# Prediction of Leidenfrost Temperature in Spray Cooling for Continuous Casting and Heat Treatment Processes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{L}, is of paramount importance to metal alloy quenching since it marks the transition from very poor heat transfer in film boiling to the far superior heat transfer associated with transition boiling [1]. The above sentence defines the purpose of the study presented in this paper well.

^{−2}·K

^{−1}changes at 80 s into a nucleate boiling regime with HTC of about 4000 W·m

^{−2}·K

^{−1}. The Leidenfrost temperature is about 800 °C. The results of the experiment shown in Figure 1 demonstrate the great importance of knowledge of the Leidenfrost temperature for design and control of cooling.

^{−2}·K

^{−1}and 13,000 W·m

^{−2}·K

^{−1}.

_{L}. T

_{L}here is 180 °C for a velocity of 1 m·s

^{−1}and 320 °C for a velocity of 20 m·s

^{−1}. This result shows how the droplet velocity is even important in sprays.

^{−1}·m

^{−2}). T

_{L}is shown here for the spray and the influence of the surface roughness. For a constant droplet velocity of 14 m·s

^{−1}T

_{L}is 280 °C for polished aluminium and 240 °C for particle blasted aluminium. The above temperatures are given for spray but are much lower than in other papers.

^{−2}·s

^{−1}and proposed a function for T

_{L}:

_{L}= 536.8 G

^{0.116}

^{−2}·s

^{−1}.

^{2}·d/σ

^{−3}, v is droplet velocity in m·s

^{−1}, d is droplet diameter and σ is surface tension in N·m

^{−1}.

_{S}= G·d/µ

_{S}= G

^{2}·d/ρ·σ

^{−2}·s

^{−1}and µ is dynamic viscosity kg·m

^{−1}·s

^{−1}.

^{−1}is used because it is considered a good example for continuous casting. There are not many references in the literature for moving surfaces and spray cooling. Zhang [6] published a description of an experimental technique for an experimental study of cooling in continuous casting. Gradeck [7] shows the influence of velocity in a range from 0.5 to 1.25 m·s

^{−1}and reports a significant influence on cooling intensity both above and below T

_{L}but only [8] a minor effect on T

_{L}. Raudensky [4] gives data for a stationary experiment in contrast to the cooled surface at velocities of 2 m·min

^{−1}and 5 m·min

^{−1}. The same paper shows the Leidenfrost temperature for three sizes of mist nozzles used in continuous casting (3, 4.5 and 7 mm) operating in a water pressure range of 0.5 bar to 7 bar and a constant air pressure of 2 bar. The Leidenfrost temperature is almost exactly 600 °C for all three nozzles for a pressure of 0.5 bar. The differences grow as feeding pressure increases. For a water pressure of 7 bar T

_{L}= 710 °C for a 3 mm nozzle, T

_{L}= 770 °C for a 4.5 mm nozzle and T

_{L}= 1170 °C for a 7 mm nozzle.

^{−1}; the nozzle moved at a velocity of 4 m·min

^{−1}under the static test sample and the spray height was 300 mm. Brozova reported small differences in T

_{L}for surface roughness when Rz is between 2.2 and 35 µm and Ra is between 0.4 and 7.3 µm. Bigger differences were found for high levels of roughness (Rz over 50 µm) but the reading of T

_{L}was difficult because the dependence of the heat flux on the surface temperature was very flat, as described in [2].

^{3}/m

^{2}·s) where a defined layer of Al

_{2}O

_{3}is formed on the steel substrate. Experiments with scale thickness from 50 µm to 210 µm again showed more intensive cooling with a thicker layer of oxides, a significantly higher Leidenfrost temperature. The same paper gives a graphical comparison of experiments with water cooling and air cooling. For air cooling the scale layer only acts as a thermal barrier which decreases the intensity of heat transfer. No effects with intensification of cooling typical for liquid spray cooling can be observed for air cooling. The study presented in this paper uses samples made of rolled austenitic steel and the presence of the oxides on the surface is not considered.

^{−2}·s

^{−1}) and air flow velocity (from 25 to 50 m·s

^{−1}). In this study the cooling effect is divided into two independent parts: the effect of the water jet and the effect of the air jet. Increases in droplet velocity due to air flow are not considered. The Leidenfrost temperature grows with growing air velocity. The results for a liquid mass flow of 7 kg·m

^{−2}·s

^{−1}give a Leidenfrost temperature of 515 °C for an air velocity of 25 m·s

^{−1}and T

_{L}547 °C for an air velocity of 45 m·s

^{−1}.

## 2. Laboratory Measurements

#### 2.1. Plan of Experiments

^{−1}.

#### 2.2. Heat Transfer Coefficient and Leidenfrost Temperature Measurement

^{−1}in this study. The test plate is insulated from all sides except the sprayed surface and is made of austenitic steel to protect the surface from oxidation. K-type shielded thermocouples were positioned inside the plate with the tip at a distance of 2 mm from the cooled surface. The distribution of thermocouples allowed us to monitor the temperature field in the cooled plate (Figure 3). A computer with a data acquisition system monitored the heating process, controlled the experiment and recorded the data from the thermocouples and position sensor.

^{−1}.

#### 2.3. Water Impingement Density Measurement

^{−2}·s

^{−1}.

#### 2.4. Impact Pressure Measurement

#### 2.5. Droplet Size and Velocity

_{10}—mean diameter, D

_{32}—Sauter mean diameter, VP—absolute mean velocity, VPx mean velocity on x axis, VPy mean velocity on y axis). For correlation purposes Sauter mean diameter and absolute mean velocity are used in this study. The Sauter mean diameter (d

_{32}) is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. The value of the diameter d

_{32}is far from the average diameter. For experiment E9 the diameter d

_{32}is 316 µm and for experiment E10 the diameter d

_{32}is 132 µm (compare with Figure 7). The mean velocity for experiment E9 is 7.71 m·s

^{−1}and for experiment E10 it is 15.4 m·s

^{−1}.

## 3. Correlations

_{L}. The following parameters are available for correlations.

_{i}(l·m

^{−2}·s

^{−1}) water impingement density;

^{−1}) mean droplet velocity;

_{32}(m) Sauter droplet diameter;

_{i}·10

^{−3}/(π/6·d

_{32}

^{3}) (m

^{−2}·s

^{−1}) number of drops per square meter per second,

_{32}

^{3}·v

^{2}(J) kinetic energy of droplet (for droplet with average size and speed),

^{−1}) droplet momentum,

_{32}/η (-) Reynolds number.

^{2}” gives the average square difference between the measured HTC and the correlated HTC. $Re{s}^{2}=\frac{1}{N}\sum {\left({T}_{L,measured}-{T}_{L,corelated}\right)}^{2}$, where N is the number of HTC values used. $Re{s}^{2}$ for each tested equation is also shown in Figure 9. Not all used parameters are independent. For example, Equations (1) and (2) are equivalent to each other because the number of droplets N (used in Equation (2)) can be expressed by Q

_{i}and d

_{32}(used in Equation (1)). Both are mentioned due to the different difficulty of obtaining the required parameters.

## 4. Conclusions

_{L}in comparison to Equation (10), which uses water impingement density. If the relative residue for Equation (10) is 100 % then the residue for Equation (9) is 57 %.

_{i}is water impingement density in l·m

^{−2}·s

^{−1}, v is mean droplet velocity in m·s

^{−1}, and d

_{32}is Sauter droplet diameter in m.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of typical record of spray cooling experiment where the Leidenfrost temperature is reached (reproduced from [4], with permission from authors, 2005).

**Figure 2.**Example of HTC for one mist nozzle with different flowrate settings, Leidenfrost temperature in a range from 500 °C to over 1200 °C.

**Figure 3.**Test bench for HTC tests, insulated upper surface of test plate with thermocouples (

**left**), nozzle on moving trolley spraying test plate, deflector is open (

**right**).

**Figure 4.**Temperatures measured at a depth of 2 mm and computed surface temperatures, data for experiments E9 and E10 at position of nozzle axis.

**Figure 7.**Droplet diameter distribution for experiments E9 and E10, identical nozzle, identical water flowrate, air pressure 1.5 bar left (

**a**), air pressure 3.0 bar right (

**b**), cumulative percentage orange line.

**Figure 8.**Droplet velocity distribution for experiments 9 and 10, identical nozzle, identical water flowrate, air pressure 1.5 bar left (

**a**), air pressure 3.0 bar right (

**b**), cumulative percentage orange line.

**Figure 9.**Comparison of Equations (1)–(10) based on relative residue Res

^{2}. The parameters which were used are written under each column.

Experiment | Nozzle Type | Standoff (mm) | Water Flowrate (l·min^{−1}) |
---|---|---|---|

E1 | mist | 360 | 4 |

E2 | mist | 200 | 7 |

E3 | mist | 190 | 20 |

E4 | mist | 145 | 9 |

E5 | mist | 345 | 5 |

E6 | mist | 200 | 10 |

E7/E8 | mist | 250 | 6 |

E9/E10 | mist | 250 | 11 |

E11 | water | 250 | 6 |

E12 | water | 250 | 11 |

Correlation Number | Formula | Res^{2} |
---|---|---|

Equation (1) | ${T}_{L}=351\xb7Q{i}^{0.111}\xb7{v}^{0.174}\xb7{d}_{32}^{0.006}$ | 2096 |

Equation (2) | ${T}_{L}=706\xb7{N}^{0.111}\xb7{v}^{0.174}\xb7{d}_{32}^{0.341}$ | 2096 |

Equation (3) | ${T}_{L}=219\xb7R{e}^{0.118}\xb7Q{i}^{0.063}$ | 3724 |

Equation (4) | ${T}_{L}=608\xb7{E}^{0.014}\xb7Q{i}^{0.116}$ | 4382 |

Equation (5) | ${T}_{L}=410\xb7{E}^{0.098}\xb7{N}^{0.089}$ | 2126 |

Equation (6) | ${T}_{L}=287\xb7{H}^{-0.026}\xb7Q{i}^{0.184}$ | 4206 |

Equation (7) | ${T}_{L}=294\xb7{H}^{0.136}\xb7{N}^{0.145}$ | 2175 |

Equation (8) | ${T}_{L}=825\xb7I{m}^{0.174}\xb7Q{i}^{0.020}$ | 2521 |

Equation (9) | ${T}_{L}=868\xb7I{m}^{0.186}$ | 2546 |

Equation (10) | ${T}_{L}=474\xb7Q{i}^{0.141}$ | 4445 |

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**MDPI and ACS Style**

Hnizdil, M.; Kominek, J.; Lee, T.-W.; Raudensky, M.; Carnogurska, M.; Chabicovsky, M. Prediction of Leidenfrost Temperature in Spray Cooling for Continuous Casting and Heat Treatment Processes. *Metals* **2020**, *10*, 1551.
https://doi.org/10.3390/met10111551

**AMA Style**

Hnizdil M, Kominek J, Lee T-W, Raudensky M, Carnogurska M, Chabicovsky M. Prediction of Leidenfrost Temperature in Spray Cooling for Continuous Casting and Heat Treatment Processes. *Metals*. 2020; 10(11):1551.
https://doi.org/10.3390/met10111551

**Chicago/Turabian Style**

Hnizdil, Milan, Jan Kominek, Tae-Woo Lee, Miroslav Raudensky, Maria Carnogurska, and Martin Chabicovsky. 2020. "Prediction of Leidenfrost Temperature in Spray Cooling for Continuous Casting and Heat Treatment Processes" *Metals* 10, no. 11: 1551.
https://doi.org/10.3390/met10111551