Computational Prediction of Flow Generated Sound

1. MAE 741 Computational Prediction of Flow Generated Sound M Wang, J B Freund, Sanjiva K Lele Annual Review of Fluid Mechanics 2006, Vol 38 Suranjan Pai

2. Agenda • Significance of flow generated sound • Progress so far • Challenges Posed • Basic Theory • Terminology • Source & Propagation • Lighthill’s Theory • Numerical Evaluation • Computational Approaches • Direct Numerical Solution (DNS) • Large Eddy Solution (LES) • Reynold’s Average Numerical Solution (RANS) • Hybrid Approach • Flow Control – recent efforts Computational Prediction of Flow Generated Sound

3. Significance of flow generated sound • Associated Problems • Causes human discomfort • Affects the stealth operations of military vehicles & submarines • Tightening noise regulations at the airports • Automobiles • Mirrors • A-pillars • Windshield Wipers • Other Applications • Wind Turbine • Fans in rotating machines • Helicopter rotors • Naval Vessels • Propellers • Hydrofoils • Sonar Domes • Aircrafts • Jet Noise • Turbo Fan • Airframe • Landing Gear Computational Prediction of Flow Generated Sound

4. Progress So Far • Lighthill, James • first pioneering study in 1952 “unsteady flows through non-linear interaction of velocity fluctuations, entropy fluctuations and viscous stresses” Computational Prediction of Flow Generated Sound

5. Progress So Far • Howe M S • emphasized the role of vorticity as sound sources • In free space dominant sources are inefficient and that solid boundaries enhance noise radiation by • Creating and augmenting noisy flow features • Imposing a boundary inhomogeneity Computational Prediction of Flow Generated Sound

6. Challenges Posed • Noise generating is unsteady. • Renders steady RANS methods unsuitable • Unsteady RANS are inefficient • Vast disparity in magnitudes between fluid dynamic & acoustic disturbances • Scale separation between sound and flow esp. Jet Engines which have a high subsonic Mach No flow (M ~ 1) – there is lack of clear scale separation Computational Prediction of Flow Generated Sound

7. Terminology Computational Prediction of Flow Generated Sound

8. Source & Propagation • Two physical processes described : • Sound generation – creates acoustic energy • Propagation – alters its character • Dissipation is also an effect of propagation. Although this concept appears to be clear and unambiguous, mathematical implementation is less clear and becomes complicated with the result that flow can alter the efficiency of the acoustic source. Computational Prediction of Flow Generated Sound

9. Lighthill’s Theory • Mathematically we define a flow solution ‘q’ such that Ŋ(q) = 0 • Lighthill formulated an acoustic analogy by rearranging the above equation as L(q) = S(q) where L = linear wave propagation operator S = corresponding non-linear sound source Computational Prediction of Flow Generated Sound

10. Lighthill’s Theory • The most well known form of this analogy can be expressed as In this equation, computation of the noise comes down to two issues : • Accurate enough inversion of L • Representation of S Computational Prediction of Flow Generated Sound

11. Lighthill’s Theory Shortcomings of Lighthill theory • Truncation and numerical approximation is not well understood. • For complex value of L, a numerical solution of the adjoint Green’s Fn is used to compute far field sound, which causes some instable solutions. • Propagation effects on S increases the relative errors in ‘S’ which are reflected on the relative errors in the far field sound. Computational Prediction of Flow Generated Sound

12. Numerical Evaluation • For unsteady flow in an unconfined region, closed form solution to Lighthill analogy is : In this equation, truncation of terms is carried out by considering : • Hydrodynamic perturbations • Acoustic perturbations. Computational Prediction of Flow Generated Sound

13. Numerical Evaluation • For unsteady flow in an unconfined region, closed form solution to Lighthill analogy is : Limitation of Green’s Fn : • Green’s Fn is unavailable for complex geometries • Computation of complete Green’s Fn is expensive Computational Prediction of Flow Generated Sound

14. Computational Approaches Sound Computation Energy content of the radiated noise is very small compared to the unsteady flow. This fact gives rise to the under-listed issues : • Need for accurate boundary conditions. • Spatial resolution of the numerical schemes. • Induction of dispersion / dissipation due to discretization – exception are spectral methods. Computational Prediction of Flow Generated Sound

15. Computational Approaches Direct Numerical Solution • Usually used to avoid modeling approximations. • Solved using compressible flow equations using methods that have well understood numerical errors. • However, this method has a limitation on the Reynolds number. Computational Prediction of Flow Generated Sound

16. Computational Approaches Sound generated by turbulent vortex ring

17. Computational Approaches Vortex ring – Formation to Exit

18. Computational Approaches Large Eddy Simulation • It represents large turbulence scales in flow and also models the effects of the smaller scales. • Turbulence modeling is more robust as small scale motions are used. • However, the grid wall resolution requirement for LES is quite stringent. Computational Prediction of Flow Generated Sound

19. Computational Approaches RANS / Hybrid Methods • For time accurate simulation methods unsteady RANS provides the lowest level of flow detail and accuracy • Most recent active pursuit is going on in incorporating RANS modeling elements into LES at different levels. • RANS calculations are insufficient by themselves for sound predictions as they lack temporal information Computational Prediction of Flow Generated Sound

20. Flow Control – Recent Efforts Optimal Control of 2D mixing layer noise Computational Prediction of Flow Generated Sound

21. QuestionsSuggestions

22. References Publications : • Computational Prediction of Flow-Generated Sound Meng Wang, Jonathan B Freund, Sanjiva K Lele Annual Review of Fluid Mechanics 2006, Vol 38 • Computing aerodynamically generated noise Wells V L, Renaut R A Annual Review of Fluid Mechanics 1997, Vol 29 Text Books : • Mathematical Methods in Chemical Engineering Arvind Varma Oxford University Press, 1997 • A First Course in Turbulence H. Tennekes, J L Lumley The MIT Press, 1972 Computational Prediction of Flow Generated Sound