**3.2.2 Numerical simulations using CFD software**

Two geometrical models have been made for numerical computations: the recurrent element of the considered heat exchangers and the recurrent segment – see Fig. 10. Geometries and numerical grids have been created using Gambit pre-processor.

The models of the recurrent segments of the radiators are related to the measurement series which results were described earlier. Each model consists of one or two rows of pipes and there are ten ribs in each row. The reason for the creation of these two numerical models is to test whether the simplification of real geometries affect the results.

The testing computations have shown that for considered models non-structured meshes are useless in most cases – the calculations were not converged or gave non-physical results. So for the fundamental computations for the recurrent element the structured meshes of 170 to 250 thousands cells for single recurrent element have been chosen.

The Reynolds Stress Model of turbulence has been chosen for the fundamental computations. The standard k- and the realizable k- models have been also tested, but some problems appeared during the calculations at low velocities of the air.

The Fluent CFD software has been applied for simulations. It has been assumed that the air inlet is parallel to the X axis of the models. Except the inlet and the outlet surfaces all of the remaining planes have been assumed as the symmetry planes. First the testing computations have been performed to choose the proper numerical grid and the turbulence

correct equation for the present case (range of Reynolds numbers and the equivalent diameter of the pipes are not sufficient criteria). The Kays and London correlations (presented for the specific geometry of the heat exchanger core) seem to be the most accurately determined according to empirical findings. But it is hard to tell what the impact of differences in the geometric parameters of the heat exchangers cores used in the study is.

Fig. 9. Comparison of results obtained by different Nusselt number correlations for HE-1

Two geometrical models have been made for numerical computations: the recurrent element of the considered heat exchangers and the recurrent segment – see Fig. 10. Geometries and

The models of the recurrent segments of the radiators are related to the measurement series which results were described earlier. Each model consists of one or two rows of pipes and there are ten ribs in each row. The reason for the creation of these two numerical models is

The testing computations have shown that for considered models non-structured meshes are useless in most cases – the calculations were not converged or gave non-physical results. So for the fundamental computations for the recurrent element the structured meshes of 170

The Reynolds Stress Model of turbulence has been chosen for the fundamental computations. The standard k- and the realizable k- models have been also tested, but

The Fluent CFD software has been applied for simulations. It has been assumed that the air inlet is parallel to the X axis of the models. Except the inlet and the outlet surfaces all of the remaining planes have been assumed as the symmetry planes. First the testing computations have been performed to choose the proper numerical grid and the turbulence

heat exchanger.

**3.2.2 Numerical simulations using CFD software** 

numerical grids have been created using Gambit pre-processor.

to test whether the simplification of real geometries affect the results.

to 250 thousands cells for single recurrent element have been chosen.

some problems appeared during the calculations at low velocities of the air.

model. These computations have been realized for the air inlet temperatures of 10ºC, 20ºC or 30ºC, and the velocity ranging from 2 m/s to 20 m/s. The water temperature has been assumed equal to 90ºC, and the heat transfer coefficient inside the pipes has been calculated from the Colburn relationship.

Fig. 10. The recurrent element (left) and the recurrent fragment (right) of the heat exchanger HE-1.

The averaged value of the heat transfer coefficient at the air side has been calculated based on the known fields of temperature for the rib surface and the pipe surface as well as the average temperature of the air and the transferred heat flux – see (Bury and Składzień, 2006) for details. The results for the HE-1 exchanger obtained by using the recurrent element model are presented in Fig. 11.

Fig. 11. Heat transfer coefficient versus the air inlet velocity – HE-1 exchanger, recurrent element model.

Impact of a Medium Flow Maldistribution on a Cross-Flow Heat Exchanger Performance 133

Fig. 13. Simplified sketch of the test station (1 - ribs and pipe models, 2 - electric heaters, 3 -

Two parameters have been set as independent during experiments: the temperature of the pipe internal wall and the air flow rates. Following parameters have been recorded during

the electric heater surface temperature th1 and th2 (assumed after as the pipe inner

temperatures on the ribs surfaces in the measuring points (seven measuring points have

There have been 25 measurements realized within the framework of this project. These experiments have been divided into five measuring series differing with the set temperature of the electric heaters (from 50 to 90 degrees Celsius with ten degree step). The range of the independent parameters changes has been chosen to obtain flow conditions (Reynolds' number) similar to those from the main testing station. Selected results of experiments are presented in Table 2. Sample temperature distribution measured during experiment MS-2 is

Fig. 14. Sample infrared thermographic picture of the first rib surface – experiment MS-2.

air

**4**

**o C**

**5**

flow channel, 4 - thermocouples, 5 - infra-red camera, 6 - speculum).

the air temperature at the inlet and outlet of the ribs section ta,in and ta,out,

measurements:

the air volumetric flow rate,

surface temperature),

presented in Fig. 14.

electric power consumed by the heaters Nh,

been marked as L1, L2, L3, M, R1, R2 and R3), temperature distribution on the surface of the first rib.

**4**

The comparison of results for the recurrent element and recurrent segment is shown in Fig. 12. One may observe that the values of the air heat transfer coefficient obtained from the segment model are higher than the results from the element model. The initial difference reaches almost 22 per cent and it decreases down to 6 per cent along with the rising velocity of the air. The more significant difference for the lower velocities may be an effect of a nonfully developed turbulence. Using the recurrent fragment model allows for more accurate mapping of the real object, but also increases the computation time almost ten times.

Fig. 12. Heat transfer coefficient versus the air inlet velocity – comparison of results for the recurrent element and segment of HE-1 exchanger.

#### **3.2.3 Validation of the numerical procedure for the heat transfer coefficient determination**

A simple comparison of heat transfer coefficient values presented in subsections 3.2.1 and 3.2.2 allows to see large differences, both between the empirical correlations and numerical models. Computational results, however, appear to coincide with the results obtained using the Kays-London correlations, which were previously considered to be the most accurate. Numerical approach is very convenient for the considered problem: it allows both to reproduce the accurate geometry of the recurrent element of the actual heat exchanger, as well as to take account of the non-uniform air flow. However, requires detailed plausibility study.

An enlarged special model of a fragment of the heat exchanger HE-1 has been built in order to check the numerical procedure responsible for determination of the heat transfer coefficient from the ribs to the gas.

The model consists of four plate ribs with respective pipe sections. Two electric heaters simulate the hot water flow inside the pipes. This model is placed in a flow channel with an observation window and it is cooled by the forced air flow (see Fig. 13). The air flow rate and temperatures at the inlet and outlet are measured. The infra-red thermography technique is used for measurement of the temperature field on the surface of the first rib. Several thermocouples are also installed for measuring the temperature on the other ribs surfaces.

Fig. 13. Simplified sketch of the test station (1 - ribs and pipe models, 2 - electric heaters, 3 flow channel, 4 - thermocouples, 5 - infra-red camera, 6 - speculum).

Two parameters have been set as independent during experiments: the temperature of the pipe internal wall and the air flow rates. Following parameters have been recorded during measurements:

the air volumetric flow rate,

132 Heat Exchangers – Basics Design Applications

The comparison of results for the recurrent element and recurrent segment is shown in Fig. 12. One may observe that the values of the air heat transfer coefficient obtained from the segment model are higher than the results from the element model. The initial difference reaches almost 22 per cent and it decreases down to 6 per cent along with the rising velocity of the air. The more significant difference for the lower velocities may be an effect of a nonfully developed turbulence. Using the recurrent fragment model allows for more accurate

mapping of the real object, but also increases the computation time almost ten times.

Fig. 12. Heat transfer coefficient versus the air inlet velocity – comparison of results for the

A simple comparison of heat transfer coefficient values presented in subsections 3.2.1 and 3.2.2 allows to see large differences, both between the empirical correlations and numerical models. Computational results, however, appear to coincide with the results obtained using the Kays-London correlations, which were previously considered to be the most accurate. Numerical approach is very convenient for the considered problem: it allows both to reproduce the accurate geometry of the recurrent element of the actual heat exchanger, as well as to take account of the non-uniform air flow. However, requires detailed plausibility

An enlarged special model of a fragment of the heat exchanger HE-1 has been built in order to check the numerical procedure responsible for determination of the heat transfer

The model consists of four plate ribs with respective pipe sections. Two electric heaters simulate the hot water flow inside the pipes. This model is placed in a flow channel with an observation window and it is cooled by the forced air flow (see Fig. 13). The air flow rate and temperatures at the inlet and outlet are measured. The infra-red thermography technique is used for measurement of the temperature field on the surface of the first rib. Several thermocouples are also installed for measuring the temperature on the other ribs

**3.2.3 Validation of the numerical procedure for the heat transfer coefficient** 

recurrent element and segment of HE-1 exchanger.

**determination** 

study.

surfaces.

coefficient from the ribs to the gas.


There have been 25 measurements realized within the framework of this project. These experiments have been divided into five measuring series differing with the set temperature of the electric heaters (from 50 to 90 degrees Celsius with ten degree step). The range of the independent parameters changes has been chosen to obtain flow conditions (Reynolds' number) similar to those from the main testing station. Selected results of experiments are presented in Table 2. Sample temperature distribution measured during experiment MS-2 is presented in Fig. 14.

Fig. 14. Sample infrared thermographic picture of the first rib surface – experiment MS-2.

Impact of a Medium Flow Maldistribution on a Cross-Flow Heat Exchanger Performance 135

Selected results of simulations of the MS-1 experiment are presented in Fig. 16. The CFD analysis gives the possibility to view fields of the most important parameters in different cross sections of the object under consideration. The air velocity distribution is shown in Fig. 16 on left. The cross section plane is parallel to the flow direction and it crosses the second

The most interesting numerical results are the temperature distributions on the first rib surface (see Fig. 16 on right), as well as the experimental results. These distributions may be

 Fig. 16. The air velocity contours (left - m/s) and temperature distribution on the first rib

The main goal of the analysis is to evaluate the numerical CFD model used for computations of the heat transfer coefficient at the gas side of the considered heat exchanger. A simple comparison of measured and computed temperatures for two analyzed experiments is presented in Table 3. The first three thermocouples are placed on the first rib visible surface and are also used for calibration of the infra-red camera. The calculated surface temperature values are a little bit underestimated, as well as the air outlet temperature. The last parameter is computed as the area weighted average value for the cross section placed 2 cm

The most interesting is comparison of the temperature field for the first rib surface (see Fig. 17). Due to different color scales a direct comparison is somewhat difficult but one can see that similarity of temperature distributions is quite good, both quantitatively and

 tL1, ºC tL2, ºC tL3, ºC tM, ºC tR1, ºC tR2, ºC tR3, ºC ta,out, ºC MS-4 Measurement 40.4 41.5 34.5 43.9 39.8 40.6 33.9 33.4

MS-22 Measurement 56.2 57.7 48.0 61.1 55.4 56.5 47.2 42.9

Table 3. Comparison of experimental and numerical data for the rib temperature – sample

Simulation 40.1 40.9 33.8 43.5 39.4 39.9 33.3 32.9

Simulation 55.5 56.2 47.1 60.5 54.6 55.1 46.3 41.3

rib. One may note that the air inflow to the ribs section is quite well unified.

next compared with the infra-red thermography measurements.

surface (right - K) for the MS-1 experiment.

next to the ribs section.

qualitatively.

results.


Table 2. Selected results of measurements.

All experiments described above have been next simulated using numerical model of the laboratory stand. The same assumptions as used during creation of the models described in subsection 3.2.2 have been applied. The numerical model of the system under consideration is a part of the laboratory stand and contains the flow channel with the ribs section. The geometry of the model has been created using Gambit preprocessor and it is shown in Fig. 15 as well as the boundary conditions types. All remaining boundary conditions have been set as coupled and isolated walls for external surfaces of the model. The numerical model contains near 560 thousands of tetrahedral cells.

All performed simulations have been realized using the measured air flow rate and the electric heaters surfaces temperature as the boundary conditions. A part of simulations also considered thermal radiation. The surface to surface model of this phenomena implemented into the Fluent has been applied.

Fig. 15. Geometry of the numerical model of the test rig and boundary conditions types.

MS-1 7.03·10-3 49.5 50.2 116.5 24.0 37.5 45.3 40.0 49.4 42.3 37.3 38.0 37.9 MS-5 12.47·10-3 49.7 50.4 137.1 22.9 31.1 38.6 33.8 43.2 38.9 31.2 31.4 31.6 MS-6 7.00·10-3 59.6 60.5 143.3 24.1 40.1 46.0 41.9 53.6 46.5 39.2 38.3 37.8 MS-10 12.47·10-3 60.1 60.7 152.5 23.4 33.1 41.7 35.9 43.7 40.9 33.1 31.0 31.8 MS-11 7.03·10-3 69.6 70.7 159.6 24.2 41.9 50.1 46.3 55.2 48.7 38.2 38.2 42.3 MS-15 12.47·10-3 69.9 71.1 173.4 23.7 34.4 42.9 40.3 45.3 43.1 36.9 33.8 34.5 MS-16 7.00·10-3 79.5 80.6 179.1 24.0 44.5 52.0 45.6 56.8 48.5 41.9 41.2 42.2 MS-20 12.50·10-3 79.2 80.0 189.2 24.2 36.2 45.3 39.4 47.7 45.1 35.8 33.9 36.2 MS-21 7.03·10-3 93,7 90.4 192.0 23.9 44.8 56.1 48.3 60.1 52.4 41.8 39.7 42.1 MS-25 12.53·10-3 89.7 90.6 215.8 24.5 38.3 46.5 39.1 48.3 42.4 35.2 32.8 35.3

All experiments described above have been next simulated using numerical model of the laboratory stand. The same assumptions as used during creation of the models described in subsection 3.2.2 have been applied. The numerical model of the system under consideration is a part of the laboratory stand and contains the flow channel with the ribs section. The geometry of the model has been created using Gambit preprocessor and it is shown in Fig. 15 as well as the boundary conditions types. All remaining boundary conditions have been set as coupled and isolated walls for external surfaces of the model. The numerical model

All performed simulations have been realized using the measured air flow rate and the electric heaters surfaces temperature as the boundary conditions. A part of simulations also considered thermal radiation. The surface to surface model of this phenomena implemented

Fig. 15. Geometry of the numerical model of the test rig and boundary conditions types.

Va th1 th2 Nh ta,in ta,out tL1 tL2 tL3 tM tR1 tR2 tR3 m3/s °C °C W °C °C °C °C °C °C °C °C °C

Meas. No.

Table 2. Selected results of measurements.

contains near 560 thousands of tetrahedral cells.

into the Fluent has been applied.

Selected results of simulations of the MS-1 experiment are presented in Fig. 16. The CFD analysis gives the possibility to view fields of the most important parameters in different cross sections of the object under consideration. The air velocity distribution is shown in Fig. 16 on left. The cross section plane is parallel to the flow direction and it crosses the second rib. One may note that the air inflow to the ribs section is quite well unified.

The most interesting numerical results are the temperature distributions on the first rib surface (see Fig. 16 on right), as well as the experimental results. These distributions may be next compared with the infra-red thermography measurements.

Fig. 16. The air velocity contours (left - m/s) and temperature distribution on the first rib surface (right - K) for the MS-1 experiment.

The main goal of the analysis is to evaluate the numerical CFD model used for computations of the heat transfer coefficient at the gas side of the considered heat exchanger. A simple comparison of measured and computed temperatures for two analyzed experiments is presented in Table 3. The first three thermocouples are placed on the first rib visible surface and are also used for calibration of the infra-red camera. The calculated surface temperature values are a little bit underestimated, as well as the air outlet temperature. The last parameter is computed as the area weighted average value for the cross section placed 2 cm next to the ribs section.

The most interesting is comparison of the temperature field for the first rib surface (see Fig. 17). Due to different color scales a direct comparison is somewhat difficult but one can see that similarity of temperature distributions is quite good, both quantitatively and qualitatively.


Table 3. Comparison of experimental and numerical data for the rib temperature – sample results.

Impact of a Medium Flow Maldistribution on a Cross-Flow Heat Exchanger Performance 137

In the paper (Bury et al., 2009a) authors concluded that neglecting of thermal radiation phenomena may be a reason of discrepancies between numerical and experimental results. An additional set of simulations has been initiated taking into account thermal radiation. The results however have shown almost no differences in comparison to these shown in Table 4. This situation could be an effect of assuming dry air flow through the ribs section. This gas contains mostly two-atom particles and it is almost optically inactive regarding the

According to the results of analyses it may be noted that the CFD based numerical model portrays the physical phenomena with satisfying accuracy. Probable reasons of recorded discrepancies are some simplifications in the numerical model geometry as well as

The analyses presented in subsection 3.2 allowed to withdrawn following conclusions:

 application of available correlations for Nusselt number leads to a wide deviation of the heat transfer coefficient values; it is difficult to define the characteristic dimension in some cases; even application of Kays-London approach (assumed as the most accurate)

 the numerical models of recurrent element and recurrent segment of considered heat exchangers give the heat transfer coefficient results within the range determined by investigated correlations for Nusselt number; the results obtained by using the recurrent element and recurrent segment differ, especially at low velocities; application of the recurrent segment model seems to be more correct but it needs a lot of computing time; such approach allows for detailed representation of real geometries in numerical model.

> Measurement No. *Q* num, kW *Q* ex, kW *Q* , % HE-1/1 12.78 11.03 15.9 HE-1/2 26.44 22.61 16.9 HE-1/3 39.96 34.08 17.3 HE-1/4 11.11 9.72 14.3 HE-1/5 22.44 19.42 15.6 HE-1/6 33.48 29.11 15.0 HE-2/1 11.59 10.07 15.1 HE-2/2 16.24 14.08 15.4 HE-2/3 22.75 19.58 16.2 HE-2/4 5.10 4.48 13.9 HE-2/5 13.76 12.04 14.3 HE-2/6 22.68 19.76 14.8 HE-3/1 14.27 12.39 15.2 HE-3/2 20.02 17.31 15.6 HE-3/3 28.10 24.08 16.7 HE-3/4 6.28 5.51 14.0 HE-3/5 17.00 14.81 14.8 HE-3/6 28.14 24.30 15.8

thermal radiation.

neglecting the heat losses to the environment.

**3.3 Results of numerical simulations** 

does not assure reliable results,

Table 5. Selected computational results.

Fig. 17. Calculated (left, K) and measured (right, ºC) temperature field of the first rib surface for experiment MS-4 – air flow direction same as in Fig. 14.

The next step in the analysis was the computation and comparison of the total heat flow rates transported from the ribbed surface to the flowing air. The results for measuring series MS-1 to MS-5 and MS-21 to MS-25 are presented in Table 4. The total heat flow rates has been calculated twice based on the air enthalpy rise:



Table 4. Comparison of experimental and computational data – heat flow rates.

The relative differences (*Q* ) between experimental and numerical results have been calculated. The heat flow rates calculated based on the measured values, as it can be seen, is lower than the measured values of the electric power of the heaters. The obvious reason of this situation is the heat losses through the rear wall of the flow channel. The differences between experimental and computational heat flow rates calculated as the CFD results reach up to 18% for some cases, but the average difference is somewhat over 10%.

In the paper (Bury et al., 2009a) authors concluded that neglecting of thermal radiation phenomena may be a reason of discrepancies between numerical and experimental results. An additional set of simulations has been initiated taking into account thermal radiation. The results however have shown almost no differences in comparison to these shown in Table 4. This situation could be an effect of assuming dry air flow through the ribs section. This gas contains mostly two-atom particles and it is almost optically inactive regarding the thermal radiation.

According to the results of analyses it may be noted that the CFD based numerical model portrays the physical phenomena with satisfying accuracy. Probable reasons of recorded discrepancies are some simplifications in the numerical model geometry as well as neglecting the heat losses to the environment.
