Fluid Flow In Ducts Research Articles

A practical method for predicting the friction factor of power-law fluids in a rectangular duct

This article presents a simple and unique method for predicting the friction factor for the fully developed, laminar flow of power-law fluids in ducts with a rectangular cross-section by means of an engineering calculation for rapid equipment design. The relationship between friction factor f and the Reynolds number defined by Metzner–Reed (ReMR) for a rectangular cross-section was investigated and rearranged with very good engineering accuracy using the results of very simple correlations based on the application of the well-known and long-established coefficient for Newtonian fluid flow. The investigated value of the flow index was up to 2, and the aspect ratio ranged from 0 to 1, with calculation error not higher than 3.5%. The proposed method was compared with conventional methods from the literature, and was validated by means of numerical computations, and also with experimental data from the literature. The product of friction factor and ReMR is a linear function of geometrical parameter C and flow behavior index n and also the proposed method predicts the friction factor as accurately as conventional and traditional methods.

Generalized Reynolds number and viscosity definitions for non-Newtonian fluid flow in ducts of non-uniform cross-section

This work presents and experimental study of the generalization method of the Reynolds number and the viscosity of pseudoplastic fluid flow in ducts of non-uniform cross-section. This method will permit to reduce 1 degree of freedom of hydrodynamical and thermal problems in those ducts. A review of the state of the art has been undertaken and the generalization equation proposed for ducts of uniform cross section has been used as a starting point. The results obtained with this equation have not been found satisfactory and a new one has been proposed.Specifically, the procedure has been developed for two models of scraped surface heat exchanger with reciprocating scrapers. For both models, the scraper consists of a concentric rod inserted in each tube of the heat exchanger, mounting an array of plugs that fit the inner tube wall. The two models studied differ in the design of the plug.The procedure to perform the generalization method out of experimental data is accurately detailed in the present document.

Osteogenic potentials with joint-loading modality

Osteogenic potentials with a novel joint-loading modality were examined, using mouse ulnae as a model system. Load-induced deformation of rigid bone is known to generate interstitial fluid flow and stimulate osteogenesis. However, in most of the previous studies, loads were applied to cortical bone. In the current study, we addressed the question of whether deformation of the epiphysis underneath the joint would enhance bone formation in the epiphysis and the diaphysis. In order to answer the question, we applied lateral loads to a mouse elbow and conducted a bone histomorphometric analysis, as well as measurements of strains and streaming potentials. Compared to the no-loading control, the histomorphometric results showed that 0.5-N loads, applied to the elbow at 2 Hz for 3 min/day for 3 consecutive days, increased the mineralizing surface (two- to threefold), the rate of mineral apposition (three- to fivefold), and the rate of bone formation (six- to eightfold) in the ulna. Strain measurements indicated that strains of around 30 microstrain, induced with the joint-loading modality, were under the minimum effective strain of around 1000 microstrain, which is considered necessary to achieve strain-driven bone formation. To evaluate the induction of fluid flow with the joint-loading modality, streaming potentials were measured in separate experiments, using mouse femurs ex vivo. We found that the streaming potentials correlated to the magnitude of the load applied to the epiphysis (r(2) = 0.92), as well as the flow speed in the medullary cavity (r(2) = 0.93). Taken together, the findings of the current study support the idea of joint-loading driven osteogenesis, through a mechanism that involves the induction of fluid flow in cortical bone.

Frottements et pertes de pression des fluides non newtoniens dans des conduites non circulaires

The study of fluid flow in a duct requires characteristic parameters of the flow and dimensionless numbers to correlate and compare experimental results. For Newtonian fluids in simple configurations, the definition of the Reynolds number is quite standard, but for non-Newtonian fluid flows in ducts with arbitrary shape of cross section, the dependence of the apparent viscosity with the shear rate requires a generalization of this dimensionless number. This note proposes a general method valid for a large class of non-Newtonian fluids and for all duct shapes. An application is developed for a viscoelastic flow through a rectangular duct. Results obtained in the present investigation are in a good agreement with available correlations. To cite this article: M. Mahfoud et al., C. R. Mecanique 333 (2005).

Peritoneal Fluid Transport in CAPD Patients with Different Transport Rates of Small Solutes

Continuous ambulatory peritoneal dialysis (CAPD) patients with high peritoneal solute transport rate often have inadequate peritoneal fluid transport. It is not known whether this inadequate fluid transport is due solely to a too rapid fall of osmotic pressure, or if the decreased effectiveness of fluid transport is also a contributing factor. To analyze fluid transport parameters and the effectiveness of dialysis fluid osmotic pressure in the induction of fluid flow in CAPD patients with different small solute transport rates. 44 CAPD patients were placed in low (n = 6), low-average (n = 13), high-average (n = 19), and high (n = 6) transport groups according to a modified peritoneal equilibration test (PET). The study involved a 6-hour peritoneal dialysis dwell with 2 L 3.86% glucose dialysis fluid for each patient. Radioisotopically labeled serum albumin was added as a volume marker.The fluid transport parameters (osmotic conductance and fluid absorption rate) were estimated using three mathematical models of fluid transport: (1) Pyle model (model P), which describes ultrafiltration rate as an exponential function of time; (2) model OS, which is based on the linear relationship of ultrafiltration rate and overall osmolality gradient between dialysis fluid and blood; and (3) model G, which is based on the linear relationship between ultrafiltration rate and glucose concentration gradient between dialysis fluid and blood. Diffusive mass transport coefficients (K(BD)) for glucose, urea, creatinine, potassium, and sodium were estimated using the modified Babb-Randerson-Farrell model. The high transport group had significantly lower dialysate volume and glucose and osmolality gradients between dialysate and blood, but significantly higher K(BD) for small solutes compared with the other transport groups. Osmotic conductance, fluid absorption rate, and initial ultrafiltration rate did not differ among the transport groups for model OS and model P. Model G yielded unrealistic values of fluid transport parameters that differed from those estimated by models OS and P. The K(BD) values for small solutes were significantly different among the groups, and did not correlate with fluid transport parameters for model OS. The difference in fluid transport between the different transport groups was due only to the differences in the rate of disappearance of the overall osmotic pressure of the dialysate, which was a combined result of the transport rate of glucose and other small solutes. Although the glucose gradient is the major factor influencing ultrafiltration rate, other solutes, such as urea, are also of importance. The counteractive effect of plasma small solutes on transcapillary ultrafiltration was found to be especially notable in low transport patients. Thus, glucose gradient alone should not be considered the only force that shapes the ultrafiltration profile during peritoneal dialysis. We did not find any correlations between diffusive mass transport coefficients for small solutes and fluid transport parameters such as osmotic conductance or fluid and volume marker absorption. We may thus conclude that the pathway(s) for fluid transport appears to be partly independent from the pathway(s) for small solute transport, which supports the hypothesis of different pore types for fluid and solute transport.

Investigation of a Two-Equation Turbulent Heat Transfer Model Applied to Ducts

This investigation concerns numerical calculation of fully developed turbulent forced convective heat transfer and fluid flow in ducts over a wide range of Reynolds numbers. The low Reynolds number version of a non-linear eddy viscosity model is combined with a two-equation heat flux model with the eddy diffusivity concept. The model can theoretically be used for a range of Prandtl numbers or a range of different fluids. The computed results compare satisfactory with the available experiment. Based on existing DNS data and calculations in this work the ratio between the time-scales (temperature to velocity) is found to be approximately 0.7. In light of this assumption an algebraic scalar flux model with variable diffusivity is presented.

On non-Newtonian fluid flow in ducts and porous media

In this communication a three-shape-factor approach is developed to characterize both the flow of non-Newtonian fluids, in particular generalized Newtonian fluids, in an arbitrarily shaped duct and the flow over an isolated sphere. The flow of Herschel–Bulkley fluid and Meter fluid is studied. While the detailed solution for a Herschel–Bulkley fluid can be used to deduce the values of the shape factors, the simplified solution for a Meter fluid is also provided to enable for easy application. The interaction of macromolecules with fine capillary duct walls, i.e. the discontinuity in flow, is modeled using the Meter fluid model. At the low shear limit (or very low flow rate), the solutions of Chauveteau (1982, J. Rheol. 26, 111–142) and Kozicki et al. (1987, Chem. Engng Commun. 59, 137–160) are recovered. For a high flow rate, the present study predicts an increased pressure drop for surface-adhesive capillary and a pressure drop reduction for a wall macromolecule depleted/aligned system. The success in modeling flow in arbitrary shaped ducts and flow over isolated spheres using the same approach suggests that the present approach is also applicable to flow in porous media. When a volume averaging technique is employed to arrive at the continuum governing equations for flow of a generalized Newtonian fluid in porous media, the macroscopic viscosity is obtained. The macroscopic viscosity is the single quantity in the governing equations that must be determined for a non-Newtonian fluid flow in addition to the parameters already known for a Newtonian fluid flow. In the Newtonian limit, the macroscopic viscosity becomes identical to the Newtonian viscosity. Otherwise, the macroscopic viscosity is the apparent viscosity of the fluid under the average microscopic shear conditions in porous media. The expressions for the macroscopic viscosity for various fluids: namely, Herschel–Bulkley fluid, Meter fluid and Cross fluid, are derived in this communication. Porous medium matrix—macromolecule interactions due to flow discontinuity are studied using two phenomenological models: macromolecule retention and macromolecule alignment/depletion. In particular, the Meter fluid model is used to derive the effects of the porous medium matrix—macromolecule interactions. Predictions based on this study agree well with experimental data for flow of non-Newtonian fluids in packed beds and consolidated sandstones.

MIXED CONVECTION FLOW OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IN A HORIZONTAL RECTANGULAR DUCT

In this study we investigate three-dimensional (3-D) mixed convection fluid flow within a horizontal duct, the walls of which are assumed to be maintained at specified constant temperatures. The flow through the duct is assumed to be steady and laminar, and the results presented are mainly concentrated on those obtained when using parameter values that are typically found in hydraulic fractures, an important process used in the oil industry to enhance the production rate of an oil well. The simplified 3-D governing equations are taken to be parabolic in the streamwise direction, and the solution technique consists of a mixture of finite difference and finite element techniques and an iterative scheme. In order to simulate the fluid flow in ducts that have dimensions similar to a typical fracture, results are obtained for duct heights much greater than duct widths. It is found that in the regions of the duct, that are not in the vicinity of the top and bottom walls the numerical solution asymptotically approaches a 2-D profile. However, simplifying the initial problem to a 2-D model would fail to determine the induced vertical pressure field and the vertical velocity component, both of which are necessary in order to determine whether mixed convection effects influence the settling of proppant in fractures.

Osmotic Conductance of the Peritoneum in Capd Patients with Permanent Loss of Ultrafiltration Capacity

ObjectiveTo compare the effectiveness of osmotic pressure in the induction of fluid flow during continuous ambulatory peritoneal dialysis (CAPD) in patients with permanent loss of ultrafiltration capacity (UFC) and clinically stable patients.DesignEstimation of osmotic conductance in individual CAPD patients using data from single CAPD dwell studies.PatientsTwenty clinically stable CAPD patients with normal ultrafiltration rate (NUR group); 8 CAPD patients with permanent UFC loss due to high diffusion rate for small solutes [high diffusion rate (HDR) group]; 3 CAPD patients with permanent loss of UFC dueto high absorption rate (HAR) of peritoneal dialysate (HAR group).DesignSix-hour dwell studies were carried out in each patient using 2 L of Dianeal 3.86% dialysis fluid. Dialysate volume and the peritoneal absorption rate were measured using radioiodinated serum albumin as a marker. The dialysate volume over dwell-time curves were examined using three mathematical models of fluid transport for solutions with a crystalloid osmotic agent: model P, based on a phenomenologically derived exponential function of time; model OS, based on the linear relationship between the rate of net volume change (Qv) to the difference of osmolality in dialysate and blood; and model G, based on the linear relationship between Qv and the difference of glucose concentration in dialysate and blood.ResultsAll three models provided an accurate description of the measured dialysate volume over time curves. The osmotic conductance, defined as the coefficient of proportionality between the rate of ultrafiltration and the osmolality (or, alternatively, glucose) gradient between dialysate and blood plasma, was 30% lower in the HDR group than in the NUR group, but close to the normal value in the HAR group.ConclusionIn the HDR group the changes in the peritoneal membrane, which resulted in the increased diffusion rate of small solutes, also yielded a decrease of osmotic conductance. In contrast, the changes in the membrane in the HAR group, which resulted in increased peritoneal absorption, did not change the osmotic con ductance or the solute diffusion rate. The detailed pathophysiological mechanisms for these two different types of UFC loss failure are still unknown.

A Model for the Mechanism of Optic Nerve Sheath Fenestration

The mechanism by which optic nerve sheath fenestration relieves papilledema associated with increased intracranial pressure has not been clearly defined. A model was constructed to determine if the induction of fluid flow along the nerve sheath and through the fenestration could account for a reduction in pressure around the optic nerve, as might be expected according to Bernoulli's equation of fluid dynamics. The model states that as the velocity of a fluid increases, the pressure it exerts decreases. The model simulated fluid spaces corresponding to the intracranial vault, chiasm, and optic nerves. The unfenestrated model showed direct transmission of elevated intracranial pressure to the nerves, consistent with the production of papilledema. When one nerve was fenestrated, fluid flow along the nerve was initiated and pressure in that nerve sheath dropped substantially. In addition, pressure in the unfenestrated sheath dropped due to fluid communication across the chiasm. These lower intrasheath pressures were consistent with the bilateral resolution of papilledema after unilateral fenestration. The reduced intrasheath pressures persisted even when the intracranial pressure was again elevated to pathologic levels as long as active fluid flow continued along the nerve sheaths. Thus, induction of cerebrospinal fluid flow along the optic nerve sheath by fenestration appears to locally reduce the pressure around the optic nerve, in spite of persistently elevated intracranial pressure. This is in accordance with what would be predicted by Bernoulli's equation.

A PARTIALLY PARABOLIC CALCULATION PROCEDURE FOR DUCT FLOWS IN IRREGULAR GEOMETRIES. PART I: FORMULATION

A control volume-based, finite-element method is used in conjunction with equal-order interpolation for pressure and velocity for the calculation of fluid flow in ducts of arbitrary cross section. The effect of downstream pressure variations on the main flow is included so that flows with strong cross-sectional pressure variations are accurately resolved. Repeated sweeps of the computational domain are employed, with a plane-by-plane update of the three-dimensional pressure field.

Comparison of two numerical methods for the solution of non‐Newtonian flow in ducts

AbstractTwo numerical methods, the Galerkin finite element method (FEM) and the boundary‐fitted co‐ordinate transformation method (BFCTM), have been applied to solve inelastic non‐Newtonian fluid flow in ducts of irregular cross‐section. Three representative fluid models, namely the power‐law, the Ellis and the Bingham models, have been analysed. The application of the FEM is straightforward, while for the BFCTM the accurate estimation of viscosity on the duct boundary and the proper mesh adjustment appear to be critical for generating convergent solutions. A detailed comparison of the two numerical methods in terms of volumetric flow rate, axial velocity, shear rate, viscosity and CPU time is given. Both methods can generate accurate solutions of velocity over a wide range of variables, but the FEM requires much less computing time to reach the same level of accuracy. Only the BFCTM can be used to approximate shear rate and viscosity with reasonable accuracy.

On finite element analysis of fluid flow in ducts with boundary layer correction

A finite element analysis of fluid flow in ducts is demonstrated. The fluid is assumed incompressible and, except in the boundary layer, inviscid. The finite element program ADINAT is used to solve the potential flow portion of the analysis, and a boundary layer calculation method is employed to correct for the viscous boundary layer effects. This procedure is employed to analyze two simple problems. First, a nozzle passage from a steam turbine is considered. The results of the analysis are compared to another solution obtained using finite differences. The flow in a wind tunnel constructed at MIT is then analyzed, and the results are compared to test data.

Elastico-viscous fluid flows in ducts

Unsteady laminar flow of an elastico-viscous Oldroyd fluid in a straight duct of uniform crosssection is considered. A method for calculating drag from flux without solving for the velocity field is established and is illustrated through some examples.

Axisymmetric One-Dimensional Compressible Flow—Theory and Applications

Several generations of engineers have found that the one-dimensional approach to compressible fluid flows in ducts is extremely informative and effective. This paper extends these methods to axisymmetric flows so that they may be used to understand and estimate the behavior of azimuthally unrestrained, swirling flows. The already-established understanding of duct flows makes an elaborate investigation of the new results unnecessary. The paper contains the underlying assumptions and resulting equations, an outline of the solution technique, a comprehensive table of influence coefficients, and a variety of interesting examples peculiar to swirling flows drawn from the field of rotating machinery.

Fluid Mechanical Aspects of Antisymmetric Stress

Basic fluid mechanical concepts are reformulated in order to account for some structural aspects of fluid flow. A continuous spin field is assigned to the rotation or spin of molecular subunits. The interaction of internal spin with fluid flow is described by antisymmetric stress while couple stress accounts for viscous transport of internal angular momentum. With constitutive relations appropriate to a linear, isotropic fluid we obtain generalized Navier-Stokes equations for the velocity and spin fields. Physical arguments are advanced in support of several alternative boundary conditions for the spin field. From this mathematical apparatus we obtain formulas that explicitly exhibit the effects of molecular structure upon fluid flow. The interactions of polar fluids with electric fields are described by a body-torque density. The special case of a rapidly rotating electric field is examined in detail and the induction of fluid flow discussed. The effect of a rotating electric field upon an ionic solution is analyzed in terms of microscopically orbiting ions. This model demonstrates how antisymmetric stress and body torque can arise in ``structureless'' fluids.

Noise Generation by Fluid Flow in Ducts

On the basis of an analysis of experimental data on flow noise in ducts, the question regarding the existence of a “universal” noise-source spectrum is discussed. [This work was supported in part by the U. S. Army, the U. S. Air Force Office of Scientific Research, and the U. S. Office of Naval Research under Contract Nonr-1841(42).]

Fluid flow in ducts with a uniformly distributed leakage

An analysis of the problem is given for any power law relationship between flow rate and pressure gradient and between leakage rate and excess pressure in a duct. The results relate the pressure drop, inlet flow rate and outlet flow rate for a leaking duct to the pressure drop and flow rate in a similar leakless duct. It is shown that these quantities can be conveniently obtained using a nomogram involving a resistance constant and a leakage constant for the duct. Assumptions involved are discussed and a description is given of a model experiment which confirms the results of the theoretical treatment.

Erratum: On the One-Dimensional Theory of Steady Compressible Fluid Flow in Ducts with Friction and Heat Addition

Steady, diabatic (nonadiabatic), frictional, variable-area flow of a compressible fluid is treated in differential form on the basis of the one-dimensional approximation. The basic equations are first stated in terms of pressure, temperature, density, and velocity of the fluid. Considerable simplification and unification of the equations are then achieved by choosing the square of the local Mach number as one of the variables to describe the flow. The transformed system of equations thus obtained is first examined with regard to the existence of a solution. It is shown that, in general, a solution exists whose calculation requires knowledge only of the variation with position of any three of the dependent variables of the system. The direction of change of the flow variables can be obtained directly from the transformed equations without integration. As examples of this application of the equations, the direction of change of the flow variables is determined for two special flows. In the particular case when the local Mach number m = 1, a special condition must be satisfied by the flow if a solution is to exist. This condition restricts the joint rate of variation of heating, friction, and area at m = 1. Further analysis indicates that when a solution exists at this point it is not necessarily unique. Finally it is shown that the physical phenomenon of choking, which is known to occur in certain simple flow situations, is related to restrictions imposed on the variables by the form of the transformed equations. The phenomenon of choking is thus given a more general significance in that the transformed equations apply to a more general type of flow than has hitherto been treated. (author)

On the One-Dimensional Theory of Steady Compressible Fluid Flow in Ducts with Friction and Heat Addition

Steady, diabatic (non-adiabatic), frictional, variable-area flow of a compressible fluid is treated in differential form on the basis of the one-dimensional approximation. The basic equations are first stated in terms of pressure, temperature, density, and velocity of the fluid. Considerable simplification and unification of the equations is then achieved by choosing the square of the local Mach number as one of the variables to describe the flow. The transformed system of equations thus obtained is first examined with regard to the existence of a solution. It is shown that, in general, a solution exists whose calculation requires knowledge only of the variation with position of any three of the dependent variables of the system. The direction of change of the flow variables can be obtained directly from the transformed equations without integration. As examples of this application of the equations, the direction of change of the flow variables is determined for two special flows. In the particular case when the local Mach number M=1, a special condition must be satisfied by the flow if a solution is to exist. This condition restricts the joint rate of variation of heating, friction, and area at M=1. Further analysis indicates that when a solution exists at this point it is not necessarily unique. Finally, it is shown that the physical phenomenon of choking, which is known to occur in certain simple flow situations, is related to restrictions imposed on the variables by the form of the transformed equations. The phenomenon of choking is thus given a more general significance in that the transformed equations apply to a more general type of flow than has hitherto been treated.