A global simulation method for obtaining reduced reaction mechanisms for use in reactive blast wave flows

A finite rate chemistry solver usually consumes the largest part of the computing time in the numerical simulation of reactive flows. To reduce these costs, a global simulation method has been developed for systematically simplifying detailed reaction mechanisms and a reduced reaction mechanism for CH₄−O₂ is presented. This reduced mechanism accurately replicates the associated detailed mechanism whilst significantly reducing the required computing time. A shock induced methane combustion problem is computed by coupling the reduced reaction mechanism to a 1-D viscous compressible flow solver. As a comparison, a simulation of non-reactive shock flow having the same initial conditions is also performed. These calculations reveal some of the key features found in reactive shock flows. This article was processed by the author using Springer-Verlag TEX PJour2g macro package version 1.1     

On air-chemistry reduction for hypersonic external flow applications

In external hypersonic flows, viscous and compressibility effects generate very high temperatures leading to significant chemical reactions among air constituents. Therefore, hypersonic flow computations require coupled calculations of flow and chemistry. Accurate and efficient computations of air-chemistry kinetics are of much importance for many practical applications but calculations accounting for detailed chemical kinetics can be prohibitively expensive. In this paper, we investigate the possibility of applying chemical kinetics reduction schemes for hypersonic air-chemistry. We consider two chemical kinetics sets appropriate for three different temperature ranges: 2500 K to 4500 K; 4500 K to 9000 K; and above 9000 K. By demonstrating the existence of the so-called the slow manifold in each of the chemistry sets, we show that judicious chemical kinetics reduction leading to significant computational savings is possible without much loss in accuracy.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Pore Scale Modeling of Reactive Transport Involved in Geologic CO<Subscript>2</Subscript> Sequestration

We apply a multi-component reactive transport lattice Boltzmann model developed in previous studies for modeling the injection of a CO₂-saturated brine into various porous media structures at temperatures T = 25 and 80°C. In the various cases considered the porous medium consists initially of calcite with varying grain size and shape. A chemical system consisting of Na⁺, Ca²⁺, Mg²⁺, H⁺, CO₂^°(aq){{\rm CO}_2^{\circ}{\rm (aq)}}, and Cl⁻ is considered. Flow and transport by advection and diffusion of aqueous species, combined with homogeneous reactions occurring in the bulk fluid, as well as the dissolution of calcite and precipitation of dolomite are simulated at the pore scale. The effects of the structure of the porous media on reactive transport are investigated. The results are compared with a continuum-scale model and the discrepancies between the pore- and continuum-scale models are discussed. This study sheds some light on the fundamental physics occurring at the pore scale for reactive transport involved in geologic CO₂ sequestration.     

On Aerodynamic Forces for Viscous Compressible Flow

The paper is aimed at reviewing and adding some new results to our recent work on a force theory for viscous compressible flows around a finite body. It has been proposed to analyze aerodynamic forces directly in terms of fluid elements of nonzero vorticity and density gradient. Let ρ denote the density, u the velocity, and ω the vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two major source elements: R _e(x) =−?u ²∇ρ·∇ϕ and V _e(x) =−u×ω·∇ϕ, where ϕ is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force considered. In particular, under mild conditions, the (unique) choice of ϕ enforces that the elements R _e(x) and V _e(x) decay rapidly away from the body. Four kinds of finite body are considered: a circular cylinder, a sphere, a hemi sphere-cylinder, and a delta wing of elliptic section—all in transonic-to-supersonic regimes. From an extensive numerical study carried out for these bodies, it is found that these two elements contribute to 95% or more of the total drag or lift for all the cases under consideration. Moreover, R _e(x) due to density gradient becomes progressively important relative to V _e(x) due to vorticity as the Mach number increases. The present method of force analysis enables effective analysis and assessment of relative importance of aerodynamics forces, contributed from individual flow structures. The analysis could therefore be very much useful in view of the rapid growth in numerical fluid dynamics; detailed (either local or global) flow information is often available. The paper is dedicated to Sir James Lighthill in honor of his great contributions to aeronautics on the occasion of the publication of his collected works. Received 3 January 1997 and accepted 11 April 1997     

Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.     

Three-dimensional Linear Eddy Modeling of a Turbulent Lifted Hydrogen Jet Flame in a Vitiated Co-flow

A new methodology for modeling and simulation of reactive flows is reported in which a 3D formulation of the Linear Eddy Model (LEM3D) is used as a post-processing tool for an initial RANS simulation. In this hybrid approach, LEM3D complements RANS with unsteadiness and small-scale resolution in a computationally efficient manner. To demonstrate the RANS-LEM3D model, the hybrid model is applied to a lifted turbulent N₂-diluted hydrogen jet flame in a vitiated co-flow of hot products from lean H₂/air combustion. In the present modeling approach, mean-flow information from RANS provides model input to LEM3D, which returns the scalar statistics needed for more accurate mixing and reaction calculations. Flame lift-off heights and flame structure are investigated in detail, along with other characteristics not available from RANS alone, such as the instantaneous and detailed species profiles and small-scale mixing.     

Series Solution of Non-similarity Boundary-Layer Flows Over a Porous Wedge

Solution of non-similarity boundary-layer flows over a porous wedge is studied. The free stream velocity U _w (x) ~ a x ^m and the injection velocity V _w (x) ~ b x ⁿ at the surface are considered, which result in the corresponding non-similarity boundary-layer flows governed by a nonlinear partial differential equation. An analytic technique for strongly nonlinear problems, namely, the homotopy analysis method (HAM), is employed to obtain the series solutions of the non-similarity boundary-layer flows over a porous wedge. An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of the physical parameters on the skin friction coefficient and displacement thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.     

Stability of some shear flows for concentrated suspensions

In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H ²/a ²), where H is a dimension of the flow field, and a is the particles' radius.     

Permeability evolution induced by the precipitation of an advected solute: Effect of the microscopic and the macroscopic scales competition on the clogging mechanism

A model is proposed for coupling the one-dimensional transport of solute with surface precipitation kinetics which induces the clogging of an initially homogeneous porous medium. The aim is to focus the non-linear feedback effect between the transport and the chemical reaction through the permeability of the medium. A Lagrangian formulation, used to solve the coupled differential equations, gives semi-analytical expressions of the hydrodynamic quantities. A detailed analysis reveals that the competition between the microscopic and macroscopic scales controls the clogging mechanism, which differs depends on whether short or long times are considered. In order to illustrate this analysis, more quantitative results were obtained in the case of a second and zeroth order kinetic. It was necessary to circumvent the semi-analytic character of the solutions problem by successive approximation. A comparison with results obtained by simulations displays a good agreement during the most part of the clogging time.Nomenclature a(x, t) Capillary tube radius (L) - A _(aq) Chemical species in the aqueous phase - A _n(s) Chemical species of the solid phase - C(x, t) Aqueous concentration in a capillary tube ([mole/L³] in the case of a permanent injection - [mole/L³/L] in the case of an instantaneous injection) - C(x, t) C(x, t)/C ₀ Dimensionless aqueous concentration in a capillary tube - C ₀ Aqueous concentration imposed at the inlet and also initial concentration in an elementary volume of fluid (mole/L³) - C _i(t) Concentration in a fluid element i (mole/L³) - C(_R) (t, C_o) Aqueous concentration in a stirred reactor (mole/L³) - d_ij (t) Length belonging to the volume, inside a fluid element i, which interacts with a precipitate element j (L) - dM _ij(t) Mass exchange between a fluid element i and a precipitate element j (M) - dN ₀ Number of molecules in an elementary volume of fluid injected at the inlet of a capillary tube during dt ₀ - dN(x, t, C₀) Number of molecules in an elementary volume of fluid - dt ₀ Time injection of an elementary volume of fluid (T) - D(x, t) Dispersion coefficient (L²/T) - Da(t, x) Damköhler number - D _m Molecular diffusion coefficient (L²/T) - F(x, t) Advective flux (mole/L²/T) - k ₁ Kinetic constant of dissolution (mole/L³/T) - k ₂ Kinetic constant of precipitation ([mole/L³]^{1 - n} /T) - k ₂ Kinetic constant of precipitation in the case of a zeroth order kinetics (mole/L³/T) - K(x, t) Permeability in a capillary tube (L²) - K(x, t) K (x, t)/K₀ Dimensionless permeability - k ₀ Permeability of a capillary tube at t = 0 (L²) - L Length of a capillary tube (L) - m Molecular weight of the reactive species (M/mole) - n Stochiometry of the chemical reaction and kinetic order of the precipitation reaction - P(x, t) Precipitate concentration in a capillary tube (mole/L³) - P _j(t) Concentration in a precipitate element j (mole/L³) - P(_r) (t, C_o) Precipitate concentration in a stirred reactor (mole/L³) - Pr(x, t) Local pressure in a capillary tube - (M/T²/L³) Pr(x, t) Pr(x, t)/Pr(x, 0) Dimensionless local pressure in a capillary tube - Q(t) Flow rate (L³/T) - Q(t) Q(t)U ₀/S₀ Dimensionless flow rate - R(x, t) Chemical flux between the aqueous and the solid phase in a capillary tube (mole/L³/T) - R _i(t) Chemical flux between an aqueous element i and the solid phase (mole/L³/T) - R _(R)[t, C₀] Chemical flux between the aqueous and the solid phase in a stirred reactor (mole/L³/T) - S(x, t) Cross sectional area of a capillary tube accessible to the aqueous phase (L²) - S(x, t) S(x, t)/S₀ Dimensionless cross-sectional area - S ₀ Cross-sectional area of a capillary tube at t = 0 (L²) - tlim(x) Time at which the precipitation front concentration vanishes in the case of zeroth order kinetics (T) - t _max Time of maximum propagation of the precipitation front in the case of zeroth order kinetics (T) - tmin(x) Time at which the precipitation front arrives at x (T) - t _p L/U ₀. Time necessary for an elementary volume of fluid, moving with the velocity U ₀, to reach the oulet of the medium - t _U max Time of maximum value of the velocity field in the case of zeroth order kinetics (T) - t ₀ Time at which an elementary volume of fluid has left the inlet of a capillary tube (T) - t _0m (x, t) Time at which the last elementary volume of fluid has left the inlet of a capillary tube to reach x at a time lower or equal to t (T) - U(x, t) Fluid velocity (L/T) - U(x, t) U(x, t)/U ₀. Dimensionless fluid velocity - U _j(x, t) Fluid velocity defined from the precipitate element j (L/T) - U _l (t₀, t) Lagrangian fluid velocity (L/T) - U _l (t ₀, t) U _l (x, t)/U ₀. Dimensionless lagrangian fluid velocity - U ₀ Velocity of the fluid at t = 0 (L/T) - V _ij(t) Volume, inside a fluid element i, which interacts with a precipitate element j (L³) - x _i(t) Front position of the fluid element i (L) - x _j Front position of the precipitate element j (L) - X _front(t) Position of the precipitation front (L) - x _lim(t) Position of the precipitation front when the value of its concentration is zero (L) - xmax Position of the maximum propagation of the precipitation front in the case of zeroth order kinetics and for high value of C ₀ (L) - Xmin (t) Position of the precipitation front (L) - x _inf* ^supmax Position of the maximum propagation of the precipitation front in the case of zeroth order kinetics and for small value of C_o (L) Greek Symbols t Time step used during the numerical computation (T) - Pro Imposed pressure drop (M/L/T²) - Injection time of reactive species (T) - Density of the precipitate (M/L³) - Dynamic viscosity (M/L/T) - <Ri(t)> _infi ^supj Mean chemical flux between a precipitate element j and all the fluid elements i susceptible to interact with the precipitate element j (mole/L³/T)     

NMS Flows on S 3 with no Heteroclinic Trajectories Connecting Saddle Orbits

In this paper we find topological conditions for the non existence of heteroclinic trajectories connecting saddle orbits in non singular Morse-Smale flows on S ³. We obtain the non singular Morse-Smale flows that can be decomposed as connected sum of flows and we show that these flows are those who have no heteroclinic trajectories connecting saddle orbits. Moreover, we characterize these flows in terms of links of periodic orbits.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Boundary layer structure of oscillatory open-channel shallow flows over smooth and rough beds

The boundary layer structure of oscillatory shallow open channel flows has been studied in a wide flume. Fluorescence solution was released at a porous rough bed through a diffuser covered by gravel of 0.5 cm grain size. A planar laser-induced fluorescence (PLIF) system was used to visualise the dye plumes in both vertical and horizontal planes for a qualitative understanding of the roles of large-scale flow structures in mass transport. A variety of tests were conducted for a range of oscillatory periods (30–240 s), water depths (3–16 cm) and velocity amplitudes (0.027–0.325 m/s), which cover a wide range of oscillatory flows with Reynolds numbers Re _a varied from 0.3 × 10⁴ (laminar) to 2.1 × 10⁶ (fully turbulent). For quantitative investigation, a novel technique, namely combined laser-induced fluorescence (LIF) and 2D laser Doppler velocimetry (LDV) (LIF/LDV), was developed and used to measure the velocity and solute concentration simultaneously in a vertical plane over 50 cycles. From the dye plumes revealed by the PLIF in transitional flows, there are different patterns of flow structure and solute transport with three representative stages of acceleration, deceleration and flow reversal. In the acceleration stage, turbulence was suppressed with dye layers adhering to the surface with little vertical mass transport. In the deceleration stage, flame-like turbulent structures occurred when turbulence generation was prominent. This was investigated quantitatively by recording the percentage occurrence of the adhered smooth layers per cycle. For those smooth bed cases with Re _a < 1.8 × 10⁵, the adhered smooth dye layers type of boundary layer occupied 100% of the oscillation period. Over a sufficiently high Re _a , a rough bed can generate fully turbulent oscillatory flows without the appearance of adhering dye layers. Between these two extremes, a transitional flow regime occurs in a wide range of flow conditions: Re _a > 2.7 × 10⁴ over the rough bed and Re _a > 8.3 × 10⁶ over a smooth bed.     

Effects of corrugation angle on developing laminar forced convection and entropy generation in a wavy channel

This paper investigates the effects of corrugation angle (β) on the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The studied cases cover β = 10-, 15-, 20-, 25-, 30- and 35°, whilst Reynolds number (Re) is varied as 100, 200 and 400. The analyzed flow characteristics include recirculating flows, secondary vortices, temperature distributions, and friction factor as well as Nusselt number. In particular, the effects of corrugation angle on the distributions and magnitudes of local entropy generation resulted from frictional irreversibility (S _P ^′′′) and heat transfer irreversibility (S _T ^′′′) are separately discussed in detail in the present paper. Based on the minimal entropy generation principle, the optimal corrugation angle and favorable Re are reported.