Transition study for asymmetric reflection between moving incident shock waves

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

Numerical Simulations on Unsteady Nonlinear Transonic Airfoil Flow

Large-amplitude excitations need to be considered for gust load analyses of transport aircraft in cruise flight conditions. Nonlinear amplitude effects in transonic flow are, however, only marginally taken into account. The present work aims at closing this gap by means of systematic unsteady Reynolds-averaged Navier-Stokes simulations. The RAE2822 airfoil is analyzed for a variety of sinusoidal gust excitations at different transonic Mach numbers. Responses are evaluated with respect to lift and moment coefficients, their derivatives and the unsteady shock motion. A strong dependency on inflow Mach number and excitation frequency is observed. Generally, amplitude effects decrease with lower Mach numbers or higher excitation frequencies. The unsteady nonlinear simulations predict lower maximum lift values and lower lift and moment derivatives compared to their linear counterparts for lower frequencies in combination with large-amplitude excitations. For the mid-frequency range, trends are not as clear. Additionally, it is shown that the variables of harmonic distortion and maximum shock motion might not be reasonable indicators to predict a nonlinear response.

Simulation of transonic buffet with an automated zonal DES approach

A study of transonic buffet on the NASA Common Research Model at flight Reynolds numbers is presented. The ability of two different hybrid RANS/LES models as well as the URANS approach for resolving three-dimensional buffet motion was evaluated by means of spectral analysis. Automated Zonal DES and URANS simulations show similar results in terms of buffet frequency and spanwise propagation of buffet cells, whereas the Delayed Detached Eddy Simulation results indicate a strong interaction between flow separation and shock motion. The extracted characteristic frequencies which are associated with transonic buffet are located in a range of Sr = 0.2–0.65 for URANS and AZDES and are therefore in accordance with findings from related recent research. Furthermore, the simulation time series were investigated and a structure of spanwise moving buffet cells with varying convection speed and wavelength could be observed.

Features of the spatial organization of the body in athletes of various qualifications when hitting the ball in football

The article analyzes the angular characteristics of football players of different qualifications in the extreme phases of the impact of the middle part of the foot on a stationary ball. The angles of the knee, hip, shoulder, elbow joints involved in the impact are considered. Their quantitative values, changes and differences between them are determined. Analyzing the quantitative characteristics of the angles at different moments of the phases when performing a shot on the ball is established. Highly qualified football players have a pronounced coordination of movements in the corners of the lower extremities. In the first phase, the blow is performed due to movement in the hip joint, ending in the knee. In this case, athletes effectively use the movement in the shoulder joint in the initial phase of the impact to increase its strength. Movement in the elbow joint in the final phase to maintain balance. In low-skilled players, the coordination of movements is disturbed, both joints of the legs are equally involved in the first phase of the blow. The movement of the hands does not occur, the shoulder and elbow joints are connected only in the final phase of the movement. It is established that the angular characteristics of the knee, hip and elbow joints in the micro-phase of the support leg of the preparation phase have statistically significant differences. Also in the micro-phase shock motion of the working phase there are statistically significant differences in all four angles analyzed by us.

Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.

Experimental study of the coherent vorticity in slightly under-expanded supersonic screeching jets

The noise generation mechanism of screech tone by shock leakage in underexpended round jets is experimentally investigated by means of phase-averaged velocity fields. Two jet flows at Mach numbers 1.10 and 1.15 are measured by a particle image velocimetry apparatus simultaneously with their near acoustic fields and sorted according to their phase with respect to a screech period. The coherent vorticity fields are then computed and analyzed. They depict two distinct regions of high level of vorticity fluctuations. Thanks to the knowledge about shock leakage gathered in previous studies, the role of both regions in the acoustic generation process is identified and a region of the flow is recognized as suitable for emitting acoustic waves. Phase-averaged schlieren visualizations are also computed and used to determine the motion of the first five shocks over a screech period. For both jets, the peak shock motion is found at the fourth shock tip. This shock is also located in the region recognized as favorable for the shock leakage to be observed.