Linear Stability Analysis of Laminar Separation Bubble over NACA0012 airfoil at Low Reynolds Numbers
13 Jan 2014-
TL;DR: In this paper, a numerical linear stability code was developed to understand the T-S wave characteristics in the LSB, where the OSE was solved as a spatial stability problem where the temporal frequency is a real number and the eigen values are the spatial wave numbers.
Abstract: Low Reynolds number flows are important especially for MAV applications due to the presence of the LSB, which affects airfoil performance. The transition model of Fluent12 is used to extract the local velocity profiles and their second derivatives for flow past NACA0012 airfoil at Re=0.34X10. These form the input to a numerical linear stability code developed to understand the T-S wave characteristics in the LSB. The code solves the OrrSommerfeld equation locally for NACA0012 mean profiles at α=9 with parallel flow approach. The OSE is solved as a spatial stability problem where the temporal frequency is a real number and the eigen values are the spatial wave numbers. A complex NewtonRaphson technique is used for the Eigen value search and e method is used to predict transition. The growth of the most unstable wave is such that the amplification ratio reaches a predefined number e. Based on e method the T-S wave frequency and phase speed are predicted. The LSB is observed using the Cp and velocity vector plots from Fluent12.
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TL;DR: In this article, the authors studied the mass transport between separation bubble and main flow in flow over airfoil, using Lagrangian coherent structures (LCSs) in order to understand the nature of evolution of the separation bubble.
Abstract: The lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.
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Book•
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
01 Jan 2000
TL;DR: In this paper, a couche is used for limite, turbulence, ecoulement, and instationnaire to train a trainee in order to deal with trainee turbulence.
Abstract: Keywords: couche : limite ; turbulence ; ecoulement ; instationnaire ; compressible ; trainee Note: livre perdu et remplacer le 11.06.02 Reference Record created on 2005-11-18, modified on 2016-08-08
502 citations
TL;DR: In this paper, the authors investigated the effect of separation bubble formation and boundary layer separation on coherent structures in low Reynolds number flows and showed that roll-up vortices formed in the separated shear layer due to the amplification of natural disturbances, and these structures played a key role in flow transition to turbulence.
Abstract: Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.
281 citations
Journal Article•
TL;DR: A new correlation-based transition model has been developed, which is based strictly on local variables and is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids and massive parallel execution.
Abstract: A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids and massive parallel execution. The model is based on two transport equations, one for intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models) but from a framework for the implementation of correlation-based models into general-purpose CFD methods.
279 citations