Turbulence production

K.N.G. Bray, PA. Libby, G. Masuya, and J.B. Moss 1981, Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25 127-140. 

Rate of turbulence production (m s ) Velocity of a turbulent eddy of size X Rate of turbulence dissipation (m s ) Kolmogorov length scale (m)... 

Figure 22.7 Vertical turbulent diffu-sivity Ez versus square of stability frequency V2 in two Swiss lakes (see Eq. 22-32). (a) For Umersee (maximum depth 196 m), a basin of Lake Lucerne, the data refer to 10-100 m depth and indicate shear-produced turbulence. (b) For Zugersee (maximum depth 198 m) the values are calculated for an extreme storm of about two days duration. The data refer to the depth interval between 10 and 70 m they show a mixture between turbulence production by local shear and large-scale motion. (Fromlmboden and Wuest., 1995.)...

Gampert B, Wagner P (1982) Reduced turbulence production by increased elongational viscosity Recent contribution to fluid mechanics ed Haase W, Springer, Berlin-New York... 

In these equations summations over repeated indices are implied. The values for the empirical constants Cu = 1.44, C2e = 1.92, Gi = 1.0, and ce = 1.3 are widely accepted (Launder and Spaulding, The Numerical Computation of Turbulent Flows, Imperial Coll. Sci. Tech. London, NTIS N74-12066 [1973]). The k-e. model has proved reasonably accurate for many flows without highly curved streamlines or significant swirl. It usually underestimates flow separation and overestimates turbulence production by normal straining. The k-e model is suitable for high Reynolds number flows. See Virendra, Patel, Rodi, and Scheuerer (A1AA J., 23, 1308-1319 [1984]) for a review of low Reynolds number k-e. models. 

In this model, the velocity disturbance by the particle is from both the wake behind the particle (Rep > 20) and the vortex shedding (Rep > 400). Hence, the changes in the kinetic energy associated with the turbulence production are proportional to the difference between the squares of the two velocities and to the volume where the velocity disturbance originates. It is further assumed that the wake is half of a complete ellipsoid, with base diameter of dp (same as the particle diameter) and wake length of /w. Thus, the total energy production of the gas by the particle wake or vortex shedding is... 

The numerator is the rate of production of turbulence energy, and the denomenator is the rate of dissipation of mechanical energy by the mean field. The turbulent viscosity can therefore be described in terms of the rate of turbulence production. 

The first term on the right is the "turbulence production. The more common form of Va is... 

I Turbulence length scale (P Turbulence production -EoSvj Pstrain tensor [Eq. (49)1 P Mean pressure p Fluctuation pressure Prx Turbulence Prandtl number [Eq. (20)1... 

The solutions of equations (5.9) and (5.11) for the shear stress layer and the upper canopy layer are more complicated as we now have to account for shear stress divergence but we can note the following points. Because the shear stress layer is a region of local equilibrium (turbulence production dissipation) it is feasible to model the shear stress with a mixing length model,... 

In Figure 5.2 we show consecutive vertical profiles from the wind tunnel model study of Finnigan and Brunet [186], Although this hill is too steep to satisfy the H/L 1 limits of linear theory, upwind of the hillcrest we can still see the main features predicted by the model of Finnigan and Belcher, [189], The maximum velocity in the lower canopy occurs well before the crest and is falling by the hilltop. The difference between lower canopy and outer layer velocities is a maximum at the hilltop and maximizes the canopy top shear at that point with consequences for the magnitude and scale of turbulence production. Conversely, the difference is at a minimum halfway up the hill, where the lower-canopy velocity is maximal but the outer layer flow has not yet increased much. This effect is so marked that the inflexion point in the velocity profile at the top of the canopy has disappeared. Note also that on this steep hill we observe a large separation bubble behind the hillcrest. 

Diapycnal mixing in the turbulent regime below the surface layer was estimated by a relation according to Osborne (1980), which is based on the balance between the shear turbulent production and the work on buoyancy forces and the dissipation rate assuming a constant Richardsson flux number. 

Thus the non-linear turbulence products that were introduced by the averaging process applied to the governing equations have the same meaning as covariances. 

To enable simulations of two-phase bubbly flows [67] [65] the single phase k — e model has been extended by including a semi-empirical production term to take into account the additional turbulence production induced by the bubbles motion relative to the liquid (i.e., based on the idea of [128] [129]). In this approach it was assumed that the internal flow inside the dispersed phase (gas bubbles) does not affect the liquid phase turbulence. The shear work performed on the liquid by a single bubble, representing the additional turbulence production due to the bubble, was thus assumed to be equal to the product of the drag force and the relative velocity. 

The turbulence production term due to the relative bubble-liquid motion per unit volume is expressed as ... 

For steady-state simulations, considering the turbulence spectrum in terms of eddy size (length scale), the scales predicted by the k-e model is thus much larger than the particle size. The inclusion of turbulence production due to the bubbles relative motion is therefore based on the assumption of an inverse cascade of turbulence. 

For dynamic simulations the Ic-quantity may represent scales less than or at the same order of magnitude as the particle size. In the cases where the extra turbulence production mechanisms represent scales larger than the ones represented by the modeled part of turbulence, no extra terms should be included in the turbulence model. 

This relation was obtained using the well-known expression for steady interfacial drag and the two formulations for bubble induced turbulence production (i.e., the one given by [74], and the other one defined by [93]). 

The Reynolds stress distributions in Fig. 8.5c indicate that turbulent momentum transport is also modified at high levels of counterflow. Since the mean velocity profiles (shown in Fig. 8.4) display independence of i, but the Reynolds stress experiences enhanced transport, the overall turbulent production of the layer is considerably increased above 13%) counterflow. In fact, a comparison of the self-similar stress profiles in Fig. 8.5 indicates that a common state is achieved for < 0.13(/i, and a second common self-similar state is achieved for U2 > 0.24(7i. From 0% to 13% counterflow, the turbulent profiles collapse, indicating a mechanism for generating the turbulence that scales with the growth rate parameter o- and velocity difference AU. Above 13% counterflow, there is an increase in turbulence level across the entire cross-stream extent of the layer. This increase seems to be dependent on velocity ratio, but not on the parameter c. Since the mean profiles display similar shape, there is likely an additional mechanism for turbulence production when Ibol is greater than approximately 0.13f7i. 

In these equations, the term Pk determines the turbulence production and is given by... 

The production or source terms are due to the spray droplets and the chemical reactions, as well as to turbulence production and dissipation. The spray source terms are identifled with a superscript, s, and the chemical source terms with a superscript c. In the mass and species equations, the spray source term is which indicates the mass transfer between the liquid and gas phases, e.g., due to evaporation. The Kronecker delta, in the species equation indicates when fuel vapor is transferred to the gas phase, i.e., = 1 if m is a fuel species and... 

The studies carried out so far have explained the slip flow phenomena to a great extent. However, the use of slip phenomena for the analysis of different fluid flow problems is limited. The effect of various flow parameters, i.e., roughness, wettabilty, polarity, and presence of nanobubbles or residual gases, on slip flow phenomena need to be conclusively and systematically studied. The effect of temperature and concentration gradient on slip flow parameters needs to be properly characterized based on both molecular dynamics simulation and experiments. The effect of slip flow on turbulence production mechanism needs to be established. The development of advanced micro-/nanomanufacturing and measurement technology is expected to facilitate the systematic study of these parameters. 

Eckelmann, H., Nychas, S.G., Brodkey, R.S. and Wallace, J.M., Vorti-city and Turbulence Production in Pattern Recognized Turbulent Flow Structures, Phys. Fluids (1977), S225. 

Eidsvik (1980) proposed an entrainment model where the combined effect of mechanical and convective turbulence production was expressed by the turbulence kinetic energy parameterized by e = i.lul + 0.5w2... 

The entrainment rate in the limit of weak free convection is Bo Pedersen s (1980) interpretation of Farmer s (1975) measurements of the development of a thermal profile in an ice-covered lake in the spring season. The solar heating near the surface produced a well-mixed convective layer, and the ice sheet prevented additional turbulence production by wind shear. The mixing rate was deduced from the vertical variation of the phase of the diurnal component of the temperature signals. 

In search of a solution including turbulence production by heat convection, we need additional boundary conditions. The first assumption is that energy diffusion and pressure transport cancel each other (Cj = 0). The second assumption is that the ratio between energy... 

Drag reduction can be achieved by direct injection of microbubbles through slots or porous skin (193-196) or the generation of hydrogen by electrolysis at the wall (197). The primary parameters, independent of gas type and Reynolds number, appear to be the actual gas flow rate referenced to injector conditions of temperature and pressure (198-200) and the location of the bubbles in the turbulent boundary layer (198,199,201-203). Merkle and Deutsch (196) have provided a comprehensive review on skin friction reduction by microbubble injection. Mahadevan and co-workers (204) postulated that microbubbles like polymer solution destroy turbulence production by selectively increasing the viscosity near the buffer region. They increase the local dynamic viscosity. Pal and co-workers (205) demonstrated that microbubble and polymer solution shear stress statistics as measured by flush moimted hot film sensors are similar at equivalent value of drag reduction. 

Higher blockage ratio of the obstacles, i.e., more dense industrial structures, lead to higher turbulence production and, hence, increased flame acceleration. 

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