Stratified flow over a backward-facing step: hybrid solution by integral transforms

Ramos, Rogério; Guerrero, J.S. Pérez; Cotta, Renato M.

doi:10.1002/1097-0363(20010130)35:2<173::aid-fld88>3.0.co;2-u

Cited by 15 publications

(9 citation statements)

References 18 publications

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“…The details of the GITT approach are given as follows, as an extension to hybrid solutions previously implemented [31][32][33][34][35][36][37][38][39][40]. The GITT approach [31][32][33][34][35][36][37][38][39][40] is now applied in the solution of Eqs. ( 12) to ( 18), following previous developments on the hybrid integral transforms solution of the Navier-Stokes and energy equations in cylindrical coordinates [37][38][39][40].…”

Section: Solution Methodologymentioning

confidence: 99%

“…In order to implement the GITT approach to solve the above equations, a streamfunction formulation is employed [32][33][34][35][36][37][38][39][40]. The two-dimensional streamfunction is defined in terms of the velocity components in the r and z directions, respectively, as:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…This paper aims to address these questions and characterize the role of a temperature gradient on the flow dynamics in a variety of axisymmetric vortex breakdown regimes, as determined by Re and h. The problem is addressed using the Generalized Integral Transform Technique (GITT), which is a hybrid numerical-analytical methodology [31] that has previously been applied to fluid flow and heat transfer governed by the Navier-Stokes and energy equations [32][33][34][35][36][37][38][39][40], including cylindrical cavities [37][38][39][40]; however, a solution to the mixed convection problem in such geometry has not been implemented hitherto. Mathematical descriptions of the problem and the GITT methodology are outlined in the following section, the results are validated in Section 3.1 and are discussed in terms of flow, vorticity and temperature fields in Section 3.2; the effects of thermal gradients and induced flows on torque transmission, azimuthal velocity and heat transfer are discussed in Section 3.3, followed by some concluding remarks in Section 4.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of mixed convection on laminar vortex breakdown in a cylindrical enclosure with a rotating bottom plate

Quaresma

Cruz

Cagney

et al. 2020

International Journal of Thermal Sciences

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Vortex breakdown plays a central role in the performance of countless rotating machinery applications, many of which contain thermal gradients either inadvertently or by design. The effect of thermal gradients on vortex breakdown and further flow development in a cylindrical domain with a rotating bottom plate is examined using the Generalized Integral Transformation Technique (GITT) with a streamfunction-only formulation. A thermal gradient is imposed in the axial direction, such that the buoyancy forces oppose the base flow driven by the rotation of the lower plate, i.e. the temperature difference acts to stabilize the flow. The hybrid numerical-analytical approach is shown to accurately capture vortex breakdown phenomena for a variety of conditions involving single, double and triple recirculation bubbles. The buoyancy forces -expressed in terms of the Richardson number (Ri) -act to suppress vortex breakdown in all cases examined and led to a series of flow transitions with increasing Ri, characterized by the appearance of a stratified structure with multiple fluid layers. These flow transitions have a significant impact on the overall performance of the system. The torque coefficient decreases with Ri, compared to the base (isothermal) case following an empirical power law relationship, which is independent of Reynolds number, aspect ratio or number of fluid layers present. Flow stratification suppresses the transport of angular momentum; azimuthal velocity is shown to decline exponentially in the regions where layering occurs, accompanied by a sharp reduction in the Nusselt number, as fluid layers act to insulate the upper plate.

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Section: Solution Methodologymentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of mixed convection on laminar vortex breakdown in a cylindrical enclosure with a rotating bottom plate

Quaresma

Cruz

Cagney

et al. 2020

International Journal of Thermal Sciences

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“…Applications of GITT to convectiondiffusion problems involving porous media are abundant [11,12,17]. Regarding the solution of fluid flows, the GITT has been applied to both the primitive variables [18][19][20][21] and streamfunctiononly [22][23][24][25][26][27][28][29][30][31] formulations. The latter was usually preferred due to the automatic satisfaction of the continuity equation and better convergence characteristics, though directly applicable only to two-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid integral transforms for flow development in ducts partially filled with porous media

Lisbôa¹,

Cotta²

2018

Proc. R. Soc. A.

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A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic-numerical code developed. A detailed verification with a finite-element commercial code is also performed.

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“…Ramos et al (2001) analyzed the solution by using the GITT of the stratified backward-facing step flow problem. Numerical results were presented for the situations more frequently encountered in the literature and were used for the co-validation of more flexible fully discrete approaches.…”

Section: Introductionmentioning

confidence: 99%

Hybrid solutions obtained via integral transforms for magnetohydrodynamic flow with heat transfer in parallel-plate channels

Pontes

Macêdo

Batista

et al. 2018

HFF

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Purpose The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field. Design/methodology/approach The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties. Findings Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters. Originality/value A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.

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Stratified flow over a backward-facing step: hybrid solution by integral transforms

Cited by 15 publications

References 18 publications

Effect of mixed convection on laminar vortex breakdown in a cylindrical enclosure with a rotating bottom plate

Effect of mixed convection on laminar vortex breakdown in a cylindrical enclosure with a rotating bottom plate

Hybrid integral transforms for flow development in ducts partially filled with porous media

Hybrid solutions obtained via integral transforms for magnetohydrodynamic flow with heat transfer in parallel-plate channels

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