Investigations on Leakages in Rotary Positive Displacement Machines

Abstract

Energy efficiency has become a necessity in today's world because it reduces greenhouse gas emissions, energy import demand, and energy costs. Electric motor-driven systems (EMDS) receive the most attention among all industrial products as they consume nearly half of all the electricity used in the industry and have a high potential to improve system energy efficiency and reduce total global electricity consumption by 10%. As a result, many countries have implemented both mandatory and voluntary efficiency standards for motor-driven products, including positive displacement machines. As the performance of positive displacement machines is dependent on a variety of operating and geometric parameters, these key parameters must be investigated in order to find ways to improve these machines' energy efficiencies. Internal leakages, operating clearances, and thermo-fluid-solid interaction are critical research areas for reducing thermodynamic losses and improving performance because they are one of the most important parameters in positive displacement machines. The clearances and leakages through these clearances are important factors in determining the capacity, power consumption, and thus the efficiencies of positive displacement machines. For an accurate prediction of the leakage flow, a thorough understanding of the flow coefficients and the effect of dimensionless numbers on flow coefficients is required. The current study focuses on the experimental investigation of leakage, the derivation of flow coefficient correlations, and the application of the derived correlations to predict the performance of twin-screw compressors as a case study using SCORGTM. In the present study, the leakage flow rates through the clearance gaps (for given shapes, sizes, and pressure conditions) are calculated using isentropic nozzle equations and compared with the experimental results obtained using a test rig to derive the flow coefficients. The derived flow coefficients are presented in terms of dimensionless numbers, which include pressure ratio, β ratio, aspect ratio, Reynolds number, and Mach number for the clearances to analyze the effect of these parameters on the flow coefficients. The experimental results were compared with the analytical results, and the mean deviation of the experimental results in comparison to the analytical results for circular clearance leakages was observed as +9.1%, which is significantly less than the mean deviation for rectangular clearance (+26.8%). The flow coefficients vary from 0.88 to 0.96 and 0.74 to 0.98 for the circular clearance and rectangular clearances, respectively. As a part of the case study, the performance of twin-screw compressors is predicted using SCORGTM which is a specialized software used for design and analysis of positive displacement machines. SCORGTM uses standard flow coefficient correlation (named Model 1 in the present study) recommended by ISO5167-1 to predict the performance of the twin-screw compressor. The performances of oil-free and oil-injected twin-screw compressors of various sizes are predicted using the thermodynamic module of SCORGTM using the original flow coefficient correlation model and the experimentally derived flow coefficient correlation based models for various speed and pressure conditions. The performance predictions of oil-free twin-screw compressors (of the N35 profile) at three different speeds and at a discharge pressure of 2.0 bar were performed using all three models and compared with the experimental results (from available published literature). In comparison to the available published experimental results for an oil-free N35 profile twin-screw compressor, the proposed flow coefficient correlations (used in the SCORGTM - based Case Study) predicted the compressed airflow within 5.32% and power within 0.8%. For analysis of working/operating clearances in screw compressors, further studies using SCORGTM were conducted, and the operating clearances were derived by iteratively matching the proposed model results with the experimental results. The performance predictions using various models were extended to oil-free (with adjusted operating clearances) and oil-injected (with design clearances) twin-screw compressors of various speeds, discharge pressures, and sizes. Due to higher temperatures and poor sealing in the absence of oil, the difference in results of compressed air flow derived from the original and proposed models was greater in the case of an oil-free compressor than in the case of an oil-injected compressor. As the leakage clearance structures of most positive displacement machines can be simplified into rectangular or circular shapes, the flow coefficient empirical relationships derived and presented in this study can be used along with the isentropic nozzle equations to estimate leakage in positive displacement machines for various clearance size, shape, and pressure conditions.

Keywords: Positive Displacement Machines, Performance, Leakages, Clearances, Experiment, flow coefficient, isentropic nozzle, SCORGTM