Turbulent Flow Of non-Newtonian Fluids Research Articles

TURBULENT FLOW SIMULATION OF THE NONNEWTONIAN FLUIDS THROUGH A POROUS MEDIUM USING LES TURBULENCE MODEL

In this study, fully turbulent flow of non-Newtonian fluids is studied in a square periodic array as a porous medium, with porosity ranging from 0.5 to 0.84. Large eddy simulation (LES) is used as an effective turbulence model at a Reynolds number of 40,000. The governing equations are solved by Ansys Fluent commercial software for various porosities. The power-law and Carreau approaches are employed to model the dilatant and pseudo-plastic non- Newtonian fluids. In this study, the power-law and Carreau models are also compared. The results showed that an increase in porosity has a significant effect on flow parameters. Specifically, as porosity increases, vorticities, pressure, and velocity values increase within the computational domain. Moreover, it was observed that the Carreau model has a greater ability to obtain more realistic results in porous media domain and complex geometries.

Hydraulic Behavior in Cased and Open-Hole Sections in Highly Deviated Wellbores

Abstract In this paper, we present results from flow loop experiments with an oil-based drilling fluid with micronized barite as weight materials. The use of micronized barite allows using lower viscosity drilling fluid, providing non-laminar flow, which is advantageous for particle transport in near-horizontal sections. While transition to turbulence and turbulent flow of non-Newtonian fluids has been well studied both theoretically and experimentally, there are very few published results on the effect of wellbore wall properties on flow regime transition and turbulence. This is relevant because horizontal sections are often open hole with less well-defined surfaces than a steel casing surface. We have conducted a series of flow experiments with and without cuttings size particles in a 10-m long annular test section using steel and concrete material to represent the wellbore wall of a cased and open-hole section. In both cases, the annulus was formed by a freely rotating steel pipe of 2” outer diameter inside a 4” diameter wellbore. Experiments were conducted at 48 deg, 60 deg, and 90 deg wellbore inclination from vertical. The two materials result in different hydraulic behaviors without particles with stronger turbulence when using concrete wellbore wall material than when using steel casing. While there is a negligible difference at low flowrates, at 0.8 m/s and below, there is an increasing difference as the flowrate increases and becomes transitional to turbulence. Hole cleaning is found to differ dependent on the wall material. However, the effect on hole cleaning is less clear than for the pressure loss.

HYDRAULIC RESISTANCE AND HEAT TRANSFER IN NON-ISOTHERMAL PIPELINES, TRANSPORTING NON-NEWTONIAN OILS USING DRAG REDUCING ADDITIVES

Background Forecasting hydraulic resistance of non-isothermic turbulent flows of non-Newtonian fluids is of great industrial importance. There are practically no studies in the literature on calculating hydraulic resistance reduction using polymer additives for turbulent flows of thermally dependent non-Newtonian fluids. Aims and Objectives Calculation of hydraulic resistance and heat transfer of turbulent flows of non-Newtonian fluids in non-isothermal oil pipelines using polymeric additives. Methods Mathematical modeling and numerical calculations for determining the hydraulic resistance coefficient in non-isothermal oil pipelines transporting non-Newtonian power-law oil with parameters depending on the temperature of using drag reducing additives. Results A mathematical model has been developed for a non-isothermal oil pipeline transporting non-Newtonian power-law oil, with parameters depending on temperature using drag reducing additives.

A Review of Russian Snow Avalanche Models—From Analytical Solutions to Novel 3D Models

The article is a review of mathematical models of snow avalanches that have been proposed since the middle of the 20th century and are still in use. The main attention is paid to the work of researchers from the Soviet Union and Russia, since many of their works were published only in Russian and are not widely available. Mathematical models of various levels of complexity for avalanches of various types—from dense to powder-snow avalanches—are discussed. Analytical solutions including formulas for the avalanche front speed are described. The results of simulations of the movement of avalanches are given that were used to create avalanche hazard maps. The last part of the article is devoted to constructing models of a new type, in which avalanches are considered as laminar or turbulent flows of non-Newtonian fluids, using the full (not depth-averaged) equations of continuum mechanics. The results of a numerical study of the effect of non-Newtonian rheology and mass entrainment on the avalanche dynamics are presented.

Turbulent Flow of Polymer Fluids Over the Sand Bed in Horizontal Concentric Annulus

Turbulent flow of non-Newtonian fluids over stationary sand bed deposits are commonly encountered during the wellbore clean-out operations conducted to remove the cuttings (solids deposited as a result of drilling or post-fracking operations) from the horizontal wellbore. We have investigated the impact of the presence of a stationary sand bed deposit on the characteristics of the flow in a horizontal concentric annulus using Particle Image Velocimetry (PIV)technique. Velocity profiles, Reynolds stresses, and axial turbulence intensities are measured in the lower and upper half of the annulus to assess the impact of the sand bed on the flow. Results show that the presence of the sand bed causes the reduction of the volumetric flow rate in the lower part of the annulus with an associated decrease in the local fluid velocity and the flow turbulence. In the upper part of the annulus, however, increased level of turbulence and flat velocity profiles were observed.

Model inference using the Akaike information criterion for turbulent flow of non-Newtonian crude oils in pipelines

The friction factor is a crucial parameter in calculating frictional pressure losses. However, it is a decisive challenge to estimate, especially for turbulent flow of non-Newtonian fluids in pipes. The objective of this paper is to examine the validity of friction factor correlations adopting a new informative-based approach, the Akaike information criterion (AIC) along with the coefficient of determination (R 2). Over a wide range of measured data, the results show that each model is accurate when it is examined against a specific dataset while the El-Emam et al. (Oil Gas J 101:74–83, 2003) model proves its superiority. In addition to its simple and explicit form, it covers a wide range of flow behavior indices and generalized Reynolds numbers. It is also shown that the traditional belief that a high R 2 means a better model may be misleading. AIC overcomes the shortcomings of R 2 as a trade between the complexity of the model and its accuracy not only to find a best approximating model but also to develop statistical inference based on the data. The authors present AIC to initiate an innovative strategy to help alleviate several challenges faced by the professionals in the oil and gas industry. Finally, a detailed discussion and models’ ranking according to AIC and R 2 is presented showing the numerous advantages of AIC.

Laminar and Turbulent Flow of Non-Newtonian Fluids in Open Channels for Different Cross-Sectional Shapes

New models for the prediction of laminar and turbulent flow of non-Newtonian fluids in open channels of different cross-sectional shapes are proposed. These models are compared with three previously published models for laminar flow and five previously published models for turbulent flow using a recently extended experimental database for non-Newtonian flow in open channels of different cross-sectional shapes. Flow of three different fluids (aqueous carboxymethylcellulose solutions and kaolin and bentonite suspensions) was investigated in open channels of four different cross sections (rectangular, semicircular, trapezoidal, and triangular) at slopes varying from 1 to 5°. The new laminar model gave a closer fit to the data than those from the previously published models. However, the presence of the yield stress still presents a problem that makes flow prediction in laminar flow for such fluids not very accurate. The new model for turbulent flow gave the best fit to the flow data compared with the five previously published models, which fell within a 30% error margin. A particular advantage of both new models is that they are applicable for all the different fluids tested and the four open channel cross-sectional shapes.

A DNS Investigation of the Effect of Yield Stress for Turbulent Non-Newtonian Suspension Flow in Open Channels

The use of fixed-shape open channels in industrial processes is common in the mineral processing industry. With lack of fundamental understanding about the mechanisms involved in how a turbulent flow of a non-Newtonian carrier fluid transports suspension particles, direct numerical simulation may come into the research as a validation tool. Direct numerical simulation (DNS) of the turbulent flow of non-Newtonian fluids in an open channel is modeled using a spectral element-Fourier method. The simulation of a yield-pseudoplastic fluid using the Herschel-Bulkley model agrees qualitatively with experimental results from field measurements of mineral tailing slurries. The simulation results over-predict the flow velocity by approximately 40% for the cases considered, however, the source of the discrepancy is difficult to ascertain. The effect of variation in yield stress, flow behavior index, and assumed flow depth are investigated and used to assess the sensitivity of the flow to these physical parameters. This methodology is seen to be useful in designing and optimizing the transport of slurries in open channels.

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

A spectral element—Fourier method (SEM) for Direct Numerical Simulation (DNS) of the turbulent flow of non-Newtonian fluids is described and the particular requirements for non-Newtonian rheology are discussed. The method is implemented in parallel using the MPI message passing kernel, and execution times scale somewhat less than linearly with the number of CPUs, however this is more than compensated by the improved simulation turn around times. The method is applied to the case of turbulent pipe flow, where simulation results for a shear-thinning (power law) fluid are compared to those of a yield stress (Herschel–Bulkley) fluid at the same generalised Reynolds number. It is seen that the yield stress significantly dampens turbulence intensities in the core of the flow where the quasi-laminar flow region there co-exists with a transitional wall zone. An additional simulation of the flow of blood in a channel is undertaken using a Carreau–Yasuda rheology model, and results compared to those of the one-equation Spalart-Allmaras RANS (Reynolds-Averaged Navier–Stokes) model. Agreement between the mean flow velocity profile predictions is seen to be good. Use of a DNS technique to study turbulence in non-Newtonian fluids shows great promise in understanding transition and turbulence in shear thinning, non-Newtonian flows.

Turbulent pipe flow of shear-thinning fluids

Direct numerical simulation of the weakly turbulent flow of non-Newtonian fluids is undertaken for two different generalised Newtonian rheology models using a spectral element-Fourier method. Results for a power law (shear-thinning) rheology agree well with experimentally determined logarithmic layer correlations and with other previously published experimental work. As the flow index becomes smaller for the same Reynolds number, the flow deviates further from the Newtonian profile and the results suggest that transition is delayed. Predicted friction factors fall above those in the literature, but below the Newtonian values when a comparison is undertaken on the basis of the Metzner–Reed Reynolds number. Results for a Herschel–Bulkley model (yield stress+shear-thinning) are compared to corresponding experimental measurements and are found to be in very good agreement. Use of direct numerical simulation shows great promise in understanding transition and turbulence in non-Newtonian fluids.

A Generic Model for Calculation of Frictional Losses in Pipe and Annular Flows

Abstract A theoretical foundation of a new simulator for hydraulic calculations of mud transport is presented. It is demonstrated that it is possible to design a simulator based on theoretical concepts taken from fluid dynamics. The theory is based on a simple turbulence model, which is calibrated against direct simulations of turbulent flows, and a simple expression for suppression of turbulence at low wall strain-rates. The model predicts turbulent non-Newtonian flows, provided rheology data is available. This is an attractive feature of the model as no general non- Newtonian flow correlations are available in the literature. The output from the model is wall shear stresses and pressure drops, while the most important input is the fluid data, and in particular the fluid rheology and its dependency on pressure and temperature. Due to instabilities caused by the drill-string and variable surface roughness at the contacting walls, it is assumed that the flow is unstable or quasi-turbulent, even for low Reynolds numbers well below 1,000. Also, effects of rotation and heat transport are treated in the same fundamental manner. The effects of rotation are included by solving for the tangential velocity in addition to the axial velocity. It is shown that rotation may have a profound impact on the pressure drop. The suggested methodology is expected to increase the precision of predictions and reduce the costs of lab testing and traditional curve fitting to analytical models. The model is verified against experimental data. For most situations, we obtained good agreement with data, as well as for laminar/turbulent transitional flows. Finally, the paper indicates that traditional Fann readings, using 4 points, are inadequate for an accurate rheology determination. In order to improve the hydraulic model, more focus on rheology data is needed. Introduction An important aspect of hydraulic optimization is an accurate estimation of the equivalent circulating density (ECD), especially in long, narrow wells. For this purpose, several simulators for hydraulic calculations of drilling wells have been developed(1). One frequent problem in such simulations is the quality of rheological data that affects the selection of the rheological model. A common approach is to let the user select a rheological model from a set of predefined rheologies(2, 3). Another approach is to curve fit the data to a best fit with a selected rheology model(4). Denis and Guillot(5) found that the Fann viscometer systematically seems to overpredict pressure losses. They tested one pipe viscometer and two rotational viscometers and recommended applying a high quality viscometer instead of the inaccurate Fann viscometer. In another work, Efaghi et al.(6) had access to the training well at Louisiana State University and recorded pressure losses of mud in a 27/8 in., 3,000 ft. deep tubing, comparing Bingham and Power law rheological models. Laminar pressure losses were not predicted accurately since the viscometer shear rate was not representative of the actual laminar flow in the tubing. Valuable data of turbulent flow of non-Newtonian fluids in rough pipes was recorded by Szilas, Bobok, and Navratil(7).

Numerical Analysis of Turbulent Flow of Non-Newtonian Fluids in Eccentric Annular Passage.

A numerical analysis has been performed for developing turbulent flow of non-Newtonian fluid in eccentric annular passage. Several calculations have been carried out to examine the drag reduction with decreasing power index of power-law fluids and the reduction of skin friction factor with increasing eccentricity defined by the distance between the centers of the inner and outer pipes for Newtonian fluid. In numerical analysis, the power law model for non-Newtonian fluid and an algebraic Reynolds stress model for turbulent flow were adopted in order to predict precisely non-Newtonian flow behaviour. Boundary-fitted coordinate system was introduced as the method of coordinate transformation. The numerical results are compared with the experimental data involving stramwise velocity and fluctuating velocities in axial, radial and tangential directions. As a result of comparison with the experiment, it was found that the present method could predict well the streamwise meam-velocity in both fluids and reproduce the secondary flow of the second kind generated by anisotoropic turbulence. As for the comparison of fluctuating velocities, the agreement with experimental data is more satisfied for Newtonian fluid than for non-Newtonian fluid. The calculated results also suggest that the drag reduction with polymer solution is realized by the present method as well as the experiment and the phenomenon of decaying fluctuating velocity with decreasing power index is predicted.

Numerical Analysis of Turbulent Flow of Non-Newtonian Fluids in Curved Pipes.

A numerical analysis has been performed for developing turbulent flow of non-Newtonian fluid in curved pipe, Numerical results are shown in two cases of power-law fluids, i.e. power index 0.76 and 0.9, at Reynolds number 19000. The ratio of bend mean radius of curvature to radius is 10 and straight duct of 40 and 100 diameters are attached to the inlet and outlet of the bend, respectively. In numerical analysis, an algebraic Reynolds stress model was adopted in order to predict precisely the anisotropic turbulent flow and boundary-fitted coordinate system was introduced as the method of coordinate transformation. The numerical results are compared with the experimental data measured by laser-Doppler anemometer. Mean velocity and fluctuating velocity in axial direction are examined into detail to clarify the validity of the turbulent model and present numerical method. As a result of this research, it is found that the present method could predict well the streamwise mean-velocity in both cases of power-law fluids. As for the comparison of fluctuating velocity, characteristic features are reproduced except for the outer region of pipes. The present method predicts its value in outer regin smaller than that of the experiment, while the present method realized the phenomenon of decaying mean fluctuating velocity with decreasing power index. The results of comparison with the experimental data suggest that algebraic turbulent model is applicable to the non-Nowtonian fluid although agreement between both results is certainly not perfect in all detail.

A numerical solution for the turbulent flow of non-Newtonian fluids in the entrance region of a heated circular tube

Numerical solutions of conservation equations are obtained for turbulent flow of non-Newtonian fluids in a circular tube. The forward marching procedure of Patankar and Spalding 1 was implemented in order to obtain the simultaneous development of the velocity and temperature fields by using the apparent viscosity of fluids. Prandtl's mixing length concept is used to determine the apparent turbulent shearing stress. Furthermore, local and average Nusselt numbers are obtained in the entrance region, as well as in the fully developed region. For the case of the fully developed region, values of the Nusselt numbers are compared both with the experimental data and empirical correlations.

Determination of turbulent pressure loss of non-newtonian oil flow in rough pipes

A detailed theoretical analysis is carried out of the turbulent flow of non-newtonian fluids in rough pipes in which approximate assumptions are of negligible importance. A new friction-factor equation (BNS-equation) is obtained which is valid for turbulent flow of “power-law type” non-newtonian fluids in the transition region between smooth and wholly rough wall turbulence.

The turbulent flow of non-Newtonian fluids in the absence of anomalous wall effects

For Newtonian fluids, the engineering predictions for pressure drop in turbulent pipe flow are well established. However, in the case of non-Newtonian liquids, only a few design techniques have been proposed and these do not share a common basis with the approach for Newtonian systems. This present work attempts to provide a common basis for both Newtonian and non-Newtonian systems in situations where anomalous wall effects are absent. Previously published experimental data suggest that if the Reynolds number is calculated on the basis of the apparent viscosity at the wall then the standard Newtonian correlations can be used for the prediction of pressure drop. The use of the wall viscosity in defining the Reynolds number also serves as a test for anomalous behaviour. Any departure of the experimental data from the Newtonian turbulent friction factor correlation indicates anomalous behaviour.

Laminar-Turbulent Transition in Flow of Pseudoplastic Fluids with Yield Stresses

An analysis of the laminar-turbulent transition behavior of power law non-Newtonian fluids with yield stresses reveals that considerable interaction occurs between the characterizing parameters m and Hedstrom number for low power law indexes, m. In particular, for m < 0.4 small yield stresses tend to destabilize the flow whereas large ones stabilize it. The results of this analysis suggest that in order to obtain correct predictions and interpretations of transitional and turbulent flows of nonNewtonian fluids, a correct modeling of the viscous rheological behavior of the fluid is essential. Nomenclature A = a dimensionless parameter defined by Eq. (6) D - pipe diameter / = friction factor He - Hedstrom number, defined by Eq. (17) K = laminar-turbulent transition parameter K = maximum value of K m = power law index in rheological model Re - Reynolds number,.defined by Eq. (8) r = radial coordinate u = v/(u}, dimensionless velocity v = velocity (v} ~ mean velocity T = -du/d£ j] = consistency index in rheological model k = r/rw £ = value of £ where K = K £o = TQ/TW p — fluid density a = dimensionless parameter defined by Eq. (7) r = shear stress TO = yield stress in rheological model

A Study on Anomalous Turbulent Flows of Non-Newtonian Fluids : 3rd Report, Experiment and Analysis in Transitional Region

Transitional region of pipe flows of dilute polymer solutions is investigated. Experiment is made with HEC water solutions and the following results are obtained. Anomaly of the resistance coefficient is very small in the flow region before transition, though it is comparatively large for PEO solutions as reported in the previous paper. In this flow region a kind of fluctuations of static pressure is recognized and once the fluctuations occur, the appearance of issuing jets shows some anomalous winding effects. An approximate analysis is made on the anomaly of the resistance coefficient in the flow region before transition. The results show that the resistance coefficient becomes larger than that of Poiseuille flow and that if Reynolds numbers and the fluctuations are constant, the rate of increase of the resistance coefficient enlarges as Weissenberg number increases. Comparison between analytical results and experimental data shows an approximate agreement.

A Study on Anomalous Turbulent Flows of Non-Newtonian Fluids : 3rd Report, Experiment and Analysis in the Transition Region

A Study on Anomalous Turbulent Flows of Non-Newtonian Fluids : 3rd Report, Experiment and Analysis in the Transition Region

A Study on Anomalous Turbulent Flows of Non-Newtonian Fluids : 2nd Report, Transitional Region from Laminar to Turbulent Flow

A Study on Anomalous Turbulent Flows of Non-Newtonian Fluids : 2nd Report, Transitional Region from Laminar to Turbulent Flow