A Theory of Transitional and Turbulent Flow of Non-Newtonian Slurries Between Flat Parallel Plates

1971 ◽  
Vol 11 (01) ◽  
pp. 52-56 ◽  
Author(s):  
Richard W. Hanks ◽  
Maheshkumar P. Valia
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Frictional Resistance ◽  
Newtonian Fluids ◽  
Transitional Flow ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Large Width

Abstract A theoretical model is developed which Permits prediction of velocity profiles and frictional prediction of velocity profiles and frictional resistance factors for the isothermal flow of Bingham plastic non-Newtonian slurries in laminar, transitional, and turbulent flow between that parallel walls, in rectangular ducts of large width-to-height ratios, or in concentric annuli with radius ratios approaching unity. The theory is tested with available frictional resistance data for a range of Hedstrom numbers from 10(4) to 10(8) and a set of theoretical design curves of friction factor vs Reynolds number is developed. The model indices that for certain ranges of Hedstrom number (the non-Newtonian index) turbulence is suppressed relative to Newtonian flow behavior, whereas for other ranges of Hedstrom number, the converse is true. Introduction The handling of non-Newtonian fluids in turbulent motion is an important operation in many modern technological processes. Despite this fact, however, little has been done to develop models which are comparable to those available for Newtonian turbulent flow. In particular, a model of the transitional flow regime is notably lacking. Recently, a theory of laminar-turbulent transition for non-Newtonian slurries flowing in pipes and parallel plates was presented. A theory of parallel plates was presented. A theory of transitional and turbulent flow of Newtonian fluids in pipes and parallel plate ducts has also recently been developed. This theory permits the analytic calculation of the friction factor-Reynolds number curves as a continuous function of Reynolds number from the critical Reynolds number of laminar turbulent transition to any condition of turbulent flow. In this paper these two theories will be combined in order to develop a theory for the transitional and turbulent flow of non-Newtonian slurries in parallel plate ducts, rectangular ducts of large width-to-height ratio, or concentric annuli with radius ratios approaching unity. THEORETICAL ANALYSIS The rheological model which will be used to represent the non-Newtonian slurry behavior is the linear Bingham plastic model, ..............(1) ............(2) For this model the laminar flow curve is given by ..............(3) where q = 2v/b, b is one-half the distance between the plates, w = b(−dp/dz) is the wall shear stress, and D = o/ w. The end of the laminax flow, region is determined by the equations ........(4) .........(5) where N Rec = 4bp vc/ p is the critical Reynolds number, Dc is the critical transitional value of D and N He -16bp o/ p is the Hedstrom number expressed in terms of the hydraulic diameter for parallel plates. parallel plates. The calculation of the transitional flow field for this type of fluid will be based upon the model developed by Hanks for Newtonian fluids. SPEJ P. 52

Difference in Critical Reynolds Number Between Hagen-Poiseuille and Plane Poiseuille Flows

2001 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Poiseuille Flow ◽  
Average Velocity ◽  
Critical Reynolds Number ◽  
Inlet Section ◽  
Parallel Plates ◽  
Plane Poiseuille Flow ◽  
Contraction Ratio ◽  
Significant Difference

Abstract For plane Poiseuille flow, results of previous investigations were studied, focusing on experimental data on the critical Reynolds number, the entrance length, and the transition length. Consequently, concerning the natural transition, it was confirmed from the experimental data that (i) the transition occurs in the entrance region, (ii) the critical Reynolds number increases as the contraction ratio in the inlet section increases, and (iii) the minimum critical Reynolds number is obtained when the contraction ratio is the smallest or one, and there is no-shaped entrance or straight parallel plates. Its value exists in the neighborhood of 1300, based on the channel height and the average velocity. Although, for Hagen-Poiseuille flow, the minimum critical Reynolds number is approximately 2000, based on the pipe diameter and the average velocity, there seems to be no significant difference in the transition from laminar to turbulent flow between Hagen-Poiseuille flow and plane Poiseuille flow.

Loss Characteristics of Orifices and Nozzles

1978 ◽  
Vol 100 (3) ◽  
pp. 299-307 ◽  
Author(s):  
S. H. Alvi ◽  
K. Sridharan ◽  
N. S. Lakshmana Rao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Discharge Coefficient ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Laminar Regime ◽  
Variation Of Parameters ◽  
Turbulent Flow Regime

Loss characteristics of sharp-edged orifices, quadrant-edged orifices for varying edge radii, and nozzles are studied for Reynolds numbers less than 10,000 for β ratios from 0.2 to 0.8. The results may be reliably extrapolated to higher Reynolds numbers. Presentation of losses as a percentage of meter pressure differential shows that the flow can be identified into fully laminar regime, critical Reynolds number regime, relaminarization regime, and turbulent flow regime. An integrated picture of variation of parameters such as discharge coefficient, loss coefficient, settling length, pressure recovery length, and center line velocity confirms this classification.

Computerized Model of Transition in Circular Pipe Flows: Part 1 — Experimental Definition of the Problem

1999 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Natural Disturbance ◽  
Reynolds Numbers ◽  
Entrance Region ◽  
Circular Pipe ◽  
Experimental Investigations ◽  
Circular Pipes ◽  
Definition Of

Abstract A conceptual model was constructed for the problem of determining in circular pipes the conditions under which the transition from laminar to turbulent flow occurs, so that it becomes possible to calculate the minimum critical Reynolds number. Up until now this problem has been investigated by stability theory with disturbances at the pipe inlet. However, the minimum critical Reynolds number has not yet been obtained theoretically. Hence, the author took up the problem directly from many previous experimental investigations and found that (i) plots of the transition length versus the Reynolds number show that the transition occurs in the entrance region under the condition of a natural disturbance, and (ii) plots of the critical Reynolds number versus the ratio of bellmouth diameter to the pipe diamter show that with larger shapes of bellmouths, laminar flow will persist to higher Reynolds numbers. The problem is thus defined clearly as: Under the condition of an ordinary disturbance, the transition from laminar to turbulent flow occurs in the entrance region of a straight circular pipe, then the Reynolds number takes a minimum value of about 2000.

Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

2019 ◽  
Vol 877 ◽  
pp. 405-428 ◽  
Author(s):  
Anselmo S. Pereira ◽  
Roney L. Thompson ◽  
Gilmar Mompean
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
Temporal Dynamics ◽  
Homoclinic Orbits ◽  
Theoretical Development ◽  
Transitional Flows ◽  
Turbulent Transition ◽  
Laminar Turbulent Transition

The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

PIV and POD Investigations of Coherent Vortices Downstream Circular or Rectangular Obstacles Located Between Two Parallel Plates

2019 ◽  
Author(s):  
Fethi Aloui ◽  
Amal Elawady ◽  
Khaled J. Hammad
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Chaotic Behavior ◽  
Rectangular Channel ◽  
Experimental Investigations ◽  
Parallel Plates ◽  
Piv Measurements ◽  
Coherent Vortices ◽  
Karman Vortex ◽  
Proper Orthogonal

Abstract The study is an experimental investigations using PIV. The measurements were obtained by PIV for an unsteady laminar flow across a rectangular channel with a cross-section 300 × 30mm2, in the middle of which is located a cylindrical or a square obstacle. In the case of the cylindrical configuration and due to the confinement, PIV measurements in the range of 40 < Re < 200 clearly show that the von Karman vortex shedding appears at a critical Reynolds number which is about 66. A post-processing of these PIV measurements using the Proper Orthogonal Decomposition (POD) technique is by keeping only the first most energetic six modes, can be used as a filtering process to remove noise from instantaneous velocity signals. In the case of the square obstacle, PIV measurements obtained in the range of 30 < Re < 350 show the absence of vortex detachments and the chaotic behavior of the wake behind the obstacle beyond a certain Reynolds number. By examining the POD post-possessing results, the existence of a dynamic detachments’ regime (instantaneous breaking and coalescence of vortices), can be clearly observed. Given the chaotic behavior of the wake behind the obstacle, the application of the POD filtering process to only the first most energetic modes, cannot lead to good results.

Experimental Investigation of Flow Laminarization in a Graphite Flow Channel at High Pressure and High Temperature

2017 ◽  
Author(s):  
Francisco I. Valentín ◽  
Narbeh Artoun ◽  
Masahiro Kawaji
Keyword(s):  
Reynolds Number ◽  
High Temperature ◽  
Turbulent Flow ◽  
Flow Channel ◽  
Transitional Flow ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Reynolds Stresses ◽  
Frequency Spectra ◽  
Flow Laminarization

Hot wire anemometer (HWA) measurements of turbulent gas flow have been performed in upward forced convection experiments at pressures ranging from 0.6 MPa to 6.3 MPa and fluid temperatures ranging from 293 K to 673 K. The results are relevant to deteriorated turbulent heat transfer (DTHT) and flow laminarization in strongly heated gas flows which could occur in gas-cooled Very High Temperature Reactors. The HWA signals were analyzed to directly confirm the occurrence of flow laminarization phenomenon due to strong heating. An X-probe was used to collect radial and axial velocity fluctuation data for pressurized air and pure nitrogen flowing through a circular 16.8 mm diameter flow channel in a 2.7 m long graphite test section for local Reynolds numbers varying from 500 to 22,000. Analyses of the Reynolds stresses and turbulence frequency spectra were carried out and used as indicators of laminar, transition or fully turbulent flow conditions. Low Reynolds stresses indicated the existence of laminar or transitional flow until the local Reynolds number reached a large value, ∼11,000 to 16,000, much higher than the conventional Re = 4,000–5,000 for transition to fully turbulent flow encountered in pipe flows. The critical Reynolds number indicating the completion of transition approximately doubled as the pressure was increased from 0.6 MPa to 2.8 MPa.

scholarly journals An improved algebraic model for by-pass transition for calculation of transitional flow in pipe and parallel-plate channels

2019 ◽  
Vol 23 (Suppl. 4) ◽  
pp. 1123-1131
Author(s):  
Konrad Nering ◽  
Kazimierz Rup
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Turbulence Intensity ◽  
Parallel Plate ◽  
Algebraic Model ◽  
Transitional Flow ◽  
Internal Flows ◽  
Fully Developed Flow ◽  
Turbulent Transition ◽  
Plate Channel

Modified algebraic intermittency model developed by E. Dick and S. Kubacki was used to describe laminar-turbulent transition. In this work a modification of this model was made for simulating internal flows in pipes and parallel-plate channel. In particular, constants present in this model were modified. These modified constants are the same for different flows in pipes and parallel-plate channels. In this work, a dependence of friction factor on Reynolds number and turbulence intensity were determined as well as the localization of laminar breakdown and fully developed flow. Obtained results were compared with theoretical and experimental data presented in the literature.

On the Flow of Bingham Plastic Slurries in Pipes and Between Parallel Plates

1967 ◽  
Vol 7 (04) ◽  
pp. 342-346 ◽  
Author(s):  
Richard W. Hanks
Keyword(s):  
Laminar Flow ◽  
Theoretical Analysis ◽  
Plastic Flow ◽  
Pipe Flow ◽  
Parallel Plates ◽  
Flow Data ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Quartic Term ◽  
Laminar Turbulent Transition

Abstract The method of Caldwell and Babbitt for determining Bingham plastic rheological constants from engineering pipe flow data has been erroneously used in many previous applications. A reanalysis of extensive pipe flow data from the literature is performed. Critical Reynolds numbers corresponding to the laminar-turbulent transition calculated from these data are found to agree with theoretically calculated values for the entire flow range studied. Similar agreement is found for the authors' own data for flow of 10 slurries between parallel plates. The Bingham plastic model is shown to be a reliable representation of the flow of non-Newtonian slurries provided it is properly applied. If the Hedstrom number He= pD ro/n greater than 10, then the linear approximation method of Caldwell and Babbitt is invalid for pipe flow data obtained in systems of ordinary engineering interest, and the complete nonlinear form of the pipe flow Bingham plastic equation must be used in determining rheological parameters. Introduction Many materials of engineering interest must be handled and transported as slurries or suspensions of insoluble particulate matter in a Newtonian liquid. These suspensions frequently exhibit non-Newtonian rheological behavior which is reasonably well described by the simple Bingham plastic rheological equation. (1) Using this particular equation to describe the laminar flow characteristics of slurries was discussed at length by Caldwell and Babbitt who considered the flow of various clay slurries and sewage sludges. The model has since been used by many others. More recently the problem of predicting the laminar turbulent transition Reynolds number for Bingham plastic fluids has been treated 8 for the case of flow in pipes. This paper points out errors which have existed in the analysis of Bingham plastic flow since the work of Caldwell and Babbitt and presents a reanalysis of the laminar turbulent transition calculation for Bingham plastic flow in pipes. In addition, new data obtained for flow of Bingham plastic slurries between parallel plates, both in laminar flow and in the laminar turbulent transition region, will be presented and compared with the theoretical analysis of laminar turbulent transition for flow between parallel plates. THEORETICAL ANALYSIS PIPE FLOW The mathematical analysis of laminar flow of a Bingham plastic fluid leads to the following equation. (2) where q less than v greater than /R is a pseudo shear rate, rw is the wall shear stress xio=To/Tw, ro is the yield stress and n is the coefficient of rigidity or plastic viscosity from Eq. 1. Caldwell and Babbitt recognized that the quartic term in Eq. 2 was small compared to the other terms whenever xio less than less than 1, and that for large values of rw a plot of Eq. 2 becomes linear. The slope of such a plot with rw as ordinate is 4n and the intercept is (4/3)ro. This approximation is illustrated schematically in Fig. 1. The shaded region between the true curve and the straight-line approximation near the origin represents the contribution of the quartic term. SPEJ P. 342ˆ

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