15

3. Flows through stationary ribbedpassages.

2-Dimensional Flows

P/e =10e/D=0.0675

P/e=10e/H=0.1

16

Ribbed Channel

17

Comparisons with non-linear k- ��

18

3-Dimensional Flows

Flow Details

Body-fitted grid

19

Nusselt Number Comparisons for HeatedDuct with Staggered Ribs

20

Flow in a Ribbed U-Bend

21

Flow in a Duct with Inclined Ribs

22

Heat Transfer in a Duct with Inclined Ribs

23

Comments

� In two-dimensional flows through ribbedchannels and pipes

- Zonal Models under-predict Nusselt number- Low-Re Models predict the right Nusselt

number levels- Second-Moment closured produced the Nu

variation more faithfully- The initial form of the Differential Yap term

too strong for the second-moment closure.- The recent version of the non-linear k- �

produced satisfactory predictions.

� In three-dimensional flows through ducts andU-bends with normal ribs.

- Mean flow development predicted well byall models.

- Turbulence field better predicted by second-moment closures.

- Heat transfer comparisons lead to similarconclusions as for 2-D flows.

24

� In ducts with inclined ribs

- Flow field well predicted by zonal models

- Nusselt number distribution and levels alsowell predicted by zonal models.

- Rib induced secondary motion makes theheat transfer predictions less sensitive to themodeling of the near-wall turbulence.

25

4. Flows through rotating ribbed passages.

Rotating Duct With Normal Ribs

Mean Flow Comparisons

26

Rotating Duct With Normal Ribs

Comparisons of Turbulent Stresses

27

Flow in a Rotating Duct With Inclined RibsPredicted Effect of Rotation on Mean Motion.

28

Flow in a Rotating Duct With Inclined RibsMean Flow Comparisons

29

Heat Transfer in a Rotating Duct WithInclined RibsNu Contours

30

Heat Transfer in a Rotating Duct WithInclined Ribs

Side-Averaged Nusselt Number

____ : 2-Layer DSM ------ : 2-Layer k- �

31

Comments

� Rotation is shown to have a noticeable effect onthe mean and turbulent flow fields.

� All models tested able to reproduce the meanflow correctly.

� Effects of rotation on turbulence better capturedby the second-moment closures.

� As also found under stationary conditions, inpassages with inclined ribs, 2- layer (zonal)models produce reasonable heat transferpredictions.

32

5. Concluding Remarks

�In many heat convection problems inengineering applications, such as blade cooling,the flow is complex and three-dimensional.

�Flow features present can include

- Streamline Curvature- Secondary Motion- Flow Separation- Flow Impingement- Streamwise acceleration- Body forces such as the Coriolis and the

Centrifugal force.

�This pauses severe challenges to currentlyavailable turbulence models, especially whenit comes to the prediction of the correct wallheat transfer.

In flows affected by streamline curvature andsecondary motion, is often advantageous tomove away from the conventional wall-functions and to also employ second-momentclosures.

33

�Flow separation induced by strong curvature,is better predicted by second-moment closuresand also requires the use of high-orderdiscretization for all transport equations.

� Heat transfer in rotating passages with smoothsurfaces becomes especially difficult to predictwhen either rotational buoyancy becomessignificant, or when rotation is combined withstrong curvature.

�

For the prediction of heat transfer in passageswith normal ribs, low-Re models are essential.

�In inclined ribs, due to the presence ofsecondary motion, the thermal predictions of thezonal models are closer to the data.

�A differential length-scale correction (Yap)term, leads to further predictive improvements.

�Recently refined non-linear k- �� models offer analternative modelling route.

�Recent developments in wall-functions offerfurther possibilities.

34

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