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In laminar flow, viscous fluids must exert appropriate elastic shear stresses normal to the flow direction. This is a direct consequence of the balance of angular momentum. There is a limit, however, to the maximum elastic shear s...
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In laminar flow, viscous fluids must exert appropriate elastic shear stresses normal to the flow direction. This is a direct consequence of the balance of angular momentum. There is a limit, however, to the maximum elastic shear stress that a fluid can exert. This is the ultimate shear stress, , of the fluid. If this limit is exceeded, laminar flow becomes dynamically incompatible. The ultimate shear stress of a fluid can be determined from experiments on plane Couette flow. For water at , the data available in the literature indicate a value of of about . This study applies this value to determine the Reynolds numbers at which flowing water reaches its ultimate shear stress in the case of Taylor-Couette flow and circular pipe flow. The Reynolds numbers thus obtained turn out to be reasonably close to those corresponding to the onset of turbulence in the considered flows. This suggests a connection between the limit to laminar flow, on the one hand, and the occurrence of turbulence, on the other.
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A new technique is presented for measuring instantaneous flow rates in unsteady laminar duct flows. It is based on a relationship between flow rate and centerline-velocity history that is an exact solution to the Navier-Stokes equ...
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A new technique is presented for measuring instantaneous flow rates in unsteady laminar duct flows. It is based on a relationship between flow rate and centerline-velocity history that is an exact solution to the Navier-Stokes equations for parallel, fully-developed flow of constant-property Newtonian fluids undergoing arbitrary unsteadiness from an initially steady state. The method applies instantaneously in both forward and reversing flow and invokes the sole additional assumption that the flow is axisymmetric. The capabilities of the technique are demonstrated by using experimental measurements of the centerline velocity in a tube upstream of a fuel injector, during a series of sequential injections, to: (i) quantify the differences in the fuel masses injected in each event; and (ii) measure the cumulative masses injected over multiple events. They were found to be in good agreement with direct measurements made with a mass balance.
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Aim To get the analytical solution for laminar viscous flow in the gap of two parallel rotating disks. Methods By estimating the order of magnitude of each term in the Navier-Stokes equations to drop small terms and achieve the ...
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Aim To get the analytical solution for laminar viscous flow in the gap of two parallel rotating disks. Methods By estimating the order of magnitude of each term in the Navier-Stokes equations to drop small terms and achieve the required simplified differential equations, and by integrating the equations to obtain the solution for the flow between two rotary disks. Results Parameters related to the laminar viscous flow in the gap between two parallel rotary disks, such as the velocity, the pressure, the flowrate, the force, the shearing stress, the torque and the power were derived. Conclusion The result provides a theoretical basis and an effective method for the designs of the devices connected with the laminar viscous flow in the gap between two parallel rotary disks.
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The influence of the cross-section shape on pressure driven viscous flow through a uniform channel is assessed by presenting analytical flow solutions of velocity distribution, volume flow rate and shear stress for different cross...
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The influence of the cross-section shape on pressure driven viscous flow through a uniform channel is assessed by presenting analytical flow solutions of velocity distribution, volume flow rate and shear stress for different cross-section shapes. Next, a simplified flow model through a non-uniform constricted channel is formulated which accounts for flow inertia, viscosity and cross-section shape. The model outcome is quantified for different fluids, flows and geometrical properties relevant to physiological flows. It is seen that a commonly applied quasi-one-dimensional (1D) model is not accurate indicating the need to account for the cross-section shape.
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In this paper, we consider a novel numerical scheme for solving incompressible flows on collocated grids. The implicit potential method utilizes an implicit potential velocity obtained from a Helmholtz decomposition for the mass c...
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In this paper, we consider a novel numerical scheme for solving incompressible flows on collocated grids. The implicit potential method utilizes an implicit potential velocity obtained from a Helmholtz decomposition for the mass conservation and employs a modified form of Bernoulli's law for the coupling of the velocity-pressure corrections. It requires the solution only of the momentum equations, does not involve the solution of additional partial differential equations for the pressure, and is applied on a collocated grid. The accuracy of the method is tested through comparison with analytical, experimental, and numerical data from the literature, and its efficiency and robustness are evaluated by solving several benchmark problems such as flow around a circular cylinder and in curved square and circular ducts.
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The oil-water-gas separation is a critical aspect of the treatment of production flows in the oil industry. The segregation of gas bubbles and/or water droplets dispersed in viscous oil by an in-line swirling flow separator has be...
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The oil-water-gas separation is a critical aspect of the treatment of production flows in the oil industry. The segregation of gas bubbles and/or water droplets dispersed in viscous oil by an in-line swirling flow separator has been considered by the oil industry for topside and subsea applications. For high viscosity oils, heat transfer processes can be affected. Works addressing these applications are rare in the literature. In this way, the article presents a numerical investigation on heat transfer characteristics in a decaying swirling flow, considering the effects of viscosity dissipation due to the high viscosity of the fluid. The flow has both velocity and temperature profiles developing simultaneously in a tube with a constant diameter having a uniform wall heat flux in a laminar flow regime, particularly the behavior of heat transfer characteristics for strongly swirling numbers considering viscous dissipation. Three swirl numbers (S = 0.0, 0.3, and 0.7) and five Brinkman numbers (Br = 0.0, 0.1,0.5,1.0, and 10.0) were investigated and the effects of those parameters on the dimensionless temperature profiles, Nusselt number and viscous dissipation function were examined. The heat transfer analysis indicated that the swirling flow affects the fluid's axial and radial temperature distribution. They promoted increased fluid in wall temperature and bulk temperature and affected the local Nusselt number distribution.
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Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of...
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Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical solution.
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The flow of highly viscous fluids in pipeline fittings has previously been of little interest to mechanical engineers. More recently it has become more topical because design methods for emergency pressure relief systems on polyme...
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The flow of highly viscous fluids in pipeline fittings has previously been of little interest to mechanical engineers. More recently it has become more topical because design methods for emergency pressure relief systems on polymerization reactors need to be improved. The abrupt enlargement is of particular importance in this respect, because it regularly occurs on pipeline systems and is also an integral component part of other pipeline fittings such as orifice plates and valves. The energy lossmechanisms that occur in an abrupt enlargement will therefore occur in many other pipeline fittings. A semi-empirical, mechanistic approach was used to develop a simple, one-dimensional flow model that allowed these energy loss mechanisms to beunderstood. The energy loss predictions from the model compared well with data available in the open literature. The model was used to generate some simple design equations.
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The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier-Stokes equations are solved...
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The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier-Stokes equations are solved simultaneously with two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis, a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two- and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability (Mack mode), in addition to the first mode related to the Tollmien-Schlichting mode present in incompressible flows. The effect of reference temperature on stability characteristics is also studied. The results of the analysis reveal that the stability characteristics remain almost unchanged for the most unstable wave direction for Mach numbers above 4.0. The obtained results are compared with existing numerical and experimental data in the literature, yielding encouraging agreement both qualitatively and quantitatively.
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The need to improve the methods used when designing emergency, pressure-relief systems on polymerisation reactors, has made the flow of highly viscous fluids in pipeline fittings highly topical. This paper investigates the flow pr...
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The need to improve the methods used when designing emergency, pressure-relief systems on polymerisation reactors, has made the flow of highly viscous fluids in pipeline fittings highly topical. This paper investigates the flow processes involvedin single-phase, viscous flows in nozzles and orifice plates. These fittings were chosen because they would give an insight into the behaviour of highly viscous flows in other geometries, such as the flow upstream of the seat in a pressure relief valve.Experimental data are presented for a pipe, two conical nozzles and a sharp-edged orifice plate for laminar flows in the Reynolds number range 50-400 and for turbulent flows. The volume flow rate -- pressure drop characteristics are presented for bothnozzles and the orifice plate. The discharge momentum flow rate for the pipe, a nozzle and the orifice plate are also given. Analysis of the data shows that nozzles and orifice plates that are geometrically similar have a similar resistance to flow. It is also shown that the contraction coefficient for an orifice plate tends to unity at low Reynolds numbers.
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