Predictions on Wall Pressure Fluctuations for a Backward-Facing Step

2005 ◽  
Author(s):  
Yu-Tai Lee ◽  
Theodore M. Farabee ◽  
William K. Blake
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Turbulent Kinetic Energy ◽  
Source Term ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Backward Facing Step ◽  
Linear Source ◽  
Wall Pressure Fluctuations ◽  
Flow Past

Time-mean flow fields and turbulent flow characteristics obtained from solving the Reynolds averaged Navier Stokes (RANS) equations with a k-ε turbulence model are used to predict the frequency spectrum of wall-pressure fluctuations for flow past a backward facing step. The linear source term of the governing fluctuating pressure equation is used in deriving the final double integration formula for the fluctuating wall pressure. The integrand includes the RANS mean-velocity gradient, modeled turbulence normal fluctuation, Green’s function and the spectral model for the interplane correlation. An anisotropic distribution of the turbulent kinetic energy is implemented using a function named anisotropic factor. This function represents a ratio of the turbulent normal Reynolds stress to the turbulent kinetic energy and is developed based on an equilibrium turbulent flow or flows with zero streamwise pressure gradient. The spectral correlation model for predicting the wall-pressure fluctuations is obtained through modeling of the streamwise and spanwise wavenumber spectra. The non-linear source term in the original governing equation is considered following the conclusion of Kim’s direct numerical simulation (DNS) study. Predictions of frequency spectra for the reattachment flow past a backward facing step (BFS) are investigated to verify the validity of the current modeling. Detailed turbulence features and wall-pressure spectra for the flow in the reattachment region of the BFS are predicted and discussed. The prediction results based on different modeling characteristics and flow physics agree with the observed turbulence field.

Wall Pressure Fluctuations in the Reattachment Region of a Backward Facing Step

2007 ◽  
Author(s):  
Yu-Tai Lee ◽  
Theodore M. Farabee ◽  
William K. Blake
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Turbulent Kinetic Energy ◽  
Source Term ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Fluctuating Pressure ◽  
Wall Pressure Fluctuations

Steady mean flow fields and turbulent flow characteristics obtained from solving the Reynolds Averaged Navier Stokes (RANS) equations with a k-ε isotropic turbulence model are used to predict the frequency spectrum of wall-pressure fluctuations for flow past a backward facing step. The linear source term (LST) of the governing fluctuating-pressure equation is used in deriving the final double integration formula for the fluctuating wall pressure. The integrand of the solution formula includes the mean-flow velocity gradient, modeled turbulence normal fluctuation, Green’s function and the spectral model for the interplane correlation. An anisotropic distribution of the turbulent kinetic energy is implemented using a function named anisotropic factor. This function represents a ratio of the turbulent normal Reynolds stress to the turbulent kinetic energy and is developed based on an equilibrium turbulent flow or flows with zero streamwise pressure gradient. The spectral correlation model for predicting the wall-pressure fluctuations is obtained through modeling of the streamwise and spanwise wavenumber spectra. The nonlinear source term (NST) in the original fluctuating-pressure equation is considered following the conclusion of Kim’s direct numerical simulation (DNS) study of channel flow. Predictions of frequency spectra for the reattachment flow past a backward facing step (BFS) are investigated to verify the validity of the current modeling. Detailed turbulence features and wall-pressure spectra for the flow in the reattachment region of the BFS are predicted and discussed. DNS and experimental data for BFSs are used to develop and validate these calculations. The prediction results based on different modeling characteristics and flow physics agree with the observed turbulence field.

Modeling of Wall Pressure Fluctuations Based on Time Mean Flow Field

2004 ◽  
Vol 127 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Yu-Tai Lee ◽  
William K. Blake ◽  
Theodore M. Farabee
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Wave Number ◽  
Mean Flow ◽  
Local Flow ◽  
Outer Flow ◽  
Wall Pressure Fluctuations ◽  
Flow Activity

Time-mean flow fields and turbulent flow characteristics obtained from solving the Reynolds averaged Navier-Stokes equations with a k‐ε turbulence model are used to predict the frequency spectrum of wall pressure fluctuations. The vertical turbulent velocity is represented by the turbulent kinetic energy contained in the local flow. An anisotropic distribution of the turbulent kinetic energy is implemented based on an equilibrium turbulent shear flow, which assumes flow with a zero streamwise pressure gradient. The spectral correlation model for predicting the wall pressure fluctuation is obtained through a Green’s function formulation and modeling of the streamwise and spanwise wave number spectra. Predictions for equilibrium flow agree well with measurements and demonstrate that when outer-flow and inner-flow activity contribute significantly, an overlap region exists in which the pressure spectrum scales as the inverse of frequency. Predictions of the surface pressure spectrum for flow over a backward-facing step are used to validate the current approach for a nonequilibrium flow.

Measurement of turbulent boundary layer unsteady wall pressures beneath elastomer layers of various thicknesses on a plate

2021 ◽  
Vol 69 (3) ◽  
pp. 182-198
Author(s):  
Cory J. Smith ◽  
Dean E. Capone ◽  
Timothy A. Brungart ◽  
William K. Bonness
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Excellent Agreement ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Wall Pressure ◽  
Shear Stresses ◽  
Backward Facing Step ◽  
Wall Pressure Fluctuations ◽  
Velocity Statistics

The attenuation of turbulence-inducedwall pressure fluctuations through elastomer layers is studied experimentally and analytically. Wall pressure statistics are measured downstream from a backward facing step, with no elastomer present and beneath 2-, 3- and 4-mm-thick elastomers in a water tunnel facility. In the absence of an elastomer layer, the wall pressure spectra, cross-spectra and velocity statistics measured at the various locations downstream from the backward facing step are in excellent agreement with those reported in the archival literature. The streamwise coherence measured beneath the elastomer layers is higher than that measured in the absence of an elastomer layer, an effect which increases with increasing elastomer thickness. It is speculated that this increase in coherence level is due to the ability of the elastomer to support shear stresses, which effectively increases the area over which an eddy influences the normal stresses measured by the pressure sensors. The high-frequency filtering of the elastomers is also observed in the coherence at the smallest streamwise separation. The attenuation of the turbulent boundary layer wall pressure fluctuations through the elastomer layer using an analytical elastomer transfer function is in excellent agreement with the attenuation measured experimentally through all thicknesses of elastomer and at all the free stream velocities at which the experiments are performed.

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