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Appl. Sci. 2020, 10, x FOR PEER REVIEW Appl. Sci. 2020, 10, 6824 P(θ,0) = P(θ,L) = P e P (θ , z ) = P ( 2π + θ , z ) P=P atrecess 5 of 14 5 of 13 (3) where P is the dimensionless pressure outside of the bearing and P is the dimensionless recess err pressure. The dimensionless recess pressure Pr is calculated using the flow continuity relationship where Pe is the dimensionless pressure outside of the bearing and Pr is the dimensionless recess between the dimensionless supply pressure Ps and the orifice restrictor, as follows pressure. The dimensionless recess pressure Pr is calculated using the flow continuity relationship between the dimensionless supply pressure Ps and the orifice restrictor, as follows ΛHi − H3 · ∇P · dl = Γt[2(Ps − Pr)]1/2 (4) 1 / 2 LiL ΛHi−H3⋅∇P ⋅dl=Γ 2 P−P i The dimensionless flow coefficient is defined as follows The dimensionless flow coefficient is defined as follows ()() (4) tsr 12μ pa Γ=12μCA pa (5) Γ=3 CA ttC3paddoo ρ (5) C pa ρ Bearing performance analysis was conducted based on the governing equation above, and the Bearing performance analysis was conducted based on the governing equation above, and the bearing stiffness and damping were calculated using the governing equation derived, using the bearing stiffness and damping were calculated using the governing equation derived, using the perturbation method from Equation (1) [21,22]. The finite element method was used to conduct a perturbation method from Equation (1) [21,22]. The finite element method was used to conduct a numerical analysis, and 120 × 60 grids were used in the circumferential and axial directions. numerical analysis, and 120 × 60 grids were used in the circumferential and axial directions. 3.2. Rotordynamic Analysis 3.2. Rotordynamic Analysis Figure 3 presents a rotor dynamics analysis model for predicting the vibration characteristics of Figure 3 presents a rotor dynamics analysis model for predicting the vibration characteristics of a pump-drive turbine. The pump-drive turbine can be considered an anisotropic rotor system that a pump-drive turbine. The pump-drive turbine can be considered an anisotropic rotor system that consists of a symmetric rotor and anisotropic stator. The equation of the motion of the anisotropic consists of a symmetric rotor and anisotropic stator. The equation of the motion of the anisotropic rotor system can be written as rotor system can be written as .. . [M]q(t) + [C]q(t) + [K]q(t) = f (t) (6) [M]q(t)+[C]q(t)+[K]q(t)= f (t) (6) w wh he erre e [[M M]], , [[C C]] a an nd d [ [K K] ] d de en no ot te e g ge en ne er ra al li iz ze ed d m ma as ss s,, d da am mp pi in ng g,, a an nd d s st ti ifff fn ne es ss s m ma at tr riix x,, a an nd d e ea ac ch h c co om mp po on ne en nt t of tthe mattriix can be derriived by fifiniitte eellementt metthod.. In this study,, the rottor was modelled usiing Euller–Bernoulllii beam ellementts,, whereas tthe pump,, turbine impeller,, and tthrustt colllar were modelled using tthe equiivallent iinerttiia.. In the analytical model, each node had two ttranslational degrees of freedomananddtwtowrotraotitoantiaolndaelgdreegsroeef sfreoefdofrmee. dTohme .stTiffhneesstiafnfndedssamanpdingdoafmbpeianrgingofwebreearcianlcgulwaterde bcaslceudlaotnedthbeaasfeodreomnetnhteioanfoerdembeeanrtiinognpederbfoeramrinangcpeearnfoarlmytaicnaclethaenoarly.tical theory. Figure 3. Rotordynamic analysis model for pump-drive turbine. (C.G.: center of gravity) Figure 3. Rotordynamic analysis model for pump-drive turbine. (C.G.: center of gravity) 4. Results and Discussion 4. Results and Discussion 4.1. Validation of Theoretical Model 4.1. Validation of Theoretical Model To validate the hydrostatic bearing analysis model developed in the present study, the computed results were compared with the data available in [22]. The hydrostatic bearing in [22] was a water-lubricatedPDF Image | Development of Pump-Drive Turbine Module Super CO2 Application
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