Thermal Stress Analysis of a Turbine Stator Blade

The conditions within gas turbines are extreme. The pressure can be as high as 40 bars, and the temperature far above 1000 K. Any new component must therefore be carefully designed to be able to withstand thermal stress and vibrations due to the rotating machinery and aerodynamic loads exerted by the fluid rushing through the turbine. If a component fails, the high rotational speeds can result in a complete collapse of the whole turbine.

The most extreme conditions are found in the high pressure section, downstream of the combustion chamber where hot combustion gas flows through a cascade of rotors and stators. To prevent melting, relatively “cold” air is taken from bleeding vanes located in the high-pressure compressor casing; this cold air is then led past the combustion chamber into the turbine casing as coolant. Directly behind the combustion chamber, both internal cooling within ducts, and film cooling over the blade side surfaces are applied. Besides, a surface treatment (coating) is often added to the blades to protect them from hot corrosion. Further downstream, where the temperature is somewhat lower, it may suffice with internal cooling. For more details on gas turbines, see Ref. 1.

Since the physics within a gas turbine is very complex, simplified approaches are often used at the initial stages of the development of new components. In this tutorial, the thermal stresses in a stator blade with internal cooling are analyzed (coating and film cooling are not considered in this example).

This application requires the Structural Mechanics Module and the CFD Module or Heat Transfer Module. It also uses the Material Library.

Model Definition

The model geometry is shown in Figure 1. The stator blade profile is a modified version of a design shown in Ref. 2. The geometry includes some generic mounting details as well as a generic internal cooling duct.

Figure 1: A stator blade with mounting details.

Use the Thermal Stress interface from the Structural Mechanics Module to set up the model. The blade and the mounting details are assumed to be made of the directionally solidified (DS) GTD111 nickel-based alloy with high tensile strength (Ref. 1). This material is available in the COMSOL Material Library. In addition to the data covered by the Material Library, the linear elastic model requires a reference temperature that is set to 310 K and a Poisson’s Ratio that is set to 0.33, a number comparable to that for other stainless steels.

Figure 2 shows the cooling duct. The duct geometry is simplified and does not include details such as the ribs typical for cooling ducts (Ref. 3). Instead of simulating the complicated flow in the duct, an average Nusselt number correlation from Ref. 3 is used to calculate a heat transfer coefficient. Assume the cooling fluid to be air at 30 bar and 650 K.

Figure 2: The internal cooling duct.

The heat flux on the stator blade surfaces is calculated using the heat transfer coefficient. The pressure and suction sides are approximated as two flat plates using the local heat transfer coefficient for external forced convection. The combustion gases are approximated as air at 30 bar and 1150 K. The corresponding speed of sound is approximately 650 m/s.

Ref. 4 contains a Mach number plot of stators without film cooling. A typical Mach number is 0.45 on the pressure side (the concave side) and 0.7 on the suction side (the convex side). This corresponds to approximately 300 m/s on the pressure side and 450 m/s on the suction side.

The platform walls adjacent to the stator blades are treated in the same way as the stator itself but with the free stream velocity set to 350 m/s.

The stator blade exchanges heat with the cooling air through the boundaries highlighted in Figure 3. It is assumed that the turbine has a local working temperature of 900 K, and that the heat transfer coefficient to the stator is 25 W/(m2·K).

Figure 3: Boundaries through which heat is exchanged with the cooling air.

The attachment of the stator element to a ring support is simulated via roller and spring foundation boundary conditions on a few boundaries. All other boundaries are free to deform as a result of thermal expansion.

Results and Discussion

Figure 4 shows a temperature surface plot. The internal cooling creates significant temperature gradients within the blade. However, the trailing edge reaches a temperature close to that of the combustion gases, which indicates that the cooling might be insufficient. The side walls also become very hot, and some additional cooling can be beneficial.

Figure 4: Surface temperature plot.

Figure 5 shows a surface plot of the von Mises stress. The maximum stress does not exceed the yield stress of the material (Ref. 5), which indicates that no static failure occurs. However, the component may still be at risk for thermal fatigue, so no definite assessment can be made without conducting a more advanced analysis that includes, for example, creep and other transient effects.

Figure 5: Surface plot of the von Mises stress.

Figure 6: Surface plot of the displacement.

Notes About the COMSOL Implementation

The default suggested solver for a thermal stress analysis assumes that the displacement field and the temperature field are two-way coupled. However, in this example there is only a one-way coupling such that the temperature field is independent of the deformations. In this case, a more efficient solver can be set up where the physics are solved in series. To modify the default solver, set to in the solver node and make sure that are set to 1. Moreover, set to in each node. With these modifications, the temperature field is first solved to convergence, before the displacements are solved for.

References

1. M.P. Boyce, Gas Turbine Engineering Handbook, 2nd ed., Gulf Professional Publishing, 2001.

2. NASA, “Power Turbine”, Glenn Research Center, www.grc.nasa.gov/WWW/K-12/airplane/powturb.html.

3. J. Bredberg, “Turbulence Modelling for Internal Cooling of Gas-Turbine Blades”, Thesis for the degree of doctor of philosophy, Chalmers University of Technology, 2002.

4. P. Dahlander, “Source Term Model Approaches to Film Cooling Simulations”, Thesis for the degree of doctor of philosophy, Chalmers University of Technology, 2001.

5. http://www.cnalloys.co.uk/stainless-jethete-m152

Structural_Mechanics_Module/Thermal-Structure_Interaction/turbine_stator

Modeling Instructions

Instructions below require to select entities corresponding to a particular numbers list. For example:
Select Boundaries 113 and 139 only.
In most cases the easiest way to select them is to click the button

and paste the numbers as they are printed in the document (for example paste “113 and 139” for the example above).

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Pr_cool	0.72	0.72	Cooling Prandtl number
U_suction_side	450[m/s]	450 m/s	Gas velocity on stator suction side
U_pressure_side	300[m/s]	300 m/s	Gas velocity on stator pressure side
U_platform	350[m/s]	350 m/s	Gas velocity along platform walls
T_gas	1150[K]	1150 K	Gas temperature
p_high	30[bar]	3E6 Pa	High pressure level
mu_cool	3.1e-5[Pa*s]	3.1E-5 Pa·s	Viscosity of the cooling air
Cp_cool	770[J/kg/K]	770 J/(kg·K)	Heat capacity of the cooling air
T_cool	650[K]	650 K	Cooling air temperature
H_cool	0.01[m]	0.01 m	Characteristic length scale of cooling channels
T_work	900[K]	900 K	Working temperature
Nu_cool	400	400	Average Nusselt number in cooling channel

Geometry 1

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file turbine_stator.mphbin.

Click

To see the interior:

Click the

button in the toolbar.

The imported geometry should look as shown in the Figure 1.

In the toolbar, click

Click the

button in the toolbar.

Define a number of selections to simplify the model setup. First define the internal cooling duct boundaries.

Definitions

Cooling Duct

In the toolbar, click

In the window for , type Cooling Duct in the text field.

Locate the section. From the list, choose .

Click

In the dialog box, type 59-64, 66, 74-114 in the text field.

If you are reading an electronic version of this document, you can copy the geometric entity numbers from the text.

Click .

Click the

button in the toolbar.

Click the

button in the toolbar.

The selection is shown in Figure 2.

Proceed to select the boundaries through which the heat exchange with the rest of the turbine occurs (Figure 3).

Exchange Boundaries

In the toolbar, click

In the window for , type Exchange Boundaries in the text field.

Locate the section. From the list, choose .

Click

In the dialog box, type 1-4, 9, 11, 14, 16, 17, 21-31, 36-39, 42-58, 65, 67-72, 115-136 in the text field.

Click .

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

GTD111 DS [solid,longitudinal] (mat1)

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Poisson’s ratio	nu	0.33	1	Young’s modulus and Poisson’s ratio
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	k(T)	W/(m·K)	Basic