When the mean flow effect is taken into account in an acoustic analysis, the convective wave equation becomes the governing equation instead of the Helmholtz wave equation. The velocity potential Φ is used for the degree-of-freedom rather than the pressure, as in the case of mean flow at rest. The convective wave equation supports harmonic and modal analyses.
The mean flow velocity can be obtained from the velocity potential by solving Laplace’s equation with a defined mean flow velocity (BF,,VMEN) on the exterior surface in a static analysis. The program assigns the reference velocity potential at a node for the solution with the pure Neumann boundary condition. The result is stored in the Jobname.rmf file for preprocessing and postprocessing.
To view nodal velocity potential and element mean flow velocity, issue the following commands (the label PRES represents the velocity potential):
To apply the solved mean flow velocity to the acoustic model for a downstream harmonic or modal analysis, issue the following command for load transfer before solving:
LDREAD,VMEN,1,1,,,
Jobname,RMF
The following sophisticated material models may be included in the model with mean flow:
Non-uniform ideal gas material
The mean flow velocity in the equivalent fluid model of perforated media is assumed to be zero.
The following acoustic boundary conditions can be used with the mean flow effect:
Velocity potential (use label PRES to define)
Rigid wall
Impedance boundary condition
Artificially matched layers
The following acoustic excitation sources can be used with the mean flow effect:
Pressure
Outward normal velocity
Arbitrary nodal velocity
Mass resources
Complex force potential
The trim element with transfer admittance matrix may be used in a model with the mean flow effect. The mean flow inside the trim element is set to be at rest.
Acoustic fluid-structure interaction (FSI) can be modeled taking the mean flow effect into account.
The far-field calculation in the postprocessor does not support the mean flow effect.
Note: The solution for convective wave equation (mean flow effect) is not available for 2D acoustic elements.
Example 11.7: Acoustic Analysis with Mean Flow Effect
et,1,220,,1 ! uncoupled acoustic element et,1,220,,1,,1 ! uncoupled acoustic PML element … c0=345 rho=1.21 mach=0.3 vx=mach*c0 L=1 vn=1 … nsel,s,loc,x,0 ! select nodes on inlet nsel,a,loc,x,L ! select nodes on outlet bf,all,vmen,vx,0,0 ! define mean flow velocity on selected nodes … alls fini /solu antype,static ! static solution solve finish /prep7 ldread,vmen,1,1,file,rmf ! apply mean flow velocity as body loads … sf,all,impd,z0,z0 ! define impedance on surface … sf,all,shld,vn ! define normal velocity on surface alls finish /solu antype,harm ! harmonic solution harfrq,100 nsub,1 solve finish
If the acoustic pressure may be non-uniform on the cross section of the inlet and outlet, it is more reliable to use PML or IPML truncation rather than the impedance or radiation boundary condition for the duct with mean flow.
For more information, see Finite Element Formulation of the Convective Wave Equation in the Mechanical APDL Theory Reference.