Showing papers on "Turbulence published in 1992"

Development of turbulence models for shear flows by a double expansion technique

Abstract: Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK/■) is the ratio of the turbulent to mean strain time scale. While low‐order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two‐equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

The Atmospheric Boundary Layer

Abstract: 1. The atmospheric boundary layer 2. Basic equations for mean and fluctuating quantites 3. Scaling laws for mean and turbulent quantites 4. Surface roughness and local advection 5. Energy fluxes at the land surface 6. The thermally stratified ABL 7. The cloud topped boundary layer 8. ABL modelling and parameterisation schemes 9. The impact of the ABL on climate.

Improved two-equation k-omega turbulence models for aerodynamic flows

Abstract: Two new versions of the k-omega two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k-omega model of Wilcox, but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner 50 percent of the boundary-layer but changes gradually to the high Reynolds number Jones-Launder k-epsilon model (in a k-omega formulation) towards the boundary-layer edge. The new model is also virtually identical to the Jones-Lauder model for free shear layers. The second version of the model is called Shear-Stress Transport (SST) model. It is based on the BSL model, but has the additional ability to account for the transport of the principal shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear stress is proportional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different flowfields. The results of the BSL model are similar to those of the original k-omega model, but without the undesirable freestream dependency. The predictions of the SST model are also independent of the freestream values and show excellent agreement with experimental data for adverse pressure gradient boundary-layer flows.

Turbulence - The filtering approach

Abstract: The paper describes a new operatorial approach to the study of turbulence, based on the general algebraic properties of the filtered representations of a turbulence field at different levels. The main results of this analysis is the averaging invariance of the filtered Navier-Stokes eaquations in terms of the generalized central moments, and an algebraic identity that relates the turbulent stresses at different levels. The resolved turbulence is defined, the algebraic consistency rules that relate these resolved quantities to the turbulent stresses at different levels are derived, and their possible uses in subgrid modeling is discussed.

Three‐dimensional optimal perturbations in viscous shear flow

Abstract: Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three‐dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.

New insights into large eddy simulation

Abstract: Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

Dispersion and Deposition of Spherical Particles from Point Sources in a Turbulent Channel Flow

Abstract: The dispersion and deposition of particles from a point source in a turbulent channel flow are studied. An empirical mean velocity profile and the experimental data for turbulent intensities are used in the analysis. The instantaneous turbulence fluctuation is simulated as a continuous Gaussian random field, and an ensemble of particle trajectories is generated and statistically analyzed. A series of digital simulations for dispersion and deposition of aerosol particles of various sizes from point sources at different positions from the wall is performed. Effects of Brownian diffusion on particle dispersion are studied. The effects of variation in particle density and particle-surface interaction are also discussed.

Toward the large-eddy simulation of compressible turbulent flows

Abstract: New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 (exp 3) grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence (conducted on a coarse 32(exp 3) grid) is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

Stochastic backscatter in large-eddy simulations of boundary layers

Abstract: The ability of a large-eddy simulation to represent the large-scale motions in the interior of a turbulent flow is well established. However, concerns remain for the behaviour close to rigid surfaces where, with the exception of low-Reynolds-number flows, the large-eddy description must be matched to some description of the flow in which all except the larger-scale ‘inactive’ motions are averaged. The performance of large-eddy simulations in this near-surface region is investigated and it is pointed out that in previous simulations the mean velocity profile in the matching region has not had a logarithmic form. A number of new simulations are conducted with the Smagorinsky (1963) subgrid model. These also show departures from the logarithmic profile and suggest that it may not be possible to eliminate the error by adjustments of the subgrid lengthscale. An obvious defect of the Smagorinsky model is its failure to represent stochastic subgrid stress variations. It is shown that inclusion of these variations leads to a marked improvement in the near-wall flow simulation. The constant of proportionality between the magnitude of the fluctuations in stress and the Smagorinsky stresses has been empirically determined to give an accurate logarithmic flow profile. This value provides an energy backscatter rate slightly larger than the dissipation rate and equal to idealized theoretical predictions (Chasnov 1991).

Spectral large-eddy simulation of isotropic and stably stratified turbulence

Abstract: We first recall the concepts of spectral eddy viscosity and diffusivity, derived from the two-point closures of turbulence, in the framework of large-eddy simulations in Fourier space. The case of a spectrum which does not decrease as (Ck is Kolmogorov's constant), with α ≈ 1.32.

Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry

Abstract: An experimental study of damping and frequency of vibrating small cantilever beams in their lowest eigenstate is presented. The cantilever beams are fabricated from monocrystalline silicon by means of micromachining methods. Their size is a few millimeters in length, a few 100 µm in width, and a few 10 µm in thickness. Damping and resonance frequency are studied as a function of the ambient pressure p (1–105 Pa) and the geometry of the beam. The purpose of this research was to obtain design rules for sensors employing vibrating beams. The analysis of the experimental results in terms of a semiqualitative model reveals that one can distinguish three mechanisms for the pressure dependence of the damping: viscous, molecular, and intrinsic. For viscous damping a turbulent boundary layer dominates the damping at high pressures (105 Pa), while at smaller pressure laminar flow dominates. In the latter region, this leads to a plateau for the quality factor Q and in the former to Q p. The pressure pc at which the transition from laminar flow dominated damping to turbulent flow dominated damping occurs depends on the geometry of the beams. pc is independent on the length and decreases with both, the width and the thickness of the beams.

Comparison between rough- and smooth-wall turbulent boundary layers

Abstract: Measurements in a zero-pressure-gradient turbulent boundary layer over a mesh-screen rough wall indicate several differences, in both inner and outer regions, in comparison to a smooth-wall boundary layer. The mean velocity distribution indicates that, apart from the expected k-type roughness function shift in the inner region, the strength of the rough-wall outer region ‘wake’ is larger than on a smooth wall. Normalizing on the wall shear stress, there is a significant increase in the normal turbulence intensity and a moderate increase in the Reynolds shear stress over the rough wall. The longitudinal turbulence intensity distribution is essentially the same for both surfaces. Normalized contributions to the Reynolds shear stress from the second (Q2) and fourth (Q4) quadrants are greater over the rough wall. The data indicate that not only are Q2 and Q4 events stronger on the rough wall but their frequency of occurrence is nearly twice as large for the rough wall as for the smooth wall. Comparison between smooth- and rough-wall spectra of the normal velocity fluctuation suggests that the strength of the active motion may depend on the nature of the surface.

Suppression of turbulence in wall‐bounded flows by high‐frequency spanwise oscillations

Abstract: The response of wall‐flow turbulence to high‐frequency spanwise oscillations was investigated by direct numerical simulations of a planar channel flow subjected either to an oscillatory spanwise cross‐flow or to the spanwise oscillatory motion of a channel wall. Periods of oscillation, Tosc+=Toscuτ2/ν, ranging from 25 to 500 were studied. For 25≤Tosc+≤200 the turbulent bursting process was suppressed, leading to sustained reductions of 10% to 40% in the turbulent drag and comparable attenuations in all three components of turbulence intensities as well as the turbulent Reynolds shear stress. Oscillations at Tosc+=100 produced the most effective suppression of turbulence. The results were independent of whether the oscillations were generated by a cross‐flow or by the motion of a channel wall. In the latter case, suppression of turbulence was restricted to the oscillating wall while the flow at the other wall remained fully turbulent. Spanwise oscillations may provide a simple and effective method for control of turbulence in wall‐bounded flows.

Direct simulation of particle dispersion in a decaying isotropic turbulence

Abstract: Results of a numerical investigation of the dispersion of solid particles in decaying isotropic turbulence are presented. The 3D time-dependent velocity field of a homogeneous nonstationary turbulence is computed using the method of direct numerical simulation (DNS). The dispersion characteristics of three different solid particles (corn, copper, and glass) injected in the flow are obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 22-cubed particles for each particle type, and then by performing ensemble averaging. Good agreement was achieved between the present DNS results and the measured time development of the mean-square displacement of the particles. Questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics are also discussed.

Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct

Abstract: The mean flow and turbulent statistics obtained from the numerical simulation of the fully developed turbulent flow through a straight duct of square cross-section are reported. The Reynolds number based on the bulk velocity and hydraulic diameter is 4410. Spatial and temporal approximations of the equations of motion were derived from standard finite-difference techniques. To achieve sufficient spatial resolution 16.1 × 106 grid nodes were employed. Turbulent statistics along the wall bisectors show good agreement with plane channel data despite the influence of the sidewalls in the former flow. The mean secondary flow field consists of two counter-rotating cells symmetrically placed about the corner bisectors with their common flow towards each corner with strong evidence for the existence of a smaller and much weaker pair situated about the wall bisectors. The mean streamwise vorticity of each corner cell is found to be associated with a stronger vorticity distribution of the opposite sign having an absolute maximum on the nearest duct wall.

Large-eddy simulation of turbulent flow above and within a forest

Abstract: A large-eddy simulation has been performed of an atmospheric surface layer in which the lower third of the domain is occupied by a drag layer and heat sources to represent a forest. Subgridscale processes are treated using second-order closure techniques. Lateral boundaries are periodic, while the upper boundary is a frictionless fixed lid. Mean vertical profiles of wind velocity derived from the output are realistic in their shape and response to forest density. Similarly, vertical profiles of Reynolds stress, turbulent kinetic energy and velocity skewness match observations, at least in a qualitative sense. The limited vertical extent of the domain and the artificial upper boundary, however, cause some departures from measured turbulence profiles in real forests. Instantaneous turbulent velocity and scalar fields are presented which show some of the features obtained by tower instrumentation in the field and in wind tunnels, such as the vertical coherence of vertical velocity and the slope of structures revealed by temperature patterns.

Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow

Abstract: A direct numerical simulation (DNS) of the fully developed thermal field in a dimensional turbulent channel flow of air was carried out. The isoflux condition was imposed on the two walls so that the local mean temperature increased linearly in the streamwise direction. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained were root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and dissipation time scales. They agreed fairly well with existing experimental and numerical simulation data. Each term in the budget equations of temperature variance, its dissipation rate, and turbulent heat fluxes was also calculated. It was found that the temperature fluctuation [theta][prime] was closely correlated with the streamwise velocity fluctuation u[prime], particularly in the near-wall region. Hence, the distribution of budget terms for the streamwise and wall-normal heat fluxes, [bar u][prime][theta] and [bar v][prime][theta][prime], were very similar to those for the two Reynolds stress components, [bar u][prime]u[prime]and [bar u][prime]v[prime].

Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes

Abstract: The velocity field of homogeneous isotropic turbulence is simulated by a large number (38–1200) of random Fourier modes varying in space and time over a large number (> 100) of realizations. They are chosen so that the flow field has certain properties, namely (i) it satisfies continuity, (ii) the two-point Eulerian spatial spectra have a known form (e.g. the Kolmogorov inertial subrange), (iii) the time dependence is modelled by dividing the turbulence into large- and small-scales eddies, and by assuming that the large eddies advect the small eddies which also decorrelate as they are advected, (iv) the amplitudes of the large- and small-scale Fourier modes are each statistically independent and each Gaussian. The structure of the velocity field is found to be similar to that computed by direct numerical simulation with the same spectrum, although this simulation underestimates the lengths of tubes of intense vorticity.Some new results and concepts have been obtained using this kinematic simulation: (a) for the inertial subrange (which cannot yet be simulated by other means) the simulation confirms the form of the Eulerian frequency spectrum , where e,U0,ω are the rate of energy dissipation per unit mass, large-scale r.m.s. velocity, and frequency. For isotropic Gaussian large-scale turbulence at very high Reynolds number, CE ≈ 0.78, which is close to the computed value of 0.82; (b) for an observer moving with the large eddies the ‘Eulerian—Lagrangian’ spectrum is ϕEL11 = CELeω−2, where CEL ≈ 0.73; (c) for an observer moving with a fluid particle the Lagrangian spectrum ϕL11 = CLeω−2, where CL ≈ 0.8, a value consistent with the atmospheric turbulence measurements by Hanna (1981) and approximately equal to CEL; (d) the mean-square relative displacement of a pair of particles 〈Δ2〉 tends to the Richardson (1926) and Obukhov (1941) form 〈Δ2〉 = GΔet3, provided that the subrange extends over four decades in energy, and a suitable origin is chosen for the time t. The constant GΔ is computed and is equal to 0.1 (which is close to Tatarski's 1960 estimate of 0.06); (e) difference statistics (i.e. displacement from the initial trajectory) of single particles are also calculated. The exact result that Y2 = GYet3 with GY = 2πCL is approximately confirmed (although it requires an even larger inertial subrange than that for 〈Δ2〉). It is found that the ratio [Rscr ]G = 2〈Y2〉/〈Δ2〉≈ 100, whereas in previous estimates [Rscr ]G≈ 1, because for much of the time pairs of particles move together around vortical regions and only separate for the proportion of the time (of O(fc)) they spend in straining regions where streamlines diverge. It is estimated that [Rscr ]G ≈ O(fc−3). Thus relative diffusion is both a ‘structural’ (or ‘topological’) process as well as an intermittent inverse cascade process determined by increasing eddy scales as the particles separate; (f) statistics of large-scale turbulence are also computed, including the Lagrangian timescale, the pressure spectra and correlations, and these agree with predictions of Batchelor (1951), Hinzc (1975) and George et al. (1984).

Influence of freestream values on k-omega turbulence model predictions

Abstract: The Wilcox (1988, 1991) k-omega model for eddy-viscosity turbulence does not require damping functions in the viscous sublayer, and its equations are less stiff near the wall. It has been designed to predict the requisite wake length in equilibrium, adverse pressure-gradient boundary-layer flows. When applied to free shear layers, however, a strong dependency of its results on the freestream value of omega has been noted. This feature is presently investigated via the self-similar equations for incompressible equilibrium boundary layers.

Experimental investigation of the field of velocity gradients in turbulent flows

Abstract: We present results of experiments on a turbulent grid flow and a few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was done by a twelve-wire hot-wire probe (3 arrays × 4 wires), produced for this purpose using specially made equipment (micromanipulators and some other auxiliary special equipment), calibration unit and calibration procedure. The probe had no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results.Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor, the positiveness of the total enstrophy-generating term ωiωjsij (sij = ½(∂ui/∂xj+∂uj/∂xi), ωi = eijk∂uj/∂xk) even for rather short records and the tendency for alignment in the strict sense between vorticity and the vortex stretching vector Wi = ωjsij. An emphasis is put on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference (e.g. sijsij and ωiωjsij) as the most appropriate to describe physical processes. From the methodological point of view the main result is that the multi-hot-wire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least at moderate Reynolds numbers.

Enhanced dissipation of kinetic energy beneath surface waves

Abstract: TRANSFER of momentum from wind to the surface layer of lakes and oceans plays a central part in driving horizontal and vertical circulation of water masses. Much work has been devoted to understanding the role of waves in momentum transfer across the air–sea interface, but less is known about the energetics of the near-surface turbulence responsible for the mixing of momentum and mass into the underlying water column. In particular, it has remained unclear whether the structure of the turbulence in the surface layer can be described by analogy to wall-bounded shear flows or whether waves, either through breaking or wave–current interaction, introduce new length- and timescales which must be modelled explicitly. Here we report observations of turbulence in Lake Ontario, taken under conditions of strong wave breaking, which reveal a greatly enhanced dissipation rate of kinetic energy close to the air–water interface, relative to the predictions of wall-layer theory. Because wave breaking is intermittent, short-term measurements of the kinetic energy dissipation in the near-surface layer may therefore result in considerable underestimates, and any general treatment of upper mixed layer dynamics will have to take wave breaking explicitly into account.

Structure of a particle-laden round jet

Abstract: The interaction of solid particles with the temporal features of a turbulent flow has direct relevance to problems in particle and spray combustion and the processing of particulate solids. The object of the present study was to examine the behaviour of particles in a jet dominated by vortex ring structures. An axisymmetric air jet laden with 55 μm glass particles was forced axially with an acoustic speaker to organize the vortex ring structures rolling up in the free shear layer downstream of the nozzle exit. Visualization studies of forced and unforced flow with Reynolds number of the order of 20000 were completed using a pulsed copper vapour laser. Instantaneous photographs and videotapes of strobed forced flow show that particles become clustered in the saddle regions downstream of the vortex rings and are propelled away from the jet axis by the outwardly moving flow in these regions. Phase-averaged spatial distribution of particle number density computed from digitized photographs and phase-averaged particle velocity measurements yield further evidence that local particle dispersion and concentration are governed by convection due to large-scale turbulence structures. The large-scale structures and convection mechanisms were shown to persist for particle-to-air mass loading ratios up to 0.65.

Experiments on transition in plane Couette flow

Abstract: The first flow visualization experimental results of transition in plane Couette flow are reported. The Couette flow water channel was of an infinite-belt type with counter-moving walls. The belt and channel walls were transparent making it possible to visualize the flow pattern in the streamwise-spanwise plane by utilizing fluid-suspended reflective flakes. Transition was triggered by a high-amplitude pointwise disturbance. The transitional Reynolds number, i.e. the lowest Reynolds number for which turbulence can be sustained, was determined to be 360 ± 10, based on half-channel height and half the velocity difference between the walls. For Reynolds numbers above this value a large enough amplitude of the initial disturbance gave rise to a growing turbulent spot. Its shape and spreading rate was determined for Reynolds numbers up to 1000.

A new time scale based k-epsilon model for near wall turbulence

Abstract: A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data.

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

Abstract: The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.