Calibration of the Reynolds Stress Model for the Simulation of Gas Flows in Corrugated Tubes

Tubes with corrugated surfaces can clearly increase the overall heat transfer coefficient in comparison to smooth tubes. Due to the additional influence of different curved surfaces, the analytical calculation of the overall heat transfer coefficient and pressure drop fails for those tubes. Numerical simulations using turbulence models with two or three differential equations appropriate for isotropic turbulence are not satisfactory in this case. Since corrugated walls cause anisotropic turbulences in the near wall region, the secondary flow must be considered in the numerical simulation. Within the time averaging turbulence models (Reynolds averaged Navier stokes = RANS models), the Reynolds stress model (RSM) is the only model solving all six components of the Reynolds stress tensor and thus enabling the consideration of secondary and anisotropic turbulence. Most turbulence models are developed and calibrated for smooth wall boundary conditions. As a consequence, simulations of corrugated tubes based on isotropic turbulence models provide inadequate results when compared with measured values. This article describes the calibration of the RSM for the simulation of corrugated tubes using the values of a shell-and-tube test facility for adaptation. To calibrate the heat transfer rate, the dimensionless turbulent Prandtl number is modified. For the pressure drop calculation, the pressure strain coefficient is adjusted varying the appropriate dimensionless coefficient. Moreover, the local flow behavior in the near wall region is validated by local measurements by laser Doppler velocimetry.