Scaling analysis for aeroelastic phenomena using the navier-stokes fluid model
The scaling analysis of the Navier Stokes equation is examined and is extended to compressible aerodynamic flows where the characteristic Reynolds number is large and the Prandtl number is of order unity. A compressible flow of a Newtonian fluid is considered in the absence of body forces which obeys the perfect-gas law. Fluid properties such as the specific heat at constant pressure, gas constant, heat conduction coefficient, and the dynamic viscosity, are assumed constant. The energy equation for compressible flows leads to a second pressure perturbation estimate different from the streamwise momentum equation result. For fluid structure systems where the principal nonlinearity is in the fluid, order-of-magnitude estimates for nonlinear aeroelastic phenomena such as limit-cycle oscillations and frequency lock-in can be achieved by application of the kinematic boundary condition to the compressible flow scaling results. Copyright © 2012 by Justin W. Jaworski and Earl H. Dowell.
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