] and the Morkovin's hypothesis gives good agreement for predicting those structures [26,20].…”

Section: Introductionmentioning

confidence: 99%