THERMAL ENGINEERING

Corresponding Member of the Academy of Sciences of the USSR M. A. STYRIKOVICH,
Z. L. MIROPOLSKII, and V. K. EVA

THE EFFECT OF LOCAL INCREASES IN HEAT FLUXES ALONG THE LENGTH OF A CHANNEL ON THE BOILING CRISIS

In most published works devoted to the study of the boiling crisis under forced motion of the working medium in channels, only the case of a uniform distribution of heat fluxes along the length of the channel is considered. However, in a number of technical devices there is a clearly expressed nonuniform distribution of heat fluxes along the channel length; in particular, local increases in heat fluxes—“hot spots”—are observed (1–4).

In (5) the conclusion is drawn that “hot spots” affect the value of \(q_{\mathrm{cr}}\). In (6) an increase of \(q_{\mathrm{cr}}\) at a “hot spot” 35 mm long is noted as a function of the heat content of the working medium at the place of crisis (an increase of 100% at \(i = 306\) kcal/kg and of 4% at \(i = 510\) kcal/kg). The experiments were carried out at \(p = 141\) ata and a ratio of heat fluxes at the “spot” and in the remaining part of the rectangular channel \(\varepsilon = 2\).

In order to study this question in greater detail, the authors carried out experiments on the experimental stand of the G. M. Krzhizhanovskii Power Engineering Institute, located at the Heat and Power Center of the All-Union Thermal Engineering Institute (a detailed description of the stand is given in (7)). The experiments were carried out under conditions with restricted and free development of pulsations, i.e., both in the absence and in the presence of a compressible medium in the elements of the circuit situated between the heated tube and the inlet throttle. The experimental sections were made from a seamless tube 10/8 mm in diameter of stainless steel 1Kh18N9T and were installed vertically. Heating was effected by alternating electric current over the length \(l\). The “hot spot” was simulated on a section of tube with a thinned wall of length \(l_1\), located 10 mm from the end of the tube. The bulk of the experiments was carried out with the “hot spot” located at the upper, outlet end of the tube. The heat fluxes on it were distributed uniformly, and the ratio of the heat fluxes in the “hot spot” zone to the heat fluxes on the remaining part of the tube was 2 and 1.35. The experiments were carried out at a pressure of 100 ata, mass velocities of 2000, 850, and 400 kg/m\(^2\)·sec, and upward motion of the working medium. The relative enthalpy of the medium at the outlet from the experimental section

\[ x = \frac{i - i'}{r} \]

varied from 1.0 to \(-0.2\). The crisis was recorded by a sharp jump in wall temperature, determined from thermocouple readings or visually—from reddening of the tube wall.

Figure 1 gives summary curves of the experimental data for regimes with restricted development of pulsations in the form of the dependence of \(q_{\mathrm{cr}}\) on the steam content at the outlet from the experimental section \(x_{\mathrm{out}}\), the mass velocity \(w_g\), and the length of the “hot spot” \(l_1\), with the ratio of heat fluxes at the “spot” and in the tube \(\varepsilon = 2\). From consideration of Fig. 1 it is seen that, at all investigated mass velocities, the value of \(q_{\mathrm{cr}}\) depends substantially on the length of the “hot spot,” this influence being strong at low steam contents and almost disappearing in the region of large \(x_{\mathrm{out}}\). With increasing mass velocity \(w_g\), the region of influence of the length \(l_1\) on \(q_{\mathrm{cr}}\) narrows noticeably.

In the experiments, some decrease in \(q_{\mathrm{cr}}\) was observed in the region \(x_{\mathrm{out}}=0\); however, this effect was insignificant, since even at \(w_g=400\ \mathrm{kg}/\mathrm{m}^2\cdot\mathrm{s}\), where the strongest influence of pulsations is observed, the decrease in \(q_{\mathrm{cr}}\) in the region \(x_{\mathrm{out}}=0\) was only 17%. The discontinuity of the curve \(q_{\mathrm{cr}}=f(x_{\mathrm{out}})\), which

Fig. 1. Effect of the length of the “hot spot” \(l_1\) on the value of \(q_{\mathrm{cr}}\) under conditions of limited development of pulsations: \(p=100\) ata, \(\varepsilon=2\), \(l=160\) mm, \(d=8\) mm; \(a\)—\(w_g=2000\ \mathrm{kg}/\mathrm{m}^2\cdot\mathrm{s}\); \(b\)—\(w_g=850\); \(c\)—\(w_g=400\); 1—\(l_1=64\) mm; 2—\(l_1=16\) mm; 3—\(l_1=4\) mm.

Fig. 2. Effect of the total channel length \(l\) on the value of \(q_{\mathrm{cr}}\) under conditions of limited development of pulsations in the presence of a “hot spot” and with uniform heating. \(p=100\) ata, \(d=8\) mm. \(a, d\)—\(w_g=2000\ \mathrm{kg}/\mathrm{m}^2\cdot\mathrm{s}\); \(b, e\)—\(w_g=850\); \(c, f\)—\(w_g=400\). 1—\(l=160\) mm, \(\varepsilon=2\); 2—\(l=500\) mm, \(\varepsilon=2\); 3—\(l=945\) mm, \(\varepsilon=2\); 4—\(l=160\) mm, \(\varepsilon=1\); 5—\(l/d\ge 100\), \(\varepsilon=1\).

was observed in works \((^8,\ ^9)\) at 100 ata and \(w_g=400\) and \(850\ \mathrm{kg}/\mathrm{m}^2\cdot\mathrm{s}\), when the steam content of the working medium at the inlet to the experimental tube reached zero values, was preserved in our experiments only at \(w_g=400\ \mathrm{kg}/\mathrm{m}^2\cdot\mathrm{s}\).

Figure 2 presents data obtained under the same conditions as in Fig. 1, with different total heated tube lengths \((l=160;\ 500;\ 945\ \mathrm{mm})\).

The data obtained at \(l = 500\) and 945 mm differ little, whereas in experiments with shorter tubes \((l = 160\) mm), in the region of high steam qualities, higher values of \(q_{\mathrm{cr}}\) were obtained. This difference, reaching about 100% at \(w_g = 2000\ \text{kg}/\text{m}^2\cdot\text{s}\), \(l_1 = 64\) mm, and \(x_{\mathrm{out}} = 0.45\), decreases as the steam quality decreases and is more pronounced

Fig. 3. Effect of the length \(l_1\), \(l\), and intensity \(\varepsilon\) of the “hot spot” on the value of \(q_{\mathrm{cr}}\), and comparison with \(q_{\mathrm{cr}}\) under uniform heating in conditions of free development of pulsations. \(p = 100\) ata, \(d = 8\) mm. \(1\)—\(l_1 = 64\) mm; \(2\)—\(l_1 = 16\) mm; \(3\)—uniform heating \((\varepsilon = 1)\). \(a\)—\(w_g = 2000\ \text{kg}/\text{m}^2\cdot\text{s}\); \(b, c, d\)—\(w_g = 850\); \(v\)—\(w_g = 400\). \(a, b, v\)—\(\varepsilon = 2,\ l = 160\) mm; \(c\)—\(\varepsilon = 2\); \(d\)—\(\varepsilon = 1.35\). \(A\)—\(l = 160\); \(B\)—\(l = 500\) mm.

at greater lengths of the “hot spot” and high \(w_g\). In the region of low steam qualities \((x_{\mathrm{out}} = 0.0 \div 0.5)\) at \(w_g = 850\), and \(x_{\mathrm{out}} = 0.0 \div 0.25\) at \(w_g = 2000\ \text{kg}/\text{m}^2\cdot\text{s}\), all the data obtained for channel lengths from 160 to 945 mm practically coincide; i.e., heating of the pre-included section has no substantial effect on \(q_{\mathrm{cr}}\). This is also confirmed by the data obtained in experiments with an unheated pre-included section \((w_g = 850\ \text{kg}/\text{m}^2\cdot\text{s},\ \varepsilon = 2,\ l_1 = 64\) mm). The range of steam qualities in which heating of the section located before the “hot spot” does not affect \(q_{\mathrm{cr}}\) widens as \(w_g\) decreases.

Figure 2 also shows curves obtained under conditions of uniform heating at \(l = 160\) mm \((^9)\) and \(l/d \geq 100\) \((^{10})\). At \(l_1 = 64\) mm the values of \(q_{\mathrm{cr}}\) slightly exceed the data obtained at \(l = 160\) mm (by up to 30%), and exceed by as much as 3.5 times the \(q_{\mathrm{cr}}\) values obtained at \(l/d \geq 100\). With increasing \(w_g\) and \(l_1\), this effect decreases; thus, for example, at \(w_g = 2000\ \text{kg}/\text{m}^2\cdot\text{s}\) and \(l_1 = 64\) mm this increase is about 50%, while at \(l_1 = 16\) mm it is 2.5-fold (in comparison with data for a uniformly heated tube at \(l/d \geq 100\)).

Figure 3 presents data obtained in experiments with free development of pulsations, with and without a “spot.” In tubes

of small length ($l = 160$ mm), in the region of small $x_{\mathrm{out}}$, the influence of $l_1$ is clearly noticeable. The crisis occurs at heat fluxes considerably greater than in the case of uniform heating (an increase by a factor of 2.7 at $l_1 = 16$ mm). With increasing $w_g$ this influence weakens, especially when $x_{\mathrm{out}}$ is increased. Increasing the total length of the tube to $l = 500$ mm noticeably reduces $q_{\mathrm{cr}}$ (by approximately a factor of 2); moreover, at $l_1 = 64$ and 16 mm and $w_g = 850$ kg/m$^2\cdot$sec, the values of the critical heat fluxes practically coincide. However, $q_{\mathrm{cr}}$ on the “spot” is nevertheless substantially higher than under conditions of uniform heating. This increase is about 50% at $\varepsilon = 2$ and about 30% at $\varepsilon = 1.35$. In the experiments at $w_g = 850$ kg/m$^2\cdot$sec, $\varepsilon = 1.35$, $l = 160$ m, $l_1 = 16$ and 64 mm, almost identical values of $q_{\mathrm{cr}}$ were obtained, although the presence of the “spot” increased $q_{\mathrm{cr}}$ by more than one and a half times ($x_{\mathrm{out}} = 0$) in comparison with uniform heating.

Energy Institute
named after G. M. Krzhizhanovsky

Received
2 IV 1962

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