http://hdl.handle.net/2142/178 (No description provided) Search the Channel search https://www.ideals.uiuc.edu/simple-search http://hdl.handle.net/2142/1710 Title: Nonlinear oscillatory convection in rotating mushy layers <br/> <br/>Authors: Riahi, Daniel N. <br/> <br/>Abstract / Summary: We consider the problem of nonlinear oscillatory convection in a horizontal mushy layer rotating about a vertical axis. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the stable and unstable oscillatory solutions of the weakly nonlinear problem by using perturbation and stability analyses. It was found that depending on the values of the parameters, supercritical simple travelling modes of convection in the form of hexagons, squares, rectangles or rolls can become stable and preferred, provided the value of the rotation parameter τ is not too small and is below some value, which can depend on the other parameter values. Each supercritical form of the oscillatory convection becomes subcritical as τ increases beyond some value, and each subcritical form of the oscillatory convection is unstable. In contrast to the non-rotating case, qualitative properties of the left travelling modes of convection are different from those of the right-travelling modes, and such qualitative difference is found to be due to the interactions between the local solid fraction and the Coriolis term in the momentum-Darcy equation. <br/> <br/>Keywords: Convection http://hdl.handle.net/2142/988 Title: On nonlinear convection in mushy layers. Part 2: Mixed oscillatory and stationary modes of convection <br/> <br/>Authors: Riahi, Daniel N. <br/> <br/>Abstract / Summary: This paper presents part 2 of a study of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. Part 1 dealt with only the oscillatory modes of convection (Riahi, J. Fluid Mech. vol. 467, 2002, pp. 331–359). In the present paper we consider the particular range of parameters where the critical values of the scaled Rayleigh number R for the onset of oscillatory and stationary convection are close to each other, and we develop and analyse a nonlinear theory in such a parameter regime which takes into account those mixed stationary and oscillatory modes of convection with common wavenumber vectors. Under a near-eutectic approximation and in the limit of large far-field temperature, we first determine a number of weakly nonlinear solutions, and then the stability of these solutions is investigated. The most interesting result is the preference for a mixed solution composed of standing and stationary hexagonal modes over a relatively wide range of the parameter values and for R just above its lowest subcritical value where convection is possible. Such a preferred solution has properties mostly in agreement with the experimental results due to Tait et al. (Nature, vol. 359, 1992, pp. 406–408) in the sense that the flow is downward at the cell centres, upward at the cell boundaries and there is some tendency for channel formation at the cell nodes. <br/> <br/>Keywords: Nonlinear convection http://hdl.handle.net/2142/987 Title: On nonlinear convection in mushy layers. Part 1: Oscillatory modes of convection. With Corrigendums <br/> <br/>Authors: Riahi, Daniel N. <br/> <br/>Abstract / Summary: We consider the problem of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. We analyse the oscillatory modes of convection in the form of two- and three-dimensional travelling and standing waves. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the solutions to the nonlinear problem by using a perturbation technique, and the stability of two- and three-dimensional solutions in the form of simple travelling waves, general travelling waves and standing waves is investigated. The results of the stability and the nonlinear analyses indicate that supercritical simple travelling rolls are stable over most of the studied range of parameter values, while supercritical standing rolls can be stable only over some small range of parameter values, where the simple travelling rolls are unstable. The results of the investigation of the onset of plume convection and chimney formation leading to the occurrence of freckles in the alloy crystal indicate that the chimney of the plume can be generated internally or near the lower boundary of the mushy layer. The roles of a Stefan number, a permeability parameter and a concentration ratio on the flow instability in both linear and nonlinear regimes are also determined. <br/> <br/>Keywords: Nonlinear convection http://hdl.handle.net/2142/986 Title: Wall-induced forces on a rigid sphere at finite Reynolds number <br/> <br/>Authors: Zeng, Lanying; Balachandar, S.; Fischer, Paul <br/> <br/>Abstract / Summary: We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For Re<100, we observe the lift coefficient to decrease with both Reynolds number and distance from the wall. In this regime the present results are in good agreement with the low-Reynoldsnumber theory of Vasseur & Cox (1977), with the recent experiments of Takemura & Magnaudet (2003) and with the simulations of Kim et al. (1993). The most surprising result from the present simulations is that the wall-induced lift coefficient increases dramatically with increasing Re above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness. <br/> <br/>Keywords: Fluid mechanics http://hdl.handle.net/2142/985 Title: Two-Phase Densification of Cohesive Granular Aggregates <br/> <br/>Authors: Gioia, Gustavo; Cuitiño, Alberto M.; Zheng, S.; Uribe, T. <br/> <br/>Abstract / Summary: When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressure is applied to these aggregates, they densify by particle rearrangement. Here we introduce experimental and computational results suggesting that densification by particle rearrangement occurs in the form of a phase transition between two configurational phases of the aggregate. Then we show that the energy landscape associated with particle rearrangement is nonconvex and therefore consistent with our interpretation of the experimental and computational results. Our conclusions are relevant to many technological processes and natural phenomena. <br/> <br/>Keywords: Granular materials http://hdl.handle.net/2142/984 Title: Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory <br/> <br/>Authors: Gioia, Gustavo; Chakraborty, Pinaki <br/> <br/>Abstract / Summary: The classical experiments on turbulent friction in rough pipes were performed by Nikuradse in the 1930s. Seventy years later, they continue to defy theory. Here we model Nikuradse’s experiments using the phenomenological theory of Kolmogo´rov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existence of close ties between two milestones of experimental and theoretical turbulence. <br/> <br/>Keywords: Turbulent flow; Turbulence theory http://hdl.handle.net/2142/983 Title: Theory of detonation with an embedded sonic locus <br/> <br/>Authors: Stewart, D. Scott; Kasimov, Aslan R. <br/> <br/>Abstract / Summary: A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions. <br/> <br/>Keywords: chemically reacting flows; shocks and singularities; supersonic flows; transonic flows http://hdl.handle.net/2142/982 Title: Structure and kinematics in dense free-surface granular flow <br/> <br/>Authors: Hill, Kimberly M.; Gioia, Gustavo; Tota, Vinay V. <br/> <br/>Abstract / Summary: We show that the structure of a dense, free-surface boundary layer granular flow is similar to the structure of a laminar liquid flow: There is a strong component of order (stratification parallel to the mean flow) superposed with a mild component of disorder (self-diffusion perpendicular to the mean flow).We also show that the self-diffusion coefficient scales with the mean velocity and propose a model that relates this scaling to the ordered structure of the flow. Last, we show that the structure of the flow imprints an oscillatory signature (similar to that found in confined granular flow) on the mean velocity profile. <br/> <br/>Keywords: Boundary layers; Granular flow http://hdl.handle.net/2142/981 Title: Spinning instability of gaseous detonations <br/> <br/>Authors: Kasimov, Aslan R.; Stewart, D. Scott <br/> <br/>Abstract / Summary: We investigate hydrodynamic instability of a steady planar detonation wave propagating in a circular tube to three-dimensional linear perturbations, using the normal mode approach. Spinning instability is identified and its relevance to the well-known spin detonation is discussed. The neutral stability curves in the plane of heat release and activation energy exhibit bifurcations from low-frequency to high-frequency spinning modes as the heat release is increased at fixed activation energy. With a simple Arrhenius model for the heat release rate, a remarkable qualitative agreement with experiment is obtained with respect to the effects of dilution, initial pressure and tube diameter on the behaviour of spin detonation. The analysis contributes to the explanation of spin detonation which has essentially been absent since the discovery of the phenomenon over seventy years ago. <br/> <br/>Keywords: Gaseous detonations; Detonation physics http://hdl.handle.net/2142/980 Title: Spanwise structure and scale growth in turbulent boundary layers <br/> <br/>Authors: Tomkins, Christopher D.; Adrian, Ronald J. <br/> <br/>Abstract / Summary: Spanwise structure and growth mechanisms in a turbulent boundary layer are investigated experimentally. PIV measurements are obtained in the streamwise– spanwise (x–z)-plane from the buffer layer to the top of the logarithmic region at Reθ =1015 and 7705. The dominant motions of the flow are shown to be large-scale regions of momentum deficit elongated in the streamwise direction. Throughout the logarithmic layer, the regions are consistently bordered by vortices organized in the streamwise direction, offering strong support for a vortex packet model. Additionally, evidence is presented for the existence and organization of hairpin vortices in the region y+ <60. Statistical evidence is also presented for two important aspects of the vortex packet paradigm: vortex organization in the streamwise direction, and the clear association of the hairpin signature with local minima in streamwise velocity. Several spanwise lengthscales are shown to vary linearly with distance from the wall, revealing self-similar growth of spanwise structure in an average sense. Inspection of the data, however, suggests that individual structures do not grow strictly self-similarly in time. It is proposed that additional scale growth occurs by the merging of vortex packets on an eddy-by-eddy basis via a vortex re-connection mechanism similar to that suggested by Wark & Nagib (1989). The proposed mechanism provides a link between vortex-pairing concepts and the observed coalescence of streaky low-speed regions in the inner layer. <br/> <br/>Keywords: Boundary layer turbulence