Development of numerical analysis method of flow-acoustic resonance in stub pipes of safety relief valves

Figures & data

Figure 1. Propagation of acoustic-induced vibration from SRV to the steam dryer.

Figure 2. Mechanism of flow-acoustic resonance at the SRV stub pipe.

Figure 3. Calculation procedure of the conventional FDLBM [23].

Figure 4. Calculation procedure of the developed method.

Figure 5. Distribution of the molecule velocities c_{i α}  [26].

Table 1. Cartesian components of the molecule velocities [26], where and .

i	cix	ciy	ciz
1	0	0	0
2	0	c 1	c 2
3	0	−c 1	c 2
4	0	c 1	−c 2
5	0	−c 1	−c 2
6	c 2	0	c 1
7	−c 2	0	c 1
8	c 2	0	−c 1
9	−c 2	0	−c 1
10	c 1	c 2	0
11	−c 1	c 2	0
12	c 1	−c 2	0
13	−c 1	−c 2	0

Figure 6. Computational grid for simulation of the cavity driven flow.

Figure 7. Time-averaged flow in the cavity driven flow simulation.

Table 2. Comparison between the developed method and the conventional FDLBM [23].

Item	Developed method	Tsutahara's model [23]
Governing equation	Equation (9)	Equation (3)
Molecular velocity model	D3Q13	D3Q13
Spatial discretization	Sixth-order central difference	Sixth-order central difference
Time integration	Four-step second-order Runge-Kutta	Four-step second-order Runge-Kutta
Turbulence model	Dynamic Smagorinsky	Dynamic Smagorisnsky

Figure 8. Schematic presentation of the test facility [3].

Table 3. Physical properties of the fluid.

Item	Value
Temperature	20 [deg C]
Density	1.204 [kg/m^3]
Pressure	101.3 [kPa]
Speed of sound	343.7 [m/s]
Molecular viscosity	1.808 × 10^−5 [Pa s]

Figure 9. Computational grid for simulations of the flow-acoustic resonance.

Figure 10. Pressure fluctuations on the top of the SRV stub pipes at St = 0.36.

Figure 11. Amplitudes of the pressure fluctuations as functions of the Strouhal number.

Figure 12. Unsteady motion of the vortex at the stub pipe of SRV1 (left, vorticity; right, pressure).

Figure 13. Pressure distribution in the SRV stub pipes at St = 0.36.

Figure 14. Pressure distribution in the SRV stub pipes at St = 0.29.

Tsutahara , M. , Kataoka , T. , Shikata , K. and Takada , N. 2008 . New model and scheme for compressible fluids of the finite difference lattice Boltzmann method and direct simulations of aerodynamic sound . Comput. Fluids , 37 : 79 – 89 .

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