Investigation of Turbulent Flow Behavior in a Heated Boundary Layer

The boundary layers are known to play key roles in many engineering systems. The hydrodynamic boundary layer found in these systems is often turbulent in nature and heat transfer is involved which further increases flow complexity due to the influence of buoyancy. One of the constituent layers of the turbulent boundary layer, the inner layer, has been established as home to key dynamical turbulent phenomena which can be influenced by the buoyant force. In the mixed convection flow regime, flow inertia and buoyant force are on the same order of magnitude. In this regime, buoyant thermals rising from the wall interact with the inertia-driven turbulent flow field resulting in highly complex three-dimensional flow dynamics. Past research studies conducted in this flow regime have been mostly computational in nature with little experimental work. The current knowledge on the impact of the relative contributions by the buoyant force and flow inertia on turbulent phenomena in the mixed convection flow regime is very limited. This study reports on an investigation into the turbulent flow phenomena present in mixed convection turbulent boundary layer flow over a heated smooth horizontal flat plate. Experiments were performed in a closed loop wind tunnel where the turbulent boundary layer was heated from below. The multi-plane particle image velocimetry (PIV) technique was used to capture two-dimensional velocity fields over two planes with respect to the flow direction. Experiments were conducted over a range of Richardson numbers (Ri) between 0.0 and 2.0 to control the relative contribution of the buoyant force with respect to flow inertia. The measured velocity fields are used to describe the influence of buoyancy on the three-dimensional turbulent boundary layer flow.

Convective Scaling of Intrinsic Thermo-Acoustic Eigenfrequencies of a Premixed Swirl Combustor

Spectral distributions of the sound pressure level (SPL) observed in a premixed, swirl stabilized combustion test rig are scrutinized. Spectral peaks in the SPL for stable as well as unstable cases are interpreted with the help of a novel criterion for the resonance frequencies of the intrinsic thermo-acoustic (ITA) feedback loop. This criterion takes into the account the flow inertia of the burner and indicates that in the limit of very large flow inertia, ITA resonance should appear at frequencies where the phase of the flame transfer function (FTF) approaches −π/2. Conversely, in the limiting case of vanishing flow inertia, the new criterion agrees with previous results, which state that ITA modes may arise when the phase of the FTF is close to −π. Relying on the novel criterion, peaks in the SPL spectra are identified to correspond to either ITA or acoustic modes. Various combustor configurations are investigated over a range of operating conditions. It is found that in this particular combustor, ITA modes are prevalent and dominate the unstable cases. Remarkably, the ITA frequencies change significantly with the bulk flow velocity and the position of the swirler but are almost insensitive to changes in the length of the combustion chamber (CC). These observations imply that the resonance frequencies of the ITA feedback loop are governed by convective time scales. A scaling rule for ITA frequencies that relies on a model for the overall convective flame time lag shows good consistency for all operating conditions considered in this study.

Flow Inertia and Heat Transfer in Suddenly Expanding Annular Shear-Thinning Flows

The impact of flow inertia on flow and heat transfer in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. The equations governing conservation of mass, momentum, and energy, along with the power-law constitutive model are numerically solved using a finite-difference numerical scheme. The influence of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer augmentation, downstream the plane of expansion, is only observed for Pr = 10 and 100. The extent and intensity of recirculation in the corner region, increases with inflow inertia. Higher Reynolds and Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane.

Electron inertia and quasi-neutrality in the Weibel instability

While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when length scales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how length scales below the electron skin depth can be neglected in a kinetic treatment emerges as an unsolved problem, since all current theories suffer from drawbacks of different nature. Alternatively, we discuss fully kinetic theories that remove all these drawbacks by restricting to frequencies well below the plasma frequency of both ions and electrons. By giving up on the length scale restrictions appearing in previous works, these models are obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.

Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium

In this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

Near-critical swirling flow of a viscoelastic fluid in a circular pipe

The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.