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Mathematics 2020, 9, 50 19 of 30 Mathematics 2020, 8, x FOR PEER REVIEW 20 of 34 Figure 21. Velocity streamline at 50% span (a) and 90% span (b), at design point (N = 40,000 rpm, PR = 6.9). Figure 21. Velocity streamline at 50% span (a) and 90% span (b), at design point (N = 40,000 rpm, PR = 6.9). 6.1.3. Results at Off-Design Points 6.1.3. Results at Off-Design Points To evaluate the performance of the turbine at off-design conditions, the pressure ratio is varied from 3 to 6.9, and the turbine inlet temperature is varied from 400 K to 471.55 K, To evaluate the performance of the turbine at off-design conditions, the pressure ratio is varied for two-speed lines (30,000 rpm and 40,000 rpm). from 3 to 6.9, and the turbine inlet temperature is varied from 400 K to 471.55 K, for two-speed lines • Different Pressure ratios and Rotational Speeds (30,000 rpm and 40,000 rpm). Mach number of the flow crucially influences the aerodynamic behaviour of turbines. Different Pressure ratios and Rotational Speeds It depends on the rotational speed, pressure ratio through the stage, and speed of sound of Mach number of the flow crucially influences the aerodynamic behaviour of turbines. It depends the working fluid. The results in the previous sub-section indicated that the flow choked at on the rotational speethde, pinrtesrsupraecera(tihoetgharpoubgehtwtehensstatagteo,raandsrpoetoerd).oTfhsiosumnedanofs theatwthoerktuinrbginfleuiodp.erates at a The results in the prfievxeiodumsassusbfl-soewctiroantei,nrdegicaartdeldestshoaftttheepfrleoswsucrheorkateido.aTthtihs,einintuernsp,arecseu(lthseingsahpockwaves and performance deterioration of the turbine. However, higher values of specific power are between stator and rotor). This means that the turbine operates at a fixed mass flow rate, regardless achieved at choked flow. Therefore, the turbine is designed to operate at choked conditions of the pressure ratio. This, in turn, results in shock waves and performance deterioration of the based on the simulation of the thermodynamic cycle. In the current CFD simulations, turbine. However, higher values of specific power are achieved at choked flow. Therefore, the turbine pressure ratio and turbine speed are under the control of the designer. For each run, they is designed to operate at choked conditions based on the simulation of the thermodynamic cycle. In are changed and the simulation is re-run as shown in the next paragraphs. the current CFD simulations, pressure ratio and turbine speed are under the control of the designer. Figure 22 presents temperature distribution, Mach number distribution, and velocity For each run, they are changed and the simulation is re-run as shown in the next paragraphs. streamlines through the turbine stage for different pressure ratios and rotational speeds. At Figure 22 presents temperature distribution, Mach number distribution, and velocity PR = 3 and 40,000 rpm, Figure 22a clearly shows that there is no choking at the interspace streamlines through the turbine stage for different pressure ratios and rotational speeds. At PR = 3 between the stator exit and rotor inlet, and the Mach number at this region is lower than and 40,000 rpm, Figure 22a clearly shows that there is no choking at the interspace between the stator 0.93. However, running the turbine at off-design points results in a non-optimum turbine exit and rotor inlet, and the Mach number at this region is lower than 0.93. However, running the performance which results in deficient flow as depicted by the velocity streamlines in the turbine at off-design points results in a non-optimum turbine performance which results in deficient figure. At 50% of the rotor blade, a flow recirculation is formed at the rotor leading edge in flow as depicted bythteheprveessloucrietysidsetr(eFaimgulirnee2s2ain), btheceaufisgeuorfe.thAetno5n0-%opotifmtuhme irnoctoidrenbclaedaen,gale,fbloewfore mixing recirculation is formeoduattwthiethrothtoermleaidnisntgreeadmg.eTinhethperepsrseussreureatsiiodeis(tFhigenurien2cr2eaa),sebdectaou4s.e5owf thhielentohne-rotational optimum incidence sapnegelde,isbmefaoirnetaminiexdincgonosutatntw.iAthssthoewmnaininFsitgruearem2.2bT,hMeapchrenssuumreberaitniocreiassethsesnignificantly compared to PR = 3, reaching sonic condition (Ma = 1). Moreover, strong vortices are increased to 4.5 while the rotational speed is maintained constant. As shown in Figure 22b, Mach created downstream of the blade suction surface. number increases significantly compared to PR = 3, reaching sonic condition (Ma = 1). Moreover, The simulation is then re-run again at two different pressure ratios (PR = 3 and PR = 6.9) strong vortices are created downstream of the blade suction surface. with 30,000 rpm as shown in Figure 22c,d. It is known that turbine size is inversely proportional to the turbine speed. Therefore, the turbine size with 30,000 rpm is considered overestimated which makes the flow does not follow the blade passage properly as shown in Figure 22c,d. Mach numbers in these cases are higher than that in Figure 22a,b, although they have the same pressure ratio. However, this is justified by the higher absolute velocities. Figure 22d presents the results at PR = 6.9 and 30,000 rpm. Compared to the 40,000 rpm (Figure 22a), Mach numbers are higher due to the higher velocities as shown byPDF Image | Generation of 3D Turbine Blades for Automotive ORC
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