A power-series solution for the unsteady laminar boundary-layer flow in an expansion wave of finite width moving through a gas initially at rest

Nathaniel B. Cohen
naca-tn-3943
Jun 1957


The equations of motion and energy for the laminar boundary-layer flow in an expansion wave of finite width moving into undisturbed fluid, such as in a shock tube, were considered. Solutions in the form of infinite power series for velocity and local enthalpy functions were indicated, and the first three terms of each series were numerically evaluated. Validity of the numerical results was restricted to the region near the leading edge of the expansion wave. Skin friction and heat transfer were compared with values given by a solution which considered the expansion wave as equivalent to a line discontinuity across which existence of isentropic expansion relations was assumed. These solutions were shown to be very different, qualitatively as well as quantitatively. Singularities in the flow field were discussed in regard to both the finite-width expansion-wave and the line-expansion -wave solutions.

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