PuK - Process Technology & Components 2022

Compressors and Systems

Compressors and Systems From the research runs along the line of the smallest distance between the rotors. A sugges- connections that occur are plotted gap connections and gas exchange tion for the calculation can be found against the angle of rotation. Since in [Nad17]. the geometric change over the ro- Fig. 3: Representation of the gap types in a screw machine (greatly enlarged) Simulation and modelling Dry-running screw machines are usually simulated using numerical flow simulations (computational fluid dynamics – CFD) [Ran15, Joh05] or chamber models [Kau02]. Since CFD simulations are very computationally intensive, simulation using a multichamber model is often used when designing a screw machine. Multichamber simulation means that the interactions between the individual chambers are included in the calculation. This is ensured by an analysis of all geometry-describing parameters of the rotors [Tem07]. The calculation based on a chamber model is based on the assumption of a homogeneous state in the working chambers. The calculation is based on the conservation of mass and energy according to the first law of thermodynamics. (4) (5) tational speed is directly associated with the change over time, the only thing missing for the iterative solution of the equations is the determination of the mass flow rates that occur through the gap connections and gas exchange connections. In order to determine this within the chamber model simulation, an isentropic nozzle flow is usually used, which is then multiplied by a flow coefficient α to take the influence of friction into account: (6) In order to improve the mapping quality of the simulation, dimension- less numbers were determined in [Utr21] in order to adapt the flow coefficient to the actual boundary conditions (e. g. existing Reynolds number). This is not used in this work and instead a general flow coefficient of 0.8 is used [Sac02, Pev07]. The required chamber models are created automatically, based on a front section analysis. The prerequisite is the provision of the inter-lobe clearance or line of contact. Since the profile family under consideration is an analytical description, it is automatically available following a concrete profile generation. An exception to the fully automatic creation of the chamber models has so far been the blowhole. The methodology proposed by Rinder [Rin79] is used to determine this. Boundary conditions The investigation of the profile family according to Wu with regard to the energy conversion quality assumes that all simulated screw compressors are comparable with each other. This affects both the physical and geometric boundary conditions as well as the internal volume ratio, which depends on the operating point and the rotor geometry. This is then optimised for each rotor geometry examined to ensure that the interaction of rotors and housing has no influence on the result achieved. Table 1 summarises the examined physical and geometric boundary conditions. Table 1: Geometric and physical boundary conditions Geometric boundary conditions Male rotor Female rotor Rotor diameter [mm] 72 70.56 Lobe number [-] 4 6 Rotor length [mm] 115 Wrap angle [°] 275 -183 Revolutions per minute [1/min] 25000 Gap dimensions [μm] 81 Internal volume ratio [-] respectively optimised To calculate the individual portions of the change over time in the internal energy dU/dt, technical work dW/dt, heat dQ/dt and the exchange of enthalpy flow rates the geometry of the working chambers and the Physical boundary conditions Value Low pressure [Pa] 101300 Intake temperature [K] 293 Compression ratio [-] 3.5; 5; 6.5 Flow coefficient [-] 0.8 (all gaps) 82 PROCESS TECHNOLOGY & COMPONENTS 2022

Compressors and Systems From the research Statistical profile investigation With the 12 parameters to choose from, the rotor profile family has too many parameters, some of which have very little influence on the energy conversion quality, for direct optimisation of the parameters to make sense. Furthermore, the choice of an optimisation algorithm is problematic since it is not clear whether and to what extent the parameters interact with regard to the energy conversion quality. For this reason, a statistical evaluation (design of experiments – DOE) is used and the MINITAB software is used for this purpose. respective influencing variable. Often, α = 95 % is chosen as the expected range or confidence interval. The decision as to whether a parameter has a relevant influence on the target value can be recognised using the significance value. If the significance value is less than 1 – α, the parameter under consideration has a significant effect on the target variable. Another advantage of the DOE is that in addition to the linear influence of the parameters, quadratic influences and interactions are also taken into account [Mat05]. The results of the screening carried out indicate that parameters 1, 3, 7 and 11 as well as Table 2: Parameters and levels of statistical design of experiments, as well as direction of optimisation with regard to specific indicated power Number Parameter Low Level Reference profile High Level 1 ρ 1 1.6 2.4 2.4 ↓ 2 ρ 2 1.4 1.9 2.4 ↔ 3 u n 0.24435 0.24435 0.34907 ↓ 4 t 1 1 1,4 ↔ 5 s 0.6 0.6 1.2 ↔ 6 κ 1 1 4 ↔ 7 τ 1 4 4 ↑ 8 d 0.1 0.1 1.1 ↔ 9 γ 0.01745 0.05236 0.05236 ↔ 10 e a 20 25 25 ↔ (↑) 11 ν 0 0.34 0.34 ↑ 12 β 0 45.5 45.5 (↓) Optimisation direction the interaction between parameters 11 and 12 have a significant influence on the energy conversion quality. As the compression ratio increases, parameter 10 also gains in importance. Improvement of the screw compressor by the rotor profile In the following, the knowledge gained from the screening will be used to design a profile that has the lowest possible specific indicated power. For this purpose, the best profile configuration from the screening is used as a reference profile. The front section of this profile is illustrated in Fig. 4 . The figure also shows the blowhole area and the inter-lobe clearance. Changes in the profile parameters primarily affect these two types of gaps and therefore influence the energy conversion. The front gap, the width of which is limited by the crown circle and root circle, is constant due to the size. Since rotor length and wrap are also constant, the geometry of the housing gap is also constant. Although the maximum chamber volume also varies with the profile parameters, the influence of the gap flows on the specific indicated power is dominant. Before considering the results, the designation of the compared profiles should be explained with the help of Fig. 5. The designation re ference stands for the best machine from the screening. The pro- Part of the DOE is creating a large enough experimental design to produce trustworthy results. In order to first determine which parameters significantly influence the energy conversion quality, so-called screening is carried out. Here, a test plan is created in which two different levels are prescribed for the parameters to be examined, Table 2. The MINITAB software uses the number of free parameters to determine the tests to be performed [Mat05]. A regression analysis is then carried out during the statistical evaluation, which provides an expected range of the target variable. In addition to the expected range, the regression analysis provides a significance value p for the Fig. 4: Representation of the reference profile in the front section with marking of the projected blowhole area and the projected inter-lobe clearance PROCESS TECHNOLOGY & COMPONENTS 2022 83