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.

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.

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.

Reynolds-number dependence of wall-pressure fluctuations in a pressure-induced turbulent separation bubble

2017 ◽  
Vol 833 ◽  
pp. 563-598 ◽  
Author(s):  
Hiroyuki Abe
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Large Scale ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Local Maximum ◽  
Wall Pressure ◽  
Mean Flow ◽  
Frequency Spectra ◽  
Wall Pressure Fluctuations

Direct numerical simulations are used to examine the behaviour of wall-pressure fluctuations $p_{w}$ in a flat-plate turbulent boundary layer with large adverse and favourable pressure gradients, involving separation and reattachment. The Reynolds number $Re_{\unicode[STIX]{x1D703}}$ based on momentum thickness is equal to 300, 600 and 900. Particular attention is given to effects of Reynolds number on root-mean-square (r.m.s.) values, frequency/power spectra and instantaneous fields. The possible scaling laws are also examined as compared with the existing direct numerical simulation and experimental data. The r.m.s. value of $p_{w}$ normalized by the local maximum Reynolds shear stress $-\unicode[STIX]{x1D70C}\overline{uv}_{max}$ (Simpson et al. J. Fluid Mech. vol. 177, 1987, pp. 167–186; Na & Moin J. Fluid Mech. vol. 377, 1998b, pp. 347–373) leads to near plateau (i.e. $p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{uv}_{max}=2.5\sim 3$) in the adverse pressure gradient and separated regions in which the frequency spectra exhibit good collapse at low frequencies. The magnitude of $p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{uv}_{max}$ is however reduced down to 1.8 near reattachment where good collapse is also obtained with normalization by the local maximum wall-normal Reynolds stress $\unicode[STIX]{x1D70C}\overline{vv}_{max}$. Near reattachment, $p_{w\,rms}/-\unicode[STIX]{x1D70C}\overline{vv}_{max}=1.2$ is attained unambiguously independently of the Reynolds number and pressure gradient. The present magnitude (1.2) is smaller than (1.35) obtained for step-induced separation by Ji & Wang (J. Fluid Mech. vol. 712, 2012, pp. 471–504). The reason for this difference is intrinsically associated with convective nature of a pressure-induced separation bubble near reattachment where the magnitude of $p_{w\,rms}$ depends essentially on the favourable pressure gradient. The resulting mean flow acceleration leads to delay of the r.m.s. peak after reattachment. Attention is also given to structures of $p_{w}$. It is shown that large-scale spanwise rollers of low pressure fluctuations are formed above the bubble, whilst changing to large-scale streamwise elongated structures after reattachment. These large-scale structures become more prominent with increasing $Re_{\unicode[STIX]{x1D703}}$ and affect $p_{w}$ significantly.

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.

Simulation of turbulent boundary layer wall pressure fluctuations via Poisson equation and synthetic turbulence

2017 ◽  
Vol 826 ◽  
pp. 421-454 ◽  
Author(s):  
Nan Hu ◽  
Nils Reiche ◽  
Roland Ewert
Keyword(s):  
Flat Plate ◽  
Boundary Layers ◽  
Poisson Equation ◽  
Pressure Fluctuations ◽  
Turbulent Boundary Layers ◽  
Wall Pressure ◽  
Fluctuating Pressure ◽  
Reynolds Number Flow ◽  
Wall Pressure Fluctuations ◽  
Interaction Term

Flat plate turbulent boundary layers under zero pressure gradient are simulated using synthetic turbulence generated by the fast random particle–mesh method. The stochastic realisation is based on time-averaged turbulence statistics derived from Reynolds-averaged Navier–Stokes simulation of flat plate turbulent boundary layers at Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=2513$ and $\mathit{Re}_{\unicode[STIX]{x1D70F}}=4357$. To determine fluctuating pressure, a Poisson equation is solved with an unsteady right-hand side source term derived from the synthetic turbulence realisation. The Poisson equation is solved via fast Fourier transform using Hockney’s method. Due to its efficiency, the applied procedure enables us to study, for high Reynolds number flow, the effect of variations of the modelled turbulence characteristics on the resulting wall pressure spectrum. The contributions to wall pressure fluctuations from the mean-shear turbulence interaction term and the turbulence–turbulence interaction term are studied separately. The results show that both contributions have the same order of magnitude. Simulated one-point spectra and two-point cross-correlations of wall pressure fluctuations are analysed in detail. Convective features of the fluctuating pressure field are well determined. Good agreement for the characteristics of the wall pressure fluctuations is found between the present results and databases from other investigators.

Measurements and Predictions of a Highly Turbulent Flowfield in a Turbine Vane Passage

2000 ◽  
Vol 122 (4) ◽  
pp. 666-676 ◽  
Author(s):  
R. W. Radomsky ◽  
K. A. Thole
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Gas Turbine ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Complex Geometry ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow

As highly turbulent flow passes through downstream airfoil passages in a gas turbine engine, it is subjected to a complex geometry designed to accelerate and turn the flow. This acceleration and streamline curvature subject the turbulent flow to high mean flow strains. This paper presents both experimental measurements and computational predictions for highly turbulent flow as it progresses through a passage of a gas turbine stator vane. Three-component velocity fields at the vane midspan were measured for inlet turbulence levels of 0.6%, 10%, and 19.5%. The turbulent kinetic energy increased through the passage by 130% for the 10% inlet turbulence and, because the dissipation rate was higher for the 19.5% inlet turbulence, the turbulent kinetic energy increased by only 31%. With a mean flow acceleration of five through the passage, the exiting local turbulence levels were 3% and 6% for the respective 10% and 19.5% inlet turbulence levels. Computational RANS predictions were compared with the measurements using four different turbulence models including the k-ε, Renormalization Group (RNG) k-ε, realizable k-ε, and Reynolds stress model. The results indicate that the predictions using the Reynolds stress model most closely agreed with the measurements as compared with the other turbulence models with better agreement for the 10% case than the 19.5% case. [S0098-2202(00)00804-X]

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