INVESTIGATION OF HEAT-EXCHANGE APPARATUS WITH FINNED TUBES FOR CHEMICAL PRODUCTION

I. P. CHASHCHIN

(Presented by the conference dedicated to the anniversary of the December Plenum of the Central Committee of the CPSU)

The process of convective heat exchange is widely used in chemical technology, and heat-exchange apparatus of various designs are the most widespread type of equipment.

At present, in chemical technology, heat exchangers with smooth tubes are used mainly; their drawback is the low efficiency of convective heat exchange, especially in those cases when the physical properties of the heat-transfer media determine different values of the heat-transfer coefficients and, as a consequence, their bulkiness, which entails increased metal consumption for their manufacture.

A number of works [1—4] are devoted to questions of heat exchange during the flow of gases and liquids in channels with finned tubes under longitudinal flow around them; however, the literature contains no broad generalization of the results obtained, and there are insufficient experimental data for calculation recommendations, while at the same time the available experimental data indicate a high intensity of heat exchange.

In the present work the following questions are considered:

a) Heat transfer and hydraulic resistances during the flow of gases and droplet liquids in channels with low-finned tubes having different fin height and pitch, and the influence of finning parameters on flow turbulization.

b) Criterion equations and a method for calculating the optimal parameters of tube finning.

c) Verification of the results of laboratory investigations under production conditions and comparison of the efficiency of the heat exchangers investigated in this work with one another and with certain results, available in the literature, of investigations by other authors.

The experiments on the study of the indicated questions were preceded by work whose aim was the selection of conditions for flow around finned tubes and the shape of the fins.

For the investigation of heat transfer and hydraulic resistances, a “tube-in-tube” type heat exchanger was fabricated. The outer tube of the heat exchanger was smooth, with an internal diameter \(d_0 = 0.0505\ \text{m}\). The inner tube of the heat exchanger had spiral fins on its outer surface and, in the course of the investigations, could be replaced by another finned tube having different finning parameters. The main parameters of the installation are given in Table 1. The fins had a triangular shape and...

formed a single whole with the tube wall, which eliminates the possibility of thermal resistances arising at the junction between the fin and the main surface of the tube during heat exchange.

Table 1

The studies were carried out successively on one smooth tube and nineteen finned tubes under conditions of longitudinal flow around them. Along its length, the heat exchanger was divided into three sections, the characteristics of which are shown below.

In the experiments, air and saturated water vapor were used as the working media. Atmospheric air was supplied by a rotary gas blower through a receiver into the annular space of the heat exchanger, with a tube-diameter ratio of 2–2.4, which lies within the practically used range of diameter ratios. Inside the finned tube, water vapor condensed at a pressure close to atmospheric.

The smooth tube and the first ten finned tubes in sequence (Table 1) were also investigated for heat exchange and hydraulic resistance under conditions of heating water in the annular channel. The investigations were carried out on a unit with a closed circulation loop.

The experiments differed from one another in the flow rate of air or water and in their temperature at the inlet to the heat exchanger; in this case the Reynolds criterion $Re$ varied within the range $5 \times 10^3$—$2 \times 10^4$.

To verify the research procedure, preliminary experiments on heat transfer in a smooth tube were carried out; the results of these tests were satisfactorily described by the Krausold equation.

The temperatures of the streams were measured with chromel–copel thermocouples. Measurements of the stream temperatures at the inlet and outlet of the heat exchanger were, in addition, duplicated by control mercury thermometers.

Table 2

The temperatures of the heat-transfer surface of the fins were measured by chromel–copel thermocouples soldered to the fin surface, two in each cross section. The measured temperatures of the fin surface at individual points were averaged over the surface of the given cross section.

The air flow rate was determined by means of an orifice plate and an inclined manometer filled with distilled water. The water flow rate was measured volumetrically.

The pressure drop in the working sections of the tubes was determined through static-pressure taps. In each of the 4 cross sections along the tube height there were three holes $d = 0.5 \cdot 10^{-3}\ \text{m}$, located at an angle of $120^\circ$, which were connected to one another and to an inclined draft manometer when operating with air. When operating with water, measurement of the static-pressure differences along the length of the heat exchanger was carried out with a two-liquid differential manometer filled with bromoisobutyl and water ($\rho = 1272\ \text{kg}/\text{m}^3$).

The coefficient of frictional resistance ($\lambda_{\mathrm{fr}}$) was calculated, under isothermal conditions, for each tube section by the formula

\[ \lambda_{\mathrm{fr}} = \frac{\Delta p}{L/d_{\mathrm{e}}}\cdot \frac{2}{\rho \cdot \omega_{\mathrm{av}}^{2}} . \tag{1} \]

The equivalent diameter of the annular channel was taken as its characteristic dimension:

\[ d_{\mathrm{e}} = \frac{4f}{\Pi}. \]

The mean stream temperature was taken as the characteristic temperature.

To derive equations for heat transfer and hydraulic resistances, the experimental data obtained on the third—“clean”—section of the tube ($L/d_{\mathrm{e}} > 50$), where the influence of the inlet-flow conditions on heat transfer in the apparatus is excluded, were used.

In deriving a generalizing equation for determining the hydraulic-resistance coefficient of the tubes investigated in this work, for

the dependence of the friction coefficient on the Reynolds number $\operatorname{Re}$ and the finning parameters was taken as the basis, i.e.

\[ \lambda_{\mathrm{or}} = f(\operatorname{Re}, h/d_{\mathrm{e}}, t/d_{\mathrm{e}}). \]

As a result of the solution, an equation was obtained for determining the friction coefficient on finned tubes,

\[ \lambda_{\mathrm{or}} = 0.316 \cdot \operatorname{Re}^{-0.25} + \left(\frac{h}{d_{\mathrm{e}}}\right)^{0.72} \cdot \left(\frac{t}{d_{\mathrm{e}}}\right)^{0.877}. \tag{2} \]

For an infinitely small fin height and an infinitely small value of the pitch, which corresponds to a smooth tube, equation (2) takes the form

\[ \lambda_{\mathrm{or}} = \lambda_{\mathrm{gl}} = 0.316 \cdot \operatorname{Re}^{-0.25}. \tag{3} \]

In generalizing the experimental data on heat transfer for smooth and finned tubes for air and water, the values of the Prandtl number $\operatorname{Pr}$ and the exponent at it, equal to $m = 0.4$, were determined. The obtained value of the exponent of the criterion $\operatorname{Pr}$ is in good agreement with literature data [5].

In analyzing the experimental data it was found that, at $\operatorname{Re} = \mathrm{const}$, the curves describing heat transfer on finned tubes at a constant distance between fins $(t)$ with variation of their height $(h)$ pass through maxima. As a result, an equation was obtained relating the fin height to the distance between them at maximum heat transfer:

\[ t_{\mathrm{opt}} = 566 \cdot h^{2.64} \cdot d_{\mathrm{e}}^{-1.64}. \tag{4} \]

Using the obtained equation (4), one can, by specifying one of the finning parameters (for example the height $h$), determine the other parameter (the fin pitch $t$). With such a combination of fin height and pitch, the maximum value of the heat-transfer coefficient is obtained. In this case the magnitude of the heat-transfer coefficient can be determined from the equation obtained in processing the experimental material on the basis of the universal law of flow-velocity distribution and the Kármán model of three-layer turbulent flow. The equation for determining the heat-transfer coefficient in an annular channel for finned tubes was derived under conditions of thermal insulation of the outer surface, with the following assumptions, close to the conditions occurring in the present work:

a. The flow is stabilized.
b. The heat load is constant (on the inner wall).
c. The liquid is incompressible.
d. The physical properties of the liquid are constant.

\[ h = 0.4 \text{--} 2 \ \mathrm{mm}, \qquad t = 2 \text{--} 12 \ \mathrm{mm}, \qquad d_{\mathrm{e}} = 30 \ \mathrm{mm}. \]

As a result, the following equation was obtained, describing heat transfer in an annular channel with a finned tube under turbulent flow conditions:

\[ \frac{Nu}{Pr \cdot Re} = \frac{1} {\left[ \left(\frac{h}{d_{\mathrm{e}}}\right)^{-0.377} \cdot \left(\frac{t}{d_{\mathrm{e}}}\right)^{-0.244} \right]} \cdot \sqrt{ \frac{ \lambda_{\mathrm{gl}} + \left(\frac{h}{d_{\mathrm{e}}}\right)^{0.72} \left(\frac{t}{d_{\mathrm{e}}}\right)^{0.877} }{8} } \times \]

\[ \times \left\{ \frac{Pr}{\beta} + \frac{ \ln \left[ 1 + Pr \left(\frac{h}{d_{\mathrm{e}}}\right)^{-0.377} \cdot \left(\frac{t}{d_{\mathrm{e}}}\right)^{-0.244} \right] }{\beta} + \frac{1}{2 \cdot \beta} \left( \frac{\sqrt{b}-1}{b-1} \right) \cdot \beta \times \right. \]

\[ \times \frac{\operatorname{Re}} {12 \cdot \left(\frac{h}{d_{\mathrm{e}}}\right)^{-0.377} \cdot \left(\frac{t}{d_{\mathrm{e}}}\right)^{-0.244}} \left\{ \sqrt{ \frac{ \lambda_{\mathrm{gl}}+ \left(\frac{h}{d_{\mathrm{e}}}\right)^{0.72} \cdot \left(\frac{t}{d_{\mathrm{e}}}\right)^{0.877} }{8} } +\psi(b) \right\}^{-1}, \tag{5} \]

where

\[ b=\frac{r_2}{r_1} \]

is a parameter,

\(r_2\) is the outer radius of the channel,
\(r_1\) is the inner radius of the channel.

\[ \beta= \frac{(r_m^2-r_1^2)\cdot r_2} {(r_2^2-r_m^2)\cdot r_1}, \]

\(r_m\) is the radius corresponding to the maximum velocity.

Calculations show that, with the proper choice of fin pitch and fin height, heat transfer can be increased severalfold in comparison with heat transfer on a smooth tube, with only a small increase in energy expenditure for hydraulic resistance.

To verify the results obtained on the laboratory installation, a finned heat exchanger of the “tube-in-tube” type was fabricated according to the drawings we supplied by the Leninsk-Kuznetsk Coking Plant, and was tested under industrial conditions.

The tests, conducted over a long period of time, showed that the average heat-transfer coefficient increases, in comparison with a heat exchanger of the same type with smooth tubes, by a factor of 1.5–2.

The investigations carried out provide grounds for recommending the use of “tube-in-tube” heat exchangers with finned tubes in the petroleum-refining and chemical industries in those cases where the physical properties of the heat-transfer media determine different values of the heat-transfer coefficient (in heat exchange between gas and liquid, saturated steam and gas, saturated steam and liquid, etc.).

Conclusions

1. Nineteen spirally finned tubes and one smooth tube were investigated with respect to heat exchange and hydraulic resistance in a “tube-in-tube” type heat exchanger under longitudinal flow around the tubes. It was found that, within the range of the criterion \(\operatorname{Re}=5\cdot10^3—2\cdot10^4\), the intensity of heat exchange for all the investigated finned tubes is higher than for smooth tubes of the same diameter.

2. A definite dependence was established between the intensity of heat exchange and the fin height at a constant pitch between fins. On the basis of a generalization of the experimental data, equation (4) was obtained, which makes it possible, for a specified pitch between fins, to determine the optimal fin height (with respect to heat exchange), and conversely, for a specified fin height, to determine the optimal value of the pitch between fins.

3. On the basis of the universal law of the distribution of flow velocities and Kármán’s model of three-layer turbulent flow, the semi-empirical equation (5) was obtained, describing heat exchange in an annular channel with a spirally finned tube under turbulent flow conditions. Equation (5), in combination with equation (4), makes it possible to calculate the value of the heat-transfer coefficient for optimal finning parameters.

4. Using the results of laboratory investigations, a “tube-in-

in a tube with an internally finned tube having optimal finning parameters. In carrying out industrial tests of the heat exchanger, where semi-coking resin, possessing comparatively high viscous properties, was heated with saturated steam, the advantages of this heat exchanger over a heat exchanger with smooth tubes were confirmed (for the same heat-transfer efficiency, the dimensions of a heat exchanger with a finned tube may be 1.5–2 times smaller than those of a heat exchanger with smooth tubes).

1. The heat exchangers tested may be used in the petroleum-refining and chemical industries in cases where the physical properties of the heat carriers lead to different values of the heat-transfer coefficient (in heat exchange between oil and water, gas and water, saturated steam and a liquid, etc.). Heat exchangers with low-finned tubes can operate with aggressive media, since the technology for manufacturing fins permits the use of various metals and alloys, including carbon or stainless steel.

REFERENCES

1. Yu. V. Petrovsky, V. G. Fastovsky, L. I. Roizen. Chemical Industry, No. 9, 1960.

2. O. S. Vinogradov, P. I. Puchkov. Thermal Power Engineering, No. 10, 1964.

3. I. G. Knudsen, D. L. Katz. Chem. Engng. Progr., 46, No. 10, 490–500, 1950.

4. R. Fortescue, M. V. Hall. Problems of Nuclear Power Engineering, No. 6, 21–23, 1957. See also Journ. Brit. Nucl. Energy Confer., 2, 83–91, 1957.

5. M. A. Mikheev. Fundamentals of Heat Transfer. GEI, pp. 61–63, 1956.