Turbine Disc Thermal-Stress Example

Problem

A turbine disc has a bore temperature of 300 deg C and a rim temperature of 550 deg C. The disc material has E = 200 GPa at temperature, CTE = 13 x 10^-6 /deg C, nu = 0.3. Estimate the thermal stress at the bore from the radial temperature gradient.

Given

• Bore temperature T_bore = 300 deg C
• Rim temperature T_rim = 550 deg C
• Delta_T = 250 deg C (rim to bore)
• E = 200 x 10^9 Pa
• CTE alpha = 13 x 10^-6 /deg C
• Poisson ratio nu = 0.3

Step 1 — Thermal stress estimate

The bore thermal stress from a radial gradient can be estimated as: sigma_thermal ≈ E * alpha * Delta_T / (2 * (1 - nu)) This is an approximate formula for the thermal stress from a linear radial gradient in a disc.

Step 2 — Substitution

sigma_thermal ≈ (200 x 10^9) * (13 x 10^-6) * 250 / (2 * 0.7) sigma_thermal ≈ (200 x 10^9 * 13 x 10^-6 * 250) / 1.4 sigma_thermal ≈ (650 x 10^6) / 1.4 sigma_thermal ≈ 464 MPa Note: The bore is in tension (cooler, restraining the hotter rim). This adds to the centrifugal hoop stress.

Result

The estimated bore thermal stress from the radial gradient is approximately 464 MPa (tensile). This is a significant stress that adds to the centrifugal bore stress. The combined stress at the bore may approach the material yield strength at temperature.

Assumptions and limitations

• The formula is an approximation for a linear radial gradient
• The actual temperature profile may be nonlinear
• The formula does not account for the disc geometry (thickness variation, bore-to-rim ratio)
• The formula assumes plane stress
• Transient thermal stress during start-up may be higher than the steady-state value
• FEA with the actual temperature field is required for accurate assessment

Related Knowledge

• Thermal Stress in Turbine Discs
• Thermal Stress in Turbine Blades