Compressible turbulent boundary layers with heat transfer and pressure gradient in flow direction

Abstract

The bes t -kn own t h eor etica l works on boundary-laye r problems, esp ecia lly in t he case of co mpressible flow wi t ho ut or w ith h eat t ransfer, ar e r elated to th e la m in a r bo und ar y layer, although th e t urbulent bound a ry layer is, in practice, often more inte restin g. The la min a r bound ary layer is more ea~ily accessible to theo retical t reatm ent beca use clearly d efin ed r elation s exist betwee n t he v iscos ity !J. a nd the sh ear s tresses T . In the tu rbul ent case, empirica l relations must be in trod uced. Therefor e, a ttemp ts to get exact solu t ion s al'e no t " 'o rthwh il e, while effor ts to obta in ap prox im ate solu t io ns, based for in st a nce on t h e von Karman-Pohlha usen prin cip le (Z. An ge w. Math . u. i\! (" ech. 1, 233 and 252, 1921 ) of util iz ing in teg ra l co nditio ns, a ppear to be a ppropriate to t his problem . In th e las t few yea rs the accu r acy of su ch a pproximate solu t io ns for th e incompressible case was n oticea bl y improved by the a ppli cation of a new e ner gy in tegral co ndition in co n nectio n wi t h a new emp irical law for the dissipat ion in t u rbulent bo unda ry laye rs, stated by J . Ro tta (Ing r-Arc h . 20, 195, 1952) a nd E. Tru cke nbrod t (Ing r-Ar ch. 20, 212, 1952). The emp irical laws for di ssipa t ion a nd for t urbul ent wall fri ction , which a re n eeded in th e p resent a pprox im ate theory, are formu lated o n t h e bas is of av a ila bl e m eas urem e nts fo r in co mpressible fl ow . Ge ner ali zation to th e compressib le flow with h eat t ra nsfer is m a de from phys ical co nsiderat io ns. Calculated r esults ag ree sat isfacto ri ly wi t h ava ila ble ex p erim ental d ata. Some poss ibi li t ies for improving as well as fo r simp lify in g th e a pproximat io n theo ry a re outlined.