scholarly journals Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

2017 ◽  
Vol 826 ◽  
pp. 830-850 ◽  
Author(s):  
Mattias Brynjell-Rahkola ◽  
Nima Shahriari ◽  
Philipp Schlatter ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Sensitivity Analysis ◽  
Surface Roughness ◽  
Energy Transport ◽  
Three Dimensional ◽  
Cross Flow ◽  
Domain Size ◽  
Great Sensitivity ◽  
Discrete Surface ◽  
Roughness Size

With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner–Skan–Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the $\unicode[STIX]{x1D700}$-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

Boundary layer at a swept stagnation line of semi-infinite extent

1970 ◽  
Vol 41 (4) ◽  
pp. 737-750 ◽  
Author(s):  
Paul A. Libby ◽  
Karl K. Chen
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Cross Flow ◽  
Differential Analysis ◽  
Eigenvalues And Eigenfunctions ◽  
Stagnation Line ◽  
Infinite Extent ◽  
Dimensional Boundary ◽  
Upstream Flow

A three-dimensional boundary layer developing along a semi-infinite swept stagnation line from a starting edge and evolving into that associated with such a line of infinite extent is calculated. A series solution useful for assessing the counteracting effects of cross-flow and mass transfer near the starting edge and for providing initial data for a subsequent streamwise, numerical solution is developed. The asymptotic behaviour far from the starting edge is examined and shown to involve only eigenfunction contributions associated with the far upstream flow. However, it is not presently possible to determine the relevant eigenvalues and eigenfunctions. Numerical solutions based on a difference-differential analysis yield the entire development of the boundary layer and indicate the streamwise length required for the case of the boundary layer at an infinite stagnation line to be obtained.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Boundary Layer Effects in the Turbulent Spiral Vortex Flow of a Compressible Fluid

1968 ◽  
Vol 183 (1) ◽  
pp. 179-188 ◽  
Author(s):  
B. F. Scott
Keyword(s):  
Boundary Layer ◽  
Vortex Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Radial Pressure ◽  
Vortex Chamber ◽  
Adiabatic Wall ◽  
Spiral Vortex ◽  
Momentum Integral

Because of the characteristically narrow impeller tip width in a proposed supersonic centrifugal compressor design, boundary layer effects in the vortex chamber are likely to be significant. The radial pressure gradient in the chambers sweeps retarded fluid towards the centre of curvature of the streamlines, thereby creating a ‘cross-flow’ in the boundary layer which is three-dimensional. Although the flow geometry has axial symmetry, the cross-flow is not independent of the streamwise flow. The momentum—integral method is adopted, together with assumptions concerning the velocity profiles; the energy equation is solved with the assumption of an adiabatic wall. Simultaneous solution of the free stream and boundary layer equations yields results emphasizing the critical dependence of the transverse deflection and growth of the boundary layer on the whirl component of the velocity. Separation cannot be predicted, but effects in the free stream can be estimated when the perturbations are small. Although the results are related to compressor performance, the method is generally applicable in situations where the idealizing assumption of spiral vortex flow is acceptable.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Three-Dimensional Calculation of Wall Boundary Layer Flows in Turbomachines

1987 ◽  
Author(s):  
W. L. Lindsay ◽  
H. B. Carrick ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Cross Flow ◽  
Flow Profile ◽  
Boundary Layer Flows ◽  
Wall Boundary Layer ◽  
Boundary Layer Development ◽  
Flow Through ◽  
The Cross

An integral method of calculating the three-dimensional turbulent boundary layer development through the blade rows of turbomachines is described. It is based on the solution of simultaneous equations for (i) & (ii) the growth of streamwise and cross-flow momentum thicknesses; (iii) entrainment; (iv) the wall shear stress; (v) the position of maximum cross-flow. The velocity profile of the streamwise boundary layer is assumed to be that described by Coles. The cross-flow profile is assumed to be the simple form suggested by Johnston, but modified by the effect of bounding blade surfaces, which restrict the cross-flow. The momentum equations include expressions for “force-defect” terms which are also based on secondary flow analysis. Calculations of the flow through a set of guide vanes of low deflection show good agreement with experimental results; however, attempts to calculate flows of higher deflection are found to be less successful.

Boundary Layers over Infinite Yawed Wings

1960 ◽  
Vol 11 (4) ◽  
pp. 333-347 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Free Flow ◽  
Momentum Thickness ◽  
Displacement Thickness

SummaryA method of calculating turbulent boundary layers on infinite yawed wings is given, making use of a method of calculating turbulent boundary layers due to Spence and of an analogy between three-dimensional and axi-symmetric boundary layers. It is also shown that the displacement thickness is equal to that computed using chordwise components and that the streamwise momentum thickness is approximately equal to the chordwise momentum thickness. Shock-free flow and small boundary layer cross-flow are assumed.

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