Equilibrium and non-equilibrium turbulent boundary layers

Devenport, William J.; Lowe, K. Todd

doi:10.1016/j.paerosci.2022.100807

Cited by 45 publications

(19 citation statements)

References 179 publications

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“…The excessive energy generated at the trip height seemingly affects the outer flow region more significantly than the inner near-wall region. This is in line with the prevalent observation that the outer region requires a longer evolution distance than the inner one to reach a full equilibrium state (Devenport & Lowe 2022).…”

Section: Development Of Tripped Boundary Layer Towards An Equilibrium...supporting

confidence: 90%

“…These large scales also do not show clearly discernible 'footprints' on the near-wall region. The characteristics as observed may, to some extent, explain why the near-wall region is usually observed to experience a shorter development distance than the outer flow region before reaching an equilibrium state (Devenport & Lowe 2022).…”

Section: Evolution and Impact Of Large-scale Disturbances Of Trippingmentioning

confidence: 68%

“…These large scales also do not show clearly discernible ‘footprints’ on the near-wall region. The characteristics as observed may, to some extent, explain why the near-wall region is usually observed to experience a shorter development distance than the outer flow region before reaching an equilibrium state (Devenport & Lowe 2022). The related physical understanding also provides a useful basis for implementing the two-scale method for a tripped turbulent boundary layer, more particularly for sizing a locally embedded fine-mesh block for resolving the trip itself in relation to other fine-mesh blocks embedded in the near-wall region for the rest of the boundary layer.…”

Section: Physical Tripping For Scale-resolving Turbulent Boundary Lay...mentioning

confidence: 78%

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Two-scale solution for tripped turbulent boundary layer

Chen

2023

J. Fluid Mech.

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Recent findings on the Reynolds-number-dependent behaviour of near-wall turbulence in terms of the ‘foot-printing’ of outer large-scale structures call for a new modelling development. A two-scale framework was proposed to couple a local fine-mesh solution with a global coarse-mesh solution by He (Intl J. Numer. Meth. Fluids, vol. 86, 2018, pp. 655–677). The methodology was implemented and demonstrated by Chen & He (J. Fluid Mech, vol. 933, 2022, p. A47) for a canonical turbulent channel flow, where the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for a conventional wall-resolved large-eddy simulation (WRLES) to $O(R{e^1})$ . The present work extends the two-scale method to turbulent boundary layers. A two-dimensional roughness element is used to trip a turbulent boundary layer. It is observed that large-scale disturbances originating at the trip have a much shorter lifetime and weaker foot-printing signatures on near-wall flow compared to those long streaky coherent structures in well-developed wall-bounded turbulent flows. Modal analyses show that the impact of trip-induced large scales can be adequately captured by a locally embedded fine-mesh block. For the tripped turbulent boundary layer, a Chebyshev block-spectral mapping is adopted to propagate source terms from the local fine-mesh blocks to the global coarse-mesh domain, driving to a target solution for the upscaled equations. The computed mean statistics and energy spectra are in good agreement with corresponding experimental data, WRLES and direct numerical simulation (DNS) results. The overall mesh count– $Re$ scaling is estimated to reduce from $O(R{e^{1.8}})$ for the full wall-resolved LES to $O(R{e^{0.9}})$ for the present two-scale solution.

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Section: Development Of Tripped Boundary Layer Towards An Equilibrium...supporting

confidence: 90%

Section: Evolution and Impact Of Large-scale Disturbances Of Trippingmentioning

confidence: 68%

Section: Physical Tripping For Scale-resolving Turbulent Boundary Lay...mentioning

confidence: 78%

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Two-scale solution for tripped turbulent boundary layer

Chen

2023

J. Fluid Mech.

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“…The profile for u + turns below the log law in the case of a concave wall and above in the case of a convex wall (see Kim and Rhode 2000). In three-dimensional turbulent boundary layer flows, a streamwise and a spanwise component of the mean velocity arise (defined in a local coordinate system with the x-axis aligned with the freestream or with the wall shear stress vector), and a spanwise pressure gradient results in flow skewing (see Devenport and Lowe 2022). A wall law for the mean-velocity component aligned with the wall shear stress and the transverse component perpendicular to it is described in van den Berg (1973), van den Berg (1975), which accounts for streamwise and spanwise pressure gradients.…”

Section: Introductionmentioning

confidence: 99%

An Empirical Wall Law for the Mean Velocity in an Adverse Pressure Gradient for RANS Turbulence Modelling

Knopp

2022

Flow Turbulence Combust

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An empirical wall law for the mean velocity in an adverse pressure gradient is presented, with the ultimate goal of aiming at the improvement of RANS turbulence models and wall functions. For this purpose a large database of turbulent boundary-layer flows in adverse pressure gradients from wind tunnel experiments is considered, and the mean velocity in the inner layer is analysed. The log law in the mean velocity is found to be a robust feature. The extent of the log-law region is reduced in ratio to the boundary layer thickness with increasing strength of the pressure gradient. An extended wall law emerges above the log law, extending up to the outer edge of the inner layer. An empirical correlation to describe the reduction of the log-law region is proposed, depending on the pressure-gradient parameter and on the Reynolds number in inner viscous scaling, whose functional form is motivated by similarity and scaling arguments. Finally, there is a discussion of the conjecture of the existence of a wall law for the mean velocity, which is governed mainly by local parameters and whose leading order effects are the pressure gradient and the Reynolds number, but whose details can be perturbed by higher-order local and history effects.

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“…Equilibrium two-dimensional boundary layers typically have a region near the wall where the total shear stress is nearly constant, approximately 0.95 ≤ τ total /τ w ≤ 1 for sufficiently high Reynolds numbers. Devenport and Lowe (2022) demonstrate the derivation of 2D zero-pressure gradient boundary layer equations that produce this behavior, showing that as the viscous shear stress decreases rapidly outside the viscous sublayer, the turbulent shear stress increases to balance out the total shear stress. In non-zero pressure gradient flows, a linear gradient of the total shear stress will be present instead.…”

Section: Introductionmentioning

confidence: 84%

Structural aspects of the attached turbulent boundary layer flow over a hill

et al. 2023

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Three-dimensional turbulent boundary layers under strong pressure gradients and curvature are the rule in real-world flow applications but are typically not well predicted by turbulence models due to isotropic eddy viscosity or equilibrium assumptions. Validation-quality data in complex 3D flows is necessary for continued efforts to improve simulation accuracy. The BeVERLI (Benchmark Validation Experiments for RANS/LES Investigations) Hill bump model, designed specifically for validation experiments, was tested in the Virginia Tech Stability Wind Tunnel to collect validation experiment data on the three-dimensional (3D) boundary layer flow over a 3D hill. Laser Doppler velocimetry measurements on the bump model were used to study the mean flow and turbulence structure and evaluate the impact of pressure gradient and curvature upon the total shear stress in the boundary layer and evaluate the impact of pressure gradient and curvature upon the total shear stress behavior in the near-wall region. From analysis of the BeVERLI Hill flow, including the boundary layer just upstream of the hill, and comparison with the 3D flow around a wing-body junction of Ölçmen et al (2001), it is shown that none of the stations studied exhibit a constant shear stress region over any significant region of the boundary layer. One station on the hill, located in a region Structural Aspects of the Attached Turbulent Boundary Layer Flow Over a Hill with strong spanwise and streamwise pressure gradients, experiences an apparent return to an equilibrium shear stress for x + 2 < 30 due to significantly increased production of u ′ 1 u ′ 2 and u ′2 2 at this station.

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Equilibrium and non-equilibrium turbulent boundary layers

Cited by 45 publications

References 179 publications

Two-scale solution for tripped turbulent boundary layer

Two-scale solution for tripped turbulent boundary layer

An Empirical Wall Law for the Mean Velocity in an Adverse Pressure Gradient for RANS Turbulence Modelling

Structural aspects of the attached turbulent boundary layer flow over a hill

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