Sonic Eddy Model of the Turbulent Boundary Layer

The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

Wake behind circular cylinder excited by spanwise non-uniform disturbances

We studied a modification of wake behind a circular cylinder using a plasma actuator. The plasma actuators were arranged in the spanwise direction of the cylinder to give temporal periodic disturbances having Strouhal number St = 0.18-2.3 with a burst ratio BR = 20 and 40%. The Reynolds number was set in a rage of Re = 4200 to 8400. Two types of plasma actuator were prepared; one is a single strip of the actuator placed at each side of the cylinder to give a spanwise uniform disturbance, and another is an array of small piece of actuators placed at the same location to create a spanwise non-uniform disturbance with temporal phase difference, φ = 0 or π, between adjacent electrodes. A conventional two-component PIV and stereo PIV was used to measure the flow field. Figure 1 shows the instantaneous spanwise component of vorticity at Re = 4200 evaluated by two-component PIV. Under no disturbance condition, the laminar shear layer extends straight to around x / d = 1.5 and then forms a wake vortex, as shown in Fig.1(a). In the case of spanwise non-uniform forcing with St = 1.09 and φ =π, rapid roll up of the initial shear layer leads to arrangement of wake vortices closer to the cylinder., as shown in Fig.1(b). With higher Strouhal number case with St = 1.09 and φ = 0, shown in Fig.1(c), a series of fine scale vortices are generated behind both side of the cylinder without forming regular Karman vortices. The spanwise non-uniform forcing was effective to suppress the formation of large scale vortices just behind the cylinder. Figure 2 shows surface of constant vorticity magnitude and vortex lines under St =1.09 and φ = π case. These were computed from a phase-averaged threecomponents velocity field evaluated by stereo PIV. The value of the surface was selected to display the boundary layer formed on the cylinder, and the vortex lines are selected to visualize the vortex structure formed in the following shear layer. A bundle of vortex lines are shaped in a wavy pattern along spanwise direction with 180 degrees out of phase to the adjacent bundle upstream of downstream. This structure, so called ‘chain-line fence structure’ was already found in planar free shear layer [Nygaard, K.J. and Glezer, A., 1990, Phys. Fluids A, 2, 461] and planar jet [Sakakibara, J., Anzai, T., 2001, Phys. Fluids, 13, 1541], but it became evident to create it in the wake of circular cylinder in this study.

Far Wake and Its Relation to Aerodynamic Efficiency

Correlations were found between the aerodynamic efficiency and the mean and fluctuating quantities in the far wake of a wall-to-wall SD7003 model and an AR 4 flat plate. This correlation was described algebraically by modeling the wake signature as a function of wing geometry and initial conditions. The model was benchmarked against experimental results to elicit the wing performance as a function of angle of attack by interrogating the wake. In these algebraic models, the drag coefficient along with other initial conditions of the turbulent generator (either airfoil or wing) were used to reconstruct the Reynolds Stress distribution and the momentum deficit distribution in the turbulent wake. Experiments were undertaken at the United States Air Force Research Labs Horizontal Free Surface Water Tunnel (AFRL/HFWT). These experiments build on previous results obtained at the University of Dayton Low Speed Wind Tunnel (UD-LSWT) on a cylinder, an AR 7 SD7062 wing, and a small remote control twin motor aircraft. The Reynolds stress and the momentum deficit of the turbulent generators were experimentally determined using Particle Image Velocimetry (PIV) with a minimum of 1000 image pairs averaged at each condition. The variation of an empirical factor (γ) used to match the Reynolds stress and momentum deficit distributions showed striking correlation to the variation of drag and aerodynamic efficiency of the turbulent generator. This correlation suggests that the wing performance information is preserved in the free shear layer 10 chord lengths downstream of the trailing edge (TE) of the wing irrespective of the dimensionality of the flow.

Fluid Dynamics of a Bistable Diverter Under Ultrasonic Excitation—Part I: Performance Characteristic

This paper investigates an ultrasonically driven bistable fluidic diverter at inlet nozzle Mach numbers of up to Mn = 0.3 and operating pressure ratios of up to Pr = 1.1. Part I examines the switching characteristics with respect to nondimensional parameters of excitation amplitude, frequency, required energy, switching time and inlet total pressure. It is shown that to promote switching at turbulent jet Mach numbers of up to Mn = 0.3 it is necessary to excite a jet preferred mode of St = 0.45 which differs from previously reported laminar jet operation of the similar device. For the reference case the switching time amounts to 1.2 ms suggesting oscillation frequencies of up to 500 Hz. Part II is a combined experimental and numerical study that examines the triggered instability modes in the free shear layer using large eddy simulations (LES) and visualizes the flow field using Particle Image Velocimetry (PIV).

Evaluation of Reattaching Shear-Layer in Compressible Turbulent Flows: A Large Eddy Simulation Approach

The boundary-layer separation and subsequent reattachment due to the free shear-layer and Shockwave interaction have a significant impact on the aerothermal design of supersonic aerospace systems. This problem is prevalent in high-speed flights and can significantly affect the skin friction, aerodynamic loads, and heat transfer. In recent years, considerable progress has been achieved in the prediction of turbulent compressible flows using high-fidelity models. However, the prediction of reattaching free shear-layer and shockwave interactions still needs to be modified for accurate predictivity. The objective of this study is to investigate the ability of a new computational fluid dynamics model to predict these critical flow phenomena accurately. The new high-fidelity model is based on a collocated central scheme, which has the advantage of being a Riemann free solver, and therefore easy to implement on unstructured grids. It is developed to capture any discontinuities at shocks while it is able to capture broadband spatial and temporal variations in turbulent flows with minimal dissipation and dispersion. Large Eddy Simulation is performed on a compression corner at a Mach number of 2.92 and a high Reynolds number. The geometry of the model is specifically designed to isolate the reattachment process of a high-speed separated flow. To examine the accuracy of the predicted results, results of velocity profiles in the free shear-layer, boundary layer development, turbulent fluctuations, and pressure are compared to an experimental effort by Princeton. Excellent agreement is observed, and it is recommended that the model can be used to investigate the physics of the shock unsteadiness due to interaction with a free shear-layer.