REPRESENTING PRESENCE OF SUBSURFACE CURRENT TURBINES IN OCEAN MODELS Manhar Dhanak Florida Atlantic University Graduate Student: Zaqie Reza 1
Momentum Equations 2
Effect of inclusion of Coriolis force on flow (Stommel, 1948) 3
Flow streamlines for different Reynolds number with a fixed Rossby number (Bryan, 1963) 4
5
Momentum Equations (Cf. Harrison et al., 2010) 6
Examine flow past turbine using Fluentbased Reynolds Averaged Navier Stokes (RANS) equations and finite-volume it method k ε turbulence model Circular cylindrical domain Structured t mesh 7
Blade and Hub Characteristics NACA Five-Digit Series 638xx sections (Bahaj et al, 2003) Rotor radius 3m Blade length 2.625m Hub radius 0.375m Number of blades Twist Foil Type 3 15 degree NACA 638xx 8
Meshed Domain 9
Validation of the Model U 0 = 1.73 m/s, ; Bhj Bahaj et al, 2003 10
Velocity Axial Component m/s x/d = -0.5 x/d = -0.15 x/d = -0.1 x/d = 0 x/d = 0. 1 x/d = 0.25 x/d = 0.5 x/d = 1 x/d = 2 Uo = 1.73 /sec TSR = 5 11
Velocity Axial Component 12
Flow velocity Axial component 13
Velocity Axial Component 14
Flow field Pathlines Pathlines of particles released from the turbine surface 15
Velocity Tangential Component 16
Velocity Radial Component 17
Eddy Viscosity Turbulent viscosity i (m 2 /s)) Contours of turbulent viscosity from inlet to outlet along a section parallel to the flow and cutting thru the blade 18
Summary RANS computation of flow past a turbine provides quantification of local effect on the flow field. Parametric study of the local flow field being considered for accurate characterization of the related force terms in the large scale ocean model. Next step: Compute ocean model flow with the local force terms to determine and characterize impact of turbine Consideration of arrays of turbines. 19
Background and Motivation The Gulf Stream is one of the world s most intensively studied current systems It is a source of constant flow of ocean currents with a definite pattern. It passes very close along the coast of Florida. Because of the density variation, ocean currents carry a large amount of energy when compared with wind energy. The Center for Ocean Energy Technology (COET) has proposed the installation of the ocean current turbines in the COET has initiated i i the study in various fields of study pertaining i to turbines. So that technically-feasible and environmentally-friendly systems can be developed. 20
Meshed Domain Mesh type Tetra - prism 21
Eddy Viscosity Eddy viscosity for uniform and sheared in-flow velocity profiles 22
Comparison Axial Velocity 23
Comparison Axial Velocity 24
Sheared Velocity Profile 25
Flow field Tangential Velocity Tangential velocity (m/s)of the nodes on the blade of the turbine 26
Objective The objective of this research is to analyze the flow past an ocean current turbine using a finite volume Navier-Stokes CFD solver Highlights g A full 3-D RANS approach in a moving reference frame employing periodicity condition Validation of the model with experimentally determined data Flow field study for a generic turbine in uniform and shearing flows and effect of flow on different pitch angles. Wake visualization Eddy viscosity it effects and study of its dependence d on flow field conditions 27
The Software -Fluent Uses control volume approach Two types of solvers Pressure based solver low speed incompressible flows Density based solver - high speed compressible flows Two types of solution algorithm Segregated - equations are solved sequentially (i.e. segregated) from one another Coupled - a coupled system of equations comprising the momentum equations and the pressure-based continuity equation. More robust but time consuming 28
Governing equations: The equation of conservation of mass, or continuity equation: dρ dt The momentum balance equation: Rotating Reference Frame:. ρv 0 d dt ρv. ρv v p.τ ρg F Rotating reference frame renders a problem which is unsteady in the stationary (inertial) frame, steady with respect to the moving frame. For a steadily rotating frame, it is possible to transform the equations of fluid motion to the rotating frame such that steady-state solutions are possible. 29
The transformed fluid velocities are Relative velocity: v r v u r Whirl velocity: u r ω xr Transformed governing equations Continuity: ρ x. ρv r 0 Rotating reference frame Balance of Momentum: ρv. ρv v ρ 2ω xv ω xω x r x r r r r p. τ r F 30
Turbulence Modeling Turbulent flow fluctuating velocity fields and transported quantities Computationally expensive to simulate these fluctuations. Two approaches RANS Reynolds averaging (ensemble averaging) RANS Filtering of small scale resolution Large Eddy Simulation (LES) Whole range of turbulence quantities are modeled Ensemble averaged continuity and momentum equations ρ x x i ρu i 0 t ρu i x j ρu i u j ρ µ u i u j 2 x i x j x j x i 3 δ u i ij ρu x j x i u j j 31
Flow field Radial Velocity Area averaged values for radial velocity(m/s) along the axial direction 32
RANS Reynolds stresses additional terms after averaging ρu i u j Reynolds stress are modeled in terms of eddy viscosity coefficients and mean velocity. The eddy viscosity coefficients can only be determined numerically. k- ε Model Two equation model i.e two transport equations to represent the turbulent properties to ρk ρku t x i µ µ t k G i x j σ k x k G b ρε Y M S k j ρε ρεu t x i µ µ t ε ε C i x j σ ε x 1ε j k G k C 3ε G b C 2ε ρ ε2 k S ε Additional variables - k - turbulent kinetic energy, ε -turbulent dissipation k determines the energy in turbulence and ε the scale of turbulence Eddy viscosity: µ t ρc µ k 2 ε 33
Concept of y+ A mesh which provides accurate results at laminar flow may not be acceptable for turbulent flow situations. Near wall region can be divided into three Inner layer - Viscous shear dominates Outer layer - turbulent shear dominates Overlap layer both type of shear are equally important 34
Concept of y+ Turbulence modeling depends on how well the inner layer is modeled y+ is a non dimensional length scale which gives an estimation of the height of the first cell height y: y yv ν v τ w ρ Shear velocity: where is the shear velocity τ w Viscous sublayer - At y 5, the velocity profile is linear Buffer Layer When 5 y 30, the velocity profile is neither logarithmic(as in logarithmic overlap layer) nor linear as in viscous sublayer. This layer is uncertain and care should be taken to not have cells in this region. 35
Near wall modeling The k-ε models are valid for fully turbulent flows i.e flow in the regions far away from the walls. Therefore consideration has to be given to make these models suitable for wall-bounded flows. Whereas Spalart-Allmaras and k-w models are suitable to be applied throughout the boundary layer, provided that the mesh is properly resolved. There are two approaches to modeling near-wall region. Wall function approach Near-wall model approach 36
Mesh hgeneration Most critical part of CFD simulation The quality of mesh decides the accuracy of results Mesh types can be classified into three structured, unstructured and hybrid Hexahedral Elements Excellent near solid boundaries High degree of control. Time consuming Prismatic Elements Tetrahedral Elements Triangles extruded into wedges. Useful for resolving near wall gradients Difficult to cluster in the lateral direction due to the underlying triangular structure. They are used to fill the volume between the surfaces. Pyramid Elements Pyramid elements are used to transition from hexahedral elements to tetrahedral elements. 37
Mesh Type Description Advantages Disadvantages Structured Laid out in a regular repeating pattern called blocks Unstructured Utilizes an arbitrary collection of elements to fill the domain. Hybrid Utilizes some form of structured mesh in local regions while using unstructured mesh in the bulk of the domain. High degree of control. Mesh can be done flow oriented Post processing made easy Time consuming Requires a high degree of expertise. Require less user Lack of user time or effort. Faster solution. Both structured and unstructured meshes can be used simultaneously. The shape and distribution of the mesh can be controlled locally. control when laying out the mesh. User control limited to boundaries of fthe mesh. They can be difficult to use and require user expertise. Hybrid methods are less robust than unstructured methods. 38
Cell Squish Cell Equivolume skew on Tri/Tetra elements Measure of deviation in orthogonality with respect to cell faces. max 1 A i r c0/xfi A i r c0/xfi A i is the surface area vector and r c0/xfi is the distance between centroid of a cell to its face center. Cell squish of 1 means worst quality cell. It is a measure of volume deviation in cells Equivolume skew optimal mesh volume-mesh volume optimal mesh volume Face Squish Calculated ltdfrom the products of each surface area vector, and dthe vector that thtconnects the centroids of fthe two adjacent cells as 1 A i r c0/c1 A i r c0/c1 A i is the surface area vector and r c0/c1 is the distance between centroids. Face squish of 1 means worst quality cell. Aspect Ratio Measure of stretching of a cell. It is computed as the ratio of the maximum value to the minimum value of any of the following distances; the distances between the cell centroid and face centroids, and the distance between the cell centroid and nodes Aspect ratio = A/B 39
Forces acting on an airfoil section θ P = Pitch angle α = Angle of attack φ = Angle of relative flow U 0 = Inflow velocity U rel = Relative velocity Ω = Rotational velocity F L = Lift force F D = Drag force F N = Normal force F T = Thrust force 40
Important Turbine Definitions Tip Speed Ratio The Tip Speed Ratio (TSR) is an important parameter for wind turbine design. It represents the ratio between the tip speed and the undisturbed wind speed. TSR λ ΩR U 0 where R is the radius of the wind turbine and is the angular velocity of the rotor. Power Coefficient The power coefficient is ratio of power P extracted by the turbine to maximum power in the freestream. It is given by the expression: C P P 1 3 2 ρu 0 A 41
Important Turbine Definitions Induction factors The incoming flow is affected by the presence of rotor. The flow velocity at the blade is hence not equal to the water speed, but a reduced one. As given by the Actuator Disk Theory, axial induction factor, a is expressed as a U 0 U d U 0 where is the flow velocity at the disk or in other words flow velocity at the turbine.the amount of axial induction factor decides the amount of power extracted by the turbine. Also the velocity at the disk is given by U d U 0 U 1 2 where is the flow velocity downstream 42
Future Work Comparison of performance characteristics between different turbines in varying operating conditions With better computational resource create structured mesh to make enhanced wall treatment and run simulations using k-ωω turbulence model- for greater accuracy Compare eddy viscosity effects with varying inflow velocities and velocity profiles 43
Boundary Conditions Velocity Used to define the flow velocity, along with all relevant scalar inlet properties of the flow, at flow inlets. Outflow Flow exits where the details of the flow velocity and pressure are not known prior to solving the flow problem. The solver extrapolates the required information from the interior. Usually used where exit flow is close to fully developed condition. Symmetry Used when the physical geometry of interest, and the expected pattern of the flow/thermal solution, has mirror symmetry. Can also be used to model zero-shear slip walls in viscous flows. Zero flux of all quantities across a symmetry boundary Wall Used to bound fluid and solid regions. Periodic Used when the physical geometry of interest and the expected pattern of the flow/thermal solution have a periodically repeating nature 44
Thank You 45
Velocity Axial Component 46