# HCF and LCF Analysis of a Generic Full Admission Turbine Blade

^{*}

## Abstract

**:**

_{2}liquid rocket engine (LRE). For this numerical example, the LCF loading turned out to be dominant. Creep turned out to be negligible.

## 1. Introduction

- A 3D thermal FE analysis.
- A 3D structural FE analysis.
- A post processing (cyclic strain based) LCF analysis.

## 2. Numerical Analysis Method

#### 2.1. LRE Turbine-Blade FE Analysis Method Outline

- The usage of a commercial FE program package [8].
- The temperature dependent parameters of the turbine-blade material.
- The geometry of single and two half turbine blades, the related disk section and the related rotor section of the first rotor stage of the considered turbo pump.
- Additionally, all of the structural FE analyses are based on:
- ○
- bi-linear elasto-plasticity with the von Mises yield criterion and kinematic hardening,
- ○
- additive split of the total strain into thermal, elastic, plastic and creep strain,
- ○
- classical three-parameter model approach for taking into account secondary creep (multiplicative combination of Norton’s stress power law and the exponential activation energy law) in order to take into account the dependency of the creep strain rate ${\dot{\epsilon}}_{creep}$ on both the stress $\sigma $ and temperature $T$ by means of a single equation, Equation (1), as, e.g., suggested in [9]:

#### 2.1.1. HCF and Creep Related FE Analysis Method

- A stationary thermal 3D FE analysis, simulating the thermal field during the stationary hot run.
- A quasi-stationary structural 3D FE analysis (with thermal strains calculated from the thermal field of the abovementioned thermal FE analysis) with six load steps $L{S}_{1,HCF\&creep}$ to $L{S}_{6,HCF\&creep}$:
- ○
- $L{S}_{1,HCF\&creep}$ (for the time range $t=0\mathrm{s}$ to $t=1\mathrm{s}$): thermal strains from the abovementioned stationary thermal FE analysis. Although from the post-processing HCF analysis point of view, this loading could be integrated into load step 3, it is useful to separate it in order to show the negligible influence of the quasi-static thermal loading to the stresses, obtained by the FE model.
- ○
- $L{S}_{2,HCF\&creep}$ (for the time range $t=1\mathrm{s}$ to $t=2\mathrm{s}$): additional spin loading (modelling centrifugal forces under high temperature). Although from the post-processing HCF analysis point of view, this loading could be integrated into load step 3, it is useful to separate it in order to show the dominant influence of the spin-loading to the stresses obtained by the FE model.
- ○
- $L{S}_{3,HCF\&creep}$ (for the time range $t=2\mathrm{s}$ to $t=3\mathrm{s}$): an additional 0.75 ∙ the (circumferential and axial) average gas bending load (originating @ the stator row). This load step results in the minimum stress of the stationary hot run of the turbine and therefore is directly needed for the post-processing HCF analysis of the turbine blade.
- ○
- $L{S}_{4,HCF\&creep}$ (for the time range $t=3\mathrm{s}$ to $t=4\mathrm{s}$): an additional 0.5 ∙ the (circumferential and axial) average gas bending load (originating @ the stator row). Therefore, load step $L{S}_{4,HCF\&creep}$ combines full thermal, full centrifugal and 1.25 ∙ the (circumferential and axial) average gas bending load (originating @ the stator row). This load step results in the maximum stress of the stationary hot-run of the turbine and therefore is directly needed for the post-processing HCF analysis of the turbine blade.
- ○
- $L{S}_{5,HCF\&creep}$ (for the time range $t=4\mathrm{s}$ to $t=540\mathrm{s}$): completely unchanged boundary conditions (for modelling both stress relaxation at the maximum HCF-loaded point and the build-up of radial creep deformation at the tip of the blade for the full duration of the stationary hot run of the turbine). According to [11], the hot-run duration of the reference engine is 540 s.
- ○
- $L{S}_{6,HCF\&creep}$ (for the time range $t=540\mathrm{s}$ to $t=542\mathrm{s}$): reduction of thermal strains, spin load, circumferential and axial gas bending loads to zero (for obtaining the residual creep deformation after the end of a single hot run).

#### 2.1.2. LCF-Related FE Analysis Method

- A fully transient thermal 3D FE analysis of the thermal loading of two complete engine operation cycles with twelve load steps $L{S}_{1,therm.trans.}$ to $L{S}_{12,therm.trans.}$. The reason for this two-cycle thermal FE analysis is some shakedown of the cyclic strain, obtained by the follow-on elasto-plastic structural FE analysis from the first to the second loading cycle. The second half $L{S}_{7,therm.trans.}$ to $L{S}_{12,therm.trans.}$ of the load steps are identical to the first half $L{S}_{1,therm.trans.}$ to $L{S}_{6,therm.trans.}$ of the load steps. Therefore, only the first half $L{S}_{1,therm.trans.}$ to $L{S}_{6,therm.trans.}$ of the load steps is described in detail:
- ○
- $L{S}_{1,therm.trans.}$ (for the time range $t=0\mathrm{s}$ to $t=1\mathrm{s}$): Linearly ramping up to chill-down boundary conditions (${T}_{bulk,impeller}=36\mathrm{K}$ at the impeller position of the FE model while keeping ambient bulk temperature at the surface of the turbine blade).
- ○
- $L{S}_{2,therm.trans.}$ (for the time range $t=1\mathrm{s}$ to $t=6300\mathrm{s}$): Keeping identical chill-down boundary conditions as at the end of the previous load step $L{S}_{1,therm.trans.}$. The chill-down duration (of 105 minutes) is chosen according to [14].
- ○
- $L{S}_{3,therm.trans.}$ (for the time range $t=3600\mathrm{s}$ to $t=6301\mathrm{s}$): Linearly ramping up the blade surface bulk temperature to the hot-run condition ${T}_{bulk,blade}=800\mathrm{K}$ while keeping ${T}_{bulk,impeller}=36\mathrm{K}$ at the impeller position of the FE model.
- ○
- $L{S}_{4,therm.trans.}$ (for the time range $t=6301\mathrm{s}$ to $t=6841\mathrm{s}$): Keeping identical hot-run boundary conditions as in the previous load step $L{S}_{3,therm,trans.}$. The hot-run duration (of 540 s) is chosen according to [11].
- ○
- $L{S}_{5,therm.trans.}$ (for the time range $t=6841\mathrm{s}tot=6842\mathrm{s}$): Linearly ramping down the blade surface bulk temperature to ambient condition ${T}_{bulk,blade}=295\mathrm{K}$ while keeping ${T}_{bulk,impeller}=36\mathrm{K}$ at the impeller position of the FE model.
- ○
- $L{S}_{6,therm.trans.}$ (for the time range $t=6842\mathrm{s}$ to $t=17000\mathrm{s}$) Keeping identical shut-down boundary conditions as in load step $L{S}_{5,therm.trans.}$. This (relatively long) duration of $L{S}_{6,therm.trans.}$ was chosen to ensure stationary thermal conditions before the transition to the second full loading cycle.

- For the follow-on (one-way coupled) quasi-stationary structural 3D FE analysis:
- ○
- Thermal strains from the abovementioned thermal FE analysis.
- ○
- Centrifugal forces (during spin up, stationary hot run and spin down).
- ○
- Average gas bending load, originating at the stator row (during spin up, stationary hot run and spin down).

#### 2.2. Post-Processing Fatigue-Life Analysis Methods of LRE Turbine Blades

#### 2.2.1. Post-Processing HCF Analysis Method

- The mean stress ${\sigma}_{m,HCF\&creep}$ of the stationary hot run of the turbo pump according to Equation (3):$${\sigma}_{m,HCF\&creep}=\frac{{\sigma}_{max,princ.,L{S}_{3,HCFcreep,.}max.space}+{\sigma}_{max,princ.,L{S}_{4,HCFcreep,}max.space}}{2}$$

- Similarly, the stress amplitude ${\sigma}_{a,HCF\&creep}$ of the stationary hot run of the turbo pump is calculated according to Equation (4):$${\sigma}_{a,HCF\&creep}=\frac{{\sigma}_{max,princ.,L{S}_{4,HCFcreep,}max.space}-{\sigma}_{max,princ.,L{S}_{3,HCFcreep,}max.space}}{2}$$

- Finally, the number of HCF cycles to failure ${N}_{f,HCF}$ is calculated by applying the modified Goodman equation (Equation (5)) as suggested in [15]:$${N}_{f,HCF}=\sqrt[{B}^{\prime}]{\frac{{\sigma}_{a,HCF\&creep}}{{A}^{\prime}\left(1-\frac{{\sigma}_{m,HCF\&creep}}{{C}^{\prime}}\right)}}$$
_{2}atmosphere.

#### 2.2.2. Post-Processing LCF Analysis Method

- As first step of the post-processing LCF analysis of the turbine blade, the minimum over-time and minimum over-all FE mesh node value of the minimum principal total mechanical strain ${\epsilon}_{min.princ.,min{.2}^{nd}cycle,min.space}$ of the turbine blade is extracted from the structural 3D FE analysis of the second full loading cycle (based on the transient thermal FE analysis).

- Subsequently, two of the values this triple minimum is related to are fixed:
- ○
- The (minimum principal strain) direction, which the value ${\epsilon}_{min.princ.,min{.2}^{nd}cycle,min.space}$ refers to;

- ○
- The node of the FE mesh, which the value ${\epsilon}_{min.princ.,min{.2}^{nd}cycle,min.space}$ refers to.

- For these two fixed values (of direction and spatial location), the maximum normal strain ${\epsilon}_{fixed-dir.,max{.2}^{nd}cycle,fixed-loc.}$ of the full second loading cycle is determined.

- Subsequently, the total mechanical strain range $\Delta {\epsilon}_{LCF}$ of the highest LCF-loaded point of the turbine blade is calculated according to Equation (6):$$\Delta {\epsilon}_{LCF}={\epsilon}_{fixed-dir.,max{.2}^{nd}cycle,fixed-loc.}-{\epsilon}_{min.princ.,min{.2}^{nd}cycle,min.space}$$

- Finally, the number of LCF cycles to failure ${N}_{f,LCF}$ of the turbine blade is calculated according to the modified Langer equation (Equation (7)) as suggested in [16]:$${N}_{f,LCF}={10}^{{10}^{{B}_{0}{\mathit{log}}_{10}\left(\Delta {\epsilon}_{LCF}+{B}_{1}\right)+{B}_{2}}}$$

## 3. Material, Material Parameters, Geometry and Loading Conditions

^{st}rotor row of a gas-generator-driven hydrogen turbo pump [6] of a 1 MN thrust class LRE was selected as reference turbine blade for this paper.

#### 3.1. Material of the Reference Turbine Blade

- “Super Waspaloy” was foreseen as blade material in the initial phase of the development;
- However, for cost efficiency reasons, Inconel 718 was selected at a later stage of the development of the turbo pump of the 1 MN thrust class gas-generator reference LRE.

#### 3.2. Material Parameters of the Reference Turbine Blade

#### 3.2.1. Thermal FE Analysis Parameters of the Reference Turbine-blade Material

#### 3.2.2. Structural FE Analysis Parameters of the Reference Turbine-blade Material

- The natural logarithm is applied to Equation (1), resulting in Equation (8):$$ln{\dot{\epsilon}}_{creep}=ln{C}_{1}+{C}_{2}ln\sigma -\frac{{C}_{3}}{T}$$

- And $ln\sigma $ and $\frac{1}{T}$ are used as dependency (input) parameters for obtaining the natural logarithm of the creep strain rate $ln{\dot{\epsilon}}_{creep}$ as a function value of Equation (8).

#### 3.2.3. Fatigue-Life Analysis Parameters of the Reference Turbine-Blade Material

#### HCF Analysis Parameters of the Reference Turbine-Blade Material

_{2}-test-related) HCF analysis parameters for Inconel 718, needed for applying Equation (5), are:

#### LCF Analysis Parameters of the Reference Turbine-Blade Material

#### 3.3. Assumed Turbine-Blade Geometry

_{2}, both a larger rotational speed and larger turbine power (in comparison to the LOX turbopump) are necessary for the LH

_{2}turbopump of LOX + LH

_{2}LREs (although the hydrogen mass-flow rate is just a relatively small fraction of the total propellant mass-flow rate). Therefore, the blade of a LH

_{2}turbopump is selected as a (worst-case) reference turbine blade. Furthermore, a turbine blade of the 1

^{st}rotor stage of a two-stage turbopump can be assumed (for the following reasons) as the higher loaded turbine blade (in comparison to the blade of the 2nd rotor stage):

- Highest temperature directly from the gas generator or (in case of other engine cycles) the pre-burner or the (expander LRE) cooling circuit (and therefore, usually most severely thermally reduced material properties);
- Highest share of the total turbine work [19].

_{2}turbine was selected as reference turbine blade for this paper.

^{st}rotor stage of the 1 MN thrust class gas generator LRE reference hydrogen turbo pump is shown in Figure 7. This cross section was pieced together from the leading- and trailing-edge radii, the blade thickness and the chord length given in Table 5 and from a cross-section drawing, extracted from [21]. The cross section shown in Figure 7 (composed of six circle sections and two straight lines) is C

^{1}-continuous (that means, a closed turbine-blade cross-section curve is ensured and sharp corners are avoided in the cross-section curve, but discontinuities of the curvature radii of the abovementioned 6 circle sections and two straight lines are accepted).

#### 3.4. Assumed Turbine-Blade Loading Conditions

^{st}stage of turbine (both given in Table 6) and from the mean blade speed.

#### 3.5. Boundary Conditions of the Reference Turbine Blade

#### 3.5.1. Boundary Conditions for the HCF- and Creep-Related FE Analyses

#### Boundary Conditions for the Stationary Thermal FE Analysis of the Reference Turbine Blade

- A: The impeller temperature (36 K);
- B: The total temperature of the turbine driving gas (from the gas generator) in the local coordinate system of the blade (800 K).

#### Boundary Conditions for the HCF- and Creep-Related Quasi-Stationary Structural FE Analysis of the Reference Turbine Blade

#### 3.5.2. Boundary Conditions for the LCF-Related FE Analyses

#### Boundary Conditions for the Transient Thermal FE Analysis of the Reference Turbine Blade

#### Boundary Conditions for the LCF-Related Quasi-Stationary Structural FE Analysis of the Reference Turbine Blade

^{nd}full loading cycle of the turbine (in the time range $t=17000\mathrm{s}$ to $t=34000\mathrm{s}$) are identical to load steps $L{S}_{1,LCF}$ to $L{S}_{6,LCF}$.

#### 3.6. FE Meshing of the Reference Turbine Blade

## 4. Results

#### 4.1. FE Analysis Results

#### 4.1.1. Thermal FE Analysis Results

#### Results of the (HCF-Related) Stationary Thermal FE Analysis of the Reference Turbine Blade

- directly for the structural FE analysis of the (from the thermal point of view, stationary) hot run of the turbo pump (as shown in Section 4.1.2),
- indirectly also for the post-processing HCF analysis of the reference turbine blade (as shown in Section 4.2).

#### Results of the (LCF-Related) Transient Thermal FE Analysis of the Reference Turbine Blade

- directly for the quasi-stationary structural FE analysis of the complete operating cycle of the turbo pump (pre-cooling, start-up, stationary hot-run, and shut-down of the turbo pump as shown in Section 4.1.2); from the time-dependent thermal field shown in Figure 11 and Figure 12, the thermal strains of the structural analysis are calculated (by multiplying the difference between the thermal field and the reference temperature by the coefficient of thermal expansion),
- indirectly for the post-processing LCF analysis of the reference turbine blade (as shown in Section 4.2).

#### 4.1.2. Results of the Quasi-Stationary Structural FE Analysis of the Reference Turbine Blade

#### Results of the HCF-Related Structural FE Analysis

#### Creep-Related Results of the Structural FE Analysis

#### Results of the LCF-Related Structural FE Analysis

#### 4.2. Post-Processing Fatigue Life Analysis Results

#### 4.2.1. Post-Processing HCF Analysis Results of the Reference Turbine Blade

#### 4.2.2. Post-Processing LCF Analysis Results of the Reference Turbine Blade

## 5. Discussion and Outlook

- This experimental data is (with HCF life values between 1 Mcycle to failure and 10 Mcycles to failure) several orders of magnitude smaller than the predicted HCF life of the reference turbine blade. A large uncertainty of the predicted HCF life of the reference turbine blade based on these HCF test results with uniaxial probes has to be assumed under these circumstances.
- The experimental HCF data is related to ambient temperature—whereas the hot-run temperature of the reference turbine blade is assumed to be 800 K.
- These two drawbacks will be eliminated in the near future at DLR Lampoldshausen by the following two measures:
- Additional HCF tests with Inconel 718 samples (under loading conditions, expected to result in the fatigue-life magnitude of the reference turbine blade).
- Elevated temperature correction of one or several of the parameters of the Goodman Equation (5).

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Temperature−dependent thermal conductivity of the blade material of the reference turbo pump as taken from [17].

**Figure 2.**Temperature−dependent specific heat of the blade material of the reference turbo pump according to [17].

**Figure 3.**Temperature−dependent coefficient of thermal expansion (CTE) of the blade material of the reference turbo pump according to [18].

**Figure 4.**Temperature−dependent modulus of elasticity of the blade material of the reference turbo pump according to [18].

**Figure 5.**Assumed temperature−dependent bi-linear elasto−plastic behavior of the blade material (Inconel 718) of the reference turbo pump according to [18].

**Figure 6.**Colored plane: $ln$−transformed secondary creep behavior of the blade material (Inconel 718) of the reference turbo pump; black squares: data from [10], used for least squares fitting the 3 parameters of Equation (1) by using the bilinear Equation (8).

**Figure 7.**C

^{1}-continuous cross section of the selected turbine blade (with blade thickness indicated by full inner circle, leading edge radius r1 and trailing edge radius r2).

**Figure 8.**(

**Left**): convective boundary condition faces of the thermal FE analyses; (

**right**): turbine-blade driving-gas-related pressure boundary of the structural FE analysis.

**Figure 9.**Mesh, used for all of the finite element analyses of the reference turbine blade and the related disc and rotor section; lefthand side: full FE mesh; center and righthand side: FE mesh zooms in the vicinity of the highest HCF- and LCF-loaded areas, respectively.

**Figure 10.**Main result of the stationary thermal FE analysis of the hot run of the reference turbine blade and the related disc and rotor section.

**Figure 11.**Thermal fields of the reference turbine blade and related disk and rotor section at selected points in time (at pre cooling and start-up of the turbo pump).

**Figure 12.**Thermal fields of the reference turbine blade and related disk and rotor section at selected points in time (early phase of the hot run of the engine).

**Figure 13.**Variation in time of the temperature of the highest LCF-loaded point (transition from the suction side of the blade to the disk).

**Figure 14.**Distribution of the maximum principal stress of the reference turbine blade for the two HCF-determining load cases $L{S}_{3,HCF\&creep}$ and $L{S}_{4,HCF\&creep}$—including position locator of the maximum HCF loading point (located at the transition between the leading edge of the blade and the disk).

**Figure 15.**Variation in time of the circumferential deflection of the tip of the reference turbine blade as result of the HCF- and creep-related FE analysis.

**Figure 16.**Equivalent creep strain and maximum principal stress of the highest HCF−loaded point for a single full operating cycle of the reference turbo pump.

**Figure 17.**Distribution of the minimum principal strain about 9 s after the 2

^{nd}start−up of the turbine.

**Figure 21.**Modified-Langer-equation-based LCF analysis of the highest LCF−loaded point of the reference turbine blade (with a total mechanical strain range of 2.0%).

Creep Parameter | Value | Unit |
---|---|---|

${C}_{1}$ | 4.539$\xb7{10}^{-105}$ | ${\mathrm{s}}^{-1}{\mathrm{MPa}}^{-{C}_{2}}$ |

${C}_{2}$ | 15.57 | - |

${C}_{3}$ | 8.677$\xb7{10}^{4}$ | K |

Structural Analysis Parameter | Value | Unit |
---|---|---|

Poisson’s ratio $\nu $ | 0.31 | - |

Density $\varrho $ | 8192 | kg/m^{3} |

**Table 3.**Ambient temperature, high-pressure GH

_{2}-test-related parameters of Inconel 718, applied to the HCF analysis according to Equation (5).

HCF Analysis Parameter | Value | Unit |
---|---|---|

${A}^{\prime}$ | 15,168 | MPa |

${B}^{\prime}$ | −0.2451 | - |

${C}^{\prime}$ | 1089 | Mpa |

**Table 4.**Inconel 718 parameters for $T=811\mathrm{K}$, as used for the LCF analysis of the turbine blade according to the modified Langer equation (Equation (7)).

LCF Analysis Parameter | Value | Unit |
---|---|---|

${B}_{0}$ | −0.3553 | - |

${B}_{1}$ | −0.4582 | - |

${B}_{2}$ | 0.5357 | - |

**Table 5.**Geometric data of the (1 MN thrust class gas generator LRE related) reference turbine blade.

Geometric Parameters | Value | Unit | Reference |
---|---|---|---|

Mean blade diameter ${d}_{mean}$ | 240 | mm | [6] |

Number ${n}_{1ststatorrow}$ of blades of the 1^{st} stator row | 23 | - | [6] |

Number ${n}_{1strotorrow}$ of blades of the 1^{st} rotor row | 106 | - | [6] |

Total height $h$ of the blade | 12.5 | mm | [21] |

Leading edge radius ${r}_{lead}$ of the blade (r1 as shown in Figure 7) | 0.209 | mm | [21] |

Trailing edge radius ${r}_{trail}$ of the blade (r2 as shown in Figure 7) | 0.157 | mm | [21] |

Transition radius ${r}_{fillet}$ disk—blade (fillet radius) | 0.55 | mm | [21] |

Blade thickness $t$ (full circle shown in Figure 7) | 3.8 | mm | [21] |

Chord length $c$ of the blade | 9 | mm | [21] |

**Table 6.**The 1

^{st}rotor row blade loading conditions of the hydrogen turbo pump of the 1 MN thrust class gas generator reference LRE.

Loading Conditions | Value | Unit | Reference |
---|---|---|---|

Total temperature at the inlet of the 1^{st} turbine stage(related to the global/fixed coordinate system) | 873 | K | [6] |

Rotational speed $n$ of the reference LRE H_{2} turbo pump | 35.68 | krpm | [6] |

Rotational speed ${\omega}_{rad}$ of the reference LRE H_{2} turbo pump(as calculated from the line above) | 3736 | rad/s | - |

Output power ${P}_{out,total}$ of the reference LRE hydrogen turbine | 14.29 | MW | [6] |

Relative power split between the 1^{st} and the 2^{nd} rotor stage of the 1 MN thrust class gas generator LRE hydrogen turbo pump. | 60:40 | % | [19] |

Output power ${P}_{out,1ststage}$ of the 1^{st} stage of the 1 MN thrust class reference LRE hydrogen turbine (as calculated from the two table lines above) | 8574 | kW | - |

Quotient: Total temperature, related to the relative (rotating) coordinate system of the turbine blade/total temperature, related to the global (fixed) coordinate system | 0.917 | - | [21] |

Total temperature in the relative (rotating) coordinate system of the turbine blade of the 1st rotor stage (as calculated from the very 1 ^{st} and the above-line of this table) | 800 | K | - |

Static pressure at the inlet of the 1^{st} rotor stage of the 1 MN thrust class reference H_{2} turbo pump | 4.18 | MPa | [21] |

Static pressure at the outlet of the 1^{st} rotor stage of the 1 MN thrust class reference H_{2} turbo pump | 3.57 | MPa | [21] |

Mean static pressure of the 1^{st} rotor stage of the 1 MN thrust class reference H_{2} turbo pump (as calculated from the two table lines above) | 3.88 | MPa | - |

Total temperature at the H_{2} inlet of the 1 MN reference thrust chamber(assumed as total temperature at the H _{2} outlet of the 1 MN reference H_{2} turbo pump, and therefore applied as impeller temperature of the turbo pump) | 36 | K | [22] |

**Table 7.**Boundary conditions for the stationary thermal FE analysis of the hot-run of the reference turbine blade.

Impeller Position Boundary [Face A of Figure 8] | Blade and Outer Disk Surface Boundary [Face B of Figure 8] | |
---|---|---|

bulk temperature ${T}_{bulk}$ [K] | 36 | 800 |

film coefficient ${h}_{film}$ [kWm^{−2} K^{−1}] | 1000 | 50 |

**Table 8.**Structural boundary conditions for the quasi-stationary structural FE analysis of a single HCF loading cycle and full hot-run duration creep of the reference turbine blade.

Load Step Number | Time Range of the Load Step [s] | Spin Loading [rad/s] | Static Pressure (Normal to the Surface) [MPa] | Component Pressure, Acting in Axial Direction of the Turbine [MPa] | Component Pressure, Acting in Circumferential Direction of the Turbine [MPa] |
---|---|---|---|---|---|

$L{S}_{1,HCF\&creep}$ | 0–1 | 0 | 0 | 0 | 0 |

$L{S}_{2,HCF\&creep}$ | 1–2 | 3736 | 0 | 0 | 0 |

$L{S}_{3,HCF\&creep}$ | 2–3 | 3736 | 3.88 | 0.112 | 0.377 |

$L{S}_{4,HCF\&creep}$ | 3–4 | 3736 | 3.88 | 0.186 | 0.629 |

$L{S}_{5,HCF\&creep}$ | 4–540 | 3736 | 3.88 | 0.186 | 0.629 |

$L{S}_{6,HCF\&creep}$ | 540–542 | 0 | 0 | 0 | 0 |

**Table 9.**Boundary conditions for the transient thermal FE analysis of a single loading cycle of the reference turbine blade.

Impeller Position Boundary [Face A of Figure 8] | Blade and Outer Disk Surface Boundary [Face B of Figure 8] | ||||
---|---|---|---|---|---|

Load Step Number | Time Range $t$ of the Load Step [s] | Bulk Temperature ${T}_{bulk,impeller}$ [K] | Film Coefficient ${h}_{film,impeller}$ [kWm ^{−2} K^{−1}] | Bulk Temperature ${T}_{bulk,blade}$ [K] | Film Coefficient ${h}_{film,blade}$ [kWm ^{−2} K^{−1}] |

$L{S}_{1,therm.trans.}$ | 0–1 | 36 | 1000 | 295 | 0.2 |

$L{S}_{2,therm.trans.}$ | 1–6300 | 36 | 1000 | 295 | 0.2 |

$L{S}_{3,therm.trans.}$ | 6300–6301 | 36 | 1000 | 800 | 50 |

$L{S}_{4,therm.trans.}$ | 6301–6841 | 36 | 1000 | 800 | 50 |

$L{S}_{5,therm.trans.}$ | 6841–6842 | 36 | 1000 | 295 | 0.2 |

$L{S}_{6,therm.trans.}$ | 6842–17,000 | 36 | 1000 | 295 | 0.2 |

**Table 10.**Structural boundary conditions for the LCF-related quasi-stationary structural FE analysis of a full hot run of the reference turbine blade.

Load Step Number | Time Range of the Load Step [s] | Spin Loading [rad/s] | Static Pressure (Normal to the Surface) [MPa] | Component Pressure, Acting in Axial Direction of the Turbine [MPa] | Component Pressure, Acting in Circumferential Direction of the Turbine [MPa] |
---|---|---|---|---|---|

$L{S}_{1,LCF}$ | 0–1 | 0 | 0 | 0 | 0 |

$L{S}_{2,LCF}$ | 1–6300 | 0 | 0 | 0 | 0 |

$L{S}_{3,LCF}$ | 6300–6301 | 3736 | 3.88 | 0.112 | 0.377 |

$L{S}_{4,LCF}$ | 6301–6841 | 3736 | 3.88 | 0.186 | 0.629 |

$L{S}_{5,LCF}$ | 6841–6842 | 0 | 0 | 0 | 0 |

$L{S}_{6,LCF}$ | 6842–17,000 | 0 | 0 | 0 | 0 |

Result Description | 3D FE Analysis Value | Unit |
---|---|---|

Maximum principal stress ${\sigma}_{max,princ.,L{S}_{3,HCF\&creep}}$$\mathrm{as}\mathrm{obtained}\mathrm{by}\mathrm{load}\mathrm{step}L{S}_{3,HCFcreep}$ of the FE analysis at the maximum loading point of the 3D model. | 463 | MPa |

Maximum principal stress ${\sigma}_{max,princ.,L{S}_{4,HCF\&creep}}$$\mathrm{as}\mathrm{obtained}\mathrm{by}\mathrm{load}\mathrm{step}L{S}_{4,HCFcreep}$ of the FE analysis at the maximum loading point of the 3D model. | 517 | MPa |

Cyclic stress ${\sigma}_{c,HCF\&creep}$ of the stationary hot-run at the maximum loading point. | 54 | MPa |

Stress amplitude ${\sigma}_{a,HCF\&creep}$ of the stationary hot-run at the maximum loading point. | 27 | MPa |

Mean stress ${\sigma}_{m,HCF\&creep}$ of the stationary hot-run at the maximum loading point. | 490 | MPa |

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## Share and Cite

**MDPI and ACS Style**

Riccius, J.R.; Zametaev, E.B.
HCF and LCF Analysis of a Generic Full Admission Turbine Blade. *Aerospace* **2023**, *10*, 154.
https://doi.org/10.3390/aerospace10020154

**AMA Style**

Riccius JR, Zametaev EB.
HCF and LCF Analysis of a Generic Full Admission Turbine Blade. *Aerospace*. 2023; 10(2):154.
https://doi.org/10.3390/aerospace10020154

**Chicago/Turabian Style**

Riccius, Jörg R., and Evgeny B. Zametaev.
2023. "HCF and LCF Analysis of a Generic Full Admission Turbine Blade" *Aerospace* 10, no. 2: 154.
https://doi.org/10.3390/aerospace10020154