Analysis on Turbulent Flows using Large-eddy Simulation on the Seaside Complex Terrain Takeshi Kamio, Makoto Iida, Chuichi Arakawa The University of Tokyo, Japan
Outline Backgrounds and Purposes Complex Terrain Computational Setups Result 1 Mean wind speed, turbulence Result 2 Power spectrum Conclusions
Background Wind Simulators For the predictions of power production and etc 1. Linear Model (for Flat Terrain) WAsP, 2. Nonlinear Model (for Complex Terrain) LAWEPS,MASCOT,LOCALS, RIAM-COMPACT (In Japan), Tasks Prediction of the turbulence characteristics
Purpose 1. Large-eddy Simulation (LES) for the wind on the complex terrain site 2. Assessment of the turbulence Turbulence Intensity Power spectrum
fs(f)/σ 2 = an/(1+bn) c Power spectrum density model(psd) Model for the spectrum of wind in the field f:frequency S(f):Power spectrum σ:standard deviation of wind speed n:non-dimensional frequency, n=fh/u (U: Mean wind speed, H:Length scale) a, b, c: PSD parameters -> Calculate the parameters and length scale Left: Imamura et al.(2004) right:hasegawa et al. (2005) Table: Kaimal s PSD Parameters (for Flat Terrain) Velocity component a b c n p u 105 33 5/3 0.0427 v 17 9.5 5/3 0.148
Complex Terrain 1000km Tokyo Ichiki-kushikino Fig. Overview SITE-K (Ichiki-Kushikino) Located in western area of Japan Complex terrain The measurements were carried out over 3 years in the project(*) *NEDO Project The new technology development for the wind and other renewable (Basic and application)
Numerical Model (1) MSSG(Multi-Scale Simulator for the Geoenvironment) Earth Simulator Center, Japan Agency for the Marine-Earth Science and Technology (JAMSTEC) Called as MSSG (sounds like Message ) MSSG-A (Atmospheric part of MSSG) Compressive Navier-Stokes Smagorinsky LES Highly paralleled and vectorized Large number of grids available on the Earth Simulator v 0 t v p g vv 2 v f F t P gw v P P v 1 2 T 1 Φ t P RT :Deviation of density P P P :Deviation of puressure f,,, ΦF,
Numerical Model (2) MSSG(Multi-Scale Simulator for the Geoenvironment) Earth Simulator Center, Japan Agency for the Marine-Earth Science and Technology (JAMSTEC) From Website : http://www.jamstec.go.jp/esc/research/mssg/index.ja.html
3.2km Numerical Setups (1) Case:west wind Nesting Method of 2 Domains 8.8km Fig. Domain Inlet boundary is located in sea Fig. Setups of Domains and grids Fig. Grids (upper: Domain-I, lower: Domain-II) Domain Domain ([m]x[m]x[m]) Grid Size ([m]x[m]x[m]) Grids Ⅰ 8800x3200x2460 20.0x20.0x3.0(min) 440x160x64=4.5x10 6 Ⅱ 2400x2400x24600 10.0x10.0x3.0(min) 240x240x64=3.7x10 6
Numerical Setups (2) Inlet boundary Steady wind Outlet boundary Radiative Ground surface boundary Wall function Roughness model 2 Category(Next page) Sea/Land Re=8.0 10 8 U=12 m/s, L=1000 m Generally : Difficult to know This study : Sea wind (= Steady wind) Table Setups of domains, grids and boundary conditions Inlet Boundary Outlet Boundary Side and Top Boundary Ground Surface Boundary Table Inflow Conditions Stable flow Radiative Slip Wall function Mainstream wind speed [m/s] 12.0 Boundary layer height [m] 1000 Vertical wind speed profile parameter in boundary layer 1/5 Turbulence No
Computational Domains, Grids, Surface Condition (a) Computational Domains and Grids (b) Surface Blue: Sea, Green: Land Fig. Computational Setups
Results - Visual MAST-A MAST-B MAST-A MAST-B MAST-A MAST-B Wind Wind Wind (a) Streamlines (b) Iso-surface of vorticity (c) Vortex core
Height [m] Height [m] Result - Mean wind speed, turbulence at MAST-A 600 600 500 500 Vector Image 400 0 5 10 Wind Speed [m/s] 400 0 0.2 0.4 Turbulence Intensity Mean wind speed Comparison in 4<U[m/s]<6 Turbulence Intensity Vector Image (Movie)
Height [m] Height [m] Result - Mean wind speed, turbulence at MAST-B 500 500 400 400 Vector Image 300 0 5 10 Wind Speed [m/s] 300 0 0.2 0.4 Turbulence Intensity Mean wind speed Comparison in 4<U[m/s]<6 Turbulence Intensity Vector Image (Movie)
Comparison of mean wind speed and turbulence intensity Better agreement Power Spectrum Analysis -5/3 law Table Errors of Mean wind speed and Turbulence intensity at 50m height Errors U err [%] T err [%] Note Mast A 19% 7.5% 4-6[m/s] Case W Mast B 2% 53.1% 4-6[m/s] Power Spectrum Density model (PSD) Calculate the PSD Parameters and the Length Scale Parameter Fig. Power spectrum
fs(f)/σ 2 Power spectrum density model(psd) Model for the spectrum of wind in the field fs(f)/σ 2 = an/(1+bn) c (1) f:frequency S(f):Power spectrum σ:standard deviation of wind speed n:non-dimensional frequency, n=fh/u (U: Mean wind speed, H:Length scale) a, b, c: PSD parameters n p = 1/b(c-1) (2) n p :Peak Non-dimensional frequency Calculate the parameters with the Least Square Fitting of the function and the data Length scale H 1. H=50 m (Measuring Height) 2. Calculate H as a variable Table: Kaimal s PSD Parameters (for Flat Terrain) Frequency - Power spectrum fh/u Non-dimensional Frequency - PSD Velocity component a b c n p u 105 33 5/3 0.0427 v 17 9.5 5/3 0.148
Power spectrum density model(psd) ~ Parameters ~ Different from Kaimal s parameters The features of the complex and turbulence wind. Length scale H 1. About 10m for u component 2. About 50m for v component 3. Knowledge for the resolution of the computational analysis Table PSD parameters from the numerical result (H=50[m]) Mast A B Mast A B Comp onent H [m] a b c n p u 50.0 24.4 14.0 1.52 0.139 v 50.0 10.2 2.22 2.47 0.307 u 50.0 5.86 0.776 4.67 0.351 v 50.0 12.2 1.11 4.40 0.265 Table PSD parameters from the numerical result (H[m] as a variable) Compo nent H [m] a b c n p u 14.4 84.7 48.6 1.51 0.0399 v 45.8 11.1 2.43 2.47 0.281 u 3.23 90.8 12.0 4.67 0.0227 v 43.5 14.1 1.28 4.4 0.230
fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 fs(f)/σ 2 Power spectrum density model(psd) ~ Plots ~ fh/u (a) component u at Mast A fh/u (b) component v at Mast A fh/u (a) component u at Mast A fh/u (b) component v at Mast A fh/u (c) component u at Mast B Fig. PSD (Case W, H=50[m]) fh/u (d) component v at Mast B fh/u (c) component u at Mast B fh/u (d) component v at Mast B Fig. PSD (Case W, H as a variable)
Conclusions Large eddy simulation of the turbulent wind The steady wind was reasonable when the inlet boundary was located in the sea. The numerical results agreed with the observations for the mean wind speed and turbulence intensity Power Spectrum Density Model (PSD) Calculated the PSD parameters and the Length Scale H H=10 m for u component, H=50 m for v component Future Works Comparison of the spectrum with the measuring data Discussion about the component of the turbulence
Acknowledgement The CFD code MSSG was developed in the Earth Simulator Center of Japan Agency for the Marine-Earth Science and Technology (JAMSTEC) and they had also assisted the simulations for the computational resources. Some part of this study were supported by the New Energy and Industrial Technology Development Organization (NEDO) project "The new technology development for the wind and other renewable (Basic and application)".
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