Theoretical Study of Fully Developed Turbulent Flow in a Channel, Using Prandtl’s Mixing Length Model

This research used the common decomposition of the velocity and pressure in an average part and a fluctuating part, for high Reynolds number, of the Navier-Stokes equation, which leads to the classic problem of turbulent closure. The Prandtl’s mixing length model, based on the Boussinesq hypothesis and traditionally used for free shear flows, was chosen and adapted for internal flows to solve the closure problem. For channel flows, Johann Nikuradse proposed a model for the Prandtl mixing length. In the present paper, which has an academic character, the authors made a return to the model of the mixing length of Prandtl and the model of Nikuradse, to solve turbulent flows inside a plane channel. It was possible to develop an ordinary differential model for the velocity in the direction of the flow whose solution occurs computationally in a simple but extremely accurate way when compared with Direct Numerical Simulation databases. For the viscous stress on the wall, it was possible to determine the exact mathematical solution of the ordinary differential equation. It is a model of great academic value and even to be used as reference for verification of computational codes destined to the solution of complete numerical and computational models.

Physicochemical Properties of Pyrolysis Bio-Oil from Sugarcane Straw and Sugarcane in Natura

Under the renewable energy context, sugarcane biomass pyrolysis has been growing as a convenient route to produce bio-oil, which can be set into the chemical industry and refineries as building blocks or combustion fuel. In this work sugarcane straw was submitted to direct pyrolysis in a fluidized bed pilot plant at 500°C, in presence of air. Sugarcane in natura was also pyrolysed as a model for comparison, in order to determine the viability of processing different sources of raw biomass. The physicochemical characterization of the biomass precursors as well as of the bio-oils was also carried out, which points both biomass feedstocks as suitable for bio-oil production in terms of viscosity, surface tension, density and acidity. The bio-oil obtained from sugarcane in natura presented higher carbon and hydrogen content as well as lower oxygen content. On the other hand, the metal content is higher in the bio-oil obtained from sugarcane straw, in special the iron and potassium contents were 807 ppm and 123 ppm against 27 ppm and 1 ppm in the bio-oil from sugarcane in natura. Aliphatic and aromatic compounds as well as carbohydrates scaffolds were identified as the main components of the bio-oil. GC-MS analyses showed aromatic products from lignine fragmentation and free sugars and sugar derivatives.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step,fully adaptive in space,hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions.The method is based on the hybrid level set/front-tracking approach proposed in[H.D.Ceniceros and A.M.Roma,J.Comput.Phys.,205,391-400,2005].Geometric,interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance(level set)function,which is evaluated fast and to machine precision,is used as a fluid indicator.The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in[S.Shin,S.I.Abdel-Khalik,V.Daru and D.Juric,J.Comput.Phys.,203,493-516,2005]whose success for greatly reducing parasitic currents has been demonstrated.The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude.To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic,adaptive mesh refinements.This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step,linearly implicit time integration scheme.We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications:the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability,an example of bubble ascending dynamics,and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.