# Experimental Characterization of an Adaptive Supersonic Micro Turbine for Waste Heat Recovery Applications

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## Abstract

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_{el}) are commercially used as expansion machines in waste heat recovery (WHR) systems such as organic Rankine cycles (ORCs). These highly loaded turbines are generally designed for a specific parameter set, and their isentropic expansion efficiency significantly deteriorates when the mass flow rate of the WHR system deviates from the design point. However, in numerous industry processes that are potentially interesting for the implementation of a WHR process, the temperature, mass flow rate or both can fluctuate significantly, resulting in fluctuations in the WHR system as well. In such circumstances, the inlet pressure of the ORC turbine, and therefore the reversible cycle efficiency must be significantly reduced during these fluctuations. In this context, the authors developed an adaptive supersonic micro turbine for WHR applications. The variable geometry of the turbine nozzles enables an adjustment of the swallowing capacity in respect of the available mass flow rate in order to keep the upper cycle pressure constant. In this paper, an experimental test series of a WHR ORC test rig equipped with the developed adaptive supersonic micro turbine is analysed. The adaptive turbine is characterized concerning its off-design performance and the results are compared to a reference turbine with fixed geometry. To create a fair data basis for this comparison, a digital twin of the plant based on experimental data was built. In addition to the characterization of the turbine itself, the influence of the improved pressure ratio on the energy conversion chain of the entire ORC is analysed.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Swallowing Capacity of a Supersonic Turbine

_{throat}< 1). ${A}_{throat}$ represents the throat area of the nozzle, ${p}_{t,in}$ the absolute total inlet pressure, ${T}_{t,in}$ the absolute total inlet temperature, $\kappa $ the isentropic exponent and ${R}_{i}$ the specific gas constant. ${M}_{thorat}$ is the isentropic Mach number at the throat of the nozzle.

_{throa}

_{t}= 1, M

_{out}> 1), Equation (3) can be applied. As choking occurs, the mass flow rate and the inlet pressure show a linear dependence. In the choked condition of the nozzle, the mass flow is independent of the outlet pressure.

#### 2.2. ANH Concept and Its Implementation

#### 2.2.1. Fixed ANH Turbine (F-ANH)

#### 2.2.2. Manually Adjusted Turbine Geometry (M-ANH)

#### 2.2.3. Automatically Adjusted Turbine Geometry (A-ANH)

#### 2.3. The ORC Test Rig

#### 2.4. Energy Conversion Chain and Considered Conversion Steps

#### 2.5. Semi-Empirical Model as Basis of Performance Evaluation

- Exhaust gas (XG-IN) composition (CO
_{2}, H_{2}O, N_{2}, O_{2}) - Exhaust gas mass flow rate
- Exhaust gas inlet temperature (XG-IN)
- Efficiency of the pumps (simulated as a single pump)
- Thermal capacity ($U\times A)$ values, approximated by a power law approach for the evaporator (EVAP)
- Constant turbine inlet temperature of 190 °C (independent of mass flow rate)
- Efficiency of the turbine
- Condenser (COND) efficiency (by implementing a certain heat leakage)
- Degrees of subcooling of the working fluid (MM-C-OUT) in the condenser
- Cooling water inlet temperature (CW-IN)

## 3. Results and Discussion

#### 3.1. Swallowing Capacity and Turbine Inlet Pressure

#### 3.2. Turbine Efficiency for the Different Turbine Configurations

#### 3.3. Turbine Efficiency, Reversible Cycle Efficiency and ORC Efficiency Calculated with the Digital Twin

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$A$ | area | (m^{2}) |

$\dot{H}$ | enthalpy flux | (J/s) |

$h$ | specific enthalpy | (J/s) |

$\kappa $ | isentropic exponent | (-) |

$M$ | Mach number | (-) |

$\dot{m}$ | mass flow rate | (kg/s) |

$\eta $ | efficiency | (%) |

$P$ | power | (W) |

$p$ | pressure | (Pa) |

$PR$ | pressure ratio | (%) |

$\dot{Q}$ | heat flux | (W) |

${R}_{i}$ | specific gas constant | (J/kg/K) |

$T$ | temperature | (K) |

$U\xb7A$ | thermal capacity | (W/K) |

$\dot{X}$ | exergy flux | (J/s) |

Subscripts | ||

corr | corrected | |

EC | electrical chain | |

EG | exhaust gas | |

EV | evaporator | |

el | electric | |

HU | heat utilization | |

IE | isentropic expansion | |

is | isentropic | |

ORC | organic Rankine cycle | |

rev | reversible | |

st | static | |

sup | supplied | |

t | total | |

ut | utilized | |

WHR | waste heat recovery | |

Abbreviations | ||

ANH | adjustable nozzle height | |

EAF | electric arc furnace | |

EV | end value | |

MV | measured value | |

PCM | phase change material | |

VTG | variable turbine geometry | |

WHR | waste heat recovery |

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**Figure 1.**Meridional cut (

**a**) and blade-to-blade cut (

**b**) of the implemented adjustable nozzle height concept.

**Figure 2.**Photograph (

**a**) and P&ID scheme (

**b**) of the experimental ORC plant at the University of Bayreuth.

**Figure 5.**Turbine efficiency (measured and interpolated) of the A-ANH configuration in dependency on the mass flow rate and turbine outlet pressure.

**Figure 6.**Polynomial fits of the turbine efficiency of the A-ANH configuration in dependency on the mass flow rate percentage for three different turbine outlet pressures.

**Figure 7.**Normalized corrected mass flow rate (swallowing capacity) as a function of the working fluid mass flow rate.

**Figure 9.**Total-to-static isentropic turbine efficiency for F-ANH and M-ANH (

**a**) and for F-ANH and A-ANH (

**b**) as a function of the pressure ratio (PR).

**Figure 10.**Total-to-static isentropic turbine efficiency and reversible cycle efficiency in dependency on the working fluid mass flow rate, calculated by the digital twin for 0.35, 0.40 and 0.45 bar turbine outlet pressure.

**Figure 11.**ORC efficiency ${\eta}_{ORC}$ in dependency on the working fluid mass flow rate, calculated by the digital twin for 0.35, 0.40 and 0.45 bar turbine outlet pressure.

$\frac{{\dot{\mathit{m}}}_{\mathit{O}\mathit{R}\mathit{C}}}{{\dot{\mathit{m}}}_{\mathit{O}\mathit{R}\mathit{C},\mathit{d}\mathit{e}\mathit{s}\mathit{i}\mathit{g}\mathit{n}}}$ | ${\dot{\mathit{m}}}_{\mathit{O}\mathit{R}\mathit{C}}$ | ${\dot{\mathit{Q}}}_{\mathit{E}\mathit{G},\mathit{u}\mathit{t}}$ | ${\mathit{P}}_{\mathit{e}\mathit{l},\mathit{d}\mathit{e}\mathit{s}\mathit{i}\mathit{g}\mathit{n}}$ |
---|---|---|---|

(%) | (g/s) | (kW_{th}) | (kW_{el}) |

50 | 160 | 90–102 | 4.0 |

60 | 192 | 106–116 | 5.6 |

70 | 224 | 125–133 | 7.2 |

80 | 256 | 139–150 | 8.8 |

90 | 288 | 160–168 | 10.4 |

100 | 320 | 178–184 | 12.0 |

Component | Type |
---|---|

Heat supply | Propane gas burner |

Pumps | Centrifugal and piston diaphragm pump (both with variable frequency drive) |

“Evaporator” | Plate and Shell type heat exchanger |

Expander | Quasi-Impulse Cantilever turbine in F-ANH, M-ANH and A-ANH configuration |

Condenser | Plate heat exchanger |

Heat rejector | Air cooler |

Measured Parameter | Type | Measuring Range | Accuracy of Measurement |
---|---|---|---|

Turbine inlet temperature | Omega PR-22-3-100-A-M3-150-M12 | −30–350 °C | 1 °C |

Turbine inlet pressure | Omega PAA23SYC-10-M12 | 0–10 bar | 1.5% of EV |

Turbine outlet pressure | Omega PAA23SY C-2-M12 | 0–2 bar | 1.5% of EV |

Mass flow rate | ABB CoriolisMaster FCB330 | 0–416,667 g/s | 0.4% of MV |

Power | Sieb & Meyer 0362111OF | 0–20 kW | N/A |

Module | Measuring Range | Accuracy of Measurement |
---|---|---|

NI 9207 | 0–22 mA | 0.87% of MV + 0.05% of EV |

NI 9208 | 0–22 mA | 0.76% of MV + 0.04% of EV |

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**MDPI and ACS Style**

Popp, T.; Weiß, A.P.; Heberle, F.; Winkler, J.; Scharf, R.; Weith, T.; Brüggemann, D.
Experimental Characterization of an Adaptive Supersonic Micro Turbine for Waste Heat Recovery Applications. *Energies* **2022**, *15*, 25.
https://doi.org/10.3390/en15010025

**AMA Style**

Popp T, Weiß AP, Heberle F, Winkler J, Scharf R, Weith T, Brüggemann D.
Experimental Characterization of an Adaptive Supersonic Micro Turbine for Waste Heat Recovery Applications. *Energies*. 2022; 15(1):25.
https://doi.org/10.3390/en15010025

**Chicago/Turabian Style**

Popp, Tobias, Andreas P. Weiß, Florian Heberle, Julia Winkler, Rüdiger Scharf, Theresa Weith, and Dieter Brüggemann.
2022. "Experimental Characterization of an Adaptive Supersonic Micro Turbine for Waste Heat Recovery Applications" *Energies* 15, no. 1: 25.
https://doi.org/10.3390/en15010025