Coupling of an unsteady aerodynamics model with a computational fluid dynamics solver. Momentum source methods are an efficient means of representing airfoils in Navier-Stokes CFD simulations. Momentum source terms are added to the Navier-Stokes equations instead of resolving the solid boundary of the airfoil with a mesh. These source terms are calculated using an aerodynamics model. This approach is useful where the overall performance and midto far-field influence of a wing or rotor are desired and details of the flow field near the blade are not the objective of the simulation. One example is simulation of rotorcraft operations where the objective may be to assess an operation's feasibility in terms of control margins, rather than to inform rotor design decisions. Coupling an aerodynamics model to a CFD solver is straightforward in cases where the airflow relative to the blade is steady. Unsteady conditions require an unsteady aerodynamics model, complicating the coupling with the CFD solver. A coupling method is proposed whereby the incident velocity is extracted from the CFD solution and corrected using a theory based approximation for the unsteady induced velocity. The steady-state momentum source method is demonstrated for 2D and 3D simulations and the unsteady coupling method is validated against experiments on a pitching airfoil and verified for blade-vortex interactions. The unsteady coupling method enables meaningful incident velocities to be extracted from unsteady flow-fields, as shown by agreement with experiments and simulations using analytical expressions for the incident velocity in place of the CFD solver.
A series of Direct Numerical Simulations (DNS) of the flow through a staggered tube bundle has been performed over the range 1030 ≤ Rem ≤ 5572 to capture the flow transition that occurs at the matrix transition point of Rem ≈ 3000. The matrix transition is the point at which a second frequency becomes prominent in tube bundles. To date, this is the highest published Reynolds number at which a DNS has been performed on cross-flow over a tube bundle. This study describes the flow behaviour in terms of: the mean flow field, Strouhal numbers, vortex shedding, 3-D flow features, and turbulence properties. These results support the hypothesis that the transition in the vortex shedding behaviour at Rem ≈ 3000 is similar to that which occurs in single cylinder flow at the equivalent Reynolds number. The visualisations presented also demonstrate the nature of the shedding mechanisms before and after the matrix transition point.
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