Available online at ScienceDirect. Energy Procedia 83 (2015 ) Václav Dvo ák a *, Tomáš Vít a

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1 Available online at ScienceDirect Energy Procedia 83 (205 ) th International Conerence on Sustainability in Energy and Buildings Numerical investigation o counter low plate heat exchanger Václav Dvoák a *, Tomáš Vít a a Technical University o Liberec, Studentska 2, Liberec, 467, Czech Republic Abstract Flow and heat transer in a recuperative counter low plate air-to-air heat exchanger were investigated numerically using Fluent sotware. It was employed previously developed methods to generate a computational mesh and assumed a zero thickness o the plates to calculate the low in an air-to-air heat exchanger. Pressure loss and eectiveness were evaluated as unctions o inner velocity. Obtained numerical data were substituted by suggested unctions dependent on the Reynolds number. A unction or the loss coeicient was based on the presumption that losses consist o local losses and riction losses. The unction or the Nusselt number used the ordinary power unction o the Reynolds number or orced convection. The eect o material thickness on pressure loss and eectiveness was illustrated. Even a very thin material or the plate signiicantly aects pressure loss, while the eect on the eectiveness depended on the thermal conductivity o plate material used. From this results, it is obvious that a thin as possible material is crucial or creating the most eective recuperative air-to-air heat exchanger with high eectiveness and low pressure loss, while the properties o the material itsel are unimportant. We compared numerical data with data obtained by measuring a real heat exchanger. The results or eectiveness corresponded well and corrections made were negligible. The results or pressure loss diered signiicantly, but this dierence was lowered by correcting or plate thickness. 205 The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility o KES International. Peer-review under responsibility o KES International Keywords: Heat exchanger, CFD;. Introduction Energy recovery is one o the ways to reduce the energy consumption o buildings. The main component o any energy recovery devices are heat exchangers. Development o recuperative heat exchangers in recent years has ocused on increasing their eectiveness. Another challenge is the development o so-called enthalpy exchangers or * Corresponding author. Tel.: address: vaclav.dvorak@tul.cz The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility o KES International doi:0.06/j.egypro

2 342 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) simultaneous heat and moisture transport, i.e. transport o both sensible and latent heat, as presented by Vít et al. in work []. To develop heat exchangers, methods o computational luid dynamics are increasingly used, but there are still some problems to transmit the calculation results to the manuacturing process. Nomenclature A area o heat exchange surace (m 2 ) c isobaric speciic heat capacity (J kg - K - ) p C coeicient in C correction or riction coeicient () d gap between plates, channel high (m) riction coeicient () L length o the heat exchanger (m) m mass low rate (kg s - ) n exponent in criterial equation or Nusselt number () Nu Nusselt number () v velocity (m s - ) p pressure (Pa) Re Reynolds number () t temperature ( C) s plate pitch (m) U overall heat transer coeicient (W m -2 K - ) plate thickness (m) dierence (-) thermal conductivity o luid air (W m - K - ) thermal conductivity o plate material (W m - K - ) kinematic viscosity o air (m 2 s - ) density (kg m -3 ) eectiveness o heat recovery () F inal loss coeicient o the heat exchanger () local loss coeicient o the heat exchanger () S To simulate a heat exchanger, it is necessary to create a model and a computational mesh and then use computational luid dynamic (CFD) sotware. When assembling the heat exchanger, complicated and irregular narrow channels are created. These channels are split into small volumes (elements). The inal meshes are structured or unstructured with dierent element sizes. Several other researchers have dealt with the design o plate heat exchangers and have investigated the perormance and loss o pressure o exchangers using numerical simulations. Most o them used an unstructured mesh or their calculations. Gherasim et al., in work [2], presented a comparison o various grids or a plate heat exchanger modeled by a tetrahedral mesh. In order to assess the inluence o the grid resolution on the solution, ive grids were created and tested by meshing the volumes with dierent interval sizes. Laminar and turbulent regimes were simulated. The evolution o the average pressure and average temperature o the hot luid over transversal sections along the length o the plate was investigated. In general, the dierences between the series or the turbulent case were larger than those or the laminar case. It was discovered that the two grids with the smallest elements provided very similar results. In terms o temperature, the obtained results were close or grids with smaller elements. For pressure, quite a large dierence between the grid with smallest elements and the grid with the largest ones was discovered.

3 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) Subsequent researchers have used numerical simulations to investigate plate heat exchangers with chevron (undulated) proiles. Tsai [3] and Liu [4], or example, dealt with these heat exchangers and their dierent geometries. Their conclusions regarding temperature and pressure loss were similar to Gherasim [2]. Novosád, in work [5], investigated the inluence o oblique waves on the heat transer surace. The main diiculty aced in this work was the creation o custom geometry. Each version had to be modeled separately and meshed. Each model had to be loaded into the solver, the boundary conditions set, and subsequently evaluated by calculation. The disadvantages o the repeated generation o computational meshes are: It is slow, meshes made in dierent models are not similar, and parameterization o the model is problematic. Further, even a small change o geometry requires the whole process o model creation and mesh generation to be gone through again. As a result, there is a high probability o introducing errors into the model and obtaining a low quality o mesh cells. It is necessary to setup the solver, boundary conditions, and all models or all computed variants. Furthermore, meshes are not similar, i.e. the size, shape, and height o cells adjacent to walls are not the same or dierent topologies. Thereore, Dvoák, in works [6] and [7], developed a new method or generating computational variants. This method was based on a dynamic mesh, which is provided by Fluent sotware. The meshes were created by pulling, which is similar to the own production process, i.e. it the pulling direction is perpendicular to the plates. The main advantage is that this type o variant generation is automatic and controlled by in-house sotware. All computational variants thus have a similar mesh. Furthermore, Dvoák and Novosád, in work [8], investigated the inluence o mesh quality and density on the numerical calculation o a heat exchanger with undulations in a herringbone pattern. They compared the results o the numerical calculation obtained or unstructured meshes made manually with structured but deormed meshes and examined the eect o computational cell size and the number o layers o computational cells across hal o the channel. They ound that very coarse meshes can yield both too high and unrealistic eectiveness and pressure loss compared to other results. It seems that or deormed meshes, which are structured, the appropriate element size is 0.7 mm, although this size is sometimes not suitable or unstructured meshes. The aim o this work was to calculate a real counter low heat exchanger and to compare numerical results with experimental. 2. Methods Fig.. Schema o a plate heat exchanger model and boundary conditions. The schema o the numerical model o the plate heat exchanger is shown in Fig.. The plate heat exchanger had a typical shape, with inlet cross-low sections in a triangular shape, which served to distribute the airlow across the heat exchanger beore it entered the counter-low section in the middle o the exchanger. The white line in Fig. represents the ideal path along which the air lowed. Due to the way the plate heat exchanger was assembled, we

4 344 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) calculated the low and heat transer around two plates. A periodical boundary condition was applied on the upper and the lower boundary conditions, which were parallel to the heat exchanger plates. We employed a previously developed method to create the computational mesh and to shape the plates o the heat exchanger, see works [6, 7]. The proper density o the mesh was subsequently conirmed in work [8]. An incompressible luid (air), with properties independent o temperature, was used: thermal conductivity (W m - K - -6 ), kinematic viscosity (m 2 s - ), and density. 225 (kg m -3 ). We used mass low inlets as inlet boundary conditions with speciied temperatures o 0 and 20 C, as well as various mass low rates, to obtain the characteristics o the heat exchanger. Outlet boundary conditions were speciied by static pressure. The two main properties o recuperative heat exchangers used in HVAC systems are the coeicient o eectiveness and pressure loss. Both are dependent on the mass low rate o air and are evaluated rom numerical data. The coeicient o eectiveness (or eectiveness) is an eiciency o the transer o sensible heat. Most recuperative heat exchangers in air conditioning systems work in isobaric mode, where mass low rates o warm and cold air are equal, i.e. m e m. Assuming parity between speciic heat capacities, i c p e c, we can write the p i eectiveness as T T T T T T e2 e e2 e i i2, () t Ti Te Ti Te where T i (K is the inlet temperature o internal air, T e (K) is the inlet temperature o external air, and T e2 () is the outlet temperature o external air. The coeicient o eectiveness obtained by numerical calculation as a unction o mass low rate is shown in Fig. 2a. The dierence in total pressure loss between the inlet and outlet was used to assess a drop in pressure p p 0 p 02, (2) where p 0 (Pa) is the mass-averaged total pressure in the inlet and p 02 (Pa) is the mass-averaged total pressure in the pressure outlet. Pressure drop as a unction o the mass low rate, which was obtained by numerical calculation, is shown in Fig. 2b. 3. Results Eiciency (%) Eiciency Calculation Measurement 0. Correction Mass low rate (kg m -3 ) a) b) 50 Measurement Correction Fig. 2. (a) Eectiveness as a unction o mass low rate; (b) Pressure drop as a unction o mass low rate. As can be seen rom Fig. 2, the eectiveness decreased at a higher mass low rate, while the drop in pressure Pressure drop (Pa) Pressure drop Mass low rate (kg m -3 ) Calculation

5 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) increased. We can also see that there was relatively good agreement among numerical results; the calculation overestimated the eectiveness obtained by measurement by 3%. The dierences between the calculated and measured pressure drop was bigger; the calculation underestimated the pressure drop by 75% or the lowest mass low rate and by 9% or the highest. The dierences can be explained by assuming a zero thickness o the material o the heat exchanger plates and neglecting heat resistance o the plates. To correct our numerical results, it was necessary to take the inluence o the plate thickness into account. To better understand these trends and to allow urther analysis, we substituted the obtained data with suitable unctions. We expected pressure losses, which were responsible or a drop in pressure, to consist o riction losses and local losses. Due to the low Reynolds number, we assumed a dominant laminar low. Thereore, we assumed the ollowing orm o pressure loss p 2 v L, (3) S 2 2d 0 where d (m) is the gap between the plates o the heat exchanger, L (m) is the length o the heat exchanger or the length o the path the air lows through, () is the riction coeicient, and S () is the sum o the coeicients o local losses, which is obtained rom numerical results. For our case we obtained S 24.. For laminar low, we assumed the riction coeicient to be directly dependent on the Reynolds number by equation 64, (4) Re 2 by introducing the deinition o Re into equation (3) and dividing it by dynamic pressure v 2 we arrived at the ollowing orm o the inal coeicient o pressure losses F S L d 32 C Re, (5) where C () is the correction or the riction coeicient obtained rom the numerical results. In our case, we obtainedc This quite high value is was caused by the low in the so-called inlet cross-low sections o the heat exchanger, where the velocity was higher than in the counter-low section. The dependence o the loss coeicient on the Reynolds number is shown in Fig. 3a. As can be seen, the suggested equation (5) can easily substitute or the obtained numerical data. For evaluating heat transer, we assumed a dependence o the Nusselt number on the Reynolds number n Nu CRe, (6) where the constants evaluated rom the results were C and n Prandt number is considered to be constant or air in the expected temperature range and is included in the constant C. Comparison o the numerical calculation and a substitution with equation (6) is shown in Fig. 3b. Again, the suggested equation substituted easily or original data. As stated above, the numerical results were obtained or a zero thickness o the material o the heat exchanger due to several reasons. First, it was easier to model the heat exchanger without any real thickness o the plates. Second, the heat transer rom one air to the second one is mainly inluenced by the heat transer rom the air to the walls, while the conduction through the plates is usually negligible. It is due to the higher heat resistance o the boundary layers compared to heat resistance o the thin plates, which are usually about 0. (mm) thick. The third

6 346 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) reason or using plates with zero thickness was that the inal thickness o the heat exchanger was not known. Manuacturers o recuperative heat exchangers or HVAC systems consider the whole cross section o the heat exchanger without considering the thickness o the plates. Thereore, it was necessary to adjust the obtained numerical data according to the actual thickness o the heat exchanger plates. 70 Loss coeicient 25 Nusselt number Loss coeicient F () Numerical calculation 0 Equation (5) Reynolds number () a) b) Nusselt number () Numerical calculation Equation (6) Reynolds number () Fig. 3. (a) Loss coeicient evaluated rom the numerical results as a unction o the Reynolds number; (b) Nusselt number evaluated rom the numerical results as a unction o the Reynolds number. To do this, the previously introduced equations were used. We also assumed that these characteristics did not change or a non-zero thickness o the material o the heat exchanger. The real space between plates is given by this dierence d s, (7) where s (m) is the plate pitch and (m) is the plate thickness. Similarly, the characteristic dimension 2 d will decrease. For a non-zero thickness and or a given mass low rate o air through the heat exchanger, the velocity increases according to the reciprocal value, yet the Reynolds number remains the same, i.e. Re Re. To calculate the loss coeicient o the heat exchanger, we simply introduced the correct space t into equation (5), but it was necessary to consider the dierent dynamic pressures. Then, the equation (5) turns into the ollowing orm 2 s L 32 F S C s s Re. (8) The dependence o pressure losses due to a non-zero material thickness is plotted in Fig. 4a. The ratio o F F is a unction o ratio s and Re in the diagram. As can be seen, even with a very minimal thickness o the material and a ratio o s 0. 05, the pressure losses increased by (2 3)%. For extremely thick material, e.g. s 0.25, the drop in pressure reached 00% and was higher or lower Reynolds numbers. The inluence o material thickness on heat transer is more complex. The Nusselt number remains unchanged because it is dependent only on the Reynolds number, which does not change with material thickness. However, the heat transer convection changes due to a change in the characteristic dimension. The material thickness also aects thermal conduction in the material itsel. The overall heat transer coeicient in the presented heat exchanger coniguration was given by equation

7 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) U, 4( s ) Nu (9) where (W m - K - ) is the thermal conductivity o air and (W m - K - ) is the thermal conductivity o the plate material. To calculate the eect o the change in heat passage on the total transerred heat in the heat exchanger, it was also necessary to take into account the change o the temperature gradient across the heat exchanger. Assuming the same low rates and constant value o speciic heat in both streams the heat balance can be expressed as c T U AT ( ), m p (0) where m (kg s - ) is the mass low rate o the air, c p is the speciic heat capacity (J kg - K - ), A (m 2 ) is the area o heat exchange surace, and T (K) is the highest temperature dierence. The let side o the equation represents heat lux obtained by one air stream and given by the second air stream. The right side o the equation represents heat lux through the plates. By rearranging equation (0), we get the ollowing ormula or eectiveness UA. mc UA p () As estimated rom ormula (), the eectiveness will be higher or lower mass low rates and or higher coeicientsu. The eect o material thickness and thermal conductivity is plotted in Fig. 4b. As can be seen, or a thermal conductivity o plate material higher than W m - K -, the eect o material thickness on eectiveness was positive, but an additional rise in eectiveness was minimal or 0. 2 W m - K - and became negligible or W m - K -. On the other hand, or low thermal conductivity, i.e W m - K -, the eect o material thickness was negative because the thermal resistance o the plates became relevant. Ratio F ' / F () Change in pressure drop due to material thickness Re = Re = 000. Re = / s () a) b) Eiciency () Change in eectivness due to material thickness / s () Fig. 4. (a) Change in losses due to material thickness as a unction o the ratio material thickness as a unction o the ratio s and the Reynolds number; (b) Change in eectiveness due to s and thermal conductivity (W m - K - ). The results o the corrections or our case are shown in Fig.. We can see that a correction that took plate thickness and thermal conductivity into account yielded an even higher eectiveness than eectiveness obtained by calculations. The overall correction increased the calculated eectiveness by 0.9%. The inluence o plate thickness

8 348 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) on pressure drop was more signiicant, and in our case, the correction increased the calculated pressure drop by 24%. However, the measured pressure drop was still distinctly higher. This high dierence in pressure drop can be explained by several eects that were not taken into account during the calculations: the eect o plate roughness, the eect o plate deormation, and the eect o other imperections and dierences between the shapes o the numerical model and the real plates o the heat exchangers. 4. Conclusion Flow and heat transer in a recuperative counter low plate heat exchanger were investigated numerically using Fluent sotware. We employed previously developed methods to generate a computational mesh and assumed a zero thickness o the plates to calculate the low in an air-to-air heat exchanger. Pressure loss and eectiveness were evaluated as unctions o inner velocity. Obtained numerical data were substituted by suggested unctions dependent on the Reynolds number. A unction or the loss coeicient was based on the presumption that losses consist o local losses and riction losses. The unction or the Nusselt number used the ordinary power unction o the Reynolds number or orced convection. We used these unctions to illustrate the eect o material thickness on pressure loss and eectiveness. We discovered that even a very thin material or the plate signiicantly aects pressure loss, e.g. i the thickness o the material was only 5% o the plate pitch, the pressure losses were increased by at least 2% compared to a zero thickness and was higher or lower Reynolds numbers. The eect o plate thickness on the eectiveness depended on the thermal conductivity o plate material used. I the thermal conductivity coeicient was W m - K -, the eectiveness decreased with plate thickness because the thermal conductivity became relevant. I W m - K -, the eectiveness even increased with plate thickness, but any additional rise in eectiveness became negligible or W m - K -. From this results, it is obvious that a thin as possible material is crucial or creating the most eective recuperative air-to-air heat exchanger with high eectiveness and low pressure loss, while the properties o the material itsel are unimportant. We compared numerical data with data obtained by measuring a real heat exchanger. The results or eectiveness corresponded well; the calculations overestimated measured eectiveness by 3% and corrections made were negligible. The results or pressure loss diered signiicantly; the calculation underestimated the measured pressure drop by (9 75)%, but this dierence was lowered by correcting or plate thickness. This high dierence in pressure loss can be explained by several eects that were not taken into account during calculations: the eect o plate roughness, the eect o plate deormation, and the eect o other imperections and dierences between the shapes o the numerical model and the real plates o the heat exchangers. Acknowledgements The author grateully acknowledges the inancial support rom the Czech Technological Agency under project TACR TA Reerences [] Vít T, Novotný P, Nguyen V, Dvoák V. Testing method o materials or enthalpy wheels. Recent Advances in Energy, Environment, Economics and Technological Innovation, Paris, France, 29th 3st October; 203. [2] Gherasim I, Galanis N., Nguyen CT. Heat transer and luid low in a plate heat exchanger. Part II: Assessment o laminar and two-equation turbulent models. International Journal o Thermal Sciences 50; 20. p [3] Tsai YCh, Liu FB, Shen, P T. Investigation o eect o oblique ridges on heat transer in plate heat exchangers. International Communications in Heat and Mass Transer 36; p [4] Liu FB, Tsai YCh. An experimental and numerical investigation o luid low in a cross-corrugated channel. Heat Mass Transer 46; 200. p [5] Novosád J, Dvoák V. Investigation o eect o oblique ridges on heat transer in plate heat exchangers. Experimental Fluid Mechanics 203, November ; 203. p [6] Dvoák V. A method or optimization o plate heat exchanger. 8th International Conerence on Circuits, Systems, Communications and Computers, Santorini Island, Greece, July 7-2; 204.

9 Václav Dvořák and Tomáš Vít / Energy Procedia 83 ( 205 ) [7] Dvoák V. Optimization o plate heat exchangers with angled undulations in herringbone pattern. The 7th International Meeting on Advances in Thermoluids, Kuala Lumpur, Malaysia, November, 26-27; 204. [8] Dvoák V, Novosad J. Inluence o mesh quality and density on numerical calculation o heat exchanger with undulation in herringbone pattern. 9th International Conerence on Circuits, Systems, Communications and Computers, Zakynthos, Greece, July 6-20; 205 (submitted).