0
TECHNICAL PAPERS

# Direct Numerical Simulations of Transitional Flow in Turbomachinery

[+] Author and Article Information
J. G. Wissink

Institute for Hydromechanics, University of Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germanywissink@ifh.uni-karlsruhe.de

W. Rodi

Institute for Hydromechanics, University of Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germanyrodi@ifh.uni-karlsruhe.de

J. Turbomach 128(4), 668-678 (Feb 02, 2006) (11 pages) doi:10.1115/1.2218517 History: Received February 02, 2005; Revised February 02, 2006

## Abstract

An overview is provided of various direct numerical simulations (DNS) of transitional flows in turbine-related geometries. Two flow cases are considered: the first case concerns separating flow over a flat plate and the second case flows in turbine cascades. In the first case, in which $Re=60,000$, either an oscillating oncoming flow (1) or a uniform flow with and without oncoming turbulent free-stream fluctuations (2) is prescribed at the inlet. In both subcases (1) and (2), separation is induced by a contoured upper wall. In (1), the separated boundary layer is found to roll up due to a Kelvin-Helmholtz (KH) instability. This rolled-up shear layer is subject to spanwise instability and disintegrates rapidly into turbulent fluctuations. In (2), a massive separation bubble is obtained in the simulation without oncoming free-stream fluctuations. A KH instability is eventually triggered by numerical round-off error and is followed again by a rapid transition. With oncoming turbulent fluctuations, this KH instability is triggered much earlier and transition is enhanced, which leads to a drastic reduction in size of the separation bubble. The second case, concerning flow in turbine cascades, includes (1) flow in the T106 turbine cascade with periodically oncoming wakes at $Re=51,800$ and (2) flow and heat transfer in a MTU cascade with oncoming wakes and background turbulence at $Re=72,000$. In the simulation of flow in the T106 cascade with oncoming wakes, the boundary layer along the downstream half of the suction side is found to separate intermittently and subsequently rolls up due to a KH instability leading to separation-induced transition. At times when the wakes impinge separation is suppressed. In the simulations of flow around a MTU turbine blade, evidence of by-pass transition in the suction-side boundary-layer flow is observed while the pressure-side boundary layer remains laminar in spite of significant fluctuations present. In agreement with the experiments, the impinging wakes cause the heat transfer coefficient to increase significantly in the transitional suction-side region close to the trailing edge and by about 30% on the pressure side. The large increase in heat transfer in the pre-transitional suction-side region observed in the experiments could not be reproduced. The discrepancy is explained by differences in spectral contents of the turbulence in the oncoming wakes.

<>

## Figures

Figure 16

Time-averaged shape factor H along the suction side and comparison to Experiment C

Figure 17

Simulations I & II: Time-averaged Nusselt number Nu as a function of the normalized wall-coordinate; comparison to experiments

Figure 18

Simulation M2: Two snapshots showing instantaneous vortical structures along the pressure side of the blades

Figure 19

Contours of the instantaneous v-velocity, illustrating the appearance of turbulent spots near the trailing edge in the suction side boundary layer (simulation M2)

Figure 1

Computational domain at midspan

Figure 2

Energy spectrum of the free-stream disturbances added at the inlet

Figure 3

Evolution of the separation bubble during one period of inflow oscillation. The contours correspond to negative phase-averaged friction velocity. (a) Simulation O1, (b) simulation O2, and (c) simulation O3.

Figure 4

Simulation O1: sequence of isosurfaces of the spanwise vorticity. Label “I” identifies the roll of recirculating flow and label “II” the remainder of the separation bubble as discussed previously.

Figure 5

Simulation O3: sequence of isosurfaces of the spanwise vorticity. Label “I” identifies the roll of recirculating flow discussed previously.

Figure 6

Spectra of the v-velocity at four points, P1–P4. The location of the points is identified in the lower graphs showing contours of the time-averaged spanwise vorticity.

Figure 7

Isosurfaces of the spanwise vorticity. (a) Simulation F1 and (b) simulation F3.

Figure 8

Time-averaged shape factor H; comparison of simulations F1, F2, and F3

Figure 9

Computational domain of the T106A cascade at midspan

Figure 10

Wall static-pressure coefficient for simulations T1 (a) and T2 (b) and comparison to experiment (16)

Figure 11

Phase-averaged fluctuating kinetic energy in the passage between blades (simulation T2)

Figure 12

Simulation T2: snapshots showing instantaneous vortical structures near the suction side

Figure 13

Simulation T2: Roll-up of separated shear layer

Figure 14

Wall static-pressure coefficient for simulations M1 (a) and M2 (b) as a function of the normalized wall coordinate s∕s0 and comparison to experiment

Figure 15

Simulation M2: Snapshots showing instantaneous vortical structures in the passage between blades

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections