Formation of a large radiation-induced fire

In connection with ecological and climatic problems and, in particular, the nuclear winter theory much attention has recently been paid to the study of the possible consequences of large fires and explosions [1–5]. Below, on the basis of the model proposed in [6, 7] we investigate the initial stage of development of a fire induced by the light emitted by a powerful explosion in the atmosphere. The situation above the seat of combustion (the aerodynamics of the layer of air adjacent to the ground, the configuration and characteristics of the smoke cloud formed) is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1992.     

Convective transport of combustion products in the atmosphere above large fires

A nonstationary axisymmetric model of the development of a turbulent convective combustion product column above a fire in a stratified atmosphere is proposed. The model takes into account the compressibility of the gas and the diffusion of the aerosol particles and makes it possible to predict the dynamics of ascent of the convective column, the height of the cloud and the distribution of the aerosol in the atmosphere. The numerical and experimental data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 47–52, July–August, 1990.     

Smoke Control of Fires in Subway Stations

We investigate the effectiveness of the smoke control scheme of the Gong-Guan subway station (GGSS), a typical subway station of the Taipei Rapid Transit System and whose mechanical control systems are also standard in modern subway station design. Three-dimensional smoke flow fields under various kinds of fires are computed by computational fluid dynamics techniques and the results are illustrated on various cross-sectional planes. Results indicate that the stack effect plays a deterministic role in smoke control when a fire occurs near the stairwell; under such circumstances, no mechanical smoke control is necessary. When a fire occurs in other places, such as at the end or the center of the platform, the current mechanical control schemes of GGSS are effective; namely, the smoke can be well controlled, either it is confined to a small region or is evacuated from the station, leaving the four exits free of smoke so that the passengers can escape through them. The effect of the platform edge door (PED) on smoke control is also investigated. With the PED, the effectiveness of the present smoke control system for fires occurring on the chassis of a train, a serious fire in the subway station, increases. We also propose an innovative smoke control scheme with a PED, which turns out to be much more efficient in evacuating smoke than that currently used. This study provides both valuable information for the design of passenger evacuation routes in fires as well as criteria for the design of a smoke control system for subway stations. Received 12 August 2002 and accepted 22 October 2002 Published online 14 February 2003 RID="*" ID="*" The financial supports for this research from both the SinoTech Engineering Consultant Inc. and the National Science Council under Grant NSC 89-2212-E-002-61 are gratefully appreciated. Communicated by H.J.S. Fernando     

Modelling and simulation of fires in vehicle tunnels

Applying a low‐Mach asymptotic for the compressible Navier–Stokes equations, we derive a new fluid dynamics model,which should be capable to model large temperature differences in combination with the low‐Mach number limit. The model is used to simulate fires in vehicle tunnels, where the standard Boussinesq‐approximation for the incompressible Navier–Stokes seems to be inappropriate due to the high temperatures developing in the tunnel. The model is implemented using a modified finite‐difference approach for the incompressible Navier–Stokes equations and tested in some realistic fire events. Copyright © 2004 John Wiley & Sons, Ltd.     

Spectral Properties of Dynamical Systems, Model Reduction and Decompositions

In this paper we discuss two issues related to model reduction of deterministic or stochastic processes. The first is the relationship of the spectral properties of the dynamics on the attractor of the original, high-dimensional dynamical system with the properties and possibilities for model reduction. We review some elements of the spectral theory of dynamical systems. We apply this theory to obtain a decomposition of the process that utilizes spectral properties of the linear Koopman operator associated with the asymptotic dynamics on the attractor. This allows us to extract the almost periodic part of the evolving process. The remainder of the process has continuous spectrum. The second topic we discuss is that of model validation, where the original, possibly high-dimensional dynamics and the dynamics of the reduced model – that can be deterministic or stochastic – are compared in some norm. Using the “statistical Takens theorem” proven in (Mezić, I. and Banaszuk, A. Physica D, 2004) we argue that comparison of average energy contained in the finite-dimensional projection is one in the hierarchy of functionals of the field that need to be checked in order to assess the accuracy of the projection.     

Calculation of the blast effect in brittle rock (fracturing by crushing,formation of cleavage cracks,and separation)

An algorithm is presented for calculating the dynamics of the development of a blast in solid, brittle fracturing rocks. The stages of the phenomenon arising and alternating in various sequences depending on the mechanical properties of the rock and power of the blast are examined in detail.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 104–120, September–October, 1970.The author thanks S. S. Grigoryan for constant attention to this study.     

Nonlinear waves on the surface of a charged liquid. Instability,bifurcation, and nonequilibrium shapes of the charged surface

Plane nonlinear waves in shallow water are described by the Kortewegde Vries equation [1–3]. The present paper contains theoretical investigations of nonlinear waves and nonlinear equilibrium shapes on the surface of a charged liquid. The influence of the field on the velocity and shape of a hydrodynamic soliton is considered. The bifurcation of the equilibrium shapes is investigated. Problems of the equilibrium shapes of a charged liquid are solved in the nonlinear formulation of the dynamics of nonlinear solitary forms (lunes, trenches) on the surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 94–102, May–June, 1984.     

Flow of linear molecules through a 4:1:4 contraction–expansion using non-equilibrium molecular dynamics: Extensional rheology and pressure drop

In this work, non-equilibrium molecular dynamics simulations are used to generate the flow of linear polymer chains (monomer-springs with FENE potential) and a Lennard–Jones fluid (Newtonian fluid) through a contraction–expansion (4:1:4) geometry. An external force field simulating a constant pressure gradient upstream the contraction region induces the flow, where the confining action of the walls is represented by a Lennard–Jones potential. The equations of motion are solved through a multiple-step integration algorithm coupled to a Nosé-Hoover dynamics [S. Nose, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511–519], i.e., to simulate a thermostat, which maintains a constant temperature. In this investigation, we assume that the energy removed by the thermostat is related to the viscous dissipation along the contraction–expansion geometry. A non-linear increasing function between the pressure drop and the mean velocity along the contraction for the linear molecules is found, being an order of magnitude larger than that predicted for the Lennard–Jones fluid. The pressure drop of both systems (the linear molecules and Lennard–Jones fluid) is related to the dissipated energy at the contraction entry. The large deformation that the linear molecules experience and the evolution of the normal stress at the contraction entry follow a different trajectory in the relaxation process past the contraction, generating large hysteresis loops. The area enclosed by these cycles is related to the dissipated energy. Large shear stresses developed near the re-entrant corners as well as the vortex formation, dependent on the Deborah number, are also predicted at the exit of the contraction. To our knowledge, for the first time, the excessive pressure losses found in experimental contraction flows can be explained theoretically.     

Motion of a cylindrical cavity near a free boundary of a liquid

The dynamics of a cylindrical cavity in a liquid with no allowance for vertical displacement are considered in [1–3]. The present study investigates the pulsation motion of a cylindrical cavity near a free boundary of a liquid, allowing for displacement of the axis of the cavity in the vertical direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1988.     

Method of contour dynamics for plane flows of an ideal fluid

The method of contour dynamics is generalized for plane flows of a general form when, apart from vortices, distributed mass sources (or sinks) are present in the fluid. The laws of variation of the vorticity and divergence of the fluid particles with time are obtained for this case which makes it possible to use the method of contour dynamics for piecewise-constant vortex sink distributions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–19, September–October, 1993.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

Nonequilibrium stretching dynamics of dilute and entangled linear polymers in extensional flow

We propose an extension of the FENE-CR model for dilute polymer solutions [M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech. 29 (1988) 382–432] and the Rouse-CCR tube model for linear entangled polymers [A.E. Likhtman, R.S. Graham, Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation, J. Non-Newtonian Fluid Mech. 114 (2003) 1–12], to describe the nonequilibrium stretching dynamics of polymer chains in strong extensional flows. The resulting models, designed to capture the progressive changes in the average internal structure (kinked state) of the polymer chain, include an ‘effective’ maximum contour length that depends on local flow dynamics. The rheological behavior of the modified models is compared with various results already published in the literature for entangled polystyrene solutions, and for the Kramers chain model (dilute polymer solutions). It is shown that the FENE-CR model with an ‘effective’ maximum contour length is able to describe correctly the hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation also observed and computed by Doyle et al. [P.S. Doyle, E.S.G. Shaqfeh, G.H. McKinley, S.H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech. 76 (1998) 79–110] and Li and Larson [L. Li, R.G. Larson, Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow, Rheol. Acta 39 (2000) 419–427] using Brownian dynamics simulations of bead–spring model. The Rolie–Poly model with an ‘effective’ maximum contour length exhibits a less pronounced hysteretic behavior in stress versus birefringence in start-up of uniaxial extensional flow and subsequent relaxation.     

Wave dynamics of mixed,periodically nonstationary flows of a spontaneously condensing vapor

A study is made of the dynamics of mixed flows of a condensing vapor with nonequilibrium phase transitions and gas-dynamic discontinuities in channels of variable area in the presence of periodically nonstationary boundary conditions at the entrance. The results are given of a numerical investigation of the flows of superheated and spontaneously condensing water vapor in a supersonic nozzle. It is shown that the periodic nonstationarity of the flow at the entrance can lead to a qualitative rearrangement of the flow structure in the presence of spontaneous condensation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–121, November–December, 1980.     

Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Action of an explosive plastic wave on a plate

The action of a transient loading on an infinitely elastic plate, freely covering the surface of an ideal compressible liquid, was discussed in [1–3]. A review of work on the dynamics of a plate under the action of a transient loading is given in [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 131–136, July–August, 1976.     

Numerical investigation and self-similar solutions of the glacier-ocean interaction problem

The mathematical modeling of the heat and mass transfer processes in glaciers is an effective means of investigating and predicting their development. A full explanation of the problem of constructing appropriate mathematical models is given in [1–5]. By analyzing the equations involved [3, 6] it is possible to establish the principal factors and dimensionless numbers determining glacier dynamics and provide justification for neglecting the secondary terms. In particular, a simplified closed system of differential equations for the detailed calculation of all the hydrodynamic characteristics of the glacier can be obtained for K_hj « 1 up to O(K _h ² ), where K_h is the ratio of the vertical and horizontal scales of the ice mass investigated (K_h 10^–4–10^–6). In this case many of the qualitative characteristics of glacier dynamics are preserved even in one-dimensional models within the subisothermal approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1986.     

Nonlinear capillary waves in thin films of viscous liquid and breaking of the films

A study is made of the dynamics of a thin film of viscous liquid with allowance for the influence of capillary forces and long-range van der Waals forces. Asymptotic solutions are found to problems of the dynamics of films in communication with a region of reduced pressure. It is shown that at a certain instant such a film breaks at its edge. The critical parameters that determine the instant of breaking are found and the form of the solution in the stage of breaking is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 47–55, July–August, 1982.     

Non-linear dynamics of a drill-string with uncertain model of the bit–rock interaction

The drill-string dynamics is difficult to predict due to the non-linearities and uncertainties involved in the problem. In this paper a stochastic computational model is proposed to model uncertainties in the bit–rock interaction model. To do so, a new strategy that uses the non-parametric probabilistic approach is developed to take into account model uncertainties in the bit–rock non-linear interaction model. The mean model considers the main forces applied to the column such as the bit–rock interaction, the fluid–structure interaction and the impact forces. The non-linear Timoshenko beam theory is used and the non-linear dynamical equations are discretized by means of the finite element method.     

基于混沌理论的室内轰燃判据

根据混沌理论,在研究大量小规模室内火灾实验结果的基础上,得到了一种新的、通过温度变化率 表征的轰燃判据;利用大规模室内火灾的实验结果,对该判据的实用性进行了初步验证。结果表明:这一判据 可以应用于预测大规模实际室内火灾中轰燃的发生。     

Numerical study of the dynamics of a vapor envelope round a heated solid particle in a liquid

A study is made of the radial motion of a vapor envelope surrounding an isolated spherical particle in an unbounded mass of liquid. It is assumed that the liquid is viscous and incompressible and that the temperature is distributed uniformly in the solid particle. A model of a calorifically perfect gas is used for the vapor phase. The same assumptions are made as in Rayleigh's formulation for the problem of the dynamics of a single bubble: that the process is spherically symmetric and that the pressure P₂ (t) in the vapor phase is homogeneous. The justification for making these assumptions in problems of the dynamics of gas, vapor, and vaporgas bubbles is discussed in [1–5]. In this paper, the collapse of the vapor layer and the boiling of the liquid on the surface of the heated particle are not considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 154–157, July–August, 1985.