Turbulent Production Term Research Articles

Characterization of Turbulent Flow in a Flume with Surfactant

Summary The drag reducing effect of a surfactant additive from the alkylpolyglycosides family was investigated experimentally. In thepresent study, PIV measurements were done to investigate theturbulent flow in the streamwise-spanwise plane of a flume aty 1 580, in the buffer zone, where about 80% of the energy pro- Fig. 4 PDF’s of the u rms8 O U q for water —circles– and surfactant—squares–. u rms8 —x,z– ˜ −—u—x,z– A −u—x,z–‰– 2 ‰and the PDF is rep-resenting the spatial distribution of the rms values, normalizedby the flow-rate velocity U q .Fig. 5 Two-point—auto–correlation function R uu of the stream-wise velocity along the streamwise x and spanwise z coordi-nates, for water —circles and plus symbols– and for surfactant—square and triangular markers–, respectively.Table 1 Statistical properties of the Reynolds stress A −u 8 w 8 ‰ O U q2 .Statistics Maximum Minimum Average Std. dev. SkewnessWater 0.05 20.035 0.35310 23 0.0045 0.93Surfactant 0.03 20.035 0.35310 24 0.0032 0.003Table 2 Statistical properties of the turbulent energy production term

Investigation on the characteristics of turbulence transport for momentum and heat in a drag-reducing surfactant solution flow

Simultaneous measurements of the velocity (u and ν in the streamwise and wall-normal directions, respectively) and temperature fluctuations (θ) in the thermal boundary layer were carried out for a heated drag-reducing surfactant solution flow in a two-dimensional channel by means of a two-component laser Doppler velocimetry and a fine-wire thermocouple probe. The drag-reducing fluid tested was a dilute aqueous solution of a cationic surfactant, cetyltrimethylammonium chloride (CTAC), with 30 ppm concentration. Measurements were performed for CTAC solution flows at an inlet temperature of 31 °C and at three Reynolds numbers of 3.5×104, 2.5×104, and 1.5×104, respectively, and for water flow at the Reynolds number of 2.5×104. Drag reduction (DR) and heat transfer reduction (HTR) for the three CTAC solution flows were DR(HTR)=33.0(20.2), 70.0(77.3), and 65.1(77.0) percentage, respectively. At a high HTR level, a large temperature gradient appeared when y+<50 in the measured range (the superscript “+” denotes normalization with inner variables). Temperature fluctuation intensity, θ′+, and the streamwise turbulent heat flux, u+θ+¯, were enhanced in the layer with large temperature gradient for the drag-reducing flow, whereas the wall-normal turbulent heat flux, −ν+θ+¯, was depressed throughout the measured range. The depression of −ν+θ+¯ was due to a cause similar to that of the depression of the Reynolds shear stress −u+ν+¯, i.e., in addition to the decrease of ν′+, decorrelation between the two variables occurred. The decrease of −ν+θ+¯ resulted in HTR, which was similar to that of the decrease of −u+ν+¯ resulted in DR for the drag-reducing flow by additives. The turbulence production terms, −u+ν+¯(∂U+/∂y+) and −ν+θ+¯(∂Θ+/∂y+) where U and Θ are mean velocity and temperature, were reduced in the drag-reducing CTAC solution flows. The estimated power spectra of temperature fluctuations implied that the drag-reducing surfactant additive depressed the turbulence at high frequencies or at small scales, whereas it increased the turbulent energy at low frequencies or at large scales. The profiles of the eddy diffusivities for momentum and heat in the CTAC solution flows were both decreased. The turbulent Prandtl number deviated from that of the water flow near the heated wall with a value close to the molecular Prandtl number of the solvent.

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

失速付近における層流剥離泡の非定常的挙動について−乱れエネルギーの生産に関する考察−

A laminar separation bubble formed on a NACA 0012 airfoil at a chord Reynolds number of 1.3×105 has been investigated to discuss the bubble behavior near stall. The flow is oscillating between a small separation-reattachment bubble formed near the leading-edge and a large separated region extending over the airfoil surface at a frequency of about 2Hz. Phase averaged turbulent energy production term have been obtained. Results indicate that the behavior of growth and decay of the phase averaged turbulent stress has strong correlation with the behavior of the phase averaged turbulent energy production.

Integral Solution for the Mean Flow Profiles of Turbulent Jets, Plumes, and Wakes

Integral methods are used to derive similarity solutions for several quantities of interest including the cross-stream velocity, Reynolds stress, the dominant turbulent kinetic energy production term, and eddy diffusivities of momentum and heat for axisymmetric and planar turbulent jets, plumes, and wakes. A universal constant is evaluated for axisymmetric and planar plumes. The cross-stream velocity profiles show that jets and axisymmetric plumes experience an outflow near the axis and an inflow far away from it. The outflow is attributed to the decay of the centerline velocity with downstream distance, and the extent and magnitude of outflow correlates with the streamwise decay of the centerline velocity. It is also shown that the entrainment velocity should not in general be equated to the product of the entrainment coefficient and the centerline velocity. It is found that, due to similar governing equations, profiles for jets and plumes are qualitatively similar. Our results show that the derived quantities are strong functions of streamwise and cross-stream positions, in contrast to previous approaches that assumed constant (in the cross-stream direction) eddy viscosity and thermal diffusivity. The turbulent Prandtl number is approximately equal to unity which matches the value quoted in the literature.

Effects of Loaded Particles on Turbulence and Scalar Diffusion in a Mixing Layer

A direct numerical simulation (DNS) based on a finite volume method is applied to a particle-laden turbulent mixing layer in order to examine effects of loaded particles on turbulence and scalar diffusion. Trajectories of all particles are individually pursued with a Lagrangian method. The results show that the small particles, whose response time, τp, is smaller than the Kolmogorov time scale, τk, reduce the turbulent intensities of streamwise and transverse velocity fluctuations upstream of the mixing layer. However, the streamwise slope of turbulent intensities becomes high as compared to particle-free flow downstream of the mixing layer. Because source terms, which are energy exchange and turbulent production terms for the turbulent intensity of streamwise velocity fluctuation and pressure strain correlation term for that of transverse velocity fluctuation, are increased. Furthermore, the small particles increase the mean squared values of the concentration fluctuations.

On the evolution of maximum turbulent kinetic energy production in a channel flow

The Reynolds number effects on turbulent kinetic energy production and mean transport terms in near-wall turbulent channel flow are investigated analytically and with the help of direct numerical simulations (DNS). Using the momentum equation for turbulent channel flow, an analytical expression for the envelope of turbulent kinetic energy production curves is derived. It is shown that this envelope coincides with the wall-normal position at which the turbulent and viscous shear stress are equal. The DNS results carried out corroborate this finding and assess other quantitative details, namely the evolution of the peak of kinetic energy production and of its wall-normal position in terms of the Reynolds number. Empirical relations for the envelopes of the mean momentum transport terms and for their extrema position are also derived.

Time-Accurate Simulations and Acoustic Analysis of Slat Free Shear Layer

Unsteady computational simulations of a multi-element, high-lift configuration are performed. Emphasis is placed on accurate spatiotemporal resolution of the free shear layer in the slat-cove region. The excessive dissipative effects of the turbulence model, so prevalent in previous simulations, are circumvented by switching off the turbulence-production term in the slat cove region. The justifications and physical arguments for taking such a step are explained in detail. The removal of this excess damping allows the shear layer to amplify large-scale structures, to achieve a proper non-linear saturation state, and to permit vortex merging. The large-scale disturbances are self-excited, and unlike our prior fully turbulent simulations, no external forcing of the shear layer is required. To obtain the farfield acoustics, the Ffowcs Williams and Hawkings equation is evaluated numerically using the simulated time-accurate flow data. The present comparison between the computed and measured farfield acoustic spectra shows much better agreement for the amplitude and frequency content than past calculations. The effect of the angle-of-attack on the slat's flow features radiated acoustic field are also simulated presented.

Existence and positivity of a system k-ε with a production term of the Rayleigh-Taylor type

In this paper, we study a modelization of the turbulence which allows us to have a control on the positivity of the kinetic turbulence energy k and the dissipation growth rate of the energy ε. We use for that purpose the maximum principle on a new system modelling the turbulence, written on the variables θ and φ first introduced by Lewandowski (θ = k/ε, φ = ε 2/ k 3). Estimates on θ and φ are given for a turbulent system with a Rayleigh-Taylor type term under a hypothesis of low compressibility of the mean flow, which is more general than the hypothesis of Lewandowski. In a second part, we study a simpler convection diffusion system (the diffusion is a constant) in which there is still the Rayleigh-Taylor term. We show that the presence of this term gives greater solutions of the k, ε system, hence proving that these terms are turbulent kinetic energy production terms.

Measurements and modeling of Reynolds stress and turbulence production in a swirl-supported, direct-injection diesel engine

Measured and numerically predicted components of the mean rate-of-strain tensor 〈Sij〉 and the Reynolds stress 〈u′ru′θ〉 are examined and compared to elucidate the source and scrutinize the modeling of late-cycle turbulence production in swirl-supported, direct-injection diesel engines. The experiments are performed with combustion in the engine inhibited, to eliminate the complicating influence of heat release on turbulence generation and to reduce the problem to one more closely approximating constant-density turbulence. Both the measurements and the calculations indicate that the primary influence of the mean flow swirl on turbulence production is confined to two separate periods: (1) shortly after the end of injection and (2) in the late-cycle period, when large positive levels of 〈u′r,u′θ〉 are observed. Formation of the positive Reynolds stress coincides with the development of a negative radial gradient in mean angular momentum, indicating an unstable mean flow field. At this time, the measured velocity fluctuations show a large increase, approximately doubling in magnitude compared to fluctuations measured without fuel injection. Predicted velocity fluctuations, obtained via k-e turbulence modeling, show a similar late-cycle increase, although the magnitude of the increase is not quantitatively captured. To evaluate its applicability during the period in which the unstable, negative radial gradient in angular momentum is present, the isotropic eddy viscosity hypothesis is examined. The Reynolds stress estimated from the measured 〈Srθ〉 using the eddy viscosity hypothesis is found to mimic the measured stress with reasonable accuracy, and the measured and calculated r-θ plane turbulence production terms are shown to have excellent qualitative and quantitative agreement. The quantitative agreement, however, appears largely providential, as the measured and predicted values of 〈Srθ〉 differ by a factor of 2. This discrepancy is compensated for by the underpredicted turbulent kinetic energy and seemingly high values of the dissipation.

Numerical simulation of the high Reynolds number slit nozzle gas–particle jet using subgrid-scale coupling large eddy simulation

Large eddy simulation (LES) model in which the effect of the particle existence on subgrid-scale flows have been taken into account is proposed. The kinetic energy of the subgrid-scale flow to obtain a turbulent viscosity coefficient of the subgrid-scale flow in the LES has been calculated in assuming that the interaction terms between the gas and particles, the turbulent production term and the viscous dissipation term were balanced with each other in the kinetic energy equation of the subgrid-scale turbulent flow. Using this model, three-dimensional Navier–Stokes equations and the Lagrangian particle motion equations are simultaneously solved to describe the high Reynolds number ( Re=10 4) gas–particle jet flow and the effect of particle existence on it. The calculated results of air and particle turbulent characteristics which are mean velocity, turbulent intensity and Reynolds stress distributions are in good agreement with experimental data measured by a laser Doppler velocimeter. The existence of particles usually reduces the grid-scale turbulence in the high Reynolds number developed turbulent jet. On the other hand, the particle existence which is some kind of flow disturbance produces grid-scale fluctuations in the initial and the transitional regions of the jet and then it increases the air turbulent intensity. When particle size is much smaller than the grid size, the particle existence reduces the subgrid-scale turbulence. However, when the product of the gas and particle relative velocity and the particle concentration gradient is very large, the particle existence is able to increase the subgrid-scale turbulence.

An Implicit Multigrid Method for the Simulation of Chemically Reacting Flows

The application of multigrid methods is complicated if the set of governing equations contains strongly nonlinear source terms. This is the case for finite-rate chemistry as well as for turbulence conservation equations. In most cases strong nonlinearities within the chemical production rates prevent convergence of standard multigrid methods. This paper investigates different approaches to treating chemical and turbulent production terms on coarse grids in order to enable convergence. Independent of combustion, supersonic flows require special care during restriction and prolongation if strong shock waves occur. A full coarsening four-level nested multigrid method is used for all conservation equations including those of turbulence and species transport. Strong convergence accelerations are achieved by a local source term-dependent damping of the restricted residual error. Several test cases with and without combustion demonstrate the efficiency and accuracy of the proposed multigrid algorithm.

Helicity fluctuations and turbulent energy production in rotating and non-rotating pipes

In this paper finite-difference second-order accurate direct simulations have been used to investigate how the helicity density fluctuations change when a turbulent pipe rotates about its axis. In this case the rotation axis is parallel to the near wall vortical structures which play a fundamental role on the wall friction and turbulence production. The helicity density is the trace of the tensor γij′=〈vi′ωj′〉 whose elements form the components of v′×ω′. When the momentum equations are written in rotational form the turbulence energy production term splits into two parts, one related to the convection of the large scales and the other related to the energy cascade to the small scales. From data of direct simulations the changes of the turbulent production term profile with the rotation have been explained by the pdf of the v′×ω′ components. The links between the changes on the pdf of the v′×ω′ and the modifications of the vortical structures have been also investigated. The joint pdf of the dissipation with the helicity density has shown that the dissipation is highly correlated with regions of very low helicity density in the non-rotating pipe. When the pipe rotates the helicity density increases and the dissipation decreases. Since a drag reduction is one of the results of the background rotation, in this paper, it has been speculated that the alignment between velocity and vorticity could be a common feature in drag reducing flows.

The direct numerical simulation of a turbulent channel flow with analyses of the database

The database of fully developed turbulent channel flow at low Reynolds number is set up through direct numerical simulations. The budget of dissipation-rate of turbulent kinetic energy is calculated and some existing models for the transport equation of the dissipation rate are evaluated. A new model for the turbulent production and viscous destruction terms is given. It makes a considerable improvement in the near-wall behavior. A new flow structure contributing much to high kurtosis levels in transverse velocity fluctuation in viscous sublayer is found. The common characters they possessed are described.

Surface Wave–Turbulence Interactions. Scaling ϵ(z) near the Sea Surface

A freely rising profiler was used to collect vertical microstructure profiles in the upper oceanic boundary layer under various atmospheric and sea conditions. Near the sea surface, the rate of viscous dissipation of turbulence kinetic energy, ε, exhibited a range of behaviors under different forcing conditions. Sometimes, ε was closely balanced by the wind stress production of turbulence kinetic energy. At other times, ε was greatly enhanced relative to wind stress production and exhibited an exponential depth deny. In these instances, simple scaling laws predicted for turbulence near a solid surface severely underestimate turbulent mixing near the ocean surface. Plausible explanations for enhanced ε(z) near the sea surface will have to address the effects of wave-turbulence interactions. The authors propose two different mechanisms to explain the behavior of ε near the surface, leading to two scaling schemes. The first mechanism requires high levels of turbulence kinetic energy, created by wave breaking at the surface, to be transported downward away from the surface by the motion of the swell. This transport is then locally balanced by ε. The second mechanism requires a rotational wave field and significant wave stresses that balance the turbulence Reynolds stresses. Energy drawn from the wave field to the mean flow, via the wave stresses, is in turn drawn from the mean flow by the turbulence production term, which is balanced by ε.

A cascade-transport model for turbulent shear flows

A simple model for local spectral resolution in turbulent shear flows is developed. The original cascade model of Desnyanski and Novikov contains time derivatives, spectral transfer, and viscous dissipation terms for shell-averaged turbulent energy. The model is adapted for shear flows by the addition of a convective derivative, a turbulence production term, and a turbulent transport term. Both production and transport are based on a spectral distribution of the eddy viscosity. When integrated over all scales, the model reduces to the κ equation of κ-ε models, whereas in uniform mean flows it reduces to the original cascade model. Calibration of the model constants is achieved based on experimental results for homogeneous shear flow.

Fundamental studies on the control of turbulent boundary layers. Computation of effects on the characteristics of boundary layers, pressure decrease near the entrance convex curvature passage, and adverse pressure gradient along the convex curvature surface.

A Simple type (Model 2) of the turbulent stress model developed by Launder, Reece and Rodi is adopted changing to a high-Reynolds-number turbulence model, to estimate the accelerated effects for double conditions: convex curvature, and adverse pressure gradient. To evaluate the accuracies of the model and the numerical computation method, the velocity profiles, turbulent stress profiles and quantities of turbulent energy production terms are calculated, and compared with the experimental values for CASE IIP. The condition CASE IIP consists of two conditions: convex curvature radius R=500mm, and weak adverse pressure gradient dcp/dx=0.2674(1/m). As a result, it is clarified that the effects of the double conditions are more accelerated than the total of the individual effects, and the boundary layers on the convex surface are highly developed.

ＮＡＣＡ６３−００９翼型上に生ずるＳｈｏｒｔ ＢｕｂｂｌｅとＬｏｎｇ Ｂｕｂｂｌｅの測定

An experimental study on the structure of the short bubble and the long bubble formed on NACA 63-009 airfoil has been made. Mean velocities, turbulent stresses and turbulent triple products were measured. Results show that the turbulent stresses attain maxima near the reattachment point for the short bubble. For the long bubble, these stresses start to increase just after the laminar separation point and attain maxima far before the flow reattaches to the airfoil surface. Turbulent energy balances were estimated from results. It is shown that the turbulent energy production term has the largest contribution to the growth of turbulent energy compared with the other terms.

Fundamental studies on the control of turbulent boundary layers. (The effects of a rapid pressure decrease at the start of the convex surface curvature on turbulent boundary layer characteristics).

Turbulent boundary layer characteristics are studied experimentally under two different conditions: with a rapid pressure decrease at the start of the convex surface curvature (CASE I), and without a pressure decrease (CASE II). It is clear that there are distinct differences in the turbulent boundary layer characteristics between the two conditions. The causes of the marked differences are discussed in detail, evaluating the turbulent stress production terms in turbulent stress transport equations. The effect of the pressure decrease in CASE I makes [∂u/∂y] increase rapidly in the region close to the convex surface, which increases the stress production terms. Furthermore, u'2^^- increases. The effect of the convex curvature in CASE II reduces the Reynolds stress in the layer under the influence of the [ku] term in the equation. Then the negative region of the stress appears. There are distinct differences between the two conditions with respect to mean velocity characteristics affected by the turbulent characteristics.

Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windug. The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.