Energy storage via high-energy density composite flywheels
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1 Energy storage via high-energy density composite flywheels Brian C. Fabien Department of Mechanical Engineering University of Washington Seattle, WA Energy storage via high-energy density composite flywheels p.1/34
2 Presentation overview Introduction - Motivation - Basic Principle Energy storage via high-energy density composite flywheels p.2/34
3 Presentation overview Introduction - Motivation - Basic Principle Stacked-ply disk design problem Energy storage via high-energy density composite flywheels p.2/34
4 Presentation overview Introduction - Motivation - Basic Principle Stacked-ply disk design problem Disk construction Energy storage via high-energy density composite flywheels p.2/34
5 Presentation overview Introduction - Motivation - Basic Principle Stacked-ply disk design problem Disk construction Testing and evaluation Energy storage via high-energy density composite flywheels p.2/34
6 Presentation overview Introduction - Motivation - Basic Principle Stacked-ply disk design problem Disk construction Testing and evaluation Conclusion Energy storage via high-energy density composite flywheels p.2/34
7 Some energy storage technologies Lead acid battery: 18 Wh/kg Energy storage via high-energy density composite flywheels p.3/34
8 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Energy storage via high-energy density composite flywheels p.3/34
9 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Hydrostorage: 300 Wh/m 3 Energy storage via high-energy density composite flywheels p.3/34
10 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Hydrostorage: 300 Wh/m 3 Composite flywheels: 100 to 1000 Wh/kg Energy storage via high-energy density composite flywheels p.3/34
11 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Hydrostorage: 300 Wh/m 3 Composite flywheels: 100 to 1000 Wh/kg Compressed air: 2000 Wh/m 3 Energy storage via high-energy density composite flywheels p.3/34
12 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Hydrostorage: 300 Wh/m 3 Composite flywheels: 100 to 1000 Wh/kg Compressed air: 2000 Wh/m 3 Gasoline: Wh/kg Energy storage via high-energy density composite flywheels p.3/34
13 Some energy storage technologies Lead acid battery: 18 Wh/kg Nickel-cadmium battery: 31 Wh/kg Hydrostorage: 300 Wh/m 3 Composite flywheels: 100 to 1000 Wh/kg Compressed air: 2000 Wh/m 3 Gasoline: Wh/kg Hydrogen: Wh/kg Energy storage via high-energy density composite flywheels p.3/34
14 Flywheel Energy Storage (FES) FES usage - Electrical load leveling - Batteries for electrical vehicles - Pulsed power supplies FES design challenges - Bearings - Drive/generator - Containment - Flywheel Energy storage via high-energy density composite flywheels p.4/34
15 Flywheel Energy Storage - Basic ideas A kinetic energy storage device Maximum energy density: α = 1 2 ( Iω 2 f ) ( ρV ) Wh/kg I - moment of inertia of the disk (kg-m 2 ), ω f - failure speed of the disk (rad/s), ρ - density (kg/m 3 ), V - volume (m 3 ). Energy storage via high-energy density composite flywheels p.5/34
16 Flywheel Energy Storage - Schematics Bearings Renewable Power Source Motor/Generator Flywheel Motor coils Motor magnets Housing T T B B Flywheel Energy storage via high-energy density composite flywheels p.6/34
17 Stacked-ply Flywheel tangential ply radial ply Alternate layers of radial and tangential plies Can fiber angle variation improve performance? How can such disks be constructed? Energy storage via high-energy density composite flywheels p.7/34
18 Constitutive relationship 1 r o r φ fiber direction r i σ θθ 2 σ rr σ 11 σ 22 τ 12 Ply stiffness relationship Q 11 Q 12 0 = Q 21 Q 22 0 } 0 0 {{ Q 66 k} [Q] k k ǫ 11 ǫ 22 γ 12 k Energy storage via high-energy density composite flywheels p.8/34
19 The k-th ply stiffness σ rr σ θθ τ rθ k = Q rr Qrθ Qr6 Q rθ Qθθ Qθ6 Q r6 Qθ6 Q66 } {{ } [ Q(φ)] k k ǫ rr ǫ θθ γ rθ k Energy storage via high-energy density composite flywheels p.9/34
20 Stiffness components Q rr Q rθ Q 22 Q 66 Q r6 Q θ6 = Q 11 cos 4 φ + Q 22 sin 4 φ + (2Q Q 66 ) cos 2 φ sin 2 φ = Q 12 (cos 4 φ + sin 4 φ) + (Q 11 + Q 22 4Q 66 ) cos 2 φ sin 2 φ = Q 11 sin 4 φ + Q 22 cos 4 φ + (2Q Q 66 ) cos 2 φ sin 2 φ = (Q 11 + Q 22 2Q 12 2Q 66 ) cos 2 φ sin 2 φ + Q 66 (cos 4 φ + sin 4 φ) = (Q 11 Q 12 2Q 66 ) cos 3 φ sin φ (Q 22 Q 12 2Q 66 ) cos φ sin 3 φ = (Q 11 Q 12 2Q 66 ) cosφsin 3 φ (Q 22 Q 12 2Q 66 ) cos 3 φ sin φ. Energy storage via high-energy density composite flywheels p.10/34
21 Ply properties Q 11 = Q 22 = E 11 1 ν 12 ν 21 E 22 1 ν 12 ν 21 Q 12 = Q 21 = ν 21E 11 1 ν 12 ν 21 Q 66 = G 12 Energy storage via high-energy density composite flywheels p.11/34
22 Laminate constitutive relations σ rr σ θθ τ rθ = [A(φ)] ǫ rr ǫ θθ γ rθ ( 1 [A(φ)] = λ [ Q(90 )] +(1 λ) }{{} 2 [ Q(φ)] [ Q( φ)] tang. stiffness }{{} radial stiffness λ = total thickness of tangential reinforcement plies total thickness of laminate. ) Energy storage via high-energy density composite flywheels p.12/34
23 Laminate constitutive relations (cont.) ǫ rr ǫ θθ γ rθ Effective strain-stress S rr S rθ 0 = S rθ S θθ 0 } 0 0 {{ S 66 } [S(φ)] σ rr σ θθ 0 where [S(φ)] = [A(φ)] 1 is the effective compliance matrix σ 11 σ 22 τ 12 k = [T(φ)] k [ Q(φ)] k [S(φ)] σ rr σ θθ 0. Energy storage via high-energy density composite flywheels p.13/34
24 Coordinate trasformation T(φ) = cos 2 φ sin 2 φ 2 cos φ sin φ sin 2 φ cos 2 φ 2 cos φ sin φ cosφsin φ cos φ sin φ cos 2 φ sin 2 φ. Energy storage via high-energy density composite flywheels p.14/34
25 Stress state Equilibrium: d dr (r σ rr ) σ θθ + ρω 2 r 2 = 0 Energy storage via high-energy density composite flywheels p.15/34
26 Stress state Equilibrium: d dr (r σ rr ) σ θθ + ρω 2 r 2 = 0 Compatibility: r dǫ θθ dr + ǫ θθ ǫ rr = 0 Energy storage via high-energy density composite flywheels p.15/34
27 Stress state Equilibrium: d dr (r σ rr ) σ θθ + ρω 2 r 2 = 0 Compatibility: r dǫ θθ dr + ǫ θθ ǫ rr = 0 States: x 1 = σ rr ρω 2 r 2 o, x 2 = σ θθ ρω 2 r 2 o, x 3 = φ, x 4 = r/r o = τ Energy storage via high-energy density composite flywheels p.15/34
28 Stress state Equilibrium: d dr (r σ rr ) σ θθ + ρω 2 r 2 = 0 Compatibility: r dǫ θθ dr + ǫ θθ ǫ rr = 0 States: x 1 = σ rr ρω 2 r 2 o, x 2 = σ θθ ρω 2 r 2 o, x 3 = φ, x 4 = r/r o = τ Control variable: = derivative of fiber angle: u = dφ/dτ Energy storage via high-energy density composite flywheels p.15/34
29 Stress state Equilibrium: d dr (r σ rr ) σ θθ + ρω 2 r 2 = 0 Compatibility: r dǫ θθ dr + ǫ θθ ǫ rr = 0 States: x 1 = σ rr ρω 2 r 2 o, x 2 = σ θθ ρω 2 r 2 o, x 3 = φ, x 4 = r/r o = τ Control variable: = derivative of fiber angle: u = dφ/dτ Nondimensional compliance: S θθ = E 11 S θθ and S rθ = E 11 S rθ. Energy storage via high-energy density composite flywheels p.15/34
30 State equations ẋ 1 = ( x 2 x 1 x 2 4) /x4, ẋ 2 = [ x 1 ( x4 S rθ u S rr) Srθ x 2 4 ẋ 3 = u, ẋ 4 = 1. +x 2 ( x4 S θθ u + S θθ)] / [x4 S θθ ], where ẋ i = dx i /dτ, i = 1, 2, 3, 4, S θθ = ds θθ/dφ, and S rθ = ds rθ/dφ. Energy storage via high-energy density composite flywheels p.16/34
31 Flywheel Performance Energy density: α = ω2 f ( r 4 o r 4 i r 2 o r 2 i ) [Wh/kg] Energy storage via high-energy density composite flywheels p.17/34
32 Flywheel Performance Energy density: α = ω2 f ( r 4 o r 4 i r 2 o r 2 i ) [Wh/kg] Design problem: Find the radial-ply fiber orientation that will maximize ω f. Energy storage via high-energy density composite flywheels p.17/34
33 ailure theories: When does the disk fail? Maximum stress failure criterion Maximum strain failure criterion Tsai-Wu failure criterion Energy storage via high-energy density composite flywheels p.18/34
34 Optimization results Compare 4 designs: Benchmark design: φ(τ) = 0. J σ, maximum stress failure criterion. J ǫ, maximum strain failure criterion. J TW, Tsai-Wu failure criterion. Energy storage via high-energy density composite flywheels p.19/34
35 Fiber orientation Benchmark J σ J ε J TW 1 Fiber angle, φ (radians) r/r o Energy storage via high-energy density composite flywheels p.20/34
36 Benchmark design Energy storage via high-energy density composite flywheels p.21/34
37 Maximum stress design Energy storage via high-energy density composite flywheels p.22/34
38 Maximum strain design Energy storage via high-energy density composite flywheels p.23/34
39 Tsai Wu design Energy storage via high-energy density composite flywheels p.24/34
40 Effective radial stress Effective radial stress Benchmark J σ J ε J TW r/r o Energy storage via high-energy density composite flywheels p.25/34
41 Effective tangential stress 0.55 Benchmark J σ 0.5 J ε J TW Effective tangential stress r/r o Energy storage via high-energy density composite flywheels p.26/34
42 Radial ply stress σ Radial ply stress, σ Benchmark J σ J ε J TW r/r o Energy storage via high-energy density composite flywheels p.27/34
43 Tangential ply stress σ Benchmark J σ J ε J TW Tangential ply stress, σ r/r o Energy storage via high-energy density composite flywheels p.28/34
44 Energy density Disk Maximum Maximum Tsai-Wu design stress strain Benchmark J σ J ǫ J TW Energy storage via high-energy density composite flywheels p.29/34
45 Flywheel construction Energy storage via high-energy density composite flywheels p.30/34
46 Fiber layout Benchmark design Energy storage via high-energy density composite flywheels p.31/34
47 Fiber layout Optimized design Energy storage via high-energy density composite flywheels p.32/34
48 Tangential strain Energy storage via high-energy density composite flywheels p.33/34
49 Conclusions Fiber angle optimization can improve energy density Energy storage via high-energy density composite flywheels p.34/34
50 Conclusions Fiber angle optimization can improve energy density Failure criteria is significant Energy storage via high-energy density composite flywheels p.34/34
51 Conclusions Fiber angle optimization can improve energy density Failure criteria is significant Optimized radial plies can be constructed Energy storage via high-energy density composite flywheels p.34/34
52 Conclusions Fiber angle optimization can improve energy density Failure criteria is significant Optimized radial plies can be constructed Behavior as predicted by classical lamination theory Energy storage via high-energy density composite flywheels p.34/34
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