To support reduced order modeling of heat transfer for reentry bodies we develop an approximate solution method is identified that provides good estimates for the local wall derivative (and thereby the skin friction and Nusselt numbers) for a wide range of self-similar laminar formulations. These formulations include: Blasius flow, axisymmetric and planar stagnation flows and the Faulkner-Skan flows. The approach utilized is simply an extension of the classical Weyl formulation for the Blasius equation. Using this solution form estimates that naturally represent combined flow behaviors are represented without post-solution interpolation. An important example, namely axisymmetric stagnation equally combined with laminar zero pressure gradient (flat plate) flow, shows a difference of 10% between the pre-solution combination developed here and s simple post-solution arithmetic average. Clearly, the nonlinearity inherent to these solutions prevails in terms of these simple solutions. Compressible extensions to the basic incompressible result are achieved by including a near wall Chapman-Rubesin term making these solutions suitable for adiabatic wall problems. Direct comparison of the wall gradient estimation procedure developed here demonstrates excellent agreement with empirically fit blunt body heat transfer models such as the asymptotically consistent model of Kemp et. al. which are deemed more appropriate than the classical stagnation point scaling approaches.
展开▼
