Calculation Of Turbulent Flow And Sound In A Suddenly Expanded Pipe With Porous Inserts

The flow over a backward facing step is widely found in fluid machinery and process equipment.Its main flow characteristic is the vortical separation in the downstream of the step.The distribution of the downstream velocity is non-uniform,and vibration and noise are therefore occur because the interaction between the fluid and the solid wall.Such side effects are harmful to safety and environment.Porous material and structure are commonly used in flow rectifying and noise silencing in the pipes.However,in the practical application process,the choice of porous material parameters is basically dependent on the experiences of design and operation staff.Improperly selected parameters may not only increase the flow resistance within the pipeline,but also the vortex movement in downstream of the step may not be eliminated.In this paper,the effects of different porous materials on the flow field and sound field in the sudden expansion channel are studied,which can be used as a reference for the application of rectifier and muffler in the pipeline.Firstly,the N-S equation is subjected to volume averaging and time-averaged processing.The flow control equations describing the interior of the porous medium are obtained.Compared with the controlling equations for flows in free-space,the flow equations in the porous medium have the added terms of the Forchheimer and the Brinkman corrections which are due to the inertial and viscous resistances,respectively.The turbulence stress was calculated using the k-ε model,and the interface between the porous medium and the pure fluid was set to be a porous medium boundary condition.Through the control variable method,the change of the flow field with the permeability,the position and the thickness of the inserts in the two-dimensional and three-dimensional sudden expansion channel are studied respectively.The results show that the increase in the thickness of the porous inserts or the decrease in the permeability could increase the pressure loss in the channel,and they play a primary role in the change of the pressure loss.The intensity of vorticity and velocity fluctuations in the pipe decrease with increasing permeability.The vorticity in the porous inserts is related to the permeability of the material.For the unsteady inflow which contains a harmonic wave,all the fluctuation amplitudes of pressure signal,axial velocity,turbulent kinetic energy and the dissipation rate of turbulence are reduced when the fluid flows through the porous insert.However,the phase of these waves is retained to be not changed.On the basis of flow field calculation,the software ACTRAN is used to calculate the acoustic calculation.Surfaces on both sides of the pipe are defined as the acoustic mode surface to simulate the infinite pipe.The calculation of sound field shows that the porous material inserts has effectively restrained the noise in the low frequency region.And as the frequency increases,the propagation direction of the acoustic wave is deflected from the axial to the radial direction.