Van Driest Model Research Articles

A mixing‐length model for magnetohydrodynamic flows in channels and ducts with wall‐parallel magnetic field

AbstractA spanwise magnetic field leads to turbulent drag reduction in channel flow of a conducting liquid due to the selective Joule damping of certain flow structures. This effect can be captured by a simple modification of Prandtl's classical mixing‐length idea. The mixing length over which a turbulent fluctuation loses its momentum is not only constrained geometrically but also by magnetic damping. We therefore introduce a magnetic damping length that is proportional to friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean between wall distance and this damping length. By combining this ansatz with the van‐Driest model for turbulent stresses in channel flow we obtain a satisfactory prediction for the mean velocity distribution in magnetohydrodynamic channel flow with spanwise field for different Reynolds and Hartmann numbers. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.

Surface instability of the liquid turbulent flows in the open inclined channels

The flow of a viscous liquid layer in an open inclined channel under the turbulent mode is considered in this paper. To describe turbulent viscosity, the Van Driest model is used. The spectrum of characteristic values of the problem on linear stability of a plane-parallel flow is studied numerically. Parameters of the maximal growth waves are found out, the surface tension effect is studied, and theoretical results are compared with experimental data.

Modeling of gas absorption into turbulent films with chemical reaction

A mathematical model has been developed to predict the rates of gas absorption in turbulent falling liquid films with and without the first order homogeneous reaction and external gas phase mass transfer resistance. The eddy viscosity model used to describe the flow distribution is the van Driest model, modified in the outer region of the film by the use of an eddy diffusivity deduced from gas absorption measurements. The results are given for special cases to illustrate the effects of turbulence, reaction rate and gas phase resistances on the concentration profiles and the rates of gas absorption.

Effect of mass transfer on turbulent friction during condensation inside ducts

This paper quantifies the effect of mass transfer (suction) on wall friction for turbulent vapour flow inside ducts during condensation. Correlations are presented for the friction factor in terms of the suction rate, and are utilized in estimating the frictional pressure change in condenser tubes. These correlations are derived from the numerical integration of the velocity profile through the turbulent boundary layer, based on the Van Driest model for the Prandtl mixing length. Predictions of the frictional pressure drop during the condensation of steam in an air-cooled duct correspond to within ±5% of experimental measurements.

Pressure Drop and Heat Transfer in Turbulent Duct Flow: A Two-Parameter Variational Method

A two-parameter variational method is introduced to calculate pressure drop and heat transfer for turbulent flow in ducts. The variational method leads to a Galerkin-type solution for the momentum and energy equations. The method uses the Prandtl mixing length theory to describe turbulent shear stress. The Van Driest model is compared with experimental data and incorporated in the numerical calculations. The computed velocity profiles, pressure drop, and heat transfer coefficient are compared with the experimental data of various investigators for fully developed turbulent flow in parallel plate ducts and pipes. This analysis leads to development of a Green’s function useful for solving a variety of conjugate heat transfer problems.

Navier–Stokes Analysis of Turbine Blade Heat Transfer

Comparisons with experimental heat transfer and surface pressures were made for seven turbine vane and blade geometries using a quasi-three-dimensional thin-layer Navier–Stokes analysis. Comparisons are made for cases with both separated and unseparated flow over a range of Reynolds numbers and free-stream turbulence intensities. The analysis used a modified Baldwin-Lomax turbulent eddy viscosity model. Modifications were made to account for the effects of: (1) free-stream turbulence on both transition and leading edge heat transfer; (2) strong favorable pressure gradients on relaminarizations; and (3) variable turbulent Prandtl number on heat transfer. In addition, the effect on heat transfer of the near-wall model of Deissler is compared with the Van Driest model.

Analysis of ventilation shock losses by finite element method

This paper presents an analysis of ventilation shock losses using the two-dimensional finite element method. It outlines the finite element formulation, in which the ventilation air flow is assumed to be a steady-state, viscous, incompressible and fully developed turbulent flow. In addition, the modified version of Van Driest model is assumed for the effective kinematic viscosity.

On the Frictional Damping of the Rolling of a Circular Cylinder

The frictional damping of the rolling motion of a circular cylinder is nonlinear. Although negligible at full scale, it may be important in model scale. The damping force is calculated using Fourier analysis of the frictional force on the surface of a cylinder with a vertical axis executing simple harmonic oscillations about its axis. Calculations of the velocity profile in the fluid near the oscillating cylinder, needed for the calculations of the frictional force, are carried out in the laminar and turbulent case using the boundary-layer approximation. For Reynolds shear stress modeling, the mixing length concept of Prandtl and an analogy to van Driest's model are used. The resulting nonlinear partial differential equation of the parabolic type is solved numerically using the Du Fort-Frankel explicit finite-difference scheme.

ビンガム流体の圧力損失に関する研究

In order to predict the relation between friction factor and Reynolds number forBinghain plastic fluid flow in circular smooth pipes, an improved mixing-length distribution is proposed in this paper. The distribution (i.e. Eq.(18)) is a modification of Van Driest's model for Newtonian fluid flow that is obtained through the results of the other researchers' studies about Newtonian and Bingham plastic fluid flow and the authors' mixing-length distribution for pseudo-plastic fluid flow in circular smooth pipes.The proposed mixing-length distribution makes it possible to predict the pressure loss of Bingham plastic fluid flow in circular smooth pipes since 163 out of 194 experimental data shown in Fig. 8 are within ±7% of the theoretical values. A set of theoretical design curves of friction factor versus Reynolds number is calculated and shown in Fig. 9.

Pressure Loss of Pseudo-Plastic Fluid Flow in Pipes

In order to predict both the velocity profile and the relationship between friction factor and Reynolds number for pseudo-plastic fluids flow in smooth pipes, and improved mixing-length distribution is proposed in this paper. This distribution is a modification of Van Driest's model for Newtonian fluids flow obtained by referring to the results of the other researcher's studies about Newtonian and pseudo-plastic fluids. It seems that this mixing-length distribution is suitable for estimating and calculating both the velocity profile and the pressure loss for Newtonian and pseudo-plastic fluids flow in circular smooth pipes through the analyzed results as compared with experimental results. A set of design curves of friction factor versus Reynolds number is presented.