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A lot of properties were studied by different scientists of
which the SAND GRAIN ROUGHNESS HEIGHT and the size of SAND GRAIN were defined
by Schlichting and Nikraudse respectively. Depending upon the ks+ value there
are 3 ranges that came to exsistence

< 4 hydraulically smooth regime  470 
fully rough regime

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It was nonted that all the rougness
function collapsed in only one regime that is FULLY ROUGH REGIME


Fundamentally there aer various wasysto
achieve a desirsed value of K+ by changing k/ ?

And Re?

IT has benn verified that different
flows having the same K+ should produce the same U+ .The deviatuijns were found only in
one case for Re?
= 120 . Hence Re? =180 was chosen as Reynolds numbers for DIRECT NUMERICAL
SIMULATION for sinusoidal pipe roughness. The difference between MEAN

For rough and smooth wall cases and for  constant Re ? are used for the computation of
values for  U+ .Roughness and flow are relates in
such a way thtat when flow approaches hydrodynamically smooth conditios and
roughness decreasas the statics more ssenstive to domain size.Plotting the
graph of MEAN VELOCITY STATICS provides the differences in immediate viscinity
of rough wall.



5. Summary and concluding remarks


A thourough study of TRI in a radiative
turbulent channel

flow has been performed. The
modification of the temperature field upon varying the

optical thickness has been extensively
investigated with the aid of temperature variance

budgets and turbulent temperature
spectra.We see that there are different magnitudes and qualitative behaviours
of TRI when different optical depths are put to test, and

highlight specifically the contrasting
effects of radiative absorption and emission on


For a low optical thickness (?        ) the role of absorption is limited to

modification of mean profiles since  there is no change in local

thermal fluctuations  due to incident radiation (G) . On the other
hand the whole temperature spectrum can be disrupted by emission,stabilizing
temperature and reducing thermal fluctuations mainly in the

channel core. The
direct effect of radiation on temperature variation is thus dependent  only on emission, and has a relatively small
impact due to the low absorption coefficient

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