scholarly journals Analysis of Unsteady Laminar Boundary Layer Flow by an Integral Method

1973 ◽  
Vol 95 (2) ◽  
pp. 237-247 ◽  
Author(s):  
R. W. Miller ◽  
L. S. Han
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Integral Method ◽  
Momentum Equation ◽  
Asymptotic Solutions ◽  
Mean Flow ◽  
Boundary Layer Flows ◽  
Approximate Integral ◽  
Layer Flow

An approximate integral method of analysis is developed for unsteady laminar boundary layer flows. The case of a flat plate in a free stream with small harmonic velocity oscillations about a steady mean is used to formulate the method. Results are compared with the available experimental data. The essence of the method is to: First obtain asymptotic solutions for limiting cases of the flow under consideration. Then, assume velocity profiles with sufficient generality to include the asymptotic solutions. The profile form functions are determined by applying integral relations (velocity weighted averages of the momentum equation) and compatibility conditions (normal derivatives of the momentum equation evaluated at the boundary). As an example of the method, the second-order mean flow correction is determined for oscillating flow over a flat plate.

scholarly journals The Simulation of Vortex Structures Induced by Different Local Vibrations at the Wall in a Flat-Plate Laminar Boundary Layer

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 563 ◽  
Author(s):  
Weidong Cao ◽  
Zhixiang Jia ◽  
Qiqi Zhang
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Maximum Amplitude ◽  
Vortex Structures ◽  
Mean Flow ◽  
Flow Shear ◽  
Local Vibration ◽  
Compact Finite Difference Scheme ◽  
Derivative Term

The compact finite difference scheme on non-uniform meshes and the Fourier spectral hybrid method are used to directly simulate the evolution of vortex structures in a laminar boundary layer over a flat plate. To this end, two initial local vibration disturbances, namely, the positive–negative and the negative–positive models, at the wall were adopted. The numerical results show that the maximum amplitudes of vortex structures experience a process of linear growth and nonlinear rapid growth. The vertical disturbance velocity and mean flow shear and the derivative term of the stream-wise disturbance velocity and the span-wise disturbance velocity, are important factors for vortex structure development; the high- and low-speed stripe and the stream-wise vortex are consistent with structures seen in full turbulence. The maximum amplitude of the negative–positive model grows more quickly than that of the negative–positive model, and the detailed vortex structures are different for the two models. The mean flow profiles both become plump, which leads to the instability of the laminar boundary layer. The way in which the disturbance is generated with different local vibrations influences the dynamics of vortex structures in a laminar boundary layer.

scholarly journals Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat plate

1988 ◽  
Vol 186 ◽  
pp. 223-241 ◽  
Author(s):  
B. Y. Wang ◽  
I. I. Glass
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Expansion Method ◽  
Boundary Layer Flows ◽  
Two Phase ◽  
Displacement Thickness ◽  
Slip Region ◽  
Two Phases

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

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