# Effects of Fuel Input on Pulsation Reactor Behavior—An Experimental Study

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## Abstract

**:**

## 1. Introduction

#### 1.1. Pulsation Reactors for Material Treatment

#### 1.2. Pulsating Combustion & the Theory of Pulsation Reactors

- 1.
- Ignition & combustion (A→B): The combustible mixture (air and gaseous fuel) is driven into the combustion chamber where it is ignited. To initialize the operation, a spark plug is typically used. Once self-excited periodic combustion is present, no additional energy source is needed and the spark plug might be switched off.
- 2.
- Expansion (B→C): The combustion is accompanied by a rapid increase of temperature and pressure, pushing the combustion products further towards the end of the exhaust pipe. The excess pressure causes mechanical valves to close completely, preventing both a flow into the combustion chamber and a potential backflow. May aerodynamic valves are used, a fraction of the flue gas might also travel back through the inlet valves.
- 3.
- Intake (C→D): Inertia of the outward traveling gases eventually causes the pressure in the combustion chamber to fall below the ambient pressure, resulting in a fresh mixture being sucked into the combustion chamber.
- 4.
- Compression (D→A): As a consequence of the negative gauge pressure in the combustion chamber, a portion of the flue gas originally moving downstream through the tailpipe reverses its direction and is pulled back into the combustion chamber. The inertia of the fluid entering from both sides of the combustion chamber results in the pressure rising above the ambient level. As the fresh mixture gets in contact with the hot combustion products, it is re-ignited and the cycle repeats.

## 2. Method

#### 2.1. Investigated PR Characteristics

- (a)
- Operation frequency: ${f}_{PR}$
- (b)
- Amplitude of pressure oscillations: ${p}_{A}$
- (c)
- Amplitude of velocity oscillations: ${v}_{A}$
- (d)
- Temperature in the tailpipe: T

#### 2.2. Experimental Setup

#### 2.3. Operation Points

#### 2.4. Data Processing & Related Calculations

## 3. Results & Discussion

#### 3.1. Pressure Data Results

#### 3.2. Temperature Data Results & the Energy Balance

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Arabic | |

A | Area |

c | Speed of sound |

${c}_{p}$ | Heat capacity at constant pressure |

f | Frequency |

${f}_{PR}$ | Operation frequency of the pulsation reactor |

${f}_{S}^{\left(p\right)}$ | Sampling frequency of the pressure sensor |

${h}_{f}$ | Enthalpy of formation (mass-specific) |

$\Delta \dot{H}$ | Enthalpy flow change |

$\Delta {\dot{H}}_{chem}$ | Chemical energy flow change |

L | Length |

$\dot{m}$ | Mass flow rate |

M | Molar mass |

p | Pressure |

${P}^{\left(in\right)}$ | Power input |

${P}_{eff}^{\left(in\right)}$ | Effective power input |

${P}_{\rho}^{\left(in\right)}$ | Power density input |

${\dot{Q}}_{L}$ | Heat loss |

r | Specific gas constant |

t | Time |

T | Period/thermodynamic temperature |

$TH{D}_{F}$ | Total harmonic distortion |

v | Velocity |

V | Volume |

$\overline{V}$ | Combustion chamber to the tailpipe volume ratio |

$\dot{V}$ | Normal flow rate |

Y | Mass fraction |

Greek | |

$\gamma $ | Heat capacity ratio |

$\lambda $ | Air-fuel equivalence ratio |

$\rho $ | Density |

$\chi $ | Mole fraction |

Indices | |

$\left(avg\right)$ | Average |

A | Air/amplitude |

$A/M$ | Amplitude-to-mean value ratio |

G | Gas |

$\left(in\right)$ | Input |

M | Mean value |

## Abbreviations

$CC$ | Combustion chamber |

$CDO$ | Combustion-driven oscillations |

$DFT$ | Discrete Fourier transform |

$HR$ | Helmholtz resonator |

$OP$ | Operation point |

$PIV$ | Particle Image Velocimetry |

$PR$ | Pulsation reactor |

$RMS$ | Root mean square |

$TP$ | Tailpipe |

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**Figure 1.**Schematic of a pulsation reactor [6].

**Figure 3.**The experimental pulsation reactor setup. The actual orientation is vertical. All dimensions are in millimeters.

**Figure 4.**Operation points displayed graphically in the ${P}_{\rho}^{\left(in\right)}-\lambda $ plane. Since the airflow rate was always varied by the same value, the increment of the air–fuel equivalence ratio is not constant and alters depending on the power density input. Thus, the maximum $\lambda $ for which stable pulsations were reached does not necessarily have to represent the operation limit. That applies primarily for lower values of ${P}_{\rho}^{\left(in\right)}$.

**Figure 6.**Oscillating pressure part for one specific operation point displayed depending on the cycle time (time normalized by the period). The solid blue curve shows the actually measured data, while the dashed red curve represents the theoretical oscillations following an ideal sine function. Each subplot displays the pressure at one location along the tailpipe: (

**a**) $T{P}_{1}$, (

**b**) $T{P}_{2}$, (

**c**) $T{P}_{3}$, (

**d**) $T{P}_{4}$.

**Figure 8.**Average total harmonic distortion displayed relative to air–fuel equivalence ratio for several power density input values.

**Figure 9.**Operation frequency of a pulsation reactor displayed relative to air–fuel equivalence ratio for several power density input values.

**Figure 10.**Measured PR operation frequency (${f}_{PR}$) compared with the theoretical frequency of a Helmholtz resonator (${f}_{HR}$) calculated using relation (1).

**Figure 11.**Pressure amplitude along the TP for one specific power density input. The solid lines connect the original data and the dashed curves display the pressure profile extrapolated to the tailpipe end, which was obtained through an approximation of the original data by a polynomial of the second order.

**Figure 12.**Average tailpipe pressure amplitude displayed relative to air–fuel equivalence ratio for several power density input values.

**Figure 13.**The average velocity amplitude and the average mean velocity ratio displayed together with the average mean velocity.

**Figure 15.**Average tailpipe temperature displayed relative to air–fuel equivalence ratio for several power density input values.

**Figure 16.**Total pulsation reactor heat loss normalized by the effective power input displayed relative to air–fuel equivalence ratio for several power density input values.

**Table 1.**Overview of the measured operation points in terms of the air–fuel equivalence ratio, $\lambda $ (the central part of the table), and of the power density input, ${P}_{\rho}^{\left(in\right)}$ (the bottom part of the table). The OPs are determined by a combination of the gas and the airflow rate - ${\dot{V}}_{G}$ and ${\dot{V}}_{A}$, respectively. The use of a hyphen means that stable pulsating combustion could not be reached for the particular flow rate combination.

${\dot{\mathit{V}}}_{\mathit{G}}$ [Nm^{3}/h] | 0.75 | 1.00 | 1.25 | 1.50 | 1.75 | 2.00 | 2.25 | 2.50 | 2.75 | |
---|---|---|---|---|---|---|---|---|---|---|

${\dot{\mathit{V}}}_{\mathit{A}}$ [Nm^{3}/h] | ||||||||||

10 | - | 1.04 | - | - | - | - | - | - | - | |

15 | 2.08 | 1.56 | 1.25 | 1.04 | 0.89 | - | - | - | - | |

20 | - | 2.08 | 1.66 | 1.39 | 1.19 | 1.04 | 0.92 | 0.83 | 0.76 | |

25 | - | - | 2.08 | 1.73 | 1.49 | 1.30 | 1.16 | 1.04 | 0.95 | |

30 | - | - | - | 2.08 | 1.78 | 1.56 | 1.39 | 1.25 | 1.13 | |

35 | - | - | - | - | 2.08 | 1.82 | 1.62 | 1.46 | 1.32 | |

40 | - | - | - | - | - | - | 1.85 | 1.66 | 1.51 | |

45 | - | - | - | - | - | - | - | 1.87 | 1.70 | |

50 | - | - | - | - | - | - | - | - | 1.89 | |

55 | - | - | - | - | - | - | - | - | 2.08 | |

${\mathbf{P}}_{\mathbf{\rho}}^{\left(\mathbf{in}\right)}$ [kW/m^{3}] | 1100 | 1467 | 1834 | 2200 | 2567 | 2934 | 3301 | 3667 | 4034 |

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**MDPI and ACS Style**

Dostál, J.; Heidinger, S.; Klaus, C.; Unz, S.; Beckmann, M.
Effects of Fuel Input on Pulsation Reactor Behavior—An Experimental Study. *Processes* **2023**, *11*, 444.
https://doi.org/10.3390/pr11020444

**AMA Style**

Dostál J, Heidinger S, Klaus C, Unz S, Beckmann M.
Effects of Fuel Input on Pulsation Reactor Behavior—An Experimental Study. *Processes*. 2023; 11(2):444.
https://doi.org/10.3390/pr11020444

**Chicago/Turabian Style**

Dostál, Jakub, Stefan Heidinger, Christian Klaus, Simon Unz, and Michael Beckmann.
2023. "Effects of Fuel Input on Pulsation Reactor Behavior—An Experimental Study" *Processes* 11, no. 2: 444.
https://doi.org/10.3390/pr11020444