Modelling the new stress for improved drag reduction predictions of viscoelastic pipe flow (original) (raw)
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A NEW k-ε MODEL FOR VISCOELASTIC DRAG REDUCING PIPE FLOW
paginas.fe.up.pt
The new stress term in the time-average momentum equation of the modified generalised Newtonian fluid model of Cruz and Pinho (2003) is modeled for improved predictions of turbulent viscoelastic flows. The modified generalised Newtonian model was introduced by Pinho (2003) to mimic viscoelastic effects of fluids exhibiting drag reduction in turbulent pipe flow. The new stress quantifies the cross-correlation between the fluctuating viscosity and the fluctuating rate of strain and had been neglected in the k-ε low Reynolds number model originally developed by Cruz and Pinho (2003). The inclusion of this model for the new stress improves the predictions of turbulent kinetic energy ( k + ) in drag reducing pipe flow at the cost of a negligible deterioration in the prediction quality of other quantities for some of other fluids tested and for which the literature provides data. The original model of has also been modified to correct for a mistake and this was shown to improve the predictions for all fluids except for the solution of 0.125%PAA used to calibrate the model.s.
Paper CIT04-0344 A NEW k-ε MODEL FOR VISCOELASTIC DRAG REDUCING PIPE FLOW
2015
Abstract. The new stress term in the time-average momentum equation of the modified generalised Newtonian fluid model of Cruz and Pinho (2003) is modeled for improved predictions of turbulent viscoelastic flows. The modified generalised Newtonian model was introduced by Pinho (2003) to mimic viscoelastic effects of fluids exhibiting drag reduction in turbulent pipe flow. The new stress quantifies the cross-correlation between the fluctuating viscosity and the fluctuating rate of strain and had been neglected in the k-ε low Reynolds number model originally developed by Cruz and Pinho (2003). The inclusion of this model for the new stress improves the predictions of turbulent kinetic energy ( k+) in drag reducing pipe flow at the cost of a negligible deterioration in the prediction quality of other quantities for some of other fluids tested and for which the literature provides data. The original model of Cruz and Pinho (2003) has also been modified to correct for a mistake and this w...
A Reynolds stress model for turbulent flows of viscoelastic fluids
Journal of Turbulence, 2013
A second order closure for predicting turbulent flows of viscoelastic fluids is proposed in this work and its performance is assessed by comparing its predictions with experimental data for fully-developed pipe flow. The model is an extension of an existing Reynolds stress closure for Newtonian fluids and includes low Reynolds number damping functions to properly deal with wall effects. The model was modified to take into account viscoelasticity, especially in the pressure strain term. The new damping functions depend on rheological characteristics of the fluids, as was the case with previous developments of k-ε models for viscoelastic fluids by Cruz and Pinho [1] and Cruz et al. [2].
Simulating drag reduction phenomenon in turbulent pipe flows
Mechanics Research Communications, 2008
Drag reduction using polymeric additives is an interesting phenomenon in turbulent pipe flows which was first discovered by Toms . Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. First Int. Cong. Rheol. 2,[135][136][137][138][139][140][141]. Due to its industrial importance, the phenomenon has been the subject of much study in the past, in both theoretical and experimental domains alike. As to the mechanisms involved, it has been argued that polymeric additives act through affecting the structure of turbulent bursts near the wall by boosting the extensional viscosity of the base fluid (see [Lumley, J.L., Blossey, P., 1998. Control of turbulence. Ann. Rev. Fluid Mech. 30, 311-327]). In practice, drag reduction as large as 90% has been achieved with concentration as low as 20 ppm of certain high-molecular-weight flexible polymers. Prediction of such huge drag reductions obtained using polymeric additives has not been possible in the past partly, because of the limitations of the computational facilities and also because of the inadequacies of the constitutive equations used for the simulations. Recently, Pinho [Pinho, F.T., 2003. A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k-e type closure. J. Non-Newtonian Fluid Mech. 114, 149-184] modified the generalized Newtonian fluid (GNF) model in such a way that it could take into account the extensional viscosity (a measure of the elastic behavior of a fluid) in addition to the shear viscosity (a measure of the viscous behavior of a fluid). Based on this idea, Pinho (2003) derived the first time-averaged turbulent flow formulations for viscoelastic fluids. These formulations were used by Cruz and Pinho [Cruz, D.O.A., Pinho, F.T., 2003. Turbulent pipe flow predictions with a low-Reynolds number k-e model for drag reducing fluids. J. Non-Newtonian Fluid Mech. 114, 109-148] and Cruz et al. [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. Non-Newtonian Fluid Mech. 121, 127-141] by embedding the low-Reynolds turbulence model of Nagano-Hishida [Nagano, Y., Hishida, M., 1987. Improved form of the k-e model for wall turbulent shear flows. J. . They performed several simulations using this well-known turbulence model and showed that it can well predict the large drag reduction observed in practice for some polymeric additives. But for certain other polymers the prediction were found not to be so great. In this work, it will be shown that better predictions can be obtained for these polymers if use is made of another low-Reynolds number k-e turbulence model called Launder-Sharma model . Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1, 131-138] for the simulations.
Development of a Reynolds Stress Model to Predict Turbulent Flows with Viscoelastic Fluids
2006
A second order closure for predicting turbulent flows of viscoelastic fluids is proposed in this work and its performance is assessed by comparing its predictions with experimental data for fully-developed pipe flow. The model is an extension of an existing Reynolds stress closure for Newtonian fluids and includes low Reynolds number damping functions to properly deal with wall effects. The
Modeling of viscoelastic turbulent flow in channel and pipe
Physics of Fluids, 2008
This paper investigates turbulent flows with or without polymer additives in open channels and pipes. Equations of mean velocity, root mean square of velocity fluctuations, and energy spectrum are derived, in which the shear stress deficit model is used and the non-Newtonian properties are represented by the viscoelasticity ␣ *. The obtained results show that, with ␣ * increment, ͑1͒ the streamwise velocity fluctuations is increased, ͑2͒ the wall-normal velocity fluctuation is attenuated, ͑3͒ the Reynolds stress is reduced, and ͑4͒ there is a redistribution of energy from high frequencies to the low frequencies for the streamwise component, but dimensionless distribution over all frequencies almost remains the same as that in Newtonian fluid flows. Good agreement between the derived equations and experimental data in small drag-reduction regime is achieved, which indicates that the present model is workable for Newtonian/non-Newtonian fluid turbulent flows.
A LOW REYNOLDS k-ε MODEL FOR VISCOELASTIC FLUIDS
A low Reynolds number k - ε model was developed for predicting drag reducing turbulent flows of elastic fluids. The rheology of the fluid was modelled by a Generalized Newtonian model modified to mimic relevant effects of extensional viscosity. A new damping function, that takes wall effects into account, is also proposed. The predictions of friction factor, mean velocity and turbulent kinetic energy compare favourably with data from the literature for various polymer solutions. The advantage of this model is that it only needs input data from the rheology of the fluid and the bulk velocity of the flow in contrast to existing models for drag reducing fluids which must be modified on a case by case basis .
Flow of non-newtonian fluids in a pipe
Journal of Non-Newtonian Fluid Mechanics, 1990
Measurements of mean axial velocity and of the three normal stresses have been obtained in fully developed pipe-flow with four concentrations of a polymer (sodium carboxymethyl cellulose) in aqueous solution and with water and viscous Newtonian fluids encompassing a range of Reynolds numbers from 240 to 111,000. The results quantify the delay in transition from laminar to turbulent flow caused by shear-thinning, the suppression of turbulent fluctuations particularly in the radial and tangential components of normal stress, and the drag reduction at the higher Reynolds numbers. They also confirm that the maximum drag reduction asymptote is appropriate to these shear-thinning solutions 0377-0257/90/$03.50 0 1990 Elsevier Science Publishers B.V.
CFD Simulation of the Flow Pattern for Drag Reducing Fluids in Turbulent Pipe Flows
Journal of Chemical Engineering of Japan, 2007
In the present work, the flow pattern in pipe flows has been simulated for drag reducing fluids using a low Reynolds number k-ε ε ε ε ε model. The model uses a non-linear molecular viscosity and damping function to account for near wall effects. The comparison between the predictions and the experimental profiles of axial velocity and kinetic energy are in good agreement. A systematic study has been undertaken to investigate the effect of rheological parameters and to consider the modification to the flow that arises in the presence of a fluid yield stress.
International Journal of Heat and Fluid Flow, 2006
An anisotropic low Reynolds number k-e turbulence model has been developed and its performance compared with experimental data for fully-developed turbulent pipe flow of four different polymer solutions. Although the predictions of friction factor, mean velocity and turbulent kinetic energy show only slight improvements over those of a previous isotropic model [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. [127][128][129][130][131][132][133][134][135][136][137][138][139][140][141], the new turbulence model is capable of predicting the enhanced anisotropy of the Reynolds normal stresses that accompanies polymer drag reduction in turbulent flow.