ASTM - Intensive Quenching Systems - Engineering and Design 2010 - N I Kobasko, M A Aronov, J A Powell, G E Totten

CHAPTER 2 n TRANSIENT NUCLEATE BOILING AND SELF-REGULATED THERMAL PROCESSES 39
Fig. 13—Depiction of how thermocouples were arranged and accurately
flattened to the wall of spheres and polished by French [26].
One of the serious investigations of quenching processes
was performed by French in 1926–1930 [26]. At the time, he
prepared and utilized unbelievably accurate spheres, cylinders,
and plates, which were instrumented with thin thermocouples.
Spheres were made from steel and copper. Fig. 13 shows how
accurately spheres were prepared for investigations.
The experimental results from French’s studies are summarized
in Table 15, which shows that during quenching of
the spheres in a cold 5 % water alkaline solution, film boiling
is absent. Also, independently of size of sphere, the wall
temperature decreases very quickly from 975°C to 150°C
within one second, which would seem impossible. However,
using computational methodology, such as finite element
analysis, it is possible to solve this heat transfer problem as
an inverse problem (IP). Details and methods of solving the
inverse problem are provided in Chapter 13.
A regularization method for solving an IP problem was
developed by Tikhonov [37]. This method was used and further
developed by various authors [38–42]. Some results of
computations using the software IQLab [40] are shown in
Figs. 14 and 15. Fig. 14 shows that the heat flux density is
very high at the very beginning of the quenching process and
varies smoothly as the process proceeds. Fig. 15 shows that
the maximum heat transfer coefficient (more than 200,000
W/m 2 K ) is achieved at the time of 2 seconds. Furthermore,
the heat transfer coefficient decreases exponentially and
reaches 30,000 W/m 2 K within 20 seconds after immersion.
To be sure that these large values are reliable, the critical
heat flux densities were determined (see Chapter 3, Section
3.4). The results of these calculations are shown in
Table 16 for the critical heat flux densities for water and
aqueous salt solutions and alkaline solutions.
TABLE 15—Time required for the surface of steel spheres of different sizes to cool to different
temperatures when quenched from 875°C (1,605°F) in 5 % NaOH-water solution at 20°C and
moving at 3 feet per second (0.914 m/s), according to French [26]
Time (s)
Average size
700°C 600°C 500°C 400°C 300°C 250°C 200°C 150°C
1/4 inch (6.35 mm) 0.025 0.030 0.033 0.040 0.06 0.10 0.21 1.05
0.025 0.040 0.050 0.063 0.12 0.23 0.42 0.67
0.030 0.040 0.043 0.050 0.09 0.13 0.23 0.36
0.027 0.037 0.043 0.051 0.09 0.15 0.29 0.69
1/2 inch (12.7 mm) 0.033 0.040 0.050 0.053 0.07 0.11 0.15 0.43
0.035 0.038 0.046 0.060 0.09 0.13 0.22 0.49
0.032 0.050 0.073 0.090 0.11 0.14 0.32 0.92
0.016 0.043 0.050 0.083 0.17 0.24 0.35 0.65
0.020 0.040 0.060 0.077 0.10 0.15 0.26 0.53
0.028 0.042 0.058 0.071 0.11 0.15 0.26 0.60
1 inch (25.4 mm) 0.035 0.040 0.045 0.060 0.08 0.10 0.15 0.40
0.050 0.050 0.080 0.083 0.11 0.19 0.40 1.20
0.028 0.040 0.045 0.064 0.14 0.21 0.34 0.71
0.020 0.020 0.050 0.086 0.19 0.32 0.32 0.99
0.033 0.042 0.055 0.074 0.13 0.21 0.35 0.82
2.5 inches (63.5 mm) 0.025 0.040 0.060 0.065 0.08 0.10 0.29 0.65
0.020 0.030 0.040 0.050 0.07 0.13 0.25 0.80
0.030 0.043 0.070 0.100 0.15 0.20 0.31 0.52
0.020 0.040 0.075 0.120 0.19 0.23 0.35 0.84
0.020 0.043 0.080 0.130 0.21 0.28 0.39 0.56
0.023 0.039 0.065 0.093 0.14 0.19 0.32 0.59