channel simulation Kristen M. Thyngα and Thomas Rocβ αOceanography, Texas A&M University; βDepartment of Marine Energy, IT Power Ltd. [email protected], [email protected] Introduction • Turbines have been modeled in an ocean modelling code, ROMS, without many of the restrictions that such models typically have • Want to evaluate power capture by two array layouts • Want to understand the effects of turbines on a represen- tative ﬂow system Numerical Model Figure 1: Simpliﬁed headland domain with overlaid magniﬁed views of the regular (left) and staggered (right) array layout. Green dots represent the TCT location. • Run in ROMS: hydrostatic, 3D, parallelized • Horizontal resolution of ∆x = 30 m, ∆y = 10 m, 20 vertical layers in 100 meter depth • k-ω turbulence closure scheme is used • West/ east open and north/south no-slip walls • M2 tide, linear density proﬁle, N=0.01 s−1 • Quadratic bottom friction with CD = 3 × 10−3 Turbine Model Force term in momentum equations, representing the tur- bine in a grid cell: F = − 1 2 ρAdCU2 d , ρ: ﬂuid density, Ad: rotor-disc area of the turbine, Ud: ﬂow velocity at turbine, C: function of the coefﬁcient, Ct. Added terms to simulate reduced turbulence length scales (Pk) and additional production of wake turbulence due to the turbine’s presence (Pω): Dk Dt = ∂ ∂z KM σk ∂k ∂z + Ps + PB − ε + Pk Dω Dt = ∂ ∂z KM σω ∂ω ∂z + ω k (c1Ps + c2PB − c3εFwall + Pω) , k: turbulent kinetic energy, KM: vertical eddy viscosity, Ps, PB: shear production, buoyancy production, ε: turbulent dissipation rate, ω: turbulent frequency, Fwall: wall function. The added terms to represent the turbine are given by Pk = Cp U3 d ∆x − Cd Udk ∆x ; Pω = Cω P2 s ε , ∆x: grid spacing of the porous disc, Cp, Cd, Cω: functions of ∆x and turbine properties. Array Layout Effect on Power Capture Local calculation of power capture of a 10 device farm: Plocal = 1 T 10 N n t 2ρAdU2 dN,t (U∞N,t − UdN,t ) × ∆t. N: turbine index, U∞N (UdN,t ): u-velocity component of un- perturbed (perturbed) ﬂow at Nth turbine location (for a given time index t). Global approach: Available Power = n t i,j,k 1 2 ρ v∞t,i,j,k 2 × ∆Vi,j,k × ∆t, i, j, k: index in x, y, z directions, v∞t,i,j,k : unperturbed ﬂow velocity norm, ∆Vi,j,k: control volume of (i, j, k)th cell. Remaining Power = n t i,j,k 1 2 ρ vt,i,j,k 2 × ∆Vi,j,k × ∆t, vt,i,j,k : ﬂow velocity norm. Power dissipated by the present of the TCT farm: Power Capture = Available Power − Remaining Power. These local and global approaches permit a complemen- tary investigation of the power extraction induced by the two-considered TCT farm layouts on the tidal system. Extraction by array (MW): Regular Array Staggered Array Local Calculation 6.008 6.051 Global Calculation 7.5348 6.1845 Array Hydrodynamic Impacts Difference in max speed and TKE between initial and reg- ular turbine array case. Positive (red) values: initial case has larger max values. Negative (grey): turbine array case has larger values. Line plots to the left (bottom) of the main plot area show the along- (across-) channel averages, with coloring same: ( a ) Speed ( b ) Turbulence kinetic energy Properties shown at hub height. Overlaid arrows are velocity vectors, overlaid signal shows time po- sition in tidal cycle (free surface), and inset plot shows headland tip area, magniﬁed. All snap- shots are taken at the same time on ebb tide: ( a ) Initial case: speed ( b ) Regular array: speed ( a ) Initial case: vertical vorticity ( b ) Regular array: vertical vorticity ( a ) Initial case: turbulence kinetic energy ( b ) Regular array: turbulent kinetic energy Mean kinetic power density. The values for the ini- tial simulation are shown in colored, ﬁlled contours and corresponding values for the regular array simu- lation are overlaid in black contours and labeled. Conclusions • The global approach leads to a more realistic result. • Coherent structures found in the speed, vorticity, and tur- bulent kinetic energy are disrupted near the headland tip due to the presence of turbines, leading to a weakened system downstream. • The path of a large lee headland eddy is slightly altered, and all effects have potentially signiﬁcant impacts for a real system. EWTEC 10th European Wave and Tidal Energy Conference Tenth European Wave and Tidal Energy Conference 2013, 2-5 September 2013, Aalborg, Denmark