Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number.

Viscoelastic Thermovibrational Flow Driven by Sinusoidal and Pulse (Square) Waves

The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.

The Role of Elasticity in the Vortex Formation in Polymeric Flow around a Sharp Bend

Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works.

Combined Influence of Fluid Viscoelasticity and Inertia on Forced Convection Heat Transfer From a Circular Cylinder

In this study, the combined influence of fluid viscoelasticity and inertia on the flow and heat transfer characteristics of a circular cylinder in the steady laminar flow regime have been studied numerically. The momentum and energy equations together with an appropriate viscoelastic constitutive equation have been solved numerically using the finite volume method over the following ranges of conditions: Reynolds number, 0.1≤Re≤20; elasticity number (= Wi/Re, where Wi is the Weissenberg number), 0≤El≤0.5; Prandtl number, 10≤Pr≤100 for Oldroyd-B and finitely extensible nonlinear elastic-Peterlin (FENE-P) (with two values of the chain extensibility parameter L2, namely 10 and 100) viscoelastic fluid models including the limiting case of Newtonian fluids (El = 0). New extensive results are presented and discussed in terms of the streamline and isotherm profiles, drag coefficient, distribution of the local and surface averaged Nusselt number. Within the range of conditions embraced here, the separation of boundary layers (momentum and thermal) is seen to be completely suppressed in an Oldroyd-B fluid whereas it is accelerated for a FENE-P fluid in comparison with that seen for a Newtonian fluid otherwise under identical conditions. At a fixed elasticity number, both the drag coefficient and average Nusselt number are seen to be independent of the Reynolds number beyond a critical value for an Oldroyd-B fluid. In contrast, the drag coefficient decreases and the average Nusselt number increases with Reynolds number for a FENE-P fluid at a constant value of the elasticity number. Finally, a simple correlation for the average Nusselt number for a FENE-P fluid is presented which facilitates the interpolation of the present results for the intermediate values of the governing parameters and/or its a priori estimation in a new application.

Analytical Solution of UCM Viscoelastic Liquid with Slip Condition and Heat Flux over Stretching Sheet: The Galerkin Approach

This paper provides a substantial amount of study related to coupled fluid flow and heat conduction of an upper-convected-Maxwell viscoelastic liquid over a stretching plane with slip velocity. A new model, presented by Christov, for thermal convection is employed. The partial differential equations are converted to ordinary differential equations by using appropriate transformation variables. The transformed equations are solved analytically by using the Galerkin method. For the sake of soundness, a comparison is done with a numerical method, and good agreement is found. The impacts of various parameters like slip coefficient, elasticity number, the thermal relaxation time of heat flow, and the Prandtl number over the temperature and velocity fields are studied. Furthermore, the Cattaneo–Christov heat flux model is compared with Fourier’s law. Additionally, the present results are also verified by associating with the published work as a limiting case.

Mechanisms of formation vortex structures at the liquid-gas interface with an adsorption layer

Experimental results of a homogeneous (along the coordinate transverse to the stream) flow instability during the interaction with a film of surfactant adsorbed at the flat interface are presented. The flow was formed at a point-like heat by radiation and a source of surfactants (acetone drops). It is proved that a small value of the film shear viscosity is one of the requirements for the vortices formation process. The possibility to use the dimensionless parameter (the elasticity number) to describe the system behavior in 3D geometry is shown. A potential mechanism for the vortices origin is proposed. The results of the visualization of the water surface uniform flow around a solid sphere are presented.

Analytical Solution of Sloshing in a Cylindrical Tank with an Elastic Cover

Coupled fluid-structure is significant in many aspects of engineering applications such as aerospace fuel tanks, the seismic safety of storage tanks and tuned liquid dampers. Numerical investigation of the effects of thin plate cover over a cylindrical rigid fuel tank filled by an inviscid, irrotational, and incompressible fluid is investigated. Governing equations of fluid motion coupled by plate vibration are solved analytically. A parameter study on the natural frequency of coupled fluid-structure interaction is performed. The results show the non-dimensional natural frequency of coupled fluid-structure is a function of mass ratio, plate elasticity number and aspect ratio. This function is derived numerically for high aspect ratios which in companion with a semi-analytical could be used in the engineering design of liquid tanks with a cover plate.

Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow

In this work, we compute numerically breakage/coalescence rates and size distribution of surfactant-laden droplets in turbulent flow. We use direct numerical simulation of turbulence coupled with a two-order-parameter phase-field method to describe droplets and surfactant dynamics. We consider two different values of the surface tension (i.e. two values for the Weber number, $We$, the ratio between inertial and surface tension forces) and four types of surfactant (i.e. four values of the elasticity number, $\unicode[STIX]{x1D6FD}_{s}$, which defines the strength of the surfactant). Stretching, breakage and merging of droplet interfaces are controlled by the complex interplay among shear stresses, surface tension and surfactant distribution, which are deeply intertwined. Shear stresses deform the interface, changing the local curvature and thus surface tension forces, but also advect surfactant over the interface. In turn, local increases of surfactant concentration reduce surface tension, changing the interface deformability and producing tangential (Marangoni) stresses. Finally, the interface feeds back to the local shear stresses via the capillary stresses, and changes the local surfactant distribution as it deforms, breaks and merges. We find that Marangoni stresses have a major role in restoring a uniform surfactant distribution over the interface, contrasting, in particular, the action of shear stresses: this restoring effect is proportional to the elasticity number and is stronger for smaller droplets. We also find that lower surface tension (higher $We$ or higher $\unicode[STIX]{x1D6FD}_{s}$) increases the number of breakage events, as expected, but also the number of coalescence events, more unexpected. The increase of the number of coalescence events can be traced back to two main factors: the higher probability of inter-droplet collisions, favoured by the larger number of available droplets, and the decreased deformability of smaller droplets. Finally, we show that, for all investigated cases, the steady-state droplet size distribution is in good agreement with the $-10/3$ power-law scaling (Garrett et al., J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163–2171), conforming to previous experimental observations (Deane & Stokes, Nature, vol. 418 (6900), 2002, p. 839) and numerical simulations (Skartlien et al., J. Chem. Phys., vol. 139 (17), 2013).