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1.
Two-phase flows with interface modeled as a Boussinesq–Scriven surface fluid are analysed concerning their fundamental mathematical
properties. This extended form of the common sharp-interface model for two-phase flows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves
as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres
for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable,
but nonzero velocities may lead to problems which linearly are not well-posed. This phenomenon does not occur in absence of
surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase flows with surface viscosity. 相似文献
2.
Prediction of separation flows around a 6:1 prolate spheroid using RANS/LES hybrid approaches 总被引:2,自引:0,他引:2
Zhixiang Xiao Yufei Zhang Jingbo Huang Haixin Chen Song Fu 《Acta Mechanica Sinica》2007,23(4):369-382
This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated
flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the
detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the
SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation
of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode
for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid
methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme
with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel
with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried
out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting
for the effect on grids and fundamental turbulence models, is obtained for the separation flows.
The project supported by the National Natural Science Foundation of China (10502030 and 90505005). 相似文献
3.
N. M. Astaf’eva 《Fluid Dynamics》1998,33(1):61-70
A numerical analysis technique and its results for viscous incompressible flows in the annulus between two concentric coaxial
spheres generated by the rotation of the boundary spheres in the same or opposite directions are presented. It is shown that
in the course of its development, the main flow passes through three characteristic stages which differ significantly from
each other (qualitatively as well as quantitatively) with respect to meridional circulation and azimuthal flow. Depending
on the fluid layer thickness, different stages of main flow development may precede the loss of stability; this determines
the differences in the mechanisms of loss of stability of the main flow and in the nature of the secondary flows. The calculated
results are compared with the experimental data.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 75–86, January–February,
1998. 相似文献
4.
We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian). 相似文献
5.
The accurate prediction of turbulent swirling flows requires the use of a differential Reynolds-stress transport model to
close the time-averaged Navier–Stokes equations. The performance of such model is largely determined by the way in which the
fluctuating pressure–strain correlations are approximated. A number of alternative approximations are available, all of which
depend explicitly on the mean vorticity tensor. Such dependence renders a constitutive relation inconsistent with the principle
of Material Frame Indifference (MFI). In this paper, an objective model (i.e. one which is consistent with MFI) for the pressure–strain
correlations is presented. This model, which was developed using Tensor Representation Theory, has fewer terms than the conventional
alternatives and is therefore easier to implement in computational codes. Moreover, the model was calibrated to correctly
reproduce the relative stress levels in both free and wall-bounded flows without the need to employ wall-damping corrections.
The performance of this model is assessed using experimental data from both weakly- and strongly-swirled jets. Comparisons
are also made with results obtained using three widely-used alternative models for the pressure–strain correlations. It is
found that the objective model, although simpler in formulation than the others, yields results that are generally in closer
correspondence with the data. The paper also reports on the prediction of mass transfer in a swirling jet. The case considered
was that of a co-axial, strongly-swirled flow with an outer annular air stream and an inner helium jet. Swirl was imparted
to the outer stream only. The concentration of helium was predicted using a differential scalar-flux transport closure. Close
agreement was obtained with the measured concentrations. Analysis of the predicted mass fluxes revealed that the turbulent
diffusivity is strongly anisotropic in this flow. 相似文献
6.
A. A. Chensokov 《Journal of Applied Mechanics and Technical Physics》1998,39(4):513-523
Quasi-linear integrodifferential equations that describe vortex flows of an ideal incomparessible liquid in a narrow curved
channel in the Eulerian-Lagrangian coordinate system are considered. The necessary and sufficient conditions for hyperbolicity
of the system of equations of motion are obtained for flows with a monotonic velocity depth profile. The propagation velocities
of the characteristics and the characteristic form of the system are calculated. A particular solution is given in which the
system of integrodifferential equations changes type with time. The solution of the Cauchy problem is given for linearized
equations. An example of initial data for which the Cauchy problem is ill-posed is constructed.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39,
No. 4, pp. 38–49, July–August, 1998. 相似文献
7.
M. I. Muchnaya 《Fluid Dynamics》1986,21(6):860-866
Simplified Navier-Stokes equations have found application as an alternative to the complete Navier-Stokes equations for the
simulation of viscous gas flows in regions of large dimensions, when there is a predominant direction of the flow [1–4]. In
the present paper, flows in wind tunnel nozzles are investigated on the basis of this model. Flows in conical and profiled
axisymmetric hypersonic nozzles are calculated in a wide range of Mach and Reynolds numbers. Good agreement with the experiment
is obtained. The important role of viscous-inviscid interaction in nozzles for large hypersonic Mach numbers is shown.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–26, November–December, 1986.
The representation of the nature of flows in hypersonic nozzles given here arose as a result of repeated discussions of the
results of the calculations with my colleagues: V. N. Vetlutskii, V. L. Ganimedov, G. P. Klemenkov, Yu. G. Korobeinikov, and
V. I. Pinchukov, for which the author is deeply grateful to them. 相似文献
8.
F. Gallaire D. Gérard-Varet F. Rousset 《Archive for Rational Mechanics and Analysis》2007,186(3):423-475
We study the stability of two-dimensional solutions of the three-dimensional Navier–Stokes equations, in the limit of small
viscosity. We are interested in steady flows with locally closed streamlines. We consider the so-called elliptic and centrifugal
instabilities, which correspond to the continuous spectrum of the underlying linearized Euler operator. Through the justification
of highly oscillating Wentzel–Kramers–Brillouin expansions, we prove the nonlinear instability of such flows. The main difficulty
is the control of nonoscillating and nonlocal perturbations issued from quadratic interactions. 相似文献
9.
A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of
a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows
in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The
resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations
between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient
and external electric field, and the coefficients in this linear relation are calculated with the use of microequations.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008. 相似文献
10.
M. S. Kotel’nikova B. A. Lugovtsov 《Journal of Applied Mechanics and Technical Physics》2007,48(3):331-339
The region of instability of the Hill-Shafranov viscous MHD vortex with respect to azimuthal axisymmetric perturbations of
the velocity field is determined numerically as a function of the Reynolds number and magnetization in a linear formulation.
An approximate formulation of the linear stability problem for MHD flows with circular streamlines is considered. The further
evolution of the perturbations in the supercritical region is studied using a nonlinear analog model (a simplified initial
system of equations that takes into account some important properties of the basic equations). For this model, the secondary
flows resulting from the instability are determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 40–50, May–June, 2007. 相似文献
11.
A. Yu. Kazakov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):235-242
This paper studies the problem of pairs of horizontal shear flows of weakly stratified fluids with identical mass, momentum,
and energy fluxes. The initial problem is reduced to a system of two scalar equations for the main- and perturbed-flow parameters
by using bifurcation methods. The existence conditions for nontrivial branches of conjugate flows close to the main flow are
investigated.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 79–88, March–April, 2009. 相似文献
12.
S. N. Aristov 《Fluid Dynamics》1998,33(6):929-932
New exact solutions of the Navier-Stokes equations are obtained for steady-state three-dimensional conical flows. In this
class of flows the velocity decreases in inverse proportion to the distance from the source and the input equations reduce
to two-dimensional ones. It is shown that in the spherical coordinate system the equations of motion reduce to a single nonlinear
equation with respect to a scalar function which depends on the polar angles. The case in which this equation reduces to the
integrable Liouville equation is discussed. This makes it possible to obtain a wide class of three-dimensional solutions in
analytic form.
Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 144–148, November–December,
1998.
The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00063). 相似文献
13.
14.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2006,47(6):800-811
The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal
fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant
vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations
resulting from the nonlinear interaction of the specified shear flows is established.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006. 相似文献
15.
The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than
the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been
proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work
of Parmar et al. (Phil Trans R Soc A 366:2161–2175, 2008). Comparisons with experimental and computational data for both stationary
spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration
of the unsteady force.
相似文献
16.
We develop new comparison principles for viscosity solutions of Hamilton–Jacobi equations associated with controlled gradient
flows in function spaces as well as the space of probability measures. Our examples are optimal control of Ginzburg–Landau
and Fokker–Planck equations. They arise in limit considerations of externally forced non-equilibrium statistical mechanics
models, or through the large deviation principle for interacting particle systems. Our approach is based on two key ingredients:
an appropriate choice of geometric structure defining the gradient flow, and a free energy inequality resulting from such
gradient flow structure. The approach allows us to handle Hamiltonians with singular state dependency in the nonlinear term,
as well as Hamiltonians with a state space which does not satisfy the Radon–Nikodym property. In the case where the state
space is a Hilbert space, the method simplifies existing theories by avoiding the perturbed optimization principle. 相似文献
17.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(1):12-23
An approximate system of equations that describe unsteady flow of an inviscid non-heat-conducting gas in a narrow channel
of varying area is derived. Generalized characteristics and hyperbolicity conditions are obtained for this system of equations.
In connection with characteristics theory, the average Mach number and the flow criticality condition are introduced. Exact
solutions that describe steady transonic channel flows are investigated.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 15–27, January–February, 1998. 相似文献
18.
Supersonic flows near flying vehicle elements are calculated in the approximation of the full Navier-Stokes equations for
a viscous compressible heat-conducting gas with different values of free-stream. Mach and Reynolds numbers and angles of attack.
The main laws of the flow near the lifting surface. and in the inlet are obtained.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 98–108, March–April, 2009. 相似文献
19.
P. K. Volkov 《Fluid Dynamics》1994,29(4):500-507
The steady rise of a vapor bubble in a liquid moving in a vertical tube is modeled by means of the Navier-Stokes equations.
The shape of the vapor bubble (drop) and the structure of the flow are determined by numerically solving the equations inside
and outside the drop. The calculations are made on the interval of intermediate values of the dimensionless parameters and
describe the transition to piston-type motion. The solutions obtained are compared with the existing experimental and approximate
data for creeping flows.
Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 76–86, July–August,
1994. 相似文献
20.
Bert Vreman Bernard J. Geurts N. G. Deen J. A. M. Kuipers J. G. M. Kuerten 《Flow, Turbulence and Combustion》2009,82(1):47-71
Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed.
The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as
encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of
modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes
equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation
of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions
are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles
on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened
and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas
phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent
with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which
the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have
a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent
particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase
flow with volume fractions around one percent. 相似文献