On the optimaL response of q-vortex
Rodríguez-García, Jesús Óscar,Blanco-Rodríguez, Francisco José,Parras-Anguita, Luis,Del-Pino-Peñas, Carlos Manuel
- Published
- 2016-09-01
- Language
- en
Abstract
Wingtip vortices represent a hazard for the stability of the following airplane in airport highways. These flows have been usually modeled as swirling jets/wakes, which are known to be highly unstable and susceptible to breakdown at high Reynolds numbers for certain flow conditions, but different to the ones present in real flying airplanes. A very recent study based on Direct Numerical Simulations (DNS) shows that a large variety of helical responses can be excited and amplified when a harmonic inlet forcing is imposed. In this work, the optimal response of q-vortex (both axial vorticity and axial velocity can be modeled by a Gaussian profile) is studied by considering the time-harmonically forced problem with a certain frequency ω. We first reproduce Guo and Sun’s results for the Lamb-Oseen vortex (no axial flow) to validate our numerical code. In the axisymmetric case m = 0, the system response is the largest when the input frequency is null. The axial flow has a weak influence in the response for any axial velocity intensity. We also consider helical perturbations |m| = 1. These perturbations are excited through a resonance mechanism at moderate and large wavelengths as it is shown in Figure 1. In addition, Figure 2 shows that the frequency at which the optimal gain is obtained is not a continuous function of the axial wavenumber k. At smaller wavelengths, large response is excited by steady forcing. Regarding the axial flow, the unstable response is the largest when the axial velocity intensity, 1/q, is near to zero. For perturbations with higher azimuthal wavenumbers |m| > 1, the magnitudes of the response are smaller than those for helical modes. In order to establish an alternative validation, DNS has been carried out by using a pseudospectral Fourier formulation finding a very good agreement.
Full text
Maximum gain response (decimal logarithm) Rmax(k, 1/q) obtained at m=1 for Reynolds number Re=5000. Frequency ω at which the maximum response is obtained at m=1 and 1/q=0. ON THE OPTIMAL RESPONSE OF Q-VORTEX JESUS O. RODRIGUEZ-GARCIA (MECHANICAL ENGINEERING, THERMAL AND FLUIDS. UNIVERSITY OF MALAGA ); FRANCISCO J. BLANCO-RODRIGUEZ (MECHANICS. UNIVERSITY OF CORDOBA ); LUIS PARRAS (MECHANICAL ENGINEERING, THERMAL AND FLUIDS. UNIVERSITY OF MALAGA ); CARLOS DEL PINO (MECHANICAL ENGINEERING, THERMAL AND FLUIDS. UNIVERSITY OF MALAGA ) Wingtip vortices represent a hazard for the stability of the following airplane in airport highways. These flows have been usually modeled as swirling jets/wakes, which are known to be highly unstable and susceptible to breakdown at high Reynolds numbers for certain flow conditions, but different to the ones present in real flying airplanes. A very recent study [1] based on Direct Numerical Simulations (DNS) shows that a large variety of helical responses can be excited and amplified when a harmonic inlet forcing is imposed. In this work, the optimal response of q-vortex (both axial vorticity and axial velocity can be modeled by a Gaussian profile) is studied by considering the time-harmonically forced problem with a certain frequency ω. We first reproduce Guo and Sun’s results [2] for the Lamb-Oseen vortex (no axial flow) to validate our numerical code. In the axisymmetric case m = 0, the system response is the largest when the input frequency is null. The axial flow has a weak influence in the response for any axial velocity intensity. We also consider helical perturbations |m| = 1. These perturbations are excited through a resonance mechanism at moderate and large wavelengths as it is shown in Figure 1. In addition, Figure 2 shows that the frequency at which the optimal gain is obtained is not a continuous function of the axial wavenumber k. At smaller wavelengths, large response is excited by steady forcing. Regarding the axial flow, the unstable response is the largest when the axial velocity intensity, 1/q, is near to zero. For perturbations with higher azimuthal wavenumbers |m| > 1, the magnitudes of the response are smaller than those for helical modes. In order to establish an alternative validation, DNS has been carried out by using a pseudospectral Fourier formulation [3] finding a very good agreement. References [1] Guo, Z.-W., Sun, D.-J., Optimal response in the Lamb–Oseen vortex. Physics Letters A 375 (36) 3191–3195 (2011). [2] Viola, F., Arratia, C., Gallaire, F., Mode selection in trailing vortices: harmonic response of the nonparallel Batchelor vortex. Journal of Fluid Mechanics 790, 523–552 (2016). [3] Delbende, I., Chomaz, J.-M., Huerre, P., Absolute/convective instabilities in the Batchelor vortex: a numerical study of the linear impulse response. Journal of Fluid Mechanics 355, 229–254 (1998).
