Computational and experimental study of annular photo-reactor hydrodynamics

The performance of ultraviolet (UV) reactors used for water treatment is greatly influenced by the reactor hydrodynamics due to the non-homogeneity of the radiation field. Reliable modeling of the reactor flow structures is therefore crucial for the design process. In this study, the turbulent flow through two characteristic annular UV-reactor configurations, with inlets concentric (L-shape) and normal (U-shape) to the reactor axis, was investigated through computational fluid dynamic (CFD). The modeling results were evaluated with the velocity profiles from particle image velocimetry (PIV) experiments. The influence of mesh structure and density, as well as three turbulence models: Standard κ–, Realizable κ–, and Reynolds stress model (RSM), on the simulation results were evaluated. Mesh-independent solutions were achieved at mean cell volumes of 5 × 10⁻⁹ m³. The Realizable κ– displayed the best overall match to the experimental PIV measurements. In general, the CFD models showed a close agreement with the experimental data for the majority of the reactor domain and captured the influences of reactor configuration and internal reactor structures on the flow distribution. The validated CFD hydrodynamic models could be integrated with kinetic and radiation distribution models for UV-reactor performance simulation.     

The consistency of pressure‐gradient approximations used in multi‐dimensional shock hydrodynamics

This paper presents a study of the consistency properties of the pressure‐gradient approximation used in multi‐dimensional finite‐element shock hydrodynamics codes today. In specific, consideration is given to the so‐called ‘bent‐element blues’ problem associated with the pressure‐gradient approximation when using the Q1Q0 element. On arbitrary grids comprised of distorted elements, the piecewise‐constant representation of the pressure field leads to a low‐order pressure‐gradient approximation at the global (nodal) level. This results in spurious nodal forces that are not aligned with the pressure gradient. There are several side‐effects of this behavior that include (a) incorrectly exciting physical modes in problems that exhibit unstable behavior, e.g. Rayleigh–Taylor problems (both magnetic and hydrodynamic), (b) potentially seeding hourglass modes, and (c) exhibiting non‐stationary behavior for steady‐state problems. A series of commonly used pressure‐gradient approximations are reviewed and evaluated based on linear consistency—the ability of the approximation to annihilate constant terms and exactly reproduce a linear gradient. The deeper theoretical issues associated with the proper selection of function spaces for the finite‐element hydro formulation are not discussed here. There are two gradient approximations that use piecewise‐constant data and deliver a consistent pressure‐gradient approximation on arbitrary grids. The first is the well‐known least‐squares gradient construction, and the second is a corrected gradient approximation that imposes linear consistency at the (global) nodal level. At the time of this writing, the corrected gradient approximation appears to be the most viable candidate for resolving the consistency issues associated with the Q1Q0 element technology. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical solutions of liquid metal flows by incompressible magneto‐hydrodynamics with heat transfer

A two‐dimensional incompressible magneto‐hydrodynamic code is presented in order to solve the steady state or transient magnetized or neutral convection problems with the effect of heat transfer. The code utilizes a numerical matrix distribution scheme that runs on structured or unstructured triangular meshes and employs a dual time‐stepping technique with multi‐stage Runge–Kutta algorithm. The code can be used to simulate the natural convection with internal heat generation and absorption and nonlinear time‐dependent evolution of heated and magnetized liquid metals exposed to external fields. Copyright © 2008 John Wiley & Sons, Ltd.     

Comprehensive experimental investigation of the hydrodynamics of large-scale, 3D,oscillating bubble plumes

An extensive study of the most important hydrodynamic characteristics of fairly large-scale bubble plumes was conducted using several measurement techniques and a variety of tools to analyze the data. Particle image velocimetry (PIV), double-tip optical probes (OP) and photographic techniques were extensively applied to measure bubble and liquid velocities, void-fraction and bubble sizes. PIV measurements in a vertical plane crossing the centre of the injector provided the instantaneous velocity fields for both phases, as well as hydrodynamic parameters, such as the movement of the axis of the plume and its instantaneous shape. Statistical studies were performed using image processing to determine the distribution of the apparent instantaneous plume diameter and centreline position. An important finding was that there is little instantaneous spreading of the bubble plume core; the spreading of the time-averaged plume width (as measured from the time-averaged void-fraction and time-averaged liquid velocity fields) is largely due to plume meandering and oscillations. The liquid-phase stress tensor distributions obtained from the instantaneous velocity data indicate that, for the continuous phase, these stresses scale linearly with the local void-fraction in the range of 0.5% < α < 2.5%. The bubbles were found to be ellipsoidal, with shape factor e ≈ 0.5.     

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.     

On circulation in relativistic hydrodynamics

In this paper it is shown that the relativistic analogue of the circulation in classical hydrodynamics is the integral

$$C = \int {\left( {{\text{1 + }}\frac{i}{{c^{\text{2}} }}} \right)} {\text{ }}U_\alpha dx^\alpha ,$$     

Shock waves in reactive hydrodynamics

Using the weakly non-linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations in Eulerian coordinates governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a reactive hydrodynamic medium. We derive the transport equations for the amplitudes of resonantly interacting waves. The evolutionary behavior of non-resonant wave modes culminating into shock waves is also studied.      

Kelvin-Helmholtz instability in relativistic hydrodynamics

An attempt is made to generalize the standard formalism of the linear analysis of the hydrodynamic instability of flows of an ideal fluid to the case of relativistic flows (in the framework of the special theory of relativity). The stability of a two-dimensional flow with shear discontinuity is investigated as a concrete example.     

Equations of foam hydrodynamics

A closed system of differential equations describing a foam as a viscoelastic compressible continuum is obtained on the basis of the general theory of the mechanics of deformable continua [3–5]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–95, September–October, 1988.     

An experimental study on the flow behavior of micellar solutions

At higher concentration levels, the inner structure of micellar solutions cannot be detected directly by optical means. Nevertheless, the flow behavior of the micellar solutions reflects their micellar structures. Hence, in this study the material behavior of micellar surfactant solutions was investigated by rheometrical means in steady and oscillatory shear flows. The flow behavior of the solutions was found to be strongly dependent on the concentration of the surfactants. At very low concentrations, the surfactant solution shows Newtonian behavior. With increasing concentration, a transition to shear thinning behavior and increasing viscoelasticity was found. The complex material structure is modeled according to the flow behavior by discrete and continuous relaxation time spectra, depending on the concentration. Received: 3 May 2000/Accepted: 18 September 2000     

The energy equation in wetting hydrodynamics

Creeping flow with a free boundary is considered in a neighborhood of a moving three-phase contact line. The energy equation is invoked to solve the closure problem of wetting theory.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–117, November–December, 1996.     

Neighbour lists in smoothed particle hydrodynamics

Since smoothed particle hydrodynamics (SPH) is based on interactions with the closer neighbouring particles, implementing the neighbour list is a key point in terms of the high performance of the code. The efficiency of the method depends directly on how to build and use the neighbour list. In the present work, the available searching algorithms for SPH codes are analyzed. Different gridding algorithms are evaluated, the gains in efficiency obtained from reordering of particles is investigated and the cell‐linked list and Verlet list methods are studied to create the neighbour list. Furthermore, an innovative searching procedure based on a dynamic updating of the Verlet list is proposed. The efficiency of the algorithms is analyzed in terms of computational time and memory requirements. Copyright © 2010 John Wiley & Sons, Ltd.     

Boundary-integral modeling of cochlear hydrodynamics

A two-dimensional model that captures the essential features of the vibration of the basilar membrane of the cochlea is proposed. The flow due to the vibration of the stapes footplate and round window is modeled by a point source and a point sink, and the cochlear pressure is computed simultaneously with the oscillations of the basilar membrane. The mathematical formulation relies on the boundary-integral representation of the potential flow established far from the basilar membrane and cochlea side walls, neglecting the thin Stokes boundary layer lining these surfaces. The boundary-integral approach furnishes integral equations for the membrane vibration amplitude and pressure distribution on the upper or lower side of the membrane. Several approaches are discussed, and numerical solutions in the frequency domain are presented for a rectangular cochlea model using different membrane response functions. The numerical results reproduce and extend the theoretical predictions of previous authors and delineate the effect of physical and geometrical parameters. It is found that the membrane vibration depends weakly on the position of the membrane between the upper and lower wall of the cochlear channel and on the precise location of the oval and round windows. Solutions of the initial-value problem with a single-period sinusoidal impulse reveal the formation of a traveling wave packet that eventually disappears at the helicotrema.