renewable energy course#01
TRANSCRIPT
Review of Fluid Dynamics
Air is virtually incompressible for V <100 m/s
Conservation of Energy – Bernoulli's Equation
Conservation of Momentum
Viscosity
Turbulence
Friction in Pipe Flow
Lift and Drag Forces – Fluid & Turbine Machinery
Conservation of EnergyP.E. lost + W.D. by Pressure Forces = Gain in K.E. + Frictional Losses
Bernoulli's Equation (Frictionless fluid)
Or (Head of fluid)
Ideal Fluid – Zero Viscosity, Thermal Conductivity & Compressibility
When power Pth is added to the fluid and Q= Au (volume
flow rate) and (c m T2 – c m T1) is the net heat gained
Conservation of Momentum
(A1 u1 Δt) (ρu1) / Δt = A1 u12 ρ = Momentum / sec
Force = (A2 u22 – A1 u1
2)ρ = m• (u2 – u1)
Viscosity – Flow between two parallel plates
Shear Stress = Force / Area = τ = µ (∂u / ∂y)
µ = Dynamic Viscosity
v = µ / ρ = Kinetic Viscosity Diffusivity
Turbulence
Reynolds Number = R = u D / v, D = pipe diameter
R > 2300 Turbulent
Turbulence increases heat transfer
Friction in Pipe Flow
f‘ = 4f = pipe friction coefficients
Pipe Roughness parameter ξ
Friction coefficient f for pipe flow
From graphFrom Table
Lift and Drag Forces
Power Coefficient Versus Tip Speed
Axial Force on Wind Turbines
Actuator Disc – Bernoulli's Principle
neglecting changes
in ρ and z
Static Pressure Difference = Dynamic Pressure Difference
Axial Forces
Axial Forces
Torque
Blade Element Theory – Stream Tube Theory