# Unsteady Flow Loss Mechanism and Aerodynamic Improvement of Two-Stage Turbine under Pulsating Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. CFD Set-Up

#### 2.2. CFD Validation

## 3. Flow Loss Analysis of Two-Stage Turbine under Pulsating Conditions

_{s,1–6}) is obtained by the isentropic process from point 1 to point 6. Similarly, the maximum expansion power produced by the fluid at location 2 is denoted as P

_{s,2–6}. Thus, the power loss in HPT volute can be expressed as Equation (10). In the calculation of the loss in rotor component, the actual power output of the rotor needs to be excluded, as shown in Equations (11) and (14). Since there is a phase lag between the upstream and downstream components, the direct subtraction may result in a negative value of the power loss. Obviously, this is physically incorrect. Therefore, the profiles of the power versus time of the downstream component are advanced to be in phase with that of the upstream component. This manipulation method will not affect the cycle-averaged power since the exit pressure p

_{6}is kept constant.

## 4. Aerodynamic Performance Improvement

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | amplitude | |

c_{p} | specific heat ratio at constant pressure | J/kg K |

m | mass flow rate | kg/s |

N | Reduced speed | rpm/K^{0.5} |

n | rotation speed | rpm |

P | power | kW |

p | pressure | Pa |

R_{g} | gas constant | J/kg K |

r | radius | mm |

T | temperature or pulse period | K or s |

t | time | s |

Acronyms | ||

BSR | blade speed ratio | |

CFD | computational fluid dynamics | |

EXP | experiment | |

HPT | high-pressure turbine | |

LPT | low-pressure turbine | |

MFP | mass flow parameter | |

T-T | total to total | |

T-S | total to static | |

Greek symbols | ||

$\gamma $ | adiabatic exponent | |

$\eta $ | efficiency | |

$\mathsf{\pi}$ | expansion ratio | |

$\mathsf{\tau}$ | torque | Nm |

$\mathsf{\phi}$ | coefficient | |

$\mathsf{\omega}$ | angular velocity | rad/s |

Subscripts and superscripts | ||

1–6 | locations in the two-stage turbine | |

a | actual | |

ave | average | |

in | inlet | |

inst | instant | |

s | isentropic | |

t | stagnation condition |

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**Figure 2.**Calculation domain of the two-stage turbine: (

**a**) the geometry of two turbine stages; (

**b**) mesh of the two turbine stages.

**Figure 3.**Total (

**a**) pressure and (

**b**) temperature profiles imposed at the inlet of the calculation domain; (

**a**) total pressure; (

**b**) total temperature.

**Figure 4.**Validation of the computational fluid dynamics (CFD) model under steady condition, HPT expansion ratio ${\pi}_{h}=2.2$(T-S); (

**a**) turbine efficiency; (

**b**) mass flow parameter.

**Figure 6.**Schematic of the two-stage turbine and the locations for monitor; (

**a**) HPT volute; (

**b**) Cross-sectional view of the two-stage turbine.

**Figure 7.**The impacts of pulse amplitude on turbine theoretical power, actual power and isentropic efficiency.

**Figure 9.**The flow losses in each component during a pulse period; (

**a**) the pulse amplitude is 0.4 A; (

**b**) the pulse amplitude is 1.0 A; (

**c**) the pulse amplitude is 1.6 A.

**Figure 11.**The circumferential-averaged incidence angle at different span of the HPT rotor as a function of time; (

**a**) HPT rotor with 1.0 A pulse amplitude; (

**b**) HPT rotor with 1.6 A pulse amplitude.

**Figure 12.**The circumferential-averaged incidence angle at different span of the LPT rotor as a function of time; (

**a**) LPT rotor with 1.0 A pulse amplitude; (

**b**) LPT rotor with 1.6 A pulse amplitude.

**Figure 13.**The entropy contour at 20%, 50% and 80% span of the LPT rotor at different times when the pulse amplitude is 1.6 A; (

**a**)peak time, 20% span; (

**b**)peak time, 50% span; (

**c**)peak time, 80% span; (

**d**)100% T, 20% span; (

**e**)100% T, 50% span; (

**f**)100% T, 80% span.

**Figure 14.**Comparisons of different blade designs; (

**a**) blade profiles at blade tip; (

**b**) 3D view of the rotor blade.

**Figure 15.**The entropy contour and velocity plot at 80% span of the rotor; (

**a**) case 1, BSR = 0.35; (

**b**) case 2, BSR = 0.35; (

**c**) case 3, BSR = 0.35; (

**d**) case 1, BSR = 0.95; (

**e**) case 2, BSR = 0.95; (

**f**) case 3, BSR = 0.95.

**Figure 16.**The rotor instantaneous isentropic efficiency during a pulse period in case 1: (

**a**) under high-load pulsating flow; (

**b**) under low-load pulsating flow.

**Figure 17.**The rotor instantaneous isentropic efficiency during a pulse period in case 2: (

**a**) under high-load pulsating flow; (

**b**) under low-load pulsating flow.

**Figure 18.**The rotor instantaneous isentropic efficiency during a pulse period in case 3: (

**a**) under high-load pulsating flow; (

**b**) under low-load pulsating flow.

Geometrical Feature | Dimension |
---|---|

Volute A/R (mm) | 15 |

Rotor inlet diameter (mm) | 84 |

Rotor inlet height (mm) | 9.3 |

Rotor exit tip diameter (mm) | 69 |

Rotor tip gap (mm) | 0.5 |

Number of blades | 12 |

Geometrical Feature | Dimension |
---|---|

Stator tip diameter (mm) | 128 |

Stator hub diameter (mm) | 92 |

Number of vanes in stator | 19 |

Rotor tip diameter (mm) | 132 |

Rotor hub diameter (mm) | 90 |

Rotor tip gap (mm) | 0.5 |

Number of blades in rotor | 20 |

Maximum Skewness | Minimum Orthogonal | Maximum Aspect Ratio |
---|---|---|

0.918 | 0.105 | 23.59 |

$\mathbf{Minimum}\text{}\mathbf{Face}\text{}\mathbf{Angle}\text{}(\xb0)$ | $\mathbf{Maximum}\text{}\mathbf{Face}\text{}\mathbf{Angle}\text{}(\xb0)$ | Maximum Element Volume Ratio | |
---|---|---|---|

HPT rotor | 30.47 | 149.67 | 6.09 |

LPT stator | 55.14 | 112.54 | 3.76 |

LPT rotor | 29.42 | 151.38 | 10.19 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, R.; Li, W.; Zhuge, W.; Zhang, Y.
Unsteady Flow Loss Mechanism and Aerodynamic Improvement of Two-Stage Turbine under Pulsating Conditions. *Entropy* **2019**, *21*, 985.
https://doi.org/10.3390/e21100985

**AMA Style**

Zhao R, Li W, Zhuge W, Zhang Y.
Unsteady Flow Loss Mechanism and Aerodynamic Improvement of Two-Stage Turbine under Pulsating Conditions. *Entropy*. 2019; 21(10):985.
https://doi.org/10.3390/e21100985

**Chicago/Turabian Style**

Zhao, Rongchao, Weihua Li, Weilin Zhuge, and Yangjun Zhang.
2019. "Unsteady Flow Loss Mechanism and Aerodynamic Improvement of Two-Stage Turbine under Pulsating Conditions" *Entropy* 21, no. 10: 985.
https://doi.org/10.3390/e21100985