A study of Reynolds-stress closure model

A hybrid model of the Reynolds stress closure was developed. This model was tested for various sizes of step flow, and the computed Reynolds stress behavior was compared with experimental data. The third order closure model was reviewed. Transport equations for the triple velocity correlation were developed and implemented in a numerical code to evaluate the behavior of the triple velocity products in various regions of the flow field including recirculating, reattaching, and redeveloping flow domains

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region

Numerical study of a separating and reattaching flow by using Reynolds-stress tubulence closure

The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure - strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion

Improvement of the second- and third-moment modeling of turbulence: A study of Reynolds-stress closure model

Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model

A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables

Groundwater recharge in Panjab State (India) using tritium tracer

Vertical recharge to groundwater due to the 1972 monsoon plus supplemental irrigation has been measured at 21 sites in the state of Panjab (1ndia) using tritigm tracer. Average recharge is found to be equivalent to 8.5 cm of water. This is about 18% of the average rainfall and 12% of the total watering

Cascades: A view from Audience

Cascades on online networks have been a popular subject of study in the past decade, and there is a considerable literature on phenomena such as diffusion mechanisms, virality, cascade prediction, and peer network effects. However, a basic question has received comparatively little attention: how desirable are cascades on a social media platform from the point of view of users? While versions of this question have been considered from the perspective of the producers of cascades, any answer to this question must also take into account the effect of cascades on their audience. In this work, we seek to fill this gap by providing a consumer perspective of cascade. Users on online networks play the dual role of producers and consumers. First, we perform an empirical study of the interaction of Twitter users with retweet cascades. We measure how often users observe retweets in their home timeline, and observe a phenomenon that we term the "Impressions Paradox": the share of impressions for cascades of size k decays much slower than frequency of cascades of size k. Thus, the audience for cascades can be quite large even for rare large cascades. We also measure audience engagement with retweet cascades in comparison to non-retweeted content. Our results show that cascades often rival or exceed organic content in engagement received per impression. This result is perhaps surprising in that consumers didn't opt in to see tweets from these authors. Furthermore, although cascading content is widely popular, one would expect it to eventually reach parts of the audience that may not be interested in the content. Motivated by our findings, we posit a theoretical model that focuses on the effect of cascades on the audience. Our results on this model highlight the balance between retweeting as a high-quality content selection mechanism and the role of network users in filtering irrelevant content

Fictitious Photon Mass in Radiative Bhabha Scattering

This thesis consists of four chapters. The first chapter is devoted to introduction. In the second chapter fundamental definitions and results required in the sequal are given. In the third chapter an Opial type inequalities involving fractional derivatives. The later chapter includes Opial type inequalities involving Riemann-Liouville fractional derivatives of two functions.Bu tez, dört bölümden oluşmaktadır. İlk bölüm giriş kısmına ayrılmıştır. İkinci bölümde çalışmamız için gerekli olan temel kavramlar verilmiştir. Üçüncü bölümde, kesirli türevler içeren Opial tipli eşitsizlikler için bazı sonuçlar verildi. Son bölümde iki değişkenli fonksiyonlar için Riemann-Liouville kesirli türevlerini içeren Opial tipli eşitsizliklerin bazı sonuçları verildi