Development of a Reynolds Stress Model to Predict Turbulent Flows with Viscoelastic Fluids (original) (raw)
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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].
PERFORMANCE OF THE k-ε AND REYNOLDS STRESS MODELS IN TURBULENT FLOWS WITH VISCOELASTIC FLUIDS
2000
The performance of a newly developed low Reynolds number second order closure for viscoelastic fluids is compared with that of an existing k-ε model using experimental data for fully-developed flow of various polymer solutions in circular pipes of Escudier et al. (1999) and Resende et al. (2005). New developments were made to account separated flows, removing the dependence of 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.
Modelling the new stress for improved drag reduction predictions of viscoelastic pipe flow
Journal of Non-Newtonian Fluid Mechanics, 2004
A model is proposed for the new stress term in the momentum equation of a modified generalised Newtonian fluid that is used 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 [J. Non-Newt. Fluid Mechanics 114 ]. With the inclusion of this new stress, the predictions of turbulent kinetic energy (k + ) in drag reducing pipe flow are significantly improved at the cost of a slight deterioration in the prediction of other quantities for some of the fluids. The value of the coefficient C in the original model of Cruz and Pinho was also modified to correct 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. Comparison of predictions with DNS results for a FENE-P model showed large overprediction of drag reduction and emphasize the need for improvements in extensional rheometry.
A NEW k-ε MODEL FOR VISCOELASTIC DRAG REDUCING PIPE FLOW
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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.
Journal of Non-Newtonian Fluid Mechanics, 2016
Most Direct Numerical Simulation (DNS) of turbulent flow of generalized Newtonian (GN) fluids presented to date have shown significant discrepancy between experimental measurement and simulation. In addition to DNS, empirical correlations using different rheology models fitted to the same shear rheogram have also shown to give significantly different results. Important to note is that for turbulent flow predictions it is a common practice to use a shear rheogram which is measured at shear rates well below the values encountered in turbulent flows. This paper highlights the importance of obtaining high shear rate rheology in reducing these discrepancies. Further, it is shown that if high shear rate rheology is used in rheology characterisation, the choice of rheology model has little influence on the results. An important aside is that accurate prediction of laminar flow gives absolutely no confidence that a rheology model is acceptable in modelling the turbulent flow of the same fluid. From an analysis of instantaneous shear rates in the predicted turbulent flow field, the probability distribution of the non-dimensionlised shear rates in the near-wall region appears to collapse onto a universal curve. Based on this, we propose that the maximum shear rate required in rheology characterisation should be at least twice the shear rate corresponding to the mean wall shear stress.
Velocity distributions and normal stresses in viscoelastic turbulent pipe flow
AIChE Journal, 1966
Pitot tube readings in a viscoelastic turbulent stream are discussed theoretically, and are shown to be made up by a first normal stress contribution, an integral normal stress contribution, and a kinetic contribution. These three contributions are of comparable orders of magnitude. The integral of a Pitot tube scanning curve is shown to yield a momentum average factor of direct physical relevance. Experimental data show that the normal stress contributions ore not negligible even in the central region of the pipe, although turbulent flow conditions were reached. Observed values of the relevant parameters are discussed. Laminor Flow When the liquid is in laminar flow, time-average and instantaneous values coincide, and Equation (5) reduces to the equation given originally by Savins (12). Savins proposed the use of Equation (5) , together with an independent evaluation of the velocity distribution. as a means for measuring the first normal stress difference ux*-uTU. In order to make this possible, he assumed that the second norma1 stress difference cr*q U is zero. Some comments concerning this assumption seem in order. Although it is by now accepted that the so-called 'Weissenberg hypothesis," namely ora = ogu, has no a priori justification, experimental evidence (8, 12) indicates that the second normal stress difference is indeed minor as compared to the first one. This does not, however, permit the integral normal stress contribution to be dropped
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...
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.
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 .