Unsteady entrance flow in a 90 degrees curved tube

A numerical model enabling the prediction of the axial and secondary velocity fields in three-dimensional configurations at moderate Reynolds numbers and Womersley parameters is presented. Steady and unsteady entrance flows in a 90° curve tube (d = [fraction one-sixth]) under various flow conditions are analysed. The good quality agreement between axial and secondary velocities for a sinusoidally varying flow rate at a Womersley parameter of a = 7.8, obtained from a finite-element calculation, and those obtained from laser-Doppler measurements justify the use of the numerical model. Halfway into the deceleration phase for a sinusoidally varying flow rate (200 <Re <800, a = 7.8) a strong resemblance is found to the steady flow case (Re = 700). In contrast with steady flow, near the inner wall reversed axial flow regions are found halfway into and at the end of the deceleration phase. Throughout the flow cycle the Dean-type secondary flow field highly influences axial flow resulting in a shift of the maximal axial velocity towards the outer wall, C-shaped axial isovelocity lines and an axial velocity plateau near the inner wall. Further downstream in the curved tube the Dean-type secondary vortex near the plane of symmetry is deflected towards the sidewall (’tail’–formation), as is also found for steady flow. An increase of the Womersley parameter (a = 24.7) results in a constant secondary flow field which is probably mainly determined by the steady component of the flow rate. A study on the flow phenomena occurring for a physiologically varying flow rate suggests that the diastolic phase is only of minor importance for the flow phenomena occurring in the systolic phase. Elimination of the steady flow component (- 300 <Re <300) results in a pure Dean-type secondary flow field (no ‘tail’-formation) for a = 7.8 and in a Lyne-type secondary flow field for a = 24.7. The magnitude of the secondary velocities for a = 24.7 are of O(10-2) as compared to the secondary velocities for a = 7.8.