Abstract:Analysis of pressure losses in laminar flows through annuli fitted with longitudinal grooves has been carried out. The additional pressure gradient required in order to maintain the same flow rate in the grooved annuli, as well as in the reference smooth annuli, is used as a measure of the loss. The groove-induced changes can be represented as a superposition of a pressure drop due to a change in the average position of the bounding cylinders and a pressure drop due to flow modulations induced by the shape of … Show more
“…Equations (3.5), (3.6a), (3.7a), (3.10) and (3.11) represent an alternative problem formulation. This particular formulation is better suited for the theoretical analysis while (3.5)-(3.8) is better suited for the numerical solution [20].…”
Section: Field Equations Suitable For the Numerical Solutionmentioning
confidence: 99%
“…We shall keep two forms of (4.2c) and (4.2e) as the use of boundary conditions in the form of derivatives is more computationally efficient (see Section 7) while the specification of Ψ T along the walls is more convenient for the enforcement of the flow rate constraint [20].…”
Section: Discretization Of the Field Equationsmentioning
confidence: 99%
“…An analytical mapping of the irregular physical domain to a rectangular computational domain can help improve the accuracy at the cost of increased complexity of the field equations [13,14]. However, such mappings are available only for a limited class of geometries [1] and reconstruction of the coefficient matrix during each time step can add to the overall computational cost by a substantial margin [14][15][16][17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…The efficiency has been increased by an order of magnitude through the development of specialized solvers which account for the special structure of the coefficient matrix [38,39]. The method has been used to identify the laminar drag-reducing grooves [16][17][18][19][20] and to study the effects of various grooves on the flow stability [40][41][42][43][44][45][46]. This work is focused on the development of an efficient algorithm suitable for the analysis of changes in the pressure gradient required to drive a specified flow rate through a vibrating channel.…”
“…Equations (3.5), (3.6a), (3.7a), (3.10) and (3.11) represent an alternative problem formulation. This particular formulation is better suited for the theoretical analysis while (3.5)-(3.8) is better suited for the numerical solution [20].…”
Section: Field Equations Suitable For the Numerical Solutionmentioning
confidence: 99%
“…We shall keep two forms of (4.2c) and (4.2e) as the use of boundary conditions in the form of derivatives is more computationally efficient (see Section 7) while the specification of Ψ T along the walls is more convenient for the enforcement of the flow rate constraint [20].…”
Section: Discretization Of the Field Equationsmentioning
confidence: 99%
“…An analytical mapping of the irregular physical domain to a rectangular computational domain can help improve the accuracy at the cost of increased complexity of the field equations [13,14]. However, such mappings are available only for a limited class of geometries [1] and reconstruction of the coefficient matrix during each time step can add to the overall computational cost by a substantial margin [14][15][16][17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…The efficiency has been increased by an order of magnitude through the development of specialized solvers which account for the special structure of the coefficient matrix [38,39]. The method has been used to identify the laminar drag-reducing grooves [16][17][18][19][20] and to study the effects of various grooves on the flow stability [40][41][42][43][44][45][46]. This work is focused on the development of an efficient algorithm suitable for the analysis of changes in the pressure gradient required to drive a specified flow rate through a vibrating channel.…”
“…This is achieved when the boundary layer thickness becomes smaller than the rough height and leading the flow resistance to be bulk dominant. The studies of Hall & Joseph [9], Moradi & Floryan [10], Greidanus et al [11] and Zhu et al [12] can be include in this category.…”
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