- apart of practical importance of jets in various applications, they are also
Fig.I-42 Characteristic features of a turbulent submerged jet. Note that jet width
(a conditionally defined quantity) increases linearly with downstream distance from
the virtual origin. On jet edges, turbulent vortices entrain nonturbulent outer fluid
- this leads to intermittent character of turbulence there. Note also that there is
a development region downstream from the nozzle.
pedagogically important objects. Their turbulent structure is relatively simple, as opposed to turbulent flows influenced by presence of nearby walls, which are more complicated. In particular, the turbulence length scale in jets is practically constant (- this means that the character of flow is determined by vortices of almost the same size) across the whole cross section. Tollmien in 1926 solved the turbulent jet flowfield using the algebraic model of turbulence, assuming that the lengths scale is constant in each transverse cross section and proportional there to the local jet width: = k . The weakness of the algebraic model is that it predicts zero turbulence on jet axis (where there is zero transverse gradient of time-mean velocity) and too low turbulence near the axis.

- is a more difficult object for study, because - according to Fig.I-43 - it is possible to to discriminate there three differently behaving layers,
Fig.I-43
not sharply separated but continously merging. In the outer layer , the conditions are rather similar to those in the jet. Similarly as in the jet, calculations lead to acceptable results with = k . . In the inner layer , turbulence is influenced by the presence of the wall: the nearer to the wall we focus our attention, the smaller are the turbulent vortices responsible for the main proportion of turbulent transport of momentum. The dependence of turbulence scale on the distance from the wall may be, in the
Fig.I-44
first approximation, taken as linear: = . Almost the whole turbulent boundary layer may be therefore modelled using the simple model of the length distribution due to Escudier, Fig. I-44. At the very wall (as long as it is sufficiently smooth) there is the third component of the boundary layer: the viscous sublayer , strongly influenced by the molecular viscosity . In spite of its extremely small thickness, it represents e.g. the most important heat transfer resistance in transport of heat across a turbulent boundary layer.
Large vortices in the outer layer reach to nonturbulent outer fluid and move it into the boundary layer. From the values of the intermittence coefficient (ratio of time during which a probe senses turbulent flow to the overall measurement time) in Fig.43 it is possible to see that nonturbulent fluid reaches for some nonnegligible amount of time as near to the wall as = 0.4 . On the other hand, at the nominal edge of the turbulent boundary layer, at = , the flow will be found really turbulent for only 7 % of total observation time and turbulence sometimes reaches as far as to = 1.2 from the wall. In the inner layer, the shear stress is constant .. and this means that also the friction velocity does not change. Inserting = into the algebraic model expression in
Fig.I-45
Fig.I-39 leads to

This may be integrated:

- which leads to the logarithmic shape of the velocity profile, Fig.I-45, usually written by means of the dimensionless "wall co-ordinates"


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This is page Nr. I12 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

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