Simulation Model of an Automatic Commercial Ice Machine

Transcription

1 Purdue Univerity Purdue e-pub International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2016 Simulation Model of an Automatic Commercial Ice Machine Haithem Murgham Univerity of Dayton, United State of America, David Myzka Univerity of Dayton, United State of America, Vijay Bahel Emeron Climate Technologie, Rajan Rajendran Emeron Climate Technologie, Kurt Knapke Emeron Climate Technologie, See next page for additional author Follow thi and additional work at: Murgham, Haithem; Myzka, David; Bahel, Vijay; Rajendran, Rajan; Knapke, Kurt; Shivahankar, Sureh; and Wynn, Kyaw, "Simulation Model of an Automatic Commercial Ice Machine" (2016). International Refrigeration and Air Conditioning Conference. Paper Thi document ha been made available through Purdue e-pub, a ervice of the Purdue Univerity Librarie. Pleae contact epub@purdue.edu for additional information. Complete proceeding may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratorie at Herrick/Event/orderlit.html

2 Author Haithem Murgham, David Myzka, Vijay Bahel, Rajan Rajendran, Kurt Knapke, Sureh Shivahankar, and Kyaw Wynn Thi article i available at Purdue e-pub:

3 2281, Page 1 Simulation of an Automatic Commercial Ice Maker Haithem MURGHAM 1, David MYSZKA 1 *, Vijay BAHEL 2, Rajan RAJENDRAN 2, Kurt KNAPKE 2, Sureh SHIVASHANKAR 2, Kyaw WYNN 2 1 Univerity of Dayton, Department of Mechanical and Aeropace Engineering Dayton, OH, USA murghamh1@udayton.edu, dmyzka@udayton.edu 2 Emeron Climate Technologie, Applied Mechanic Sidney, OH, USA Vijay.Bahel@emeron.com, Rajan.Rajendran@emeron.com, Kurt.Knapke@emeron.com, Sureh.Shivahankar@emeron.com, Joe.Wynn@emeron.com * Correponding Author ABSTRACT Automatic commercial ice making machine that produce a batch of cube ice at regular interval are known a cuber. Such machine are commonly ued in food ervice, food preervation, hotel, and health ervice indutrie. The machine are typically rated for the weight of ice produced over a 24 hour period at ambient air temperature of 90 F and water inlet temperature of 70 F. Thee cuber typically utilize an air-cooled, vapor-compreion cycle to freeze circulating water flowing over an evaporator grid. Once a ufficient amount ice i formed, a valve witche to enable a harvet mode, where the compreor dicharge ga i routed into the evaporator, thereby releaing ice into a torage bin. The U.S. Department of Energy ha et a target of reducing energy uage by 10-15% by Engineering model are not publicly available to ait deigner in achieving the new energy regulation. Thi paper preent an engineering imulation model that addree thi need. Thi model imulate the tranient operation of a cuber ice machine baed on fundamental principle and generalized correlation. The model calculate time-varying change in the ytem propertie and aggregate performance reult a a function of machine capacity and environmental condition. Rapid what if analye can be readily completed, enabling engineer to quickly evaluate the impact of a variety of ytem deign option, including the ize of the air-cooled heat exchanger, finned urface, air / water flow rate, ambient air and inlet water temperature, compreor capacity and/or efficiency for freeze and harvet cycle, refrigerant, uction/liquid line heat exchanger and thermal expanion valve propertie. Simulation reult from the model were compared with the experimental data of a fully intrumented, tandard 500 lb capacity ice machine, operating under variou ambient air and water inlet temperature. Key aggregate meaure of the ice machine performance are: 1) cycle time (duration of freeze plu harvet cycle), 2) energy input per 100 lb of ice, and 3) energy uage during 24 hour. For thee meaure, the model accuracy i within 5% for a variety of operating condition. 1. INTRODUCTION The U.S. Department of Energy (2015) ha revied the energy efficiency tandard for automatic commercial ice maker (ACIM) that produce 50 lb to 4000 lb per day. A major egment of the ACIM market are elf-contained unit that produce a batch of cube ice at regular interval. Thee machine, known a cuber, are primarily ued in retaurant, hotel, convenience tore, and hopital. Cube weight typically range from approximately 1/6 to 1/2 oz and each manufacturer uually produce a unique hape (cubic, rectangular, crecent, and pillow) to ditinguih themelve from other manufacturer (Wetphalen et al., 1996). To ait in the deign of ACIM ytem, Varone (1995) developed an empirically baed imulation model. Since the deign change neceary to meet the new tandard will likely exceed the bound of an empirical model, a phyic-baed ACIM imulation model i deired to ae the performance implication.

4 2281, Page 2 Phyic-baed imulation model for the teady-tate operation of a vapor-compreion, refrigeration ytem have been etablihed everal decade ago (Domanki and Didion, 1983, Fiher and Rice, 1983). Thee model continue to erve a the bai for more recent enhancement uch a alternative refrigerant (Arora and Kahik, 2008) and complex ytem circuit (Bahel and Shivahankar, 2014). The teady-tate model are ufficient for mot refrigeration application, where the ytem achieve a table operating mode and continue to run in that mode for a majority of time. Engineering model for the ice machine preent a particularly challenging application. The ice machine exhibit entirely tranient behavior, a the operation continually cycle between the ice formation mode and ice harvet mode. Bendapudi et al. (2008) dicu variou approache for tranient imulation model. Of particular interet for ACIM modeling include refrigeration ytem during variable evaporator load (Chi and Didion, 1982, Macarthur, 1984), tartup condition (Li and Allleyne, 2010) and hot-ga bypa (Hoffenbecker et al., 2004) a ued during ice harvet mode. Tranient model for the heat exchange between refrigerant flowing through the evaporator tubing to water flowing over an ice forming grid do not exit in the literature and were developed by the author. Once etablihed, the imulation model enable prediction of component condition, load under different operating environment, and aement of ytem deign change. The remainder of the paper i organized a follow. The decription of the ice machine component and operation i decribed in Section 2. Section 3 preent the model theory. An overview of the model i provided in Section 4. Section 5 preent the reult and comparion to an intrumented ice maker. 2. ICE MAKER DESCRIPTION A chematic of a cuber i given in Fig. 1. Thi ACIM conit of two major ubytem: the vapor compreion refrigeration ytem and water upply/circulation/purge ytem. The typical refrigeration ytem component include a compreor, air-cooled condener, thermotatic expanion device, liquid line/uction line interchanger, and an evaporator that conit of copper tubing attached to copper or tainle teel grid forming the ice making urface. During harvet, a hot-ga olenoid valve witche and channel refrigerant directly from compreor to evaporator, which melt a boundary layer and releae the ice. The water ytem conit of a water ump, circulation pump, platic tubing and an evaporator water ditributor. A potable water upply connection upply control valve and purge drain control water inflow and from the ice maker. Condener Condener Fan Hot Ga Valve Evaporator Grid Expanion Valve Compreor Circulation Pump Drain Water Fill Heat Exchanger Figure 1: Schematic of an ACIM that produce batche of cube. Wetphalen et al. (1996) decribed the conventional, batch, ice making proce a follow: a. Water fill the ump, which uually contain 10 40% more water than required to make a given batch of ice. b. The refrigeration ytem i activated and ump water i circulated over the evaporator plate. During the freeze cycle, the compreor, condener fan (for air-cooled machine) and the water circulating pump are activated.

5 2281, Page 3 c. The water i cooled down and gradually freeze on the evaporator grid plate. d. Ice build up on the plate to the proper ice batch weight a detected by ome mean: ump water level, compreor uction preure, or thickne of ice on the grid plate. e. Upon reaching the precribed ice weight, the machine witche to the harvet mode. f. Mot machine ue hot ga harvet, in which hot refrigerant vapor i directed directly from the compreor to the evaporator to warm the evaporator and melt enough ice to free the cube from the plate. Typically about 5-10 percent of the ice i melted during the harvet proce. Once free, the ice fall by gravity into the torage bin below. During the harvet proce the condener fan for air-cooled machine i off and the water circulating pump may be operating, depending on the deign. Some machine ue a limited amount of hot ga for melting combined with mechanical mean for removing the ice. g. During the harvet proce, water remaining in the ump i purged from the ytem and freh, potable water i fluhed through the ytem to remove impuritie. h. Water fill the ump and the ytem return to the freeze mode a detected by evaporator temperature and/or time. 3. ACIM SIMULATION MODEL THEORY The tranient ice machine model incorporate a combination of algebraic and time-baed differential equation for the main component, a in the vapor-compreion ytem model created by Qiao et al. (2012). The pecific operating condition include the ambient air temperature T a and the upply water temperature T. Compreor: The compreor model involve only algebraic equation. A detailed by Stroeker (1998), the amount of ma flow m d delivered by the compreor to the component of the ice machine i dependent on compreor peed, compreor uction denity c, diplacement V d and volumetric efficiency v i m V (1) d v A polytropic approach can be ued to determine power conumption of the compreor, which i influenced by the evaporator preure p e, condener preure p c, compreor efficiency d, and polytropic exponent, c d ( 1) / 1 p 1 c W k d Vd p (2) e k pe Alternatively, compreor manufacturer conventionally provide rating information acro an operating map in accordance with AHRI Standard 540 (2004). The compreor performance value are tabulated over a range of evaporator aturation temperature T e and condener aturation temperature T c. The tabular data i fit to a tencoefficient, third-order polynomial equation of the form X C C T C T C T C T T C T C T C T T C T T C T (3) e 3 c 4 e 5 e c 6 c 7 e 8 e c 9 e c 10 c where X can repreent power conumption W k or ma flow m d. The appropriate rating coefficient C i are determined by a regreion and are provided by compreor manufacturer for engineer deigning a ytem or component. Rice and Dabiri (1981) developed adjutment to Eq. (3) for the level of uction ga uperheat. An energy balance on the vapor in the compreor chamber i ued to determine the temperature exiting the compreor T d. Fiher and Rice (1983) etablihed a compreor hell lo factor f q to compenate for heat tranfer through the compreor wall to the ambient air. Expanion Valve: The expanion valve operate during the freeeze portion of the cycle and alo involve only algebraic equation. The valve retrict flow and create a preure differential between the low-ide evaporator and the high-ide condener. Since refrigerant liquid at temperature T l and denity l i expected through the expanion valve, the one-dimenional, incompreible flow equation propoed by Jame and Jame (1987) i ued to model the device, m A ( p p ) (4) l l 2 l c e W S

6 2281, Page 4 An effective valve flow area of A l i fixed for an orifice or capillary tube expanion valve. Thermal expanion valve (TXV) or electronic expanion valve (EXV) provide a feedback ytem (mechanical or electronic) that alter A l to maintain a certain level of evaporator uperheat T h = T ev - T e, where T ev i the temperature of the vapor exiting the evaporator. The feedback gain G l and time contant v erve a input into the expanion valve model, l l b ev h A A G ( T T ) T (5) where T b i the ening element (thermobulb) temperature and A i a teady tate flow area. Since the feedback for a TXV i purely mechanical, a time delay i aociated with the temperature repone of the ening bulb. The repone lag i modeled by dt / dt ( T T ) / (6) b Air-Cooled Condener: The condener i modeled by dividing the total volume of the heat exchanger into N c decrete element along it legnth and uing a finite-difference method a detailed by Bendapudi et al. (2008). A outlined in Ge and Cropper (2005), condener heat rejection Q i computed uing the effectivene-ntu method, where c i the condener effectivene, N b c ev v c Q c ccp ( Tc Ta ) (7) c i i1 C i a heat capacity, p c T i the refrigerant temperature in the ith element c i of the condener, and T a i the ambient temperarure. Wang and hi collaborator developed appropirate model for the heat tranfer correlation of fin and tube heat exchanger that depend on condener fan flow V a, fin material and geometry, including mooth (2000), corrugated (1999), wavy (2001) and louvered (1999). The refrigerant propertie within the heat exhanger i governed by a conervation of refrigerent ma and energy along with preure drop due to friction. Thee equation are integrated to remove the patial dependence, reulting in a lumped-parameter, time-baed, ordinary differential equation. Evaporator: Heat tranfer from the water and into the refrigerant within the evaporator include the interface through the water, ice, evaporator grid, plate, tubing and refrigerant. A with the condener, the refrigerant within the evaporator tube i divided into into N e decrete element. A lumped reitance model i ued to determine the evaporator heat flow, Ne 1 Q e ( Te Tw ) (8) i R i1 where T i the refrigerant temperature in the ith element of the evaporator, T e W i the time varying circulation i water temperature, and R T i the effective reitance. The thermal reitance involve: 1) convection from the flowing water, 2) conduction through the ice being formed, 3) conduction through the evaporator tube, 4) the convection to the refrigerant within the evaporator tube. Thee individual interface component are Ti R 1/( W A ) R /( k A ) 1 W 2 I I I R /( k A ) R 1/( ) 3 g g g 4 e A i i e (9) with the cumulative reitance being R T R R R R i i (10) For the different zone: 1) The convection coefficient for a flowing liquid over a plate i denoted W and A W i the urface area of ice in contact with the flowing water. 2) The thermal conductivity of ice i k I, A I i the urface area of the grid, and I i the ice thickne. 3) The thermal conductivity of the evaporator grid and plate i k g, A g i the urface area of the plate, and g i the effective thickne of the evaporator plate. 4) The convection coefficient for

7 2281, Page 5 the two-phae refrigerant in the ith element of the evaporator i and A e e i the urface area of the evaporator i tube. Appropriate correlation were elected for the thermal conductivitie and heat tranfer coefficient (Incropera, 2006). The ice thickne I i zero at the tart of the freeze cycle and increae in relation to the cumulative evaporator heat tranfer Q e t. The conduction through the ice i oberved to be the dominant reitance. Circulating Water: At the tart of the freeze cycle, the circulating water ha a total ma M at a temperature W 0 T. At the end of the freeze cycle, an amount of water ha been tranformed into ice, having ma M W I. The 0 remaining water in the ump ha a ma MW F MW M and temperature 0 I T. Prior to the tart of the W F ubequent cycle a ma M of water at a temperature W S T i upplied to the ump. Since the amount of water W S circulating i contant for each freeze cycle, MW S M. A the upply water mixe with the remaining water in I the ump, the reulting temperature of the circulating water at the tart of the freeze cycle i T W0 M T M M WS WS WF WF (11) Liquid/Suction Line Heat Exchanger: Suction line heat exchanger heat flow Q between the compreor uction line at T c and the condener liquid line at temperature T cl. The value Q i baed on an effective contact width w of the tubing, the length of contact L and an appropriate heat tranfer coefficient, W0 T Q L w T T ) (12) ( c cl Hot Ga Valve: A the ice machine imulation witche to harvet mode, an alternate flow path permit refrigerant dicharged from the compreor to flow through a bypa retriction defined by A v and directly into the evaporator. With the bypa retriction, the compreor dicharge preure p d, and ma flow through the hot ga valve m i governed by v m A ( p p ) (13) v v 2 d d e During the freeze cycle, A v = 0. A the hot ga valve i opened during harvet (A v 0), the condener and expanion valve are bypaed. The governing equation for the other component in the ytem remain unchanged in the harvet mode. The tate potulate i an important principle of thermodynamic that i required to aemble the equation decribing each component. The tate potulate aert that the tate of a compreible ubtance i completely defined by two independent propertie (Sontag, 2008). That i, two given propertie of a uperheated refrigerant are ufficient to determine any other thermodynamic property. For intance, with value of T c and p e at the compreor inlet, the compreor uction denity c and enthalpy h c can be determined by uing refrigerant databae uch a RefProp (Lemmon et al., 2010). To reduce computation time, Laughman (2012) created look-up table that tore thermodynamic propertie for elected refrigerant that are generated from a databae. The look-up table are ued to quickly determine neceary tate variable of the refrigerant a it flow through the component. The theorie and equation preented above are general and equally apply to the freeze cycle and harvet. During the harvet, the bypa valve i opened and heat i removed from the ice and into the evaporator. The imulation will increment through time t until a pecified number of freeze and harvet cycle are encountered. Implicit routine within the SimScape TM modeling environment (Mathwork, 2015) are ued to olve et of overall algebraic and differential equation a needed uch, that Kirchhoff' firt and econd law are atified at the node where component are connected. That i, all through variable (ma flow rate and heat flow rate) need to um to zero and all the acro variable (preure and enthalpy) hould be equal.

8 2281, Page 6 4. MODEL OPERATION OVERVIEW The model of the ACIM i executed a follow: 1. Simulation begin with a pecified ma of ice to be formed within evaporator grid, M I, and phyical parameter uch a condener dimenion V c, and evaporator dimenion V e. 2. Water upply at a deignated temperature T i mixed with water in the ump. w 3. A tartup ytem (evaporator and condener) preure p p i deignated, refrigerant charge (ma) i e0 c 0 calculated. 4. The tranient imulation begin with the freeze tage. A chematic of the ACIM model operating in freeze mode i hown in Fig. 2. Figure 2: Ice machine model operating in freeze mode. 5. Evaporator heat flow Q e i baed on tandard refrigerant-ide heat exchanger model. Water-ide equation involve cutom developed equation for heat tranfer from evaporator tube wall to flowing water through an increaing ice reitance. 6. Once the pecified amount of ice ha been formed (M I ) with correponding thickne ( I ), the harvet mode i initiated. A chematic of the ACIM model operating in harvet mode i hown in Fig. 3. Figure 3: Ice machine model operating in harvet mode.

9 2281, Page 7 7. Hot-ga bypa valve i opened during the harvet cycle, routing the compreor dicharge line directly into the evaporator. During harvet, a retriction area A v i implemented within the bypa valve. 8. Harvet i complete when a pecified percentage of the ice i melted. 9. Water inlet at a deignated temperature T i ued to replenih the ma of ice harveted ice, and mixed with W S exiting water in the ump. 10. The imulation return to the freeze tage (Step 6). 5. RESULTS A 500lb, intrumented ACIM wa equipped with enor to meaure the operational characteritic of the machine. The intrumented machine wa run at variou operating point defined by the ambient temperature and the water inlet temperature. A ummary of the experimental value (E) and the prediction made by the imulation model (S) are given in Table 1. Alo provided i the percent abolute value of error () between the experiment and imulation. Table 1: Comparion of ummary reult between experimental reult and imulation model. 100/110 F 90/70 F 70/50 F E S E S E S Cycle time (min.) % % % Ice per 24 hr. (lb.) % % % Energy input per 100 lb. (kwh) % % % Energy input per 24 hr. (kwh) % % % Figure 4-5 provide a comparion of the tranient repone of preure, temperature and compreor power at variou location on the ice machine. Figure 4: Graphical repreentation of the tranient comparion at 110/100 F.

10 2281, Page 8 Figure 5: Graphical repreentation of the tranient comparion at 90/70 F. 6. CONCLUSIONS Thi paper outlined a tranient imulation model of the operation of an automatic commercial ice maker. The model i baed on fundamental, phyic-baed principle of individual ytem component. Governing equation for the compreor, condener, expanion valve, and connecting tubing were adapted from prior reearch available in the literature. A cutom evaporator model wa developed to decribe the heat tranfer between the refrigerant and water flowing over an ice-formation grid. Simulation reult from the model were compared with the experimental data of a fully intrumented, tandard 500 lb capacity ice machine, operating under variou ambient air and water inlet temperature. Key aggregate meaure of the ice machine performance include the freeze and harvet cycle time, energy input per 100 lb of ice, and energy uage during 24 hour. For thee meaure, the model accuracy i within 5% for a variety of operating condition. REFERENCES AHRI Standard 810 (I-P) & 811 (SI), (2016). Performance Rating of Automatic Commercial Ice Maker, Air Conditioning, Heating, and Refrigeration Intitute, Arlington, VA. ANSI/AHRI. (2004). Standard for Performance Rating of Poitive Diplacement Refrigeration Compreor and Compreor Unit, Air-Conditioning, Heating, and Refrigeration: Standard 540, Arlington, VA. Arora, A., Kahik, S., (2008). Theoretical Analyi of a Vapour Compreion Refrigeration Sytem with R502, R404A and R507A, International Journal of Refrigeration, 33(3), pp ASHRAE (1988) Method of Teting for Rating Unitary Air-Conditioning and Heat Pump Equipment: Standard 37, Air-Conditioning, Heating, and Refrigeration Intitute, Arlington, VA. Bahel, V., Shivahankar, S., (2014). Uing Simulation Model to Reduce Sytem Deign Time and Cot, International Refrigeration and Air Conditioning Conference. Paper Bendapudi S., Braun, J., Groll, E. (2008). A Comparion of Moving-Boundary and Finite-Volume Formulation in Centrifugal Chiller, International Journal of Refrigeration, 31(8), pp Chi, J., Didion, D., (1982). A Simulation of the Tranient Performance of a Heat Pump, International Journal of Refrigeration, 5(3), pp

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