Quasi One-dimensional Flow Research Articles

Theoretical analysis and numerical validation of the mechanisms controlling composition noise

A new definition of entropy fluctuation is provided in this paper, that allows properly separating entropy and mixture composition fluctuations. This decomposition into linearly independent variables prevents from overestimating compositional noise in indirect noise prediction. When considering quasi one-dimensional flow in nozzles, a new resulting system of linearized Euler equations is obtained. Two analytical solutions of this system of equations are investigated in this study, one dedicated to low-frequency perturbations and another one for all frequency perturbations. This new theory is then validated by comparing the model predictions with direct numerical simulation of nozzle flows in which composition fluctuations are pulsed. To do so, new Navier–Stokes characteristics boundary conditions to account for the new properly defined entropy wave are provided. Furthermore, non-reflecting inlet boundary conditions have been newly derived, relaxing on the axial mass-flow rate, static temperature and species mass fractions. Finally, a parametric study based on an air-kerosene (equivalent C10H20) mixture and an ideal framework shows that composition noise can reach a maximum of 10% of entropy noise for lean combustion and choked nozzle while for rich combustion, composition noise and entropy noise show comparable levels.

The characteristics of ventilated pool fires of Daegok-Sosa subway lines using Model-Scale tunnels and stations

The characteristics of ventilated pool fires for Daegok-Sosa subway lines with a length of 15.12 km in Seoul, South Korea were studied. The model-scale tunnels and stations were built in scale 1:50 and temperature distribution, smoke (Carbon Monoxide (CO)) spreading, back-layering phenomenon and longitudinal ventilated flow velocity were systematically investigated. Present subscale model was based on the Froude number similitude and a heptane pool fire was used as the heat source. Heat release rate of pool fire in model-scale tunnel was 1.13 kW corresponding to an equivalent 20 MW in full scale. The occurrence of smoke back-layering phenomenon could be observed by whether the upstream temperature rose at a certain position during the whole process of the fire test. In the single line parallel tunnel, the smoke was restricted to downstream of fire source, however, in the double track tunnel the smoke back layering slightly occurred in upstream region of fire source and then it soon disappeared. The smoke propagated far downstream side and the tunnel safety measures should be taken for passenger’s safe evacuation from the CO toxic gas. The longitudinal air velocities in upstream side near the fire source were accelerated and were about 11% higher than the downstream velocities in single line parallel tunnel and more than 20% higher in double track tunnel caused by the blocking effect of fire source. A generalized quasi one-dimensional flow network solver was employed to calculate the longitudinal air velocity in tunnels using the finite volume Ghost Junction Method (GJM) which were compared with the present experimental data. The required minimum longitudinal air velocities (2.0 m/sec for single line parallel tunnel and 2.5 m/sec for double track tunnel) specified in the Korean railway facility technical standards were well satisfied in this experiment.

Non-Ideal Compressible Fluid Dynamics: A Challenge for Theory

The possibility that compression as well as rarefaction shocks may form in single phase vapours was envisaged first by Bethe (1942). However calculations based on the Van der Waals equation of state indicated that the latter type of shock is possible only if the specific heat at constant volume cv divided by the universal gas constant R is larger than about 17.5 which he considered too large to be satisfied by real fluids. This conclusion was contested by Thompson (1971) who showed that the type of shock capable of forming in arbitrary fluids is determined by the sign of the thermodynamic quantityto which he referred to as fundamental derivative of gas dynamics. Here v, p, s and c denote the specific volume, the pressure, the entropy and the speed of sound. Thompson and co-workers also showed that the required condition for the existence of rarefaction shocks, that Γ may take on negative values, is indeed satisfied for a number of hydrocarbon and fluorocarbon vapours. This finding spawned a burst of theoretical studies elaborating on the unusual and often counterintuitive behaviour of shocks with rarefaction shocks present. These produced both results of theoretical character but also results suggesting the practical importance of Non-Ideal Compressible Fluid Dynamics in general. The present paper addresses some of the challenges encountered in connection with the theoretical treatment of the associated flow behaviour. Weakly nonlinear acoustic waves of finite amplitude serve as a starting point. Here mixed rather than strictly positive nonlinearity generates a wealth of phenomena not possible in perfect gases. Examples of steady flows where these non-classical effects play a decisive role (and which may be useful also for future experimental work) are quasi one-dimensional nozzle flows and transonic two-dimensional flows past corners. The study of viscous effects concentrates on laminar flows of boundary layer type. Here non-classical phenomena are caused by the uncommon smallness of the Eckert number but also by the unconventional Mach number dependence on p in the external inviscid flow region.

A quasi one-dimensional bleed flow rate model for terminal normal shock stability in mixed compression supersonic inlet

Ninety-degree (normal) bleed slots have been used to stabilize the terminal normal shock in the throat of a mixed compression supersonic inlet. In this study, a quasi-one-dimensional bleed flow rate model, consisting of a constant-area channel with a pair of normal slots symmetrically located along the upper and lower endwalls, is developed. The bleed flow rate is shown to be a function of the terminal normal shock position within the slot. Some key factors, such as the bleed discharge coefficient, taken from the Bragg model, were derived from the basic laws of conservation for a one-dimensional simplification. Furthermore, numerical simulations based on Reynolds-averaged Navier–Stokes equations were performed to analyze the flow characteristics around the bleed slots. The predictions of the bleed flow rate model agree well with computational fluid dynamics results. This method may be helpful to predict the stability of the terminal normal shock in mixed compression supersonic inlets.

AN IMPROVED MODEL FOR REDUCED-ORDER PHYSIOLOGICAL FLUID FLOWS

An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.

Numerical Simulation of the Inter-Equation Couplings in All-Speed Flows via the Method of Proper Closure Equations

In the classical finite-volume method, the governing partial differential equations are first integrated on a control volume to obtain balance equations containing integration point flux quantities. Profile assumptions are made afterwards to relate the integration point flux terms to nodal values, and to finally obtain the set of algebraic governing equations. To numerically model the pressure-velocity coupling on a colocated grid arrangement, two integration point velocity definitions have been traditionally employed to avoid non-physical oscillatory solutions. The method of proper closure equations (MPCE), already used to solve steady incompressible flows, advocates a procedure in which a single velocity concept is needed in the numerical solution of flow equations on colocated grids. In this article, the implementation of the MPCE in the numerical solution of unsteady and compressible flows is discussed. Numerical tests, including quasi one-dimensional flows at all speeds and the flow in a shock tube, show that the method successfully models the transient behavior as well as the compressibility effects and discontinuities in fluid flow problems.

B243 準一次元通路内を運動する知的粒子流の状態変化と情報伝達

Traffic, pedestrian and creature's flows etc. are seemed to be a crowd of intellectual particles. The crowd sometimes has been analyzed phenomenologically, statistically or kinematically. The features of the behavior of crowd depend on the many factors as personality, individual velocity, peculiar velocity, intelligence and educated level of the crowd, etc. In the present paper, a crowd of pedestrian was analyzed by using a direct simulation of molecular dynamics method. The interaction between the pedestrians was presented by Morse potential, which was selected by preliminary simulation. A quasi one-dimensional pedestrian flow was simulated to discuss the relation between the individual walking speed and the local density and the propagating information of the state of crowd. Consequently, the physics of the crowd motion was discussed in detail from the viewpoint of thermo-fluid dynamics.

압력비에 따른 박리 노즐 유동의 수치적 해석

Axisymmetric separated flows in a converging-diverging conical nozzle are investigated through numerical simulations for various pressure ratios. We employ AUSM scheme for spatial derivatives and Pulliam`s 2nd order subiteration time stepping scheme for implicit time integration. Numerical results indicate that the separated flow structures are very complex when compared to the simple quasi-one dimensional flow. Depending on the pressure ratio, the flow within the nozzle is either separated or non-separated. Various separated flow patterns with distinctive features are illustrated and discussed in detail.

BOUNDARY ELEMENT APPROACH TO TRANSIENT HEAT PIPE ANALYSIS

A transient heat pipe was modeled by a quasi steady state one-dimensional vapor flow and a transient two-dimensional wall and wick heat conduction. The assumption of quasi steady state vapor was based on the fact that the vapor dynamics have a much smaller timescale than the wall conduction. A boundary element method was proposed to solve the transient two-dimensional heat conduction problem. The vapor flow dynamics was solved by a numerical approach, including two iterative “estimate-correction” processes. Comparisons with previous experimented and numerical studies verified the model and the solution methods. This work provides an effective means of transient heat pipe analysis.

Shock waves in flow of an incompressible liquid in collapsing pipes: Application to large blood vessels

Flow of a liquid in collapsing pipes is of great interest for problems in the mechanics of blood circulation, since collapse can take place in many blood vessels. This effect forms the basis for a large number of diagnostic and therapeutic methods, and also for methods of investigating the system of blood circulation. Consequently the mechanics of collapsing pipes has been studied intensively of late [1], but the available studies are far from exhausting the theoretical or the applied aspects of the problem. This applies also to the study of discontinuous solutions such as shock waves which describe steep fronts of opening or narrowing of a blood vessel. The most studied phenomenon is unsteady flow caused by change in the external pressure [2]. There is an explanation in [3–6] of the effect on the process of formation of discontinuities in collapsing pipes due to such factors as friction on the wall, distributed lateral outflow, the presence of a stagnant zone in the flow, and viscoelasticity of the wall. The origin of some acoustic phenomena in the arteries is connected by some with the propagation of discontinuities; these phenomena include Korotkov sounds, used in the determination of the arterial pressure of blood [1, 7]. The present study considers quasione-dimensional flow of a viscous incompressible liquid in a collapsing pipe of finite length and made of a nonlinear viscoelastic material; there is a study of the conditions in which discontinuities arise in such systems, and an investigation of the structure of shock waves with allowance for the effect of the surrounding tissues.

Thermally induced low-frequency oscillations

This paper discusses nonlinear thermally induced oscillations in quasi-one dimensional flows in ducts. In practice such oscillations are frequently observed in furnaces and combustion chambers. The problem considered involves entropy disturbances which are convected through a nozzle at the end of a tube, thereby producing an acoustic wave which propagates upstream and leads to a modulation of the mass flow at the inlet of the tube. Alternatively, if the rate of heat addition (i. e. the rate of fuel addition in the case of a combustion chamber) responds only weakly or not at all to the oscillating pressure at the inlet, the modulated air flow produces an entropy oscillation (due to the oscillating equivalence ratio in the case of a combustor) downstream of the zone of heat addition (reaction zone). To obtain general stability limits for this kind of self-induced oscillation, a second-order analysis is developed which leads to a nonlinear wave equation. The convection of entropy disturbances introduces nonlinear memory effects which are responsible for a non-local character of the wave equation. The wave equation is solved with the help of a numerical evolution scheme, making use of a suitable scaling transformation which does not change the form of the equation.

Averaging transfer equations in porous media with random inhomogeneities

The inhomogeneity of real porous structures and the consequent inhomogeneity of the velocity field of the fluid or gas are the reasons for the dispersion of fluid masses during transfer in porous media. This dispersion has a considerable influence on the quantitative and qualitative characteristics of many processes in oil extraction. The author consider the transfer of an admixture by a quasione-dimensional flow of constant mean velocity, the fluctuation of which is a statistically homogeneous random field.

An experimental study on shock-induced combustion of hydrogen

An experimental study on the shock-induced combustion of hydrogen was made by stabilizing flame behind the normal shock wave of a Mach reflected shock pattern, generated in a high temperature airstream of Mach number 1.91. The stagnation temperature was varied from 1000 to 1400°K to find its effects on the shock configurations and the flame induction length. It was found that the exothermic chemical reaction behind the normal shock wave causes it to increase in size and to move upstream. The flow expansion behind the normal shock wave has quenched downstream portion of the induced flame, but a quasi one-dimensional reactive flow calculation has revealed that effect of the expansion on the induction length is not so important as compared to that of chemical kinetics.

On the application of boundary conditions to time dependent computations for quasi one-dimensional fluid flows

Abstract A study is made of the influence of boundary and initial conditions on time-dependent finite-difference solutions of quasi-one-dimensional duct flows. Several questions are addressed: (1) Under what conditions will a time-dependent solution converge to a steady-state supersonic flow, (2) Under what conditions will it converge to subsonic flow and (3) What conditions are necessary to insure a particular unique solution for subsonic flows. The results provide an orientation, or way of thinking, about the role of such conditions in time-dependent solutions of steady-state flows. The results also show that supersonic solutions are readily obtained by holding only pressure and temperature fixed at the duct inlet, and allowing velocity to float. However, subsonic solutions require pressure, temperature and velocity to be fixed at both the duct inlet and exit. If no conditions are held fixed at the exit, the results always converge to the supersonic solution, even if the fixed inlet mass flow is less than critical. In such a case, the program appears to generate additional mass flow between the inlet and throat, sufficient to choke the flow. These results also have some impact on two- and three-dimensional time-dependent solutions where subsonic flow is present on some or all portions of the flow boundaries.

Nonequilibrium Nozzle Expansions of Carbon Dioxide from a High-Enthalpy Reservoir

NUMERICAL study is presented of nonequilibrium nozzle expansions of carbon dioxide from a reservoir at high specific enthalpy /z0 ranging from 3 to 85 x 1010 cm2 sec2. TThe effect of uncertainties in the relevant reaction rates and of assumptions made about the vibrational energy of the molecular components' is examined. The results show that the gas composition at large area ratios does not separately depend on reservoir pressure and temperature, but depends only on reservoir specific entropy. Contents The nozzle flow problem consists of the solution of the conservation equations for mass, momentum and energy in conjunction with an equation specifying the equilibrium condition of the gas and the reaction rate equations, the boundary streamline being defined by the nozzle shape. With the assumption of quasi-onedimensional flow the problem is reduced to a set of ordinary differential equations with the nozzle cross-sectional area A as an input. A conical nozzle with 7.5° semiangle is considered. An inviscid, thermally and electrically nonconducting gas is considered, consisting of the species, C, O, CO2, CO, O2, CO+, O + , C+ and electrons, in proportions such that the mixture may be totally recombined to CO 2. A conventional equilibrium gas

Construction of approximate solutions to two-dimensional potential problems of electrohydrodynamics

After transformation to new variables the system of equations describing planar potential electrohydrodynamic flows with a small interaction parameter is converted to a single equation. The particular solution of this equation, which is the electrohydrodynamic analog of Hamel's solution in the dynamics of a viscous liquid, is found. Two types of flows, described by simplified equations, can be distinguished when certain constraints are imposed on the manner in which the electrical parameters vary along the coordinate lines and the terms of the equation correspondingly estimated. These flows are the jet and quasione-dimensional flows of the charged component in a curvilinear electrostatic field and a supper-posed two-dimensional potential flow of the carrier medium. Solutions to the approximate equations are obtained for certain particular cases.

On radial flow of a conducting gas in crossed fields

An earlier treatment of quasi-onedimensional flow of a conducting gas in crossed fields (Q.A.M., 19, 177 (1961)) is extended to radial flow with azimuthal magnetic field. The usual simplifying assumptions are made, including constant specific heats; and different flow situations are illustrated by means of phase diagrams (drawn for γ = 1.33 \gamma = 1.33 ). One of the differences between radial flow ( E E = const.) and that in exponentially diverging channels ( E / B E/B = const.) is the possibility of a smooth transition from supersonic to subsonic motion that seems to exist for a certain range of strongly divergent radial channels.