Grid Generation for CFD Analysis and Design of a Variety of Twin Screw Machines

A detailed study of the fluid flow and thermodynamic processes in positive displacement machines requires 3D CFD modeling in order to capture their real geometry, including leakage gaps. However, limitations in the conventional computational grids, used in commercial software packages, exclude their use for classical twin screw machines. The screw compressor rotor grid generator (SCORG) is a customized grid generation tool developed to overcome these limitations. This paper shows how it can be further extended to include non-conventional rotor designs, such as those with variable lead or profile variation and even internally geared machines with conical rotors. Other arrangements possible with this improvement include multiple gate rotors to increase volumetric displacement or dual lead, high wrap angle rotors for very high-pressure differences and vacuum applications. A case study of a water-injected twin screw compressor is included to demonstrate its use for both detailed flow analysis and design.


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Today screw machines are regarded as highly reliable and compact systems for energy 27 conversion. The twin screw and single screw compressors are the most widely used types of 28 industrial compressors. Figure 1 presents the geometry of a pair of a twin screw compressor. Opening 29 of the space between the rotor lobes to the suction port fills the gas into the passages formed between 30 them and the casing, until the trapped volume is a maximum. Further rotation leads to cut off the

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There is a lack of 3D computational methods available for design and analysis of such screw 46 machines. Screw compressor rotors with a variable lead are still at the research stage, although a patent on this concept dates back to 1969 [2]. This describes a helical screw compressor with a 48 continuously variable lead for the lobes of the male and gate rotors. Figure 3a shows the meshing of 49 twin screw rotors with variable helical lead. It has been shown that for the same rotor lengths, 50 diameter, wrap angles and lobe profiles the variable pitch rotors can be designed to provide higher 51 pressure ratios and larger discharge port opening areas, thus reducing the exit throttling losses [2].

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Advantages of variable pitch rotors, can also be comprehended if the rotor diameters are made to 53 vary from suction to the discharge. Figure 3b shows an example of a parallel axis variable profile twin 54 screw rotors. As the rotors of a screw machine turn during operation, the fluid volume in between 55 them is deformed (compressed or expanded) and the CFD grid which represents the fluid volume 56 also needs to deform. Without capturing this deformation it is not possible to capture the real three structure interaction, etc have been reported in [3,4,6]. Sauls and Branch [7] used the results from 72 CFD calculations to develop an improved one-dimensional thermodynamic model for refrigerant screw compressors, by extracting calibration coefficients that influence the pressure variation during 74 the discharge process. Mujić [8] presented an optimisation of the discharge port area based on flow 75 behaviour in the discharge chamber. CFD model was used for relative comparison of port geometry 76 modifications and their influence on predicted pressure pulsations has been used to judge sound 77 spectrum and noise level from the compressor. These noise levels predicted by CFD solutions have 78 been used for designing discharge ports with reduced noise levels. Mujić [8] in his thesis presented a 79 3D CFD coupled model in which the boundary conditions for the discharge port were obtained as 80 time varying data from 1D thermodynamic chamber models. The procedure was implemented for 81 Star CCM+ solver. It was found that the results predicted by the coupled model for sound pressure 82 levels were closer to the full 3D CFD models and also in close agreement with the experimental 83 measurements. Such an approach simplified the numerical analysis and also provided faster results 84 from the CFD models. Vierendeels et al. [9] were the first to implement a grid generation algorithm 85 for block structured mesh from the solution of the Laplace equation for twin screw compressors and 86 pumps using differential methods. The use of differential methods requires the PDE to be solved for 87 every rotor position and then the grid generation has to be repeated from the equipotential and 88 gradient lines. In his thesis, Vande Voorde [10] presented the principles of solving the initial Laplace 89 equation and then using it to construct a block structured deforming mesh. Based on this grid 90 generation, flow in a double tooth compressor and a twin screw compressor was analysed and the 91 results were compared with experimental data over a range of discharge pressures and rotor speeds.

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A detailed comparison of the algebraic and differential methods has been presented by Rane and 93 Kovačević [1,11]

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generator has been presented. The quality of numerical cells and their distribution obtained by this 120 differential method is greatly improved making the grid suitable for multiphase models such as oil completely smooths the transition of the partitioning rack curve between the two rotors thus improving grid node movement and robustness of the CFD solver [20]. Further, application of An analytical grid generation of screw machine working domain is explained in Kovačević et.al 130 [3,4]. It includes separating domains of the screw rotors by a rack curve [5] and forming independent

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One of the objectives of the elliptic PDE mesh generation implemented in SCORG was to improve

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The smooth rack obtained by this procedure is supplied back to a second stage of boundary 183 distribution calculation resulting in a new conformal distribution. This conformal distribution is 184 further used as a boundary condition for final differential mesh generation. As a result a significant 185 improvement in the mesh quality is achieved. Figure 6 shows the comparison of the cell orthogonal 186 quality between the algebraic meshes and the elliptic meshes. Figure

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functionality also allows a covariation of rotor lead as well as rotor profile. An example of uniform 250 lead and variable profile rotor is Figure 3b and the grid generated by SCORG is shown in Figure 9.

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In this algorithm, the additional computational effort required is to calculate the 2D grid data in every 252 cross section as compared to that of a uniform pitch rotor grid generation calculation. The assembly 253 of the grid from 2D to 3D structure was completely redesigned in order to provide flexibility to 254 generate grids for variable geometry rotors. The inputs for the geometry of the rotor can be provided

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The volumetric displacement of these rotors was smaller than that of the uniform profile rotors.

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Analysis of variable profile rotors showed a steeper internal pressure rise but there was no reduction      (1)

Empirical form
Such that, ≫ ,̂ The enthalpy source in energy equation applied for air phase is defined as is the latent heat due to evaporation at discharge pressure. Such an empirical model also enables 371 the use of constant thermodynamic properties for the water-liquid in the calculations. Four cases 372 were calculated in this study and the corresponding operating conditions are as shown in Table 1.

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Fluid properties were defined as in Table 2 with air as the primary phase and water-liquid as 376 the secondary phase. Pressure boundary conditions were specified at the suction and discharge.

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Solver parameters were set at higher stability conditions. SST k-Omega turbulence model was 378 applied. Results from CFD analysis are presented in this section. They reflect a state when full 11.0 379 bar discharge pressure has been reached in the discharge port and 1-2 cycles of calculation were 380 continued at these operating conditions. The cycle averaged temperature data were collected during 381 the simulation.

Internal compression chamber pressure
383 Figure 13 shows the rise of pressure in the compression chamber with main rotor rotation for same pressure inside the chamber. Because of the high under-compression which can be observed by 386 the steep pressure rise at 350º rotor angle, a strong pressure pulse is generated in the discharge port.  If water was not injected in the compressor, the temperature of air would have exceeded 380℃ 397 at 11.0 bar discharge pressure. In the analysed cases, water has been injected at 10℃.

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The water mass of 0.009 Kg/sec was determined so as to achieve saturated air at the exit with 406 power dissipation of approximately 30 kW. But these estimates did not account for transient affects.
CFD calculation has therefore resulted in higher than saturation exit temperatures. Additionally the 408 leakage of gas during compression adds to the accumulation of energy in the compression chamber 409 which further raises the gas temperature. Cases 2 and 4 were designed such that the mass flow rate 410 of water is 5 times and 10 times that of the saturation mass of Case 2 respectively with the aim of 411 achieving a discharge temperature lower than 200℃. The limit of 200℃ is due to the maximum 412 temperature that the compressor bearings and housing can withstand during operation. It can be 413 observed from Table 1 that the temperature of 205℃ is achieved at 4500 rpm and 187℃ is achieved 414 at 6000rpm with increased mass flow of water. Figure 14 presents the distribution of air temperature 415 inside the compressor. An iso-surface generated with water-liquid volume fraction of 0.01% is also 416 shown in the figure. The temperature in the suction port is lower on the gate rotor side, but on the 417 main rotor side shows higher air temperature. This indicates that the leakage is higher from the tip 418 of the main rotor as compared to the gate rotor and also that the cooling is more effective on the gate 419 rotor side as compared to the main rotors side for the same mass of injected water. The temperature 420 on the gate rotor is higher than on the main rotor close to the discharge port. Water-liquid is observed 421 in the region where air temperature is below the saturation temperature at 11.0 bar. Evaporation 422 effect is visible in the compression chamber opened to the discharge port and also in the discharge 423 port i.e. no liquid water is present here. In comparison to Case 2, Case3 showed about 50℃ lower 424 cycle average temperature.

Evaporation effect
426 Figure 15 shows the representative water-vapour formation and cooling of air. Figure 15a shows the 427 air temperature distribution on the main rotor surface, in the end leakage and in a plane through the 428 discharge port. Figure 15b shows the region where liquid water is getting converted to vapour. Figure   429 15c shows the distribution of liquid water on the main rotor surface and Figure 15d shows the latent

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The availability of computational grid for such screw rotors now makes it possible to evaluate the 457 flow and thermal field in the working chambers of these machines.

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The test case of water injected twin screw compressor is an example of multi-phase flow

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 Results show higher cooling at 4500 rpm than at 6000 rpm for the same water mass flow rate.

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Total mass of water injected and its residence time in the compression chamber is higher at 464 lower speed resulting in greater heat transfer and cooling. At 4500 rpm the compression 465 power is lower than at 6000 rpm. Therefore the same mass of water will provide higher 466 cooling at lower speeds.

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 When water mass required just for saturation is injected, the exit temperature exceeds 300 C.

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By injecting five times higher water mass flow, cycle average temperature close to 200 C 469 could be achieved.

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 In this compressor design, water cooling effect was higher on the Gate rotor side due to early

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injection. An increase in the water injection on main rotor side can help to achieve better 472 temperature uniformity.

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 Tip leakage is higher on Main rotor side and this results in non-uniform temperature on the 474 housing.

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The test case demonstrated that physical mechanism such as injection of water in the 476 compression chamber and evaporation during the compression cycle is still at a primitive level where 477 simplification of the evaporation mechanism was required to avoid excessively high computational

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It is anticipated that more customized grid generation tools such as SCORG will need to be 483 developed as further positive displacement screw machine designs are explored and their 484 computational models are demanded. Additional 3D CFD methods that can provide robust grid re-485 meshing algorithms or meshless methods will also need to be evolved that can be used for flow 486 computation in complex deforming domains of these machines.