Analysis of the Inner Fluid-Dynamics of Scroll Compressors and Comparison Between CFD Numerical and Modelling Approaches

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Article Analysis of the Inner Fluid-Dynamics of Scroll Compressors and Comparison between CFD Numerical and Modelling Approaches

Giovanna Cavazzini * , Francesco Giacomel, Alberto Benato , Francesco Nascimben and Guido Ardizzon

Department of Industrial Engineering, University of Padova, 35131 Padova, Italy; [email protected] (F.G.); [email protected] (A.B.); [email protected] (F.N.); [email protected] (G.A.) * Correspondence: [email protected]; Tel.: +39-049-827-6800

Abstract: Scroll compressors are widely adopted machines in both refrigeration systems and heat pumps. However, their efficiency is basically poor and constitutes the main bottleneck for improving the overall system performance. In fact, due to the complex machine fluid dynamics, scroll design is mainly based on theoretical and/or semi-empirical approaches. Designs strategies that do not guarantee an in-depth analysis of the machine behavior can be supplemented with a Computation Fluid Dynamics (CFD) approach. To this purpose, in the present work, the scroll compressor inner fluid dynamics is numerically analyzed in detail using two CFD software and two different modelling strategies for the axial gap. The analysis of the fluid evolution within the scroll wraps reveals unsteady phenomena developing during the suction and discharge phases, amplified by the axial clearance with negative impact on the main fluid flow (e.g., −13% of average mass flow rate for an axial gap of 30 µ) and on the scroll performance (e.g., +26% of average absorbed power for an axial gap of 30 µ). In terms of accuracy, the k-ε offers good performance on the estimation of average quantities Citation: Cavazzini, G.; Giacomel, F.; but proves to be inadequate for capturing the complexity of the unsteady phenomena caused by the Benato, A.; Nascimben, F.; Ardizzon, G. Analysis of the Inner axial gap (e.g., −19% of the absorbed power in case of perfect tip seal). The need for considering Fluid-Dynamics of Scroll specific geometric details in design procedures is highlighted, and guidelines on the choice of the Compressors and Comparison most suitable numerical model are provided depending on the analysis needs. between CFD Numerical and Modelling Approaches. Energies 2021, Keywords: positive displacement machine; scroll; CFD analysis; unsteady phenomena; axial gap; 14, 1158. https://doi.org/10.3390/ turbulent model en14041158

Received: 4 February 2021 Accepted: 17 February 2021 1. Introduction Published: 22 February 2021 Scroll-type compressors/expanders are Positive Displacement (PD) machines largely adopted in refrigeration systems, heat pumps, and power units. As an example, Publisher’s Note: MDPI stays neutral Murthy et al. [1] performed a review on expanders types used in vapor compression with regard to jurisdictional claims in refrigeration systems while Fukuta et al. [2] presented an investigation aimed to recover the published maps and institutional afﬁl- throttling loss in trans-critical CO2 refrigeration cycles. Byrne et al. [3] and Legros et al. [4] iations. presented a thermodynamically based model to design the scroll compressor for heat pumps and Organic Rankine Cycles (ORCs), respectively. In addition, Song et al. [5] focused on scroll expanders for ORC applications and demonstrate the great potential of these machines in the ORC energetic and exergetic performance improvements (for more Copyright: © 2021 by the authors. details on ORCs optimization, see, e.g., [6–8]). Licensee MDPI, Basel, Switzerland. So, it is clear that scroll-type compressors and expanders are receiving great interest This article is an open access article from researchers and the main reason of their success downs to their simple and compact distributed under the terms and structure. In practice, there is only one moving element that guarantees a positive impact on conditions of the Creative Commons the machine dimensions, reliability, and even noise. However, their design strategy has not Attribution (CC BY) license (https:// been improved over the years and it is still based on standard theoretical approaches and/or creativecommons.org/licenses/by/ thermodynamical methods, considering the volumes to displace as the key parameter for 4.0/).

Energies 2021, 14, 1158. https://doi.org/10.3390/en14041158 https://www.mdpi.com/journal/energies Energies 2021, 14, 1158 2 of 28

the machine design [3,9]. Design strategies that lead to building machines characterized by medium-to-poor efficiency in turn negatively affect the overall performance of the systems in which they are installed [2,10]. Unlike hydraulic machines, wind turbines, and axial compressors/turbines (see, e.g., [11–15]), whose design and performance received a significant boost by the birth and development of Computation Fluid Dynamics (CFD), scroll devices and PD machines in general suffer from both innovative design approaches and performance enhancements, resulting from the challenges of applying CFD to these machines and arising from the need for deforming mesh, fluid real equations (with further complications in case of combination with the lubrication oil), and long computational time. In a nutshell, in a PD machine, the pocket volume is continuously deformed during the shaft revolution. The motion that originates is a complex and time-dependent fluid- dynamic phenomena detectable only with mesh able to “follow” the deformation imposed by the machine moving part without losing its quality. In fact, for small deformations of the fluid domain, the original mesh maintains sufficient quality. However, in PD machines, the pocket volume variation, imposed by the moving part, is continuous in time and significantly deforms the mesh. So, several issues can arise by maintaining the original mesh: Quality decay, uncontrolled modifications of the mesh refinements, possible mesh collapse near contact points between stator and moving parts, etc. To overcome these issues, throughout the years, researchers proposed several meshing approaches but only three are the most applied: (a) Immersed Boundary Method (IBM) [16]; (b) key-frame remeshing [17]; and (c) adaptive meshing. The IBM was developed for simulating the flow of a solid body inside a fluid region without deforming or remeshing the mesh because of the body motion [18]. Unlike the others, this method considers the time-dependent body motion not at mesh level but directly in the flow equations. To do this, two different meshes are built: A background mesh for the whole domain, not considering the solid walls of the body, and a “solid” one for the moving body. In the zones where the solid mesh overlaps the background mesh, the flow equations are properly adapted. This approach solves the issue of the mesh quality decay, typical of body fitted meshes, but it increases the challenges in solving the equations in the nearby of the boundary. The key-frame remeshing technique [17] faces the issue of the time-dependent body motion at mesh level and completely re-meshes the grid if the cell quality falls below certain thresholds. This method guarantees the mesh quality and the solution consistency but requires huge computation time for the meshing process due to the need of a complete re- mesh of the fluid domain. Moreover, during the re-meshing process, the node locations are modified as well as the node distribution. This means that the solver is forced to interpolate the results between the current time step and the previous one, which is characterized by a different grid. So, interpolation errors can occur. The third technique, called “mesh adaption”, is one of the most adopted approach for PD machines and it is mainly based on the adaptation through deformation of structured hexahedral grids in each step of the simulation. In this regard, the scientific literature highlights several strategies that differ from one another for the choice of the main grid topology and the algorithm adopted for controlling the mesh adaptation. Classic and improved Laplacian-based approaches are widely and successfully adopted in this field [19,20]. There are two other strategies reported in literature: The Smoothed Particle Hydrody- namics (SPH) approach and the overset grid approach. The SPH is a challenging mesh-free Lagrangian approach proposed in literature mainly for turbomachines [21] with rare applications to PD ones [22]. The overset grid approach subdivided the grid into multiple grids, which can be generated independently one from the other. This approach does not result in outperforming the more consolidated meshing approach and it has not been widely applied in simulations of PD machines [23]. Energies 2021, 14, 1158 3 of 28

Over the years, the development of the above-mentioned meshing techniques has made possible the successful application of the CFD on PD machines. Stosic et al. [24], in 1996, was one of the first to use CFD to investigate the fluid flow in scroll, adopting a quasi-steady flow approach, while De Bernardi [25], in 2000, applied CFD to demonstrate the powerfulness of the approach in the physical understanding of the lubrication process. More recently, the CFD has been used by Angel et al. [26] to investigate the impact on scroll compressor performance of intermediate discharge ports and by Abdulhussain [27] to study the mixing of two-phase refrigerant dual ports through a variable speed scroll compressor. Differently, Morini et al. [28] proposed an integrated Reverse-Engineering CFD methodology to study how to convert a commercial scroll compressor into an expander for a micro-ORC system. Hence, the scroll performance investigation by means of CFD allowed: (i) To analyze in more detail the inner fluid dynamics and (ii) to work on the identification of the factors affecting their performance [5]. Cavazzini et al. [29] proposed, for the first time, a CFD- based optimization approach aimed at maximizing the efficiency of a scroll compressor, by the optimization of a selected number of design parameters. Their analysis highlighted the relevance of some design parameters over others. In particular, the orbit radius and the discharge port size and shape resulted in affecting the scroll performance. So, the analysis outcomes highlight the need of optimizing these parameters in view of performance maximization. Regarding the discharge port, in the considered design operating condition, the solution envisages a bean shape following the scroll spirals. The main reason for this result is its capability of limiting the onset of a clearance, reducing the built-in volume ratio. The influence of the leakage flow on the machine performance is also confirmed by several experimental and analytical studies [2,30,31]. As an example, Fukuta et al. [30] analyzed the leakage flow rate effects on the scroll performance, investigating a scroll compressor from both a theoretical and experimental viewpoint. The analysis showed a clear impact of the axial clearance on the machine performance and the influence of geometrical parameters on the tip seal efficiency. To study the leakage flow mechanism and its main affecting factors more in depth, several researchers focused on clearance and gaps within the scroll geometry. The first studies facing this topic were the ones performed by Cui [32,33]. He investigated the unsteadiness related to the discharge process of a scroll compressor, highlighting the influence of the leakage flow on this process and its complexity (unsteady 3D and transonic characteristics). In 2017, Singh et al. [34] carried out a CFD simulation to analyze the behavior of a scroll expander for a transcritical CO2 refrigeration system. A 2D approach is adopted and the authors focused their attention on the radial gap, demonstrating that the expansion process is affected by the leakage path between the rotor and the stator. In addition, they observed a resulting vortex in the expansion pocket, inducing a periodic fluctuation in the fluid velocity. A similar CFD simulation is carried out by Emhardt et al. [35] to investigate the influence of the radial clearance on the performance of a scroll expander applied to small- scale ORC. In fact, decreasing the radial clearance from 200 µm to 75 µm, allows, on the one hand, to increase the isentropic efficiency from 31.9% to 53.9% but, on the other hand, to reduce the specific power output from 864.2 W to 336.5 W. The same research group also found that constant wall thickness scroll expander characterized by large built-in volume ratios allowed to achieve higher performance in small-sized ORC [36]. Unlike the previous studies focusing on the radial clearance, the first studies modelling the axial gaps of a scroll expander were those of Song et al. [37,38]. They present the flow field within a large axial clearance of 100 µm confirming the onset of high-velocity values in the radial direction. The above-mentioned works clearly highlighted the complexity and unsteadiness of the flow field within the scroll together with the key role played by geometrical details and clearances in the definition of scroll performance. However, to the authors’ knowledge, Energies 2021, 14, 1158 4 of 28

no one has ever identified the root causes of the unsteadiness during the suction and discharge phase. Moreover, no one has ever considered the influence of the numerical approaches (e.g., turbulence model) and modelling strategies (gaps, tip seal, etc.) on the simulation accuracy. For example, the benefits in terms of result accuracy deriving from different modelling approaches have not been compared with the corresponding need of finer and finer grids and of greater computing effort, poorly matching with an optimization procedure. To this purpose, in the present work, the authors study the inner fluid dynamics of the scroll in depth with a particular focus on the suction and discharge phases. They also consider the influence of different CFD approaches on the result accuracy to highlight their strengths and weaknesses depending on the simulation goals. The paper is organized as follows. In Section2, the geometrical characteristics of the under-investigation scroll compressor are described, while, in Section3, the two CFD software and the corresponding numerical approaches are presented. In Section4, the main results are outlined and discussed, while in Section5, the concluding remarks are given.

2. The Scroll Compressor Geometry To properly validate the numerical models and evaluate their accuracy, a literature experimental analysis is chosen as a reference test case [39]. The scroll geometry, used in the test case, is defined according to the design procedure based on the equidistant curve approach. This procedure obtains the two spirals of the scroll as an offset of a continuous midline. It allows to define the complete meshing profiles (CMP) of the scroll, comprehensive of both the central and the peripheral profiles, simultaneously. This procedure was also adopted in [29] thanks to the reduced number of equations to handle in the scroll design optimization procedure. Since it allows to control the clearance volumes and the flank gaps, it perfectly fits even in this study. Indeed, the scroll geometry is obtained by combining the design of the peripheral profiles (for example as the involute of a circle) with the Perfect Meshing Profile (PFM) technique. In this manner, the scroll profiles meshing in the center is improved and the gaps are limited to the maximum. On the other hand, the design procedure proposed by Wang et al. [39] makes it possible from the very beginning to perfectly match the profiles even in the centers, in this way limiting further leakages due to imperfect profile interactions. The midline of the proposed geometry is obtained by the combination of a circular involute with a circular arc (Figure1a) according to the following equations:

x = x + R cosθ Circular arc arc θ C m f or θe[γ + π, γ + π + λ] (1) yarc θ = yC + Rmsinθ

π xinv θ = Rbcosθ + Rb θ + 2 sinθ Circular involute π f or θe[ϕ, ϕend] (2) yinv θ = Rbsinθ + Rb θ + 2 cosθ

where (xC, yC) are the coordinates of the center of the circular arc while Rm is the radius of the circular arc at the midline. γ is the modified angle (angle between the center of the arc and the x axis) while λ is the central angle of the circular arc. Rb is the radius of the involute generating circle while ϕ and ϕend are the starting and ending angle of the involute, respectively. The two scroll profiles are then obtained by offsetting the midline in both directions by half of the orbit radius Ror (Figure1b). The design parameters of the scroll geometry are taken from Wang et al. [39] since it is chosen as reference test case for evaluating the numerical model accuracy. The orbit radius Ror is assumed equal to 5.5 mm, whereas the orbiting scroll is only translated by 5.47 mm, leaving a flank gap of 30 µm. The spirals have a thickness of 4.5 mm and a height of 40 mm with an axial gap of 50 µm. The discharge port is located at the scroll center, tangential to the fixed spiral at the final meshing point, with a diameter equal to 0.8 of the last pocket diameters. Energies 2021, 14, 1158 5 of 28 Energies 2021, 14, x FOR PEER REVIEW 5 of 29

Figure 1. CompleteFigure 1. meshingComplete proﬁles meshing (CMP): profiles (a) ( midlineCMP) midline angles; angles (b) main and geometrical parameters parameters..

The two scroll profiles are then obtained by offsetting the midline in both directions 3. Numerical Models by half of the orbit radius Ror (Figure 1b). TAshe stateddesign above, parameters there areof the three scroll main geometry meshing are techniques taken from able Wang to handle et al. [39] the issuesince ofit isthe chosen time-dependent as reference mesh test deformationcase for evaluating typical the of scrollnumerical machines. model The accuracy aim of. thisThe studyorbit is not to discuss the strengths and the weaknesses of these techniques. Obviously, in radius Ror is assumed equal to 5.5 mm, whereas the orbiting scroll is only translated by literature, there are reviews and comparisons among them but not from a design point of 5.47 mm, leaving a flank gap of 30 µm. The spirals have a thickness of 4.5 mm and a height view. In particular, if the problem is approached from a design procedure perspective, there of 40 mm with an axial gap of 50 µm. The discharge port is located at the scroll center, is a need to focus on key geometrical details (i.e., the axial gap) and available numerical tangential to the fixed spiral at the final meshing point, with a diameter equal to 0.8 of the models. For this reason, the authors adopt the adaptive meshing technique, a consolidate last pocket diameters. meshing approach in PD machines analysis. Then, they compare the numerical approaches proposed by two commercial software, Pumplinx 5.0 [40] and TwinMesh 2019 [41], because 3. Numerical Models they modelled the axial gap in a different way. AsTwin stated Mesh above is a, there grid generatorare three main specifically meshing developed techniques for able rotary to handle PD machines. the issue of It thegenerates time-dependent and optimizes mesh the deformation computational typical grids of scroll of the machines machine. forThe each aimtime of this step study of the is notsimulation. to discuss The the step strengths corresponds and the to weaknesses a specific rotation of these angle techniques of the. rotor Obviously and, in, in general, literature,the angle there increment are reviews is assumedand comparisons equal to among 1◦ or 2◦ them, as suggested but not from by [ 42a design–44]. This point software of view. is Incomplementary particular, if the to Ansysproblem CFX is approached 19.0 [45] and from allows a design to build procedure the grids perspective, prior to the there launch is aof need the simulation.to focus onAt key the geometrical beginning ofdetails each (i. timee., the step, axial a proprietary gap) and available Fortran routine numerical [41] modelsloads the. For new this mesh reason, (depending the authors on adopt the rotor the adaptive position) meshing in the CFD technique solver, anda consolidate the mesh meshingdeformation approach is added in toPD the machines set of differential analysis. equations. Then, they In compare this way, theno interpolationnumerical ap- is proachesrequired betweenproposed time by two steps; commercial a technique software, that avoids Pumplinx the typical 5.0 [40] interpolation and TwinMesh errors 2019 that [41]occurred, because during they the modelled remeshing the phase.axial gap in a different way. TwinTwin Mesh Mesh is allows a grid togenerator split the specifically simulation developed domain into for differentrotary PD volumes machines to. It apply gen- eratesthe most and suitable optimizes meshing the computational strategy for each grids volume. of the machine In particular, for each a scroll time geometry step of the is simulationsubdivided. The in three step maincorresponds fluid domains: to a specific The rotation stator domain angle of (including the rotor and, inlet in and general, outlet thepipes angle and increment stationary is parts assumed of the equal working to 1° pockets),or 2°, as suggested the rotor domain,by [42–44] and. This the software rotor axial is complementarygap domain (Figure to Ansys2). All CF theX 19.0 domains [45] and are allows meshed to build independently the grids prior and connectedto the launch in ofthe the simulation simulation solver. At the via beginning a fluid-fluid of Generalizedeach time step, Grid a proprietary Interface (GGI) Fortran due routine to the time- [41] loadsdependent the new connection mesh (depending of the rotor on domain the rotor with position) the stator in one.the CFD solver and the mesh deformation is added to the set of differential equations. In this way, no interpolation is required between time steps; a technique that avoids the typical interpolation errors that occurred during the remeshing phase. Twin Mesh allows to split the simulation domain into different volumes to apply the most suitable meshing strategy for each volume. In particular, a scroll geometry is subdivided in three main fluid domains: The stator domain (including inlet and outlet pipes and stationary parts of the working pockets), the rotor domain, and the rotor axial gap Energies 2021, 14, x FOR PEER REVIEW 6 of 29

domain (Figure 2). All the domains are meshed independently and connected in the sim- Energies 2021, 14, 1158 6 of 28 ulation solver via a fluid-fluid Generalized Grid Interface (GGI) due to the time-dependent connection of the rotor domain with the stator one.

FigureFigure 2. Fluid 2. Fluid domains domains of Twin of Twin Mesh Mesh [44] [.44 ].

RegardingRegarding the therotor rotor domain, domain, affected affected by the by thetime time-dependent-dependent rotor rotor movement, movement, Twin Twin MeshMesh adopt adoptss a 2D a 2Dtopology topology characterized characterized by an by O an-type O-type grid, grid, characterized characterized by hexahedral by hexahedral elements,elements, around around the therotor rotor curvature. curvature. This This grid grid is built is built for foreach each possible possible rotor rotor position position adoptingadopting the thesame same topology topology and and node node numbers numbers as well as well as the as thesame same refined refined resolution resolution boundaboundaryry layers layers with with higher higher aspect aspect ratio ratio towards towards rotor rotor and and housing housing walls walls.. This This is is a pre- precon- conditiondition thatthat guarantees to avoid the need of interpolations between time time steps. steps. Regard- Regarding the mesh quality, smoothing methods are applied to guarantee adequate quality values for ing the mesh quality, smoothing methods are applied to guarantee adequate quality val- the desired quality criteria (minimum element angle, aspect ratio, etc.). The 2D meshes are ues for the desired quality criteria (minimum element angle, aspect ratio, etc.). The 2D then extruded to obtain the 3D ones of the rotor domain. meshes are then extruded to obtain the 3D ones of the rotor domain. The rotor axial gap is discretized by a structured high-resolution grid that allows to The rotor axial gap is discretized by a structured high-resolution grid that allows to take into account the tip seal leakage flow caused by the gap. take into account the tip seal leakage flow caused by the gap. The grids of the scroll geometry previously presented and generated by Twin Mesh [41] The grids of the scroll geometry previously presented and generated by Twin Mesh are loaded in Ansys CFX 19.0 [45] for carrying out a transient numerical simulation [46]. [41] are loaded in Ansys CFX 19.0 [45] for carrying out a transient numerical simulation As previously said, for each rotor position (defined by a rotation angle increment of 2◦), [46]. As previously said, for each rotor position (defined by a rotation angle increment of the Fortran routine changes the rotor domain grid, loads the new one optimized for that 2°), the Fortran routine changes the rotor domain grid, loads the new one optimized for specific position, but without interpolation needs. that specificUnlike position Twin, Mesh,but without which interpolation is a grid generator needs. requiring the combination with the AnsysUnlike CFX Twin solver, Mesh PumpLinx, which is a is grid a CFD generator software requiring that allows, the combination in a unique environment,with the An- to sys generateCFX solver, the grid,Pump defineLinx is the a numericalCFD software model, that and allows, carry outin a theunique simulation. environment, to generateAs the TwinMesh, grid, define PumpLinx the numerical automatically model, and generates carry aout structured the simulation. mesh for both the stator andAs theTwinMesh, rotor domains, PumpLinx but withautomatically a different generates meshing a technique. structured For mesh the for rotor, both it adoptsthe sta- the tor proprietaryand the rotor Conformal domains, Adaptativebut with a different Binary-tree meshing (CAB) technique. algorithm For [47 ],the generating rotor, it adopt cartesians the hexahedraproprietary cells Conformal in a volume Adaptative enclosed Binary by a group-tree (CAB) of surfaces. algorithm Close [47] to, the generating boundary, car- CAB tesianautomatically hexahedra cells adjusts in a thevolume grid enclosed shape to by conform a group to of thesurfaces. surfaces Close and to criticalthe boundary, geometry CABedges. automatically In order to adjusts fit critical the grid geometrical shape to features, conform CAB to the modifies surfaces the and cell critical size by geometry progressive edges.division In order of the to meshfit critical cells geometrical in half (binary features, grid). CAB modifies the cell size by progressive divisionThe rotor of the topology mesh cells is cylindrical,in half (binary and grid). the automatic mesh generator adopts a multi- blockThe rotor strategy, topology searching is cylindrical for key geometrical, and the automatic points to mesh subdivide generator the domain adopts ina multi six parti-- blocktions strategy, (Figure search3). ing for key geometrical points to subdivide the domain in six partitions (FigurePartitions 3). from 1 to 3 are meshed as long fluid volumes with evenly distributed nodes and hexahedral oriented in parallel with the rotor outline. Partitions from 4 to 6 belong to the central part of the scroll near the discharge port and allow the contact points. They are modelled as small gaps in agreement with all the other commercial software, Twin Mesh included. In these partitions, the grid is generated starting from lines of normal to solid walls so as guarantee a high level of orthogonality. Ecliptic smoothing techniques are Energies 2021, 14, 1158 7 of 28

adopted to optimize the grid in highly distorted areas (i.e., sharp corners), and a sweep Energies 2021, 14, x FOR PEER REVIEWmethod is applied. When the rotor moves into a new position, corresponding to7 of a 29 new time step, the procedure is repeated. More details on the meshing strategy in the discharge area are given in [48].

FigureFigure 3. 3.RotorRotor meshing meshing strategy strategy in PumpLinx: in PumpLinx: Rotor Rotor domain domain partition partitionss [48] [.48 ].

PartitionsThe main from difference 1 to 3 are between meshed as this long mesh fluid generation volumes with procedure evenly distributed and the Twin nodes Mesh andone hexahedral are regarding oriented the in axial parallel gap, with which the is rotor not considered,outline. Partitions and is from meshed 4 to 6 as belong a separate to thehigh-resolution, central part of the structured scroll near grid. the Indischarge PumpLinx, port the and leakage allow the paths contact in the points axial. They gapare are not Energies 2021, 14, x FOR PEER REVIEW 8 of 29 modelledfully meshed. as small The gaps reason in agreement is that the with sealing all the action other of commercial the tip seal issoftware assumed, Twin constant Mesh and included.perfectin In time these with partitions, a consequent the grid null is generated radial leakage starting ﬂow from in the lines axial of gap normal (see to Figure solid4 ). walls so as guarantee a high level of orthogonality. Ecliptic smoothing techniques are adopted to optimize the grid in highly distorted areas (i.e., sharp corners), and a sweep method is applied. When the rotor moves into a new position, corresponding to a new time step, the procedure is repeated. More details on the meshing strategy in the discharge area are given in [48]. The main difference between this mesh generation procedure and the Twin Mesh one are regarding the axial gap, which is not considered, and is meshed as a separate high- resolution, structured grid. In PumpLinx, the leakage paths in the axial gap are not fully meshed. The reason is that the sealing action of the tip seal is assumed constant and perfect in time with a consequent null radial leakage flow in the axial gap (see Figure 4).

FigureFigure 4.4. PumpLinxPumpLinx approach to axial gap modelling modelling..

Therefore, the leakage path is simplified in a Z-shaped fluid volume, which is meshed assuming the flux of mass, momentum, heat, and turbulence from one volume pocket to the other is null [49]. This simplification assumes that the high-pressure value characterizing the inside pocket—in comparison with the low-pressure value in the outside pocket—continuously pushes the tip seal to the outer side of the groove, guaranteeing a perfect sealing (Figure 4). Unfortunately, this assumption only partially reflects the real dynamics of the process. In fact, the real behavior is characterized by unsteady time-dependent reversals of the outside-inside pressure gradient. Moreover, it does not consider the inner imperfection in the sealing, due to the need for limiting the friction losses, a necessary condition for making the scroll movement possible. Lastly, the leakage volume stops at the ends of the spiral shape (Figure 5).

Figure 5. Example of the start and end of the tip seal volumes in a scroll compressor. Energies 2021, 14, x FOR PEER REVIEW 8 of 29

Energies 2021, 14, 1158 8 of 28 Figure 4. PumpLinx approach to axial gap modelling.

ThereforeTherefore,, the leakageleakage path path is issimplified simplified in a in Z-shaped a Z-shaped fluid volume, fluid volume which, iswhich meshed is meshedassuming assuming the flux ofthe mass, flux momentum,of mass, momentum, heat, and turbulenceheat, and turbulence from one volume from one pocket volume to the pocketother isto null the [other49]. This is null simplification [49]. This simplification assumes that theassumes high-pressure that the high value-pressure characterizing value characterithe insidezing pocket—in the inside comparison pocket—in with comparison the low-pressure with the low value-pressure in the value outside in pocket—the out- sidecontinuously pocket—continuously pushes the tippush seales tothe the tip outerseal to side the outer of the side groove, of the guaranteeing groove, guaranteeing a perfect asealing perfect (Figure sealing4 ).(Figure Unfortunately, 4). Unfortunately, this assumption this assumption only partially only reflects partially the reflect real dynamicss the real dynamicsof the process. of the process In fact,.the In fact real, the behavior real behavior is characterized is characterized by unsteady by unsteady time-dependent time-de- pendentreversals reversal of the outside-insides of the outside pressure-inside pressure gradient. gradient Moreover,. Moreover, it does not it does consider not consider the inner theimperfection inner imperfection in the sealing, in the duesealing to the, due need to forthe limitingneed for the limiting friction the losses, friction a necessarylosses, a necessarycondition condition for making for the making scroll movementthe scroll movement possible. Lastly, possible. the Last leakagely, the volume leakage stops volume at the stopsends at of the the end spirals of shape the spiral (Figure shape5). (Figure 5).

Figure 5. Example of tip sealFigure volumes 5. Example in a scroll of compressor: the start and (a end) end of of the the tip tip seal seal volumes volumes; in (b a) startscroll of compressor the tip seal. vol-umes.

The resulting fluid domain is certainly simplified since it forms a single computational domain with the tip seal volumes, and no flux of mass, momentum, heat, and turbulence from one volume pocket to the low-pressure one should be numerically solved [49]. To analyze the influence of these two different meshing strategies on the numerical viewpoint, particular attention needs to be paid to avoiding the influence on the results of the third factors. First, a sensitivity analysis based on the average inlet mass flowrate is carried out with and without the axial gap for both software, resulting in the number of nodes reported in Table1.

Table 1. Number of grid nodes in the different cases.

Software Without Axial Gap With Axial Gap TwinMesh—Ansys CFX 250,000 520,000 PumpLinx 250,000 450,000

The resulting number of elements for the main ﬂuid domain is similar in both cases with an equal number of elements per dimension (Figure6). For example, in the case without an axial gap, the following node distribution is ﬁxed for both software: 180 elements in the θ-direction, 12 elements in the radial direction, and 10 elements in the axial direction. In the case considering the axial gap, the differences in the total number of nodes are mainly due to the different strategy for modelling the gap (Figure6b). Energies 2021, 14, x FOR PEER REVIEW 9 of 29

The resulting fluid domain is certainly simplified since it forms a single computational domain with the tip seal volumes, and no flux of mass, momentum, heat, and turbulence from one volume pocket to the low-pressure one should be numerically solved [49]. To analyze the influence of these two different meshing strategies on the numerical viewpoint, particular attention needs to be paid to avoiding the influence on the results of the third factors. First, a sensitivity analysis based on the average inlet mass flowrate is carried out with and without the axial gap for both software, resulting in the number of nodes reported in Table 1.

Table 1. Number of grid nodes in the different cases.

Software Without Axial Gap With Axial Gap TwinMesh—Ansys CFX 250,000 520,000 PumpLinx 250,000 450,000

The resulting number of elements for the main fluid domain is similar in both cases with an equal number of elements per dimension (Figure 6). For example, in the case without an axial gap, the following node distribution is fixed for both software: 180 elements in the θ-direction, 12 elements in the radial direction, and 10 elements in the axial direc- Energies 2021, 14, 1158 tion. In the case considering the axial gap, the differences in the total number of nodes are 9 of 28 mainly due to the different strategy for modelling the gap (Figure 6b).

(a) PumpLinx grid (b) TwinMesh grid

FigureFigure 6. Overview 6. Overview of the ofPumpLinx the PumpLinx grid (a grid) and ( adetail) and of detail the TwinMesh of the TwinMesh grid at grid the atdischarge the discharge in case in of case the ofmodel the modelwith with axial gap.axial gap.

The settings of the reference test case [39] are also fixed in both cases. In particular, a pressure ratio of 7:1 (pin = 1 bar, pout = 7 bar) with a rotation rate of 3000 rpm is fixed. The fluid is assumed to be an ideal gas with constant properties (Tin = 293 K) beside the density. Regarding the solver scheme, a high-resolution, second-order scheme (Upwind for PumpLinx and Backward Euler Transient for CFX) is adopted in both cases with first-order turbulence numeric [49]. The time step is fixed equal to a rotation angle increment of 2◦. The turbulence is considered with a Shear Stress Transport (SST) turbulent model in CFX, whereas with a k-ε model in PumpLinx, since neither the SST nor the k-ω are available for this software. However, it must be pointed out that the k-ε model is the state-of-the-art turbulence model in CFD simulations carried out on scroll geometries, as it is clearly highlighted in Table 6 of [5] and confirmed by the most recent CFD studies on scrolls [35,36]. So, the difference in turbulent model is considered useful to evaluate the accuracy of the k-ω model in comparison with the state-of-the-art k-ε approach. No-slip wall condition is fixed on the walls. The simulations are performed over a total of five complete revolutions of the scroll rotor. The scroll fluid dynamics reaches convergence after two, or maximum three, revolutions.

4. Results and Discussion This section presents the results of the simulations carried out with the two approaches and discusses their strengths and weaknesses in the analysis of a scroll compressor. As said, the two approaches differ not only in the modelling/meshing strategy of the axial gap, but also in the turbulence model. All these differences in the approach are the result of the different “philosophy”, underpinning the development of the two software. Energies 2021, 14, 1158 10 of 28

On one side, the CFX approach is inherently aimed at reproducing as much accuracy as possible in the machine flow field, searching for a high level of adherence to the real geometry, even at gap level, and to the multi-scale fluid dynamics. On the other side, the PumpLinx software aims at reproducing the macro aspects of the scroll fluid dynamics, prioritizing the adoption of simplified and time-saving modeling solutions. To capture the influence of these two approaches on the results, the comparison between them is carried out at different levels (from macro- to micro-scale) and for different models (with and without axial gap) and the resulting accuracy in comparison with the experimental results is evaluated.

4.1. Scroll Simulation without Axial Gap The scroll fluid dynamics is extremely complex and characterized by several unsteady phenomena whose development is strictly related to the so called “porting process”, i.e., the suction and discharge process of the fluid mass flow. Figures7 and8 show the vector plots, captured by CFX, in two different sections of the scroll (mid-span and axial) for three different instants during the last revolution (Figure9—1 revolution = 0.02 s). At t1 the orbiting scroll is located farthest from the inlet port (Figure7). The filling of the inlet pocket is just started, and the instantaneous mass flow rate is close to its peak value (Figure9). Large recirculating zones are induced by the interaction between the mass flow entering in the inlet pocket and the outside wall of the orbiting scroll. This interaction forces the flow to reverse direction giving rise to vortexes, clearly affecting the Energies 2021, 14, x FOR PEER REVIEW 11 of 29 flow field near the inlet duct (Figure7). The vortexes extend for the whole radial direction and involve half of the pocket width (Figure8).

(a) t1 = 0.069 (b) t2 = 0.073 (c) t3 = 0.079

FigureFigure 7. 7. VVectorector plots plots of of the the flow ﬂow field ﬁeld at at mid mid-span-span for for three three different different instants instants during during the the last last revolution revolution (CFX) (CFX)..

(a) t1 = 0.069 (b) t2 = 0.073 (c) t3 = 0.079 Figure 8. Vector plots of the flow field on an axial section plane for three different instants during the last revolution (CFX).

At t1 the orbiting scroll is located farthest from the inlet port (Figure 7). The filling of the inlet pocket is just started, and the instantaneous mass flow rate is close to its peak value (Figure 9). Large recirculating zones are induced by the interaction between the mass flow entering in the inlet pocket and the outside wall of the orbiting scroll. This interaction forces the flow to reverse direction giving rise to vortexes, clearly affecting the Energies 2021, 14, x FOR PEER REVIEW 11 of 29

Energies 2021, 14, 1158 (a) t1 = 0.069 (b) t2 = 0.073 (c) t3 = 0.079 11 of 28 Figure 7. Vector plots of the flow field at mid-span for three different instants during the last revolution (CFX).

Energies 2021, 14, x FOR PEER REVIEW 12 of 29

(a) t1 = 0.069 (b) t2 = 0.073 (c) t3 = 0.079 flow field near the inlet duct (Figure 7). The vortexes extend for the whole radial direction FigureFigure 8. Vector 8. Vector plots plots of the ofand ﬂow the involve ﬁeldflow onfield anhalf on axial ofan theaxial section pocket section plane width plane for three for(Figure three different different8). instants instants during during the last the revolution last revolution (CFX). (CFX).

FigureFigure 9. Evolution over timetime ofof thethe mass mass flow flow rate rate at at the the inlet inlet port, port, and and pressure pressure at theat the inlet inlet port port during during the lastthe threelast three orbit orbitrevolutions revolutions of the o rotatingf the rotating scroll: scroll: CFX inlet CFX mass inlet flow mass (solid flow line), (solid PumpLinx line), PumpLinx inlet mass inlet flow mass (dash-dot flow (dash line),-dot and line) CFX, inletand CFXpressure inlet (dottedpressure line). (dotted line).

The location of the inlet port in front of the orbiting scroll continuously modifies the radial distance between the inlet port and the moving wall of the orbiting scroll, reproducing the unsteady “tumble” phenomenon typical of the internal combustion engines. Indeed, as shown in Figure 8, the surface of the orbiting scroll moves towards the inlet port, reducing the radius of the vortexes whose rotation rate is consequently increased to maintain their constant moment of momentum (net of the losses). In the second part of the suction phase, the outside surface of the scroll moves away from the inlet port, increases the vortexes radius, and hence, progressively decreases their intensity (Figure 9). This phenomenon is further amplified by the progressive reduction of the inlet mass flow rate. When the mass flow rate reaches its minimum (푡4 in Figure 9), the vortexes almost disappear (Figure 10). Energies 2021, 14, 1158 12 of 28

The location of the inlet port in front of the orbiting scroll continuously modifies the radial distance between the inlet port and the moving wall of the orbiting scroll, reproducing the unsteady “tumble” phenomenon typical of the internal combustion engines. Indeed, as shown in Figure8, the surface of the orbiting scroll moves towards the inlet port, reducing the radius of the vortexes whose rotation rate is consequently increased to maintain their constant moment of momentum (net of the losses). In the second part of the suction phase, the outside surface of the scroll moves away from the inlet port, increases the vortexes radius, and hence, progressively decreases their intensity (Figure9). This phenomenon is Energies 2021, 14, x FOR PEER REVIEWfurther amplified by the progressive reduction of the inlet mass flow rate. When the13 mass of 29

ﬂow rate reaches its minimum (t4 in Figure9), the vortexes almost disappear (Figure 10).

Figure 10. Vector plots of the flow field at mid span and on the axial section plan for 푡 = 0.085 (CFX) Figure 10. Vector plots of the ﬂow ﬁeld at mid span and on the axial section plan for t4 4= 0.085 (CFX).

Figure.Figure9 9also also depicts depicts the the evolution evolution over over time time of of the the inlet inlet mass mass flow flow rate rate captured captured by by PumpLinx.PumpLinx. The generalgeneral trendtrend isis toto somesome extendextend similar.similar. TheThe averageaverage valuevalue ofof thethe massmass flowflow raterate isis almostalmost equalequal inin the two simulations:simulations: 0.010553 kg/s kg/s in in CFX CFX vs. vs. 0.0104830.010483 kg/s kg/s in inPumplinx Pumplinx,, and and approximate approximate with with a sufficient a sufficient accuracy accuracy (an error (an errorless than less 5%) than the 5%) experi- the . experimentalmental mass flow mass rate flow 푚 ratė = 0m.011= 0.011kg/s [39]kg/s. However,[39]. However, CFX captured CFX captured a greater a greater peak value peak valueof the ofmass the flow mass rate flow (+24% rate (+24%for CFX for vs. CFX +11.6% vs. +11.6%for Pumplinx for Pumplinx with respect with respectto the average to the averagevalue) and value) a pulsating and a pulsating behavior, behavior, amplified amplified in the first in part the of first the part suction of the phase suction (from phase time (from0.69 to time 0.73). 0.69 This to 0.73).pulsating This pulsatingbehavior, behavior,whose frequency whose frequency is half ofis the half machine of the machine rotation rotationfrequency frequency (25 Hz vs. (25 50 Hz Hz vs. corresponding 50 Hz corresponding to a period to a periodof 0.04 ofs vs 0.04. 0.02 s vs. s), 0.02is clearly s), is clearly linked linkedto the perturbation to the perturbation of the inlet of the pressure inlet pressure (Figure (Figure 8). As8 given). As givenbelow below,, the perturbation the perturbation seems provoked by the inertia phenomena developing in the discharging pockets, which causes pressure drops propagating up to the scroll inlet. Figure 11 depicts the vector plots of the flow field at the scroll discharge on two different locations. The first section plan is normal to the scroll axis and coincides with the discharge port, while the second one is the same axial section plane of Figure 7 with a view limited to the discharge area. The vector plots refer to six different instants which are also highlighted in Figure 12, reporting the evolution over time of the outlet mass flow rate, as determined by CFX (solid line) and PumpLinx (dash-dot line). In t1, the scroll has almost concluded the discharge of the fluid mass (Figure 12) and the flow field does not present vortexes or separation zones (Figure 11). Then, the remaining fluid mass of the last pocket is progressively pushed out from the discharge port by the movement of the orbiting scroll. This movement indeed causes, at the same time, the Energies 2021, 14, 1158 13 of 28

seems provoked by the inertia phenomena developing in the discharging pockets, which Energies 2021, 14, x FOR PEER REVIEW 14 of 29 causes pressure drops propagating up to the scroll inlet. Figure 11 depicts the vector plots of the flow field at the scroll discharge on two different locations. The first section plan is normal to the scroll axis and coincides with the reductiondischarge port,of the while volume the secondof the discharging one is the same pocket axial and section the planestart of of the Figure discharge7 with a of view the limited to the discharge area. The vector plots refer to six different instants which are also second last pocket (see t2 and t5 in Figure 11). The mass flow discharged by the scroll sig- nificantlyhighlighted increases in Figure due 12 to, reporting this double the contribution, evolution over reaching time of its the peak outlet, and mass then flow decreas rate,ing as determined by CFX (solid line) and PumpLinx (dash-dot line). while the scroll completely opens the discharge port (see t6, t7, and t8 in Figure 11).

(a) t1 = 0.069 (b) t2 = 0.073 (c) t5 = 0.074

(d) t6 = 0.076 (e) t7 = 0.078 (f) t8 = 0.08

Figure 11. VectorVector plotsplots ofof thethe ﬂowflow ﬁeldfield atat thethe scrollscroll dischargedischarge locatedlocated onon thethe dischargedischarge portport (of(of circularcircular shape)shape) and on an axial sectionsection planplan(rectangular (rectangular shape) shape) (CFX). (CFX) The. The zero-velocity zero-velocity area area on on the the discharge discharge port port is related is related to the to widththe width of the of wall the wall of the orbiting scroll, partially blocking the discharge area. of the orbiting scroll, partially blocking the discharge area. This analysis highlights two interesting fluid-dynamic phenomena:  During the first part of the discharge phase, the flow field is perturbed by jets of mass flow coming out from pressurized discharging pockets (see t5 and t6 Figure 11). These jets are combined with counter-rotating vortexes and separation zones. This behavior explains the main peak and the subsequent smaller one in the evolution of the outlet mass flow rate (Figure 12), due to the combined discharge of the two pockets (see t5 and t6 in Figure 11).  The discharging process is characterized by inertia phenomena, affecting the pressure level in the discharging pockets. At the beginning of the discharge phase, the pressurized discharging pockets push out the fluid mass, with a con- Energies 2021, 14, x FOR PEER REVIEW 15 of 29

sequent rapid decrease in local pressure (Figure 13). This pressure drops reasonably to propagate up to the inlet suction pocket through the radial clearance, providing an explanation for the trend of the inlet pressure and mass flow rate in the CFX analysis (Figure 9). Clearly, PumpLix is able to capture the main characteristics of the flow field development in the scroll (Figure 14). However, there are some discrepancies that can justify the slightly different trend of the instantaneous mass flow rate. For example, at t5 the mass flow discharged by the last pocket is less intense (Figure 14), resulting in a smaller peak in Figure 12. At t6 the two jets of mass flow and the main vortex are captured but the structure of secondary flows developing in the discharging duct is less defined, resulting in a more regular discharge of mass flow at the scroll outlet. Despite the general agreement in trends between the software, Figure 12 clearly shows that CFX captured a more perturbed evolution over time, in line with the extremely unsteady flow field at the scroll Energies 2021, 14, 1158 14 of 28 discharge.

Figure 12. InstantaneousInstantaneous mass mass flow ﬂow rate rate at at the the outlet outlet port port during during the the last last three three orbit orbit revolutions revolutions of of the the rotating rotating scroll: scroll: CFX CFX (solid line) vs. Pumplinx Pumplinx (dash (dash-dot-dot line).

In t1, the scroll has almost concluded the discharge of the fluid mass (Figure 12) and the flow field does not present vortexes or separation zones (Figure 11). Then, the remaining fluid mass of the last pocket is progressively pushed out from the discharge port by the movement of the orbiting scroll. This movement indeed causes, at the same time, the reduction of the volume of the discharging pocket and the start of the discharge of the second last pocket (see t2 and t5 in Figure 11). The mass flow discharged by the scroll significantly increases due to this double contribution, reaching its peak, and then decreasing while the scroll completely opens the discharge port (see t6, t7, and t8 in Figure 11). This analysis highlights two interesting fluid-dynamic phenomena: • During the first part of the discharge phase, the flow field is perturbed by jets of mass flow coming out from pressurized discharging pockets (see t5 and t6 Figure 11). These jets are combined with counter-rotating vortexes and separation zones. This behavior explains the main peak and the subsequent smaller one in the evolution of the outlet mass flow rate (Figure 12), due to the combined discharge of the two pockets (see t5 and t6 in Figure 11). • The discharging process is characterized by inertia phenomena, affecting the pressure level in the discharging pockets. At the beginning of the discharge phase, the pressurized discharging pockets push out the fluid mass, with a consequent rapid decrease in local pressure (Figure 13). This pressure drops reasonably to propagate up to the inlet suction pocket through the radial clearance, providing an explanation for the trend of the inlet pressure and mass flow rate in the CFX analysis (Figure9). Energies 2021, 14, 1158 15 of 28 Energies 2021, 14, x FOR PEER REVIEW 16 of 29

a) 푡 = 0.0725 b) 푡 = 0.0733

c) 푡 = 0.0741 d) 푡 = 0.075

Figure 13. Contour plots of theFigure pressure 13 at. Contour the scroll plots discharge of the locatedpressure on at the the discharge scroll discharge port (of located circular on shape) the discharge and an axial port (of section plan (rectangular shape).circular shape) and an axial section plan (rectangular shape).

Clearly, PumpLix is able to capture the main characteristics of the flow field development in the scroll (Figure 14). However, there are some discrepancies that can justify the slightly different trend of the instantaneous mass flow rate. For example, at t5 the mass Energies 2021, 14, 1158 16 of 28

flow discharged by the last pocket is less intense (Figure 14), resulting in a smaller peak in Figure 12. At t6 the two jets of mass flow and the main vortex are captured but the structure of secondary flows developing in the discharging duct is less defined, resulting in a more regular discharge of mass flow at the scroll outlet. Despite the general agreement in Energies 2021, 14, x FOR PEER REVIEW 17 of 29 trends between the software, Figure 12 clearly shows that CFX captured a more perturbed evolution over time, in line with the extremely unsteady flow field at the scroll discharge.

a) 푡1 = 0.069 b) 푡2 = 0.073 c) 푡5 = 0.074

d) 푡6 = 0.076 e) 푡7 = 0.078 f) 푡8 = 0.08

FigureFigure 14. 14. VectorVector plots of the flow ﬂow field ﬁeld at the scroll discharge located on an axial section plan (PumpLinx).

TheThe main reason for this difference seems to be the turbulent model. As previously highlighted,highlighted, PumpLinx PumpLinx adopts adopts the the k k--εε model,model, which which is is widely u usedsed in the prediction of severalseveral turbulent ﬂowflow calculationscalculations due due to to its its robustness, robustness, economy, economy and, and reasonable reasonable accuracy accu- racyfor a for wide a wide range range of ﬂows. of flows. However, However, it has been it has also been demonstrated also demonstrated that this modelthat this performs model performspoorly when poorly faced when with faced non-equilibrium with non-equilibrium boundary layersboundary as in layers the case as in of the “tumble” case of motion “tumble”at the motion entrance at the [50 ].entrance [50]. In this case, the k-ε model is not able to properly capture the unsteady phenomena affecting the scroll fluid dynamics. Therefore, the mass flow rate peaks are underestimated and the mass flow rate at the scroll inlet presents a more regular trend (Figure 9). Regarding the power absorbed at the scroll shaft, PumpLinx determines a smaller power in comparison with CFX (Figure 15). This seems mainly linked to the underestimation of the fluid-dynamic losses associated with the unsteady phenomena developing within the scroll, which are not completely captured by PumpLinx. Energies 2021, 14, 1158 17 of 28

In this case, the k-ε model is not able to properly capture the unsteady phenomena affecting the scroll fluid dynamics. Therefore, the mass flow rate peaks are underestimated and the mass flow rate at the scroll inlet presents a more regular trend (Figure9). Re- garding the power absorbed at the scroll shaft, PumpLinx determines a smaller power in Energies 2021, 14, x FOR PEER REVIEW 18 of 29 comparison with CFX (Figure 15). This seems mainly linked to the underestimation of the fluid-dynamic losses associated with the unsteady phenomena developing within the scroll, which are not completely captured by PumpLinx.

FigureFigure 15. 15. ComparisonComparison of of power power absorbed absorbed at at the the scroll scroll shaft shaft between between CFX CFX (solid (solid line) line) and PumpLinx (dash (dash-dot-dot line) line)..

InIn summary, summary, when when the the axial axial gap gap is is neglected neglected,, the the comparison comparison between between the the modelling modelling strategystrategy adopted by by thethe two two software software highlights highlights that that the the combination combination between between Twin-Mesh Twin- Meshand CFX and allows CFX allows a more a accuratemore accurate overview overview of the fluid of the dynamics fluid dynamics within the within scroll the machine. scroll machineIn this regard,. In this the regard, turbulence the turbulence model (for examplemodel (for the example SST model) the plays SST amodel) key role plays in the a casekey roleof flow in the fields case characterized of flow fields by characterized separation zones by separation and unsteady zones phenomena, and unsteady such phenomena as the jets, suchof mass as the flow jets rate of previously mass flow discussed. rate previously The in-depth discussed. evaluation The in- ofdepth the flowevaluation field makes of the it floweasier field to identify makes theit easier geometrical to identify details the affecting geometrical the scroll details performance. affecting the For example,scroll perfor- CFX manceallows. toFor highlight example, the CFX influence allows ofto thehighlight inlet port the locationinfluence on of the the trend inlet ofport the location instantaneous on the trendmass of flow the rate.instantaneous However, mass it must flow be rate. pointed However out, thatit must the be average pointed values out that of the aver- main ageperformance values of the parameters main performance are comparable parameters for the are software, comparable but thefor simplifiedthe software, modelling but the simplifiedstrategy proposed modelling by strategy PumpLinx proposed allows by to PumpLinx reduce the allows computational to reduce the time. computational This can be timea benefit. Thiswhen can be the a benefit CFD simulation when the isCFD included simulation in an is optimization included in an procedure, optimization requiring pro- hundreds, if not thousands, of simulations. In this case, average performance values cedure, requiring hundreds, if not thousands, of simulations. In this case, average perfor- characterized by sufficient accuracy can represent a good compromise between accuracy mance values characterized by sufficient accuracy can represent a good compromise be- and computational time. To stress this time-saving approach, the simulation of the scroll tween accuracy and computational time. To stress this time-saving approach, the simula- is repeated adopting a first-order solver scheme in PumpLinx, further speeding up the tion of the scroll is repeated adopting a first-order solver scheme in PumpLinx, further computing process. The development of the main flow field is sufficiently captured even speeding up the computing process. The development of the main flow field is sufficiently in this case. However, the accuracy of the average values is reduced. In fact, the average captured even in this case. However, the accuracy of the average values is reduced. In fact, mass flow rate decreases from 0.010485 kg/s to 0.010012 kg/s, increasing the numerical the average mass flow rate decreases from 0.010485 kg/s to 0.010012 kg/s, increasing the error—with respect to the experimental value—up to 9%, whereas the absorbed average numerical error—with respect to the experimental value—up to 9%, whereas the absorbed power is overestimated (from 2.75 kW to 3.23 kW). average power is overestimated (from 2.75 kW to 3.23 kW).

4.2. Scroll Simulation with Axial Gap Another key aspect to consider in the analysis of a scroll and, more generally, of a volume displacement machine is the axial gap modelling. Experimental studies clearly demonstrated that the relevance of the axial gap is even greater than that of the radial gap due to the longer sealing length [30,31]. So, depending on the CFD goals, it is extremely important to define the appropriate modelling strategy to consider the axial gap. As given in Section 3, TwinMesh and PumpLinx adopt two different strategies for the axial gap modelling. The first one makes it possible to consider the radial leakage Energies 2021, 14, x FOR PEER REVIEW 19 of 29

through the axial clearance. The other one models the gap as equipped with perfect tip seal, preventing the radial leakage from pockets, and allowing only the tangential leakage along the wrap in the tip seal (Figure 4). The difference in the two modelling approaches can be appreciated by the result comparison. Figure 16 shows the instantaneous inlet mass flow rates as a function of time in

Energies 2021, 14, 1158 four different cases: CFX with axial gap (blue solid line), CFX without axial gap 18(blue of 28 dash-dot line), PumpLinx with the perfect tip seal (red solid line), and PumpLinx without axial gap (red dash-dot line). There is no significant difference in results between the PumpLinx cases with and without4.2. Scroll axial Simulation gap. The with perfect Axial seal Gap prevents radial leakages in the axial gap from the com- pressedAnother pocket keys back aspect to the to suction consider area in. the The analysis average of mass a scroll flow and, rate more is only generally, slightly ofre- a ducedvolume (0.01038 displacement kg/s vs. machine 0.01048 kg/s is the) and axial the gap reason modelling. of this Experimentalreduction is the studies increase clearly in tangentialdemonstrated leakage that, gaining the relevance the small of the contribution axial gap is of even the leakage greater thantangential that of flow the radialin the gaptip sealdue. to the longer sealing length [30,31]. So, depending on the CFD goals, it is extremely importantOn the toother define side the, in appropriate the CFX results modelling, the mass strategy flow to rate consider pulsation, the axial also gap.experienced in theAs case given without in Section axial 3gap, TwinMesh (Figure 9), and is significantly PumpLinx adopt amplified two differentby the introduction strategies for of thethe axial axial gap. gap modelling. The first one makes it possible to consider the radial leakage throughThe flow the axial fields clearance. reflect this The behavior other onesince models they change the gap significantly as equipped during with perfectone revo- tip lutionseal, preventing of the scroll the (Figure radial 17 leakage and Figure from pockets, 18). At the and beginning, allowing only t1, the the velocity tangential at the leakage en- trancealong reaches the wrap values in the around tip seal 40 (Figure m/s while4). the flow rate is so intense to be deviated by the wall ofThe the difference orbiting scroll, in the creating two modelling two side approaches vortexes close can to be the appreciated inlet duct by(Figure the result 16). Then,comparison. the flow Figure rate progressively 16 shows the instantaneousdecreases during inlet the mass revolution, flow rates reaching as a function values of close time toin zero four ( differentt3). The flow cases: field CFX within with the axial suction gap (blue pocket solid is line),characterized CFX without by velocity axial gap close (blue to zero,dash-dot and line),even PumpLinxthe tumble withmotion, the perfectlinked tipto sealthe flow (red solidrate entrance, line), and almost PumpLinx disappears without (Figureaxial gap 18). (red dash-dot line).

FigureFigure 16. 16. EvolutionEvolution over over time time of of the the mass mass flow ﬂow rate rate at at the the inlet inlet port port during during the the last last three three orbit orbit revolutions revolutions of of the the ro rotatingtating scroll:scroll: CFX CFX with with axial axial gap gap (blue (blue solid solid line) line),, CFX CFX without without axial axial gap gap (blue (blue dash dash-dot-dot line) line),, Pump PumpLinxLinx with with the the perfect perfect tip tip seal seal ((redred solid solid line) line),, and and PumpLinx PumpLinx without without axial axial gap gap (red (red dash dash-dot-dot line) line)..

There is no significant difference in results between the PumpLinx cases with and without axial gap. The perfect seal prevents radial leakages in the axial gap from the compressed pockets back to the suction area. The average mass flow rate is only slightly reduced (0.01038 kg/s vs. 0.01048 kg/s) and the reason of this reduction is the increase in tangential leakage, gaining the small contribution of the leakage tangential flow in the tip seal. On the other side, in the CFX results, the mass flow rate pulsation, also experienced in the case without axial gap (Figure9), is significantly amplified by the introduction of the axial gap. Energies 2021, 14, 1158 19 of 28

The flow fields reflect this behavior since they change significantly during one revolution of the scroll (Figures 17 and 18). At the beginning, t1, the velocity at the entrance reaches values around 40 m/s while the flow rate is so intense to be deviated by the wall of the orbiting scroll, creating two side vortexes close to the inlet duct (Figure 16). Then, the flow rate progressively decreases during the revolution, reaching values close to zero (t3). The flow field within the suction pocket is characterized by velocity close to zero, and even the tumble motion, linked to the flow rate entrance, almost disappears (Figure 18). This is due to the radial leakage in the axial gap (not considered in the PumpLinx cases), moving back from discharge up to the scroll inlet pocket. When this flow leaks from a high-pressure pocket to a low-pressure pocket, its pressure content slightly pressurizes the low-pressure pocket. This is of course a dynamic process that is strictly linked to the instantaneous evolution of the pressure within the pockets during one revolution of the scroll. To better clarify this process and the interconnections between factors, it is mandatory to compare the evolution over three cycles of the instantaneous mass flow rate at the inlet and outlet ports with the pressure at the inlet port (Figure 19). There is a clear cause-and-effect relationship between the three trends. At the instant t1, the discharge process of the mass flow rate is in its final phase (dash-dot line in Figure 19). The pockets D, already merged, are discharging the residual compressed air at a constant rate and the air pressure in the subsequent pockets C is close to the maximum value (Figure 20a). Therefore, the pressure difference between pockets D and C is small, resulting in a poor radial leakage flow in the axial gap between those pockets (Figure 20c). Similar situation characterizes the pockets A, which have just started the compression process: Their pressure is almost equal to that of the suction pocket and the leakage flow is minimum (Figure 20a,c). At this instant, the pressure at the inlet port is lower than Energies 2021, 14, x FOR PEER REVIEWthat of the environment and the gradient pressure favors the entrance of new air20 of mass, 29 as

demonstrated by the maximum value of the inlet mass ﬂow rate (Figure 19).

a) 𝑡 = 0.069 b) 𝑡 = 0.073 c) 𝑡 = 0.079

FigureFigure 17. VectorVector plots plots of ofthe the flow ﬂow field ﬁeld at mid-span at mid-span for three for threedifferent different instants instants during the during last revolution the last revolution (CFX with (CFXaxial with gap). axial gap).

Energies 2021, 14, x FOR PEER REVIEW 20 of 29

a) 푡1 = 0.069 b) 푡2 = 0.073 c) 푡3 = 0.079

Energies 2021, 14, 1158 20 of 28 Figure 17. Vector plots of the flow field at mid-span for three different instants during the last revolution (CFX with axial gap).

Energies 2021, 14, x FOR PEER REVIEW 21 of 29

Figure 18. Vector plots of the flow field on an axial section plane for three different instants during the last revolution (CFX with axial gap).

This is due to the radial leakage in the axial gap (not considered in the PumpLinx cases), moving back from discharge up to the scroll inlet pocket. When this flow leaks from a high-pressure pocket to a low-pressure pocket, its pressure content slightly pressurizes the low-pressure pocket. This is of course a dynamic process that is strictly linked to the instantaneous evolution of the pressure within the pockets during one revolution a) 푡1 = 0.069 of the scroll. b) 푡2 = 0.073 c) 푡3 = 0.079 To better clarify this process and the interconnections between factors, it is manda- Figure 18. Vector plots of the ﬂowtory ﬁeldto compare on an axial the sectionevolution plane over for three three cycles different of the instants instantaneous during the mass last revolutionflow rate at (CFX the with axial gap). inlet and outlet ports with the pressure at the inlet port (Figure 19).

FigureFigure 19. Evolution 19. Evolution over over time time during during the the last last three three orbit orbit revolutions revolutions of of the the rotating rotating scroll scroll of of the: the:mass mass flowflow raterate atat thethe inlet port (blueinlet port solid (blue line), solid mass line), flow mass rate flow at the rate discharge at the discharge port (red port dash-dot (red dash line)-dot and line) pressure and pressure at the inlet at the port inlet (green port dotted (green line). dotted line).

There is a clear cause-and-effect relationship between the three trends. At the instant t1, the discharge process of the mass flow rate is in its final phase (dash-dot line in Figure 19). The pockets D, already merged, are discharging the residual compressed air at a constant rate and the air pressure in the subsequent pockets C is close to the maximum value (Figure 20a). Therefore, the pressure difference between pockets D and C is small, resulting in a poor radial leakage flow in the axial gap between those pockets (Figure 20c). Sim- ilar situation characterizes the pockets A, which have just started the compression process: Their pressure is almost equal to that of the suction pocket and the leakage flow is minimum (Figure 20a,c). At this instant, the pressure at the inlet port is lower than that of the environment and the gradient pressure favors the entrance of new air mass, as demonstrated by the maximum value of the inlet mass flow rate (Figure 19). Energies 2021, 14, 1158 21 of 28

Energies 2021, 14, x FOR PEER REVIEW 22 of 29

A B B C

C D

D D C C B B A A

a) 푡1 = 0.069 - Pressure b) 푡3 = 0.079 - Pressure

A B

B A A

c) 푡1 = 0.069 - Velocity d) 푡3 = 0.079 - Velocity

FigureFigure 20. Contour 20. Contour plot of plot the of pressure the pressure and of and the of velocity the velocity in a section in a section plan normalplan normal to the to scroll the scroll axis and axis passing and passing through through the axial gap. Comparison between two different instants: t1 (0.069) and t3 (0.079). the axial gap. Comparison between two different instants: t1 (0.069) and t3 (0.079).

In theIn subsequentthe subsequent instants, instants, the the pressure pressure distribution distribution in in the the scroll scroll pockets pockets changes changes due due to the scroll orbiting movement. At At the the instant instant t3t,3 ,the the scroll scroll is is still still in in the the middle middle of the of thedischarging discharging phase phase and and the the pockets pockets are are characterized characterized by byincreasing increasing pressure pressure value value (Figure (Figure20b). 20 bThe). Thepressure pressure gradients gradients between between the pockets the pockets are not are negligible not negligible and favor and favoran intense an intenseradial leakage radial leakage flow from ﬂow the from discharge the discharge pockets D pockets up to the D upsuction to the pocket suction A (Figure pocket 20d). A(FigureThis radial 20d). leakage This radial flow leakagebrings part ﬂow of bringsits temperature part of its and temperature pressure content and pressure into the low- contentpressure into the pocket, low-pressure causing pocket,a small causingincrease aof small the pocket increase pressure of the pocketand temperature pressure and (Figure temperature21). This (Figure is clearly 21). demonstrated This is clearly by demonstrated the evolution by over the evolutiontime of the over inlet time pressure of the inletin Figure 19. Indeed, at t3, the inlet pressure reaches the environmental pressure value, 1 bar, and this prevents to the air mass to enter into the suction pocket, bringing the mass flow rate to null or even negative values (Figure 19). Energies 2021, 14, 1158 22 of 28

pressure in Figure 19. Indeed, at t3, the inlet pressure reaches the environmental pressure Energies 2021, 14, x FOR PEER REVIEW value, 1 bar, and this prevents to the air mass to enter into the suction pocket, bringing23 of 29 the

mass ﬂow rate to null or even negative values (Figure 19).

Figure 21. Contour plot of the temperature in a section plan normal to the scroll axis at mid-span. Figure 21. Contour plot of the temperature in a section plan normal to the scroll axis at mid-span. (t3 = 0.079). (t3 =0.079). It must be pointed out that the axial gap not only affects the inner fluid dynamics withinIt must the be scrollpointed pockets, out that but the also axial in the gap discharge not only duct.affects The the mass inner flow fluid jets dynamics coming out withinfrom the discharging scroll pocket pockets,s, but clearlyalso in capturedthe discharge in the duct. analysis The without mass flow the axialjets coming gap (Figure out 11), fromare discharging significantly pocket dampeds, clearly down captured in the simulationin the analysis with without the axial the gap axial (Figure gap (22Figure) mainly 11), arefor significantly two reasons. damped First, the down mass in flow the simulation rate discharged with the by axial the scroll gap (Figure is smaller 22) mainly due to the for twoincreased reasons. mass First, leakage the mass flowing flow back rate to discharged the entrance. by Then, the scroll the axial is smaller gap makes due a to mass the flow increasedexchange mass possible leakage between flowing the back discharging to the entrance pockets. Then due, to the the axial onset gap of pressuremakes a gradientsmass flow(see exchange contour possible plot over between the orbiting the discharging scroll width pocket in t5 sand duet7 to– the Figure onset 22 ).ofConsequently, pressure gra- the dientmasss (see flow contour rate at plot the outletover the port orbiting is more scroll uniformly width distributed in t5 and overt7 – timeFigure and 22 the). Conse- amplitude quentlyof the, the peak mass at flow the beginning rate at the of outlet the discharging port is more phase uniformly is significantly distributed reduced over time (Figure and 23 ). the amplitudeBesides of the the average peak at mass the beginning flow rate reduction, of the discharging it is important phase to highlightis significantly that, in re- terms ducedof scroll(Figure global 23). performance, the pressurizing effect of the radial leakage linked to the axial gapBesides significantly the average increases mass theflow scroll rate power reduction, consumption: it is important 3.6 kW to vs. hig 2.8hlight kW. that, in terms of Figurescroll global 23 also performance, highlights thatthe pressurizing the modelling effect approach of the radial based leakage on a perfect linked tip to seal the axialprevents gap significantly PumpLinx from increases capturing the scroll significant power differencesconsumption with: 3.6 the kW simulation vs. 2.8 kW. without axial gap. The small reduction in the average mass flow rate caused by the increased tangential leakage flow is confirmed. This reflects in the global performance, whose values are slightly increased in comparison with the previous case. For example, the average power consumption just increases from 2.7 kW to 2.9 kW. Energies 20212021,, 1414, ,x 1158 FOR PEER REVIEW 24 of 29 23 of 28

a) 𝑡 = 0.069 b) 𝑡 = 0.073 c) 𝑡 = 0.074

d) 𝑡 = 0.076 e) 𝑡 = 0.078 f) 𝑡 =0.08

FigureFigure 22. 22. VectorVector plots plots of ofthe the flow ﬂow field ﬁeld at the at thescroll scroll discharge discharge locate locatedd on the on discharge the discharge port (of port circular (of circular shape) shape)and an axial and an axial section plan (rectangular shape) (CFX with axial gap). section plan (rectangular shape) (CFX with axial gap). EnergiesEnergies 20212021,, 1414,, x 1158 FOR PEER REVIEW 2524 of of 29 28

FigureFigure 23. 23. EvolutionEvolution over over time time of of the the mass mass flow ﬂow rate rate at at the the outlet outlet port port during during the the last last three three orbit orbit revolutions revolutions of of the the rotating rotating scroll:scroll: CFX CFX with with axial axial gap gap (blue (blue solid solid line), line), CFX CFX without without axial axial gap gap (blue (blue dash dash-dot-dot line), line), PumpLinx PumpLinx with with the the perfect perfect tip tip seal seal (red(red solid solid lin line),e), and and PumpLinx PumpLinx without without axial axial gap gap (red (red dash dash-dot-dot line) line)..

5. ConclusionsFigure 23 also highlights that the modelling approach based on a perfect tip seal prevents PumpLinx from capturing significant differences with the simulation without axial Even if scroll machines present a wide application range, their efficiency is often one gap. The small reduction in the average mass flow rate caused by the increased tangential of the main bottlenecks for increasing the performance of the overall system/technology leakage flow is confirmed. This reflects in the global performance, whose values are in which they are applied. Unlike turbomachines, the design strategy of these machines slightly increased in comparison with the previous case. For example, the average power (and more in general of positive displacement machines) is limited to theoretical and/or consumptionsemi-empirical just approaches. increases from A fact 2.7 linkedkW to to2.9 the kW. complex fluid dynamics combined with challenges in applying CFD software. 5. Conclusions This paper analyses the inner fluid dynamics of a scroll machine with a particular focusEven on theif scroll influence machines of the present axial gap a wide on the application resulting range performance., their efficiency Indeed, is axial often gap one is ofone the of main the mostbottlenecks challenging for increasing aspect to the consider performance in a CFD of simulationthe overall andsystem/technology its relevance in inscroll which design they areareclearly applied. demonstrated Unlike turbomachines, by experimental the design studies. strategy of these machines (and moreTo discriminate in general betweenof positive different displacement factors machines) affecting the is scrolllimited flow to theoretical field, CFD and/or simula- semitions-empirical are carried approaches out with and. A fact without linked the to axial the complex gap. This fluid approach dynamics makes combined it possible: with (i) challengesTo study the in applying fluid evolution CFD software. within the scroll wraps and the unsteady phenomena caused by theThis porting paper processanalyses and the (ii) inner to analyze fluid dynamics the influence of a ofscroll the axialmachine clearance with a on particular the main focusfluid on flow. the influence of the axial gap on the resulting performance. Indeed, axial gap is one ofMoreover, the most sincechallenging innovative aspec designt to consider strategies in are a generallyCFD simulation based on and CFD itsfluid-dynamic relevance in scroanalyses,ll design a comparison are clearly betweendemonstrated numerical by experimental models is carried studies out. to highlight strengths and weaknessesTo discriminate of the available between approaches. different factors affecting the scroll flow field, CFD simulations areRegarding carried theout scrollwith machineand without fluid the flow axial field gap. analysis, This approach it can be concludedmakes it possible: that: i) T•o studyA tumble the fluid motion evolution arises within in the inletthe scroll pocket wraps from and the interactionthe unsteady between phenomena the mass caused flow by therate porting entering process in the and suction ii) to analyze pocket and the theinfluence outside of surface the axial of theclearance orbiting on scroll. the main The fluid flow.location of the inlet port affects the onset of this tumble motion and, hence, it shall be Moreover,considered since during innovative the scroll design design. strategies are generally based on CFD fluid-dynamic• The analyses, discharge a comparison process at the between scroll outlet numerical is perturbed models by jets is ofcarried mass flow out andto highlight unsteady strengthinertias and phenomena, weaknesses whose of the available influence approaches. is propagated up to the scroll inlet, causing the Regarding the scroll machine fluid flow field analysis, it can be concluded that: Energies 2021, 14, 1158 25 of 28

pulsation of the inlet mass flow rate. To affect these phenomena and the consequences on the inlet mass flow rate, possible modification of the discharge port geometry needs to be considered during the scroll design. The relevance of the discharge port shape on the scroll performance is also deduced in the analysis of Cavazzini et al. [29], but in their study, the root causes have not been identified. • The axial clearance increases the tangential leakage of the radial clearance and determines the onset of a radial leakage flow, whose intensity depends on the pressure gradient between pockets. When this radial leakage is not negligible, it is able to slightly pressurize the low-pressure pockets, increasing the counter-pressure and, hence, the scroll power consumption. Moreover, the pressurization of the inlet pockets is the cause of the null or reverse mass flow rate at the inlet port. This affects the average mass flow rate and power consumption, and hence, need to be considered during the design phase. As regards the CFD models, the comparison brings to the following conclusions: • The scroll fluid dynamics is characterized by unsteady separation zones mainly related to the charge (e.g., tumble motion) and discharge (e.g., mass flow jets) process, and the k-ε model, because of its characteristics, is not as accurate as other turbulent models (e.g., SST) in reproducing them. Nevertheless, its robustness and timesaving make it suitable for comparisons between different design solutions within an optimization procedure, which is a time-consuming process generally requiring hundreds, even not thousands, of simulations. • The modelling strategy based on a perfect tip seal does not reproduce accurately the influence of the axial gap on the fluid dynamics and performance of a scroll machine. Even if the pressure gradient between the pockets pushes the tip seal against the stator wall, experimental studies demonstrate that a perfect sealing can be never achieved, even in the case of high-pressure ratio, and that the radial leakage flow, which is not considered in a perfect-tip-seal modelling strategy, is a matter of fact. • The strategy based on modelling the axial gap is closer to the real operating conditions since it allows to consider the radial leakage through pockets. However, the axial clearance in this modelling strategy is assumed to be constant which is not fully consistent with the real operating condition. Indeed, the leakage flow rate is governed by a tip clearance that depends on the pressure forces acting on the tip seal, varying during the scroll revolution as a function on time. The relevance of this time-dependent behavior of the tip seal in terms of simulation accuracy is not fully negligible since the flow in the axial gap can easily reach transonic velocities with the consequent chocking of the axial gap. So, if the simulation goal is to analyze new design solutions of the tip seal for damping down mass flow rate pulsations and/or to simulate as much accurately as possible the scroll performance, it is necessary to consider this time-dependent behavior, with the consequent need for the development of a new and more complex modelling strategy.

Author Contributions: Conceptualization, G.C., A.B. and G.A.; data curation, G.C., F.G., A.B. and F.N.; formal analysis, G.C., F.G., A.B. and F.N.; investigation, G.C., F.G., A.B. and G.A.; methodology, G.C., F.G., A.B. and G.A.; writing—original draft, G.C.; writing—review and editing, G.C., A.B. and G.A.; funding, G.C. and G.A. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Abbreviations

CAB Conformal Adaptative Binary-tree CFD Computational Fluid Dynamics Energies 2021, 14, 1158 26 of 28

CMP Complete Meshing Profiles GGI Generalized Grid Interface IBM Immersed Boundary Method ORC Organic Rankine Cycle PD Positive Displacement PMP Perfect Meshing Profile SPH Smoothed Particle Hydrodynamics SST Shear Stress Transport xC, yC coordinates of the center of the circular arc . m mass flow rate pin inlet pressure pout outlet pressure Rb radius of the involute generating circle Rm radius of the circular arc at the midline Ror orbit radius Tin inlet temperature ti i-th instant of time λ central angle of the circular arc γ modified angle or angle between the center of the arc and the x axis ϕ, ϕend starting and ending angle of the involute

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