**3. Validation of Computational Model by the Experiment**

The prototype of HPHE was manufactured for the validation of the computational model. The HPHE tests were carried out in three successive measurement series. Each series was characterized by different values of air volumetric flows in the ducts caused by the change in rotational speed of the radial fans. The rotational speed of the fans was varied by fan motor speed controllers (based on TRIAC's electronic circuits). The measurement

series consisted of three tests, during which the volumetric flow rates of the fluid flowing in the channels were kept steady.

The first measurement series was carried out at average volumetric flows of approx. 530 m3/h (hot air duct) and approx. 400 m3/h (cold air), respectively.

The second measurement series was carried out with average volumetric flows of approx. 520 m3/h (hot air duct) and approx. 460 m3/h (cold air), respectively. This series is distinguished by a high-volume flow rate in the hot air duct.

The third measurement series was carried out at average volume flows of approximately 380 m3/h (hot air duct) and 370 m3/h (cold air), respectively. This series was characterized by the lowest average volumetric flows in the air channels. The range of airflows corresponds to average velocities: 1.7–2.5 m/s, which is typical for small airconditioning ducted systems (for systems with capacities < 1000 m3/h, 3 m/s velocity is considered maximal, to avoid high pressure drops). HEX studies were conducted at the experimental rig shown in Figure 20.

**Figure 20.** Diagram of the HPHE test rig: 1—HPHE; 2, 7—air filters; 3–5—electric preliminary heaters; 6, 8—air fans; 9—air cooler; 10–15—manual dampers.

The subject of the test is a HEX (1) made of finned SHP (Figure 21) for the recovery of heat from exhaust air.

**Figure 21.** Photo of the finned heat pipe.

Two air streams (hot—exhaust and cold—fresh air) pass through the HEX. The airflow arrangement is countercurrent. The HEX is made up of 32 HPs in a staggered arrangement. Each of the HP's is filled with R404A refrigerant. Based on previous research [22] the optimal amount of refrigerant in HP has been determined as 20% of its volume. Air flows through steel air ducts with a diameter of d = 0.2 m, while in the part adjacent to HPHE they transform into ducts with a rectangular flow area: 0.24 m × 0.25 m. Streams of the exhaust (hot) and fresh (cold) air flow in closed circuits. Airflow in the ducts is forced, utilizing fans (6, 8). There is one fan for exhaust and one for fresh air. The speeds of both fans are individually regulated. The air parameters are regulated by a cooler (9) and heaters (3–5). Cooler is an element of a split refrigeration system (refrigerant R404A). The air-cooled

condenser, which is expelling the heat absorbed from an air stream, is placed outside the building. The cooling capacity is regulated by manually adjusting the automatic expansion valve opening, which is metering a refrigerant flow to the cooler. Heaters are simple electric air duct heaters. There is a temperature probe upstream of every heater for the feedback to the automation system controlling the power output for obtaining the pre-set temperature. Air is drawn in through filters (2, 7) and the flow direction is controlled by mechanical dampers. The experimental rig arrangement allows for cooling only the top channel of HPHE and heating the bottom channel (Figure 19).

The air system can operate in both closed and open circuit (drawing or releasing air to outside). The experimental tests were carried out in conditions where supply and fresh air flowed in closed circuits without contact with the external air. Both HPHE flow channels were divided into 27 equal areas. In the centers of these areas, velocity and temperature measurements were taken. In each of the measurement planes, the average velocity and temperature were calculated based on 27 measurements. The temperature and velocity measurements were performed utilizing the "climate meter" probe LB-580 [25], which has the functions of a thermal anemometer, thermometer (Pt1000), and capacitive hygrometer. The mass flow rate was calculated from the average value of the velocity at the measurement planes. In each of the airflow ducts (fresh and exhaust air) there were two measurement planes—directly upstream and downstream of the HPHE. The differences between the average velocities of a single airstream did not exceed 5%. The average relative humidity of air was also checked at the inlet and outlet of HPHE, but in any of the cases no change was recorded, so no water vapor condensation occurred on the heat exchange surfaces.

The graph shown in Figure 22 specifies the values of the average heat transfer rates depending on the set temperature of the fresh (cold) air at the HPHE inlet for three measuring ranges, differing in the average air volumetric flow rates in the ducts. The experimental values were shown with error bars and computed values from the numerical model. The temperature of the fresh air at the inlet to the HPHE in the condenser section changed according to Figure 3 and in the evaporator section, it was kept at 24 ◦C. The charts were made for the air flows shown in Table 3.

**Table 3.** Exhaust and fresh air flows.


The characteristics presented in Figure 22 show that with the increase in the temperature at the inlet of the fresh air, the heat transfer rates became lower. The decrease in the average air volume flows in individual measurement series is accompanied by a decrease in the average heat transfer rates. The highest average experimental heat transfer rate, 1773 W, was obtained for the second case, for which the average temperature measurement of the fresh air at the heat exchanger inlet was equal to 1.5 ◦C. The lowest average heat flux of 592 W was obtained for the third case and the fresh air temperature of 14.70 ◦C. There is a good agreement between experimental heat transfer rates and those obtained from the model described in the following section—the average difference between measured and computed values is approximately 10%. In the high heat transfer rates region, the model output is within the estimated measurement uncertainty. Relative uncertainty is in the range of 5–8%. The model is more differing from the experimental data for the smaller heat fluxes. As can be seen in Figure 22, as fresh air inlet temperature increases, the measurement, and numerical curves diverge. The highest relative difference is 20%, the lowest is 1%. The reason for the higher discrepancy for lower heat fluxes can be the higher uncertainty of the heat pipe thermal resistance for low throughputs. The same argument could be made for the airside convective heat transfer correlation.

**Figure 22.** Average HPHE heat transfer rates . *Q* from model and experimental for varying volumetric airflow rates.

Figure 23 shows the values of the experimental HEX efficiency η defined as the ratio of the heat transfer rate absorbed by the fresh air to the value of the heat transfer rate released by the exhaust air. These values depend on the average inlet temperature of the fresh air. The graph shows the characteristics for three cases, characterized by different average fluid volumetric flow rates.

**Figure 23.** HEX efficiency η versus the fresh air temperature at the inlet to HEX for different volumetric flow rates.

Based on the above diagram, it can be concluded that the efficiency of the HEX η decreases in most cases with increasing temperature of the fresh air at the inlet. The exception is the second case, for which the average volume flows were 520 m3/h (the exhaust air duct) and 460 m3/h (the fresh air duct). At a lower average temperature (1.54 ◦C), a lower efficiency (94%) was obtained than for similar measurements at higher temperatures (97.8%). The lowest efficiency (93%) was obtained for the temperature of 16.09 ◦C, which leads to the conclusion that it is worth ensuring that the HEX works with air at possibly the lowest temperatures. The highest efficiency (98.9%) was obtained for the third measurement of the third series (2.22 ◦C). In the entire tested range, the efficiency of the HEX was in the range of approx. 93–98%.

Figure 24 shows the values of the temperature effectiveness of the heat exchanger ε. Effectiveness depends on the fresh air inlet temperature. The graph shows the characteristics for three cases, characterized by different average volumetric flow rates in the air-ducts.

**Figure 24.** HEX temperature effectiveness vs. the fresh air inlet temperature for different volumetric flow rates.

Based on the characteristics in Figure 24, it is possible to determine the ranges of the temperature effectiveness in the case of the tested HEX. The highest temperature effectiveness was recorded for the first measurement series (56%). The lowest temperature effectiveness of 49.2% was observed for measurement series characterized by the lowest volumetric airflow rates. The recorded temperature effectiveness was in the range of 49–56%. The temperature effectiveness decreased with increasing the fresh air temperature for all measurement series.
