Experimental Determination of Flow and Heat Transfer Correlations for Passive Regenerators

Transcription

1 Purdue University Purdue e-pubs International Rerigeration and Air Conditioning Conerence School o Mechanical Engineering 20 Exeriental Deterination o Flow and Heat Transer Correlations or Passive Regenerators Steanie Marie Knau University o Wisconsin-Madison Gregory Nellis University o Wisconsin-Madison Sanord Klein University o Wisconsin-Madison Follow this and additional works at: htt://docs.lib.urdue.edu/iracc Knau, Steanie Marie; Nellis, Gregory; and Klein, Sanord, "Exeriental Deterination o Flow and Heat Transer Correlations or Passive Regenerators" (20). International Rerigeration and Air Conditioning Conerence. Paer 8. htt://docs.lib.urdue.edu/iracc/8 This docuent has been ade available through Purdue e-pubs, a service o the Purdue University Libraries. Please contact eubs@urdue.edu or additional inoration. Colete roceedings ay be acquired in rint and on CD-ROM directly ro the Ray W. Herrick Laboratories at htts://engineering.urdue.edu/ Herrick/Events/orderlit.htl

2 276, Page Exeriental Deterination o Flow and Heat Transer Correlations or Passive Regenerators Steanie KNAUF*, Gregory NELLIS, Sanord KLEIN University o Wisconsin Deartent o Mechanical Engineering Madison, WI, United States *Corresonding Author: sknau@wisc.edu ABSTRACT Active Magnetic Regenerative Rerigeration (AMRR) systes are being considered as an environentally riendly alternative to vaor coression rerigeration cycles. AMRR systes use solid rerigerants rather than a synthetic working luid. With the use o an environentally sae heat transer luid, such as water or a water roylene glycol solution, the ozone deletion otential and global waring otential or AMRR is essentially negligible. Further otiization o AMRR systes is required in order or the to becoe an econoically attractive and viable substitute or current air conditioning and rerigeration units. Much o this otiization is ocused on the regenerator atrix geoetry and the theral-luid behavior o the acked bed o agnetocaloric aterial. As art o this eort, a assive single-blow test acility has been develoed at the University o Wisconsin-Madison in order to easure the riction actor and the Nusselt nuber under conditions that are aroriate or AMRR systes.. INTRODUCTION Recent increased interest in AMRR systes has led to the need or couter odels that can accurately redict their behavior and erorance in a coutationally eicient anner. Engelbrecht (2005) develoed a one-diensional nuerical odel caable o redicting the erorance o an AMRR syste. However, coarison o the odel with exeriental easureents obtained ro an AMRR rototye at Astronautics (Zi et al., 2006) showed that the odel consistently over-redicted the erorance o the syste. This discreancy is ossibly a result o inaccurate calculation o the heat transer and ressure dro associated with the regenerator. The one-diensional nuerical odel utilizes correlations ro the literature or the Nusselt nuber (Nu) as a unction o the Reynolds (Re) and Prandtl (Pr) nubers, and or the riction actor () as a unction o the Reynolds nuber. Frischann (2009) designed and constructed a assive regenerator test bed that was installed in the single blow test acility. This regenerator is being used to veriy existing correlations or, i necessary, develo a new correlation or the Nusselt nuber and/or riction actor in a bed o acked unior sheres eloying a liquid heat transer luid with a high Prandtl nuber.. The Magnetocaloric Eect Magnetic rerigeration is ade ossible by the agnetocaloric eect, which reers to the change in the entroy o a aterial due to agnetization. Understanding o the agnetocaloric eect is best achieved through an analogous coarison with the coression rocess or a coon rerigerant used in vaor coression cycles. The undaental roerty relation or a coressible substance is given by: du T ds P dv () A siilar relation can be written or a agnetocaloric substance (rovided that hysteresis is ignored): International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20 o du T ds H d VM (2) Exaination o equations () and (2) reveals that ressure (P) is coarable to the alied agnetic ield ( o H) and the agnetic oent (VM) is coarable to (the inverse o) volue (V). When the coressible rerigerant is coressed adiabatically an increase in teerature will be induced; in an analogous rocess, an adiabatic agnetization o the agnetocaloric aterial causes an increase in its teerature. The next section discusses how the agnetocaloric eect ay be used to roduce rerigeration.

3 276, Page 2.2 The AMRR Cycle Figure shows a siliied version o the AMRR cycle. During an AMRR cycle, a orous regenerator bed constructed ro a agnetocaloric aterial is exosed to a tie-varying agnetic ield and a tie-varying low o heat transer luid. cold reservoir hot-to-cold low T C T H () (4) T C T H agnetization agnetic regenerator hot reservoir deagnetization T H (2) () T H T C T C cold-to-hot low Figure : Active agnetic rerigeration cycle (Engelbrecht, 2005) The rocess begins with the syste at state () where the regenerator bed exhibits a teerature variation ro the hot reservoir to the cold reservoir teeratures. The bed is agnetized causing it to transition ro state () to state (2). There is no luid low during the agnetization rocess and thereore the teerature in the regenerator increases due to the agnetocaloric eect. The teerature distribution at state (2) (ater agnetization) thereore results in teeratures that are higher than the hot teerature reservoir (T H ) at the hot end. During the cold-to-hotlow rocess, the heat transer luid lows through the bed ro the cold reservoir to the hot reservoir. This low o luid ro the cold reservoir causes the bed teerature to decrease, as shown in state (). As a result o this rocess, luid at a higher teerature than the hot reservoir is orced ro the hot end o the bed causing a heat rejection. The bed is deagnetized causing it to transition ro state () to state (4); this rocess results in a reduction in the teerature in the regenerator leading to the distribution shown in state (4). To get ro state (4) back to state (), heat transer luid is ushed back through the bed ro the hot reservoir to the cold reservoir. The hot luid brings the bed back to its original teerature roile and causes luid at a teerature lower than the cold reservoir (T C ) to low ro the cold end o the bed, resulting in a cooling eect. 2. UW AMRR SYSTEM MODEL The UW AMRR odel is a -D transient, nuerical odel that calculates the eriodic steady state teerature o the regenerator aterial and the heat transer luid during a colete AMRR cycle (Engelbrecht, 2008). The odel is exlicit in tie and ilicit in sace and is ileented using MATLAB. The odel accets water, a solution o roylene glycol and water or a solution o ethylene glycol and water as a heat transer luid which is assued to be incoressible and thereore the density o the heat transer luid is constant. The reaining luid roerties are odeled as a unction o teerature but not ressure. Hysteresis in the agnetocaloric aterial is neglected. The theral conductivity o the agnetocaloric aterial is assued to be a unction o teerature and the entroy a unction o teerature and alied ield. Correlations ro literature are used to calculate axial disersion, Nusselt nuber, and local riction actor in the regenerator. A thorough descrition o the odel is described by Engelbrecht (2008). The UW AMRR odel results have been coared to exeriental data or a rototye AMRR utilizing a acked bed o sherical articles coosed o coercial grade gadoliniu (Gd). Figure 2 shows the redicted cooling ower as a unction o easured cooling ower or these data. It is aarent ro the igure that the UW AMRR odel consistently over redicts the cooling ower by, on average, aroxiately 20 W. International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

4 276, Page Figure 2: Predicted cooling ower as a unction o exeriental cooling ower (Engelbrecht, 2008) One likely reason or the discreancy shown in Figure 2 is that the Nusselt nuber or riction actor correlation used by the odel is inaccurate or unsuitable or the range o Reynolds nuber (Re) and Prandtl nuber (Pr) that is used to roduce the data (i.e., low Reynolds nuber and high Prandtl nuber). The Nusselt nuber is deined according to: hd Nu () k where h is the heat transer coeicient, d is the article diaeter and k is the theral conductivity o the luid. The riction actor is a unction o the Reynolds nuber (Re) and the Nusselt nuber is a unction o both the Reynolds and Prandtl (Pr) nubers as deined below. v d Re (4) Pr (5) where is the density o the luid, is the viscosity o the luid, v is the suericial velocity o the luid as deined by the ratio o the voluetric low rate o the luid to the cross-sectional area o the test section, is the kineatic viscosity o the luid and is the theral diusivity o the luid. Several correlations exist or the Nusselt nuber inside a acked shere regenerator. The UW AMRR odel currently uses a correlation develoed by Wakao and Kaguei (982): Nu. Re Pr 06. / 2 (6) Wakao However, alternative correlations or the Nusselt nuber are rovided by Kunii and Levensiel (969): and Macias Mechin et al. (99): / 2 Re Nu 28. Pr Kunii / Re Nu Pr Macias (7) (8) Figure shows the Nusselt nuber redictions or these three correlations or a Prandtl nuber o 0 and a bed orosity ( ) o 0.6. The three correlations dier by a actor o aroxiately 5 under these conditions. International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

5 276, Page 4 Discreancies between these correlations as well as the disagreeent between the UW AMRR odel and exeriental data has rovided otivation or an exeriental study o the Nusselt nuber and riction actor or a acked bed at low Reynolds nuber and high Prandtl nuber. Friction actor exerients have been conducted and the results are dislayed in a subsequent section. Nusselt nuber data is currently being collected. Figure : Nusselt nuber correlations ro the literature as a unction o Reynolds nuber with Pr = 0 and = 0.6 (Frischann, 2009). PASSIVE REGENERATOR TEST FACILITY A single-blow test acility has been develoed and constructed at the University o Wisconsin-Madison in order to exerientally deterine the Nusselt nuber and riction actor associated with low through a regenerator acking (Marconnet, 2007). The acility utilizes a assive regenerator, i.e. the aterial is not agnetocaloric. A scheatic o the test acility is shown in Figure 4. Figure 4: Passive regenerator test acility The test acility can be used to easure ressure dro across the test section (i.e., the assive regenerator) using the low loo indicated with a bold, solid line in Figure 4. Fluid is ued ro the hot teerature bath through a.8 L/in caacity agnetic low eter and a series o low control valves beore it reaches the regenerator and is exhausted into a graduated cylinder. Pressure tas on either end o the regenerator are connected to a dierential ressure transducer, range 0- sid, selected seciically to easure the sall dierential ressures generated across the test bed. Pressure dro across the regenerator is easured at a seciic low rate and used to deterine the riction actor or a given Reynolds nuber. International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

6 276, Page 5 Obtaining easureents o Nusselt nuber is a ore colex rocess that ust be erored in two stes. The irst ste is to run the cold soak loo, indicated in Figure 4 by the bold, dashed line. During the cold soak, a continual low o luid is ued through a heat exchanger where the luid is cooled by low ro the cold teerature bath. The cold luid leaving the heat exchanger asses through the regenerator; the cold soak loo is run until the test section is therally stabilized at a unior, low teerature. Iediately ollowing the cold soak, a series o valves are switched so that the hot blow loo (bold solid line) is run through the test section roducing a ste change in luid teerature driven by hot luid extracted ro the hot teerature bath. Teerature versus tie data are gathered ro the beginning o the teerature ste change until a new theral equilibriu is reached by the regenerator. The theral behavior exhibited by the regenerator can be directly related to the luid-to-atrix heat transer, which allows the Nusselt nuber to be easured or a seciic set o conditions. A detailed set o test acility oeration instructions are given by Engelbrecht (2008). 4. FRICTION FACTOR The correlation develoed by Ergun is the ost widely used equation to describe ressure dro () across a acked bed o sheres (Heggs, 2008): 2 2 v v c 2 (9) L d d where is the ean ractional void sace o the acked bed (bed orosity), L is the length o the bed, and c and are correlation constants obtained by itting exeriental data. Ergun s equation is the su o two ters that corresond to viscous and inertial ressure loss. The riction actor can be deined by nondiensionalizing the ressure gradient by the viscous ter (i.e., the irst ter) in order to obtain the viscous riction actor: 2 d c v L v 2 Re () or by nondiensionalizing the ressure gradient by the inertial ter, the second ter in Eq. (9), in order to obtain the kinetic riction actor: d c () k 2 L v Re Ergun suggests values or c = 50 and =.75. Other correlations have the sae or, but use slightly dierent constants. For exale, MacDonald et al. use c = 80 and =.8. Both the Ergun and MacDonald correlations are coared to exeriental data gathered using the assive regenerator test acility. 4. Porosity Porosity is deined as the ratio o the ree volue to the total volue o the test section. V F (2) VT Equations () and () show that the riction actor has a cubic deendence on orosity; consequently, even a sall error in the easureent o the orosity can result in a substantial isreresentation o the riction actor. Thereore, it is very iortant to obtain an accurate easureent o the orosity. The orosity can be easured using two dierent ethods. The irst ethod should be eloyed beore the regenerator bed is assebled. The total volue o the test section is easured and the ass o the acking aterial is deterined. Dividing the acking aterial ass by the density o the acking aterial rovides the acking volue and dividing the acking volue by the total volue rovides the raction o the volue that is occuied by the sheres. Subtracting the acking raction ro unity rovides the ree volue raction (i.e., the orosity) o the test section. The second ethod can be utilized ater the regenerator test section is constructed. To deterine the ree volue, the test section is illed to caacity with water. The water is then oured ro the regenerator into a graduated cylinder to deterine the ree volue. The ree volue is divided by the total volue (deterined beore construction) in International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

7 276, Page 6 order to obtain the orosity. The orosity or the regenerator used in the UW test acility was easured using both ethods and ound to be 0.56 ±0.0 and 0.58 ±0.009, resectively. The two easureents are averaged, resulting in a orosity o Exeriental Setu Pressure dro across the assive regenerator was easured using water at three dierent teeratures and a 0% roylene glycol and water solution at a single teerature. The three teeratures o water (26 C, 4 C, and 72 C) were seciically chosen to create a oderate change in viscosity and thereore in the Prandtl nuber (6.0, 4. and 2.6, resectively). The glycol solution was selected in order to rovide a very large increase in viscosity and consequently in the Prandtl nuber (24.7). Such a large range o Prandtl nubers were used in order to veriy that the Prandtl nuber o the luid does not aect the riction actor/reynolds nuber behavior. These sae luids are used during Nusselt nuber testing where the eect o Prandtl nuber is exected to be draatic. Thereore, this veriication is necessary in order to ensure that an observed eect o the Prandtl nuber on the Nusselt nuber is not an artiact o the exeriental setu or rocedure. For each run, low rates were chosen to rovide Reynolds nubers ranging ro to 225 so that a roer coarison could be achieved against Ergun and Macdonald riction actor correlations. Table shows the low rates corresonding to the Reynolds nubers or each run. Table : Flow rates and corresonding Reynolds nuber Flow Rate (L/in) Reynolds Nuber Water 26 C Water 4 C Water 72 C 0% PG 22 C A constant teerature bath was used to set the teeratures or the 4 C and 72 C runs. Two therocoules at the to o the test section and two at the botto o the test section are onitored and recorded during each test run. Data are collected starting at the highest low rate and oving to the lowest low rate. Data are then taken in the oosite order, beginning with the lowest low rate and increasing to the highest low rate, in order to ensure reeatability. 4. Friction Factor Results Figure 5 shows ressure dro as a unction o voluetric low rate or 4 C water data and 0% roylene glycol/water solution. Pressure Dro [si] Decreasing Flow Rate Increasing Flow Rate Voluetric Flow Rate [liter/in] Pressure Dro [si] Decreasing Flow Rate Increasing Flow Rate Voluetric Flow Rate [liter/in] Figure 5: Pressure dro as a unction o voluetric low rate or 4ºC water data (let) and 0% PG data (right) International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

8 276, Page 7 The let-hand side o equations () and () are used to deterine the riction actor ro the collected ressure dro data. Figure 6 shows the riction actor (both viscous and kinetic) results with uncertainty bars or all our sets o data. Also shown in Figure 6 are the Ergun and Macdonald correlations. 0 Macdonald et al. v 0 Macdonald et al. v Ergun v Measured v Measured k Macdonald et al. k Ergun v Measured v Measured k Macdonald et al. k Ergun k 0 Reynolds Nuber [-] Macdonald et al. v Ergun k 0 Reynolds Nuber [-] 0 Macdonald et al. v Ergun v Measured v Measured k Macdonald et al. k Ergun k Measured v Ergun v Macdonald et al. k Measured k Ergun k 0 Reynolds Nuber [-] 0. 0 Reynolds Nuber [-] Figure 6: Friction actor as a unction o Reynolds nuber or 26 C (uer let), 4 C (uer right), 72 C (lower let) water data and 0% PG data (lower right) The uncertainty bars in Figure 6 are deterined based on a colete uncertainty analysis or the exeriental test acility. Table 2 shows a suary o the uncertainty values or a run at.2 L/in low rate using 0% roylene glycol and water solution. As seen in the table, the ajor sources o uncertainty in the Reynolds nuber result ro uncertainty in the luid viscosity and luid velocity. Uncertainty in the orosity accounts or about 62% o the uncertainty in the kinetic riction actor with the second largest contributor being uncertainty in the luid velocity which accounts or 29% o the uncertainty. Table 2: Suary o uncertainty values or.2 L/in low rate or 0% PG solution Variable Descrition Value Variable Descrition Value Total uncertainty in the kinetic Total uncertainty in the Reynolds k riction actor.202 Re nuber Re Uncertainty in the Reynolds nuber associated with luid density 6.9 x - Re Uncertainty in the Reynolds nuber Uncertainty in the riction actor associated with ressure dro 0.56 Uncertainty in the riction actor v associated with luid velocity Uncertainty in the riction actor associated with orosity Uncertainty in the riction actor L associated with length Uncertainty in the riction actor d associated with the article diaeter Uncertainty in the riction actor associated with the luid density.40 x -6 associated with luid viscosity 0.40 Re Uncertainty in the Reynolds nuber d associated with article diaeter Re Uncertainty in the Reynolds nuber v associated with luid velocity 0.26 International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20

9 276, Page 8 Figure 7 cobines the viscous and kinetic riction actors ro all three sets o water data as well as the 0% roylene glycol and water solution data. Fro Figure 7 it is concluded that the entirety o ressure dro data exhibits the ost agreeent with the Macdonald riction actor correlation Macdonald v Ergun v Water v 24 C Water k 24 C Water v 4 C Water k 4 C Macdonald k Water v 72 C Water k 72 C 0% PG v Ergun k 0% PG k 0. 0 Reynolds Nuber [-] Figure 7: Friction actor as a unction o Reynolds nuber or all our sets o ressure dro data 5. CONCLUSIONS The riction actor data reveal that the ressure dro through the acked bed o unior sheres is ost closely reresented by the Macdonald correlation. The uncertainty analysis o the data shows alost % agreeent with the Macdonald correlation within the uncertainty band. The largest source o uncertainty in the riction actor is uncertainty in the orosity o the acked bed and thereore a eticulous easureent o this araeter is necessary in order to obtain accurate data. Future work will ocus on exeriental easureent o the Nusselt nuber or unior sheres as well as other geoetries such as acked beds o non-unior diaeter sheres, non-sherical articles, and connected atrices. REFERENCES Engelbrecht, K., 2008, A Nuerical Model o an Active Magnetic Regenerator Rerigerator with Exeriental Validation, M.S. Thesis, University o Wisconsin Madison. Engelbrecht, K., 2005, A Nuerical Model o an Active Magnetic Regenerator Rerigeration Syste, M.S. Thesis, University o Wisconsin Madison. Frischann, M., 2009, Heat Transer Coeicient Using Liquid Heat Transer Fluids or use in Active Magnetic Regenerative Rerigeration, M.S. Thesis, University o Wisconsin Madison. Heggs, P.J., 2008, Fixed Beds, In: Hewitt, G.F., Heat Exchanger Design Handbook 2008, vol. 2, Begell House, New York: Kunii, D., Levenseil, O., 969, Fluidization Engineering, Wiley, New York, NY, 54. Macias-Machin, A., Ouer, L., Wannenacher, N., 99, Heat Transer between an Iersed Wire and a Liquid Fluidized Bed, Powder Technology, vol. 66: Marconnet, A., 2007, Predicting Regenerator Perorance with a Single-Blow Exerient, M.S. Thesis, University o Wisconsin Madison. Wakao, N., Kaguei, S., 982, Heat and Mass Transer in Packed Beds, Gordon and Breach Science Publishers, New York, NY, 64. Zi, C., Boeder, A., Chell, J., Sternberg, A., Fujita, A., Fujieda, S., Fukaichi, K., 2006, Design and Perorance o a Peranent Magnet Rotary Rerigerator, International Journal o Rerigeration, vol. 29, 8:2-6. ACKNOWLEDGEMENT The authors grateully acknowledge the suort ro Astronautics or this research. In articular, Steve Jacobs, Carl Zi, and Andre Boeder have rovided valuable discussions and technical inut. International Rerigeration and Air Conditioning Conerence at Purdue, July 2-5, 20