Open-channel flow near the critical depth

Summary The stationary surface waves in a quasi-uniform flow approaching the critical conditions are shown to be possible only around a basic normal depth greater than critical.The demonstration is based on the second order equation of steady two-dimensional flow (cnoidal waves equation).     

Open-channel turbulent flow over non-uniform gravel beds

the measurements of flow over non-uniform gravel open channel have been conducted with Laser Doppler Velocimetry (LDV). The experimental results indicate that the distribution of mean velocity agrees well with the Nikuradse's law. From the distributions of resistance coefficient, reference level and turbulence intensity, the classification of small scale roughness case is obtained.Project supported by the National Science Foundation of China     

Developing flows and developed flows

This paper puts emphasis on the problem of the developing flows in the circular tube under oscillatory conditions. According to the Navier-Stokes' equations and using the method of Bessel function of imaginary argument, a system of formulas is obtained. Comparing the formulas obtained in this paper with Atabek's formulas, it may be seen that the former is simpler and more convenient. When both the formulas obtained in this paper and Atabek's formulas are reduced to the representation of developed flows, both of them are consistent. Numerical calculation results show that the computed results obtained in this paper are rather consistent with both Atabek's computed results and the experimental results.     

Open-channel waves generated by propagation of a discontinuous wave over a bottom step

This paper presents the results of theoretical and experimental studies of open-channel waves generated by the propagation of a discontinuous dam-break wave over a bottom step. The cases where the initial tailwater level is higher than the step height (the step is under water) and where this value is smaller than the step height (at the initial time, water is absent on the step) are considered. Exact solutions are constructed using modified first-approximation equations of shallow-water theory, which admit the propagation of discontinuous waves in a dry channel. On the stationary hydraulic jump formed above the bottom step, the total free-stream energy is assumed to be conserved. These solutions agree with experimental data on various parameters (types of waves, wave propagation velocity, asymptotic depths behind the wave fronts). __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 31–44, January–February, 2008.     

The upward flow of air betweem two waterfalls: An unusual choked flow problem

An experimental and theoretical investigation of the effect of air rising between two opposed waterfalls is presented. It is found experimentally that as the air flow is increased, the waterfalls are drawn more closely together until a critical air flow rate is reached at which the waterfalls collapse together. A theoretical analysis of this phenomenon is presented and the collapse condition is shown to be analogous to the choked flow of air through a nozzle the cross-sectional area of which is strongly pressure dependent. This dependency results in a very low effective “sonic” velocity and “choked” flow and the theoretical predictions are in reasonable agreement with the experiment results. The relevance of this work to the PWR refill problem is discussed.     

Some kinematical results concerning steady flows and extensional flows

Dedicated to Professor Bernard D. Coleman on his Sixtieth Birthday     

On pressure and thermal flux in gas-mixture flows and in two-phase flows

To begin with, two different definitions of pressure, thermal flux, etc. in the diffusion model and two-fluid model are given. Then the physical interpretations of the pressure and the thermal flux are provided by introducing the momentum and energy fluxes,M and ε, through a surface dS in the flow field. The quantities defined in the diffusion model are suggested when the motion of the mixture is studied as a whole, while the quantities defined in the two-fluid model are suggested when the motion of individual species is studied. The collision pressure and thermal flux in dense gas-mixtures are also discussed in detail, i.e. their origin, their expressions in the momentum and energy equations, and their distinctions from the normal partial pressure and thermal flux. A gas-particle flow can be treated as a flow of dense gas-mixtures. The long-standing controversy whether the “inertial coupling term” should exist in the momentum equation can be clarified by the two different definitions of pressure.     

Droplet-based flows in serpentine microchannels: Chemical reactions and secondary flows

Mixing is an essential operation in many microfluidic devices. Droplet-based micromixers utilize droplets for mixing enhancement. In the present study, a novel three-dimensional simulation is conducted which has the ability to capture not only the mixing process, but also the chemical reactions inside liquid droplets. This two-phase model is used for simulating the reacting flow inside a serpentine microchannel and explores the effects of droplet size and reaction rate on the production and consumption of species in droplets. It is observed that the chemical reaction in each droplet, begins from its front area. Furthermore, it is shown that the production of species does not depend on water fraction (ratio of water flow rate to total flow rate) and for all droplet sizes, only depends on the reaction rate. Moreover, different transient generated vortices and secondary flows are studied in the presence and absence of droplets and explained in details based on the position of droplets. It is found that during the passage of droplets through a microchannel bend, the number of cross-sectional vortices changes and the velocity magnitude in these secondary flows increases dramatically.     

On the surface equations in two-phase flows and reacting single-phase flows

This paper summarizes the mathematical surface equations which are useful in two-phase flows and single-phase reacting flows. The connection between the interfacial area concentration transport equation for two-phase flows and the flame surface density transport equation for turbulent reacting flows is established. Several analytical examples are given to clarify the physical significance of the different quantities involved in the different transport equations. An introduction to the mathematical treatment of anisotropic interfaces is also given. This theory is illustrated on two different numerical examples: a single inclusion in a simple shear and a single inclusion in an uni-axial elongation.     

Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows

Constitutive relations for the lift force on the particulate phase and the effect of Brownian motion are presented. These constitutive relations are derived subject to three new principles of constitutive equations. The effects of lift and Brownian motion in basic parallel flows are considered in order to determine the importance and the consequences of these effects. The relation of the Brownian motion model involving momentum balance to the diffusive model of particle motions is studied. Dimensional and scaling arguments are given.     

Swirled flows and their generalizations

New swirled flows (flows in channels, flows around bodies of revolution, and flows with a sink or source on the axis of symmetry) are studied. Group solutions constructed from a supergroup, which are generalizations of conical flows, are considered.     

On the obtaining of axisymmetric flows from plane-parallel flows

The obtaining of axisymmetric flows of incompressible and compressible fluids from plane-parallel flows by means of integral transformations relating harmonic and p-harmonic functions [1] is considered. A transformation is found that carries plane-parallel flows from elementary singularities into axisymmetric flows. It is shown that this transformation makes it possible to obtain the general form of the solution of axisymmetric problems of flow past bodies from the solution of plane-parallel problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 113–121, September–October, 1982.     

Transition of nonone-dimensional flows produced by explosions into one-dimensional flows

A particular class of flows resulting from explosions is considered and two processes are analyzed, both independently and as coupled processes: the transition of the solution to the problem of nonpoint explosion to the corresponding point regime and the transition of the solution to the problem of an explosion with nonone-dimensional initial conditions to a corresponding one-dimensional solution (not necessarily a point solution).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 93–99, July–August, 1983.     

Turbulent separation flows

Turbulent separation flows arise when objects move in the oceans and in the atmosphere, and also when a liquid or gas flows past elements of the Earth's relief, technological and industrial plant, and constructional elements. Therefore, problems of turbulent separation flows cover the entire range of velocities of continuum motions and under such varied boundary conditions that the forms, properties, and manifestations of turbulent separation are inexhaustible. The aim of the present paper is to discuss the available results and the possibilities for further development of computational models of turbulent separation flows. The somewhat nominal classification of such models given in the paper reflects essentially the sequence of their historical development.Paper presented at Fifth All-Union Symposium on Theoretical and Applied Mechanics, Alma-Ata, 1981.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–47, March–April, 1982.     

Development and stability of swirling flows

The purpose of this research is to investigate steady axisymmetric swirling flows in channels and free vortices and also to establish the role of hydrodynamic instability in the formation of the sharp changes in flow structure associated with an increased rate of rotation. On the basis of numerical solutions of the complete Navier-Stokes equations obtained by a finite-difference method swirling flows in pipes with impermeable and permeable walls and in a free vortex are investigated. The stability of the swirling axisymmetric flows is considered on the assumption of local parallelism: the problem of the normal modes developing against the background of the axisymmetric flow determined by the velocity profiles in local cross sections of the flow is solved. Attention is mainly concentrated on free vortex flows with reverse current zones, their structure and stability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–11, July–August, 1988.     

Simulation of supersonic and hypersonic flows

A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.