# Measurement of Gas Flow Rate at Gasification of Low-Melting Materials in a Flow-Through Gas Generator

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

_{0}= 2.5, 3.0 and 4.0 could be attached to the fire heater. Table 1 shows the calculated and measured parameters of the corresponding jet flow. Measurements of the real values of the flow Mach number M

_{1}were performed using a Pitot pressure sensor (Pitot pressure P

_{0}′) installed at the nozzle exit. In each experiment, the total pressure P

_{0}(t) and stagnation temperature T

_{0}(t) were recorded for calculating the mass flow rate of gases, G

_{0}(t). A jet of hot gasifying agent from the facility nozzle partly entered the GG mounted downstream along the facility axis.

## 3. Gas Generator Design

_{0,in}and stagnation temperature T

_{0,in}in the gas flow at the inlet to the LSM sample. Around the diffuser, a 36-g pyrotechnic igniter with a calorific value of about 1.5 MJ/kg was placed. It was used to ignite combustion of LSM aimed at providing heat for endothermic physical and chemical processes accompanying sample gasification. The igniter was triggered at a preset time by a command of the synchronization system. Typical igniter burning time was 0.10–0.15 s. Preliminary estimates showed that the gas temperature at the inlet of the LSM sample could theoretically reach 1300–2600 K, however the actual measured gas temperature was on the level of 1300–1500 K, thus indicating large heat loss into the walls.

_{0,out}and stagnation temperature T

_{0,out}. To measure static pressure P

_{out}and control the flow Mach number, a static pressure sensor was also mounted in the nozzle throat. After exiting the measuring nozzle, the exhaust jet was directed to the noise absorbing ventilation shaft at atmospheric pressure. For pressure measurements, pressure sensors RPD-I with a maximum pressure up to 1.0 and 2.5 MPa were used. The rated measurement error of the pressure sensors was 0.2%. The actual pressure measurement error was established by the results of numerous calibrations of the sensors in the expected pressure range. In this case, to control the set pressure, a PDE-020I reference pressure transducer was used with a basic relative error of ±0.02%. The resulting estimate of the actual pressure measurement error did not exceed 1%. For temperature measurements, tungsten-rhenium thermocouples were used. To convert the electrical signal of thermocouples into temperature readings, a standard calibration table was used. The temperature measurement error did not exceed 5%.

## 4. Test Results

## 5. Processing of Test Results

#### 5.1. Calculation of Gas Flow Rate at GG Intake

_{0}(t) and T

_{0}(t) and the approaching flow Mach number M

_{1}:

_{in}(t) = φF

_{in}ρ(t)V(t) = φF

_{in}M

_{1}P

_{0}(t)π(M

_{1})[γRT

_{0}(t)τ(M

_{1})]

^{1/2}[RT

_{0}(t)τ(M

_{1})]

^{−1}=

φF

_{in}M

_{1}π(M

_{1})τ(M

_{1})

^{−1/2}(γ/R)P

_{0}(t)T

_{0}(t)

^{−1/2}

_{in}is the cross-sectional area of the GG intake, φ is the contraction ratio of GG intake, R = 287 kJ/kg/K is the gas constant for air, γ = 1.4 is the specific heat ratio for air, π(M

_{1}) and τ(M

_{1}) are the gas-dynamic functions.

#### 5.2. Contraction Ratio of GG Intake

_{in}with the Mach number M

_{1}from the free jet emanating from the facility nozzle. In this case, the contraction ratio of the GG intake was φ = 1.0. Let us jointly consider Figure 2 and curves 2 (P

_{0,in}) in tests 1, 4, and 7 in Figure 4, Figure 5 and Figure 6. Downstream of the cylindrical section of the intake, the supersonic gas flow entered the expanding conical diffuser and accelerated to Mach number M

_{2}(M

_{2}> M

_{1}). Thereafter, due to geometric throttling in the LSM channels, the flow passed through a normal shock and became subsonic with a sharp decrease in the stagnation pressure to P

_{0,in}(M

_{2}).

_{0,in}/P

_{0}ratio. Prior to ignition triggering, the P

_{0,in}/P

_{0}ratio corresponded to the total pressure loss at elevated Mach number M

_{2}> M

_{1}. This indicated that the normal shock was located in the conical diffuser upstream of the total pressure sensor. After ignition triggering and establishment of LSM sample combustion, thermal throttling of the flow caused the normal shock to move upstream and exit the GG intake. Starting from this time instant, the P

_{0,in}/P

_{0}ratio corresponded to the total pressure loss in the normal shock at the freestream Mach number M

_{1}. A decrease in the Mach number ahead of the normal shock led, on the one hand, to a pressure rise in the flow entering the channels of LSM sample and thereby intensified the combustion and heat and mass transfer processes in sample channels. On the other hand, the head shock wave detached from the GG intake led to a decrease in the gas flow rate through the intake, i.e., to a decrease in the contraction ratio φ in Equation (1). This posed a problem of determining the realistic value of the contraction ratio φ < 1.0. The methodology for solving this problem by measuring the gas flow rate at the GG outlet is presented below. Once the contraction ratio is determined, Equation (1) can be used for calculating the mass flow rate of gasifying agent entering the GG intake.

#### 5.3. Calculation of Gas Flow Rate at GG Outlet

_{0,out}and stagnation temperature T

_{0,out}before the nozzle. The values of F*, P

_{0,out}, and T

_{0,out}were used to calculate G

_{out}using the relation:

_{out}(t) = mF*P

_{0,out}(t)T

_{0,out}(t)

^{−1/2}

^{(γ* + 1)/(γ − 1)}]

^{1/2}

_{out}is then the determination of coefficient m, as the gas composition depends on the LSM combustion completeness, as well as local instantaneous pressure and temperature. Herein, the values of γ* and R* for the gas mixture were determined by iterations using the Astra 4 thermodynamic code [29].

#### 5.4. Flow Rate of Polypropylene Gasification Products

_{in}and G

_{out}calculated based on Equations (1) and (2), respectively, for different freestream Mach numbers M

_{1}. In addition to plots G

_{in}(t) and G

_{out}(t), the calculated difference between these flow rates, ΔG = G

_{out}(t) − G

_{in}(t) is also plotted in Figure 9 to Figure 11. Clearly, this difference corresponds to the total flow rate of product gases generated by LSM sample gasification.

_{in}and G

_{out}were virtually equal. In test fires with combustion, a noticeable LSM gasification accompanied with sample combustion was detected. In these latter test fires, the gas flow rates G

_{in}and G

_{out}differed markedly. According to Figure 9, Figure 10 and Figure 11 the flow rate of gasification products (ΔG = G

_{out}(t) − G

_{in}(t)) in test fires with combustion could be constant, like in Figure 9 and Figure 10, or variable in time, like in Figure 11. The mean values of the flow rates of gasification products in Figure 9, Figure 10 and Figure 11 took the values of 0.08 kg/s at M

_{1}= 2.43, 0.10 kg/s at M

_{1}= 2.94, and 0.05–0.02 kg/s at M

_{1}= 3.81.

_{1}) and after (W

_{2}) test fire. The difference between these masses (ΔW = W

_{1}− W

_{2}) determines the amount of gasified sample material leaving the GG with exhaust gases. Based on the calculated flow rates G

_{in}and G

_{out}and measured sample masses W

_{1}and W

_{2}, one can derive the following balance equation for determining the intake contraction ratio φ:

_{1}− W

_{2}= mF*

_{t}

_{1}ʃ

^{t}

^{2}P

_{0,out}(τ)T

_{0,out}(τ)

^{−1/2}dτ − φF

_{in}M

_{1}π(M

_{1})τ(M

_{1})

^{−1/2}(γ/R)

_{t}

_{1}ʃ

^{t}

^{2}P

_{0}(τ)T

_{0}(τ)

^{−1/2}dτ

_{1}corresponds to the start of gas temperature rise after igniter triggering and time t

_{2}corresponds to the shutdown of air supply. An unknown value of the air intake contraction ratio φ can be now determined from Equation (4). Once φ is determined, the realistic value of gasifying agent flow rate at the inlet to LSM sample can be obtained. Furthermore, the value of coefficient m in Equation (3) can be refined.

_{in}dt/ʃΔGdt, varied from 1.61 to 2.86 in the test fires. This means that for obtaining 1 kg of gasification products one consumes 1.61 to 2.86 kg of gasifying agent.

## 6. Amendment

_{i}before and after test fires allowed obtaining additional useful information on the zones of maximum LSM decomposition along the sample length. Figure 12 shows the distribution of masses W

_{i}of individual blocks in a test sample, measured before and after test 3. The individual blocks are numbered from the inlet of the LSM sample. As seen, the zone of most intense LSM decomposition in this test was located between blocks 4 and 9. Figure 13 shows the photographs of all individual blocks of the LSM sample before and after test 3.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations and Nomenclature

ADC | Analog-to-digital converter | |

GG | Gas generator | |

LSM | Low-melting solid material | |

MAF | Model Aerodynamic Facility | |

ITAM SB RAS | Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences | |

c* | Characteristic exhaust velocity | m/s |

M_{0} | Design nozzle Mach number | - |

M_{1} | Air flow Mach number at the nozzle exit | - |

M_{2} | Mach number before the normal shock in diffuser | - |

P_{0}′ | Pitot pressure at the nozzle exit | Pa |

P_{0} | Total pressure of the air flow | Pa |

T_{0} | Total (stagnation) temperature of the flow | K |

G_{0} | Mass flow rate | kg/s |

P_{0,in} | Total pressure at the entrance of LSM sample | Pa |

T_{0,in} | Total temperature at the entrance of LSM sample | K |

P_{0,out} | Total pressure at the exit of LSM sample | Pa |

T_{0,out} | Total temperature at the exit of LSM sample | K |

P_{out} | Static pressure at the sound nozzle | Pa |

F_{in} | Area of intake entrance cross-section | m^{2} |

F* | Area of sonic nozzle throat cross-section | m^{2} |

G_{in} | Air flow rate through intake | kg/s |

G_{out} | Gas flow rate at the sonic nozzle throat | kg/s |

φ | Contraction ratio of intake | - |

R | Gas constant for air | J/kg/K |

R* | Gas constant for gas mixture | J/kg/K |

γ | Specific heat ratio for air | - |

γ* | Specific heat ratio for gas mixture | - |

π(M1) | Gas-dynamic function | - |

τ(M1) | Gas-dynamic function | - |

m | Dimensional coefficient | - |

W_{1} | Sample mass before test | kg |

W_{2} | Sample mass after test | kg |

W_{i} | Masses of individual blocks in the LSM sample | g |

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**Figure 3.**One of 16 identical polyethylene blocks for assembling a test sample; dimensions are given in millimeters.

**Figure 4.**Test results at M

_{1}= 2.43 (see Table 1): 1—P

_{0}; 2—P

_{0,in}; 3—P

_{0,out}; 4—P

_{out}; 5—T

_{0}; 6—T

_{0,in}; 7—T

_{0,out}.

**Figure 5.**Test results at M

_{1}= 2.94 (see Table 1): 1—P

_{0}; 2—P

_{0,in}; 3—P

_{0,out}; 4—P

_{out}; 5—T

_{0}; 6—T

_{0,in}; 7—T

_{0,out}.

**Figure 6.**Test results at M

_{1}= 3.81 (see Table 1): 1—P

_{0}; 2—P

_{0,in}; 3—P

_{0,out}; 4—P

_{out}; 5—T

_{0}; 6—T

_{0,in}; 7—T

_{0,out}.

**Figure 7.**Formation of a diverted head shock at the GG intake in test fires with LSM sample combustion.

**Figure 8.**Calculated dependences of coefficient m on temperature for PP–air mixtures with different content of PP (mass basis) at pressure 1 MPa.

**Figure 9.**Calculated time histories of flow rates G

_{in}(curve 8), G

_{out}(9) and ΔG = G

_{out}(t) − G

_{in}(t) (10) at M

_{1}= 2.43 in tests 1 to 3.

**Figure 10.**Calculated time histories of flow rates G

_{in}(curve 8), G

_{out}(9) and ΔG = G

_{out}(t) − G

_{in}(t) (10) at M

_{1}= 2.94 in tests 4 to 6.

**Figure 11.**Calculated time histories of flow rates G

_{in}(curve 8), G

_{out}(9) and ΔG = G

_{out}(t) − G

_{in}(t) (10) at M

_{1}= 3.81 in tests 7 to 9.

**Figure 12.**Masses of blocks composing LSM sample before (1) and after (2) test 3 with combustion. Burning time t

_{2}− t

_{1}= 3.46 – 1.15 = 2.31 s.

**Figure 13.**Photographs of (

**a**) upstream and (

**b**) downstream faces of blocks composing LSM sample after test 3 with combustion.

Designed M _{0} | Mean P_{0}′/P_{0} | Measured M _{1} | P_{0}, MPa | T_{0}, K | G_{0}, kg/s |
---|---|---|---|---|---|

2.5 | 0.528 | 2.43 | 1.90 | 665 | 0.85 |

3.0 | 0.346 | 2.94 | 3.20 | 830 | 0.79 |

4.0 | 0.163 | 3.81 | 3.00 | 850 | 0.32 |

Test | φ | ʃG_{in}dt,kg | m | ΔW, kg | ʃΔGdt, kg | ʃG_{in}dt/ʃΔGdt |
---|---|---|---|---|---|---|

2 | 0.751 | 0.330 | 0.0306 | 0.187 | 0.186 | 1.77 |

3 | 0.728 | 0.326 | 0.0308 | 0.176 | 0.174 | 1.86 |

5 | 0.774 | 0.444 | 0.0311 | 0.276 | 0.273 | 1.61 |

6 | 0.810 | 0.372 | 0.0312 | 0.219 | 0.216 | 1.70 |

8 | 0.662 | 0.133 | 0.0344 | 0.064 | 0.064 | 2.10 |

9 | 0.717 | 0.144 | 0.0344 | 0.050 | 0.050 | 2.86 |

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**MDPI and ACS Style**

Vnuchkov, D.A.; Zvegintsev, V.I.; Nalivaichenko, D.G.; Frolov, S.M.
Measurement of Gas Flow Rate at Gasification of Low-Melting Materials in a Flow-Through Gas Generator. *Energies* **2022**, *15*, 5741.
https://doi.org/10.3390/en15155741

**AMA Style**

Vnuchkov DA, Zvegintsev VI, Nalivaichenko DG, Frolov SM.
Measurement of Gas Flow Rate at Gasification of Low-Melting Materials in a Flow-Through Gas Generator. *Energies*. 2022; 15(15):5741.
https://doi.org/10.3390/en15155741

**Chicago/Turabian Style**

Vnuchkov, Dmitry A., Valery I. Zvegintsev, Denis G. Nalivaichenko, and Sergey M. Frolov.
2022. "Measurement of Gas Flow Rate at Gasification of Low-Melting Materials in a Flow-Through Gas Generator" *Energies* 15, no. 15: 5741.
https://doi.org/10.3390/en15155741