STUDY OF HEAT TRANSFER AND HYDRAULIC RESISTANCE OF A GAS–LIQUID FLOW IN A TUBE-IN-TUBE HEAT EXCHANGER

I. P. Chashchin, B. I. Litvinov, N. T. Shalavin

(Presented by the scientific seminar of the Department of Processes, Apparatuses, and Cybernetics of Chemical Production)

One of the ways to intensify heat transfer when working with a gas is to use gas–liquid flows, when a liquid phase—a high-boiling heat carrier—is introduced into the gas medium. Recently, papers devoted to the study of heat transfer and hydraulic resistance in two-phase flows [1–4] have appeared in the periodical literature, but these works are still few in number and do not provide grounds for generalizing conclusions. From the standpoint of accumulating experimental data in this field, we carried out an experiment to study heat transfer and hydraulic resistance in a descending gas–liquid flow.

The experiment was conducted on a tube-in-tube heat exchanger fabricated by us.

The outer tube of the heat exchanger was copper, with an internal diameter of Ø \(2 \cdot 10^{-3}\) m. The inner tube of the heat exchanger had an outside diameter of Ø \(19 \cdot 10^{-3}\) m. Along its length the heat exchanger was conventionally divided into 2 sections. This was necessitated by the need to eliminate the influence of inlet conditions, i.e., partial turbulence of the flow. To avoid heat losses to the environment, the outer tube of the heat exchanger was insulated. The heat exchanger was installed vertically.

The main parameters of the heat exchanger are given in Table 1.

Initially, experiments were carried out with a single-phase gas flow. Air and saturated water vapor were used as the working media. Atmospheric air was supplied by a compressor to the upper part of the heat exchanger, and then the flow moved from top to bottom in the annular space of the apparatus. Water vapor was condensed inside the central tube of the heat exchanger. At the heat-exchanger inlet the vapor was superheated by \(1 \div 1.5^\circ\)C.

The temperatures of the flow and of the outer wall of the inner tube of the heat exchanger were measured by chromel–copel thermocouples connected through a switch to a mirror millivoltmeter. The cold junctions of the thermocouples were thermostated at \(0^\circ\)C. The temperature of the flow and of the outer wall of the inner tube was measured at three points along the height of the heat exchanger with an accuracy of \(\pm 0.4^\circ\)C. In each section, the temperature of the flow and of the outer wall of the inner tube was measured by two thermocouples, whose readings were averaged. In addition, measurement of the flow temperature at the inlet and outlet of the heat exchanger was duplicated by mercury thermometers with a scale division of \(0.1^\circ\)C. The pressure drop during flow through the annular channel of the heat exchanger was meas—

Table 1

was measured with U-shaped manometers filled with distilled water. The air flow rate was determined by means of an orifice plate installed at the inlet of the gas stream into the heat exchanger. The orifice plate was connected to a differential manometer filled with distilled water. The flow rate of the heating steam was measured volumetrically from the amount of condensate obtained.

The experiments differed from one another in the air flow rate; in this case the Reynolds criterion varied within the range $(0.3 \div 2.5)\cdot 10^3$. The experimental data obtained on heat transfer between the surface of the inner tube and a single-phase gas stream in the section of the apparatus where $L/d > 100$ are described quite satisfactorily by the known calculation equation [5].

The experimental data on the hydraulic resistance of the gas stream coincided with the data calculated by the Darcy–Weisbach formula. The experimental data on heat transfer and hydraulic resistance were processed in criterion form.

The results of the experimental data on heat transfer and hydraulic resistance are presented in Figs. 1 and 2.

Fig. 1. Plot of experimental data on heat transfer. Designations of liquid flow rate — $Q_\mathrm{ж}$:

1 — $Q_\mathrm{ж}=0.042\ \text{m}^3/\text{h}$,
2 — $Q_\mathrm{ж}=0.029\ \text{m}^3/\text{h}$,
3 — $Q_\mathrm{ж}=0.022\ \text{m}^3/\text{h}$,
4 — $Q_\mathrm{ж}=0.016\ \text{m}^3/\text{h}$,
5 — $Q_\mathrm{ж}=0.009\ \text{m}^3/\text{h}$,
6 — $Q_\mathrm{ж}=0.04\ \text{m}^3/\text{h}$.

The air flow rate varied within the range $1.9 \div 5.7\ \text{m}^3/\text{h}$.

After this, experiments were carried out with a two-phase flow. Into the upper part of the annular space of the heat exchanger, liquid was injected into the gas stream by means of nozzles (a high-boiling heat-transfer agent—ethylene glycol). The experiments differed from one another in the air and liquid flow rates. In this case the volumetric concentration of liquid in the gas stream did not exceed 3%. At the outlet from the heat exchanger the gas-liquid flow was separated in a cyclone, and the ethylene glycol was returned again to the cycle.

Since the concentration of the liquid phase was comparatively small, all calculations were performed using formulas and relationships characterizing the gas stream. The heat-transfer data for the two-phase flow are presented in Fig. 1. The hydraulic-resistance data for the two-phase flow are presented in Fig. 2.

For processing in criterion form, the experimental data obtained in the tube section where $L/d > 100$ were used.

Fig. 2. Graph of experimental data on hydraulic resistances. Designations of liquid flow rate — $Q_{\mathrm{ж}}$:
1 — $Q_{\mathrm{ж}}=0.042\ \mathrm{m^3/h}$, 4 — $Q_{\mathrm{ж}}=0.016\ \mathrm{m^3/h}$,
2 — $Q_{\mathrm{ж}}=0.029\ \mathrm{m^3/h}$, 5 — $Q_{\mathrm{ж}}=0.009\ \mathrm{m^3/h}$,
3 — $Q_{\mathrm{ж}}=0.022\ \mathrm{m^3/h}$, 6 — $Q_{\mathrm{ж}}=0.004\ \mathrm{m^3/h}$.
The air flow rate varied within the range $1.9 \div 5.7\ \mathrm{m^3/h}$.

After processing the experimental data, semiempirical equations were obtained that describe heat transfer and hydraulic resistances for a two-phase flow within $\pm 10\%$ when the Reynolds number varies in the range $(0.70 \div 2.6)\cdot 10^3$ and the liquid flow rate in the range $0.0048 \div 0.042\ \mathrm{m^3/h}$.

$$ \mathrm{Nu}=0.0285\cdot \mathrm{Re}^{0.8}\left(\frac{Q_{\mathrm{ж}}}{Q_{\mathrm{в}}}\right)^{0.15}, \tag{1} $$

$$ \mathrm{Eu}=6.66\cdot \mathrm{Re}^{-0.398}\left(\frac{Q_{\mathrm{ж}}}{Q_{\mathrm{в}}}\right)^{0.451}. \tag{2} $$

As a result of the investigations carried out, it was established:

1. The heat-transfer coefficient from the wall to the gas flow increases with the introduction of atomized liquid. The greatest intensification of heat transfer was observed in the initial section of the tube. At a constant value of the Reynolds criterion, as the amount of atomized liquid introduced into the gas flow increases, the heat-transfer coefficient increases.

2. The hydraulic resistances increase with the introduction of liquid into the gas flow. The greatest pressure losses were observed in the initial section of the tube. At a constant value of the Reynolds criterion, as the amount of liquid introduced into the gas flow increases, the hydraulic resistances increase.

REFERENCES

1. N. M. Fedotkin, L. P. Zarudnev. Thermophysics and Heat Engineering. Kiev, 1969. Issue 15.

2. A. D. Akimenko, G. A. Zemskov, A. A. Sivortsev. Proceedings of Higher Educational Institutions, “Energetika”, vol. 10, 1969.

3. I. V. Domanskii. Applied Chemistry. Issue 4, Leningrad, “Nauka,” 1969.

4. V. M. Borishanskii, A. A. Andreevskii, A. G. Kryuchkov, B. S. Fokin. Thermal Power Engineering. Issue 4, 1968.

5. M. A. Mikheev. Fundamentals of Heat Transfer, Leningrad, Gosenergoizdat, 1956.