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Deriving forces from 2D velocity field measurements

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Abstract

We discuss how to derive a force or a force density from a measured velocity field. The first part focuses on the integral force a fluid exerts on a body, e.g. lift and drag on an airfoil. Obtaining the correct pressure is crucial; however, it cannot be measured within the flow non-intrusively. Using numerical and experimental test cases, we compare the accuracy achievable with three methods: pressure reconstruction from velocity fields via (1) the differential momentum equation, or (2) the Poisson equation, furthermore, (3) Noca’s momentum equation [Noca, JFS 13(5), 1999], which does not require pressure explicitly. The latter gives the best results for the lift, whereas the first or second approach should be used for the drag. The second part deals with obtaining the distribution of a body force density generated by an actuator. Using a stream function ansatz, we obtain a Laplace equation that allows us to compute the solenoidal part of the force distribution; however, the irrotational part is lost. Furthermore, the wall pressure must be known. We validate this approach using numerical data from a wall jet flow in a rectangular box, driven by a fictitious, solenoidal body force. Reconstructing the force distribution yields an error of less than 10−2 for most of the domain.

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Authors and Affiliations

  1. Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 51,01 19, 01314, Dresden, Germany

    Thomas Albrecht & Tom Weier

  2. ETSEIAT, UPC, Polytechnic University of Catalunya, 08222, Terrassa, Spain

    Vanessa del Campo

  3. Institute of Fluid Mechanics, Technische Universität Dresden, 01062, Dresden, Germany

    Hans Metzkes & Jörg Stiller

Authors
  1. Thomas Albrecht
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  2. Vanessa del Campo
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  3. Tom Weier
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  4. Hans Metzkes
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  5. Jörg Stiller
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Correspondence to Thomas Albrecht.

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Albrecht, T., del Campo, V., Weier, T. et al. Deriving forces from 2D velocity field measurements. Eur. Phys. J. Spec. Top. 220, 91–100 (2013). https://doi.org/10.1140/epjst/e2013-01799-9

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  • DOI: https://doi.org/10.1140/epjst/e2013-01799-9

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