The Laminar Model

COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL DEVELOPMENT

4.2 Model Specification

4.3.2 Boundary Layer Mesh on Grid 1

4.3.4.4 The Laminar Model

With all the immense research activity into turbulence modelling, many researchers struggle to compute the heat load to a blade in the laminar region. There is one model in FLUENT that is usually overlooked, namely the Laminar model, which, as its name suggests, is used for laminar flow.

FLUENT defmes laminar flow as an organised flow, which can be streamlined, where the viscous stresses dominate over the fluid inertia stresses. For no-slip wall conditions, FLUENT uses the property of the flow adjacent to the walVfluid boundary to predict the shear stress on the fluid at the wall. In the laminar flow model, this calculation simply depends on the velocity gradient at the wall, while in turbulent flows, approaches such as the near wall treatment are used, which solve for turbulence production and turbulent viscosity.

Inthe laminar flow, the wall shear stress 'fw is defmed by the normal velocity gradient at the wall as:

Eq 4-9

Where y is the distance from the adjacent wall and jJthe dynamic viscosity of the fluid.

Fluent recommends that the grid be sufficiently finetoaccurately resolve the boundary layer, thishasbeen achieved through grid independence in Grid 3. The viscous laminar model was set up using the same boundary conditions that were used in all previous simulations.

Employing the simple Laminar model significantly reduced the computational time. The results of the simulation are shown below in Figure 4-30.

Temperature Distribution Using the Laminar Model

0.8

e

0.7

~

0.6

- - Q -ElCperimental, Sohn

--FLUENT

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

xIL

0.5+ - - - , - - - . , , . . . . - - - , - - - - , - - - r - - - - . - - - , - - - . . - - - - . - - - J -1

Figure 4·30: Temperature distribution from the aerodynamic analysis for the Laminar model using the decomposed mesh

The model shows excellent temperature prediction in the laminar region. The stagnation point temperature is over predicted by a mere 1%. Onthe pressure side, the temperature prediction is exact with the data in the laminar region up to 17%axial chord where transition occurs. As expected, the model thereafter under predicts the data as it assumes laminar flow and does not model turbulence, which increases heat transfertothe blade. The same trend is observed on

the suction side, where the prediction again follows the data accurately up to 44 % axial chord where transition due to the shock wave occurs. The same under prediction is then observed on the suction side in the turbulent region. The contours of static pressure and temperature for the Laminae model are shown in Figures F-ll and F-12, respectively. From the figures the under prediction for both the temperature and pressure can clearly be seen in the turbulent regions. The model also shows no capability of modelling the shock wave on the suction side.

The Laminar model and the Spalart-Allmaras turbulence model can now be combined into a single graph, where the prediction for the laminae region can be taken from the Laminar model and the prediction for the turbulent region from the Spalart-Allmaras turbulence model. Figure 4-31 shows both the models, which clearly shows where each model is capable of predicting the temperature.

Temperature Distribution Showing the Turbulent and Laminar Model

0.8 ~Experimental.Sohn

0.7

'too

~ !

0.6

- - Spalart-A1lmaras --Laminar

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 xlL

0.5 +--..----.----.----.---..,----..,----..,----..,----..---j -1

Figure 4-31: Temperature distribution from the aerodynamic analysis showing both the Spalart-Allmaras and Laminae model using the decomposed mesh

Figure 4-32 shows the product of combining the two models into one graph. Onthe pressure side, from the leading edge stagnation point to the transition point at 17 %axial chord, the prediction from theLaminaemodeliscombined with the prediction from 17%to 100%axial chord from the Spalart-Allmaras turbulence model. On the suction side, from the stagnation

pointto the transition point at 44 % axial chord, the prediction from the Laminar model is combined with the prediction from 44 %to 100 % axial chord from the Spalart-Allmaras turbulence model.

Temperature Distribution Used for the Validation

0.8

- ^!

0.7

~

0.6

- e -Experimenta, Bohn

--FLUENT

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

xJL

0.5 + - - - , - - - , . . . . - - , - - - - , - - - , - - - - , - - - , - - , - - - - , - - - 1 -1

Figure4-32:Temperature distribution from the aerodynamic analysis showing the combined Spalart-Allmaras andLaminarmodel using the decomposed mesh

The combined model shown in Figure 4-32 is the model that validates the data and can now beused in the thermal analysis to predict the resulting thermal stresses. Figure 4-33 shows the combination of the Standard k - ^E model with enhanced wall treatment and the Laminar model, while Figure 4-34 shows the combination of the Realizablek-^Emodel with enhanced wall treatment and the Laminar model. Both the Figures show acceptable results, however, Figure 4-32 will be used to in the thermal stress calculations.

The procedure of combining the two models can be extended to any blade configuration, and is possible if the transition points on the blade are known. These can be calculated with good accuracy, as shown. Even if the approximate position can not be calculated, the turbulence models give some hint as to where transition occurs. The laminar region can be seen where the turbulence models highly over predict the experimental data, and vica versa with the Laminar model.

Temperature Distribution Using the Combined Standardk - e and Laminar Model

0.8

0.7

!

1=

0.6

_ElCperimental, Sohn

--FLUENT

0.5 +----r----.--~---,----,---r_-_._-__.-____r-__j

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

xIL

Figure 4-33: Temperature distribution from the aerodynamic analysis showing the combined Standardk-^&turbulence model with enhanced wall treatment and the

Laminar model using the decomposed mesh

Temperature Disb1bution Using the Combined Realizablek -e and Laminar Model

0.8

e

0.7

~

0.6

--&-Experimental, Sohn

--FLUENT

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

xJL

0.5 + - - . . , . - - . - - - , - - - , - - - - , - - - - r - - - , - - - - r -__,...---l -1

Figure 4-34: Temperature distribution from the aerodynamic analysis showing the combined Realizablek-&turbulence model with enhanced wall treatment and the

Laminarmodel using the decomposed mesh

4.3.4.5 Heat Transfer Results

Bohn did not perfonn heat transfer measurements on the MARK II NGV, the study was rather aimed at predicting the temperature distribution. It is also unclear as to how Bohn calculated the heat transfer, as no mention regarding the matter is made. Figure 4-35 shows Bohn's heat transfer calculation compared to that predicted by FLUENT, where Href

=

¹¹³⁵

W/m²K.

Heat Tansfer Distribution Using the Combined Spalart- Allmaras and Laminar Model

1.4

- r - - - ,

1.2

1

... 0.8 2:!

~0.6

0.4 0.2

- - Calculation, Sohn

--FLUENT

O+--...,.---r--,----.---,---"T---r---,---.----i -1 -D.8 -D.6 -D.4 -D.2 0 0.2 0.4 0.6 0.8

xIl

Figure 4-35: Heat transfer distribution from the aerodynamic analysis showing the combined Spalart-Allmaras andLaminarmodel using the decomposed mesh

The development of the heat transfer along the blade surface is analogous to that of the temperature. The heat transfer distribution predicted by FLUENT follows similar trends to Bohn's calculation. At the leading edge stagnation point, the predicted heat transfer is lower thanBohn's calculation. On the suction side up to 44 %axial chord, both graphs decrease to the same value. Bohn's graph however decreases with a steeper gradient and is considered to be more accurate in this region, as it correlates more accuratelytothe decrease in temperature in this region. The heat transfer spike is accurately modelled. The prediction there after

follows the same trend as Bohn's calculation, where both the data decrease to the trailing edge, the values are, however, lower. It is uncertain which trend is more accurate.

On the pressure side, from the stagnation point to the transition point at 22 % axial chord, Bohn's calculation again shows a decrease in the heat transfer, where as FLUENT predicts an area of little change in the heat transfer. Here again, Bohn's data follows the trend seen in the temperature more accurately than the FLUENT prediction. There after FLUENT predicts the decrease in the heat transfer spikes (caused by the cooling holes) where as from Bohn's calculation, the heat transfer spikes show very little decrease up to the trailing edge.

It can be argued that in the 1aminar region Bohn's calculation is more accurate, where the difference between the two graphs in the 1aminar region is 9 %. No conclusions can be drawn from the heat transfer distribution in the turbulent region. A proper analysis can only be made if there are experimental results to compare to. Comparing two codes or calculations has little validation meaning or accuracy.