Tham khảo tài liệu 'practical ship hydrodynamics episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Introduction 11 solution either. Even if such a solution may become feasible in the future it is questionable if it is really necessary for engineering purposes in naval architecture. Velocities and pressure may be divided into a time average and a fluctuation part to bring the Navier-Stokes equations closer to a form where a numerical solution is possible. Time averaging yields the Reynolds-averaged Navier-Stokes equations RANSE . u v w and p are from now on time averages. u0 v0 w0 denote the fluctuation parts. For unsteady flows . manoeuvring high-frequency fluctuations are averaged over a chosen time interval assembly average . This time interval is small compared to the global motions but large compared to the turbulent fluctuations. Most computations for ship flows are limited to steady flows where the terms ut vt and wt vanish. The RANSE have a similar form to the Navier-Stokes equations p ut C UUx C vUy C wuz pf 1 - Px C g Uxx C Uyy C u z - p u0u0 x C u0v0 y C u0w0 z p Vt C UVx C VVy C wvz pf 2 - Py C g Vxx C Vyy C v zz __ lii i 0 A I 7 7 A I i vifOA Pvvu v x C Vv v y C Vv w z p wt C UWx C VWy C WWz pf 3 - Pz C M Wxx C Wyy C Wzz - p u0w0 x C v0w0 y C w0w0 z They contain as additional terms the derivatives of the Reynolds stresses pu0u0 pu0v0 pu w0 pu0v0 pv0 V0 pv0w0 pu0w0 pv0w0 pw0w0 The time averaging eliminated the turbulent fluctuations in all terms except the Reynolds stresses. The RANSE require a turbulence model that couples the Reynolds stresses to the average velocities. There are whole books and conferences dedicated to turbulence modelling. Recommended for further studies is . Ferziger and Peric 1996 . Turbulence modelling will not be treated here in detail except for a brief discourse in section . It suffices to say that none of the present models is universally convincing and research continues to look for better solutions for ship flows. Because we are so far from being able to solve the actual Navier-Stokes equations we often say .
