bluuebunny/crossref_metadata_2025_split huggingface dataset:
A spectral closure for premixed turbulent combustion in the flamelet regime
Authors: Peters N. 
Published: April 2006

Premixed turbulent combustion in the flamelet regime is analysed on the basis of a field equation. This equation describes the instantaneous flame contour as an isoscalar surface of the scalar field G(x,t). The field equation contains the laminar burning velocity sL as velocity scale and its extension includes the effect of flame stretch involving the Markstein length [Lscr ] as a characteristic lengthscale of the order of the flame thickness. The scalar G(x,t) plays a similar role for premixed flamelet combustion as the mixture fraction Z(x,t) in the theory of non-premixed flamelet combustion.Equations for the mean $\overline{G}$ and variance $\overline{G^{\prime 2}}$ are derived. Additional closure problems arise for the mean source terms in these equations. In order to understand the nature of these terms an ensemble of premixed flamelets with arbitrary initial conditions in constant-density homogeneous isotropic turbulence is considered. An equation for the two-point correlation $\overline{G^{\prime}({\boldmath x},t)G^{\prime}({\boldmath x}+{\boldmath r},t)}$ is derived. When this equation is transformed into spectral space, closure approximations based on the assumption of locality and on dimensional analysis are introduced. This leads to a linear equation for the scalar spectrum function Γ(k,t), which can be solved analytically. The solution Γ(k,t) is analysed by assuming a small-wavenumber cutoff at k0 = lT−1, where lT is the integral lengthscale of turbulence. There exists a $k^{-\frac{5}{3}}$ spectrum between lT and LG, where LG is the Gibson scale. At this scale turbulent fluctuations of the scalar field G(x,t) are kinematically restored by the smoothing effect of laminar flame propagation. A quantity called kinematic restoration ω is introduced, which plays a role similar to the scalar dissipation χ for diffusive scalars.By calculating the appropriate moments of Γ(k,t), an algebraic relation between ω, $\omega,\overline{G^{\prime}({\boldmath x},t)^2}$, the integral lengthscale lT and the viscous dissipation ε is derived. Furthermore, the scalar dissipation χ[Lscr ], based on the Markstein diffusivity [Dscr ][Lscr ] = sL [Lscr ], and the scalar-strain co-variance Σ[Lscr ] are related to ω. Dimensional analysis, again, leads to a closure of the main source term in the equation for the mean scalar $\overline{G}$. For the case of plane normal and oblique turbulent flames the turbulent burning velocity sT and the flame shape is calculated. In the absence of flame stretch the linear relation sT ∼ u′ is recovered. The flame brush thickness is of the order of the integral lengthscale. In the case of a V-shaped flame its increase with downstream position is calculated.
Direct simulation of particle dispersion in a decaying isotropic turbulence
Authors: Elghobashi S. , Truesdell G. C. 
Published: April 2006

Dispersion of solid particles in decaying isotropic turbulence is studied numerically. The three-dimensional, time-dependent velocity field of a homogeneous, non-stationary turbulence was computed using the method of direct numerical simulation (DNS). A numerical grid containing 963points was sufficient to resolve the turbulent motion at the Kolmogorov lengthscale for a range of microscale Reynolds numbers starting fromRλ= 25 and decaying toRλ= 16. The dispersion characteristics of three different solid particles (corn, copper and glass) injected in the flow, were obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 223particles for each particle type, and then performing ensemble averaging. The three different particles are those used by Snyder & Lumley (1971), referred to throughout the paper as SL, in their pioneering wind-tunnel experiment. Good agreement was achieved between our DNS results and the measured time development of the mean-square displacement of the particles.The simulation results also include the time development of the mean-square relative velocity of the particles, the Lagrangian velocity autocorrelation and the turbulent diffusivity of the particles and fluid points. The Lagrangian velocity frequency spectra of the particles and their surrounding fluid, as well as the time development of all the forces acting on one particle are also presented. In order to distinguish between the effects of inertia and gravity on the dispersion statistics we compare the results of simulations made with and without the buoyancy force included in the particle motion equation. A summary of the significant results is provided in §7 of the paper.The main objective of the paper is to enhance the understanding of the physics of particle dispersion in a simple turbulent flow by examining the simulation results described above and answering the questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics.
Numerical simulation of turbulent convection over wavy terrain
Authors: Krettenauer Kilian , Schumann Ulrich 
Published: April 2006

Thermal convection of a Boussinesq fluid in a layer confined between two infinite horizontal walls is investigated by direct numerical simulation (DNS) and by large-eddy simulation (LES) for zero horizontal mean motion. The lower-surface height varies sinusoidally in one horizontal direction while remaining constant in the other. Several cases are considered with amplitude δ up to 0.15H and wavelength λ of H to 8H (inclination up to 43°), where H is the mean fluid-layer height. Constant heat flux is prescribed at the lower surface of the initially at rest and isothermal fluid layer. In the LES, the surface is treated as rough surface (z0 = 10−4H) using the Monin-Oboukhov relationships. At the flat top an adiabatic frictionless boundary condition is applied which approximates a strong capping inversion of an atmospheric convective boundary layer. In both horizontal directions, the model domain extends over the same length (either 4H or 8H) with periodic lateral boundary conditions.We compare DNS of moderate turbulence (Reynolds number based on H and on the convective velocity is 100, Prandtl number is 0.7) with LES of the fully developed turbulent state in terms of turbulence statistics and Characteristic large-scale-motion structures. The LES results for a flat surface generally agree well with the measurements of Adrian et al. (1986). The gross features of the flow statistics, such as profiles of turbulence variances and fluxes, are found to be not very sensitive to the variations of wavelength, amplitude, domain size and resolution and even the model type (DNS or LES), whereas details of the flow structure are changed considerably. The LES shows more turbulent structures and larger horizontal scales than the DNS. To a weak degree, the orography enforces rolls with axes both perpendicular and parallel to the wave crests and with horizontal wavelengths of about 2H to 4H. The orography has the largest effect for λ = 4H in the LES and for λ = 2H in the DNS. The results change little when the size of the computational domain is doubled in both horizontal directions. Most of the motion energy is contained in the large-scale structures and these structures are persistent in time over periods of several convective time units. The motion structure persists considerably longer over wavy terrain than over flat surfaces.
Nonlinear and free-surface effects on the spin-down of barotropic axisymmetric vortices
Authors: Maas Leo R. M. 
Published: April 2006

The spin-down of a barotropic axisymmetric vortex, such as observed in laboratory models, is examined analytically. In addition to the classical, self-similar Ekman decay due to viscous effects (Greenspan & Howard 1963), which is characterized by an azimuthal velocity profile with the position of its maximum velocity fixed and a decay time equal to the Ekman timescale. the effects of nonlinearity and a free surface are considered separately.The Ekman circulation in the radial and vertical planes whose strength is determined by the vorticity of the overlying fluid, leads to radial advection of the azimuthal velocity. This nonlinearity results in a nonlinear kinematic wave equation for the circulation and leads to the outward/inward propagation of the position of maximum azimuthal velocity for cyclonic/anticyclonic vortices. The associated steepening of the azimuthal velocity profile may lead to a shock formation when the absolute vorticity of the initial profile is negative at a certain radius. For anticyclonic vortices having a monotonically increasing angular velocity profile this shock formation occurs at the core. For such vortices (or arbitrary cyclonic vortices) this dynamical ‘breaking’ criterion is, despite significant differences in the physics concerned, identical to Rayleigh's kinematical criterion for the onset of centrifugal instability.For a dynamically active free-surface fluid the spin-down of a decaying vortex is prolonged by a radially dependent factor proportional to the Froude number. This conclusion holds both in a cylinder with a parabolic bottom (mimicking the shape of the free surface of a fluid in solid-body rotation) and in a flat-bottomed cylinder. In view of the constancy of background vorticity the former geometry is relevant for a comparison to geophysical f-plane vortices. The latter geometry, however, is more easily established in a laboratory experiment, but the evolution of the azimuthal velocity profile is much more complicated and depends on the initial azimuthal velocity profile in a highly convoluted way.
Frequency spectra of reactant fluctuations in turbulent flows
Authors: Kosály George 
Published: April 2006

Bilger, Saetran & Krishnamoorthy (1991) give measured values of the variance, cross-correlation coefficient, autospectra, coherence and phase shift of the reactant concentration fluctuations for an irreversible second-order reaction in an incompressible turbulent scalar mixing layer. The present paper approaches the interpretation of the measured data by evaluating the above quantities in the frozen (slow) and equilibrium (fast) chemistry limits. We assume that the limiting values bracket the corresponding intermediate rate data.The analysis leads to values that correspond with the measured variances and correlation coefficients. The paper offers simple procedures for experimenters to evaluate the fast chemistry limit of the spectral characteristics from the measured mixture fraction fluctuations. The investigation of the limiting spectra suggests that, in the frequency region considered in the Bilger et al. measurements, the shape of the autospectrum is quite insensitive to the chemistry rate. The cross-spectrum is much more sensitive to the chemistry than the autospectrum. The analysis predicts correctly that the coherence decreases with increasing frequency while the phase stays equal to π until the decrease of the coherence leads to indeterminate phase results.
Oscillatory flow in a stepped channel
Authors: Tutty O. R. , Pedley T. J. 
Published: April 2006

Two-dimensional, unsteady flow of a viscous, incompressible fluid in a stepped channel has been studied by the numerical solution of the Navier–Stokes equation using an accurate finite-difference method.With a sinusoidal mass flow rate, the problem has three governing parameters: the Reynolds number, the Strouhal number, and the step height. The effects on the flow of varying all three parameters has been investigated systematically. In appropriate parameter regimes, a strong ‘vortex wave’ is generated during the forward phase when the flow is over the step into the expansion. Secondary effects on the wave can result in a complex flow pattern with each major structure of the flow consisting of an eddy with more than one core. No such wave is found during the reverse phase of the flow. The generation and development of the wave is examined in some detail, and our results are compared and contrasted with those of previous studies, both experimental and theoretical, of flow in non-uniform vessels.
Highly accelerated, free-surface flows
Authors: Longuet-Higgins Michael S. 
Published: April 2006

Accelerations exceeding 20gin surface waves have been observed both in experiments and in numerically computed flows with a free surface. The present paper describes a family of analytic solutions which display such behaviour. They are expressible in parametric form as z =Fsinh ω + iGcosh ω + γω + iH, whereF, GandHare functions of the timetonly, and γ is linear int. ω is a complex parameter which is real at the free surface. The functionsF(t) andG(t) satisfy two nonlinear, coupled ODEs, which can be solved numerically. Typically the solutions pass through an ‘inertial shock’, or singularity in the time, where the displacements vary ast2/3, the velocities ast1/3 and the accelerations ast-4/3. In this class of solution the free surface develops a cusp ast→ ∞. In a special case,FandGvary ast4/7and the cusp is reached in finite time. Gravity is neglected, but plays a part in setting up the initial conditions for the highly accelerated flow.In future papers it will be shown that more general solutions exist in which the acceleration is momentarily large but bounded.
Mach reflection of a large-amplitude solitary wave
Authors: Tanaka Mitsuhiro 
Published: April 2006

Reflection of an obliquely incident solitary wave by a vertical wall is studied numerically by applying the ‘high-order spectral method’ developed by Dommermuth & Yue (1987). According to the analysis by Miles (1977a, b) which is valid when ai [Lt ] 1, the regular type of reflection gives way to ‘Mach reflection’ when ai/(3ai)½ ≤ 1, Where ai is the amplitude of the incident wave divided by the quiescent water depth d and ψi is the angle of incidence. In Mach reflection, the apex of the incident and the reflected waves moves away from the wall at a constant angle (ψ*, say), and is joined to the wall by a third solitary wave called ‘Mach stem’. Miles model predicts that the amplitude of Mach stem, and so the run-up at the wall, is 4ai when ψi = (3ai)½.Our numerical results shows, however, that the effect of large amplitude tends to prevent the Mach reflection to occur. Even when the Mach reflection occurs, it is ‘contaminated’ by regular reflection in the sense that all the important quantities that characterize the reflection pattern, such as the stem angle ψ*, the angle of reflection ψr, and the amplitude of the reflected wave ar, are all shifted from the values predicted by Miles’ theory toward those corresponding to the regular reflection, i.e. ψ* = 0, ψr = ψi, and ar = ai. According to our calculations for ai = 0.3, the changeover from Mach reflection to regular reflection happens at ψi ≈ 37.8°, which is much smaller than (3ai)½ = 54.4°, and the highest Mach stem is observed for ψi = 35° (ψi/(3ai)½ = 0.644). Although the ‘four-fold amplification’ is not observed for any value of ψi considered here, it is found that the Mach stem can become higher than the highest two-dimensional steady solitary wave for the prescribed water depth. The numerical result is also compared with the analysis by Johnson (1982) for the oblique interaction between one large and one small solitary wave, which shows much better agreement with the numerical result than the Miles’ analysis does when ψi is sufficiently small and the Mach reflection occurs.
Mixing by a turbulent plume in a confined stratified region
Authors: Cardoso Silvana S. S. , Woods Andrew W. 
Published: April 2006

An experimental and theoretical study of the mixing produced by a plume rising in a confined stratified environment is presented. As a result of the pre-existing stable stratification, the plume penetrates only part way into the region; at an intermediate level it intrudes laterally forming a horizontal layer. As time evolves, this layer of mixed fluid is observed to increase in thickness. The bottom front advects downward in a way analogous to the first front in the filling box of Baines & Turner (1969), while the lateral spreading of the plume occurs at an ever-increasing level and an ascending top front results. We develop a model of this stratified filling box; the model predicts the rate at which the two fronts advance into the environment.It is found that stratification in the environment, when smooth, has no significant influence on the dynamics of the descending front. We show that the rate of rise of the ascending front is determined by the turbulent mixing occurring at the spreading level. Entrainment of environmental fluid from above into the overshooting plume is significant; as a result, a density interface develops at this level. Asymptotically, the system reaches a state in which a bottom convecting layer, with an almost homogeneous density, deepens in a stratified background. The model proposed for this large-time behaviour is based on the simple energetic formulation that a constant fraction of the kinetic energy supplied by the plume, for mixing across the interface, is converted into potential energy of the convective layer. Our experimental results suggest an efficiency of approximately 50 % for this conversion.We discuss our results in the light of previous studies on turbulent penetrative convection and conclude that the theory developed should be valid for an intermediate range of values of the Richardson number characterizing the dynamic conditions at the interface. The model is applied quantitatively to the process of cooling of a room wherein stratification is relevant. The geological problem of replenishment of a magma chamber by a light input of magma is also analysed.
A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils
Authors: Kinnas Spyros A. , Fine Neal E. 
Published: April 2006

The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result.The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT's cavitation tunnel.
Mixing of a viscoelastic fluid in a time-periodic flow
Authors: Niederkorn T. C. , Ottino J. M. 
Published: April 2006

We present an experimental and computational investigation of mixing of a viscoelastic fluid in two-dimensional time-periodic flows generated in an eccentric cylindrical geometry. The objective of the study is to investigate the impact of fluid elasticity on the morphological structures produced by the advection of passive tracers in chaotic flows. The relevant dimensionless numbers that quantify the rheological differences with respect to the Newtonian fluid are the Deborah number (De), defined as the ratio of the fluid timescale to the flow timescale, and the Weissenberg number (We), defined as the product of the fluid timescale and the mean shear rate. The effects of elasticity are investigated in the limit of slow flows, De ≈ 0 and We < 0.1. The experimental window of We is limited to Newtonian behaviour on the low end and the transition to three-dimensional flow on the high end; experiments show that this window is small, 0.02 < We < 0.1. Typical values of the Reynolds number and the Strouhal number are O(0.001) and O(0.1), respectively.Results from experiments with a constant-viscosity elastic fluid and computations using the upper-convected Maxwell constitutive equation are presented. Even though the streamlines for the elastic flow are nearly indistinguishable from the Newtonian flow, small deviations in the velocity field produce large effects on chaotically advected patterns. Elasticity affects both the asymptotic coverage of a dyed passive tracer and the rate at which the tracer is stretched. In all cases the tracer undergoes exponential stretching, but on a longer timescale as the elasticity increases. According to flow conditions, elasticity might increase or decrease the degree of regularity; however, island symmetry does not seem to be affected. Similar phenomena are observed in both the experiments and computations; therefore, an analysis of the chaotic dynamics of the periodic flow using numerical techniques is possible.