*3.2.2 T106 turbine cascade*

T106 turbine cascade experiment was designed to investigate the interaction of a convected wake and a separation bubble on the suction surface of a highly loaded low-pressure turbine blade. In these experiments by Stieger et al. [35], five-blade cascade of T106 profile was placed downstream of a moving bar wake generator in order to simulate an unsteady wake passing environment of a turbomachine. In the experiment, the flow conditions correspond to a Reynolds number of nearly 91,000 based on the chord length of the T106 profile and the inlet velocity. The

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**Figure 6.**

**Figure 5.**

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications*

experimental turbulence intensity is specified to be 0.1%. Geometric details of the experimental cascade setup are given in **Table 2**. Comparison of the experimental and numerical pressure coefficient distributions for T106 cascade for the steady case is depicted in **Figure 7**. Looking at **Figure 7**, it is observed that the separation bubble on the blade predicted by the B-C model and the two-equation γ-Reθ model

Two twisted and tapered 10-meter diameter turbine blades that use the S809 airfoil profile are tested in the NASA Ames Research Center wind tunnels [36, 37]. In the experiments, the NREL wind turbine rotation speed was set to 72 RPM for all

**Figure 8** compares the pressure coefficient distributions over various spanwise locations on the turbine blades at the freestream velocity of 7 m/s. It is observed

is slightly smaller in size than the experimentally measured bubble.

**3.3 3-D wing test cases from low to high speeds**

cases, whereas the wind speeds varied from 7 to 25 m/s.

*Pressure coefficient distribution comparison for the S809 airfoil at 1̊.*

*3.3.1 Low speed rotating wind turbine blade*

*S809 airfoil transition location comparison.*

*DOI: http://dx.doi.org/10.5772/intechopen.83520*

**Figure 4.** *S809 airfoil (a) lift coefficients and (b) drag coefficients at M = 0.15 and Re = 2 M.*

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications DOI: http://dx.doi.org/10.5772/intechopen.83520*

#### **Figure 5.**

*Boundary Layer Flows - Theory, Applications and Numerical Methods*

subsequent variable pressure gradient region is obtained.

**3.2 Airfoil and turbomachinery test cases**

quite well by all the models (**Figure 6**).

*3.2.2 T106 turbine cascade*

*3.2.1 S809 airfoil*

the laminar region was rather inaccurate. Finally, for the T3C5 case, solution of the zero-equation B-C model [20], Menter et al. one-equation γ model [22], and WA-γ model [24] well agree with the experiment in the laminar region, the onset of transition is also fairly good with some delay, and again quite good agreement in the

The S809 airfoil is a 21% thick profile, which specifically designed for horizontal-axis wind turbine applications. The S809 airfoil was tested in a low-turbulence wind tunnel (Tu = 0.2%) by Somers [34] at Re number of 2 million (based on chord length) and a Mach number of 0.15. Comparison of the numerical results by Langtry and Menter [11] γ-Reθ, Walters and Cokljat [14] k-kL-ω, and Medida [31] SA-γ-Reθ and B-C models [20] with the experimental data is given in **Figures 4**–**6**. In general, all transition models agree well with the experimental data until the stall angle. Although the lift and drag coefficients (**Figure 4**) are rather inaccurate after the stall angle, it is observed that the experimental measurements of the transition locations are quite successfully predicted by all models (**Figure 5**). Also, comparing the experimental and numerical pressure coefficient distributions on the S809 airfoil at 1̊ angle of attack, it is observed that the separation bubble is predicted

T106 turbine cascade experiment was designed to investigate the interaction of a convected wake and a separation bubble on the suction surface of a highly loaded low-pressure turbine blade. In these experiments by Stieger et al. [35], five-blade cascade of T106 profile was placed downstream of a moving bar wake generator in order to simulate an unsteady wake passing environment of a turbomachine. In the experiment, the flow conditions correspond to a Reynolds number of nearly 91,000 based on the chord length of the T106 profile and the inlet velocity. The

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**Figure 4.**

*S809 airfoil (a) lift coefficients and (b) drag coefficients at M = 0.15 and Re = 2 M.*

*S809 airfoil transition location comparison.*

experimental turbulence intensity is specified to be 0.1%. Geometric details of the experimental cascade setup are given in **Table 2**. Comparison of the experimental and numerical pressure coefficient distributions for T106 cascade for the steady case is depicted in **Figure 7**. Looking at **Figure 7**, it is observed that the separation bubble on the blade predicted by the B-C model and the two-equation γ-Reθ model is slightly smaller in size than the experimentally measured bubble.

#### **3.3 3-D wing test cases from low to high speeds**

#### *3.3.1 Low speed rotating wind turbine blade*

Two twisted and tapered 10-meter diameter turbine blades that use the S809 airfoil profile are tested in the NASA Ames Research Center wind tunnels [36, 37]. In the experiments, the NREL wind turbine rotation speed was set to 72 RPM for all cases, whereas the wind speeds varied from 7 to 25 m/s.

**Figure 8** compares the pressure coefficient distributions over various spanwise locations on the turbine blades at the freestream velocity of 7 m/s. It is observed

**Figure 6.** *Pressure coefficient distribution comparison for the S809 airfoil at 1̊.*

#### *Boundary Layer Flows - Theory, Applications and Numerical Methods*


**Table 2.**

*Geometric details of the T106 cascade experimental setup.*

that both fully turbulent and the transitional solutions differ very slightly and both agree well with the experimental data. The skin friction contours and the surface streamlines obtained by Medida [31], Potsdam et al. [38], and Aranake et al. [39] for the same freestream velocity are compared to the B-C model and the S-A model solutions in **Figure 9**.

#### *3.3.2 High subsonic flow over 3-D swept wing*

DLR-F5 wing tested by Sobieczky [40] is a 0.65 m span wing with 20° sweep angle and an average chord length of 150 mm. The wing is mounted to the tunnel wall with a smooth blending region, and the angle of attack is set to be 2°. The square cross-section wind tunnel has dimensions of 1 × 1 × 4 meters. The experimental inlet Mach number and the turbulence intensity are specified as M = 0.82 and Tu <0.35%, respectively. The corresponding Re number based on the average chord is 1.5 million. In the experiment, the transition locations are determined by the sublimation technique, whereas measurements of pressure coefficients at different spanwise stations are available. In 1987, a workshop with several researchers were took place in Gottingen [41], where the results were compared against the experimental data.

**Figure 10** shows the pressure coefficient distributions at different span locations. It is observed that the fully turbulent and the transitional solutions are very

#### **Figure 7.**

*Comparison of numerical and experimental pressure coefficient distributions on the T106 blade for Re = 91,000.*

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**Figure 9.**

*Comparison of numerical skin friction contours obtained by several researchers.*

**Figure 8.**

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications*

*Comparison of pressure coefficient distributions for the NREL phase IV blade for U = 7 m/s freestream velocity.*

*DOI: http://dx.doi.org/10.5772/intechopen.83520*

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications DOI: http://dx.doi.org/10.5772/intechopen.83520*

#### **Figure 8.**

*Boundary Layer Flows - Theory, Applications and Numerical Methods*

Blade chord 198 mm Blade stagger 59.3° Cascade pitch 158 mm Inlet flow angle 37.7° Design exit flow angle 63.2° Bar diameter 2.05 mm Axial distance from bars to leading edge 70 mm

that both fully turbulent and the transitional solutions differ very slightly and both agree well with the experimental data. The skin friction contours and the surface streamlines obtained by Medida [31], Potsdam et al. [38], and Aranake et al. [39] for the same freestream velocity are compared to the B-C model and the S-A model

DLR-F5 wing tested by Sobieczky [40] is a 0.65 m span wing with 20° sweep angle and an average chord length of 150 mm. The wing is mounted to the tunnel wall with a smooth blending region, and the angle of attack is set to be 2°. The square cross-section wind tunnel has dimensions of 1 × 1 × 4 meters. The experimental inlet Mach number and the turbulence intensity are specified as M = 0.82 and Tu <0.35%, respectively. The corresponding Re number based on the average chord is 1.5 million. In the experiment, the transition locations are determined by the sublimation technique, whereas measurements of pressure coefficients at different spanwise stations are available. In 1987, a workshop with several researchers were took place in Gottingen [41], where the results were compared against the

**Figure 10** shows the pressure coefficient distributions at different span locations. It is observed that the fully turbulent and the transitional solutions are very

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**Figure 7.**

*Re = 91,000.*

solutions in **Figure 9**.

**Table 2.**

experimental data.

*3.3.2 High subsonic flow over 3-D swept wing*

*Geometric details of the T106 cascade experimental setup.*

*Comparison of numerical and experimental pressure coefficient distributions on the T106 blade for* 

*Comparison of pressure coefficient distributions for the NREL phase IV blade for U = 7 m/s freestream velocity.*

**Figure 9.**

*Comparison of numerical skin friction contours obtained by several researchers.*

**Figure 10.**

*Pressure coefficient distributions for the DLR-F5 wing at M = 0.82 and Re = 1.5 M.*

similar to each other. **Figure 11** compares the skin friction contours of different numerical models with the experiment [40]. As seen, the B-C model predicts a somewhat similar transition and separation region with the experiment obtained by the sublimation and pressure measurement techniques.

Finally, in order to emphasize the difference between the fully turbulent and the transitional solutions, comparison of the skin friction coefficients at 80% span on

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with the one-equation S-A turbulence model [28].

**4. Conclusions**

*model at 80% span on the DLR-F5 wing.*

**Figure 12.**

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications*

the DLR-F5 wing is depicted in **Figure 12**. It can be clearly observed that the B-C model predicts marked extent of laminar regions for both the suction and pressure sides of the wing, which is in agreement with the contours shown in **Figure 11**.

*Comparison of the skin friction coefficients predicted by the S-A turbulence model and the B-C transition* 

Local correlation-based transition models in the sense of empirical correlations incorporated into Reynolds-averaged Navier-Stokes methods have been discussed. A logical path for the development of such models is highlighted such that a variety of combinations of turbulence and transition equations lead to different modeling alternatives. For instance, the pioneering work by Menter et al. [1] two-equation γ-Reθ transition model sums up to a total of four-equation model by the incorporation of the two-equation k-ω SST turbulence model of Menter et al. [27]. In the same line of development but in a leaner approach, Walters and Cokljat [14] developed a three-equation k-kL-ω model. Similarly, Medida [31] developed a three-equation S-A-γ-Reθ transition model that is a sum of the Menter et al. [1] twoequation γ-Reθ transition model and the one-equation S-A turbulence model [28]. In fact, in a recent work, Menter [22] reached to the conclusion that the Re<sup>θ</sup> equation was rather redundant. Without any loss of accuracy, Menter produced a leaner three-equation k-ω SST-γ transition model by incorporating a novel oneequation intermittency transport γ-model [22] with the two-equation k-ω SST turbulence model of Menter et al. [27]. In the same line of thought, Nagapetyan-Agarwal constructed the so-called two-equation transition model of WA-γ [24] by incorporating the Wray-Agarwal (WA) wall-distance-free one-equation turbulence model [23] based on the k-ω closure with the one-equation intermittency transport γ-equation of Menter et al. [22]. These two models paved the way for developing yet another leaner transition model by Bas et al. [19] with the introduction of the algebraic Bas-Cakmakcioglu (B-C) model by incorporating an algebraic γ-function

The Bas-Cakmakcioglu (B-C) [19] model qualifies as a zero-equation model that solves for an intermittency function rather than an intermittency transport (differential) equation. The main approach behind the B-C model follows again the pragmatic idea of further reducing the total number of equations. Thus, rather than deriving extra equations for intermittency convection and diffusion, already

*DOI: http://dx.doi.org/10.5772/intechopen.83520*

**Figure 11.** *Skin-friction coefficient comparisons for the DLR-F5 wing.*

*Transition Modeling for Low to High Speed Boundary Layer Flows with CFD Applications DOI: http://dx.doi.org/10.5772/intechopen.83520*

**Figure 12.**

*Boundary Layer Flows - Theory, Applications and Numerical Methods*

*Pressure coefficient distributions for the DLR-F5 wing at M = 0.82 and Re = 1.5 M.*

the sublimation and pressure measurement techniques.

similar to each other. **Figure 11** compares the skin friction contours of different numerical models with the experiment [40]. As seen, the B-C model predicts a somewhat similar transition and separation region with the experiment obtained by

Finally, in order to emphasize the difference between the fully turbulent and the transitional solutions, comparison of the skin friction coefficients at 80% span on

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**Figure 11.**

*Skin-friction coefficient comparisons for the DLR-F5 wing.*

**Figure 10.**

*Comparison of the skin friction coefficients predicted by the S-A turbulence model and the B-C transition model at 80% span on the DLR-F5 wing.*

the DLR-F5 wing is depicted in **Figure 12**. It can be clearly observed that the B-C model predicts marked extent of laminar regions for both the suction and pressure sides of the wing, which is in agreement with the contours shown in **Figure 11**.
