Conference on Modelling Fluid Flow (CMFF’15)The 16th International Conference on Fluid Flow Technologies

Budapest, Hungary, September 1-4, 2015

D

Balázs Farkas1, Viktor Szente2, Jeno Miklós Suda3

1 Corresponding Author. Department of Fluid Mechanics, Budapest University of Technology and Economics. Bertalan Lajos u. 4 - 6,H-1111 Budapest, Hungary. Tel.: +36 1 463 2464, Fax: +36 1 463 3464, E-mail: farkas@ara.bme.hu2 Department of Fluid Mechanics, Budapest University of Technology and Economics. E-mail: szente@ara.bme.hu3 Department of Fluid Mechanics, Budapest University of Technology and Economics. E-mail: suda@ara.bme.hu

ABSTRACTBy the nature of their working process, the clear-

ances within the volumetric compressors are sub-jected to complex deformations. Therefore, deform-ing mesh has to be used to simulate transient effectswith CFD codes. Using dynamic meshing makes thesimulation of essential phenomena such as leakageflows and heat transfer effects quite challenging be-cause the desired mesh quality close to the bound-aries and within the narrow seal cavities is not easilymaintainable in every instant as a result of deformingnumerical domain. To achieve the desired mesh qual-ity several methods are available. ANSYS Fluenthas inbuilt smoothing and re-meshing options whichgive relatively limited control to the user. To over-come this issue predefined meshes can be used whichcan assure appropriate resolution at certain positionsof the rolling cylinder which can help to keep themesh quality within acceptable limit for the wholecycle. For more elaborate solution the mesh can bealso fully controlled by using user defined functionswhich allows for creating unique meshing algorithmfor the given problem. The aim of this study is tocompare the accessible models within ANSYS Flu-ent and find a proper meshing method which allowsto provide accurate prediction about the performanceof a rolling piston compressor in the early stage ofthe design process.

Keywords: CFD, dynamic meshing, rolling pistoncompressor

1. INTRODUCTIONBecause of the urgent need to use environmen-

tally friendly energy resources, many new progres-sive solutions have been developed or are under on-going development in recent years. Part of thesesolutions extract electric power from geothermalsources which can be an efficient way when eas-ily accessible high thermal energy sources are avail-able. However recently further efforts have been

made to extract electric power from low enthalpyheat sources. Same sources are already widely usedfor air conditioning and heating purposes mainly forsmall individual households. Nevertheless, powergeneration using low enthalpy heat sources is morechallenging since the low temperature ratio alreadyrestricts the thermal efficiency of the applied ther-modynamic cycle. Therefore, the efficiency of theindividual components used to realize the thermo-dynamic cycle has to be as high as possible to pro-vide a cost efficient solution, even if waste amountof heat is available from the source. In case of con-ventional solutions the compressor and the expanderare key elements of the system. To get the high-est efficiency, choice of the construction type for thegiven purpose is as important as the careful designand manufacturing is. Here the traditional rollingpiston type compressor design was used as a platformand was further improved as it is shown in Figure 1to achieve sufficiently high performance. The vane

DISCHARGE PORT

VANE

CYLINDER

PISTON

SUCTION PORT

Figure 1. Velocity distribution within the rotatingpiston compressor designed by Magai [1]

which separates the high and low pressure cham-bers was redesigned and it is directly driven from thecrankshaft of the piston which provides constant gapbetween the vane and piston, regardless the rotationspeed without using extensive constrictive force and

increasing the friction induced losses. The piston issolidly mounted on the crankshaft and does not rollalong the inner surface of the cylinder. This designmakes it similar to the trochoidal compressors, whichdo not require extremely small and expensive man-ufacturing tolerances because of the closed sealingborder of the compression space and neither do theyneed oil for sealing [2].

To verify the theory, Computational Fluid Dy-namics (CFD) tool was chosen to estimate the perfor-mance of this new design. Although CFD is knownto be a very economical tool during evolutionary de-sign process [3], most of the positive displacementcompressor related studies are focused on develop-ing and using concentrated parameter models sincethese components were considered as mainly ther-modynamic devices. But within the past decade thehavoc caused by fluid dynamics in destroying the ef-ficiency has started gaining attention due to the press-ing need for making these machines more energy ef-ficient and reliable.

In 2004 two papers were presented at the Inter-national Compressor Engineering Conference in Pur-due by the same company introducing a parametricCFD study related to the effect of the design of thenotch [4] and suction piping [5] in meaning of noiseand efficiency in case of a given double dischargecompressor architecture. In both cases STAR-CD,a general CFD software was used for the simula-tions. The applied meshing techniques were not dis-cussed in details but figures presented in [4] showa quadratic mesh within the cylinder with extendedregion of highly skewed elements around piston-cylinder gap and close to the vane. Despite theseanomalies, the results resembled well the theory. In[5] where experimental tests were also conducted,the numerically predicted efficiency was also alignedwell with the test results to verify the theory. Moreimportantly, the trends in the change of performanceparameters caused by geometry modifications, werepredicted in good fashion.

In a study from 2010 by Liang et al. [6] two dif-ferent kind of rolling piston compressors were inves-tigated which were implemented with pressure ac-tivated discharge valves. The same solvers for thesolution and governing the motion of the deformingmesh were used as in the above mentioned studies,but no further details were enclosed either. The pre-dictions were also compared with experimental re-sults. The error of the cooling capacity and powerwith the simulation and experiment test were lessthen 7%. The pressure rise vs. cranckshaft anglediagram of the simulation result is also claimed tobe very close to the experiment test, although evi-dent discrepancies can be observed on the presentedgraphs. Hui Ding et al. [7] from 2014 presented anew approach for simulating the applied dischargereed valve. For the simulations the PumpLinx CFDpackage were used which is specially targeted forsimulating volumetric machines. According to the

figures the applied meshing and re-meshing algo-rithms result in a good quality mesh within the wholecomputational domain where no highly distorted el-ements could been picked up. Here no further detailsabout the applied meshing methods were enclosed ei-ther. Impressively, a whole revolution was claimed tobe simulated within five hours on a general purposequad-core Intel Xeon CPU at 2.67GHz machine. Thepredictions seemed to be aligned well with the the-ory, but obtained results were not compared to ex-perimental test results.

Although deforming meshing seems to be ine-ludible, in the study of Brancher & Deschamps [8]the effect of the rotating rolling piston on the suc-tion and discharge losses was estimated by steady3D CFD solutions at different crankshaft angles. Thepredicted effective flow area and effective force areacoefficients were implemented into a lumped param-eter model. As a result significant improvement inthe performance estimation were confirmed by ex-perimental data.

2. SIMULATION MODEL3D representation of the of the numerical do-

main resembling the Magai design compressor is pre-sented on Figure 2(a). Since in this case the model

(a) (b)

Figure 2. Comparison between original Magaitype compressor geometry (a) and the redesignedmodel compressor geometry (b)

compressor is symmetrical, the numerical domainwas divided into two and only one half of it wasmodeled and it was completed by using symmetryboundary condition at the symmetry plane. The ini-tial mesh was created using ANSYS Workbench butduring the simulation the mesh was controlled byFluent’s dynamic mesh models [9]. The domainwas meshed by triangular elements on the frontalfaces which were then extruded to the axial direc-tion parallel to the crankshaft creating wedge typeelements as it is shown on Figure 3(a). During thetransient computation the mesh was only regeneratedon the frontal base mesh and this frontal mesh wasthan projected to the parallel mesh surfaces similarlyas the base mesh was initially created. In ANSYSfluent terminology it is referred as 2.5D approach.The node points on the cylinder remained station-

(a) (b)

Figure 3. Comparison of the numerical mesh fororiginal Magai type compressor geometry (a) andfor the redesigned model geometry (b)

ary and the nodes on the piston and vane surfacesfollowed rigid body like motion, which means thatthey kept their position respect to each other mean-while the piston and the vane were rotated along theiraxes. To control the node points on the base sur-face spring/Laplace based smoothing and re-meshingalgorithms were used. Both algorithms are part ofthe Fluent’s dynamic mesh models. As the distor-tion of the cells increases by the large scale move-ments, ANSYS Fluent agglomerates cells that vio-late the initially defined skewness or size criteria andlocally re-meshes the agglomerated cells or faces. Ifthe new cells or faces satisfy the skewness criterion,the mesh is locally updated with the new cells withthe solution interpolated from the old cells. Other-wise, the new cells are discarded and the old cellsare retained [9]. This solution results in relativelyeasy model setup since only the rigid body motionof the moving parts has to be predefined by the userby external User Defined Functions (UDF’s) and therest is taken care by the Fluent’s inbuilt algorithms.The maximum size of the cells in the tangential di-rection on the surfaces were limited by the gap be-tween the moving elements to gain appropriate meshquality within the small clearances. The deforminggrid has to provide a connected domain of constantarea which means that no parts of the flow domaincan be isolated from the rest, therefore even in thesmallest gap a one cell high layer has to be remained.Rest of the base surface is discretized with constantsize elements which resulted in unreasonable resolu-tion outside the boundary regions. Several attemptswere made to preserve the initial mesh quality butin every case after the first revolution of the pistonthe computational domain got overlayed with homo-geneous size distribution elements. This method re-sulted in eminently time consuming simulations. Thesimulation for one revolution took almost five dayson a quad-core i7 k2600 processor when the meshcounted 2 · 105 cells in average, and the simula-tion was parallelized for all four cores available inone processor. The idea to use predefined meshes atgiven crankshaft angles were dropped when attemptsto model the check valve were implemented. This isbecause unlike in case of a piston which rotates at a

constant speed the position of the check or reed valveat a given crankshaft angle cannot be predicted in ad-vance [10].

2.1. Redesigned model and new re-meshing approach

Because of the unexpectedly long solution time,the old model was replaced and the new computa-tional domain is shown in Figure 2 (b). Here thevane was replaced by an impermeable blade with in-finitesimal thickness which significantly reduces thecomplexity of the original geometry. The new dis-cretization is presented in Figure 3 (b) in comparisonwith the original mesh. The mesh contains only hex-aghedral elements. The position of the mesh nodeswithin the cylinder were fully controlled by an exter-nal UDF using designated macros provided by AN-SYS Fluent. The re-meshing process is illustratedin Figures 4 (a) and (b). During the rotation of the

P

O

A

A' V

(a)

O

A'

A

P

V

(Blade)Vane

(b)

Figure 4. Illustration of the new meshing pro-cess by two meshes taken at (a) 0o and (b) 135o

crankshaft angles

piston the axial position of the nodes do not change,which means that the nodes do not move parallel tothe direction of the crankshaft. The motion of thenodes on the piston resembles a rigid body like mo-tion, where the point P, which is the center of thepiston, point V, which is the bottom point of the vaneon the piston, and point A, which is an arbitrary nodepoint on the piston surface, retain their position inrespect to each other at each instant of the cylindermotion. This rigid body motion is described by themotion of the imaginary O-V rod which is part ofthe simple O-P-V crank mechanism where point Ois the center of the cylinder and also defines the po-sition of the axis of the crankshaft. The crankshaftangle is defined by the angular position of the O-P section which rotates around point O. The move-ment of point V is restricted to the vertical directionwhich also means that the blade keeps its vertical po-sition during the rotation of the cylinder. This mo-tion resembles the motion of a piston in a hingedvane compressor [11]. The position of an arbitraryA’ node point on the cylinder surface is than definedas the projection of point A from the piston surfacealong the straight O-A-A’ line. The rest of the points

between A and A’ are distributed equally within thestraight A-A’ section. This equal distribution is op-tional and not restricted by the method. Also, themethod can be adapted to different blade thicknesses.Using the same settings discussed in the followingsection the simulation of one revolution took approx-imately twelve hours on the same architecture usingjust one core of the quad-core processor. The meshholds constant number of 2 · 104 cells. At this point,parallelization was not implemented in the prewrittenUDF code, since the achieved simulation time wasalready acceptable. Also, by running different casesin parallel, the available computational capacity wassuitably utilized by the simultaneously running serialprocesses.

3. COMPARISON BETWEEN THE DIF-FERENT MODELS

For performance estimations, the compressorwas throttled back by adding a porous layer up-stream from the exit of the outlet pipe. The porousmedia was modeled by the addition of the Darcy-Forchheimer type source term to the standard fluidflow equations. For both models, the outlet pipe wasconnected across a non-conformal mesh interface [9]to the cylinder and the geometry of the outlet pipewas identical in both cases. In case of the simplifiedmodel the inlet pipe was also connected in the sameway to the cylinder. The inlet and outlet pipe tan-gential position for the simplified model was definedso that compression process would have the same ex-tension as it is in the case of the original model. Thesolver was used with the standard settings. To modelturbulent quantities, realizable k-ε turbulence modelwas used, both at the inlet and the outlet the ambi-ent temperature and pressure was imposed as bound-ary conditions. For the preliminary computations thewalls were considered to be adiabatic. The workingfluid was taken as ideal compressible air.

Because of the meshing considerations, the mov-ing elements are not connected directly to their coun-terparts at the sealings, therefore here the flow is re-stricted by a porous domain defined within a nar-row area limited to couple of cells within a givenradius around the theoretical contact points. Herethe porous resistance was also defined by Darcy-Forchheimer source term. In both cases, the viscousresistance was set to the maximum allowed value, forwhich the stability of the solution is ensured.

The models were tested at two distinct throttlingconfiguration. The predicted variation of the pressureat the cylinder exit just upstream the porous zone isshown in Figures 5 (a) and (b). The results align rela-tively well in both low and high throttling cases. Al-though, despite that the same loading was imposedfor both models, the predicted pressure ratio reachedhigher values in case of the redesigned and simpli-fied model compressor (Fig. 2 (b)) than in case of theoriginal design resembling the exact geometry of theMagai compressor (Fig. 2 (a)). Hence, the gradient of

the curves representing the actual pressure rise in themodel compressor is slightly higher, both in Fig. 5(a) and (b).

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 45 90 135 180 225 270 315 360

∆p/∆

p max

[-]

Crankshaft angle [deg]

Magai typ. comp.Model comp.

(a)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 45 90 135 180 225 270 315 360

∆p/∆

p max

[-]

Crankshaft angle [deg]

Magai typ. comp.Model comp.

(b)

Figure 5. Pressure difference between the in-let and the outlet normalized with the maximumvalue at (a) high and (b) low throttling conditions,predicted by the original model resembling theMagai type compressor geometry and the simpli-fied model compressor

In case of the model compressor, the predictedvolumetric efficiency was 93% at lower throttling and90% at higher throttling. On the other hand, the samevalues are consecutively 88% and 84% in case ofthe original Magai type compressor model. The dis-crepancies are the result of the higher leakage flowpredicted by the original model. In the original ge-ometry there are two extra sealings connected to thevane which were not taken into the account in thesimplified model. However, the leakage flow can beadjusted by changing the viscous resistance of theporous zone at the sealing contact positions, and partof the vane blade can be turned to be permeable tosimulate the leakage across the vane. Still, there isnot much chance to significantly improve the predic-tions before relevant measurement data are availablefor appropriate tuning.

4. COMPRESSOR AND DISCHARGEVALVE

Rolling piston compressors are usually imple-mented with a discharge valve to prevent back flow

when the discharge port is connected to a high pres-sure reservoir. The applied valves are usually sim-ple reed valves made of high-grade steel. However,the Magai type compressor was planned to be cou-pled with a commercially available pneumatic checkvalve for the duration of the first test period becauseof practical reasons. The numerical model is pre-sented in Figure 6.

Valve disc

Core mesh Outer meshUpper stationary end

Lower stationary end

Figure 6. The numerical model of the dischargevalve in closed and fully opened position

Ds II.

Ds I.

Figure 7. Representation of the different setups

The core and the outer part of the mesh is con-nected across a non-conformal mesh interface. Thecore part between the upper and lower stationary endis dynamic and follows the movement of the pressureactivated valve disc. The position of the node pointswithin this dynamic region is controlled by ANSYSFluent’s smoothing algorithm and no re-meshing wasapplied. This solution can be only used with the sim-plified compressor model, since the smoothing algo-rithm is not accessible when the 2.5D model is active.Because of the vane design of the Magai type com-pressor, the tangential distance between inlet and theoutlet ports is relatively high compared to the tradi-tional rolling piston type compressor architectures.This can result in decreased volumetric efficiency,

0.8 1

1.2 1.4 1.6 1.8

2 2.2 2.4 2.6 2.8

3

0 90 180 270 360 450 540 630 720

p out

/pin

[-]

Crankshaft angle [deg]

Ds I.Ds II.

Figure 8. Ratio between the inlet and the cylin-der outlet pressure in function of the Crankshaftangle in case Ds I. and Ds II.

since the effective compressed volume is reduced. Toinvestigate the effect of the tangential separation ofthe inlet and outlet ports, two distinct designs weretested as it is shown in Figure 7. In both cases loadingwas imposed by the increased pressure at the outletboundary, which resembles a scenario when the out-let port is connected to a pressurized system. Thisratio was set to be relatively low and the pressure atthe outlet boundary is twice as high as the inlet pres-sure. Figure 8 show the variation of the pressure ra-tio between the cylinder outlet pressure upstream thedischarge valve and the inlet ambient pressure. Thereis no significant difference between the two curves.However, in case of DsI., when the in-take and thedischarge ports are closer to each other, the pressur-ization starts earlier and the discharge process takeslonger. There is a distinct overshoot in maximumpressure compared to the outlet pressure at the out-let boundary, which is the result of the throttling im-posed by the sudden area change between the cylin-der and the discharge pipe, and also of the additionalthrottling imposed by the discharge valve itself. The

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 90 180 270 360 450 540 630 720

Rel

ativ

e va

lve

lift [

-]

Crankshaft angle [deg]

Ds I.Ds II.

Figure 9. The relative valve lift in function of theCrankshaft angle in case Ds I. and Ds II.

relative valve lift is presented in Figure 9. The arearatio between the outlet port and free surface of theopened valve is 0.95. The variation of the valve liftalso confirms the longer discharge process in case ofDs I., although no significant difference can be ob-

served. However the predicted volumetric efficiencyis dropped from 94% to 86% as the angular distancewas increased between the inlet and outlet ports fromDs I. to Ds II..

5. CONCLUSIONTo improve the performance of the traditional

rolling piston type compressors, a new design wasintroduced. To verify the expectations regarding theredesigned system the CFD model of the new geom-etry was prepared and tested.

To increase the computational efficiency and re-duce computational, original model was simplifiedand a new 3D moving mesh approach was intro-duced.

The new method was compared to the originalalgorithm which was provided by the ANSYS Fluentsolver.

Despite some marginal discrepancies, the viabil-ity of the new method was proven although no finalconclusion can be withdrawn before sufficient exper-imental data will be available.

The new moving mesh approach has proved thepotential for further development and the possibilityto adapt it for more complex geometries. Finally, amore complex compressor model coupled with a dis-charge valve was introduced to investigate the effectof the increased angular separation between the suc-tion and the discharge port.

It was estimated that it has moderate effect on theoverall performance at low pressure ratios. If thesetrends can be experimentally confirmed than a futureparametric study can be conducted with a new modelto find an optimal design.

6. ACKNOWLEDGEMENTThis research has been supported by the New

Széchenyi Plan under contract No. KMR_12-1-2012-0199.

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