MATHEMATICAL MODELLING OF THE CENTRIFUGAL COMPRESSOR

Faults frequently occur in the sensors and actuators of process machines to cause shutdown and process interruption, thereby creating costly production loss. centrifugal compressors (CCs) are the most used equipment in process industries such as oil and gas, petrochemicals, and fertilizers. A compressor control system called an anti-surge control (ASC) system based on many critical sensors and actuators is used for the safe operation of CCs. In this paper, an advanced active fault-tolerant control system (AFTCS) has been proposed for sensor and actuator faults of the anti-surge control system of a centrifugal compressor. The AFTCS has been built with a dedicated fault detection and isolation (FDI) unit to detect and isolate the faulty part as well as replace the faulty value with the virtual redundant value from the observer model running in parallel with the other healthy sensors. The analytical redundancy is developed from the mathematical modeling of the sensors to provide estimated values to the controller in case the actual sensor fails. Dual hardware redundancy has been proposed for the anti-surge valve (ASV). The simulation results of the proposed Fault-tolerant control (FTC) for the ASC system in the experimentally validated CC HYSYS model reveal that the system continued to operate in the event of faults in the sensors and actuators maintaining system stability. The proposed FTC for the ASC system is novel in the literature and significant for the process industries to design a highly reliable compressor control system that would continue operation despite faults in the sensors and actuators, hence preventing costly production loss.

This study aims to quantify and assess qualitatively the impact of modeling simplifications used to represent inertial and aerodynamic loads on the stresses and structural deformations of a centrifugal compressor in operation. The research object is the compressor of the high-pressure line of the DGEN 380 bypass turbine engine. Based on the virtual dynamometer WESTT CS/BV, the gas-dynamic parameters at the entrance to the centrifugal compressor and after the stage are determined. These values were used as initial parameters for numerical flow analysis. As part of the numerical strength analyses, a series of several load configurations were carried out: spin only, spin and inlet pressure normally applied on the working surface of the rotor blade, spin and outlet pressure normally applied on the working surface of the rotor blade, and one-way fluid–structure interaction analysis taking into account the aerodynamic loads with and without spinning. Based on the simulations, the level of similarity of a given load configuration with the last analysis, adopted as the reference, was determined. It was observed that in terms of the stress state, the rotational analysis taking into account the pressure on both sides of the blade gives satisfactory results, but the strain values are overestimated. The results obtained and the method of evaluation of compressor results can be used in research in the area of aviation, automotive, and refrigeration industries.

Turbochargers are widely used to help reduce the environmental impact of automotive engines. However, a limiting factor for turbochargers is compressor surge. Surge is an instability that induces pressure and flow oscillations that often damages the turbocharger and its installation. Most predictions of the surge limit are based on low-order models, such as the Moore–Greitzer model. These models tend to rely on a characteristic curve for the compressor created by extrapolating the constant speed lines of a steady-state compressor map into the negative mass flow region. However, there is little validation of these assumptions in the public literature. In this article, we develop further the first-principles model for a compressor characteristic presented in Powers, K., Brace, C., Budd, C., Copeland, C., & Milewski, P., 2020, “Modeling Axisymmetric Centrifugal Compressor Characteristics From First Principles,” J. Turbomachinery, 142(9), with a particular emphasis on reverse flow. We then perform experiments using a 58 mm diameter centrifugal compressor provided by Cummins Turbo Technologies, where we feed air in the reverse direction though the compressor while the impeller is spinning in the forward direction to obtain data in the negative mass flow region of the compressor map. This demonstrated experimentally that there is a stable operating region in the reverse flow regime. The recorded data showed a good match with the theoretical model developed in this article. We also identified a change in characteristic behavior as the impeller speed is increased, which, to the authors’ knowledge, has not been observed in any previously published experimental work.

Currently existing regulatory documents assume that refrigeration compressors are tested as part of test rigs with heat-exchange equipment. Given the high energy intensity of centrifugal compressors, the drive power of which in cooling mode with a cold capacity of up to 8.0 MW can be 2.0 or more MW, the creation of test rigs for preliminary and acceptance tests at the manufacturer’s factory requires a large investment. An alternative to the considered refrigeration centrifugal compressors test method is a test on a test rig in which the agent is partially condensed. In this case, an evaporator and a full-sized condenser are not required. The mathematical model of the refrigeration centrifugal compressors developed by JSC VNIIKHOLODMASH, allows testing of the refrigeration centrifugal compressors in model conditions, when the entire compressor operation cycle at the test rig is carried out in the area of superheated steam. Since the refrigeration centrifugal compressors mathematical model is based on physical simulation of compression processes in model stages at different values of conditional Mach numbers, dimensionless characteristics of model stages can be used to calculate the characteristic of the created compressor when operating under new conditions. The implementation of the model test method provides reduction of testing time due to absence of phase changes of the agent, improves the accuracy of the obtained results, reduces of power consumption, simplifies the test rig, and reduces consumption of the agent for filling the rig and water for cooling the agent.

Performance analysis of NH3/CO2 cascade refrigeration system using CO2 centrifugal compressor with gas bearing

Turbocharging technique has played a critical role not only for improving automotive engine performance, but also for reducing fuel consumption and exhaust emissions both in Spark Ignition and Compression Ignition engines. In the research described in this paper, a 1D centrifugal compressor model has been developed for simulating turbocharger flow and performance. The model takes into account energy conservation and transfer which includes the losses determined from the compressor geometry. The losses including incident loss, friction loss, clearance loss, backward loss and volute loss were simulated by the thermodynamics model, rather than from the characteristic performance curves obtained experimentally. The proposed model was validated against experimental data and it showed simulating and experimental results are in very good agreement at three different rotational speeds, in particular near the surge line, though the deviation begins to increase as mass flow rate goes up. With current results, it has suggested the proposal is suitable for predicting the compressor performance curves such as outlet pressure, efficiency and losses for any centrifugal compressor. In addition, surge line obtained from the simulation result can be used to define stable operation range.

For several decades in the process industry, critical plant operations demanding continuous run time have used high speed turbocompressors, most commonly driven by induction motors. Transient disturbances, caused by grid and motor-terminal upsets, are common occurrences in three-phase induction motors. Such upsets can arise during start-up as well as steady state operating conditions, and can have an impact on the driven equipment. Common upset conditions include startup line bursts, voltage unbalances, two-phase & three-phase short circuits, and bus-transfers & reclosures. These transient upsets not only impact the motor, but also have a torsional influence on the motor-compressor drive-train. Understanding the significance of these upsets, and how it impacts the driven equipment is thus an important part of machinery design and the component selection process for centrifugal compressors. This paper presents a qualitative approach to analyzing these transient conditions arising from induction motors, and the resulting effects on driven equipment such as centrifugal compressors. As the compression industry continues to develop into a globally integrated market, it becomes even more important to understand these effects; to ensure that a consistent global strategy exists to control these upsets and to mitigate some of the ill-effects resulting from torsional bursts on the drive train. A review of the current industry standards and mitigation techniques has also been presented.

Oil-free pressurized air is needed in several industrial fields, i.e. paper mills and in electronics manufacturing. The pressure level is rather high, 600 – 900 kPa, and the compressor type usually used in these applications are dry screw compressors and gearbox-driven centrifugal compressors. However, drawbacks of these kinds of compressors are wearing of the components, high maintenance costs and increased energy consumptions during the life-time. To tackle these drawbacks, the prototype of a two-stage centrifugal compressor was designed, manufactured and tested. Both compressor impellers and the electric motor are on the same shaft, and magnetic bearings are used to make the machine oil-free. Due to the high pressure level and two compressor stages, the centrifugal compressor needs to run at relatively high rotation speed. When the compressor has more than one wheel, the compressor power can be reduced and the overall efficiency increased with intercooling. In a two-stage compressor this means that the pressurized air after the first stage is cooled near to ambient temperature. As a result the compressor consumes less power, but intercooling causes a pressure loss to the system, which has to be taken into account. The compromise is needed with the same mass flow rate compressor stages is very restrictive, as the specific speeds can not vary much. The main difference comes from the different volume flows, as the density in the second stage is higher than in the first stage. The final optimizing of the efficiency takes into account the mechanical requirements with shaft critical speeds. The operation of the two-stage air compressor driven by a high-speed motor is rated at the point 800 kPa(g), 0.9 kgs−1, 300 kW and 60 000 rpm, respectively. The compressor stages are equipped with vaneless diffusers to maximize the operational range. The aerodynamic design based on the traditional in-house practice is verified with computerized flow dynamics using the Finflo-solver. The calculation does not include the volute, and the differences between the CFD results and the in-house design results are larger in the first stage of the compressor. Both compressor stages have been properly measured in a comprehensive test program following the measurement standards. The performances of the compressor stages at 80% speed are similar to the design data. At design speed both the efficiencies and pressures are lower than expected and the results indicate a need to improve the aerodynamic design.

The accuracy of a CFD model of a turbo-machine might depend on a number of factors: turbulence model, quality of the mesh model, boundary conditions, solver settings, consideration of secondary geometric factors, etc. The purpose of this work is to develop practical recommendations for CFD calculations of centrifugal compressors based on the validation of a model of NASA High Efficiency Centrifugal Compressor experimental radial compressor stage. Results of a grid independence test are presented, and the optimal grid size for the High Efficiency Centrifugal Compressor stage is identified as comprising 3 million elements. CFD-calculations of an experimental stage were performed with different turbulence models. The obtained data was compared with the NASA experimental data considering integral (total pressure ratio, mass flow rate, adiabatic efficiency) and differential parameters (static pressure distribution downstream the vaned diffuser). The required CFD computational time for different turbulence models was calculated. Based on the results of this research, recommendations were formulated for the application of SST, k–ε, BSL EARSM and GEKO turbulence models for numerical modeling of centrifugal compressors.

Methodology for experimental validation of a CFD model for predicting noise generation in centrifugal compressors

In view of the difficulty in establishing a precise centrifugal compressor model in the practical industrial processes, the paper use process data and adopt data-driven modelling method to build up centrifugal compressor model based on RBF neural network; In the light of the difficulty in achieving RBF network's neurons theoretically, the collaborative clustering was adopted. Through an example, it is indicated that collaborative clustering solve the neurons of RBF network well and the constructed model has a good performance in predicting the important performance parameter of centrifugal compressor - pressure ratio, implying that the constructed data-driven model can act as an important tool to serve production process.

In connection with reduction of volumes of transporting of gas through the gas-transport system of Ukraine the issue of the day is the rational loading of the compressor stations taking into account the technical state of gascompressor units. The mathematical model was developed in the article on principles of fuzzy logic, that gave an opportunity to define the technical state of gascompressor units that are working in parallel taking into account such parameters as the productivity of supercharger, expense of fuel gas, pressure and temperature on an entrance, pressure and temperature on the exit of centrifugal supercharger, temperature of products of combustion on an exit from the turbine of LP, frequency of rotation of shaft of the supercharger, temperature and pressure of environment, vibrospeed and vibroacceleration, speed of accumulation product of triggering in agile olive, concentration oxide nitrogen and carbon in exhaust-gas.
 The expense of fuel gas, that is measured by facilities of regular automation, depends on many factors such as atmospheric pressure, ambient temperature, physical and chemical properties of fuel gas, technical state and type of turbo-engine. All that grounds to consider the expense of fuel gas an unclear value. Experimental researches on the base of Bohorodchany compressor station showed, that unclear value the "expense of fuel gas" has Gauss function of belonging. Therefore the task of choice of optimal amount of aggregates working in parallel is formalized as a task of integer of the linear programming, the criterion of optimality in that is a cost of fuel gas that consumes the compressor station taking into account the technical state of gascompressor units and unclearness of expense of fuel gas.
 Efficiency of the worked out method is confirmed by calculations that are based on industrial data received during exploitation of Bohorodchany compressor station.

PurposeThis paper aims to investigate the flow of two-layered non-Newtonian fluids with different viscosities in an axisymmetric elastic tube.Design/methodology/approachA mathematical model was considered for this study to describe the flow characteristics of two-layered non- Newtonian Jeffrey fluids in an elastic tube. Because Jeffrey fluid model is a better model for the description of physiological fluid motion. Further, this model is a significant generalization of Newtonian fluid model. Analytical expressions for flux, stream functions, velocities and interface velocity have been derived in terms of elastic parameters, inlet, outlet and external pressures. The effects of various pertinent parameters on the flow behavior have been studied.FindingsThe volumetric flow rate was calculated by different models of Mazumdar (1992) and Rubinow and Keller (1972); from this it was found that the flux of Jeffrey fluid is more in the case of Rubinow and Keller model than Mazumdar. A comparative study is made between single-fluid and two-fluid models of Jeffrey fluid flows and it was observed that more flux and higher velocities were observed in the case of two-fluid model rather than single-fluid model. Furthermore, when both the Jeffrey parameter tends to zero and ratios of viscosities and radii are unity, the results in this study agree with those of Rubinow and Keller (1972).Originality/valueTo describe the fluid flow in an elastic tube with two-layered systems, the models and solutions developed here are very important. These results will be highly suitable in analyzing the rheological characteristics of blood flow in a small blood vessel because of their elastic nature.

Being able to measure 3-D flow velocity and volumetric flow rate effectively in the cardiovascular system is valuable but remains a significant challenge in both clinical practice and research. Currently, there has not been an effective and practical solution to the measurement of volume flow using ultrasound imaging systems due to challenges in existing 3-D imaging techniques and high system cost. In this study, a new technique for quantifying volumetric flow rate from the cross-sectional imaging plane of the blood vessel was developed by using speckle decorrelation (SDC), 2-D high-frame-rate imaging with a standard 1-D array transducer, microbubble contrast agents, and ultrasound imaging velocimetry (UIV). Through SDC analysis of microbubble signals acquired with a very high frame rate and by using UIV to estimate the two in-plane flow velocity components, the third and out-of-plane velocity component can be obtained over time and integrated to estimate volume flow. The proposed technique was evaluated on a wall-less flow phantom in both steady and pulsatile flow. UIV in the longitudinal direction was conducted as a reference. The influences of frame rate, mechanical index (MI), orientation of imaging plane, and compounding on velocity estimation were also studied. In addition, an in vivo trial on the abdominal aorta of a rabbit was conducted. The results show that the new system can estimate volume flow with an averaged error of 3.65% ± 2.37% at a flow rate of 360 mL/min and a peak velocity of 0.45 m/s, and an error of 5.03% ± 2.73% at a flow rate of 723 mL/min and a peak velocity of 0.8 m/s. The accuracy of the flow velocity and volumetric flow rate estimation directly depend on the imaging frame rate. With a frame rate of 6000 Hz, a velocity up to 0.8 m/s can be correctly estimated. A higher mechanical index (MI = 0.42) is shown to produce greater errors (up to 21.78±0.49%, compared to 3.65±2.37% at MI = 0.19). An in vivo trial, where velocities up to 1 m/s were correctly measured, demonstrated the potential of the technique in clinical applications.

Comparison of two axial fans for cooling of electromechanical actuators at variable pressure