The effects of passive wall porosity on the linear stability of boundary layers

A two-dimensional and quasi three-dimensional model has been developed which enables the stability characteristics of laminar boundary layer flows over porous surfaces to be evaluated. The theory assumes the porosity to be continu- ous over a fixed portion of the computational domain. The chosen configuration also assumes a continuous plenum chamber, of variable depth, beneath the thin porous boundary. It has been suggested that surfaces of this type may be of use in the delay of a laminar boundary-layer's transition to turbulence. Hence, a pro- gram of study, involving both simulation and experimentation, was initiated to catalogue the effects of porosity. The numerical model consists of two sets of coupled solutions; one describing the cavity dynamics and the other describing the flow above the porous surface. The two systems are coupled together using their common wall boundary condi- tion. This is defined in terms of a complex function which attempts to model the effects of the viscous and inertial stresses within the fluid as it periodically flows through the wall into the cavity. Essentially, the function defines the magnitude and phase relationship between the pressure across the porous boundary and the flow through it. The cavity dynamics are determined by an analytical solution to the Orr-Sommerfeld equation in the absence of a mean flow field. The upper boundary condition for this flow is provided by the admittance function of the porous surface. The Orr-Sommerfeld equation is then solved again for the boundary layer flow - with the mean flow provided by solutions to the Falkner-Skan (or Falkner-Skan-Cooke) group of similarity profiles. This solution uses the admittance function to define its lower boundary condition. A high accuracy spectral technique, using Cheby- shev polynomials, is used for the integration of the Orr-Sommerfeld equation. Numerical simulations suggest that the appropriate selection of cavity depth and porosity fraction can lead to a complete suppression of the Toflmien-Schlichting instability for the case of zero pressure gradient. The model also suggests that The cavity dynamics are determined by an analytical solution to the Orr-Sommerfeld equation in the absence of a mean flow field. The upper boundary condition for this flow is provided by the admittance function of the porous surface. The Orr-Sommerfeld equation is then solved again for the boundary layer flow - with the mean flow provided by solutions to the Falkner-Skan (or Falkner-Skan-Cooke) group of similarity profiles. This solution uses the admittance function to define its lower boundary condition. A high accuracy spectral technique, using Cheby- shev polynomials, is used for the integration of the Orr-Sommerfeld equation. Numerical simulations suggest that the appropriate selection of cavity depth and porosity fraction can lead to a complete suppression of the Toflmien-Schlichting instability for the case of zero pressure gradient. The model also suggests that surface produced a self-sustained cavity oscillation whose magnitude could be up to 40% of the free-stream flow speed. These oscillations were found to be caused by a shear layer instability, self-excited by the feedback of disturbances caused by the shear layer's own impingement on the downstream cavity edge. A theoretical model for the instability has been developed which gives qualitative agreement with the experimental results. However, various cavity baffle configurations ul- timately failed to remove the instability. Hence, linear experiments on the 10% porous surface were not possible. The final two chapters of the thesis concern the stability of a general three- dimensional boundary layer when the PPW boundary condition is applied. Flows with varying degrees of streamwise pressure gradient and sweep were considered. It was noted, for the zero sweep case, that flows which exhibited viscous instabil- ity with decelerating fluid (tending towards inviscid instability) performed rather poorly when influenced by the PPW boundary condition. Furthermore, a wholly inviscid mechanism, such as that exhibited by the crossflow instability, was seen to have massively increased growth rates under the action of passive wall poros- ity. These two observations where seen as independent evidence in support of the prediction that the PPW boudary-condition is only theoretically of use when instabilities are wholly viscous.