Wind Turbine Aero-Structural Simulation

A three-bladed horizontal-axis wind turbine sits in a 12 m/s wind and turns at 2.22 rad/s. The question is what aerodynamic load that produces on a blade, and what the blade does under it.

Answering it takes two physics domains. A steady RANS solution in a rotating reference frame predicts the pressure field on the blade surface; that field is then mapped onto a separate structural mesh, where an orthotropic composite shell model predicts deformation, stress and root reactions. The coupling runs one way only: the structure never feeds its deformation back to the flow.

Only one blade is solved. Rotational periodicity across a 120° sector stands in for the other two, on the assumption that all three blades and their inflow are identical. That single assumption cuts the cost of the aerodynamic problem by roughly a factor of three, and it is the first thing this page holds up to scrutiny.

Each stage consumes the previous one's output, so an error anywhere propagates forward silently. A structural stress contour looks exactly the same whether the pressure field feeding it was converged or not.

A rotor is neither steady nor small. Solved literally, it needs a moving mesh, a transient solution and the full 360° of azimuth. Two modelling decisions remove all three costs, and both are worth stating precisely because both buy their speed with an assumption.

The rotating reference frame. Instead of rotating the mesh, the governing equations are written in a frame that rotates with the rotor. The blade is then stationary relative to its own cell zone, the flow field around it stops changing with time, and a steady solver is legitimate. The price is two extra acceleration terms in the momentum equation.

There is no Euler term, because Ω is constant at a fixed operating point. Fluent introduces both source terms once frame motion is enabled on the fluid cell zone, which means the entire physical difference between a rotating and a stationary analysis lives in a setting that is easy to leave switched off and impossible to see in a contour plot afterwards.

The 120° sector. A three-bladed rotor repeats itself every 360°/3 = 120°, so one sector containing one blade can represent the whole machine if the two radial faces are joined as a rotational periodic pair. Flow variables leaving one face re-enter at the other, rotated by 120°.

The first result to check is kinematic, because it is the one with an exact answer. Blade velocity in the stationary frame reaches 98.05 m/s at the tip against 98.12 m/s from ΩR by hand, a difference of 0.07 %. That single number verifies the rotation rate, the axis, the units and the 1 m root offset at once. It says nothing whatever about the aerodynamics.

Torque follows from integrating the surface pressure and shear moment about the rotor axis. The supplied course result gives a one-blade torque of 137,115 N·m, and the rest is arithmetic: three blades at 2.22 rad/s give 0.913 MW of mechanical rotor power, against 6.496 MW of kinetic power passing through the 6,137 m² swept area.

Convergence is not an iteration count. A run that stops at the number of iterations it was asked for has demonstrated nothing except that the loop finished. What matters is whether the residuals are small and the engineering outputs have stopped moving, judged together.

The figure below is the integral static pressure on the blade wall, logged every iteration of my own run of the baseline case. It is the quantity the structural analysis ultimately consumes, so it is the right thing to watch.

Three further numerical questions sit above that one, in the order they need answering:

This is what makes the analysis one-way. Pressure crosses from fluid to structure; deformation does not cross back. The aerodynamic solution therefore remains that of the undeformed blade, and the local twist that actually sets angle of attack is never updated. For a first aero-structural estimate at a moderate operating point that is a reasonable trade, and the tip deflection below is what decides whether it holds.

The interpolation itself deserves more suspicion than it usually gets. Mapping between non-matching meshes is a numerical operation with its own error, and a coverage report showing 100 % of target nodes received a value is not evidence that the load survived the trip. Two meshes can both be fully covered and still disagree about the total force.

The blade is a slender, twisted, hollow composite shell: an aerodynamic skin over an internal spar, both tapering from root to tip. It is modelled as curved shell surfaces carrying an assigned thickness rather than as a solid meshed through its wall.

For a rigidly rotating mass distribution, the total radial force reduces exactly to the total mass times the square of the angular speed times the centre-of-mass radius, no matter how the mass is spread along the span. That makes it computable by hand, independently of the finite element model, from three quantities the model reports.

The supplied structural results give a maximum equivalent (von Mises) stress of approximately 33.36 MPa, at the junction where the spar transfers bending load into the skin. That location is physically sensible, and it is also exactly the sort of place where a value is sensitive to CAD simplification, to how the spar and skin are connected, and to local mesh density.

Against the 537 MPa tensile strength quoted for the material, the ratio is about 16.

Every choice below buys something and costs something. Listing the cost beside the benefit is what separates a model from a set of settings.

More specifically, and in no particular order of severity:

None of the following has been run. It is the ordered plan for turning the current model into one whose numbers could carry an engineering argument, with the largest source of uncertainty attacked first.