Effect of Suction on the Stability of Supersonic Boundary Layers. Part I—Second-Mode Waves

1991 ◽  
Vol 113 (4) ◽  
pp. 591-597 ◽  
Author(s):  
A. A. Al-Maaitah ◽  
A. H. Nayfeh ◽  
J. A. Masad
Keyword(s):  
Mach Number ◽  
Boundary Layers ◽  
Mass Flux ◽  
Two Dimensional ◽  
Second Mode ◽  
Wave Numbers ◽  
Stabilizing Effect ◽  
Dimensional Boundary ◽  
The Stability ◽  
And Shifts

The effect of suction on the second (Mack) mode of instability in supersonic and hypersonic two-dimensional boundary layers is investigated. The results show that suction has a stabilizing effect on these waves; it reduces the peak amplification and shifts it toward a higher frequency. In the presence of suction, the most amplified Mack mode remains two-dimensional. The effectiveness of suction in stabilizing Mack waves decreases as the Mach number increases. Variations of the growth rates of the most amplified Mack mode and the corresponding frequencies and wave numbers with mass flux are found to be almost linear. The frequencies and wave numbers corresponding to the most amplified Mack mode increase by increasing the suction level.

Effect of Suction on the Stability of Supersonic Boundary Layers. Part II—First-Mode Waves

1991 ◽  
Vol 113 (4) ◽  
pp. 598-601 ◽  
Author(s):  
J. A. Masad ◽  
A. H. Nayfeh ◽  
A. A. Al-Maaitah
Keyword(s):  
Boundary Layers ◽  
Mass Flux ◽  
Growth Rates ◽  
Two Dimensional ◽  
Viscous Instability ◽  
Dimensional Boundary ◽  
Mach Numbers ◽  
The Stability

The effect of suction on the first mode of instability of compressible two-dimensional boundary layers is investigated. Suction is found to be more effective in stabilizing the viscous instability, and hence it is more effective at low Mach numbers. Suction decreases the amplification rates at all frequencies and narrows down the band of unstable frequencies. Moreover, for a given frequency, suction decreases the amplification rates at all streamwise locations. Variations of the growth rates of the most amplified first-mode waves with mass flux are found to be almost linear.

Modeling of External Pressure Gradient Influence on the Stability of Disturbances in the Boundary Layers of Compressed Gas

2013 ◽  
Vol 8 (4) ◽  
pp. 64-75
Author(s):  
Sergey Gaponov ◽  
Natalya Terekhova
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
External Pressure ◽  
Transition To Turbulence ◽  
Compressed Gas ◽  
High Mach ◽  
The Stability ◽  
Very High

This work continues the research on modeling of passive methods of management of flow regimes in the boundary layers of compressed gas. Authors consider the influence of pressure gradient on the evolution of perturbations of different nature. For low Mach number M = 2 increase in pressure contributes to an earlier transition of laminar to turbulent flow, and, on the contrary, drop in the pressure leads to a prolongation of the transition to turbulence. For high Mach number M = 5.35 found that the acoustic disturbances exhibit a very high dependence on the sign and magnitude of the external gradient, with a favorable gradient of the critical Reynolds number becomes smaller than the vortex disturbances, and at worst – boundary layer is destabilized directly on the leading edge

On the stability of plane shock waves

1957 ◽  
Vol 2 (4) ◽  
pp. 397-411 ◽  
Author(s):  
N. C. Freeman
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Plane Shock ◽  
Two Dimensional ◽  
Small Perturbations ◽  
Diverging Channel ◽  
Maximum Stability ◽  
The Stability ◽  
Fourier Type

The decay of small perturbations on a plane shock wave propagating along a two-dimensional channel into a fluid at rest is investigated mathematically. The perturbations arise from small departures of the walls from uniform parallel shape or, physically, by placing small obstacles on the otherwise plane parallel walls. An expression for the pressure on a shock wave entering a uniformly, but slowly, diverging channel already exists (given by Chester 1953) as a deduction from the Lighthill (1949) linearized small disturbance theory of flow behind nearly plane shock waves. Using this result, an expression for the pressure distribution produced by the obstacles upon the shock wave is built up as an integral of Fourier type. From this, the shock shape, ξ, is deduced and the decay of the perturbations obtained from an expansion (valid after the disturbances have been reflected many times between the walls) for ξ in descending power of the distance, ζ, travelled by the shock wave. It is shown that the stability properties of the shock wave are qualitatively similar to those discussed in a previous paper (Freeman 1955); the perturbations dying out in an oscillatory manner like ζ−3/2. As before, a Mach number of maximum stability (1·15) exists, the disturbances to the shock wave decaying most rapidly at this Mach number. A modified, but more complicated, expansion for the perturbations, for use when the shock wave Mach number is large, is given in §4.In particular, the results are derived for the case of symmetrical ‘roof top’ obstacles. These predictions are compared with data obtained from experiments with similar obstacles on the walls of a shock tube.

scholarly journals Damage zone propagation and support pressure estimation around two access tunnels of the Barapukuria coalmine in Bangladesh: a two-dimensional numerical modeling approach

2015 ◽  
Vol 3 (2) ◽  
pp. 14
Author(s):  
Md. Rafiqul Islam ◽  
Mohammed Omar Faruque ◽  
Ryuichi Shinjo
Keyword(s):  
Damage Zone ◽  
Support Pressure ◽  
Two Dimensional ◽  
Weak Rocks ◽  
Strength Factor ◽  
Internal Support ◽  
Dimensional Boundary ◽  
Pressure Estimation ◽  
The Stability ◽  
Two Stages

<p>The present study uses a two-dimensional boundary element method (BEM) numerical analysis to predict damage zone propagation associated with the required support pressure estimation around the two access tunnels of Barapukuria coalmine in northwest Bangladesh. Two tunnels at different depths are presented here. The stability of the two tunnels that was driven through the weak rocks' strata of Gondwana formation is examined at depths below the surface 290 m and 453 m. The two tunnels involve horseshoe-shaped design. The shallower tunnels, which are located below the surface 290 m, are presented by model A. The deeper tunnels, which are located below the surface 453 m, are presented by model B. Both tunnels are horseshoe-shaped with a height and span of about 4.5 m and 4 m, respectively. The modeling analysis was carried out in two stages to predict the damage zone and required support pressure. The first stage considered the model without support installation. The second stage measured the model with non-uniform internal support pressure installation. It is reasonable to mention that prior and subsequent to the support pressure estimation, three important parameters, like- strength factor, failure trajectories, and deformation boundaries in the vicinity of the two tunnels have been computed properly. Final results reveal that the strength factor values ranged from 0.33 to 0.99 would create the intense deformation at the roof and sidewalls. The damage zone would be extended from 0.64 to 0.74 m towards the roof and sidewalls. The damage zone would be ranged from 1.95 to 2.21 m, for shallower and deeper tunnels, respectively. For shallower tunnels, the required support pressure would be ranged from 4.0 to 9.0 MPa. For deeper tunnels, the essential support pressure would be ranged from 7.0 to 14 MPa.</p>

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