Discuss about the Design Optimisation and Application of Rotary.
Currently, many industries and homes are resolving to use the alternative sources of energy which are renewable and environmentally friendly. People and industries are currently storing energy such that in case there is the need for an alternative energy to boost the supply of the grid, then these energy storage devices are used. Some of the energy storage devices that are currently being used include flywheel energy storage system, pumped-hydro, battery energy storage, and compressed air energy storage systems.
In 1928 was the year when the first theory of gas compression was developed by a Japanese scholar, Nahuse. However, the first practical compressor was invented later in 1934 a Swedish by the name Lysholm. This compressor had a 3/3 profile combination. Later on, many improvements were seen on the subsequent compressor designs. The twin-screw rotary compressor came into existence in 1960. It came along with many benefits such as lower cost, reduced size, higher capacity as well as options for high compression ratios operation. ?In the recent past, a lot of studies and research has been conducted on techniques for improving the rotor design and adiabatic and volumetric efficiencies (Wan et al, 2017).
Rotary air compressors are classified into two that is a single screw and twin screw air compressors. The screw air compressor can be used for the purposes of air compression through the screw action to attain an air pressure of 150 psi (10 atm) and output volume of 57m?3?/min (2000 cubic feet per minute). This compressed air can then be channeled to the compressed air energy storage system. The figure below shows the features of a rotary screw compressor that can be used for the purposes of air compression before channeling the compressed air to the energy storage system:
Compression of air generates heat; the air is warmer after the process of compression. During the process of expansion, heat is removed from the system. In case no heat is added, then the air will be much colder after expansion (Avinash et al, 2015). This heat produced during the compression of air by rotary air compressor can be stored and used during expansion. The figure below shows how the compressed air from the rotary air compressor will be channeled to the compressed air energy storage system (Taheri & Gadow 2017):
The development of appropriate screw compressor design for CAES or any other function critical processes such as advanced computerized designs, computational fluid dynamics, mathematical modelling, and experimental validation amongst others (Byeon et al, 2017). This paper focusses on mathematical modelling and advanced computerized design tool to optimize a better screw compressor for the compressed air energy storage and other applications. Screw machines are gaining popularity today for fluid compression and expansion jobs and are continuously replacing vane and reciprocating compressors (Bianchi et al, 2015). This calls for more research on design optimisation in order to come up with the ultimate best design that has higher adiabatic and volumetric efficiencies.
Screw air compressors are mechanical machines that raise the pressure of the gas by reducing the volume of the gas. Oil injected twin-screw air compressor is a simple device with twin rotational screw. Here, the lubricant (oil) is injected knowingly into the gas stream for absorbing the compression heat. This allows for an increased pressure ratio in a single stage without intercooling and at the same time offers crucial protection of the compressor from gases that may cause corrosion (He et al, 2018).
The rotors are a form of helical gears which have a uniform lead and parallel axes (Chua, 2015). Their rotors make line contact and have a meshing criterion normal to their axes in the transverse plane similar to the spur gears (Lim et al, 2017).
To begin the rotor profiling procedure, their first derivatives together with the coordinates of the profile points in the transverse plane of a rotor must be known. The condition for envelope meshing for screw rotors gives the condition of meshing either directly if the generating curves are presented on the rack of the rotor, or numerically if the curves are presented on the compressor rotors (Wang et al, 2018). This basically provides a general procedure by enabling the use of several arc curves. Furthermore, deriving the primary arc curves numerically allows such an approach even when only the primary curve coordinates are known, and their derivatives unknown.
The elements of the rack-generated ‘N’ profile are given as follows. The primary curves are outlined on the rack: C-D is a circle having a radius of r3 on the rack,
C-B is a straight-line,
A-B is a parabola having a constraint radius r1,
G-H-A are trochoids produced by circles of radii r4 and r2 from the gate and main in that order.
G-E is a straight-line
F-E and D-E are circles on the rack
For the rotor optimisation, rotor addendum, r0 and three rotor radii, r1, r2, and r3 are used as the main variables.
The rotor transverse plane coordinates together with rotor length and rotor lead are the basis of calculation of full compressor and rotor geometry such as rotor displacement, throughput cross-section, discharge and suction port coordinates, leakage flow and sealing line cross-section. Consequently, they will be used as input variables for the calculation of the screw rotor thermodynamic process. In addition, the built-in volume ratio is used together with the rotor addendum and the rotor radii as an optimisation variable. Whenever there is a variation in the input variables, r0, r1, r2, and r3 a recalculation operation must be done and perform a full transformation for the purposes of obtaining the current compressor and rotor geometry.
The thermodynamic and the flow processes algorithm applied has a mathematical model that comprises of a set of equations describing all the science of the screw compressor such as rotation angle and time, operating volume as well as mass and energy flow. These equations are then subjected to the processes of suction, discharge, and compression within the machine.
This mathematical model has a feature that uses energy equation in a form that generates internal energy rather than an enthalpy. This feature makes this model more convenient computationally, more so when investigating real fluids properties. Moreover, internal energy can only be presented as a function of specific volume and temperature only, thus pressure will be computed directly thereafter. The internal energy and volume derive all the thermodynamic and fluid properties remaining within the machine cycle then the computation is performed through several cycles until the solution converges (MA et al, 2015).
The equation of the conversion of internal energy is given by;
Where ???? is the main rotor rotation angle h=h(????) is the specific enthalpy ????=????(?q?) is the mass flowrate p=p(????) is the fluid pressure in the control volume of the working chamber
Q?=?Q?(?q?) is the transfer of heat between the surrounding of compressor and fluid
V=V?(?q?) is the compressor working chamber control volume
In the above equation subscripts in and out denotes inflow and outflow respectively.
The following equation denotes mass continuity
The instantaneous density ????= (????) is acquired from the instantaneous mass m which is in the control volume, thus the size of the instantaneous volume, V is given by ????=m/V.
The discharge and suction port flow are defined by their velocities and cross-sectional area. The compressor geometry provides the cross-sectional area, A which is regarded as a periodic function of the angle of rotation, ????.
Leakage is also significant in the total flow rate and plays a substantial role since it has an effect on the delivered mass flow rate, thus subsequently affecting the adiabatic and volumetric efficiencies of the compressor.
A substantial modification of the thermodynamic process in a screw rotary compressor occurs during oil or other fluids injection on the screw compressor for the purposes of sealing, lubrication or cooling. The gases and their condensate that mixes or comes out of the injected fluid should be separately accounted for. Fluids or oil is injected into the rotor compressor mainly for the purposes of cooling the gas and lubrication (Rane et al, 2014).
For oil-filled compressors, parameters such as injected oil, the temperature of inlet oil, and position of injection must be included in the optimisation as variables (He et al, 2015).
Runge-Kutta fourth order method is used to numerically solve the equation of internal energy, U, and mass, m using the appropriate boundary and initial conditions. The solution convergence is obtained after the difference between two successive compressor cycles is adequately small, since the initial conditions were selected arbitrarily (Wu et al, 2017).
Numerical/mathematical model of the compressor physical processes offers a basis for a more accurate calculation of the desired integral characteristics with an increased accuracy degree. The most significant properties are adiabatic efficiency, specifically indicated power, indicated power, isothermal efficiency, indicated efficiency, power utilization coefficient, compressor mass flow rate etc. (Bianchi & Cipollone, 2015).
A contemporary computer has the capacity and power to allow for a full multivariable optimisation of the compressor design as well as the profile of the rotor simultaneously. The total number of optimisation variables used was nine and they include; four radii, r0, r1, r2, and r3 for rotor profile parameters, built-in-volume ratio parameter for the compressor geometry, oil flow and compressor speed which are operating variables and position of injection and temperature which are oil optimisation parameters (Järvisalo et al, 2015).
A box-constrained simplex method was adopted in this case to obtain the local minima. A simplex is stochastically selected by the box method that represents an independent variable matrix and arrives at the optimisation target through calculation. Later on, these calculations are compared with the initial calculations then performing their minimizations. The constrained box method calculation results may minimize one or more optimisation variables (Thackery et al,
2017). Thus, offering an added flexibility to the compressor optimisation.
The optimisation results arrive at an estimation of the global minimum after being fed into the expandable database of the compressor. Later on, the database together with other test results can be used for the acceleration of the minimization process.
The dry air compressor exhibited 1-3 bar pressure for the discharge and suction pressure, while the oil flooded compressor showed a pressure of 1-8 bar for the discharge and suction. The condensation and evaporation temperatures were 40 and 5 degrees Celsius respectively for R-134A. All the compressors had their male rotor outer diameters and centre distance kept constant at 128.45 and 90 mm in that order.
The criterion of optimisation was the lowest compressor specific power. Owing to that, three rotor profiles which are distinctively different were computed. They include one for oil-flooded air, another for oil-free air and the other for refrigeration compression. Figure 4-6 gives the illustration (Kovacevic et al, 2014). Table 1 below gives their geometrical profiles as well as the compressor optimisation results.
For instance, detailed analysis of the gate rotor addendum can lead to a conclusion that the addendum and the size of the area of the rotor blow-hole are proportional. Thus, smaller r0 should be made so that the blow-hole area can be minimised. Ideally, r0 should be equal to or less than zero. However, its reduction would result in a reduction in the cross-sectional area of the fluid flow, thus a corresponding decrease in the flow rate and volumetric efficiency. Therefore, a lower limit for the value of r0 is appropriate in order to get the best results (Gopalakrishnan et al, 2014).
The compressor design parameters, as well as the screw compressor profile obtained by calculation, must be put into consideration under extreme caution, as in the case of multivariable optimization result. This is because of the fact that multivariable optimisation is prone to only finding local minima, that may not be the best global optimisation result (Fujimoto et al, 2015). Thus, before arriving at the final compressor design decision extensive calculation is in order. Figure 9: specific power as a function if compressor built-in speed and volume
Further analysis was carried out for the dry air compressor due to its compression which is almost similar to that of an adiabatically compressed ideal gas where the isentropic exponent has a value of 1.4 which is relatively large. Radii r0-r3 are considered for the influence of optimisation variables on the specific power of the compressor (Qin et al, 2017). Figure 6 illustrates the influence of the gate rotor tip addendum and the gate rotor radius, r0 and r3 respectively n addition to the radii of the main rotor, r1, and r2. Figure 7 illustrates the influence of compressor speed and compressor built-in volume ratio.
Conclusions
This research has conducted a comprehensive multivariable optimisation of the rotary screw compressor operating conditions as well as its geometry for the establishment of the ultimate best design of the compressor for any application, especially compressed air energy storage. This is attributed to the use of computer program which offers the lobe segment general specifications with respect to several parameters and that can lead to the generation of various shapes of lobes. Thus, the working volume and the instantaneous area of cross-section could be repetitively computed with respect to the angle of rotation. The computer program contains a mathematical model of the fluid flow and the thermodynamic processes together with the models of processes that exist in real machines, for instance, variable fluid leakage, losses due to friction and heat loss to the surrounding, fluid flooding and other fluid injection and other effects. These factors are expressed in a differential manner with respect to an increase in the angle of rotation. These equations’ numerical solutions aid in the calculation of compressor efficiencies, power, screw compressor flow, specific power amongst others.
An example of a rack generated profile in ? configuration rotors of 106mm was applied for showing how optimisation allows for both higher efficiency and better delivery without at a constant tip speed. To achieve a defined optimisation target, the multivariable optimisation of the machine geometry together with its working conditions/parameters apply such rotor geometrical parameters as compressor built-in ratio, injection position, temperature and oil flow, compressor speed, as well as the main and gate tip radii.
References
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Byeon, S. S., Lee, J. Y., & Kim, Y. J. (2017). Performance Characteristics of a 4× 6 Oil-Free Twin-Screw Compressor. Energies, 10(7), 945.
Chua, M. H. (2015). Experimental investigation of inlet air temperature on input power in an oil-flooded rotary screw air compressor. The University of Alabama.
Fujimoto, H., Nishimura, H., & Kawabata, N. (2015). U.S. Patent No. 9,057,374. Washington, DC: U.S. Patent and Trademark Office.
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