Examination of the Stability of Disturbed Boundary-Layer Flow by a Numerical Method

1969 ◽  
Vol 12 (12) ◽  
pp. II-139
Author(s):  
Stefan Loer
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Boundary Layer Flow ◽  
Layer Flow ◽  
The Stability

scholarly journals Numerical Solutions of Unsteady Boundary Layer Flow with a Time-Space Fractional Constitutive Relationship

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1446
Author(s):  
Weidong Yang ◽  
Xuehui Chen ◽  
Yuan Meng ◽  
Xinru Zhang ◽  
Shiyun Mi
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Constitutive Relationship ◽  
Elastic Behavior ◽  
Unsteady Boundary Layer ◽  
Time Space ◽  
Layer Flow ◽  
Fractional Parameter

In this paper, we develop a new time-space fractional constitution relation to study the unsteady boundary layer flow over a stretching sheet. For the convenience of calculation, the boundary layer flow is simulated as a symmetrical rectangular area. The implicit difference method combined with an L1-algorithm and shift Grünwald scheme is used to obtain the numerical solutions of the fractional governing equation. The validity and solvability of the present numerical method are analyzed systematically. The numerical results show that the thickness of the velocity boundary layer increases with an increase in the space fractional parameter γ. For a different stress fractional parameter α, the viscoelastic fluid will exhibit viscous or elastic behavior, respectively. Furthermore, the numerical method in this study is validated and can be extended to other time-space fractional boundary layer models.

The stability of boundary-layer flow over single-and multi-layer viscoelastic walls

1988 ◽  
Vol 196 ◽  
pp. 359-408 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Single Layer ◽  
Viscous Sublayer ◽  
Rigid Base ◽  
Theoretical Treatment ◽  
Dynamical Condition ◽  
Compliant Walls ◽  
Layer Flow ◽  
The Stability

In this paper, we are concerned with the linear stability of zero pressure-gradient laminar boundary-layer flow over compliant walls which are composed of one or more layers of isotropic viscoelastic materials and backed by a rigid base. Wall compliance supports a whole host of new instabilities in addition to the Tollmien-Schlichting mode of instability, which originally exists even when the wall is rigid. The perturbations in the flow and the compliant wall are coupled at their common interface through the kinematic condition of velocity continuity and the dynamical condition of stress continuity. The disturbance modes in the flow are governed by the Orr-Sommerfeld equation using the locally-parallel flow assumption, and the response of the compliant layers is described using a displacement-stress formalism. The theoretical treatment provides a unified formulation of the stability eigenvalue problem that is applicable to compliant walls having any finite number of uniform layers; inclusive of viscous sublayer. The formulation is well suited to systematic numerical implementation. Results for single- and multi-layer walls are presented. Analyses of the eigenfunctions give an insight into some of the physics involved. Multi-layering gives a measure of control over the stability characteristics of compliant walls not available to single-layer walls. The present study provides evidence which suggests that substantial suppression of disturbance growth may be possible for suitably tailored compliant walls.

scholarly journals The centrifugal instability of the boundary-layer flow over slender rotating cones

2014 ◽  
Vol 755 ◽  
pp. 274-293 ◽  
Author(s):  
Z. Hussain ◽  
S. J. Garrett ◽  
S. O. Stephen
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Rotating Disk ◽  
Alternative Formulation ◽  
Centrifugal Instability ◽  
Half Angle ◽  
Layer Flow ◽  
The Stability ◽  
Experimental And Theoretical Studies ◽  
Numerical Approaches

AbstractExisting experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

The effect of buoyancy forces on the boundary-layer flow over a semi-infinite vertical flat plate in a uniform free stream

1969 ◽  
Vol 35 (3) ◽  
pp. 439-450 ◽  
Author(s):  
J. H. Merkin
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Method ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Leading Edge ◽  
Series Solutions ◽  
Buoyancy Forces ◽  
Layer Flow ◽  
Vertical Flat Plate

The boundary-layer flow over a semi-infinite vertical flat plate, heated to a constant temperature in a uniform free stream, is discussed in the two cases when the buoyancy forces aid and oppose the development of the boundary layer. In the former case, two series solutions are obtained, one of which is valid near the leading edge and the other is valid asymptotically. An accurate numerical method is used to describe the flow in the region where the series are not valid. In the latter case, a series, valid near the leading edge is obtained and it is extended by a numerical method to the point where the boundary layer is shown to separate.

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