3.1. Effect of the Cooling Water Flow Rate
Figure 2 presents variations of temperatures along the experimental model at Re
in ≈ 9500), different inlet flue gas temperatures and in cases when the cooling water flow rate was 60 kg/h and 120 kg/h. The dew point temperature (t
dp-in) was calculated as indicated in [
24]. The obtained t
dp-in was in the range between ~59 and 63 °C. The inlet cooling water temperature (t
cw-in) measured in the inlet water mixer was about 8–9 °C.
From the results shown in
Figure 2, it is clear that the dew point temperature (curve 4) is well above tube wall temperature (curve 2), and hence water vapor condensation should start on the internal wall of the tube already from the beginning of the tube. This was confirmed by the heat transfer results (Nu
t, see
Figure 3).
As
Figure 2a shows, the flue gas temperature (curve 1) rapidly decreased by approx. 20 °C from x/d = 0 to x/d ≈ 25, and then only a small temperature decrease between x/d ≈ 25–40 was obtained. After that, the temperature gradually decreased until the end of the tube. Then, as some amount of vapor had condensed and the temperature difference between the tube wall and flue gas had decreased (
Figure 2a, curves 1 and 2), the heat transfer also started to decrease. Nonetheless, it was still high and at x/d ≈ 170 of the tube, the Nu
t ≈ 110 (
Figure 3a).
Curve 3 (see
Figure 2a) shows that the cooling water temperature was increasing from x/d ≈ 170 (inlet) until x/d = 0 (the outlet). The change in temperature until x/d ≈ 85 was not significant; however, it became more expressed from x/d ≈ 85. This means that the heat gained by the water in this part of the condensing heat exchanger was rather high due to the prevailing condensation process and high heat transfer (
Figure 3a; Nu
t varied in the range of 110–150). In this case, the water temperature increase through all the test section was about 21 °C, i.e., from ≈ 9 °C to ≈ 30 °C.
The results of temperature distributions for almost the same flue gas inlet parameters, but at a higher cooling water flow rate are presented in
Figure 2b. For the flue gas temperature (
Figure 2b, curve 1), two clear zones of the linear temperature change could be distinguished: one is from x/d = 0 until x/d ≈ 70, where a steep temperature decrease is obtained, and the other from x/d ≈ 70 until x/d ≈ 170, where much less of a decrease is obtained.
Figure 2b (see curves 2 and 3) shows that the temperatures of the cooling water and tube wall have similar characters. The water temperature increase in this case (
Figure 2b, curve 3) is not as clearly expressed as it was with a lower cooling water flow rate (
Figure 2a, curve 3). The cooling water temperature increases from the beginning of the section, i.e., from x/d ≈ 170, and until x/d ≈ 70 the increase is only by 3–4 °C (
Figure 2a, curve 3). From x/d ≈ 70 until the outlet (x/d = 0), there is even more increase, i.e., ~9–10 °C. The heat transfer (
Figure 3a) in the distance between x/d = 0 and x/d ≈ 70 was high (Nu
t is in the range between 180–160) and confirmed the increased temperature of the cooling water, which was due to vapor condensation, and the release of latent heat. As the most amount of water vapor was condensed in the initial part of the tube, the heat transfer from x/d ≈ 70 until x/d ≈ 170 was rapidly decreasing (
Figure 3a). However, at the end of the tube, it continued to be rather high (Nu
t ≈ 50), yet was still smaller than in the case of the water flow rate of 60 kg/h.
For both cases presented in
Figure 2a and b, the condensation efficiencies were about 52% and 62%, respectively. Thus, the cooling water flow rate increased by two times, showing no substantial increase neither in heat transfer (
Figure 3a), nor in condensation efficiency.
At a higher inlet flue gas temperature (
Figure 2c), the flue gas temperature decreases abruptly until x/d ≈ 90, yet farther along the tube the decrease is more constant (
Figure 2c, curve 1). The comparison of this case with the previous one (see
Figure 2a) reveals that the distance where more sudden flue gas temperature decrease is observed extends further, i.e., from x/d ≈ 20 to x/d ≈ 90. The characteristics of the wall and cooling water temperatures are similar (
Figure 2c, curves 2 and 3). The water temperature from x/d ≈ 170 increases slightly until x/d ≈ 95. From x/d ≈ 95 until the outflow, the temperature increases more, i.e., from ≈15 °C until ≈35 °C and is by about 4–5 °C higher compared to the case of a lower inlet flue gas temperature (
Figure 2a).
As the dew point temperature is higher than the tube wall temperature (
Figure 2c, curves 2 and 4), good conditions for condensation occur from x/d = 0 (
Figure 3b) until x/d ≈ 90. Here Nu
t varies in the range of ≈ 100–120. Then, Nu
t decreases slightly but remains between ≈95 and 110 till the end of the test section.
The temperatures of the flue gas, the tube wall, and the cooling water show similar tendencies in the case when the cooling water flow rate was 120 kg/h (
Figure 2d). Compared to the case presented in
Figure 2c, the temperatures were slightly lower and the increase in the water temperature was not as evident as it was in the case before (cf.
Figure 2c).
The characteristics of heat transfer at a higher cooling water flow rate are very similar to that of a lower flow rate (
Figure 3b).
Condensation efficiencies determined for the experiments when the cooling water flow rate was 60 kg/h and 120 kg/h were in the range between 54 and 58%. The results of [
13] show that even in an internally finned tube, the maximum condensation efficiency was only about 20%. But in this case, the tube was very short, only x/d ≈ 9. The tube used in our experiments was about 20 times longer, and therefore, the surface for vapor condensation was much larger, which resulted in a much higher condensation efficiency.
Figure 4 presents a comparison of the Nu
t distribution along the model for both the flue gas inlet temperatures and different cooling water flow rates. The results show that if the flue gas inlet temperature is higher, Nu
t remains almost constant along the tube irrespective of the cooling water flow rate.
For lower flue gas inlet temperatures, Nut changes similarly along the tube for both water flow rates, but the results indicate that more intense condensation takes place only in a half of the test section, i.e., until x/d ≈ 80–90; farther, Nut is decreasing.
Temperature distributions at Re
in ≈ 21,000 are presented in
Figure 5. As the Figure shows, that the characteristics are not the same as in
Figure 2 (case of lower Re
in). Moreover, in
Figure 5, the dew point temperature (curve 4) is higher than the wall temperature (curve 2).
As depicted in
Figure 5a, the flue gas temperature (curve 1) is almost constantly decreasing along the tube with some small fluctuations at the end.
Temperatures of the tube wall and cooling water (
Figure 5a, curves 2 and 3) change very similarly along the length of the model.
An intensive increase in the water temperature is observed from x/d ≈ 0 until x/d ≈ 30. Farther, the increase becomes less significant. Until the outlet, the cooling water temperature increases by 43 °C, i.e., from 10 °C to 53 °C (
Figure 5a, curve 3). This temperature variation is almost opposite in comparison to the results presented in
Figure 2a. The characteristics of the wall temperature (
Figure 5a, curve 2) are similar to the water temperature. Although, the wall temperature is lower compared to the dew point temperature, the difference between them at the beginning of the tube is small, i.e., 2–3 °C (cf.
Figure 5a, curves 2 and 4). That is why the condensation is not intensive at that point (
Figure 6a). As the mentioned temperature difference increases with the increase of x/d (
Figure 5a), the Nu
t also increases until x/d ≈ 100 (
Figure 6a). Farther along the tube, it remains almost constant with some fluctuations and after that starts to decrease. The decrease in heat transfer happens most likely because of the decreased water vapor mass fraction in the flue gas, despite the fact that the temperature difference between the flue gas and the tube wall remains almost constant until the end of the test section.
When the cooling water flow rate was increased, the characteristics of temperatures changed (
Figure 5b) in comparison to those presented in the case of a lower water flow rate (
Figure 5a).
When the water flow rate was higher (
Figure 5b), two zones of flue gas temperature decrease could be also distinguished: one from x/d = 0 until x/d ≈ 110 where a sharp temperature decrease was observed, and the other from x/d ≈ 110 until the end of the tube, where a much less decrease was observed.
From x/d ≈ 170 (the inlet) until x/d ≈ 110, the cooling water temperature increased slightly, by about 3 °C, i.e., from ≈9 °C to ≈12 °C. After that, the water temperature increase until the outflow was much better expressed: it increased by about 23 °C, i.e., from ≈12 °C to ≈35 °C. This suggests that water vapor condensation should result in higher heat transfer in the range x/d = 0–120, than in the range x/d ≈ 120–170; indeed, the distribution of the Nu
t presented in
Figure 6a confirms that, although it is not very clearly pronounced. As the temperature difference between the dew point and the tube wall temperatures at the beginning of the tube (
Figure 5b, curves 2 and 4) is much larger in comparison with the results presented in
Figure 5a, the heat transfer in the case of a larger cooling water flow rate is also higher (
Figure 6a). However, at the water flow rate of 120 kg/h, the heat transfer is nearly constant (Nu
t ≈ 275) until x/d ≈ 120. Farther on, till the end of the tube, there is a slight decrease in Nu
t.
The condensation efficiencies obtained in the cases when the cooling water flow rates were 60 kg/h and 120 kg/h were about 50%.
The temperature distributions at higher inlet flue gas temperatures and different cooling water flow rates presented in
Figure 5c,d do not differ much from the cases at lower inlet flue gas temperatures (
Figure 5a,b). The difference is slightly higher temperature values when the flue gas inlet temperature is increased.
In the case presented in
Figure 5c, the difference between the wall and dew point temperatures at the beginning of the tube is small, and therefore the heat transfer is rather low (
Figure 6b, Nu
t ≈ 25). However, as the difference between those two temperatures increases, the condensation heat transfer also increases rapidly and at x/d ≈ 120 the maximum value of Nu
t ≈ 415 is reached. As a certain part of the water vapor had condensed until x/d ≈ 120, the influence of condensation heat transfer gained a weakening character, and thus, the heat transfer from x/d ≈ 120 until x/d ≈ 170 was decreasing. Despite that, the Nu
t at the tube end remained high, i.e., Nu
t ≈ 300 (
Figure 6b).
For cooling water flow rate of 120 kg/h, due to a larger temperature difference between the wall and dew point (
Figure 5c), the heat transfer at the initial part of the heat exchanger was much intense (
Figure 6b, Nu
t ≈ 175) in comparison with the water flow rate of 60 kg/h. Farther along the tube, it increased slightly up to Nu
t ≈ 225 at x/d ≈ 120. After that, due to previously discussed reasons, it started decreasing. At the tube end, the Nu
t remained high (
Figure 6b, Nu
t ≈ 190).
The condensation efficiencies at water flow rates of 60 kg/h and 120 kg/h were determined to be almost the same, i.e., about 42%. The efficiencies in the case of Rein ≈ 21,000 were smaller than in the case of Rein ≈ 9500. This happened because the flue gas of a higher Rein number moves faster through the experimental setup, spends less time in it and, therefore, a decreased condensation efficiency is obtained.
For comparison purposes, all the local Nusselt number distribution results for Re
in ≈ 21,000 are presented in
Figure 7. As the Figure shows, at a higher cooling water flow rate, Nu
t remains more constant along the tube. This leads to a conclusion that the condensation in this case is more even.
3.2. Effect of the Cooling Water Temperature
To reveal the effect of cooling water temperature on the distribution of temperatures along the tube and on the local Nut number, an additional series of experiments was performed with the cooling water inlet temperature (tcw-in) of about 14–15 °C and the flow rate of 120 kg/h (≈2 L/ min).
There are no significant differences between the results obtained for higher and lower cooling water inlet temperatures (cf.
Figure 2b and
Figure 8a): the temperature values are only slightly higher in
Figure 8a. Moreover, the difference in the temperatures of the flue gas, the tube wall, and the water in the case of a higher cooling water inlet temperature is smaller than in the case of a lower cooling water inlet temperature.
Smaller temperature differences resulted in the decreased influence of condensation heat transfer, and, therefore, from x/d = 0 until about x/d = 100, the Nu
t was smaller in comparison to a lower cooling water inlet temperature (
Figure 9). From x/d ≈ 100 until the tube end, the Nu
t was decreasing and was the same for both water inlet temperatures.
Condensation efficiencies for the cases with water inlet temperatures of ≈8 °C and ≈14 °C did not differ significantly and were about 60 and 50%, respectively, indicating that a more intense condensation was obtained at a lower cooling water inlet temperature.
Temperature distribution results obtained for a higher flue gas inlet temperature presented in
Figure 8b do not indicate any drastic changes in comparison with similar flue gas inlet temperatures, but lower cooling water temperature (
Figure 2d). Here (
Figure 8b) it should also be noted that the tube wall and water temperatures are by a few degrees higher than at a lower water inlet temperature (
Figure 2d).
Only negligible differences in the Nu
t obtained in the case of a lower and a higher cooling water inlet temperatures were determined from the beginning of the tube until x/d ≈ 90–100 (
Figure 10). After that, Nu
t was decreasing. However, when the cooling water inlet temperature was lower, the Nu
t stabilized and remained in the range of 78–88, while when the temperature was higher, the Nu
t decreased sharply until the end of the tube. Hence, the results show that only a certain length of the pipe is involved in higher condensation heat transfer. The condensation efficiencies in this case do not differ significantly and for t
cw-in ≈ 8 °C, it is ≈58% and for t
cw-in ≈ 15 °C it is ≈52%.
The comparison of the Nu
t distribution in the condensing heat exchanger (
Figure 11) shows that it remains almost constant until about x/d ≈ 80–90, and starts to decrease farther on. Hence, only a certain length of the heat exchanger is efficiently used for condensation heat transfer.
The temperature distribution results for higher Re
in numbers are presented in
Figure 12. The results (
Figure 12a) are similar to the already discussed earlier (
Figure 5b). The only difference is a little higher tube wall and cooling water temperatures for a higher inlet flue gas temperature as compared to a lower cooling water inlet temperature (
Figure 5b).
Some changes along the tube were determined in the Nu
t (
Figure 13). When the cooling water inlet temperature was lower, the Nu
t remained almost constant along the tube, while at a higher water inlet temperature at the beginning of the tube, the Nu
t was smaller (Nu
t ≈ 175). But it was constantly increasing until x/d ≈ 90, where in the x/d range ≈90–130 it reached almost the same value as at a lower cooling water inlet temperature. Then, a slight decrease in Nu
t was noticed for both cases. However, at a lower water inlet temperature, the Nu
t stabilized, while at a higher temperature, the Nu
t was decreasing constantly. The distribution of the Nu
t at higher water inlet temperatures indicates that the condensation process is not even along the tube, yet it has expressed minimums and maximums.
The condensation efficiencies determined in the analyzed case were similar: 42% and 39%. Higher efficiency was obtained at a lower cooling water inlet temperature.
The temperature distribution results presented in
Figure 12b are also typical: the flue gas temperature decreases constantly, the water temperature increases, the characteristics of the tube wall and cooling water temperatures are similar (c.f.
Figure 5d). Temperature differences between the flue gas, tube wall, and cooling water are slightly smaller at a higher cooling water inlet temperature (
Figure 12b).
Smaller temperature differences have a certain impact on heat transfer and therefore change the distribution of the Nu
t along the tube (
Figure 14). The comparison of the Nu
t for different water inlet temperatures shows that in the initial part of the tube, at the water inlet temperature of ≈8 °C, the Nu
t is larger than at t
cw-in ≈ 15 °C. When t
cw-in ≈ 8 °C, Nu
t increases slightly along the tube up to x/d ≈ 110, where it reaches a maximum value of ≈220 and then starts decreasing. For the case of the cooling water inlet temperature of ≈15 °C, the variation of the Nu
t along the tube is more expressed. From the inlet, the Nu
t increases intensively up to x/d ≈ 100–110, where the Nu
t is ≈260. After that, the Nu
t starts decreasing with even greater intensity until the end of the tube and reaches almost the same value as in the beginning of the tube (Nu
t ≈ 115).
The difference between the condensation efficiencies in this case was about 9%, i.e., ≈42% and ≈31% for the lower and higher cooling water inlet temperatures, respectively.
The comparison of Nu
t shows (
Figure 15) that the most even Nu
t along the tube was obtained at a lower cooling water inlet temperature. A higher water inlet temperature causes unevenness of the Nu
t, and the tube length where the most effective condensation takes places becomes rather short, i.e., in the x/d range ≈80–130.