Continuum Mechanics and Thermodynamics

, Volume 30, Issue 2, pp 279–290

# Temperature distribution of a simplified rotor due to a uniform heat source

• Sarah Welzenbach
• Tim Fischer
• Felix Meier
• Ewald Werner
• Sonun Ulan kyzy
• Oliver Munz
Original Article

## Abstract

In gas turbines, high combustion efficiency as well as operational safety are required. Thus, labyrinth seal systems with honeycomb liners are commonly used. In the case of rubbing events in the seal system, the components can be damaged due to cyclic thermal and mechanical loads. Temperature differences occurring at labyrinth seal fins during rubbing events can be determined by considering a single heat source acting periodically on the surface of a rotating cylinder. Existing literature analysing the temperature distribution on rotating cylindrical bodies due to a stationary heat source is reviewed. The temperature distribution on the circumference of a simplified labyrinth seal fin is calculated using an available and easy to implement analytical approach. A finite element model of the simplified labyrinth seal fin is created and the numerical results are compared to the analytical results. The temperature distributions calculated by the analytical and the numerical approaches coincide for low sliding velocities, while there are discrepancies of the calculated maximum temperatures for higher sliding velocities. The use of the analytical approach allows the conservative estimation of the maximum temperatures arising in labyrinth seal fins during rubbing events. At the same time, high calculation costs can be avoided.

### Keywords

Rotating cylindrical body Temperature field Thermal analysis Labyrinth seal system

### List of symbols

a

Contact half length (m)

$$c_p$$

Specific heat ($$\frac{\text {J}}{\text {kg}\,\text {K}}$$)

$$\delta$$

Heat penetration depth (m)

h

Heat transfer coefficient ($$\frac{\text {W}}{\text {m}^\text {2}\,\text {K}}$$)

$$h_{0}$$

Reference heat transfer coefficient ($$\frac{\text {W}}{\text {m}^\text {2}\,\text {K}}$$)

$$h^{*}$$

Dimensionless heat transfer coefficient (–)

$$\kappa$$

Thermal diffusivity ($$\frac{\text {m}^\text {2}}{\text {s}}$$)

$$\lambda$$

Thermal conductivity ($$\frac{\text {W}}{\text {m}\,\text {K}}$$)

$$\lambda _{0}$$

Reference thermal conductivity ($$\frac{\text {W}}{\text {m}\,\text {K}}$$)

$$\lambda ^{*}$$

Dimensionless thermal conductivity (–)

Pe

Peclet number (–)

$$\dot{q}$$

Heat source intensity ($$\frac{\text {W}}{\text {m}^\text {2}}$$)

r

$$\rho$$

Density ($$\frac{\text {kg}}{\text {m}^\text {3}}$$)

s

Sliding distance (m)

T

Temperature ($$^\circ \text {C}$$)

$$T_{\text {max}}$$

Maximum temperature ($$^\circ \text {C}$$)

$$T_{\text {max}}^{\text {analytical}}$$

Maximum temperature (analytical approach) ($$^\circ \text {C}$$)

$$T_{\text {max}}^{\text {2D}}$$

Maximum temperature (two-dimensional model) ($$^\circ \text {C}$$)

$$\theta$$

Spatial function of the temperature profile (–)

$$u_z$$

Displacement (m)

v

Circumferential/sliding velocity ($$\frac{\text {m}}{\text {s}}$$)

x

x-coordinate (m)

$$\xi$$

Dimensionless x-coordinate (–)

y

y-coordinate (m)

z

z-coordinate (m)

$$\zeta$$

Dimensionless z-coordinate (–)

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## Notes

### Acknowledgements

The authors acknowledge the financial support from the Deutsche Forschungsgemeinschaft through the project “Rub-in processes in turbines - experimental investigation and modeling” (WE 2351/14-1). The authors appreciate the technical input of the MTU Aero Engines, given by Dr. Beate Schleif.

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© Springer-Verlag GmbH Germany 2017

## Authors and Affiliations

• Sarah Welzenbach
• 1
• Tim Fischer
• 1
• Felix Meier
• 1
• Ewald Werner
• 1
• Sonun Ulan kyzy
• 2
• Oliver Munz
• 3
1. 1.Institute of Materials Science and Mechanics of MaterialsTechnical University of MunichGarchingGermany
2. 2.Metals and AlloysUniversity of BayreuthBayreuthGermany
3. 3.Institute of Thermal TurbomachineryKarlsruhe Institute of TechnologyKarlsruheGermany