The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and no-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive ‘O’-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (∼ 80–150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.
A numerical solution procedure for the ensemble-averaged, compressible, time-dependent Navier-Stokes equations is applied to predict the flow about a cascade of airfoils operating in the transonic flow regime. The equations are solved by the consistently split, linearized block implicit (LBI) method of Briley and McDonald. Boundary conditions are set so as to specify upstream total pressure and downstream static pressure. Turbulence is modeled by a mixing length model. Predictions are made for flow through a compressor cascade configuration. The method yields converged solutions within a relatively small number of time steps ( ≈ 150), which give good comparisons with experimental data.
SummaryA method is presented for predicting the behaviour of a two-dimensional supersonic turbulent near-wake during the recompression process. In contrast to most previous extensions of Crocco-Lees strong interaction theory, the proposed analysis includes a transverse momentum integral equation. In addition, a modified strip method for conservation of streamwise momentum replaces the usual integral equations. Although a straightforward treatment of the equations results in the appearance of a singularity analogous to the well-known Crocco-Lees critical point, it is shown that solutions can be obtained which do not exhibit a singular behaviour, either by posing the problem as a boundary-value problem rather than an initial-value problem or by making a suitable approximation which suppresses the quasi-elliptic behaviour of the equations. Both procedures lead to an unambiguously defined uniqueness condition for the near-wake recompression solution.
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