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Energies 2019, 12, x FOR PEER REVIEW Energies 2019, 12, 2791 case 2). Second, a time step of 10 Energies 2019, 12, x FOR PEER REVIEW 18 of 22 s, giving a total number of 123-time steps (case 3). Finally, a time step of 10 s, with a total number of 1232-time steps (case 4), this case was not economical regarding the time step was set on 5 × 10−4 s, giving a total number of 24-time steps (this setup is referred to as −4 the simulation time and was used as a reference to evaluate the accuracy of other cases. Figure 23 case2)).. Second, a time step of 10 s,s,ggivivininggaatototatallnnuumbbeerrooff112233--titmimeesstteepss((ccaassee33))..Finally,,attiime − 5 compares the deviation of the total to total efficiency ( ) and total to static efficiency ( ) of the sttepoff1100 s,s,wwitihthaatototatal lnnuumbbeerrooff11223322-t-itmimeesstteeppss((ccaassee44)),,tthiisscassewasnotteconomiicallregardiing optimum outflow turbine at its best efficiency point, obtained from cases 1 to 3 with respect to the tthe siimullattiion ttiime and was ussed ass aarreeffeerreencceettooeevvaaluluaatteetthheeaacccuurraaccyyooffooththeerrccaasseess. . Fiigure 23 results of case 4. According to Figure 23, case 3 shows minor deviation from the case 4 (1% in and compares the deviation of the total to total effifficiency (η ) and total to static effifficiency (η ))off tthe t−t t−s 0.73% in ) but is more economical in terms of the computational cost. Therefore, case 3 with the opttiimum ouutflflow turbine at iits best effifficiiency poiint,, obtained from cases 1 tto 3 wiitth rrespectt tto tthe time step of 10 was selected as the final transient model to simulate the optimum outflow turbine’s ressullttssoffcase4.. According to Figure 23, case 3 shows minor deviation from the case 4 (1% iin ηt−t and efficiency in an unsteady fashion. In addition, Figure 23 shows that there is a 2% deviation in the 0..73%iinη ) )bbuut tisismmoorereeceoconnoommicicaal linintetermrmssooffththeeccoomppuutatatitoionnaallccoosstt..Therrefforre,,case3wiitthtthee t − s and less than 1% deviation in the of the MRF model (case 1) and the transient model (case 3) at −4 ttiimestep of 1100 wwasaseslelcetcetdedasasththeefifninaal ltrtarannsiseiennt tmooddeel ltotossimimuulalatetettheeopttiimumouttflflowtturbiine’’s effifficciieenccyiinanunstteadyffashiion.. In addition, Figure 23 shows that there is a 2% deviation in the η t−t At best efficiency point e1 the maximum efficiency point. andlleessstthhaann11%ddeevviaiatitoionnininththeeη ofothfethMeRMFRmFomdeold(ecals(cea1s)ea1n)datnhdethraentsriaenstiemnotdmelo(dcealse(c3a)seat3t)haet t−s mthaexmimauxmimeuffimcieefnficyiepnocyinpt.oint. 10 8 18 of 22 18 of 22 10 6 8 4 6 2 4 0 2 0 Computational Model Case2 Case3 Case4 Cas At bTe-Tst effiTc-iSency point T-T T-S Cas e2 Case3 Case4 Case 1 Figure 23. Time step study of the transient model and comparison of the deviation of Cases 1 to 3 Computational Model Figure 23. Time step study of the transient model and comparison of the deviation of Cases 1 to 3 from from the Case 4. the Case 4. Figure 23. Time step study of the transient model and comparison of the deviation of Cases 1 to 3 As the main concern of this study, the plot of the total to static efficiency ( ) of the optimum As the main concern of this study, the plot of the total to static efficiency (η ) of the optimum from the Case 4. t−s outflow turbine over the entire flow coefficient is compared for the MRF and the transient model in outflow turbine over the entire flow coefficient is compared for the MRF and the transient model in FigurAe 2s4t.hIetmisaoibnvcionucsetrhnaot fththeiesffistcuiednyc,ythpeloptlsoitnobfoththemtootadletlos fsotalltoicwesffaicsiiemniclyar(tren)d,oafntdhethoepstitmeaudmy Figure 24. It is obvious that the efficiency plots in both models follows a similar trend, and the steady model (MRF) has slightly overestimated the efficiency of the turbine for the whole flow coefficients. mouotdfleolw(MtuRrFb)inheasovsleigrhthtleyeonvteiresftloimwacteodeftfhiceieenffit icsiecnocmypoafrtehdeftourrbthineeMfoRrFthaendwthoeletrflaonwsiecnotemffiocdienltisn. Considering the volume of the computations in the optimisation studies, benefits of using the steady CFoignusridee2r4i.nIgt itsheobvvoilouumsethoaftttheeceofmficpieuntactyiopnlostisninthbeootphtmimoidsaetlisofnolsltouwdsieas,sbimenileafirttsreonfdu,saingdtthesteady model in this study strongly outweigh the 2% discrepancy and the MRF model can be regarded as an modelli(nMthRiFs)shtuadsyslsigtrhotnlygloyvoeuretwsteimigahtethdeth2%e edffiiscireenpcaynocyf tahnedtuthrbeiMneRfFormtohdeewl chaonlebfelorwegacordefefdicaiesnatns. accurate model. aCcocunrsaidterminogdtehl.e volume of the computations in the optimisation studies, benefits of using the steady model in this study strongly outweigh the 2% discrepancy and the MRF model can be regarded as an accurate model. 1 0.8 Optimum outflow turbine MRF Optimum outflow turbine Transient MRF Transient 0.6 0.8 0.4 0.6 0.2 0.4 1 0 0.20 0.5 1 φ 1.5 2 2.5 0 Figure 24. Comparison of effifficiency of the optimum outflflow turbine using MRF model (Case 1) and 0 0.5 1 φ 1.5 2 2.5 the transient model (Case 3). (Vertical axis: total-to-static efffificiency,, Horizontal axis: ffllow coeffifficient). Figure 24. Comparison of efficiency of the optimum outflow turbine using MRF model (Case 1) and The performance of the optimised outflow turbine, obtained from the transient model, was The performance of the optimised outflow turbine, obtained from the transient model, was the transient model (Case 3). (Vertical axis: total-to-static efficiency, Horizontal axis: flow coefficient). compared to the existing unidirectional axial and radial turbines (in their direct mode) in the compared to the existing unidirectional axial and radial turbines (in their direct mode) in the literature [16,22]. As Figure 25 illustrates, the outflow turbine has a peak efficiency of 71%, which has a literature [16,22]. As Figure 25 illustrates, the outflow turbine has a peak efficiency of 71%, which has The performance of the optimised outflow turbine, obtained from the transient model, was 21% improvement compared to the radial geometry suggested in [22]. It should be noted that the radial a 21% improvement compared to the radial geometry suggested in [22]. It should be noted that the compared to the existing unidirectional axial and radial turbines (in their direct mode) in the literature [16,22]. As Figure 25 illustrates, the outflow turbine has a peak efficiency of 71%, which has a 21% improvement compared to the radial geometry suggested in [22]. It should be noted that the η t-s η t-s % Devia%tionDeinvieaftfiiocnieincyefficiencyPDF Image | Unidirectional Radial-Air-Turbine OWC Wave Energy Converters
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