A finite-difference procedure is employed to predict the turbulent flow in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction. The flows were treated as “parabolic” and the turbulence model used involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. Agreement with experimental data is good for a constant-area duct at low rotation, but less satisfactory for a divergent duct at larger rotation. It is argued that a “partially-parabolic” procedure will be needed to predict the latter flow correctly.

A calculation procedure is described for three-dimensional duct-flow situations which are partially-parabolic in nature, i.e. those in which convective influences pass only downstream, diffusive influences are directed across the stream, but influences are transmitted from downstream regions to upstream ones by way of pressure. The numerical calculation procedure handles such flows economically; it stores the pressure as a three-dimensional array, but other variables two-dimensionally. As an illustration, the results from an application of the calculation procedure are compared with those of a parabolic calculation procedure.

SummaryThe paper describes the application of a recently developed numerical scheme to the computation of the flow in a curved duct. The flow situation is partially-parabolic in nature as there are significant elliptic effects, which are transmitted through the pressure field. The turbulence model used comprises two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. It has been observed that the predictions using the new procedure agree very satisfactorily with the experimental data. Comparisons are also made with the predictions of a fully-parabolic calculation procedure.

A finite-difference procedure is employed to predict the development of turbulent flow in curved pipes. The turbulence model used involves the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. The predicted total-velocity contours for the developing flow in a 180° bend are compared with the experimental data. Predictions of fully developed velocity profiles for long helically wound pipes are also presented and compared with experimental measurements.

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A calculation procedure for three-dimensional parabolic flows is applied to predict the velocity and temperature fields in helically coiled pipes. The curvature produces a secondary flow and causes departures from the symmetric velocity profile of Poiseuille flow. Predictions are presented of flow and heat transfer in the developing and fully developed regions. Comparisons of the developing and fully developed velocity profiles with experimental data exhibit good agreement. The development of the wall temperature for the case of axially uniform heat flux with an isothermal periphery has been compared with experimental data and the agreement is good. Predictions for fully developed temperature profiles and heat-transfer coefficients also exhibit good agreement with experimental data. Effects of the Dean number on the friction factor and heat transfer are presented.