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Modification of the $k-ω_0$ model for roughness

Paul Durbin, Zifei Yin

Abstract

Surface roughness plays a substantial role in many flows for which Reynolds averaged prediction is needed. The transformation used in the k-omega0 model is extended to rough surfaces by adding an effective origin. The log-layer offset is computed as a function of this effective origin, thereby creating a correspondence between effective origin and equivalent sandgrain roughness. A formula is derived for the virtual origin of the fully rough log law. It is shown how the present model is consistent with the fully rough limit.

Modification of the $k-ω_0$ model for roughness

Abstract

Surface roughness plays a substantial role in many flows for which Reynolds averaged prediction is needed. The transformation used in the k-omega0 model is extended to rough surfaces by adding an effective origin. The log-layer offset is computed as a function of this effective origin, thereby creating a correspondence between effective origin and equivalent sandgrain roughness. A formula is derived for the virtual origin of the fully rough log law. It is shown how the present model is consistent with the fully rough limit.
Paper Structure (8 sections, 15 equations, 7 figures)

This paper contains 8 sections, 15 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Log-layer offset
  3. The $k-\omega_0$ equations
  4. The $\omega_0=0$ boundary condition
  5. Shear stress, $\omega_0\propto\tau_w/\mu$, boundary condition
  6. Fully rough limit
  7. Comparisons
  8. Discussion

Figures (7)

  • Figure 1: Calibration curve, $\omega_0=0$ boundary condition
  • Figure 2: Effects of roughness via the model.
  • Figure 3: Calibration curve, $\omega_0\propto\tau_w/\mu$ boundary condition
  • Figure 4: Effects of roughness with the $\omega_0\propto\tau_w/\mu$ boundary condition.
  • Figure 5: Profiles using virtual origin, $y_+ + y_{0+}$.
  • ...and 2 more figures