A Comprehensive Model of a Novel Rotating Spool Compressor

Transcription

1 Purdue Univerity Purdue e-pub International Compreor Engineering Conference School of Mechanical Engineering 01 A Comprehenive Model of a Novel Rotating Spool Compreor Craig Bradhaw cbradha@purdue.edu Greg Kemp Joe Oroz Eckhard A. Groll Follow thi and additional work at: Bradhaw, Craig; Kemp, Greg; Oroz, Joe; and Groll, Eckhard A., "A Comprehenive Model of a Novel Rotating Spool Compreor" (01). International Compreor Engineering 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

2 114, Page 1 A Comprehenive Model of a Novel Rotating Spool Compreor t Craig BRADSHAW 1, Greg KEMP *, Joe OROSZ 3, Eckhard GROLL 4 1 Ray W. Herrick Laboratorie and Cooling Technologie Reearch Center, Wet Lafayette, IN Fax ( ), E mail cbradha@purdue.edu Torad Engineering, 1005 Union Hill Road, Suite Alpharetta, GA Phone , Fax , E mail greg.kemp@toradengineering.com 3 Torad Engineering, 1005 Union Hill Road, Suite Alpharetta, GA Phone , Fax , E mail joe.oroz@toradengineering.com 4 Ray W. Herrick Laboratorie Wet Lafayette, IN Fax ( ), E mail groll@purdue.edu * Correponding Author ABSTRACT A comprehenive imulation model of a novel rotating pool compreor i preented. The pool compreor provide a new rotating compreion mechanim with eaily manufactured component. Compared with other rotary compreor, the pool compreor preent the additional advantage of relocating the face ealing urface to the outer radiu of the device. A detailed analytical geometry model of the pool compreor i preented which include the geometry of the vane. Thi geometry model i included in a comprehenive model that include ubmodel for friction, leakage, and heat tranfer. The reult of the comprehenive model were validated uing experimental data from a prototype compreor. The prototype compreor ha an overall diplacement of 3.9 cm 3, and wa operated at rotational peed between 1750 and 350 rpm and preure ratio between.1 and.9 uing R410A a the working fluid. The model predict the volumetric and overall ientropic efficiencie of the prototype compreor to within 6.3% and 11.% MAE, repectively. The trend and pread in the data indicate that additional effort hould be focued on the operation of the active ealing element within the compreor. 1. INTRODUCTION The rotating pool compreor i a novel rotary compreor mechanim mot imilar to the liding vane compreor. Primary difference are decribed by Kemp et al. (008, 010) and include three key difference from a liding vane compreor. The vane i contrained by mean of an eccentric cam allowing it dital end to be held in very cloe proximity to the houing bore (typically le than 0.30mm) while never contacting the bore. The rotor ha affixed endplate that rotate with the central hub and vane forming a rotating pool. The practical ue of dynamic ealing element to minimize leakage between the uction and compreion pocket a well a between the proce pocket and the compreor containment Thee difference are hown in Figure 1 which preent a cutaway view of a rotating pool compreor with the key geometric feature highlighted. International Compreor Engineering Conference at Purdue, July 16-19, 01

3 114, Page Figure 1: Cutaway view of rotating pool compreor mechanim with key component highlighted. Due to the ever increaing need for increaed performance envelope and energy efficiency, air conditioning and refrigeration ytem technologie have greatly evolved over the lat 30 year. Shortly after the inception of vapor compreion ytem, the market wa dominated by two type of compreor, the reciprocating compreor for maller cooling capacity ytem and the centrifugal compreor for larger cooling capacity ytem. Thi wa dictated, for the mot part, from a knowledge bae and manufacturing capability (Soumeri, 010). Thi gave way to variou compreor deign implemented over the next 30 year that capitalized on newer manufacturing technology and met the ever increaing efficiency requirement dictated by regulation. By example ASHRAE 90.1 ha mandated an improvement in chiller efficiency of 61% ince 1977 while employing refrigerant with lower cycle efficiency (Lord, 009). Thi ha produced a current technical profile in the market that encompae at leat even fundamental device type in variou configuration with variou optimum technical feature. More demand for higher efficiency component ha reulted in a renewed interet in detailed compreor modeling to predict the performance of novel compreor. A recent approach to compreor modeling, called the comprehenive approach, ha provided a complete analyi of poitive diplacement compreor. The comprehenive modeling approach relie on the unteady ma and energy balance of a control volume, imilar to that of Ooi and Wong (1997), with ub-model for each of the key phyical phenomenon. Kim and Groll (007) utilized the comprehenive approach for the modeling of a novel bowtie compreor. Thi type of compreor i baed on the Beard-Pennock mechanim, which provide capacity control in a fixed volume device. Jovane (007) applied the comprehenive approach to a novel rotary compreor, called a z-compreor. More recently, Mathion et al. (008) developed a comprehenive model for a two-tate rotary compreor, which provided inight into the optimum intermediate preure for the bet cycle and compreor efficiency. Thi work wa continued by applying the approach to a rotary compreor with vapor injection a well a the novel rotary pool compreor (Mathion, 011). Bell (011) preented another recent addition to the application of comprehenive modeling by examining the impact of oil flooding on croll compreor. The comprehenive model provided a deeper inight into the unique internal performance of a croll compreor flooded with oil. Thi allowed for a numerical optimization of croll wrap for ue in oil flooding, which may have been cotly and time conuming to obtain experimentally. Finally, Bradhaw et al. (011) applied the comprehenive modeling approach to a linear compreor for electronic cooling. The variety of compreor type analyzed diplay the veratility of thi modeling approach, which i why it i utilized in thi work. Firt, an analytical model of the pool compreor geometry i preented, which will then be utilized in a comprehenive model. The reult from thi model are then compared againt experimental reult from a prototype compreor. International Compreor Engineering Conference at Purdue, July 16-19, 01

4 114, Page 3. GEOMETRY MODEL OF A ROTATING SPOOL COMPRESSOR The analytical expreion decribing the pool compreor geometry are decribed in thi ection. Figure how implified pool compreor geometry and identifie the polar coordinate ued in the analyi. At any intant in the compreor rotation, the ga occupie either the uction, compreion, or dicharge chamber. Thee chamber are eparated by the gate and the point referred to a Top Dead Center (TDC) a hown in Figure. Thi figure how the center of rotation (point O), at the rotor center, the leading (point A) and trailing (point B) end of the compreor vane a well a the vane center (point C). Figure : Simplified pool compreor planar geometry chematic highlighting global coordinate (left) and additional geometric vector (right). To calculate the volume of the pool compreor a vector decribing the poition of the pool houing (tator) relative to the axi of rotation i developed. Utilizing the law of coine, thi vector can be written in term of the houing radiu and eccentricitie, which are contant, and the angle of rotation of the rotor, r = ecoθ + e co θ e + R (1) where the lower limit of the eccentricity i given a: e = R R () r Then, to identify the movement aociated with the tip eal, the vector from point O to C i calculated a follow: r = eco( θ π ) (3) The vector decribing the length of the vane a a function of rotor angle i decribed a, c International Compreor Engineering Conference at Purdue, July 16-19, 01

5 114, Page 4 where the length of the vane ha an upper limit of, r = R r = R eco( θ π ) (4) v v c g R = R e (5) v Finally, the vector decribing the movement of the vane tip eal can be written a, rt = r rv (6) The vector decribed above parameterize the key urface within a rotary pool compreor a a function of the rotor angle. Thu, the area of the uction, compreion, and dicharge chamber can be evaluated a a function of the rotor angle a well and calculated uing: θ θ 1 1 ( ) = r 0 0 A θ r dθ r dθ 1 1 A r d r d A θ + π θ + π c ( θ ) = θ r θ ( θ ) θ θ 1 1 A ( θ ) r dθ r dθ A ( θ ) A ( θ ) π π d = r c θ + π θ + π (7) for 0 < θ < π, and repeated for π < θ < π. A the expreion given in Equation (1) i unable to be integrated in cloed form, the olution to each area integration i computed numerically uing a finite difference method. Additionally, the rotor i lightly inet into the pool houing at the location of the TDC, thi i known a the TDC relief. The depth of the TDC relief i an input to the geometry model and at thee angular location, r = Rr. Finally, the volume of each chamber can be computed by realizing that the geometry i planar, V ( θ ) = A( θ ) h (8).1 Spool Vane Geometry The previou analyi aume that the vane doe not take up any of the volume within the compreor chamber. To account for thi inaccuracy the following analyi i ued to calculate the volume of the vane and tip eal within each chamber at each rotor angle. Figure 3 how a cloe up of the vane geometry ued for thi analyi with the key dimenion identified. The vane alo employ planar geometry and thu, the vane analyi begin by calculating the area of the ection of the vane that i within the rotor, which i fixed: 1 w A R w R 1 v v, r = tan + r v r Rr (9) International Compreor Engineering Conference at Purdue, July 16-19, 01

6 114, Page 5 Figure 3: Cloe-up chematic of implified pool vane and dynamic tip eal geometry included in model. Then, the total variable area of the vane a it move throughout the rotation, including the area within the rotor, i calculated a follow: ( 1 ( ) θ ) A = R w w w tan + r w r R 8 v, v v v v t v t t c v Finally, ince the only area of concern i the area puhed into one of the compreor chamber, the net gate area become: v v, v v, r (10) A = A A (11) where the area of the vane at point B i calculated in a imilar way with the vector offet by π. Uing the gate area, the chamber volume calculated in the previou ection are modified a follow, V 1 = V A v h A V 1 1 c = Vc A v h A A v h B V 1 d = Vd A v h B (1) for 0 < θ < π, and repeated for π < θ < π. Additional conideration for the ituation when the vane pae through the TDC plane are alo conidered and included in the reult but the analyi i omitted from thi work for brevity. The reult of the geometry analyi are hown in Figure 4, which preent the final chamber volume and rate of change of chamber volume for each of the three chamber over one rotation of the pool rotor. International Compreor Engineering Conference at Purdue, July 16-19, 01

7 114, Page 6 5 Suction Vol. Compreion Vol. Dicharge Vol Suction Vol. Compreion Vol. Dicharge Vol Volume [cm 3 ] dv / dθ [cm 3 /rad] π π θ [rad] 3π π 10 0 π π θ [rad] 3π π Figure 4: Reult of pool geometry model, chamber volume (left) and derivative of volume (right) a a function of rotor angle for pool compreor prototype RCP 4. a preented in Oroz et al. (01). Moving from the angle of 0 toward π, the uction volume initially tart near zero and diplay a mall expanion and compreion prior to, which i eaier to oberve in the right figure. Thi i a reult of a combination of the π TDC relief region and the vane geometry. The TDC relief region i the mall region near the TDC plane that the pool houing i manufactured with the ame radiu a the rotor. Thi elongate the leakage gap acro the TDC plane and reduce uction to dicharge leakage. Since the radiu of the tator and rotor are the ame in thi region the chamber volume i only impacted by the movement of the vane, which i beneath the rotor urface at thi location. When the vane move from TDC further into the uction chamber, pat the TDC relief region, the vane begin to move out of the rotor, decreaing the volume, but the uction chamber begin to form a a reult of the difference in radii of the rotor and tator. However, until roughly π, the movement of the vane dominate the chamber volume 4 development which lead to a mall compreion volume before the uction proce occur. The remaining uction proce occur until π, when the backide of the vane (point B) pae through the TDC plane and begin to generate another uction chamber. The ga in the previou uction chamber become the compreion volume. Thi volume continue to expand until 3 π. Then, the chamber volume decreae until π, when the front ide of the vane (point A) pae through the TDC plane. The compreion chamber then become the dicharge chamber a the back ide of the gate (point B) rotate through another half rotation, puhing the ga out the dicharge chamber. The proce in all chamber i periodic about every half rotation and an entire proce take one and a half rotation to complete. Thu, for each rotation, two uction, compreion, and dicharge procee occur. 3. COMPREHENSIVE MODEL DEVELOPMENT A comprehenive compreor modeling approach i utilized to predict the performance of the rotating pool compreor. Thi approach ha been preented in detail previouly for other poitive diplacement compreor (Bradhaw et al. 011, Bell 011, Mathion et al. 008, 011). The approach relie on a governing et of equation which are derived from a ma and energy balance within the working volume of a poitive diplacement compreor: International Compreor Engineering Conference at Purdue, July 16-19, 01

8 114, Page 7 d ρ 1 dv 1 = ρ ( min mout ) dθ V + ɺ ɺ dθ ω (13) dv u ρ 1 ρh uv + ρv + Q + m h m h dt dθ ρ θ ω = dθ u ρv T ( ɺ ɺ in in ɺ out out ) (14) Thee equation are enforced in each compreor chamber for each rotor angle. The equation alo require input from a variety of ub-model including friction, leakage, valve, and heat tranfer ub-model. The heat tranfer ubmodel utilize a piral heat exchange model to calculate the convective heat tranfer coefficient. The correlation wa developed for different geometrie but it ha been hown to be uitable for rolling piton compreor, which have a imilar internal geometry to a pool compreor (Mathion, 008). The valve model employed i a dynamic valve model with two mode of operation, a preented in Kim and Groll (007) and Bradhaw et al. (011). The friction model account for friction between the tator (houing) and rotor in the TDC relief region, from the tip eal on the tator (houing), and from the pool eal. An oil film hear model i utilized with the gap between each urface a an input to the friction and the leakage model. 3.1 Ma Flow and Leakage Model Figure 5 how a chematic of the 10 leakage path accounted for in the model. The leakage path acro the TDC region and acro the pool eal are modeled a compreible flow with friction (fanno flow), ince the ratio of the leak path to height i high. All remaining leak path are modeled a ientropic compreible flow through a nozzle. The leakage gap width for the pool eal, tip eal, and TDC clearance were ued to adjut the model reult. Reaonable etimation for thee gap are known but they are difficult to meaure accurately. The remaining leakage gap are meaured and thi additional geometry information i ued a input to the leakage model. The ma flow through the uction and dicharge opening are alo modeled a ientropic compreible flow through a nozzle.!"%#!"#!"$#!"# Figure 5: Schematic of leak path conidered in the comprehenive model, looking at the planar view (left) and the normal view (right). 4. MODEL RESULTS COMPARED WITH EXPERIMENTAL RESULTS The comprehenive model reult are compared with experimental data from the prototype pool compreor RCP 4. preented in Oroz et al. (01), which ha a diplaced volume of 3.9 cm 3. Thi data wa collected utilizing the International Compreor Engineering Conference at Purdue, July 16-19, 01

9 114, Page 8 hot-ga bypa load tand alo preented in Oroz et al. (01). The compreor wa operated at rotational peed from 1750 to 350 rpm and uction condition at 905 kpa and 11 C preure and uperheat, repectively, uing R410A a the working fluid. The dicharge preure wa varied to achieve preure ratio between.1 and.9. Uing the geometry preented in Section and the overall model from Section 3 with the appropriate geometric input to repreent RCP 4., the comprehenive model i compared to experimental data. Figure 6 how parody plot comparing the experimental volumetric and overall ientropic efficiencie compared with the model predicted value. The Mean Abolute Error (MAE) of each comparion i 6.3% and 11.% for the volumetric and overall ientropic efficiencie, repectively Simulated ηvol [ ] % Simulated ηo,i % +15% % Experimental η vol [ ] Experimental η o,i Figure 6: Model predicted volumetric (left) and overall ientropic (right, error within marker width) efficiencie of the prototype pool compreor. The volumetric efficiency on the left of Figure 6 how that while mot point are predicted within 10% there i a trend in the error. Thi i indicative of the model not capturing all of the actual compreor behavior. The overall ientropic efficiency how increaed catter and error. An increae in error in the overall ientropic efficiency i typical a thi metric include error from all of the ub-model combined. However, the amount of error in a mall range of experimental efficiencie i alo indicative of a trend in the actual performance that i not captured. 5. CONCLUSIONS AND FUTURE EFFORTS An analytical model of the rotating pool compreor geometry i preented which include the chamber volume and the vane geometry. Thi model i incorporated into a comprehenive compreor model decribing the rotating pool compreor. The model reult are compared againt tet data collected uing a prototype pool compreor at a variety of rotational peed and operating condition. The comprehenive model predict the volumetric efficiency within a reaonable amount of error. However, the trend in the error indicate that one or more of the ub-model do not accurately capture the behavior of the compreor. Thi i alo een in the overall ientropic efficiency where the error i exacerbated. While the trend i not obviou from thi comparion the level of error indicate that there are till model inaccuracie. International Compreor Engineering Conference at Purdue, July 16-19, 01

10 114, Page 9 Kemp et al. (01, 01a) preent reult that indicate a high level of enitivity of the experimental performance to change of the deign of both the pool eal and tip eal. Both eal are dynamic, activated eal, which are actuated by the preure differential created by the compreor. The leakage and friction ub-model aume that the pool eal and tip eal function the ame regardle of the peed or operating condition. Thi behavior i inaccurate and the impact of an improved ub-model for both the tip eal and pool eal warrant further invetigation. NOMENCLATURE A c Area of compreion chamber, m A d Area of dicharge chamber, m A Area of uction chamber, m A v Area of vane within working chamber, m A v,r Area of vane within the rotor, m A v,v Total area of compreor vane, m e Eccentricity of compreor, m h Enthalpy, kj kg -1 h Height of tator (houing), m mɺ Ma flow in, kg -1 in mɺ Ma flow out, kg -1 Q ɺ R r R R v r r out Heat tranfer rate, W Radiu of rotor, m Radiu of tator (houing), m Radiu of vane, m Vector decribing rotor urface, m r v Vector decribing poition of vane tip, m r t Vector decribing poition of tip eal, m r c Vector decribing center of the vane, m T Temperature, K u Internal energy, kj kg -1 V c Compreion chamber volume, m 3 V d Dicharge chamber volume, m 3 V Suction chamber volume, m 3 wt Width of tip eal, m wv Width of vane, m Greek Letter θ Rotor angle, rad ρ Denity, kg m -3 ω Rotational peed, rad -1 REFERENCES Bell, I Theoretical and Experimental Analyi of Liquid Flooded Compreion in Scroll Compreor. PhD thei, Purdue Univerity. Bradhaw, C., Groll, E., Garimella, S A comprehenive model of a miniature-cale linear compreor for electronic cooling. International Journal of Refrigeration. 34(011), Jovane, M Modeling and analyi of a novel rotary compreor. PhD thei, Purdue Univerity. Kemp, G., Elwood, L., Groll, E., 010. Evaluation of a Prototype Rotating Spool Compreor in Liquid Flooded Operation. In: Proceeding of the International Compreor Engineering Conference. Purdue Univerity, Wet Lafayette, IN USA. No Kemp, G., Garrett, N., Groll, E., 008. Novel Rotary Spool Compreor Deign and Preliminary Prototype Performance. In: Proceeding of the International Compreor Engineering Conference. Purdue Univerity, Wet Lafayette, IN USA. No Kemp, G., Oroz, J., Bradhaw, C., Groll, E., 01. Spool Compreor Tip Seal Deign Conideration and Teting. In: Proceeding of the International Compreor Engineering Conference. Purdue Univerity, Wet Lafayette, IN USA. No Kemp, G., Oroz, J., Bradhaw, C., Groll, E., 01. Spool Seal Deign and Teting for the Spool Compreor. In: Proceeding of the International Compreor Engineering Conference. Purdue Univerity, Wet Lafayette, IN USA. No Kim, J., and Groll, E Feaibility tudy of a bowtie compreor with novel capacity modulation. International Journal of Refrigeration, 30(8): Lord, R., 009. Sytem Level Efficiencie and Strategy to Enable their Ue and Improvement. Technical Report, Carrier Corp. Mathion, M., Braun, J., Groll, E Modeling of a two-tage rotary compreor. HVAC&R Reearch, 14(5): Mathion, M Modeling and Evaluation of Advanced Compreion Technique for Vapor Compreion Equipment. PhD thei, Purdue Univerity. International Compreor Engineering Conference at Purdue, July 16-19, 01

11 114, Page 10 Ooi, K., and Wong., T A computer imulation of a rotary compreor for houehold refrigerator. Applied Thermal Engineering, 17(1): Oroz, J., Kemp, G., Bradhaw, C., Groll, E., 01. Performance and Operating Characteritic of a Novel Rotating Spool Compreor. In: Proceeding of the International Compreor Engineering Conference. Purdue Univerity, Wet Lafayette, IN USA. No Soumerai, H.., 010. Hitory in the Air Conditioning and Refrigeration Indutry: Breakthrough of Large Poitive Diplacement Rotary Compreor in the Second Half of the 0 th Century. ASHRAE Web Publication; A Look Back at HVAC&R. International Compreor Engineering Conference at Purdue, July 16-19, 01