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1.
A modified second order viscoelastic constitutive equation is used to derive a k–l type turbulence closure to qualitatively assess the effects of elastic stresses on fully-developed channel flow. Specifically,
the second order correction to the Newtonian constitutive equation gives rise to a new term in the momentum equation involving
the time-averaged elastic shear stress and in the turbulent kinetic energy transport equation quantifying the interaction
between the fluctuating elastic stress and rate of strain tensors, denoted by P
w
, for which a closure is developed and tested. This closure is based on arguments of isotropic turbulence and equilibrium
in boundary layer flows and a priori P
w
could be either positive or negative. When P
w
is positive, it acts to reduce the production of turbulent kinetic energy and the turbulence model predictions qualitatively
agree with direct numerical simulation (DNS) results obtained for more realistic viscoelastic fluid models with memory which
exhibit drag reduction. In contrast, P
w
< 0 leads to a drag increase and numerical breakdown of the model occurs at very low values of the Deborah number, which
signifies the ratio of elastic to viscous stresses. Limitations of the turbulence model primarily stem from the inadequacy
of the k–l formulation rather than from the closure for P
w
. An alternative closure for P
w
, mimicking the viscoelastic stress work predicted by DNS using the Finitely Extensible Nonlinear Elastic-Peterlin fluid model,
which is mostly characterized by P
w
> 0 but has also a small region of negative P
w
in the buffer layer, was also successfully tested. This second model for P
w
leads to predictions of drag reduction, in spite of the enhancement of turbulence production very close to the wall, but
the equilibrium conditions in the inertial sub-layer were not strictly maintained. 相似文献
2.
The flow initiated by a hot gas cloud (thermal) in a stratified atmosphere is calculated on the basis of theκ-ε turbulence model and the transport model for the Reynolds stresses and turbulent fluxes and the results obtained are compared
The nonlocal nature of the turbulent transport in a vortex ring and its effect on certain flow characteristics are explained
In particular, the calculations carried out using the Reynolds stress model show much slower cooling of the temperature-vortex
torus than those based calculated on theκ-ε-model Modification of theκ-ε-model to take the effect of curvature of the streamlines approximately into account makes it only partially possible to reproduce
the results obtained on the basis of the Reynolds stress model
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–20, January–February,
1999.
The research was carried out with support from the Russian Foundation for Basic Research (project No. 95-01-00544a). 相似文献
3.
Philip Schaefer Markus Gampert Jens Henrik Goebbert Lipo Wang Norbert Peters 《Flow, Turbulence and Combustion》2010,85(2):225-243
Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Re
λ
between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)3. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then
obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation
ε in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other.
The high Reynolds number version of the k-ε-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is
found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does.
In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles
of the kinetic energy k and the dissipation ε. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138,
2008), is used to examine the Menter–Egorov ε model equation. An expression for the evolution of ε is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the
length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which
with increasing Reynolds number approach the empirical values. 相似文献
4.
In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann equation based on the minimization
problem for the entropy under moments constraints (Levermore in J. Stat. Phys. 83:1021–1065, 1996; Schneider in M2AN 38:541–561,
2004). In particular the moment constraints and corresponding coefficients are linked with the eigenfunctions and eigenvalues
of the linearized collision operator through the Chapman–Enskog expansion. Then we deduce from this expansion a single relaxation term of BGK type. Here we stop the moments constraints at order two in the velocity v and recover the ellipsoidal statistical model (Holway in Rarefied Gas Dynamics, vol I, pp 193–215, 1966).
相似文献
5.
R. A. W. M. Henkes 《Applied Scientific Research》1996,57(1):43-65
With a single numerical method the performance of three classes of turbulence models is compared for different types of attached
boundary layers, for which direct numerical simulations or experiments are available in the literature. The boundary-layer
equations are solved with the following turbulence models: an algebraic model, two-equation models (k-ε andk-ω), and a differential Reynolds-stress model. The test cases are the channel flow, and boundary layers with zero, favourable
and adverse streamwise pressure gradient. The differential Reynolds-stress model gives the best overall performance, whereas
the performance of the algebraic model and thek-ω model is reasonably good. The performance of thek-ε model is less good for boundary layers with a non-zero streamwise pressure gradient, but it can easily be improved by an
additional source term in the ε equation, which is also applied in the considered differential Reynolds-stress model. 相似文献
6.
Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and
improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction
was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of
the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds
number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as
follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles
increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates
of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the
bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate
experimental data are required for quantitative validation of the ε equation. 相似文献
7.
A. Marshall P. Venkateswaran D. Noble J. Seitzman T. Lieuwen 《Experiments in fluids》2011,51(3):611-620
Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U
0 ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be
varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness
exhibit complex and not yet fully understood dependencies upon both U
0 and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high
gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly.
This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion
studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200)
over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely,
without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca
(Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge
on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters
using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This
paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length
scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio. 相似文献
8.
The paper reports on the application of the Time-dependent Reynolds-Averaged Navier–Stokes (T-RANS) approach to analysing
the effects of magnetic force and bottom-wall configuration on the reorganisation of a large coherent structure and its role
in the transport processes in Rayleigh–Bénard convection. The large-scale deterministic motion is fully resolved in time and
space, whereas the unresolved stochastic motion is modelled by a `subscale' model for which the conventional algebraic stress/flux
expressions were used, closed with the low-Re number (k)-(ε)-(θ2) three-equation model. The applied method reproduces long-term averaged mean flow properties, turbulence second moments,
and all major features of the coherent roll/cell structure in classic Rayleigh–Bénard convection in excellent agreement with
the available DNS and experimental results. Application of the T-RANS approach to Rayleigh–Bénard convection with wavy bottom
walls and a superimposed magnetic field yielded the expected effects on there organisation of the eddy structure and consequent
modifications of the mean and turbulence parameters and wall heat transfer.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
V. K. Golubev V. A. Medvedkin 《Journal of Applied Mechanics and Technical Physics》2000,41(3):416-420
The dependence of the detonation velocity of aNIL-1 low-density sheet explosive on density is found in the range of charge densities0.1–0.3 g/cm
3. The equation of state of theNIL-1 detonation products with a linear dependence of the effective isentropic exponent of unloading on the density of an explosive
that is acceptable for applied calculations is proposed. Calculated estimates of the mechanical action of anNIL-1 explosion on obstacles from several powerful explosive compositions are given.
Institute of Experimental Physics, Sarov 607190. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No.
3, pp. 43–47, May–June, 2000. 相似文献
10.
We consider a mixed boundary-value problem for a Poisson equation in a plane two-level junction Ωε that is the union of a domain Ω0 and a large number 3N of thin rods with thickness of order
. The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The homogeneous Dirichlet conditions and inhomogeneous Neumann conditions are given on the sides
of the thin rods from the first level and the second level, respectively. Using the method of matched asymptotic expansions
and special junction-layer solutions, we construct an asymptotic approximation for the solution and prove the corresponding
estimates in the Sobolev space H
1(Ωε) as ε → 0 (N → +∞).
Published in Neliniini Kolyvannya, Vol. 9, No. 3, pp. 336–355, July–September, 2006. 相似文献
11.
Large-eddy simulation of a turbulent reactive jet with and without evaporating droplets is performed to investigate the interactions
among turbulence, combustion, heat transfer and evaporation. A hybrid Eulerian–Lagrangian approach is used for the gas–liquid
flow system. Arrhenius-type finite-rate chemistry is employed for the chemical reaction. To capture the highly local interactions,
dynamic procedures are used for all the subgrid-scale models, except that the filtered reaction rate is modelled by a scale
similarity model. Various representative cases with different initial droplet sizes (St
0) and mass loading ratios (MLR) have been simulated, along with a case without droplets. It is found that compared with the bigger, slow responding droplets
(St
0 = 16), smaller droplets (St
0 = 1) are more efficient in suppressing combustion due to their preferential concentration in the reaction zones. The peak
temperature and intensity of temperature fluctuations are found to be reduced in all the droplet cases, to a varying extent
depending on the droplet properties. Detailed analysis on the contributions of respective terms in a transport equation for
grid-scale kinetic energy (GSKE) shows that the droplet evaporation effect on GSKE is small, while the droplet momentum effect
depends on St
0. When the MLR is sufficiently high, the bigger (St
0 = 16) droplets can have profound influence on GSKE, and consequently on the formation and evolution of large-scale flow structures.
On the other hand, the turbulence level is found to be lower in the droplet cases than in the pure flame case, due to the
dissipative droplet dynamic effect. 相似文献
12.
Towards better uncertainty estimates for turbulence statistics 总被引:1,自引:0,他引:1
Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which
occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general
distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent
triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”,
are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be
presented with statistical uncertainty error bars on all turbulence quantities.
Received: 11 December 1995 / Accepted: 12 April 1996 相似文献
13.
A. P. Kuryachii 《Fluid Dynamics》1998,33(1):48-55
The results of calculating a supersonic turbulent boundary layer on a heated surface on the basis of the algebraic two-parameter
(k-ε) and four-parameter (k-ε-θ
2-ε
6) models of turbulence are compared with experimental data. Emphasis is placed on the ability of the models to predict the
behavior of the friction and heat-transfer coefficients on a heated surface. The optimal model of turbulence is chosen. The
possibility of improving the efficiency of viscous drag reduction by localizing the regions of heat addition to the boundary
layer is demonstrated on the basis of numerical calculations.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–68, January–February,
1998.
This research was carried out with financial support from the International Scientific and Technological Center (project No.
199). 相似文献
14.
Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density
ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible
flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth
scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant
jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume
base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation
frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different
density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport
equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The
roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent
jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5%
level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like
behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws,
characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and
good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional
to x
−1/3 in the plume-like region consistent with the experimental observation, but is different from the x
−1 law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field
strongly depend upon the ratio of the ambient density to plume density ρa/ρ0. The increase of ρa/ρ0 under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase
in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed
and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased
with the increase of ρa/ρ0.
Received 16 June 2000 and accepted 26 June 2001 相似文献
15.
C.G. Speziale 《Theoretical and Computational Fluid Dynamics》1999,13(3):161-166
A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated
to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent
flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow
– the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear
K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero
when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it
too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics
in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are
also discussed.
Received 19 February 1998 and accepted 23 October 1998 相似文献
16.
A. P. Kuryachii 《Fluid Dynamics》1998,33(6):876-881
A solution of the coupled nonstationary boundary-value problem of turbulent flow around a flat heat-conducting plate of finite
thickness having local regions with volume heat sources is given. For modeling the heat transfer in the boundary layer, thek-ε turbulence model is used. It is shown that the thermal conductivity of the plate material significantly affects the surface
distributions of both temperature and local friction.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–86, November–December,
1998.
The work received financial support from the International Scientific and Engineering Center (project No.199). 相似文献
17.
We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω ɛ that is the union of a domain Ω0 and a large number 2N of thin rods with thickness of order ɛ =
(N
−1). Depending on their lengths, the thin rods are divided into two levels. In addition, the rods from each level are ɛ-periodically
alternated. Inhomogeneous Neumann boundary conditions are given on the vertical sides of the thin rods of the first level,
and homogeneous Dirichlet boundary conditions are given on the vertical sides of the rods of the second level. We investigate
the asymptotic behavior of a solution of this problem as ɛ → 0 and prove a convergence theorem and the convergence of the
energy integral.
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 241–257, April–June, 2005. 相似文献
18.
V. V. Aristov 《Fluid Dynamics》1998,33(2):280-283
Free supersonic underexpanded jets are studied using a direct method conservative splitting scheme for solving the Boltzmann
equation. Numerical solutions for a jet flowing into a vacuum and into a fluid-filled space are presented for the following
ranges of the parameters: Knudsen number 10−6<Kn<∞ and pressure ratio 10<n<∞. The solutions are compared with experimental data. Instabilities associated with free turbulence effects in the mixing
layer are detected for low Kn numbers.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–157, March–April, 1998.
The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-00829). 相似文献
19.
C. Tunç 《Nonlinear Oscillations》2006,9(4):536-551
We consider the equation X
(4) + Φ(X″)X‴ + F(X,X′)X″ + G(X′) + H(X) = P(t,X,X′,X″,X‴) in two cases: P ≡ 0 and P ≠ 0. In the case P ≡ 0, the asymptotic stability of the zero solution X = 0 of the equation is investigated; in the case P ≠ 0, the boundedness of all solutions of the equation is proved.
Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 548–563, October–December, 2006. 相似文献
20.
A physicochemical and fluid dynamic model is formulated for the numerical simulation of the flow field in a reactor for titanium
dioxide production, the turbulence motion is described by theKε equation, the governing equations are solved by the SIMPLER algorithm devised by Partankar and Spalding. The velocity, tmperature
and concentration fields are obtained for three cases: A) with chemical reaction and thermal insulation on the walls; B) with
chemical reaction and wall temperature is 450K; C) without chemical reaction and thermal insulation on the walls, and the
physicochemical numerical simulation for the titanium dioxide production has been done. The results of the paper can be used
as a theoretical guide for the engineers in the design of such reactors. 相似文献