{
  "id": "1606.01415",
  "version": "v1",
  "published": "2016-06-04T20:28:05.000Z",
  "updated": "2016-06-04T20:28:05.000Z",
  "title": "Predictions of canonical wall bounded turbulent flows via a modified $k-ω$ equation",
  "authors": [
    "Xi Chen",
    "Fazle Hussain",
    "Zhen-Su She"
  ],
  "comment": "22 pages, 14 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified $k-\\omega$ equation for canonical wall bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number ($Re$). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the $k-\\omega$ equation. Three innovations are introduced: First, an adjustment of the Karman constant to 0.45 is set for the overlap region with a logarithmic MVP. Second, a wake parameter models the turbulent transport near the centerline. Third, an anomalous dissipation factor represents the effect of a meso layer in the overlap region. Then, a highly accurate (above 99\\%) prediction of MVPs is obtained in Princeton pipes, improving the original model prediction by up to 10\\%. Moreover, the entire SMKP, including the newly observed outer peak, is predicted. With a slight change of the wake parameter, the model also yields accurate predictions for channels and boundary layers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-04T20:28:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76F55"
    ],
    "keywords": [
      "canonical wall bounded turbulent flows",
      "mean kinetic energy profile",
      "boundary layer",
      "overlap region",
      "wake parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}