In the calculation of acoustic radiation, we re-derive the Green's function of the wave equation with uniform flow, and establish a three-dimensional acoustic radiation formula. From the three-dimensional formula, the acoustic radiation of the object oscillates under two-dimensional and low Mach number is established. The near-field and far-field formulas are calculated using the far-field formula.
Mathematical model of the problem Flow calculation model The airfoil surface is a complex curve. The computational grid of the physical space is not uniform, so the curve coordinate system is adopted. Since the airfoil can move, a moving mesh is needed. In this paper, the time-discrete of the momentum equation of the incompressible NS equation is expressed by the semi-implicit scheme using the inverse velocity flux; the convection term is the MUSCL-like style of vanLeer; the diffusion term is transformed into the velocity value on the cell boundary by the Gaussian formula; The method carries out the coexistence of pressure and velocity, and the algebraic equation uses the iterative method combined with the GMRES method and the incomplete Lu decomposition (pre-optimal).
The simplified structure-spring system is solved by the well-known Newmark Lu method. Acoustic Radiation Calculation Model We re-derived the Green's function of the wave equation with uniform inflow conditions. This Green's function is used to generalize the Ffowes-Wiliams-Hawkings equation and convert it into two-dimensional. The write is the Lighthill tensor, the off is the fluid stress on the boundary S, the subscript A is the two-dimensional integral domain, and a' and å® are the components of the velocity and acceleration at any point on the object in the Cartesian coordinate system, respectively.
Gas is the projection of the relative velocity on the surface of the object on the surface normal, and vc is the area enclosed by the inside of the object. There are three types of sources in the above formula: the first is a volume quadrupole, which is derived from the unstable wake region of the object; the second is the surface dipole, which is derived from the fluid stress on the object surface; the last three terms The movement of the source objects, they are dipoles and quadrupoles, respectively. The first item is the contribution of the quadrupole and the second is the role of the dipole.
The calculation results show that the vortex shedding of the fixed cylinder in the uniform flow is numerically simulated by the above method. The grid of 81x61 is used, and the dimensionless time step is 0.002. Under the case of Re 2 and 7519 respectively, The position is at (l0, 1000) (the radius of the cylinder is taken as 1), the change in sound density over time and the corresponding spectrum. visible:
(1) The contribution of dipoles is much larger than that of quadrupoles;
(2) Re hour waveform rule, the spectrum is concentrated in one frequency component, and the waveform and spectrum have high frequency components when high R.
Sound density changes with time and pre-spectrum, left 10. (a) side pole, quadrupole. For the quadrupole to the cylinder, we also calculated the motion of the cylindrical oscillation and the cylindrical spring system. Due to space limitations, only the latter calculation results are given here. In the kneading motion of the cylindrical-spring system, locked and unlocked states occur. In the locked state, the vortex shedding frequency is consistent with the system natural vibration frequency, and the frequency of the cylindrical oscillation displacement and the lift coefficient change are all single. In the unlocked state, there are two different frequencies, and the oscillation displacement of the cylinder is in a tempo phenomenon, and the lift is basically a single frequency.
It can be seen that in the case of cylindrical motion, dipole and quadrupole contribute to the increase of sound density, especially the contribution of object motion can not be neglected. In the case of locking, the motion of the object contributes the most to the change of sound density. The series of calculations for the airfoil flow shows that there is no significant separation of the airfoil surface when the angle of attack is 6. and 12. When the angle of attack reaches 30, the airfoil exhibits a similar vortex shedding phenomenon to the cylinder. At this time, the Strouhal number is about 0.29. Through the calculation of the time history of the force of Re=1000 and the angle of attack of 30.NACAOO12, it is found that after a certain transition time, the airfoil force shows a stable period phenomenon, reflecting The periodic detachment of the vortex.
However, the change in fluid dynamics at this time is different from the similar sinusoidal variation of the cylindrical force, showing a stronger nonlinearity. The time-varying curve at the sound density at (100, 1000) is also not very regular, and the transition time required for the sound density to start to stabilize is also longer. Time history of sound density (a) Dipole, He Siji is our two-dimensional wing-spring system, the degree of freedom is 2, which is the up and down oscillation and the rotation around the elastic center. We choose the two degrees of freedom vibration to be equal, corresponding to the situation where the two degrees of freedom have the greatest impact.
(a) and (b) are time-varying curves of the time-of-failure displacement for the structural frequencies of 1.155 and 1.055, respectively. We have seen the rhythm of the airfoil torsional vibration, which is the coexistence of the vortex frequency and the natural vibration frequency, and the rhythm of the translational oscillation is not obvious. When the natural vibration frequency is 1.055, we find that as time goes by, the vibration of the system will gradually develop to a resonance state, the amplitude is obviously increased, and it exists in the degree of freedom of translation and torsion, and its amplitude is damping. The effect is limited to a certain range, which may also be a locking phenomenon.
Conclusion The calculation reveals some phonological mechanisms of underwater vortex-induced noise and the relationship between the evolution of vortices and acoustic radiation. Dynamic mesh technology is a good way to solve such problems when objects move in the flow field. The vortex separation of the cylindrical one spring system and the airfoil-spring system catastrophic motion produces similar tempo and resonance under certain conditions. The calculation results of the sound field show that the monopole term cannot be ignored.
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