Development of formulation Q1As method for quadrupole noise prediction around a submerged cylinder Available online at www sciencedirect com + MODEL ScienceDirect Publishing Services by Elsevier Inter[.]
+ MODEL Available online at www.sciencedirect.com 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 February 2017; accepted 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 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 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: jhs@jnu.ac.kr (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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 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 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), v r0 v2 Tij 2 V r ¼ c vt vxi vxj 1ị Tij ẳ rvi vj ỵ 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), v p0 v v V2 p0 ¼ ðr0 jdðf ÞjÞ ðpni dðf ÞÞ c2 vt2 vt vxi v2 ỵ Hf ịTij vxi xj ð3Þ where f represents the moving surface as an implicit definition by the function f x; tị ẳ 0, and f > 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): Z _ _ b M r r v v r n n i i 0 dS 4pPThickness ¼ rð1 Mr ị r1 Mr ị f ẳ0 ret # Z " r0 cvn ðMr M Þ dS 4ị ỵ r Mr ị 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 _ b M pcosq r i i dS 4pPLoading ẳ 2ỵ cr1 Mr ị cr1 Mr ị f ẳ0 ret # Z " pcosq ðMr M Þpcosq þ dS þ r ð1 Mr Þ r ð1 Mr Þ Z 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 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 _ _ Un ỵ Ur dShị r1 Mr Þ2 ret # Z " _ run r M ỵ cMr M ị dS hị r ð1 Mr Þ ret S Z _r L dShị ỵ cr1 Mr Þ S ret # Z " Lr Mr dShị ỵ r Mr ị3 ret S Z Lr r M_ r ỵ cMr M ị dShị ỵ cr Mr ị ỵ S 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), 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 to vortex eddies up to Z ∞ f >0 Z f >0 Trr v dUdt ỵ vt r 3Trr Tii dUdt ỵ c r2 Z f >0 Zt ∞ Zt ∞ 3Trr Tii dUdt r3 ð8Þ where dU is an element of the collapsing sphere g ẳ t t ỵ r=c ẳ 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 > By using Eq (9), Eq (8) becomes v2 4pPQuadrupole ¼ c vt2 Zt Z f ỵ ẳ0 Qrr v dGdt ỵ vt r Zt gẳ0 Z ret 7ị Zt 3Qrr Qii dGdt ỵ c r2 f ỵ ẳ0 Zt gẳ0 Z 3Qrr Qii dGdt r3 10ị f þ ¼0 g¼0 The notation G indicates the intersection of the object with the collapsing sphere, and f ỵ ẳ 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 object Eq (7) can be written in a formulation of retarded time considering integration by t Z v2 Qrr 4pPQuadrupole ¼ 2 dS c vt rj1 Mr j ret f ỵ ẳ0 Z v ỵ c vt f ỵ ẳ0 3Qrr Qii r j1 Mr j Z ỵ f ỵ ¼0 3Qrr Qii r j1 Mr j dS ret ð11Þ dS ret Using the relationship between the observer time derivatives and the source time derivatives, v=vtjx ẳ ẵ1=1 Mr ịv=vtjx ret , leads to the formulation Q1A in surface integral form, Z Kr1 Kr2 Kr3 ỵ 4pPformulation Q1A ẳ ỵ dS; 12ị c2 r cr r ret f ỵ ẳ0 where Kr1 ¼ Kr2 ¼ Kr3 ¼ Q€rr ð1 Mr ị 3ỵ Q_ii Mr Qrr ỵ 3M_ r Q_rr Mr ị ỵ 3M_ r Qrr Mr ị 4Q_Mr ỵ 2QMr_ ỵ M_ r Qii ð1 Mr Þ ð1 Mr Þ3 ð1 M ÞQ_rr 2M_ r QMr Mi M_ i Qrr ỵ ð1 Mr Þ 6M_ r ð1 M ịQrr ỵ Mr ị 2QMM ð1 M ÞQii ð1 Mr Þ3 6ð1 M 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 ỵ Fig Medium-sized cavitation tunnel and position of a hydrophone 3ð1 M Þ Qrr ð1 Mr Þ 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 ỵ 4pPformulation Q1As ẳ ỵ dS c2 r cr r3 ret f ỵ ẳ0 13ị 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 m (L W D), as shown in Fig The test section has a width of 0.6 m and a height of 0.6 m The noise measurements were recorded using a Bruăel & Kjổr 8103 Fig 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 Noise analysis of a cylinder Five steps were conducted for the noise analysis of the circular cylinder, as shown in Fig 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 Fig Summary of the underwater experiments for a single cylinder in the test section: (a) Setting, (b) Test section diagram Fig Flow chart of quadrupole noise calculation Table Mesh model for calculation Fig View of the bottom grid surface Mesh Model Case Case Case 1600 660 10 1280 528 10 960 396 10 Table 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 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 Yỵ) 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 m/ s to 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 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 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 Fig Comparison of pressure coefficient around a cylinder for mesh models Table 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 shows the flow simulation results for the pressure coefficient with the results of the mesh convergence tests, for m/s The red, blue, and black lines show the results of the pressure coefficient for the three mesh models Fig shows that they are in good agreement with each other Table verifies that the Strouhal number of the simulation compares well with that from other research with a similar Reynolds number, Re ¼ 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 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 m/s and 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 shows comparisons of the noise predicted around the cylinder for a velocity of m/s received at the designated receiver point at Re ¼ 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 shows that the three results had a similar decreasing tendency for the sound pressure level (SPL) from 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 Comparisons of acoustic results for mesh models Fig Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 105: (a) Whole frequency scale from 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 Fig Comparisons of sound pressure level spectrum underwater obtained from different method at Re ¼ 1.2 105: (a) Whole frequency scale from 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 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 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 indicate the results of the formulation Q1As method for three cases with different models The results were very close, with a 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 shows comparisons of the predicted results and the experiments at m/s The results of the experiment also had the same distinctive frequency characteristics regarding the background noise as those with 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 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 m/s and 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 m/s and m/s, the results of the experiments and the formulation Q1As method increased the difference to 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 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 m/s and 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 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 + MODEL Y.-S Choi et al / International Journal of Naval Architecture and Ocean Engineering xx (2017) 1e8 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 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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 ... 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),... for the noise analysis of the circular cylinder, as shown in Fig OpenFOAM was used for the CFD calculations and the acoustic calculations of the formulation Q1As method The results of the analysis... 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 and 1A of Farassat