Tidal current turbine power capture and impact in an idealized channel simulation

Poster presented at the European Wave and Tidal Energy Conference (EWTEC) in 2013.

Transcript

1. Tidal current turbine power capture
   and impact in an idealised channel
   simulation
   Kristen M. Thyngα and Thomas Rocβ
   αOceanography, Texas A&M University; βDepartment of Marine Energy, IT Power Ltd.
   kthyng@tamu.edu, thomas.roc@itpower.co.uk
   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
   

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