Reynolds and Mach number effects in compressible turbulent channel flow

Modesti, Davide; Pirozzoli, Sergio

doi:10.1016/j.ijheatfluidflow.2016.01.007

Cited by 155 publications

(186 citation statements)

References 40 publications

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“…As shown in previous works [11,12,15,16,23,24,30], the semilocal wall coordinate y is effective in accommodating changes in viscous scales due to variable properties, thus providing a meaningful representation for the turbulent velocity statistics. Therefore, all wall-normal profiles are plotted as a function of y in the present work.…”

Section: Scalar Statisticsmentioning

confidence: 85%

“…In all such cases, the effects of thermophysical property variations can be strong enough to modulate turbulence and the traditional approach of treating temperature as a passive scalar no longer holds. Although turbulence modulation in a turbulent channel flow due to variable thermophysical properties has been investigated in great detail in high-Mach-number flows [9][10][11][12] and in low-Mach-number flows [13][14][15][16], the effect of property variations on scalar transport is not well understood. Lee et al [17] studied the influence of wall heating on turbulent thermal boundary layers with variable viscosity and observed variations in mean scalar, scalar fluctuation, and scalar flux, relative to a reference isothermal flow.…”

Section: Introductionmentioning

confidence: 99%

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Scalar statistics in variable property turbulent channel flows

2017

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Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ, viscosity μ, and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Re τ ≡ Re τ √ (ρ/ρ w )/(μ/μ w ) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Re τ is the friction Reynolds number based on wall values), and the local Prandtl number Pr = Pr w (μ/μ w )/(λ/λ w ) (Pr w is the molecular Prandtl number based on wall values). Near-wall gradients in Re τ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Re τ variations and only exhibits a Pr -dependent shift.

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Section: Scalar Statisticsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Scalar statistics in variable property turbulent channel flows

2017

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“…Recent channel flow DNS [22] and boundary layer experiments [42] have indeed shown that genuine compressibility effects on the typical flow scales are small, if any, and may be conveniently accounted for through variable-property extension of incompressible scaling formulas. Another subject of great interest in compressible flows is the transport of passive scalars, an essential building block in the understanding of mixing processes and combustion.…”

Section: Introductionmentioning

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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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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“…For example, the density or viscosity significantly changes in flows of supersonic aircraft, rocket propulsion systems, heat exchangers, chemically reacting flows, or the flow in the Sun's convection zone. In general, strong thermophysical property variations alter the conventional behaviour of turbulence and cause scaling laws of constant property flows to fail (Bradshaw 1977;Lele 1994;Coleman et al 1995;Duan et al 2010;Lee et al 2013;Modesti & Pirozzoli 2016). From past studies it is known that differences between adiabatic supersonic boundary layers and incompressible isothermal flows can be corrected by simply accounting for mean density variations -an example is the van Driest velocity transformation -as long as the turbulent Mach number remains small, M ′ < 0.3 (Smits & Dussauge 2006).…”

Section: Introductionmentioning

confidence: 99%

“…This is known as Morkovin's hypothesis (Morkovin 1962). However, for flows with strong wall heat transfer, the van Driest velocity transformation fails to provide a reasonable collapse (Duan et al 2010;Modesti & Pirozzoli 2016). Recently, Trettel & Larsson (2016) and Patel et al (2016) have proposed a transformation that provides a collapse for supersonic channel flows with isothermal walls, and low-Mach-number volumetrically heated channel flows.…”

Section: Introductionmentioning

confidence: 99%

Scaling and modelling of turbulence in variable property channel flows

Pečnik

Patel

2017

J. Fluid Mech.

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We derive an alternative formulation of the turbulent kinetic energy equation for flows with strong near-wall density and viscosity gradients. The derivation is based on a scaling transformation of the Navier-Stokes equations using semi-local quantities. A budget analysis of the semi-locally scaled turbulent kinetic energy equation shows that for several variable property low-Mach-number channel flows, the 'leading-order effect' of variable density and viscosity on turbulence in wall bounded flows can effectively be characterized by the semi-local Reynolds number. Moreover, if a turbulence model is solved in its semi-locally scaled form, we show that an excellent agreement with direct numerical simulations is obtained for both low-and high-Mach-number flows, where conventional modelling approaches fail.

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Reynolds and Mach number effects in compressible turbulent channel flow

Cited by 155 publications

References 40 publications

Scalar statistics in variable property turbulent channel flows

Scalar statistics in variable property turbulent channel flows

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

Scaling and modelling of turbulence in variable property channel flows

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