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Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder
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ScienceDirect Publishing Services by Elsevier International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 http://www.journals.elsevier.com/international-journal-of-naval-architecture-and-ocean-engineering/
Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder Yo-Seb Choi a,b, Woen-Sug Choi a,b, Suk-Yoon Hong a,b, Jee-Hun Song c,*, Hyun-Wung Kwon d, Han-Shin Seol e, Chul-Min Jung f a
Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea b Research Institute of Marine Systems Engineering, Seoul National University, Seoul, Republic of Korea c Department of Naval Architecture and Ocean Engineering, Chonnam National University, Yeosu, Republic of Korea d Department of Naval Architecture and Ocean Engineering, Koje College, Koje, Republic of Korea e Advanced Ship Research Division, Korea Research Institute of Ships and Ocean Engineering, Daejeon, Republic of Korea f The 6th R&D Institute-3rd Directorate, Agency for Defense Development, Changwon, Republic of Korea Received 22 October 2016; revised 2 February 2017; accepted 6 February 2017 Available online ▪ ▪ ▪
Abstract Recent research has shown that quadrupole noise has a significant influence on the overall characteristics of flow-induced noise and on the performance of underwater appendages such as sonar domes. However, advanced research generally uses the Ffowcs WilliamseHawkings analogy without considering the quadrupole source to reduce computational cost. In this study, flow-induced noise is predicted by using an LES turbulence model and a developed formulation, called the formulation Q1As method to properly take into account the quadrupole source. The noise around a circular cylinder in an underwater environment is examined for two cases with different velocities. The results from the method are compared to those obtained from the experiments and the permeable FWeH method. The results are in good agreement with the experimental data, with a difference of less than 1 dB, which indicates that the formulation Q1As method is suitable for use in predicting quadrupole noise around underwater appendages. Copyright © 2017 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Quadrupole noise; Circular cylinder; Acoustic analogy; Formulation Q1As method; OpenFOAM
1. Introduction In the flow-induced noise of a given means of transportation, quadrupole noise grows in importance as speed increases. Lighthill proved the significance of quadrupole noise in aero-acoustics by discovering that it is proportional to the cube of the Mach number, for applications in the air, compared the predictions from experimental results (Lighthill, 1952). In the case of an underwater environment, quadrupole noise has not been considered as object of calculations for flow-induced * Corresponding author. E-mail address: [email protected] (J.-H. Song). Peer review under responsibility of Society of Naval Architects of Korea.
noise because it has a negligible magnitude from the point of view of radiated noise. However, researchers have recently found that quadrupole noise is important for determining the overall properties of the far-field radiated noise in an underwater environment (Ianniello et al., 2014). In addition, underwater appendages, such as sonar domes, can be affected by the self-noise produced by flow-induced noise, thus decreasing their performance. Therefore, it is important to predict the quadrupole noise generated by vortex shedding around appendages in an underwater environment. Quadrupole noise can be predicted using acoustic analogy methods that were originally developed for aero-acoustics. Lighthill (1952) was the first to produce a wave equation for an acoustic analogy with a noise source for an arbitrary flow.
http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002 2092-6782/Copyright © 2017 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Curle (1955) expanded Lighthill's analogy to also consider a stationary body, and Ffowcs Williams and Hawkings (1969) further developed the analogy by considering a moving body with arbitrary motion, which is referred to as the Ffowcs WilliamseHawkings (FWeH) analogy. The FWeH analogy has the advantage over other acoustic analogy methods that it models noise using three source terms to which physical meanings can be given: thickness noise, loading noise and quadrupole noise (Ffowcs Williams and Hawkings, 1969). However, the use of quadrupole noise in the FWeH analogy is complicated since it is non-linear and incurs in highcomputational costs. Therefore, the generation of a direct calculation method is being actively studied (Wang et al., 2006; Ansys, 2009). Schmitz and Yu (1977) calculated quadrupole noise using the two-dimensional airfoil theory, but the predicted peak amplitudes generally show poor correspondence with experimental data. Hanson and Fink (1979) also included a quadrupole source for the two-dimensional airfoil at subsonic, transonic and supersonic speeds; they, indicated that, compared with experimental data, the results improved by adding the quadrupole source. Despite the importance of the quadrupole source, it remained difficult to predict the sound source of the Lighthill stress tensor, and there was a lack of computational power to calculate it. To overcome these challenges, Farassat and Brentner (1987) developed a new quadrupole source in the FWeH analogy for a helicopter rotor; this method uses a calculation method similar to that used when the thickness and loading noises are considered surface integrals. Furthermore, a generalized formula was developed to compute the quadrupole source by using its strength, the formulation Q1A method, avoiding the calculation of time derivatives that involve significant computational costs (Brentner, 1997). A comparison between the formulation Q1A and permeable FWeH methods, which calculate quadrupole noise by computing the thickness and loading noises on a permeable surface as indirect effects was carried out in air circumstances; the results indicate that the formulation Q1A method is in better agreement with experimental data than the permeable FWeH method (Brentner and Farassat, 2003). In an underwater environment, Choi calculated the quadrupole noise around a circular cylinder using the expanded permeable FWeH method for a stationary object as indirect effects (Choi et al., 2016). However, research into the direct calculation of quadrupole noise is insufficient to date, and further improvements in accuracy are needed. In general, this study uses a hybrid method with a turbulence model and an acoustic analogy method in order to calculate the flow-induced noise with quadrupole noise around a circular cylinder in an underwater environment, reducing the computational expense. A large-eddy simulation (LES) turbulence model from CFD is used for the CFD calculations. The formulation for the stationary object, which is referred to as the formulation Q1As method, is developed from the formulation Q1A method and is used for the acoustic calculation. The solver developed for the CFD calculations, and the acoustic calculation of the formulation Q1As method is based
on the OpenFOAM platform, an object-oriented, open source CFD tool-kit (Jasak, 2009; Weller et al., 1998). Acoustic experiments and the permeable FWeH method were used to verify the results of the analysis using the formulation Q1As method and its performance. Summarizing, the formulation Q1As method is a more robust method to correctly calculate quadrupole noise compared to the permeable FWeH method. 2. Theoretical background 2.1. Quadrupole noise of acoustic analogy Lighthill first provided an analogy derived from comparing the exact equations of fluid motion with acoustic wave equations, as follows (Lighthill, 1952), 1 v 2 r0 v2 Tij 2 0 2 V r ¼ 2 c vt vxi vxj
ð1Þ
Tij ¼ rvi vj þ pij c2 r0 dij
ð2Þ
where c is the velocity of sound in a fluid, and r0 ¼ r r0 is the density perturbation. Tij is Lighthill's stress tensor, which is calculated to consider the quadrupole noise. vi and pij indicate the velocity component in the xi direction and the compressive stress tensor, respectively. Curle expanded the research of the acoustic analogy to a rigid surface (Curle, 1955). Ffowcs Williams and Hawkings developed their theory from the acoustic analogy of Lighthill by applying it to a solid object in arbitrary motion, and this method is now known as the FWeH equation, which is given as follows (Ffowcs Williams and Hawkings, 1969), 1 v 2 p0 v v V2 p0 ¼ ðr0 vn jdðf ÞjÞ ðpni dðf ÞÞ c2 vt2 vt vxi v2 þ Hðf ÞTij vxi xj
ð3Þ
where f represents the moving surface as an implicit definition by the function f ðx; tÞ ¼ 0, and f > 0 indicates the outside surface. On the right-hand side of Eq. (3), the first term is the thickness noise as a monopole source modeled from the displacement of fluid that results from the object passage. The second term is the loading noise as a dipole source resulting from the pressure distribution on the surface. The third term, expressed in the quadrupole source, is the quadrupole noise and indicates that the fluid is unsteady, as a Reynolds stress. Farassat developed formulation 1A from the FWeH equation into integral forms as follows (Farassat, 2007): 2 3 Z _ _ b M r r v v r n n i i 0 0 4 5 dS 4pPThickness ¼ 2 3 rð1 Mr Þ rð1 Mr Þ f ¼0 ret # Z " 2 r0 cvn ðMr M Þ dS ð4Þ þ 3 r 3 ð1 Mr Þ ret f ¼0
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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3 _ b M pcosq r i i 4 5 dS 4pPLoading ¼ 2þ 3 crð1 Mr Þ crð1 Mr Þ f ¼0 ret # Z " 2 pcosq ðMr M Þpcosq þ dS þ 3 r 2 ð1 Mr Þ r 2 ð1 Mr Þ Z
2
staggered vortex steer emerge considering accuracy and calculation cost.
_ pcosq
2.2. Development of formulation Q1As for a stationary object
ret
f ¼0
ð5Þ 4pPQuadrupole ¼
v2 vxi xj
Z V
Tij dV rj1 Mr j ret
ð6Þ
where r ¼ jx yj, where x and y indicate the observer position and the source position, respectively. 1 Mr is the Doppler factor and the kernel of the integration evaluated in retarded time t ¼ t r=c. The turbulence term that is represented as a quadrupole source needs to be calculated by volume integration. It is difficult to determine the volume around a solid object over which to integrate and evaluate the kernel of the integration, because of the complexity introduced by the non-linearity (Farassat and Brentner, 1987). To avoid volume integration indirectly, Di Francescantonio (1997) developed a permeable FWeH method by taking advantage of two methods, the Kirchhoff and the FWeH methods, to make a prediction for a hovering rotor. Z 4pPpermeable FWH ¼ S
2
3
_ _ 4 Un þ Ur 5 dSðhÞ rð1 Mr Þ2 ret # Z " _ run r M þ cðMr M 2 Þ
dS ðhÞ 3 r 2 ð1 Mr Þ ret S 2 3 Z _r L 5 dSðhÞ þ 4 2 crð1 Mr Þ S ret # Z " Lr Mr dSðhÞ þ 2 r ð1 Mr Þ3 ret S 2 3 Z Lr r M_ r þ cðMr M 2 Þ 5 dSðhÞ þ 4 3 cr 2 ð1 Mr Þ
þ
S
3
The formulation Q1A method was developed to make a precise, direct calculation of the quadrupole noise for a helicopter-rotor (Brentner, 1997). The formulation is calculated by conducting a surface integration of the terms composed of the quadrupole source strength, including Lighthill's stress tensor. Using these, the turbulence term in the FWeH equation is computed directly, resulting in high accuracy for the flow noise. The quadrupole noise from the quadrupole source is expressed before developing the formulation Q1A method as follows (Farassat and Brentner, 1987), 1 v2 4pPQuadrupole ¼ c vt2
where Ui is the mass-like flux, Li is the momentum flux, and h is the moving coordinate system along the control surface. The permeable FWeH method calculates the turbulence term indirectly by establishing a permeable surface. Accordingly, the quadrupole noise inside the surface is included in the calculation of the thickness and loading noises on the permeable surface as indirect effects (Wang et al., 2006; Farassat, 2007). From our experiences, the permeable surface is set with a size that includes 3 to 5 vortex eddies up to
Z
∞
f >0
Z f >0
Trr v dUdt þ vt r
3Trr Tii dUdt þ c r2
Z
f >0
Zt ∞
Zt ∞
3Trr Tii dUdt r3
ð8Þ
where dU is an element of the collapsing sphere g ¼ t t þ r=c ¼ 0 with t and t as the source and observer times, respectively. The quadrupole source strength is defined by considering the collapsing-sphere surface to facilitate computing the integration as follows, Z Qij ¼ Tij dz ð9Þ f >0
where z is in the direction normal to an object, and the z integration range is f > 0. By using Eq. (9), Eq. (8) becomes 1 v2 4pPQuadrupole ¼ c vt2
Zt
Z
∞
f þ ¼0
Qrr v dGdt þ vt r
Zt ∞
g¼0
Z
ret
ð7Þ
Zt
3Qrr Qii dGdt þ c r2
f þ ¼0
Zt ∞
g¼0
Z
3Qrr Qii dGdt r3
ð10Þ
f þ ¼0 g¼0
The notation G indicates the intersection of the object with the collapsing sphere, and f þ ¼ 0 represents the surface of the
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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object. Eq. (7) can be written in a formulation of retarded time considering integration by t Z 1 v2 Qrr 4pPQuadrupole ¼ 2 2 dS c vt rj1 Mr j ret f þ ¼0
Z
1 v þ c vt
f þ ¼0
3Qrr Qii r 2 j1 Mr j
Z þ f þ ¼0
3Qrr Qii r 3 j1 Mr j
dS ret
ð11Þ
dS ret
Using the relationship between the observer time derivatives and the source time derivatives, v=vtjx ¼ ½ð1=1 Mr Þv=vtjx ret , leads to the formulation Q1A in surface integral form, Z Kr1 Kr2 Kr3 þ 4pPformulation Q1A ¼ þ dS; ð12Þ c2 r cr 2 r 3 ret f þ ¼0
where Kr1 ¼
Kr2 ¼
Kr3 ¼
Q€rr ð1 Mr Þ
3þ
Q_ii
M€r Qrr þ 3M_ r Q_rr ð1 Mr Þ
4
þ
2 3M_ r Qrr
ð1 Mr Þ
5
4Q_Mr þ 2QMr_ þ M_ r Qii
ð1 Mr Þ ð1 Mr Þ3 3 ð1 M 2 ÞQ_rr 2M_ r QMr Mi M_ i Qrr þ 4 ð1 Mr Þ 6M_ r ð1 M 2 ÞQrr þ 5 ð1 Mr Þ 2
2QMM ð1 M 2 ÞQii ð1 Mr Þ3
6ð1 M 2 ÞQMr ð1 Mr Þ4
(B&K8103) hydrophone located at the bottom of the test section, and the recordings were analyzed using the B&K analyzer software. To ensure accurate measurements, the hydrophone had an inside rubber with the same impedance as that of the water inside the tunnel. The background noise included mechanical noise from the pump and other attached devices, because the facility was not designed for noise tests. However, those parts were distinguishable as a background noise, distinct from the major noise of the cylinder. For certain distinctions, a background noise test was conducted for various flow velocities, in order that the flow noise from the cylinder could be accurately measured. 3.2. Model
2
þ
Fig. 1. Medium-sized cavitation tunnel and position of a hydrophone.
3ð1 M 2 Þ Qrr ð1 Mr Þ
5
For a relatively stationary object with an observer position, Eq. (12), can be simplified into the formulation Q1As method as follows Z € Qrr 3Q_rr Q_ii 3Qrr Qii þ 4pPformulation Q1As ¼ þ dS c2 r cr 2 r3 ret f þ ¼0
ð13Þ 3. Experimental apparatus and procedure 3.1. Test facility Underwater acoustic tests were conducted in the mediumsized cavitation tunnel at the Korea Institute of Ocean Science & Technology (KRISO). The size of the tunnel is 12 2 8 m (L W D), as shown in Fig. 1. The test section has a width of 0.6 m and a height of 0.6 m. The noise measurements were recorded using a Bru¨el & Kjær 8103
Fig. 2 shows a picture of the cylinder installed in the test section, and a diagram of the apparatus. A single cylinder model spanning the entire width of the test section was used for the acoustic test. The cylinder measured 600 mm in length and 20 mm in diameter. Noise data could be acquired by fixing the location of the hydrophone with a distance of 300 mm from the cylinder. The free stream velocity was set to 5e6 m/s, a range that can prevent bubbles from making audible noises in the flow. In addition, preventive measures were performed on the cylinder installed in the test section. 4. Noise analysis of a cylinder Five steps were conducted for the noise analysis of the circular cylinder, as shown in Fig. 3. OpenFOAM was used for the CFD calculations and the acoustic calculations of the formulation Q1As method. The results of the analysis were compared with those of the experiment. In addition, a reliability verification was implemented by conducting mesh convergence tests. The mesh is one of the major factors affecting CFD and acoustic results. Thus, a convergence of the results for changes in the mesh can verify the reliability of the analysis results. 4.1. Geometry and mesh modeling The cylinder diameter (D) is 20 mm, and three cases of the mesh model were constructed for the calculation, as shown in
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Fig. 2. Summary of the underwater experiments for a single cylinder in the test section: (a) Setting, (b) Test section diagram.
Fig. 3. Flow chart of quadrupole noise calculation.
Table 1 Mesh model for calculation. Fig. 4. View of the bottom grid surface.
Mesh Model Case 1 Case 2 Case 3
1600 660 10 1280 528 10 960 396 10
Table 1. In general, the O-type shape domain was used to provide better quality, such as orthogonality and skewness around the cylinder, as shown in Fig. 4. The computational domain size in the outer boundary of 25D and the spanwise direction of 5D were used. To accurately calculate the boundary layers, the dimensionless wall distance (wall Yþ) on the cylinder wall was set to be lower than one. A condition of a no-slip wall was applied at the cylinder, and a constant free stream velocity was employed at the outer boundary from 5 m/ s to 6 m/s. A receiver for the acoustic calculation was placed perpendicular to the flow direction upward from the cylinder at distances of 15D. 4.2. CFD calculation
environment. Moreover, the pisoFoam solver has generic turbulence models, such as laminar, Reynolds-averaged NaviereStokes equation (RANS), and Large Eddy Simulation (LES). In this simulation, LES was used for the threedimensional CFD calculations. Regarding the LES, the subgrid scale was modeled using the Smagorinsky model. Table 2 shows additional solver settings for the CFD calculations. The PISO (Pressure Implicit with Splitting of Operators) algorithm was used for the pressureevelocity coupling. The solver settings for the CFD calculations were consulted by Zhang et al., (2015), and more details of the schemes can be seen in the OpenFOAM guide (OpenFOAM, 2011). To verify the flow simulation, mesh convergence tests were conducted using the same procedure for three cases with Table 2 Solver settings for CFD simulations. Solver settings for CFD simulations
The CFD calculations were implemented by using the standard pisoFoam solvers provided in OpenFOAM for transient solutions. The pisoFoam solver is a transient solver for incompressible flow. Thus, the usage of pisoFoam can be justified because of the incompressibility in an underwater
Scheme Time derivatives Gradient Divergence Laplacian
PISO Transient, backward Gauss linear Gauss linear Gauss linear corrected
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Fig. 5. Comparison of pressure coefficient around a cylinder for mesh models.
Table 3 Comparison of Strouhal number. Strouhal number (St) Experiment (Park, 2012) Experiment (Norberg, 2003) Simulations (Park, 2012) Simulations (Orselli et al., 2009) Result
0.195 0.190 0.198 0.191 0.2
different mesh models. Fig. 5 shows the flow simulation results for the pressure coefficient with the results of the mesh convergence tests, for 5 m/s. The red, blue, and black lines show the results of the pressure coefficient for the three mesh models. Fig. 5 shows that they are in good agreement with each other. Table 3 verifies that the Strouhal number of the simulation compares well with that from other research with a similar Reynolds number, Re ¼ 1 105 (Orselli et al., 2009; Park, 2012). Furthermore, the results of the Strouhal number for the three cases of the mesh model converged at 0.2. The above processes were equally implemented for the 6 m/s case, and similar results were obtained. Thus, the reliability of the CFD calculations could be confirmed.
300 mm. Noise predictions for the cylinder were conducted for velocities of 5 m/s and 6 m/s using the formulation Q1As method, and the results were compared to those of the permeable FWeH method. The results of the experiments with the peak frequency as the main sound source around the cylinder corresponds to the quadrupole noise from vortex shedding, which also has that peak frequency. Fig. 6 shows comparisons of the noise predicted around the cylinder for a velocity of 5 m/s received at the designated receiver point at Re ¼ 1 105 in an underwater environment. The black, blue, and red lines show the results of the experiments, the permeable FWeH method, and the formulation Q1As method, respectively. The results of the experiments at 80e100 Hz, 140e170 Hz, 360e370 Hz and 580e650 Hz had distinctive frequency characteristics that were recognized as background noise produced by electronic devices, such as pumps. Fig. 6 shows that the three results had a similar decreasing tendency for the sound pressure level (SPL) from 0 Hz to 1000 Hz. All results showed frequency characteristics with a peak at 47 Hz. The experiments gave an SPL value of 147 dB at the peak frequency, and the results of the analysis using the permeable FWeH and formulation Q1As methods provided SPL values of 160.1 dB and 147.2 dB, respectively, at the same peak frequency. Comparing the numerical and experimental spectra at the peak frequency, the noise obtained by the permeable FWeH method is 13.3 dB higher than the corresponding value from the experiment, while the result using the formulation Q1As method obtained a similar values within 0.2 dB of difference. Moreover, the results from 800 Hz
4.3. Acoustic calculation It is common for applications of the FWeH method to neglect the quadrupole noise source. As was stated in the Theoretical Background section, the formulation Q1As method enables the calculation of the quadrupole noise source. The receiver position is set equally with experiments at
Fig. 7. Comparisons of acoustic results for mesh models.
Fig. 6. Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 1 105: (a) Whole frequency scale from 0 Hz to 1000 Hz, (b) Peak value. Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Fig. 8. Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 1.2 105: (a) Whole frequency scale from 0 Hz to 1000 Hz, (b) Peak value.
to 1000 Hz showed that those obtained with the formulation Q1As method were closer to the experimental results than those obtained using the permeable FWeH method. Therefore, the computations for the 5 m/s case demonstrated the robustness of the formulation Q1As method. In addition, the same procedures for the acoustic calculation were conducted for three cases of the mesh model at 5 m/s, in order to obtain reliable acoustic calculations and support the reliability verification of the CFD calculation. The blue, red, and black lines shown in Fig. 7 indicate the results of the formulation Q1As method for three cases with different models. The results were very close, with a 1 dB difference from each other. Thus, the acoustic calculation was deemed reliable, and the reliability verification implementing the procedure above the Simulation of turbulent flow section is sufficient instead of the results of the reliability for the acoustic calculation. Fig. 8 shows comparisons of the predicted results and the experiments at 6 m/s. The results of the experiment also had the same distinctive frequency characteristics regarding the background noise as those with 5 m/s, and an additional distinct region at 680 Hze820 Hz. All results showed frequency characteristics with peaks at 56 Hz. The results of the experiments and the permeable FWeH and formulation Q1As methods provided SPL values of 151 dB, 160.6 dB, 150 dB, respectively, at the same peak frequency. The formulation Q1As method was more accurate, with 1 dB difference with the results of the experiments at the peak frequency. It also had a tendency to be closer to the results of the experiments than the permeable FWeH method at 800e1000 Hz. A comparison of the results between the 5 m/s and 6 m/s cases revealed that in all cases, the peak frequency had the same increase from 47 Hz to 56 Hz. Regarding the SPL value at the peak frequency for 5 m/s and 6 m/s, the results of the experiments and the formulation Q1As method increased the difference to 4 dB and 2.8 dB, respectively. However, the results of the permeable FWeH method had similar value of 160.1 dB and 160.6 dB. The tendency of the permeable FWeH method with respect to the velocity increments means that there is a lack of accuracy, owing to the uncertainty for setting the permeable surface. By all accounts, the formulation Q1As method is a more robust method to calculate the quadrupole noise correctly, compared to the permeable FWeH method.
5. Conclusions In an underwater environment, the prediction of quadrupole noise around a circular cylinder can be carried out by using the formulation Q1As method developed for a stationary object and based on the formulation Q1A method. Existing procedures for geometric modeling, mesh modeling, CFD calculations, noise calculations and reliability verification were conducted at velocities of 5 m/s and 6 m/s. Moreover, the results of the formulation Q1As method were compared to those from the experiments and the permeable FWeH method, establishing that it is a robust method, which can correctly calculate the quadrupole noise. The developed formulation Q1As method predicted the noise around a circular cylinder well, matching commonlyknown frequency characteristics. A comparison with the experimental data shows that the developed formulation Q1As method predicted the noise around the cylinder and the frequency characteristics with the same peak frequency as the experiments. A comparison of the two methods for calculating the quadrupole noise shows that the formulation Q1As method is more accurate than the permeable FWeH method with respect to the experimental results at the peak frequency, within 1 dB of difference. Moreover, in the high-frequency range, the results from the formulation Q1As method are closer to the experimental results than those from the permeable FWeH method. The formulation Q1As method can be used to predict quadrupole noise for objects in an underwater environment, with good performance, high overall accuracy, and better frequency characteristics than with the permeable FWeH method. Therefore, the formulation Q1As method is a robust method to calculate the quadrupole noise correctly. In further studies, the quadrupole noise will be predicted for more complex geometries to derive its general features in an underwater environment. Acknowledgements This research was funded by Advanced Naval Vessels Research Laboratory, Seoul National University, Seoul, Korea. Also, supported by Research Institute of Marine Systems Engineering, Basic Science Research Program through the
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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National Research Foundation of Korea (NRF) funded by Ministry of Education, Science and Technology (2016R1D1A1A09918294, 2015R1D1A 1A01060387) and the basic research program (PES2110) of the KRISO. References Ansys, 2009. Ansys Fluent 12.0 Theory Guide, Aerodynamically Generated Noise, pp. 421e432. Brentner, K.S., 1997. An efficient and robust method for predicting helicopter rotor high-speed impulsive noise. J. Sound Vib. 203 (1), 87e100. Brentner, K.S., Farassat, F., 2003. Modeling aerodynamically generated sound of helicopter rotors. Prog. Aerosp. Sci. 39, 83e120. Choi, W., Choi, Y., Hong, S., Song, J., Kwon, H., Jung, C., 2016. Turbulentinduced noise of a submerged cylinder using a permeable FW-H. Int. J. Nav. Archit. Ocean Eng. 8, 235e242. Curle, N., 1955. The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 231 (1187), 505e514. Di Francescantonio, D., 1997. A new boundary integral formulation for the prediction of sound radiation. J. Sound Vib. 202 (4), 491e509. Farassat, F., 2007. Derivation of Formulations 1 and 1A of Farassat. NASA/ TM-2007e214853. NASA. Farassat, F., Brentner, K.S., 1987. The uses and abuses of the acoustic analogy in helicopter rotor noise prediction. J. Am. Helicopter Soc. 33, 29e36. Ffowcs Williams, J.E., Hawkings, D.L., 1969. Sound generation by turbulence and surfaces in arbitrary motion. Philos. Trans. R. Soc. Lond. A 264 (1151), 321e342. Hanson, D.B., Fink, M.R., 1979. The importance of quadrupole sources in prediction of transonic tip speed propeller noise. J. Sound Vib. 62, 19e38.
Ianniello, S., Muscari, R., Di mascio, A., 2014. Ship underwater noise assessment by the acoustic analogy, part II: hydroacoustic analysis of a ship scaled model. J. Mar. Sci. Technol. 19, 52e74. Jasak, H., 2009. OpenFOAM: open source CFD in research and industry. Int. J. Nav. Archit. Ocean Eng. 1, 89e94. Lighthill, M.J., 1952. On sound generated aerodynamically, I: general theory. Proc. R. Soc. A221, 564e587. Norberg, C., 2003. Fluctuating lift on a circular cylinder: review and new measurement. J. Fluids Struct. 17 (1), 57e96. OpenFOAM, 2011. OpenFOAM the Open Source CFD Toolbox User Guide, pp. 123e128. Orselli, R.M., Meneghini, J.R., Saltra, F., 2009. Two and Three-dimensional Simulation of Sound Generated by Flow Around a Circular Cylinder. American Institute of Aeronautics and Astronautics, AIAA, pp. 2009e3270. Park, I.C., 2012. 2-dimensional Simulation of Flow-induced Noise Around Circular Cylinder. Thesis and Dissertations. Chungnam University. Schmitz, F.H., Yu, Y.H., 1977. Theoretical modeling of high-speed helicopter impulsive noise. In: Paper Presented at the Third European Rotorcraft and Powered Lift Aircraft Forum, Aix-en-Provence, France. Wang, M., Freund, J.B., Lele, S.K., 2006. Computational prediction of flowgenerated sound. In: Annual Review of Fluid Mechanics, 38, pp. 483e512. Weller, H.G., Tabor, G., Jasak, H., Fureby, C., 1998. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620e631. Zhang, H., Yang, J., Xiao, L., Lu, H., 2015. Large-eddy simulation of the flow past both finite and infinite circular cylinders at Re ¼ 3900. J. Hydrodyn. Ser. B 27, 195e203.
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Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder Yo-Seb Choi a,b, Woen-Sug Choi a,b, Suk-Yoon Hong a,b, Jee-Hun Song c,*, Hyun-Wung Kwon d, Han-Shin Seol e, Chul-Min Jung f a
Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea b Research Institute of Marine Systems Engineering, Seoul National University, Seoul, Republic of Korea c Department of Naval Architecture and Ocean Engineering, Chonnam National University, Yeosu, Republic of Korea d Department of Naval Architecture and Ocean Engineering, Koje College, Koje, Republic of Korea e Advanced Ship Research Division, Korea Research Institute of Ships and Ocean Engineering, Daejeon, Republic of Korea f The 6th R&D Institute-3rd Directorate, Agency for Defense Development, Changwon, Republic of Korea Received 22 October 2016; revised 2 February 2017; accepted 6 February 2017 Available online ▪ ▪ ▪
Abstract Recent research has shown that quadrupole noise has a significant influence on the overall characteristics of flow-induced noise and on the performance of underwater appendages such as sonar domes. However, advanced research generally uses the Ffowcs WilliamseHawkings analogy without considering the quadrupole source to reduce computational cost. In this study, flow-induced noise is predicted by using an LES turbulence model and a developed formulation, called the formulation Q1As method to properly take into account the quadrupole source. The noise around a circular cylinder in an underwater environment is examined for two cases with different velocities. The results from the method are compared to those obtained from the experiments and the permeable FWeH method. The results are in good agreement with the experimental data, with a difference of less than 1 dB, which indicates that the formulation Q1As method is suitable for use in predicting quadrupole noise around underwater appendages. Copyright © 2017 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Quadrupole noise; Circular cylinder; Acoustic analogy; Formulation Q1As method; OpenFOAM
1. Introduction In the flow-induced noise of a given means of transportation, quadrupole noise grows in importance as speed increases. Lighthill proved the significance of quadrupole noise in aero-acoustics by discovering that it is proportional to the cube of the Mach number, for applications in the air, compared the predictions from experimental results (Lighthill, 1952). In the case of an underwater environment, quadrupole noise has not been considered as object of calculations for flow-induced * Corresponding author. E-mail address: [email protected] (J.-H. Song). Peer review under responsibility of Society of Naval Architects of Korea.
noise because it has a negligible magnitude from the point of view of radiated noise. However, researchers have recently found that quadrupole noise is important for determining the overall properties of the far-field radiated noise in an underwater environment (Ianniello et al., 2014). In addition, underwater appendages, such as sonar domes, can be affected by the self-noise produced by flow-induced noise, thus decreasing their performance. Therefore, it is important to predict the quadrupole noise generated by vortex shedding around appendages in an underwater environment. Quadrupole noise can be predicted using acoustic analogy methods that were originally developed for aero-acoustics. Lighthill (1952) was the first to produce a wave equation for an acoustic analogy with a noise source for an arbitrary flow.
http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002 2092-6782/Copyright © 2017 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Curle (1955) expanded Lighthill's analogy to also consider a stationary body, and Ffowcs Williams and Hawkings (1969) further developed the analogy by considering a moving body with arbitrary motion, which is referred to as the Ffowcs WilliamseHawkings (FWeH) analogy. The FWeH analogy has the advantage over other acoustic analogy methods that it models noise using three source terms to which physical meanings can be given: thickness noise, loading noise and quadrupole noise (Ffowcs Williams and Hawkings, 1969). However, the use of quadrupole noise in the FWeH analogy is complicated since it is non-linear and incurs in highcomputational costs. Therefore, the generation of a direct calculation method is being actively studied (Wang et al., 2006; Ansys, 2009). Schmitz and Yu (1977) calculated quadrupole noise using the two-dimensional airfoil theory, but the predicted peak amplitudes generally show poor correspondence with experimental data. Hanson and Fink (1979) also included a quadrupole source for the two-dimensional airfoil at subsonic, transonic and supersonic speeds; they, indicated that, compared with experimental data, the results improved by adding the quadrupole source. Despite the importance of the quadrupole source, it remained difficult to predict the sound source of the Lighthill stress tensor, and there was a lack of computational power to calculate it. To overcome these challenges, Farassat and Brentner (1987) developed a new quadrupole source in the FWeH analogy for a helicopter rotor; this method uses a calculation method similar to that used when the thickness and loading noises are considered surface integrals. Furthermore, a generalized formula was developed to compute the quadrupole source by using its strength, the formulation Q1A method, avoiding the calculation of time derivatives that involve significant computational costs (Brentner, 1997). A comparison between the formulation Q1A and permeable FWeH methods, which calculate quadrupole noise by computing the thickness and loading noises on a permeable surface as indirect effects was carried out in air circumstances; the results indicate that the formulation Q1A method is in better agreement with experimental data than the permeable FWeH method (Brentner and Farassat, 2003). In an underwater environment, Choi calculated the quadrupole noise around a circular cylinder using the expanded permeable FWeH method for a stationary object as indirect effects (Choi et al., 2016). However, research into the direct calculation of quadrupole noise is insufficient to date, and further improvements in accuracy are needed. In general, this study uses a hybrid method with a turbulence model and an acoustic analogy method in order to calculate the flow-induced noise with quadrupole noise around a circular cylinder in an underwater environment, reducing the computational expense. A large-eddy simulation (LES) turbulence model from CFD is used for the CFD calculations. The formulation for the stationary object, which is referred to as the formulation Q1As method, is developed from the formulation Q1A method and is used for the acoustic calculation. The solver developed for the CFD calculations, and the acoustic calculation of the formulation Q1As method is based
on the OpenFOAM platform, an object-oriented, open source CFD tool-kit (Jasak, 2009; Weller et al., 1998). Acoustic experiments and the permeable FWeH method were used to verify the results of the analysis using the formulation Q1As method and its performance. Summarizing, the formulation Q1As method is a more robust method to correctly calculate quadrupole noise compared to the permeable FWeH method. 2. Theoretical background 2.1. Quadrupole noise of acoustic analogy Lighthill first provided an analogy derived from comparing the exact equations of fluid motion with acoustic wave equations, as follows (Lighthill, 1952), 1 v 2 r0 v2 Tij 2 0 2 V r ¼ 2 c vt vxi vxj
ð1Þ
Tij ¼ rvi vj þ pij c2 r0 dij
ð2Þ
where c is the velocity of sound in a fluid, and r0 ¼ r r0 is the density perturbation. Tij is Lighthill's stress tensor, which is calculated to consider the quadrupole noise. vi and pij indicate the velocity component in the xi direction and the compressive stress tensor, respectively. Curle expanded the research of the acoustic analogy to a rigid surface (Curle, 1955). Ffowcs Williams and Hawkings developed their theory from the acoustic analogy of Lighthill by applying it to a solid object in arbitrary motion, and this method is now known as the FWeH equation, which is given as follows (Ffowcs Williams and Hawkings, 1969), 1 v 2 p0 v v V2 p0 ¼ ðr0 vn jdðf ÞjÞ ðpni dðf ÞÞ c2 vt2 vt vxi v2 þ Hðf ÞTij vxi xj
ð3Þ
where f represents the moving surface as an implicit definition by the function f ðx; tÞ ¼ 0, and f > 0 indicates the outside surface. On the right-hand side of Eq. (3), the first term is the thickness noise as a monopole source modeled from the displacement of fluid that results from the object passage. The second term is the loading noise as a dipole source resulting from the pressure distribution on the surface. The third term, expressed in the quadrupole source, is the quadrupole noise and indicates that the fluid is unsteady, as a Reynolds stress. Farassat developed formulation 1A from the FWeH equation into integral forms as follows (Farassat, 2007): 2 3 Z _ _ b M r r v v r n n i i 0 0 4 5 dS 4pPThickness ¼ 2 3 rð1 Mr Þ rð1 Mr Þ f ¼0 ret # Z " 2 r0 cvn ðMr M Þ dS ð4Þ þ 3 r 3 ð1 Mr Þ ret f ¼0
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3 _ b M pcosq r i i 4 5 dS 4pPLoading ¼ 2þ 3 crð1 Mr Þ crð1 Mr Þ f ¼0 ret # Z " 2 pcosq ðMr M Þpcosq þ dS þ 3 r 2 ð1 Mr Þ r 2 ð1 Mr Þ Z
2
staggered vortex steer emerge considering accuracy and calculation cost.
_ pcosq
2.2. Development of formulation Q1As for a stationary object
ret
f ¼0
ð5Þ 4pPQuadrupole ¼
v2 vxi xj
Z V
Tij dV rj1 Mr j ret
ð6Þ
where r ¼ jx yj, where x and y indicate the observer position and the source position, respectively. 1 Mr is the Doppler factor and the kernel of the integration evaluated in retarded time t ¼ t r=c. The turbulence term that is represented as a quadrupole source needs to be calculated by volume integration. It is difficult to determine the volume around a solid object over which to integrate and evaluate the kernel of the integration, because of the complexity introduced by the non-linearity (Farassat and Brentner, 1987). To avoid volume integration indirectly, Di Francescantonio (1997) developed a permeable FWeH method by taking advantage of two methods, the Kirchhoff and the FWeH methods, to make a prediction for a hovering rotor. Z 4pPpermeable FWH ¼ S
2
3
_ _ 4 Un þ Ur 5 dSðhÞ rð1 Mr Þ2 ret # Z " _ run r M þ cðMr M 2 Þ
dS ðhÞ 3 r 2 ð1 Mr Þ ret S 2 3 Z _r L 5 dSðhÞ þ 4 2 crð1 Mr Þ S ret # Z " Lr Mr dSðhÞ þ 2 r ð1 Mr Þ3 ret S 2 3 Z Lr r M_ r þ cðMr M 2 Þ 5 dSðhÞ þ 4 3 cr 2 ð1 Mr Þ
þ
S
3
The formulation Q1A method was developed to make a precise, direct calculation of the quadrupole noise for a helicopter-rotor (Brentner, 1997). The formulation is calculated by conducting a surface integration of the terms composed of the quadrupole source strength, including Lighthill's stress tensor. Using these, the turbulence term in the FWeH equation is computed directly, resulting in high accuracy for the flow noise. The quadrupole noise from the quadrupole source is expressed before developing the formulation Q1A method as follows (Farassat and Brentner, 1987), 1 v2 4pPQuadrupole ¼ c vt2
where Ui is the mass-like flux, Li is the momentum flux, and h is the moving coordinate system along the control surface. The permeable FWeH method calculates the turbulence term indirectly by establishing a permeable surface. Accordingly, the quadrupole noise inside the surface is included in the calculation of the thickness and loading noises on the permeable surface as indirect effects (Wang et al., 2006; Farassat, 2007). From our experiences, the permeable surface is set with a size that includes 3 to 5 vortex eddies up to
Z
∞
f >0
Z f >0
Trr v dUdt þ vt r
3Trr Tii dUdt þ c r2
Z
f >0
Zt ∞
Zt ∞
3Trr Tii dUdt r3
ð8Þ
where dU is an element of the collapsing sphere g ¼ t t þ r=c ¼ 0 with t and t as the source and observer times, respectively. The quadrupole source strength is defined by considering the collapsing-sphere surface to facilitate computing the integration as follows, Z Qij ¼ Tij dz ð9Þ f >0
where z is in the direction normal to an object, and the z integration range is f > 0. By using Eq. (9), Eq. (8) becomes 1 v2 4pPQuadrupole ¼ c vt2
Zt
Z
∞
f þ ¼0
Qrr v dGdt þ vt r
Zt ∞
g¼0
Z
ret
ð7Þ
Zt
3Qrr Qii dGdt þ c r2
f þ ¼0
Zt ∞
g¼0
Z
3Qrr Qii dGdt r3
ð10Þ
f þ ¼0 g¼0
The notation G indicates the intersection of the object with the collapsing sphere, and f þ ¼ 0 represents the surface of the
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object. Eq. (7) can be written in a formulation of retarded time considering integration by t Z 1 v2 Qrr 4pPQuadrupole ¼ 2 2 dS c vt rj1 Mr j ret f þ ¼0
Z
1 v þ c vt
f þ ¼0
3Qrr Qii r 2 j1 Mr j
Z þ f þ ¼0
3Qrr Qii r 3 j1 Mr j
dS ret
ð11Þ
dS ret
Using the relationship between the observer time derivatives and the source time derivatives, v=vtjx ¼ ½ð1=1 Mr Þv=vtjx ret , leads to the formulation Q1A in surface integral form, Z Kr1 Kr2 Kr3 þ 4pPformulation Q1A ¼ þ dS; ð12Þ c2 r cr 2 r 3 ret f þ ¼0
where Kr1 ¼
Kr2 ¼
Kr3 ¼
Q€rr ð1 Mr Þ
3þ
Q_ii
M€r Qrr þ 3M_ r Q_rr ð1 Mr Þ
4
þ
2 3M_ r Qrr
ð1 Mr Þ
5
4Q_Mr þ 2QMr_ þ M_ r Qii
ð1 Mr Þ ð1 Mr Þ3 3 ð1 M 2 ÞQ_rr 2M_ r QMr Mi M_ i Qrr þ 4 ð1 Mr Þ 6M_ r ð1 M 2 ÞQrr þ 5 ð1 Mr Þ 2
2QMM ð1 M 2 ÞQii ð1 Mr Þ3
6ð1 M 2 ÞQMr ð1 Mr Þ4
(B&K8103) hydrophone located at the bottom of the test section, and the recordings were analyzed using the B&K analyzer software. To ensure accurate measurements, the hydrophone had an inside rubber with the same impedance as that of the water inside the tunnel. The background noise included mechanical noise from the pump and other attached devices, because the facility was not designed for noise tests. However, those parts were distinguishable as a background noise, distinct from the major noise of the cylinder. For certain distinctions, a background noise test was conducted for various flow velocities, in order that the flow noise from the cylinder could be accurately measured. 3.2. Model
2
þ
Fig. 1. Medium-sized cavitation tunnel and position of a hydrophone.
3ð1 M 2 Þ Qrr ð1 Mr Þ
5
For a relatively stationary object with an observer position, Eq. (12), can be simplified into the formulation Q1As method as follows Z € Qrr 3Q_rr Q_ii 3Qrr Qii þ 4pPformulation Q1As ¼ þ dS c2 r cr 2 r3 ret f þ ¼0
ð13Þ 3. Experimental apparatus and procedure 3.1. Test facility Underwater acoustic tests were conducted in the mediumsized cavitation tunnel at the Korea Institute of Ocean Science & Technology (KRISO). The size of the tunnel is 12 2 8 m (L W D), as shown in Fig. 1. The test section has a width of 0.6 m and a height of 0.6 m. The noise measurements were recorded using a Bru¨el & Kjær 8103
Fig. 2 shows a picture of the cylinder installed in the test section, and a diagram of the apparatus. A single cylinder model spanning the entire width of the test section was used for the acoustic test. The cylinder measured 600 mm in length and 20 mm in diameter. Noise data could be acquired by fixing the location of the hydrophone with a distance of 300 mm from the cylinder. The free stream velocity was set to 5e6 m/s, a range that can prevent bubbles from making audible noises in the flow. In addition, preventive measures were performed on the cylinder installed in the test section. 4. Noise analysis of a cylinder Five steps were conducted for the noise analysis of the circular cylinder, as shown in Fig. 3. OpenFOAM was used for the CFD calculations and the acoustic calculations of the formulation Q1As method. The results of the analysis were compared with those of the experiment. In addition, a reliability verification was implemented by conducting mesh convergence tests. The mesh is one of the major factors affecting CFD and acoustic results. Thus, a convergence of the results for changes in the mesh can verify the reliability of the analysis results. 4.1. Geometry and mesh modeling The cylinder diameter (D) is 20 mm, and three cases of the mesh model were constructed for the calculation, as shown in
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Fig. 2. Summary of the underwater experiments for a single cylinder in the test section: (a) Setting, (b) Test section diagram.
Fig. 3. Flow chart of quadrupole noise calculation.
Table 1 Mesh model for calculation. Fig. 4. View of the bottom grid surface.
Mesh Model Case 1 Case 2 Case 3
1600 660 10 1280 528 10 960 396 10
Table 1. In general, the O-type shape domain was used to provide better quality, such as orthogonality and skewness around the cylinder, as shown in Fig. 4. The computational domain size in the outer boundary of 25D and the spanwise direction of 5D were used. To accurately calculate the boundary layers, the dimensionless wall distance (wall Yþ) on the cylinder wall was set to be lower than one. A condition of a no-slip wall was applied at the cylinder, and a constant free stream velocity was employed at the outer boundary from 5 m/ s to 6 m/s. A receiver for the acoustic calculation was placed perpendicular to the flow direction upward from the cylinder at distances of 15D. 4.2. CFD calculation
environment. Moreover, the pisoFoam solver has generic turbulence models, such as laminar, Reynolds-averaged NaviereStokes equation (RANS), and Large Eddy Simulation (LES). In this simulation, LES was used for the threedimensional CFD calculations. Regarding the LES, the subgrid scale was modeled using the Smagorinsky model. Table 2 shows additional solver settings for the CFD calculations. The PISO (Pressure Implicit with Splitting of Operators) algorithm was used for the pressureevelocity coupling. The solver settings for the CFD calculations were consulted by Zhang et al., (2015), and more details of the schemes can be seen in the OpenFOAM guide (OpenFOAM, 2011). To verify the flow simulation, mesh convergence tests were conducted using the same procedure for three cases with Table 2 Solver settings for CFD simulations. Solver settings for CFD simulations
The CFD calculations were implemented by using the standard pisoFoam solvers provided in OpenFOAM for transient solutions. The pisoFoam solver is a transient solver for incompressible flow. Thus, the usage of pisoFoam can be justified because of the incompressibility in an underwater
Scheme Time derivatives Gradient Divergence Laplacian
PISO Transient, backward Gauss linear Gauss linear Gauss linear corrected
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Fig. 5. Comparison of pressure coefficient around a cylinder for mesh models.
Table 3 Comparison of Strouhal number. Strouhal number (St) Experiment (Park, 2012) Experiment (Norberg, 2003) Simulations (Park, 2012) Simulations (Orselli et al., 2009) Result
0.195 0.190 0.198 0.191 0.2
different mesh models. Fig. 5 shows the flow simulation results for the pressure coefficient with the results of the mesh convergence tests, for 5 m/s. The red, blue, and black lines show the results of the pressure coefficient for the three mesh models. Fig. 5 shows that they are in good agreement with each other. Table 3 verifies that the Strouhal number of the simulation compares well with that from other research with a similar Reynolds number, Re ¼ 1 105 (Orselli et al., 2009; Park, 2012). Furthermore, the results of the Strouhal number for the three cases of the mesh model converged at 0.2. The above processes were equally implemented for the 6 m/s case, and similar results were obtained. Thus, the reliability of the CFD calculations could be confirmed.
300 mm. Noise predictions for the cylinder were conducted for velocities of 5 m/s and 6 m/s using the formulation Q1As method, and the results were compared to those of the permeable FWeH method. The results of the experiments with the peak frequency as the main sound source around the cylinder corresponds to the quadrupole noise from vortex shedding, which also has that peak frequency. Fig. 6 shows comparisons of the noise predicted around the cylinder for a velocity of 5 m/s received at the designated receiver point at Re ¼ 1 105 in an underwater environment. The black, blue, and red lines show the results of the experiments, the permeable FWeH method, and the formulation Q1As method, respectively. The results of the experiments at 80e100 Hz, 140e170 Hz, 360e370 Hz and 580e650 Hz had distinctive frequency characteristics that were recognized as background noise produced by electronic devices, such as pumps. Fig. 6 shows that the three results had a similar decreasing tendency for the sound pressure level (SPL) from 0 Hz to 1000 Hz. All results showed frequency characteristics with a peak at 47 Hz. The experiments gave an SPL value of 147 dB at the peak frequency, and the results of the analysis using the permeable FWeH and formulation Q1As methods provided SPL values of 160.1 dB and 147.2 dB, respectively, at the same peak frequency. Comparing the numerical and experimental spectra at the peak frequency, the noise obtained by the permeable FWeH method is 13.3 dB higher than the corresponding value from the experiment, while the result using the formulation Q1As method obtained a similar values within 0.2 dB of difference. Moreover, the results from 800 Hz
4.3. Acoustic calculation It is common for applications of the FWeH method to neglect the quadrupole noise source. As was stated in the Theoretical Background section, the formulation Q1As method enables the calculation of the quadrupole noise source. The receiver position is set equally with experiments at
Fig. 7. Comparisons of acoustic results for mesh models.
Fig. 6. Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 1 105: (a) Whole frequency scale from 0 Hz to 1000 Hz, (b) Peak value. Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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Fig. 8. Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 1.2 105: (a) Whole frequency scale from 0 Hz to 1000 Hz, (b) Peak value.
to 1000 Hz showed that those obtained with the formulation Q1As method were closer to the experimental results than those obtained using the permeable FWeH method. Therefore, the computations for the 5 m/s case demonstrated the robustness of the formulation Q1As method. In addition, the same procedures for the acoustic calculation were conducted for three cases of the mesh model at 5 m/s, in order to obtain reliable acoustic calculations and support the reliability verification of the CFD calculation. The blue, red, and black lines shown in Fig. 7 indicate the results of the formulation Q1As method for three cases with different models. The results were very close, with a 1 dB difference from each other. Thus, the acoustic calculation was deemed reliable, and the reliability verification implementing the procedure above the Simulation of turbulent flow section is sufficient instead of the results of the reliability for the acoustic calculation. Fig. 8 shows comparisons of the predicted results and the experiments at 6 m/s. The results of the experiment also had the same distinctive frequency characteristics regarding the background noise as those with 5 m/s, and an additional distinct region at 680 Hze820 Hz. All results showed frequency characteristics with peaks at 56 Hz. The results of the experiments and the permeable FWeH and formulation Q1As methods provided SPL values of 151 dB, 160.6 dB, 150 dB, respectively, at the same peak frequency. The formulation Q1As method was more accurate, with 1 dB difference with the results of the experiments at the peak frequency. It also had a tendency to be closer to the results of the experiments than the permeable FWeH method at 800e1000 Hz. A comparison of the results between the 5 m/s and 6 m/s cases revealed that in all cases, the peak frequency had the same increase from 47 Hz to 56 Hz. Regarding the SPL value at the peak frequency for 5 m/s and 6 m/s, the results of the experiments and the formulation Q1As method increased the difference to 4 dB and 2.8 dB, respectively. However, the results of the permeable FWeH method had similar value of 160.1 dB and 160.6 dB. The tendency of the permeable FWeH method with respect to the velocity increments means that there is a lack of accuracy, owing to the uncertainty for setting the permeable surface. By all accounts, the formulation Q1As method is a more robust method to calculate the quadrupole noise correctly, compared to the permeable FWeH method.
5. Conclusions In an underwater environment, the prediction of quadrupole noise around a circular cylinder can be carried out by using the formulation Q1As method developed for a stationary object and based on the formulation Q1A method. Existing procedures for geometric modeling, mesh modeling, CFD calculations, noise calculations and reliability verification were conducted at velocities of 5 m/s and 6 m/s. Moreover, the results of the formulation Q1As method were compared to those from the experiments and the permeable FWeH method, establishing that it is a robust method, which can correctly calculate the quadrupole noise. The developed formulation Q1As method predicted the noise around a circular cylinder well, matching commonlyknown frequency characteristics. A comparison with the experimental data shows that the developed formulation Q1As method predicted the noise around the cylinder and the frequency characteristics with the same peak frequency as the experiments. A comparison of the two methods for calculating the quadrupole noise shows that the formulation Q1As method is more accurate than the permeable FWeH method with respect to the experimental results at the peak frequency, within 1 dB of difference. Moreover, in the high-frequency range, the results from the formulation Q1As method are closer to the experimental results than those from the permeable FWeH method. The formulation Q1As method can be used to predict quadrupole noise for objects in an underwater environment, with good performance, high overall accuracy, and better frequency characteristics than with the permeable FWeH method. Therefore, the formulation Q1As method is a robust method to calculate the quadrupole noise correctly. In further studies, the quadrupole noise will be predicted for more complex geometries to derive its general features in an underwater environment. Acknowledgements This research was funded by Advanced Naval Vessels Research Laboratory, Seoul National University, Seoul, Korea. Also, supported by Research Institute of Marine Systems Engineering, Basic Science Research Program through the
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002
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National Research Foundation of Korea (NRF) funded by Ministry of Education, Science and Technology (2016R1D1A1A09918294, 2015R1D1A 1A01060387) and the basic research program (PES2110) of the KRISO. References Ansys, 2009. Ansys Fluent 12.0 Theory Guide, Aerodynamically Generated Noise, pp. 421e432. Brentner, K.S., 1997. An efficient and robust method for predicting helicopter rotor high-speed impulsive noise. J. Sound Vib. 203 (1), 87e100. Brentner, K.S., Farassat, F., 2003. Modeling aerodynamically generated sound of helicopter rotors. Prog. Aerosp. Sci. 39, 83e120. Choi, W., Choi, Y., Hong, S., Song, J., Kwon, H., Jung, C., 2016. Turbulentinduced noise of a submerged cylinder using a permeable FW-H. Int. J. Nav. Archit. Ocean Eng. 8, 235e242. Curle, N., 1955. The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 231 (1187), 505e514. Di Francescantonio, D., 1997. A new boundary integral formulation for the prediction of sound radiation. J. Sound Vib. 202 (4), 491e509. Farassat, F., 2007. Derivation of Formulations 1 and 1A of Farassat. NASA/ TM-2007e214853. NASA. Farassat, F., Brentner, K.S., 1987. The uses and abuses of the acoustic analogy in helicopter rotor noise prediction. J. Am. Helicopter Soc. 33, 29e36. Ffowcs Williams, J.E., Hawkings, D.L., 1969. Sound generation by turbulence and surfaces in arbitrary motion. Philos. Trans. R. Soc. Lond. A 264 (1151), 321e342. Hanson, D.B., Fink, M.R., 1979. The importance of quadrupole sources in prediction of transonic tip speed propeller noise. J. Sound Vib. 62, 19e38.
Ianniello, S., Muscari, R., Di mascio, A., 2014. Ship underwater noise assessment by the acoustic analogy, part II: hydroacoustic analysis of a ship scaled model. J. Mar. Sci. Technol. 19, 52e74. Jasak, H., 2009. OpenFOAM: open source CFD in research and industry. Int. J. Nav. Archit. Ocean Eng. 1, 89e94. Lighthill, M.J., 1952. On sound generated aerodynamically, I: general theory. Proc. R. Soc. A221, 564e587. Norberg, C., 2003. Fluctuating lift on a circular cylinder: review and new measurement. J. Fluids Struct. 17 (1), 57e96. OpenFOAM, 2011. OpenFOAM the Open Source CFD Toolbox User Guide, pp. 123e128. Orselli, R.M., Meneghini, J.R., Saltra, F., 2009. Two and Three-dimensional Simulation of Sound Generated by Flow Around a Circular Cylinder. American Institute of Aeronautics and Astronautics, AIAA, pp. 2009e3270. Park, I.C., 2012. 2-dimensional Simulation of Flow-induced Noise Around Circular Cylinder. Thesis and Dissertations. Chungnam University. Schmitz, F.H., Yu, Y.H., 1977. Theoretical modeling of high-speed helicopter impulsive noise. In: Paper Presented at the Third European Rotorcraft and Powered Lift Aircraft Forum, Aix-en-Provence, France. Wang, M., Freund, J.B., Lele, S.K., 2006. Computational prediction of flowgenerated sound. In: Annual Review of Fluid Mechanics, 38, pp. 483e512. Weller, H.G., Tabor, G., Jasak, H., Fureby, C., 1998. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620e631. Zhang, H., Yang, J., Xiao, L., Lu, H., 2015. Large-eddy simulation of the flow past both finite and infinite circular cylinders at Re ¼ 3900. J. Hydrodyn. Ser. B 27, 195e203.
Please cite this article in press as: Choi, Y.-S., et al., Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder, International Journal of Naval Architecture and Ocean Engineering (2017), http://dx.doi.org/10.1016/j.ijnaoe.2017.02.002