T structure of a laminar boundary layer with massive blowing is greatly complicated in view of the viscidinviscid interactions. These interactions result in larger deflection of incident flow and also a significant alteration in the major flow variables including pressure distribution. To date various analytical models have been developed for the prediction of the flowfield. More recently, numerical studies based on the laminar boundary-layer approximation have been developed for the prediction of a boundary-layer flow structure with a prescribed pressure gradient. Methods adopted in the numerical investigation include backward shooting, Libby, Nachtsheim and Green, Liu and Nachtscheim, and matrix method Garrett, Smith, and Perkins. Although it has been shown by Liu and Nachtsheim that the backward shooting technique is stable, its computing timeis long and increases as injection rates increase. Therefore, from an economic point of view, it is highly desirable to devise another stable and yet fast numerical scheme. With this motivation, the authors tried the matrix method resulting from various finite differencing. However, for differential equations with large parasitic eigenvalues such as massive blowing problem, most differencing schemes result in a matrix with large condition number and therefore is unstable. It is the purpose of the present study to propose a fast, stable, and easy to code matrix method of which the number of nodes and rate of convergence (and therefore the computing time) are independent of injection rate.

Fast and stable numerical method for boundary-layer flow with massive blowing

The investigation reported was conducted to clarify the thermodynamic properties of C3 by further developing the limit to the partition function suggested by Strauss and Thiele (1967). A quantum solution for the energy levels of a quadratically perturbed square well potential is presented and the consistency of this limit with observed energy levels is established. In the process a more complete physical picture of the bending C3 molecules emerges. The values of entropy deduced from various measurements of graphite pressure are compared with this limit, and the thermodynamic properties predicted for the limiting case are evaluated.

A quantum model for bending vibrations and thermodynamic properties of C3.

A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.

Shooting Method for Solution of Boundary-Layer Flows with Massive Blowing

By = 0.408%, K = 50.0 for the tensile plastic loading phase and ey = 0.097%, K = 1.90 for the compression plastic phase, Eq. (2) curve-fit the data accurately. A comparison of the measured strain-time history and the theoretical prediction is shown in Fig. 5. As discussed in Ref. 1, the Bauschinger effect reduces peak amplitudes after the first maximum peak and also reduces the final deformation. After 108 /^sec, the ring vibrates elastically; this vibration eventually damps out and the ring is left with a permanent strain of 2.2%. This Note presents an experimental method for expanding rings into the plastic regime and measuring the response. This procedure and the compressive method presented in Ref. 1 provide techniques for experimentally verifying nonlinear dynamic stress-strain laws.

William C. Davy

Papers

Nonequilibrium boundary layer at a stagnation point for a hydrogen-helium stream over ablating graphite