Dynamics of fluid mixing in separated flows
Authors: Leder A. 
Published: July 2002

Separated flows at high Re (&gt;103) are highly turbulent. In some situations the turbulence generation and mixing processes associated with flow separation are desirable, e.g., in heat exchangers or in many chemical engineering applications. In others, e.g., stalled airfoils, separation must be avoided as it causes loss in pressure and kinetic energy. To control the phenomenon effectively, physical mechanisms of flow separation and related aspects, such as the growth of flow instabilities in shear layers, the process of vortex formation, and the dynamics of fluid mixing in recirculating flow regions, must be understood. In many cases numerical procedures, e.g., Navier–Stokes calculations including k-ε turbulence modeling, fail to predict real physical mechanisms in separated flows.1,2

Separated flows in the lee of bluff bodies have been studied for many years.3,4 However, accurate measurements of the magnitude and direction of velocities and the magnitude of the terms of the Reynolds stress tensor have been restricted by the unsuitability of the hot-wire anemometer in recirculating flows. The development of the pulsed-wire anemometer, flying hot-wire anemometer, and laser-Doppler anemometry (LDA) allows more reliable measurements also in turbulent separated flows.5–8

The aim of this paper is to investigate the dynamics of undisturbed fluid mixing in separated regions of 2-D, incompressible flows with visualization techniques and LDA. Measurements were performed with a vertical flat plate model, mounted in a closed-circuit wind tunnel at low blockage ratio. Because of the noninvasive character, optical techniques like LDA are more suitable to analyze complex fluid motions than pulsed-wire and flying-wire anemometry. The LDA system used to investigate turbulent flow structures consists of a two-channel version operating in backscatter mode and a specifically developed phase detector to extract phase-averaged information from recorded measurement ensembles.9 Endplates were used to get nearly 2-D behavior. Downstream of the plate the flow field exhibits a distinct periodic component at Strouhal frequency S=0.14. In the investigated Re number range, 103–105, S remains constant. The flow dynamics were visualized by the smoke-wire technique.10 Mixing between laminar external and turbulent separated fluid is evident.

The process is initiated by entrainment of external fluid into the turbulent recirculating region. Corresponding quantitative results of LDA measurements are discussed. The plots show the developing of flow structures in a section from x/D=1.0 – 4.5 and y/D=−1.0 – 1.0, where D is the dimension of the plate model. The time difference between consecutive phases is t=0.02 sec. The saddle points are emphasized by short arrows indicating streamlines. Flow visualization and LDA measurements are in good agreement concerning the overall flow motions of the turbulent structures. Dynamic behavior of the Reynolds stress terms (u′2, v′2, and u′v′) are discussed.

From these distributions the fields of phase-averaged turbulent energy production 〈P〉 could be derived. The isoline diagrams clarify that the location of extremum values in 〈P〉 are dependent on time and the position of the saddle point. In conclusion: (1) The dynamics of fluid mixing can be investigated with phase-locked LDA technique; (2) qualitative results of flow visualizations and quantitative LDA measurements support each other and shed new light upon the physics of fluid mixing; (3) extreme values of phase-averaged turbulent energy production coincide with the occurrence of saddle points in the flow field; and (4) mixing is initiated by entrainment of laminar external fluid into the turbulent recirculating region.