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Numerical study of the thermal development in a rotating cooling passage

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Abstract

In the present study, the fully developed turbulent secondary flows inside rotating square-upstream section and rectangular downstream section oriented at several angles with axis rotation are numerically simulated using the low Reynolds Non-linear \( k - \omega \), \( k - \varepsilon \) Reynolds-Stress Model (RSM), and Large Eddy Simulation (LES) models. The two flat walls are heated (leading and trailing sides), while the outer wall and the splitter plate are thermally insulated. The simulation has been done at Re = 36,000 with different rotation numbers from Ro = −0.4 to Ro = 0.4, where negative Ro values refer to counter-clock wise and positive Ro values refer to clock wise sense of rotation. This enables to investigate the effects on the thermal development of the rotation numbers. The effects of minor modifications, in cross section area at the bend exit, on thermal development, under rotating conditions, can also be explored. The interactions between secondary flows and separation lead to very complex flow patterns. To accurately simulate these flows and heat transfer, both refined turbulence models and higher-order numerical schemes are indispensable for turbine designers to improve the cooling performance. Previous studies have shown that the flow and heat transfer features through curved bends, even with a moderate curvature, cannot be accurately simulated. It is the conventional belief and practice that the usage of a proper turbulence model and a reliable numerical method for achieving accurate computations. It is shown that the present RSM model produces satisfactory predictions of the flow development inside the sharp U-bend comparing with the experiments (Iacovides et al. 2006). In the present study, three turbulence models are used to predict Nusselt number distribution. The results were further compared with the LES computations and discussed the difference between the turbulence models and the LES as well.

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Abbreviations

a, c:

Weighted average coefficients

\( C_{i} (i = 1\sim 9) \) :

Turbulence modeling constants in Eq. 3

D :

Hydraulic diameter

f k :

Coriolis force

k :

Turbulence kinetic energy

LES:

Large eddy simulation

M t :

Turbulent mach number

Nu :

Local nusselt number

P :

Mean pressure

P k :

Generation rate of \( \overline{{u_{i} u_{j} }} \)

Pr:

Fluid Prandtl number

R c :

Radius of curvature of U-bend to the midpoint of curved duct

Ro:

Rossby number (rotation number) (ΩD/W b )

Re:

Flow Reynolds number \( \left( { \equiv W_{b} D/v} \right) \)

R k , R β, R ω :

Model constants

RSM:

Reynolds-stress model

S ij :

Deformation tensor

U :

Mean velocity in cross duct direction

U i :

Mean velocity tensor

\( \overline{{u_{i} u_{j} }} \) :

Reynolds stress tensor

W :

Mean velocity in streamwise direction

W b :

Bulk velocity

x :

Crossduct direction

y :

Direction normal to the duct symmetry plane

z :

Streamwise direction

\( \delta_{ij} \) :

Kronecker delta

εijk :

Third order skew-symmetric unit tensor

\( \omega \) :

Specific dissipation rate

\( \Upomega_{ij} \) :

Vorticity tensor

\( \mu , { }\mu_{\text{t}} \) :

Laminar and turbulence viscosity

\( \alpha_{0} ,\alpha_{0}^{*} ,\beta \) :

Model constants

\( \Upphi \) :

Transport variable

ρ:

Density

ε:

Turbulence dissipation

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Acknowledgments

The original paper was presented at ASME Turbo Expo 2008: Power for Land, Sea, and Air (GT2008). The authors are grateful for ASME for granting a permission of this paper to publish in Heat and Mass Transfer.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA

    R. S. Amano, Jose Martinez Lucci, Krishna Guntur & B. Song

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  1. R. S. Amano
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  2. Jose Martinez Lucci
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  3. Krishna Guntur
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  4. B. Song
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Correspondence to R. S. Amano.

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Amano, R.S., Lucci, J.M., Guntur, K. et al. Numerical study of the thermal development in a rotating cooling passage. Heat Mass Transfer 48, 1011–1022 (2012). https://doi.org/10.1007/s00231-011-0940-3

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  • DOI: https://doi.org/10.1007/s00231-011-0940-3

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