A theoretical investigation of an averaged-structure eddy viscosity model applied to turbulent shear flows

The project is concerned with the study of a new mathematical model in which the structure of turbulence is described by averaging the effects of the eddies of various scales over the whole volume of flow. The model assumes that the turbulent stresses can be presented in a way analogous to the laminar stresses and the correlations between the point in question with those at other locations in the flow follow a distribution which may be assumed Gaussian. The model is initially applied to the steady incompressible turbulent Poiseuille flows between parallel flat plates and through circular pipes. The Navier-Stokes equations are simplified and solved analytically, with the aid of Integral Transform methods and asymptotic expansions. With the appropriate numerical values for the model constants, the approximate asymptotic solutions for the mean velocities are found in good agreement with the universal laws and with the experimental data. To test the model further, the steady incompressible turbulent boundary layer flow along the surface of a solid body is studied. It is shown that under the similarity transformations the boundary-layer equations may be simplified to give, to the first approximation, ordinary differential equations of order three. These equations are similar to the Blasius and the Falkner-Skan equations except for the presence of the additional terms representing' the turbulent effects. With the usual no-slip conditions at the wall, numerical solutions to these non-linear equations are obtained for various values of the flow parameters. For the special case when the pressure gradient related parameter n=-1, it is described how an approximate analytic solution can be obtained, by extending the existing solutions of the Falkner-Skan equation

Flaxseed dietary fibers suppress postprandial lipemia and appetite sensation in young men

Background and aim: Dietary fibers (DF) are linked to a reduced risk of life-style diseases, which relate to their physiological effects in the gastrointestinal tract. The aim was to examine whether flaxseed DF-enriched meals suppress postprandial lipemia and reduce appetite. Methods and results: Four different iso-caloric meals were tested in 18 young men in a double-blind randomized crossover design. Test meals were served after an overnight fast. DF content and source were: control (C): 1.4 g/MJ; whole flaxseed (WF): 2.4 g/MJ from whole flaxseeds; low-mucilage dose (LM): 2.4 g/MJ from flaxseed DF; high-mucilage dose (HM): 3.4 g/MJ from flaxseed DF. During the 7 h test day, subjective appetite sensation was assessed using visual analogue scales and appetite-regulating hormones, and lipemia and glycemia were measured, after which ad libitum energy intake was recorded. There was a significant time x meal effect on triacylglycerols (TG) (p = 0.02) and an 18% smaller area under the curve (AUC) for TG after meal HM compared to meal C was observed (p < 0.01). AUC for insulin was smaller after both LM and HM meals compared to C and WF meals. Higher mean ratings of satiety (p < 0.01) and fullness (p = 0.03) was seen following the HM meal compared to meal C. AUC for ghrelin, CCK and GLP-1 and ad libitum energy intake did not differ between meals, but ghrelin response exhibited a different response pattern after the mucilage-containing meals. Conclusion: These findings suggest that flaxseed DF may suppress postprandial lipemia and appetite although subsequent energy intake was not affected