Bladed Knowledge Base

What is the relaxation factor?
Category: Calculation Setup

Problem

The "Initial conditions relaxation factor" under "Additional Items" may be optionally set to a value less than 1 - this can often help in improving the initial state of the system, reducing problems such as large blade motion in the early part of a simulation. But what exactly does it do?

Solution

The relaxation factor is used to slow down the convergence in the initial condition finding algorithm, which tends to lead to better results. The algorithm uses a numerical gradient descent type approach to find a state of the system in which there is zero acceleration of the rotor, i.e. steady (equilibrium) state. With relaxation factor (R) = 1, the "next" value found by the numerical solver is used as the starting point for the following iteration. If R is less than 1 however, the starting point for next iteration is a weighted sum of the "next" value and the previous value. The lower the value of R, the larger the weight of the previous value. In the block chart below, Xn+1 is the starting point for iteration n+1, Xnew is the (hopefully) improved value found by the solver, R is the relaxation factor and Xn is the previous state. The iterations continue until zero accelerations are reached (within some tolerance).

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Keywords Relaxation factor; initial conditions; stability