Stress modelling

Arzhaev A.I., Bougaenko S.E., Smirnov Yu.I., Aladinsky V V, Makhanev V.O., Saburov Yu. Residual stress modelling and analysis for INPP primary circuit pipeline welds. Transactions of the 14th Int. Conf. on Structural Mechanics in Reactor Technology (SMiRT 14), Lyon, 1997, Vol. 1, Div, B, pp. 345-352. 

Reynolds Stress Models. Eddy viscosity is a useful concept from a computational perspective, but it has questionable physical basis. Models employing eddy viscosity assume that the turbulence is isotropic, ie, u u = u u = and u[ u = u u = u[ = 0. Another limitation is that the... 

The flow pattern is ealeulated from eonservation equations for mass and mometum, in eombination with the Algebraie Stress Model (ASM) for the turbulent Reynolds stresses, using the Fluent V3.03 solver. These equations ean be found in numerous textbooks and will not be reiterated here. Onee the flow pattern is known, the mixing and transport of ehemieal speeies ean be ealeulated from the following model equation ... 

Almost all modern CFD codes have a k - model. Advanced models like algebraic stress models or Reynolds stress model are provided FLUENT, PHOENICS and FLOW3D. Table 10-3 summarizes the capabilities of some widely used commercial CFD codes. Other commercially CFD codes can be readily assessed on the web from hptt//www.cfd-online.com This is largest CFD site on the net that provides various facilities such as a comprehensive link section and discussion forum. 

Chen, Q. Prediction of room air motion by Reynolds-stress models. Build. FInviron., vol. 31, pp. 233-244, 1996. 

Gatski, T. B., Speziale, C. G. On explicit algebraic stress models for complex turbulent flows. /. Fluid Mech., vol. 154, pp. 59-78, 1993. 

Abid, R., Ramsey, C., Gatski, T. Prediction of nonequilibriura turbulent flows with explicit algebraic stress models. AIAA J., vol. 33, pp. 2026-2031, 1995. 

An appropriate model of the Reynolds stress tensor is vital for an accurate prediction of the fluid flow in cyclones, and this also affects the particle flow simulations. This is because the highly rotating fluid flow produces a. strong nonisotropy in the turbulent structure that causes some of the most popular turbulence models, such as the standard k-e turbulence model, to produce inaccurate predictions of the fluid flow. The Reynolds stress models (RSMs) perform much better, but one of the major drawbacks of these methods is their very complex formulation, which often makes it difficult to both implement the method and obtain convergence. The renormalization group (RNG) turbulence model has been employed by some researchers for the fluid flow in cyclones, and some reasonably good predictions have been obtained for the fluid flow. 

More advanced models, for example the algebraic stress model (ASM) and the Reynolds stress model (RSM), are not based on the eddy-viscosity concept and can thus account for anisotropic turbulence thereby giving still better predictions of flows. In addition to the transport equations, however, the algebraic equations for the Reynolds stress tensor also have to be solved. These models are therefore computationally far more complex than simple closure models (Kuipers and van Swaaij, 1997). 

Our results do not support the protein stress model. However, this model may apply in cases where stress is intermittent and results in tissue loss, as observed in the study of crows (Hobson and Clark 1992). Low protein levels throughout life after weaning may have produced overall slow and reduced rate of growth rather than tissue loss. Adult rats fed protein-deficient diets after maturation show systematic losses of nitrogen from most tissues that are in proportion to their turnover rates and masses (Uezu et al. 1983). Perhaps tissue nitrogen isotope enrichment may occur under these conditions. New experiments are needed to evaluate this hypothesis. 

Tahry, S.E., Application of a Reynolds stress model to engine-like flow calculations. /. of Fluids Engineering, 1985.107(4) 444-450. 

Adverse drug reactions and the diathesis stress model... 

Diathesis stress model A multifactorial model of pathogenesis suggesting that schizophrenia is due to the complex interaction between a number of internal and external factors. 

Fig. 5. The piezospectroscopic behavior of the two ls-like levels of differently oriented, trigonal shallow acceptor complexes, based on the equivalent stress model, (a) Trigonal distortion equivalent to a stress of + 0.205 kbar (tensional). (b) Trigonal distortion equivalent to a stress of —0.810 kbar (compressional). Roman numerals denote the four possible orientations of the complexes. A4 and A5 6 denote the representations of C3v according to which the states transform in the absence of externally applied stress. The energy shifts are shown for externally applied compressional stress under applied tensional stress, the behavior of (a) and (b) is reversed, as explained in the text.

A cure against these longer CPU times is the Algebraic Stress Model (ASM) described by, e.g., Rodi (1984) and used and recommended by, e.g., Bakker (1992) and Bakker (1996). Most commercial codes do no longer support an ASM. 

Venneker et al. (2002) used as many as 20 bubble size classes in the bubble size range from 0.25 to some 20 mm. Just like GHOST , their in-house code named DA WN builds upon a liquid-only velocity field obtained with FLUENT, now with an anisotropic Reynolds Stress Model (RSM) for the turbulent momentum transport. To allow for the drastic increase in computational burden associated with using 20 population balance equations, the 3-D FLUENT flow field is averaged azimuthally into a 2-D flow field (Venneker, 1999, used a less elegant simplification )... 

---