PuK - Process Technology & Components 2022

Compressors and Systems

Compressors and Systems From the research Energetic profile optimisation of twin-screw compressors Matthias Heselmann (MSc), Prof. Dr.-Ing. Andreas Brümmer Abstract In this article, the energy conversion of twin-screw compressors is considered and analysed to what extent this can be improved by choosing a suitable profile for the rotors. In general, the energy conversion in screw compressors is significantly influenced by gap flows between the working chambers. While the front and housing gaps are essentially influenced by the size, i. e. shaft diameter and length as well as the rotor twist, the choice of profile has a decisive effect on the blowhole and the inter-lobe clearance. The normal rack generation method according to Wu, which provides 12 free parameters, is used to generate the rotor profile. The indicated power related to the intake volume flow, also known as the specific indicated power, is chosen as a measure for the energy conversion. The key profile parameters are identified using a statistical test plan. The results indicate that only 4 parameters influence the energy conversion. Through their targeted setting, an optimal compromise between blowhole area and inter-lobe clearance width is achieved, which can reduce the specific indicated power by around 3 %. Due to their periodic working cycle, screw compressors can be classified in the group of positive displacement machines. The working chambers are formed by two rotors twisted in opposite directions, which are mounted in a housing that encloses them tightly. Due to significant improvements in the manufacture of the complicated rotor geometries, the compact design and the low-maintenance operation, this type of machine is now the most commonly used type of compressor in compressed air and re frigeration technology. In general, screw machines can be divided into dry-running and wet-running machines. The reason for the subdivision results from the torque to be transmitted from the female to the male rotor [Utr19]. In the case of wet-running machines, an auxiliary fluid (usually oil) is injected into the working chamber, which lubricates the rotors and thus reduces wear in direct contact between the rotors. In addition to lubricating the rotors, the auxiliary fluid partially seals the working chambers, reduces noise emissions and dissipates a significant part of the compression heat. As a result, wet-running screw machines can achieve a compression ratio of up to 20. Usually the oil has to be separated from the gas again downstream of the compressor, which is associated with increased effort. This is not necessary for dry-running screw machines. Instead, a synchronisation gear is required to transmit the torque between the rotors in order to avoid contact between them. Since the advantages of an auxiliary fluid do not apply, the achievable compression ratio is around 5. Due to the lack of hydraulic losses, dry-running screw compressors can be operated with a rotor-tip speed of approx. 100 m/s, which is twice as high as with the wetrunning type [Rin79]. Working cycle of screw compressors As with all positive displacement machines, the periodically occurring working cycle can be classified into characteristic phases. The gas exchange work steps, consisting of suction and discharge, as well as the work phase are run through. With a screw compressor, this consists only of compression, since the screw machine works without deadspace. In order to evaluate the quality of the compressor, a pV diagram is often used, which can be represented ideally by isobaric gas exchange and isentropic compression (Fig. 1). The red arrows symbolise the direction of rotation and the red marked rotor surfaces symbolise the working chambers to which the mentioned phase refers. As already mentioned, the screw machine works without deadspace. This means that a working cycle begins when a working chamber is created and steadily increases in size from there. Axial and radial openings in the housing provide a con- Introduction Fig. 1: Idealised pV diagram of a screw compressor 80 PROCESS TECHNOLOGY & COMPONENTS 2022

Compressors and Systems From the research nection to the low-pressure port (LP port) of the system. This connection usually exists until the working chamber reaches its maximum volume. The connection to the LP port is separated by driving over the LPside control edges. Now the working phase follows. During compression, the working chamber is encapsulated in that it is only connected to other working chambers via operational gap connections, but also temporarily to the LP and high-pressure side (HP side). The further rotation of the rotors causes the chamber to become continuously smaller, thereby increasing the energy content of the working medium in the form of pressure and temperature. The duration of the compression depends on the position of the HP-side control edges, which when passed over, create a connection to the HP port. The position of the HP-side control edges defines a chamber volume V compr,end at which compression ideally ends. Thus, if the maximum chamber volume V max is put into the ratio: (1) then the internal volume ratio v i is obtained, which is independent of the pressures in the suction and pressure ports and thus has a significant influence on the partial and overload behaviour of the system. If geometric variations are carried out, care should be taken to ensure that the internal volume ratio matches the rotor geometry used (profile, twisting, etc.), otherwise misinterpretations can quickly occur [Utr21]. The last step in the working cycle is the process of discharge, in which the working fluid is pushed into the HP port by further reducing the chamber volume. This process ends when the ejecting chamber disappears. The required indicated power P i of the compressor then results from the area formed in the pV diagram together with the number of working cycles (speed n × number of lobes of the male rotor z): (2) If the required internal capacity is related to the suction conditions converted volume flow rate the volume flow rate related to suction conditions indicated power, E i of the compressor results: (3) This is the amount of energy that the compressor needs to bring a suctioned volume of fluid to the desired pressure level. This variable is very suitable for comparing the quality of compressors and should be as small as possible. Rotor profile The first patent for a screw machine dates back to 1878 [Kri78]. However, the symmetrical rotors developed by Krigar could not run due to the kinematic conditions of the gearing law. It was not until 1934 that the development of the screw machine was resumed by the chief engineer at Svenska Rotor Maskiner (SRM) Lysholm. The asymmetric profile he developed represents a further development of the pair of helical rotors patented by Krigar. These rotors were only able to run when using a synchronisation gear. In 1952, the upswing of the screw machine began with the screw profile patented by HR Nielsson (also SRM), which was no longer designed to be completely airtight at the contact lines (there is a gap there). This profile represented the starting point for many of today’s screw machine profiles [Rin87]. An overview of frequently used screw profiles is given in [Sto05]. One possibility to generate rotor profiles of screw machines is the rack method. Fig. 2 shows an example of the rotors and the parameterised rack profile in the so-called normal plane (N-N). It is perpendicular to the profile pitch plane or the tooth flank. The front section plane is denoted by T-T. The angle β between the two planes is called the helix angle and is used to project the generated profile from the N-N plane to the T-T plane. The profile used here according to Wu [Wu08] consists of 9 segments that are continuously connected to each other at C 1 . Including the helix angle, there are 12 parameters with which this screw profile can be designed. Fig. 2: Representation of the parameters for designing a rotor profile using the normal rack generation method [Wu08] Gap situation During the operation of a screw machine, relative movements occur both between the rotors and between the rotor and the housing. For this reason, gaps are necessary between the components. When dimensioning these gaps, thermal expansion, mechanical deformation, bearing clearances and manufacturing tolerances of all components involved must be taken into account [Fos03]. On the other hand, gap connections cause undesired mass flow rates between the working chambers and partly from the HP side to the LP side. Depending on the boundary conditions at the gap, such as pressure ratio, rela tive movements and geometry, the influence of the gap varies greatly. Therefore, the investigation of gap flows for the simulation of screw machines is indispensable and is carried out in [Utr18a, Utr18b, Sac02, Pev07, Utr21], among others. There are four types of gaps found in a screw machine (Fig. 3.). The front and housing gaps are formed between the rotors and the housing and connect two adjacent working chambers. Their dimensions are essentially determined by the size and the wrap angle. The blowhole and the inter-lobe clearance, on the other hand, are strongly dependent on the selected profile shape. The calculation of the blowhole area is dealt with in [Nad17, Rin79, Sin88]. For rotor pairs that have a gap, the inter-lobe clearance PROCESS TECHNOLOGY & COMPONENTS 2022 81