Computational Fluid Dynamics 114 flashing Ca Ca Ca v p 4. Fluid Induced Vibration. (FIV)          0 1020304050 Cavitation number Speed m/s Cavitation number Expon. (Cavitation number) Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 115 • • Computational Fluid Dynamics 116 Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 117                                                 ψ pp φ pp A B V c φ pp                         f r Dh                                                Computational Fluid Dynamics 118 Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 119 5. Fluid Induced Noise (FIN)                            T ij                            • • Computational Fluid Dynamics 120 Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 121 Computational Fluid Dynamics 122 [...]... the vortical flow Circumferential velocity m/s 0.20 0. 15 0.10 3 Flow rate m /s -4 0. 75 x 10 -4 Experiment 1.0 x 10 -4 1. 25 x 10 -4 0. 75 x 10 -4 CFD 1.0 x 10 -4 1. 25 x 10 0. 05 0.00 0.00 0.01 0.02 0.03 0.04 0. 05 0.06 0.07 0.08 Radius from center of vortical flow m Fig 5 Cicumferential velocity in CFD result of Moji's experiment 140 Computational Fluid Dynamics Downward velocity m/s 0.10 0.00 -0.10 3 Flow... Nuclear engineering and 132 Computational Fluid Dynamics Nuclear Engineering and Design, Goodard Institute for Analysis dates Journal of fluids and structures pressure vessel technology fluidos Journal of El método de los elementos finitos Vol 3, dinámica de Finite element in fluids New trends and applications Turbulence in fluids Noise Induced Transitions Mecánica de fluidos Fluid Dynamics of Cavitation... Fluid Instabilities Practical Approach S0 a N d r L V0 x 6 Fluid induced instabilities • • • • • • • • • • • 123 124 Computational Fluid Dynamics • • • • xi = f ( xi ) + g ( xi )·ε (t ) + ε D Σ(x j − xi ) + A cos(w·t ) + B cos(Ω·t ) 2·d Turbulence, Vibrations, Noise and Fluid Instabilities Practical Approach xi = ε ·K1 · x − K 2 · x − K 3 x 3 + η ·ζ xi = x(ε · K 1 − K 2 ) − K 3 x 3 + η ·ζ 1 25 126 Computational. .. = ε ·K1 · x − K 2 · x − K 3 x 3 + η ·ζ xi = x(ε · K 1 − K 2 ) − K 3 x 3 + η ·ζ 1 25 126 Computational Fluid Dynamics xi = x· K 1' − K 3 x 3 + η ·ζ ζ • • η Turbulence, Vibrations, Noise and Fluid Instabilities Practical Approach 127 128 Computational Fluid Dynamics 129 Turbulence, Vibrations, Noise and Fluid Instabilities Practical Approach Instantaneous frequency -3 4 x 10 2 0 -2 -4 0 200 400 600 800... 200 400 600 800 1000 Time (s) 1200 1400 1600 1800 2000 0.04 Phase 0.02 0 -0.02 -0.04 -0.06 Flow (Total -56 50) t/h 200 100 0 -100 -200 130 Computational Fluid Dynamics StdDev( F ) = 30.02 + 7 Conclusion A B2 −1 Flow(t / h) 2 131 Turbulence, Vibrations, Noise and Fluid Instabilities Practical Approach Fluid type // condition Turbulence effect Affected area • • • • “Linearity is an idea sought after, yearned... 2 CF D 10 4 10 142 Computational Fluid Dynamics the GE phenomena (open plots) occurs when the downward velocity gradient becomes large Therefore, the authors determine the second onset condition for the bubble pinch-off type of the GE phenomena empirically as * αCFD < 10 −7 ( 15) The occurrence of the GE phenomena in FRs is predicted by using these two conditions (Eqs 14 and 15) 3 .5 Application to GE... a strict solution of the axisymmetric Navier-Stokes (N-S) equation: 1 ur = − α r , 2 ⎡ ⎧ ⎛r Γ ⎪ uθ = ∞ ⎢1 − exp ⎨ − ⎜ ⎜ 2π r ⎢ ⎪ ⎝ r0 ⎣ ⎩ (3) ⎞ ⎟ ⎟ ⎠ 2 ⎫⎤ ⎪⎥ ⎬ , ⎪⎥ ⎭⎦ (4) 136 Computational Fluid Dynamics uz = α ( z − h∞ ) , (5) where r, θ and z show the radial, tangential and axial directions, respectively (ur, uθ and uz are the velocity components of each direction) α is the downward velocity gradient,... is applied to the outlet The transient CFD is performed for over 100 seconds to obtain the quasi-steady result Vessel diameter 200 mm Water depth 250 mm Inlet width 20mm Outlet diameter 12 .5 mm Fig 4 Computational mesh for CFD of Monji's experiment Figure 5 shows the comparison of the circumferential velocity distributions in the experimental and CFD results It is evident that the CFD result agrees... description of GE phenomena The GE phenomena can be observed in a lot of industrial plants with gas-liquid interfaces, e.g pump sump Therefore, the GE phenomena have been studied theoretically and 134 Computational Fluid Dynamics experimentally in many years (Maier, 1998) In the experiments, the onset condition of the GE phenomena in a reservoir tank or main pipe with branch pipe was investigated in detail As... of the vessel As for the working fluids, water and air at room temperature are employed in those simple experiments Fig 2 Schematic view of Moriya's experimental apparatus The first experiment was performed by Moriya (Moriya, 1998) As shown in Fig 2, the inner diameter of the cylindrical vessel and outlet pipe are 400 and 50 mm, respectively The water depth is kept at 50 0 mm The water is driven by a . • Computational Fluid Dynamics 120 Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 121 Computational Fluid Dynamics 122 Turbulence, Vibrations, Noise and Fluid. (Total -56 50) t/h Computational Fluid Dynamics 130 1 )/( 02.30)( 2 2 − += htFlow B A FStdDev 7. Conclusion Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 131 Fluid. number) Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach. 1 15 • • Computational Fluid Dynamics 116 Turbulence, Vibrations, Noise and Fluid Instabilities. Practical Approach.