Investigation of flow non-uniformities in the cross-flow heat exchanger with elliptical tubes

. In heat exchangers, especially those with the cross-flow arrangement, it is nearly impossible to achieve the uniform distribution of the working fluid in the tubular space with the currently used inlet and outlet chambers (in some constructions as well). The improper inflow conditions to individual tubes, including those with an elliptical cross-section - often used because of their favorable features compared to round tubes, is the cause of improper heat transfer. In this respect, transitional flow is of particular importance. This flow regime is complex and challenging to model. Therefore, it is necessary to perform experimental verification. For this purpose, an appropriate stand was built, allowing to investigate the flow of the working fluid (water) to the elliptical tubes in the cross-current heat exchanger. The paper presents the results of measurements for manifold geometry, which are currently used in practice (for heat exchanger constructions). The analysis of the measurement data confirms the non-uniform flow distribution to individual tubes of the heat exchanger. stand is developed to allow the measurements of the working fluid (water) flow rate in the elliptical tubes in the cross-flow heat exchanger. The obtained measurement results allow one to investigate the flow maldistribution in the heat exchanger with elliptical tubes.


Introduction
In many heat exchangers with the cross-flow arrangement, it is nearly impossible to achieve a proper distribution of the working fluid in the tubular space, with currently used inlet and outlet headers [1][2][3]. In addition, in this type of devices, the flow of liquid in the tubes can belong to various flow regimes including: laminar, transitional and turbulent.
The lack of uniform flow to individual heat exchanger tubes is the reason for improper heat exchange in some of them. This is particularly valid for elliptical tubes -often used because of their advantages compared to round tubes, including lower pressure drop and more favorable heat transfer conditions. The abovementioned flow maldistributions cause unfavorable high stresses, usually leading to damage to the device [3,4]. The transitional flow regime is of particular importance since the phenomena that characterize it are complex and challenging to mathematical modeling [3][4][5]. For this purpose, an appropriate stand is developed to allow the measurements of the working fluid (water) flow rate in the elliptical tubes in the cross-flow heat exchanger. The obtained measurement results allow one to investigate the flow maldistribution in the heat exchanger with elliptical tubes.

Test stand
In order to measure the flow of liquid in the cross-flow heat exchanger, a suitable test stand is built as mentioned earlier. Its characteristic feature is the possibility of testing the inlet and outlet headers of various shapes. Also, for each of them, there is a multivariate arrangement of the connectors to it, respectively: supplying and discharging the working medium. This allows investigating the influence of the geometry of heat exchanger chambers and the location of nozzle pipe on the conditions of working fluid flow (uniform or with maldistributions).
The heat exchanger in the test stand is situated vertically and consists of 20 elliptical tubes, placed in two rows (10 tubes per row in the staggered arrangement). To easily change the shape of the inlet and outlet headers, flexible connections between the inlet/outlet nozzle pipe and the feed tank are applied, by using flexible reinforced ducts. The aforementioned headers are connected to sieve plates with a typical flange-screw connection, sealed with a rubber gasket. The scheme of the stand and its general view are shown in Figure 1. It can be added that a more detailed description of this stand is given in [6]. Measurement of the instantaneous volumetric flow rate in individual tubes is carried out by using an ultrasonic Sontex Superstatic 749 flowmeters with the accuracy of 0.001 m 3 /h. The flowmeters are connected to the data acquisition system. This allowed for automatic verification of independently controlled total liquid flow in the tested system (in Figure 1 this meter was marked as No. 3). Figures 2 and 3 show examples of the inlet and outlet chambers. In addition to the chamber shape testing, it is possible to study the different positioning of the inlet and outlet nozzle pipe. Figure 4 shows a view of the heat exchanger sieve plate and an example of the inlet chamber assembly phase.   Based on Figures 2 and 3, it can be noticed that two design solutions for inlet and outlet headers can be tested. For some, the unchanging shape is characteristic (it is made up of a longitudinal section of the pipe), and for others -the unilateral increase of the internal volume (properly cut wedges are added on both sides in longitudinal direction). The numerical analyzes carried out previously show that this solution improves the flow distribution in the heat exchanger tubes [3,4].
In addition to the header construction itself, the influence of the supply and outflow nozzles on flow distribution is also examined. In order to ensure a stable inflow of water to the inlet chamber of the heat exchanger, an additional straight pipe section is installed. A similar solution is applied at the outlet header of the heat exchanger.

Study of maldistribution of the working medium flow
The paper presents the results of the measurements carried out for one of the described headers design and nozzles located on them. This is a constant (unchanging) longitudinal shape of the collectors, with the location of the nozzles in the middle of the chamber. This type of solution is often used in currently applied heat exchangers. Figure 5 presents the tested header with dimensions, and Figure 6 shows the view and dimensions of the sieve plate, with the numbering of individual tubes.                  In addition to the data presented above, it can be added that a certain, minimal discrepancy between the set flow rate (measured with the flowmeter marked in Figure 1 as 3) and actually obtained (calculated as the sum of readings from flowmeters installed on the tubes) results mainly from measurement error of the applied ultrasonic meters, which is 0.0060 [m 3 /h].

Analysis of measurement results
The presented measurement results illustrate the flow of the working fluid (water) in individual tubes of the cross-flow heat exchanger, for the laminar, transitional and turbulent regimes. The value of the Reynolds number determines the flow type. In practice, for round tubes, the following ranges are usually accepted: Re < 2100 -laminar flow, 2100 < Re < 3000 -transitional flow, Re > 3000 -turbulent flow [7].
Considering the abovementioned flow regimes, it can be noted that the first of the flow regimes (laminar) occurs in heat exchanger tubes for measurements No. 1 -5, where total flows is in the range from 1 [m 3  The measurement results confirm the assumption that maldistributions characterize the flow of the working fluid in the tubular space of the cross-flow heat exchanger. The presented measurement results indicate that the most considerable flow differences concern the tubes located under the supply nozzle pipe. In the examined heat exchanger, in tubes No. 5, 6 and 7 in the first row and No. 15 and 16 in the second row.
Visible significant flow maldistributions occur mainly for laminar and transitional flows. In the case of the latter (measurements No. 6 ÷ 8), in some tubes of the numbers above, the flow rate of the water is so low that the flow should be classified as laminar. A similar situation can be observed in the case of measurement No. 9, in this case in the majority of the tubes the flow is turbulent, but in several tubes, it belongs to the transitional flow regime. In their case, the differences in flow rate are lower compared to the remaining tubes and do not exceed 20% The measurement data obtained for the transitional flow is of great importance because this kind of regime is insufficiently studied. The obtained experimental data will be used to verify CFD simulations. Currently, further investigations of other heat exchanger headers are under development (taking into account the different location of the inlet nozzle pipe). It is planned to broaden the scope of research for turbulent flow. Additional research is also carried out to optimize the shape of the headers, aimed at improving the conditions of flow distribution in the heat exchanger. The result of this work will ensure a more uniform distribution of liquid to individual tubes of the heat exchanger.

Conclusions
The paper presents a test stand for testing water flows in a single-pass cross-flow heat exchanger with elliptical tubes. This developed setup enables the measurement of the volumetric flow rate in each of the twenty tubes of the analyzed exchanger. The results of the research are presented for laminar, transitional and turbulent flow regimes which allowed one to confirm the occurrence and to assess the maldistributions of the flow of the working medium (water) for individual tubes of the device.
For a typical cross-flow heat exchanger with straight headers in the shape of a longitudinal section of the pipe (in practice the most commonly used), with the nozzle pipe placed in their central part of the heat exchanger, it was observed that the most significant flow maldistribution occurs for the laminar flow regime. In this case, the volumetric flow rates in individual tubes of the tested heat exchanger differ up to six times. For transitional and turbulent flows, these differences are much smaller, and their maximum value, between the highest and the lowest flow rates in heat exchanger tubes, does not exceed 80%.