Turbulence averages

Turbulent, average, flat plate, forced flow... 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

Convective heating in fire conditions is principally under natural convection conditions where for turbulent flow, a heat transfer coefficient of about 10 W/m2 K is typical. Therefore, under typical turbulent average flame temperatures of 800 °C, we expect convective heat fluxes of about 8 kW/m2. Consequently, under turbulent conditions, radiative heat transfer becomes more important to fire growth. This is one reason why fire growth is not easy to predict. 

Turbulent, average, flat plate, forced flow k L sfc.at.g = = 0.0365average coefficient Based on Prandtls 1/7-power velocity law, i=(r ... 

In the following discussion, a bar over a variable indicates that the quantity is turbulence-averaged and a as a superscript of a variable means that it is the instantaneous turbulent fluctuation relative to the average value of the variable. From these definitions, it follows that the ensemble average of a turbulent fluctuation equals zero, i.e. we necessarily have ... 

The method used above to write out turbulence-averaged equations is entirely classical. While we have applied it to the dispersion of a passive scalar, it is also used for other quantities. Its apphcation to Navier-Stokes equations leads to Reynolds equations ... 

By substituting relations [8.30] into [8.20], the averaged advection-diffusion equation for the turbulence-average concentration becomes ... 

In these equations, m, denotes the components of the turbulence-average velocity. Equations [8.39] are summed over indices i and j. The k-s model uses five constants Cju, C, C2, cxk, and cts, whose values were calibrated on the basis of reference experiments. The quantity ... 

The Reynolds stresses appearing in the Reynolds equations [8.21], whose solution determines the turbulence-average velocity field, are modeled via the mixing length model (equation [8.28]) such as ... 

The first term on the right-hand side is a term of energy production by the gradient of the turbulence-average flow. Considering the equation for k, for a sheared, unidirectional averaged flow Ux z), the production term reduces to... 

Evaluate the velocity of the turbulence-average flow in each of the three streaks, using the lo rithmic law (derived from bormdary layer theories not covered in this book) ... 

Instantaneous gas flow velocities U in the flame base vicinity were obtained in [17]. Those measurements revealed low velocities conditioned by the tranquil flow in zones between the large vortices. In the lower part of the jet (at zlvj 10) the characteristic flow velocity was about 20% of the laminar flame velocity in a stoichiometric mixture. However, for z/r 30 and 50, characteristic velocities were recorded. Velocities of the order of 1.2 are in sufficient agreement with the assumption that the non-turbulent average boundary length between large vortices is measured. 

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