A Numerical Approach for Modeling of Turbulent Newtonian Fluid Flow in Eccentric Annulus

Abstract

Turbulent flow is a complicated process that frequently appears not only in nature but also in engineering applications. Numerical methods frequently are used to solve turbulent flow problems due to the trouble in solving Navier-Stokes equations.  Navier-Stokes equations including inner pipe rotation effect are solved via two different numerical techniques. The efficiency of the proposed numerical technique is compared with the obtained solutions of Newton-Raphson method. The proposed method is computationally expensive, however, it may allow tackling the non-linearity of challenging problems in hydraulics. A mechanistic model including proposed numerical method is also developed in order to predict pressure gradient for fully developed turbulent flow through fully eccentric horizontal annulus including pipe rotation. The computational frameworks are developed in MATLAB. Mathematical model is confirmed by the experimental study, which is conducted in Izmir Katip Celebi University.  Results show that computational fluid model is a capable of estimating frictional pressure gradient with an error of less than 14 %.

Keywords

• eccentric annular flow; finite difference method; mechanistic modeling; newtonian fluid; pipe rotation; turbulent flow

A Numerical Approach for Modeling of Turbulent Newtonian Fluid Flow in Eccentric Annulus

Abstract

Türbülanslı akımlar, yalnızca doğada değil mühendislik uygulamalarında da görülen karmaşık bir yapıdadır.  Navier-Stokes denklemlerinin türbülanslı çözümlerinin karmaşık ve zor olmasından dolayı sayısal yöntemler sıklıkla kullanılır. İki farklı sayısal teknik vasıtasıyla boru dönmesi hesaba katılmış Navier-Stokes denklemleri çözülmüştür. Geliştirilen sayısal yöntemin etkinliği Newton-Raphson method kullanılarak elde edilen sonuçlarla karşılaştırılmıştır. Geliştirilen sayısal metot her ne kadar işlevsel olarak ağır olsa da, hidrolikteki linear olmayan zor problemlerin çözümünü sağlamaya yol açabilir. İç içe geçmiş borular arasından geçen tam gelişmiş türbülanslı akımın içteki borunun dönmesi etkili olduğu basınç farklarının tayini için geliştirilmiş sayısal metot ile birlikte bir mekanistik model geliştirilmiştir. Sayısal hesaplamalar MATLAB’ta geliştirilen kodlarla yapılmıştır. Yapılan sayısal hesaplamalar İzmir Katip Çelebi Üniversitesi’nde yapılan deneylerin sonuçlarıyla teyit edilmiştir. Elde edilen sonuçlar, hesaplamalı akışkanlar modelinin basınç gradyanını  %14’den daha az bir hata ile tahmin ettiğini  göstermiştir.

Keywords

• eksantrik borular arasındaki akış ; sonlu farklar metodu; mekanistik modelleme; newtonian akışkan; boru dönmesi; türbülanslı akış

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