Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units

There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ=400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J. Fluid Mech.). Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows.

Direct numerical simulation of turbulent flows over superhydrophobic surfaces with gas pockets using linearized boundary conditions

Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions.

Comparison of Micro-Vortex generators in supersonic flows

An experimental comparison of several vortex generator geometries was conducted at Mach 1.5, 1.8, and 2.5 to better understand downstream vortex development as a function of device shape and Mach number. The devices had heights less than that of the boundary-layer ("micro"-vortex generators) and were either vane-shaped or of the alternative microramp geometry. LDV was used to measure two components of velocity at several stations downstream of the devices. The velocity data were then fitted to a vortex model so that vortex parameters such as circulation, core radius, and trajectory were estimated. Mach number dependence was seen for all parameters. Vortex height and core radius both tended to decrease slightly with increasing Mach number. A critical vane angle for maximum circulation was observed and also decreased with increasing Mach number. Circulation was seen to scale with wall-friction velocity for Mach 1.5 and 1.8 but not 2.5. © 2012 by W.R. Nolan and H. Babinsky.

Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Kelvin-Helmholtz-like instability of turbulent flows over riblets

The turbulent drag reduction due to riblets is a function of their size and, for different configurations, collapses well with a length scale l+g=(A+g)1/2, based in the groove cross-section Ag. The initially linear drag reduction breaks down for l+g≈11, which agrees in our DNS with the previously reported appearance of quasi-two-dimensional spanwise rollers immediately above the riblets. They are similar to those found over porous surfaces and plant canopies, and can be traced to a Kelvin-Helmholtz-like instability associated with the relaxation of the impermeability condition for the wall-normal velocity. The extra Reynolds stress associated with them accounts quantitatively for the drag degradation. An inviscid model for the instability confirms its nature, agreeing well with the observed perturbation wavelengths and shapes. The onset of the instability is determined by a length scale L+w that, for conventional riblet geometries, is proportional to l+g. The instability onset, L+w≥4, corresponds to the empirical breakdown point l+g≈11.

Canonical normal shock wave/boundary-layer interaction flows relevant to external compression inlets

The normal shock wave/boundary-layer interaction is important to the operation and performance of a supersonic inlet, and the normal shock wave/boundary-layer interaction is particularly prominent in external compression inlets. To improve understanding of such interactions, it is helpful to make use of fundamental flows that capture the main elements of inlets, without resorting to the level of complexity and system integration associated with full-geometry inlets. In this paper, several fundamental flowfield configurations have been considered as possible test cases to represent the normal shock wave/boundary-layer interaction aspects found in typical external compression inlets, and it was found that the spillage diffuser more closely retains the basic flow features of an external compression inlet than the other configurations. In particular, this flowfield allows the normal shock Mach number as well as the amount and rate of subsonic diffusion to all be held approximately constant and independent of the application of flow control. In addition, a survey of several external compression inlets was conducted to quantify the flow and geometric parameters of the spillage diffuser relevant to actual inlets. The results indicated that such a flow may be especially relevant if the terminal Mach number is about 1.3 to 1.4, the confinement parameter is around 10%, and the width is around twice or three times the height. In addition, the area expansion downstream of the shock should be limited to the conservative side of incipient stall based on incompressible diffusers. Copyright © 2013 by the authors.

Models for acoustic propagation through turbofan exhaust flows

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of previous solutions is that they do not allow for the jet nozzle to protrude a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). In this paper we use the matrix Wiener-Hopf technique, which will allow precisely the finite nacelle-jet nozzle separation to be included. The crucial step in our work is to factorise a certain matrix as a product of terms analytic and invertible in the upper/lower halves of the complex plane. The way we do this matrix factorisation is quite different in the buried and protruding nozzle cases. In the buried case our solution method is the so-called pole-removal technique. In the technically more demanding protruding case, however, we must first use Pade approximants to generate a uniformly-valid, meromorphic representation of a certain function, before the same pole-removal method can be applied. Sample results are presented, investigating in particular the effects of exit plane stagger. © 2007 by B Veitch and N Peake.

High-order detached eddy simulation, zonal LES and URANS of cavity and labyrinth seal flows

Hybrid numerical large eddy simulation (NLES), detached eddy simulation (DES) and URANS methods are assessed on a cavity and a labyrinth seal geometry. A high sixth-order discretization scheme is used and is validated using the test case of a two-dimensional vortex. The hybrid approach adopts a new blending function. For the URANS simulations, the flow within the cavity remains steady, and the results show significant variation between models. Surprisingly, low levels of resolved turbulence are observed in the cavity for the DES simulation, and the cavity shear layer remains two dimensional. The hybrid RANS-NLES approach does not suffer from this trait.For the labyrinth seal, both the URANS and DES approaches give low levels of resolved turbulence. The zonal Hamilton-Jacobi approach on the other had given significantly more resolved content. Both DES and hybrid RANS-NLES give good agreement with the experimentally measured velocity profiles. Again, there is significant variation between the URANS models, and swirl velocities are overpredicted. © 2013 John Wiley & Sons, Ltd.

Construction of habitat suitability models (HSMs) for benthic macroinvertebrate and their applications to instream environmental flows: A case study in Xiangxi River of Three Gorges Reservior region, China

Based on a long-term ecological monitoring, the present study chose the most dominant benthic macroinvertebrate (Baetis spp.) as target organisms in Xiangxi River, built the habitat suitability models (HSMs) for water depth, current velocity and substrate, respectively, which is the first aquatic organisms model for habitat suitability in the Chinese Mainland with a long-term consecutive in situ measurement. In order to protect the biointegrity and function of the river ecosystem, the theory system of instream environmental flow should be categorized into three hierarchies, namely minimum required instream flow (hydrological level), minimum instream environmental flow (biospecies level), and optimum instream environmental flow (ecosystem level). These three hierarchies of instream environmental flow models were then constructed with the hydrological and weighted usable area (WUA) method. The results show that the minimum required instream flow of Xiangxi River calculated by the Tennant method (10% of the mean annual flow) was 0.615 m(3) s(-1); the minimum instream environmental flow accounted for 19.22% of the mean annual flow (namely 1.182 m(3) s(-1)), which was the damaged river channel. ow in the dry season; and 42.91% of the mean annual flow (namely 2.639 m(3) s(-1)) should be viewed as the optimum instream environmental flow in order to protect the health of the river ecosystem, maintain the instream biodiversity, and reduce the impact of small hydropower stations nearby the Xiangxi River. We recommend that the hydrological and biological methods can help establish better instream environmental. ow models and design best management practices for use in the small hydropower station project. (C) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.