Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

Abstract

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter &Örlü, J. Fluid Mech., vol. 659, 2010, pp. 116-126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatter et al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness) Re θ < 300, all quantities agree well for both inner and outer layer for Re θ > 2000. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over-or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher Re θ irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

Wall shear stress fluctuations: Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer

“…Incompact3D uses 6th order finite difference schemes to discretise the incompressible Navier Stokes equations on a Cartesian mesh, with a pseudo-spectral Turbulent conditions have been triggered with the tripping method designed by [38], using the optimal parameters described by these authors. The tripping region is located at x = 10δ 0 and occupies the entire spanwise extent.…”

Near field development of artificially generated high Reynolds number turbulent boundary layers

“…However, as pointed out by Marusic et al (2010) and Schlatter andÖrlü (2012), on many occasions the exact tripping conditions for different experiments are not adequately described, which may lead to difficulty when comparing results with previously published data. Two studies deserve special attention with regards to the tripping effects on the downstream development of the TBL; both Erm and Joubert (1991) (experimental) and Schlatter andÖrlü (2012) (computational) concluded that, for the tested trips' geometry and location, a self-similar state (independent of the trip employed) is obtained at about Re θ > 2000 , where Re θ is the Reynolds number based on the momentum thickness, θ, the freestream velocity, U ∞ , and the kinematic viscosity, ν. This result seemed contradictory with the study of Castillo and Johansson (2002) who reported that the trip dependency was maintained up to the last station measured (Re θ > 5000).…”

“…Several of these studies thus reflect the necessity for employing appropriate trip designs, for a given flow, in order to ensure the desired boundary layer state is achieved. (Erm and Joubert, 1991;Schlatter andÖrlü, 2012).…”

Transition of Turbulent Boundary Layer with a Step Change from Smooth to Rough Surface

“…(hairpin) 형태의 난류 와 구조에 대한 연구가 많이 수행 되어져 왔으며, 현재까지도 헤어핀 구조가 난류 에너지의 생성과 운동량의 교환 등에 미치는 영향에 대하여 찬반론 적인 연구가 활발히 이루어지고 있다 (8,9,10,11) . Wu & Moin (9) 은 경계층의 직접수치모사를 통하여 층류유동에서 난류유동으로 천이가 발생할 때, 헤어핀 형태의 와 구조 가 모든 영역에 걸쳐 발생하는 것을 확인하였으며, 특히 충분히 긴 도메인을 사용하여 수행한 직접수치모사 결과 는 레이놀즈 수가 Re θ =1950에 달하는 난류경계층에서도 † 책임저자 소속 및 연락처 Corresponding Author: Mechanical and Nuclear Engineering, UNIST, UNIST-gil 50, Ulsan, 689-798, jhlee06@unist.ac.kr 이재화 헤어핀 구조가 난류에너지의 발생 (production) 및 소산 (dissipation)에 지배적인 역할을 함을 보여주었다.…”

“…Wu & Moin (9) 은 경계층의 직접수치모사를 통하여 층류유동에서 난류유동으로 천이가 발생할 때, 헤어핀 형태의 와 구조 가 모든 영역에 걸쳐 발생하는 것을 확인하였으며, 특히 충분히 긴 도메인을 사용하여 수행한 직접수치모사 결과 는 레이놀즈 수가 Re θ =1950에 달하는 난류경계층에서도 † 책임저자 소속 및 연락처 Corresponding Author: Mechanical and Nuclear Engineering, UNIST, UNIST-gil 50, Ulsan, 689-798, jhlee06@unist.ac.kr 이재화 헤어핀 구조가 난류에너지의 발생 (production) 및 소산 (dissipation)에 지배적인 역할을 함을 보여주었다. 하지 만, 다른 연구 그룹에서는 낮은 레이놀즈 수의 난류유동에 서 나타나는 헤어핀 구조가 높은 레이놀즈 수의 난류유동 에서는 발견되지 않음을 보여주었다 (11) . 또한, Adrian (12) 는 헤어핀 구조가 응집성을 가지고 공간적으로 배열되어 새 로운 헤어핀 패킷 구조를 만들어 냄을 실험적으로 보여주 었지만, Jimenez 등 …”