scholarly journals Approximate Analytical Models for Turbulent Boundary Layer Wall Pressure and Wall Shear Fluctuation Spectra and Coherence Functions

2017 ◽  
Author(s):  
Lawrence J. DeChant ◽  
Justin A. Smith ◽  
Matthew F. Barone
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Wall Pressure ◽  
Analytical Models ◽  
Wall Shear

scholarly journals Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient

2019 ◽  
Vol 877 ◽  
pp. 1007-1062 ◽  
Author(s):  
G. Grasso ◽  
P. Jaiswal ◽  
H. Wu ◽  
S. Moreau ◽  
M. Roger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Analytical Models ◽  
Function Technique ◽  
Fast Evaluation ◽  
Wall Pressure Fluctuations

This paper presents a comprehensive analytical approach to the modelling of wall-pressure fluctuations under a turbulent boundary layer, unifying and expanding the analytical models that have been proposed over many decades. The Poisson equation governing pressure fluctuations is Fourier transformed in the wavenumber domain to obtain a modified Helmholtz equation, which is solved with a Green’s function technique. The source term of the differential equations is composed of turbulence–mean shear and turbulence–turbulence interaction terms, which are modelled separately within the hypothesis of a joint normal probability distribution of the turbulent field. The functional expression of the turbulence statistics is shown to be the most critical point for a correct representation of the wall-pressure spectrum. The effect of various assumptions on the shape of the longitudinal correlation function of turbulence is assessed in the first place with purely analytical considerations using an idealised flow model. Then, the effect of the hypothesis on the spectral distribution of boundary-layer turbulence on the resulting wall-pressure spectrum is compared with the results of direct numerical simulation computations and pressure measurements on a controlled-diffusion aerofoil. The boundary layer developing over the suction side of this aerofoil in test conditions is characterised by an adverse pressure gradient. The final part of the paper discusses the numerical aspect of wall-pressure spectrum computation. A Monte Carlo technique is used for a fast evaluation of the multi-dimensional integral formulation developed in the theoretical part.

Axial Flutter Effects on the Axisymmetric Turbulent Boundary Layer Along Long Thin Circular Cylinders

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Stephen A. Jordan
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Reynolds Numbers ◽  
Wall Pressure ◽  
Analytical Models ◽  
Circular Cylinders ◽  
Reynolds Stresses ◽  
Turbulent Statistics ◽  
Oscillatory Instabilities

Experimental observations of towed sonar arrays as characterized by long thin circular cylinders indicate transverse motions that are clearly identified by low-amplitudes, low-wavelengths, and low-frequencies. Although the cylinder length (L) to radius (a) is commonly large [L/a = O(103)] with high Reynolds numbers [O(104)], the corresponding length scale involving the average skin friction [CfL/a = O(10)] remains within the many experimental determinations of short to moderate length cylinders that experience oscillatory instabilities. Prior to the present investigation, any detrimental effects of these oscillatory instabilities on the thin cylinder flow physics that serve construction of the respective semi-empirical and semi-analytical models remained chiefly unknown. Herein, we began examining those turbulent statistics via fine-scale numerical simulations to critique the pragmatic adequacy of the representative design models. We were concerned in particular about the streamwise effects on the turbulent boundary layer (TBL), skin friction and wall pressure evolutions as well as the radial distributions of the leading normal and shear Reynolds stresses. Fortunately, no major deviations (within 10%) were discovered in the TBL statistics over a characteristic range of Reynolds numbers and TBL thicknesses as compared to the axisymmetric state. However, acute spikes (both subharmonics and harmonics) were detected in the wall pressure autospectra similar to that suspected in the towed cylinder experiments, which were conducted in large tow tanks and lake-type basins. These spikes are of paramount importance and should be explored further because they may lead to signal-to-noise ratios above acceptable limits.

scholarly journals Phase relationships between velocity, wall pressure, and wall shear stress in a forced turbulent boundary layer

2016 ◽  
Author(s):  
Kevin T. Rosenberg ◽  
Subrahmanyam Duvvuri ◽  
Mitul Luhar ◽  
Beverley J. McKeon ◽  
Casey Barnard ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Wall Pressure ◽  
Wall Shear ◽  
Phase Relationships

Fluctuations in wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow

1991 ◽  
Vol 225 ◽  
pp. 545-555 ◽  
Author(s):  
D. M. Chase
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Stress Component ◽  
Wall Pressure ◽  
Inviscid Limit ◽  
Pressure Amplitude ◽  
Shear Stress Component ◽  
Wall Shear

Turbulent boundary-layer fluctuations in the incompressive domain are expressed in terms of fluctuating velocity-product 'sources’ in order to elucidate relative characteristics of fluctuating wall-shear stress and pressure in the subconvective range of streamwise wavenumbers. Appropriate viscous wall conditions are applied, and results are obtained to lowest order in this Strouhal-scaled wavenumber which serves as the expansion parameter. The spectral amplitudes of pressure and of the shear stress component directed along the wavevector both contain additive terms proportional to source integrals with exponential wall-distance weighting characteristic respectively of the irrotational and the rotational fields. At low wavenumbers, barring unexpected relative smallness of the pertinent boundary-layer source term, the rotational terms become dominant. There the wall pressure and shear-stress component have spectra that approach the same non-vanishing, wavevector-white but generally viscous-scale-dependent level and are totally coherent with phase difference ½π. The other, irrotational contributions to the shear-stress and pressure amplitudes likewise bear a simple and previously known, generally wavevector– and frequency-dependent, ratio to one another. In an inviscid limit this contribution to the pressure amplitude reduces to the one obtained previously from inviscid treatments. A representative class of models is introduced for the source spectrum, and the resulting rotational contribution to the spectral density of wall pressure and K-aligned shear stress at low (but incompressive) wavenumbers is estimated. It is suggested that this contribution may predominate and account for measured low-wavenumber levels of wall pressure.

Decay of fluctuating wall-pressure field of Mach 5 turbulent boundary layer

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1088-1096
Author(s):  
O. H. Unalmis ◽  
D. S. Dolling
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Field ◽  
Wall Pressure
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