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Research Papers

# Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer—Part II: Model Validation and Benchmarking

[+] Author and Article Information
M. Stripf, A. Schulz, H.-J. Bauer, S. Wittig

Lehrstuhl und Institut für Thermische Strömungsmaschinen, Universität Karlsruhe (TH), Kaiserstraße 12, Karlsruhe 76128, Germany

As only the roughness models without the transition model are validated in this section, the model names do not include the affix “-T” (see Ref. 1).

The turbulence intensities quoted in Refs. 17-18 are around 10% higher than the ones given in this paper and in Ref. 19. The authors apologize for this inconsistency and recommend using the new values provided here and in Ref. 19 as they are based on additional extensive measurements of the spectral distributions of turbulence.

J. Turbomach 131(3), 031017 (Apr 20, 2009) (11 pages) doi:10.1115/1.2992512 History: Received June 20, 2008; Revised August 05, 2008; Published April 20, 2009

## Abstract

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity, and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent states. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from (Durbin, , 2001, “Rough Wall Modification of Two-Layer k-ε  ,” ASME J. Fluids Eng., 123, pp. 16–21), which builds on a two-layer $k-ε$-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer $k-ε$-turbulence model by the present authors. The discrete-element model will be formulated in a new way suitable for randomly rough topographies. Part I of this paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors, as well as new experimental data from a low pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

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## Figures

Figure 1

Roughness geometry for the test cases of Hosni (4) and Chakroun (6)

Figure 2

Test cases of Hosni and co-workers (4-5): calculated and measured heat transfer distributions

Figure 3

Test cases of Hosni and co-workers (4-5): calculated and measured friction coefficients

Figure 4

Test cases of Chakroun and co-workers (6-7): freestream velocity distribution

Figure 5

Test cases of Chakroun and co-workers (6-7): calculated and measured Stanton numbers and displacement thicknesses

Figure 6

Roughness geometry for the test cases of Coleman (10-12)

Figure 7

Test cases of Coleman (10-12): freestream velocity distributions

Figure 8

Test cases of Coleman (10-12): calculated and measured Stanton numbers and friction coefficients

Figure 9

Roughness parameters for the surfaces of McClain (14)

Figure 10

Test cases of McClain (14): measured friction coefficients and calculated values using the DEM-TLV model

Figure 11

Geometry of the high and low pressure turbine cascades

Figure 12

Surface roughness and corresponding diameter and porosity distributions for the HPTV test cases

Figure 13

High pressure turbine vane test cases of Stripf and co-workers (17,19): calculated and measured heat transfer distributions

Figure 14

Comparison of the calculated and measured average heat transfer for all high pressure turbine vane test cases

Figure 15

Low pressure turbine vane test cases of Stripf (19): calculated and measured heat transfer distributions at varying roughness heights

Figure 16

Low pressure turbine vane test cases of Stripf (19): calculated and measured heat transfer distributions at varying roughness densities

Figure 17

Surface parameters for the LPTV_40rnd test case

Figure 18

LPTV_40rnd test case: calculated and measured heat transfer distributions at varying Reynolds numbers

Figure 19

Low pressure turbine vane test cases with locally varying surface roughness: calculated and measured heat transfer distributions

Figure 20

LPTV: comparison of the calculated and measured average heat transfer for all test cases

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