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Numerical Solution of Mass Flow Rate Controlled, Fully Developed, Unsteady, Turbulent Pipe Flows

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.1950
pages 1918-1929

Subhashis Ray
Institute of Thermal Engineering, Technische Universitat Bergakademie Freiberg, Gustav-Zeuner-Strasse 7, D-09596 Freiberg, Germany

Eric Werzner
Institute of Thermal Engineering, Technische Universitat Bergakademie Freiberg, Gustav-Zeuner-Str. 7, 09596 Freiberg, Germany

Dimosthenis Trimis
Institute of Thermal Engineering, Technische Universitat Bergakademie Freiberg, Gustav-Zeuner-Strasse 7, D-09596 Freiberg, Germany; Engler-Bunte-Institute Division of Combustion Technology, Karlsruhe Institute of Technology, Engler-Bunte-Ring 1, D-76131


This paper presents a method for the simulation of mass flow rate-driven, fully-developed, unsteady, turbulent pipe flow. Under the assumption of full-developed flow, all the flow variables, except pressure, are functions of only the wall normal coordinate. The pressure, on the other hand, can be assumed to be uniform over the cross-section of the pipe at a given axial location and can be considered to be dependent only on the axial direction. The applicable governing equations clearly suggest that if the pressure gradient is known as a function of time, the velocity solution as functions of time and space can be easily obtained by numerically integrating the governing equations over the pipe cross-section. From these solutions, the mass flow rates are generally calculated. Therefore, when the mass flow rate is prescribed as a function of time, one requires guessing the pressure gradient and hence has to formulate a simple and robust algorithm for its correction, so that the predefined mass flow rate is obtained. This task has been taken up and systematically presented in this paper. The performance of the proposed algorithm has been demonstrated by solving accelerating, decelerating and sinusoidally pulsating turbulent, fully-developed, pipe flows.

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