Flow-induced Noise and Vibration Analysis of a Piping Elbow with/without a Guide Vane

Tao Zhang, Yong’ou Zhang, Huajiang Ouyang and Tao Guo

1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

2. Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, Huazhong University of Science and Technology,Wuhan 430074, China

3. School of Engineering, University of Liverpool, Liverpool L69 3GH, UK

4. Beijing Institute of Spacecraft Environment Engineering, Beijing 100049, China

1 Introduction1

Pipeline systems used in industrial applications are characterized by large sizes and complexity, which have many long straight pipes and equipment connected by sharp bends (Wilsonet al., 2011; Sakakibara and Machida, 2012;Raniet al., 2014; Tanet al., 2014). Fluid flows through a sharp elbow are a very complex phenomenon. In the elbow region, the fluid near the inside of an elbow has a higher velocity while the fluid near the outside of an elbow has a lower velocity, which generates a large pressure gradient. As a result of the pressure gradient, unbalanced force appears in the fluid, which results in a secondary flow field downstream of the elbow, leading to flow-induced noise and vibration which are difficult to predict.

For turbulent flow, many experimental investigations have been carried out on the flow characteristics of curved ducts. Anwer and So (1993), So and Anwer (1993) made an experimental study of swirling turbulent flow through a curved bend. The competing effects of swirl and bend curvature on curved-pipe flow were analyzed and the recovery from swirl and bend curvature were assessed based on measurements. All measured data indicated that the flow displayed characteristics of axial symmetry and the turbulent normal stress distributions were more uniform across the pipe compared to fully developed pipe flows and the effect of bend curvature were to accelerate swirl decay in a pipe flow. Sudoet al. (2000, 2001) also did similar research with curved circular or square ducts. Besides, Takamuraet al.(2012) and Onoet al. (2011) visualized the turbulent flow in a single short elbow by means of two-dimensional particle image velocimetry. Flow-induced noise in elbows also attracts many researchers. Hambricet al. (2010) described a procedure which coupled computational fluid dynamics(CFD) and structural-acoustic models that can be used to compute the structure- and fluid-borne powers emanating from the ends of turbulence boundary layer excited by piping components. Zhanget al. (2010), Zhanget al. (2014a,2014b) and Zhanget al. (2014c) used hybrid methods based on large eddy simulation (LES) to simulate the flow-induced noise. Meanwhile, some researchers (Pittardet al., 2004;Maoet al., 2006; Firouz-Abadiet al., 2010; Niet al., 2011)have spent a significant amount of effort on studying vibration of pipes. Pa?doussis (1998) provided a comprehensive review of the related literature. He investigated linear, nonlinear and chaotic dynamics of straight and curved fluid-conveying pipes and distinguished vibrations in the plane of curvature and that perpendicular to it. Yamanoet al. (2011a, 2011b) and Shiraishiet al. (2006)studied the fluctuating pressures and the flow-induced vibration of primary cooling pipes in the Japan Sodium-cooled Fast Reactor (JSFR) with experiment and numerical simulation.

This paper combines CFD and finite element method(FEM) to predict noise and vibration induced by turbulent flow through a piping elbow with/without a guide vane.Firstly, flow distribution in a 90°piping elbow is computed through LES and the results are respectively used as acoustic source of flow-induced noise and excitation of flow-induced vibration. Secondly, the acoustic model of piping elbow is established and the flow-induced noise is simulated with Lighthill’s acoustic analogy method in commercial software Actran. Thirdly, the flow-induced vibration of piping elbow is solved based on a fluid structure interaction (FSI) code which conducts harmonic response analysis. Finally, results of flow-induced noise and flow-induced vibration with/without the guide vane are discussed.

2 Problem definition

The flow configuration in a 90°piping elbow is shown in Fig. 1. The pipe diameter (D) is 0.076 m and bend radius diameter (R) is 1.5D. It is known that the radial location of the guide vane has an evident effect on the flow regime. Modi and Jayanti (2004) carried out several simulations of different guide vane positions for the case of single guide vane in a 180°piping elbow. It was shown that the ideal radial position of a guide vane for a square duct was (RiRo)0.5considering the pressure loss of the elbow, whereRiandRoare the inner and outer radial of the guide vane, and it was the same as that found experimentally by Ito (1960) for a bend of circular cross-section. Therefore, in this paper the position of single guide vane is set to (RiRo)0.5. The thickness of guide vane is 0.003 m, and is equal to the thickness of piping wall. The flow entering the elbow region is water at 25°C, whose material properties are shown in Table 1. The pipe wall is steel, whose material properties are also shown in Table 1.

Fig. 1 90°piping elbow model

Table 1 Material properties of water at 25°C and steel

3 Numerical method

3.1 Large eddy simulation (LES)

The prediction of industrially important fluctuating flow problems, for instance, the region of turbulent flow through 90°piping elbow, can be performed using the technique of LES. LES is an approach which solves for large-scale fluctuating motions and uses “sub-grid” scale turbulence models for the small-scale motion, which means the near-wall region is not simplified by a wall-function. Instead,the boundary layer structure is resolved by refining the boundary layer mesh. Comparing with direct numerical simulation (DNS) which does resolve all scales, it costs decent time for results.

The governing equations for LES are obtained by filtering the time-dependent Navier-Stokes equations in the physical space. The filtered incompressible momentum equation can be written in the following way:

It includes the effect of the small scales and

The filtering processes effectively filter out eddies and decompose the flow variables into large scale and small scale parts. The large scale turbulent flow is solved directly and the influence of the small scales is taken into account by appropriate subgrid-scale (SGS) models. In this paper, the Smagorinsky model is adopted and theCsis set to 0.1.

3.2 Flow-induced noise

A LES and Lighthill’s acoustic analogy hybrid method is used to simulate flow-induced noise in this paper. In this method, the flow field information are obtained through LES with the CFD mesh first. Then, acoustics are simulated with commercial software Actran (Zhanget al., 2014a)using the Lighthill’s acoustic analogy theory and sound sources are solved with FEM and infinite element method(IFEM) as volume sources. The continuity equation and the momentum equation are simplified to get the Lighthill’s acoustic analogy equation:

Details and validation of this method have been given in our preliminary research (Zhanget al., 2014a, 2014b; Liuet al.,2013).

3.3 Fluid structure interaction (FSI)

FSI is a method for analysing flow-induced vibration.There exist two different forms of coupling approach:one-way coupling and two-way coupling. One-way coupling is a suitable option for cases where one field strongly affects the other field but not the other way around. Two-way coupling is a suitable option for cases where both two fields strongly affect each other. One-way coupling with no damping is used to analyse the flow-induced vibration in this paper.

The FSI algorithm is implemented using CFX Command Language (CCL) >amp; ANSYS Parametric Design Language(APDL). The FSI process for the computation of vibration is described as follows. Firstly, the nodal pressure fluctuation information and the node location information of the mesh of pipe wall are exported according to the CFD results.Secondly, the location information of nodes for structural analysis is collected from the mesh for structural analysis,and the correspondence of the location information of CFD nodes and nodes for structural analysis is built. Thirdly,according to the node to node correspondence, the interpolation between CFD nodes and nodes for structural analysis is made. The pressure simulation results of the pipe wall are translated to the loads of the flow-induced vibration simulation. The discrete loads acting on the inside wall are obtained from the averaged pressure on the small areas where individual loads are located. Finally, the loads are transformed from the time domain to the frequency domain and then the flow-induced vibration is computed with these loads. This approach had been introduced and used by Guoet al. (2012).

4 Boundary condition and mesh

Four different mean velocities (U) (2, 4, 6, 8 m/s) are simulated in this paper. The range of Reynolds number,based on the mean velocity and the hydraulic number is from 1.60×105to 6.81×105. Because LES models are by definition unsteady, proper initial conditions must be established for getting an accurate instantaneous solution.Therefore, proper initial conditions are required. For a proper inlet boundary condition, a straight piping model with diameterDand length 3Dis needed and a translational periodic interface which represents an infinite straight pipe is used. The RNGk-εmodel is used to solve for obtaining velocity profile of boundary. Inlet velocity profile at 4 m/s is shown in Fig. 2. Next, the profile data to the inlet boundary condition are prescribed and the flow across the entire elbow domain is initialized. The analysis types above are all of steady state. The final state of steady analysis is then used as the initial condition of LES.

Fig. 2 Inlet velocity boundary profile at 4 m/s

In the LES simulation, time step is set to 0.000 5 s, and 8000–12 000 time steps are taken to run until flows become statistically steady. Besides, the outlet of the elbow is in a pressure condition and the average pressure is zero, and the wall of piping elbow is no slip wall. A second order central difference has been used. Not every step is interesting, so only the last 1 000 time steps are saved and analyzed. In addition, two different meshes are used for complete simulation to cut down computation time. Different meshes are connected by general connection interface which can connect non-matching grids used in CFD. The details of the grids used in the CFD simulations are shown in Table 2 and the details of grids used in acoustic and structural simulations are shown in Table 3. The grid topology of these simulations is presented in Fig. 3. The minimum size of the mesh used in CFD is 0.05 mm and the mesh close to the guide vane is denser. The mesh in both upstream and downstream regions are obtained by gradually increasing the mesh size. In the LES computation,y+of the pipe wall is under 40 and most wall of the guide vane (except the sharp corner) is under 30. They+of the corner is less than 500.

Fig. 3 Grid topology (left: without the guide vane; right:with the guide vane)

Table 2 Details of the grids used in CFD

Table 3 Details of the grids used in the acoustic and structural simulations

In the following acoustic simulation, the wall of the elbow is set as a rigid wall while a semi-infinite duct is added onto the inlet and the outlet of the elbow. In the flow-induced vibration investigations, the wall thickness is constant, and it is much smaller than radius of curvature and the length of piping, which is modelled as a thin shell with the element type of shell 63. Furthermore, the 90°piping elbow is simply-supported and the fluid can be considered in a crude way as an increase of the density of the elbow wall.

5 Results and discussion

5.1 Flow field

The velocity vector field in the mid-plane of the bend with/without the guide vane at 2 m/s is shown in Fig. 4. In order to show velocity vectors clearly, a part of the velocity field, as marked by a box, is enlarged and presented in the same figure. The velocity vectors show the presence of vortices in the downstream region near the elbow. The vortices are caused by centrifugal force of the flow through the elbow and the vortex zone in the elbow without the guide vane is obviously larger than that with the guide vane.

Fig. 4 The velocity vector on the mid-plane of bend with/without guide vane at 2 m/s

5.2 Uniformity of velocity distribution

The velocity vector field provides qualitative information about flows, but it is difficult to quantify the effect of the guide vane on flow field using this alone. So the parameter of uniformity of velocity distribution for certain cross sections of the pipe is introduced to quantify the effect. The parameter representing the uniformity of velocity distribution at a time instant, is defined as

wherenis the number of nodes on a certain cross section;uniis the axial velocity of nodei;is the average axial velocity of a certain plane;Sistands for the edge area associated with nodei. Because of LES, uniformity at different time instants is not the same. The average uniformity over the simulated time interval is used in this paper.

Fig. 5 Variation of the uniformity of velocity distribution along with the distance from the elbow and the fluid velocity

Uniformity of velocity distribution is related to the location of cross sections and the mean velocity of flow. The location is shown in Fig. 5(a). Variation ofβwith distance from the elbow at 90°to the right at 2 m/s is shown in Fig. 5(b).βat the cross section located at 0.5Dis approximately 0.302 without the guide vane and 0.290 with the guide vane,and it decreases with the increase of distance. From 6Donwards,βbecomes almost constant at 0.186 and 0.176 respectively, which means that velocity fluctuation caused by an elbow gradually diminishes and the flow returns to normal.

Fig. 5(c) shows the relation between uniformity and velocity. The uniformity shown here is for the cross section at distance 7Dfrom the elbow at 90°, which is located in the stable flow region. Uniformity is seen to decrease with the increase of velocity. But an important point should be made here: at the same velocity, uniformity describes amplitude of velocity fluctuation. It can be seen that the guide vane reduces the amplitude of velocity fluctuation and obviously the guide vane is useful to stabilize the flow.

5.3 Sound pressure level and sound power level

Total sound pressure level and total sound power level betweenf0andf1are defined as follows:

The sound pressure level whenfD/Uis less than 5 is shown in Fig. 6. The tendency of sound pressure level has a certain correlation with pressure spectrum, but they are not all identical. The amplitude of sound pressure level at 2 m/s approximately stays the same whenfD/Uis under 3, and then it starts to decrease along with increase of dimensionless frequency. In the cases of 4, 6 and 8 m/s, the dimensionless frequency turning point of sound pressure level is about 2. Next, the sound pressure level starts to decrease. The total sound pressure level between 10 Hz and 1000 Hz is shown in Table 4. With increase of velocity, total sound pressure level becomes greater. The guide vane is seen to decrease total pressure level decline by 3.05–5.91 dB.The tendency of sound power level is similar to sound pressure level, and the guide vane decreases total sound power level by about 3.04–5.76 dB.

Fig. 6 Sound pressure level at different velocities

The total sound pressure and total sound power levels without the guide vane are all greater than those with the guide vane. Therefore, it can be concluded that the guide vane at the right location can reduce noise induced by turbulent flow through a 90°piping elbow.

Table 4 Total sound pressure level and sound power level between 10 Hz and 1 000 Hz

5.4 Vibration level analysis

The guide vane increases the mass of elbow and the stiffness of structure which would change the natural frequencies. There exists an intimate connection between the magnitude of flow-induced vibration and its natural frequencies. So it is necessary to assess guide vane’s influence on natural frequencies of the elbow. Table 5 shows the natural frequencies of the elbow without/with the guide vane.

Table 5 First six natural frequencies of elbow

Weighted vibration induced by turbulent flow is defined as

whereD0is the reference vibration (10?12m),Sithe edge area associated with nodeI, and(f) the weighted vibration with frequency.

Total weighted vibration level between the frequency off0andf1is defined as follows

where △fis the frequency resolution.

Weighted vibration level at different velocity is shown in Fig. 7. The amplitudes decrease along with increase of frequency and velocity, but they increase sharply at the natural frequencies. The total weighted vibration level of the elbow with and without the guide vane are shown in Table 6.The fourth column is the difference between the elbow without the guide vane and the one with one guide vane. It can be seen from the table that the vibration level rises up along with the increase of fluid velocity from 2 m/s to 8 m/s.Moreover, the presence of the guide vane can decrease the total weighted vibration level of elbow in all cases and the value of difference changes from 1.60 to 5.26 dB, and the bigger the velocity, the greater the vibration suppression it results in.

Table 6 Total weighted vibration displacement level between 10 Hz and 1 000 Hz

Fig. 7 Weighted vibration displacement level at different velocities

6 Conclusions

The noise and vibration induced by turbulent flow through a 90°piping elbow with/without the guide vane at different velocities are computed using LES. Flow-induced noise is simulated based on a LES/Lighthill hybrid method.Flow-induced vibration is a result of FSI. A conservative integration scheme is adopted and all nodal information is conserved in the process. The conclusions obtained in this paper are summarized as follows:

1) The range of the vortex zone in the elbow without the guide vane is larger than the case with the guide vane.Uniformity of velocity distribution decreases with the increase of distance right to the elbow and when the distance reaches some degree, uniformity becomes almost constant.

2) The guide vane decreases total weighted vibration level in the range of Reynolds numbers between 1.70′105and 6.81′105by 1.6–5.26 dB. The bigger the flow velocity, the greater the vibration suppression the guide vane results in.

3) Sound pressure level of the monitoring point has the same trend along with the increase offD/U. The guide vane decreases total sound pressure level in the range of Reynolds numbers between 1.70′105and 6.81′105by 3.05–5.81 dB and total sound power level by 3.04–5.76 dB.

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