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    M.Tech. Project Progress Report

    Enhancement Of Heat Transfer Through Air Jet

    Impingement By Using Axisymmetric Detached Ribs.

    Submitted by

    Rohan Arun Gulavani

    2009AME3486

    Under the guidance of

    Prof. Anupam Dewan Prof. Sanjeev Sanghi

    Department of Applied Mechanics

    Indian Institute of Technology Delhi

    Hauz Khas, New Delhi

    November 2010

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    Abstract

    As we know, heat transfer enhancement is getting increasing importance since last

    few years as it increases performance of any system which uses thermal energy at any

    point of operation, such as, internal combustion engines, food processing equipments,

    textiles, films and papers, processing of some metals and glass, etc. As impingement

    of any fluid on the surface certainly increases the heat transfer than the natural

    convection, researchers are concentrating over impingement with modified surface.

    One way to modify the surface is use of ribs. The function of rib is to make the flow

    turbulent, which results in enhancement of heat transfer. So in this project I am going

    to study various dimensional parameters of axisymmetric detached ribs which are

    certainly affects the heat transfer. Computational study is the main part of this project

    and for which, commercial CFD software FLUENT and GAMBIT is used.

    In this report, I simulate the air jet impingement over the flat plate as well as on plate

    with detached rib. Grid independence study, selection of turbulence model, boundary

    conditions, effect of impingement on heat transfer, and the effect of turbulent intensity

    and length scale on heat transfer and rib clearance effect ( c/d ) are the main content

    of the report.

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    Contents

    Abstract ................................ ................................ ................................ ..................... ii

    List of Figure ................................ ................................ ................................ ............ iv

    Chapter 1. Introduction ................................ ................................ .......................... 1

    Chapter 2. Literature Review ................................ ................................ ................. 2

    Chapter 3. Governing Equations ................................ ................................ ............ 5

    Chapter 4. Geometry, Boundary Conditions and Grid ................................ ............ 7

    Chapter 5. Results and Discussion ................................ ................................ ....... 10

    Chapter 6. Conclusions and Future Scope ................................ ............................ 16

    References ................................ ................................ ................................ ............... 17

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    List of Figure

    Figure 4:1 Experimental geometry considered by (Prabhu and Katti )................................ .... 7

    Figure 4:2 Computational domain................................. ................................ ........................ 8

    Figure 4:3 Grid considered in the present study................................ ................................ ..... 9

    Figure 5:1 Grid independence study................................ ................................ .....................10

    Figure 5:2 Comparisons of results using the RNG and standard k- models......................... 11

    Figure 5:3 Effect of detached rib on Nusselt number................................ ............................ 12

    Figure 5:4 Effect of turbulent intensity on Nusselt number................................ ................... 13

    Figure 5:5 Effect of turbulent length scale on Nusselt number................................ ..............14

    Figure 5:6 Effect of rib clearance ( c/d ) on heat transfer................................ ...................... 15

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    Chapter 1. IntroductionAs we know, heat transfer enhancement is getting increasing importance since last

    few years as it increases performance of any system which uses thermal energy at any

    point, such as, internal combustion engines, food processing engines, etc. During past

    few years many investigations dealing with impingement heat transfer enhancement

    have been reported in the literature. In this case, fluid under high pressure impinges

    on the surface over which we want to enhance heat transfer. Due to high pressure

    difference, the flow becomes turbulent and consequently heat transfer increases. Such

    processes have become popular in some industrial applications, such as, drying of

    food products, textiles, films and papers, processing of some metals and glass, cooling

    of gas turbine blades and outer wall of the combustion chamber, cooling of electronic

    equipments, etc.

    With impinging jets, to increase heat transfer, some scientists have used modified

    surfaces, e.g., they have used surface roughners, attached ribs, detached ribs. Based

    on several experimental studies reported in the literature, it can be concluded that in

    all situations, these techniques enhance heat transfer. In the present project, a

    computational study to consider the effect of axisymmetric detached rib on heat

    transfer from a smooth surface has been reported.

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    Chapter 2. Literature ReviewAs already mentioned, turbulence has significant effect on heat transfer, Gardon and

    Akfirat (1965) studied the effect of turbulence on the heat transfer between two-

    dimensional jet and flat plate. They also studied the effect of impingement on two

    dimensional flat-plate. Hoogendoorn (1977) has proposed Nusselt number variation at

    stagnation point and nearby region. He said that for low nozzle to plate distance

    (z/d

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    in the heat transfer coefficient for the dimpled surface as compared to the smooth

    surface. Gau and Lee (1992, 2000) reported the heat transfer augmentation to slot jet

    impinging on square ribbed and triangular ribbed walls, respectively. They performed

    both the flow visualization and local Nusselt number measurement. They found that

    reduction in heat transfer in case of triangular rib due to formation of air bubble

    enclosing cavities near stagnation point which was lower than that in case of flat

    plate. They stated that if impingement is used, flow becomes turbulent and it easily

    penetrates the cavities resulting in an increase in the heat transfer. They reported that

    square ribs are superior to triangular ribs. Gao et al. (2003) studied the effect of

    various parameters on heat transfer such as nozzle to plate distance, number of arrays

    of tabs. They found that 6 tabs array produce 6 distinct regions of high heat transfer

    while 10 and 16 tabs array produce only 5 and 8 regions, respectively. They also

    stated that for large nozzle to plate distance, Nusselt number distribution is quite

    uniform and tabs plays an important role in making the flow turbulent and enhancing

    the heat transfer.

    Some researchers have reported the detached rib experiments. Liou and

    Wang (1995) and Liou et al. (1995) studied different configurations of detached ribs

    on the walls in internal flows and reported improved thermal performance compared

    to the attached ribs. The flow visualization results of Liou et al. (1998) showed the presence of recirculating flow immediately behind the detached rib. They also

    observed an asymmetric wake behind the rib because of asymmetric flow area across

    the rib. The vortex shedding promotes the mixing of fluid and hence leads to a higher

    level of heat transfer distributions. Tsia and Hwang (1999) studied the effect of

    thermal conductivity of the attached ribs in internal flow using thermally active

    material (aluminum ribs) and thermally non-active turbulators (wood ribs). They

    concluded that higher enhancements with thermally active ribs are attributed to the rib

    conduction effects. Their experiments with fully detached ribs show that enhancement

    in heat transfer due to enhancement in turbulence. They speculated the flow over the

    detached ribs and reported shedding of vortices from the detached rib and the wall jets

    ejecting from the rib clearance.

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    Prabhu and Katti (2008) studied the effect of axisymmetric detached rib

    by normal impingement of circular jet. They studied various parameters such as

    nozzle to plate distance (z/d), clearance of rib from the plate (c/d), height of the rib

    (e/d), width of the rib (w/d), rib distance from axis of nozzle, etc. They concluded that

    there is a continuous enhancement in Nusselt numbers from stagnation point till the

    first detached rib for all the ribbed configurations studied. This behavior may be

    attributed to fluid accelerations created in the stagnation region by the clearance under

    the first rib. This result is supported by lower wall static pressure under the rib,

    compared with smooth surface.

    Yuling Shi et. al. (2002) has done computational study for impingement

    heat transfer for 2D model. They compare the results between RSM and standard k-

    turbulence model. They come to conclusion that results obtained by standard k-

    model and RSM model has very little difference and results are very well agreement

    with experimental results. They studied the effect of turbulence intensity on heat

    transfer and they come to conclusion that as intensity increases heat transfer and

    hence Nusselt number increases. Pathak et al. (2006) studied different turbulence

    models for slightly heated jet discharged in a crossflow. They also commented on the

    value of y+

    in the computation. They concluded that for the flow which is not much

    affected by the side wall, it is preferable to keep the value of y

    +

    between 20-30. Theyconcluded that for three-dimensional flow computations Reynolds stress transport

    model is seen to be performing better than the standard k- model. Saket. al. (2007)

    has investigated the effect of turbulent length scale and turbulent intensity on forced

    convection heat transfer.

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    Chapter 3. Governing EquationsContinuity equation:

    0jj

    Ux

    Vx

    !x

    - - - - - - - - - - - - - - - - - - - - (3.1)

    Momentum equation:

    , ,jii j i j j i j j i

    UUPU U u u

    x x x x x V Q V

    xxx x x! x x x x x -

    - - - - - - - - - - - - - - - - - - - (3.2)

    Energy equation:

    ? A .( ) ( ) ( )Pr

    p t

    i i ij eff

    j j t j

    c TU E p k U

    x x x

    QV X

    x x x !

    x x x - -- - - - - - - - - - - - - - - - - - (3.3)

    Where,

    2( )

    3

    j i kij eff eff eff ij

    i j k

    U U U

    x x xX H

    x x x

    x x x

    Viscous heating term plays important role in the compressible flow computations.

    Turbulent model used for computation is k- model

    Standard k- model:

    ,i

    x x x

    ti k b M

    k

    kku G G Y

    Q V Q VI

    W

    x x x

    x x x - - - - - - - - - - - - - - - - - - (3.4)

    2

    ,

    1 3 2

    i x x x

    ti k b

    u C G C G C k k

    I I I

    I

    Q I I I VI Q V

    W

    x x x

    x x x - - - - - - - - - - - - (3.5)

    Where,

    tQ denotes the turbulent viscosity and is modeled as

    2

    t

    kC

    QQ V

    I!

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    In these equations,

    kG represents the generation of turbulent kinetic energy due to mean velocity gradient

    bG represents the generation of turbulent kinetic energy due to buoyancy

    MY represents the contribution of fluctuating dilatation in compressible turbulent to the

    overall dissipation rate

    The values of the model constants used in above equations are

    1 2 31.42, 1.68, 0.09, 1.0, 1.3

    kC C C

    I I I I W W! ! ! ! !

    ,kI

    are the turbulent Prandtl numbers for I and k respectively.

    RNG k- model

    ,i

    x x xi k eff k b M k

    kku G G Y S V E Q VI

    x x x!

    x x x - - - - - - - - - - - - - - - (3.6)

    2

    ,

    1 3 2

    i x x x

    i eff k bu C G C G C S Rk k

    I I I I I I

    I I I VI E Q V

    x x x!

    x x x - - - -- - - - - (3.7)

    Where,

    RI

    is the value contributing in the constant2

    CI

    All other nomenclatures are same as standard k- equations

    The model constants are

    1 2 31.42, 1.68, 0.09, 1.0, 1.3

    kC C C

    I I I I

    ! ! ! ! !

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    Chapter 4. Geometry, Boundary Conditions and GridThe arrangement for plate, nozzle and rib is described in Fig. 4.1.

    Figure 4:1 Experimental geometry considered by (Prabhu and Katti )

    Fig. 4.1 shows the nature of geometry of problem considered for computational

    purpose. Here a nozzle of diameter 15.00 mm and is impinging air at 1.5 bar pressure.

    Steel plate of dimension 160 x 80 x 0.06 mm acts as the heater which is continuously

    provides a heat flux of 5000 W. Different dimensions of ribs and other geometries are

    considered. We will look at the effect of (1) nozzle to plate distance (z/d);

    (2) clearance (c); (3) thickness of rib (e); (4) width of the rib (w); and (5) pitch of the

    rib (p).

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    B ondi ions

    Fi 4: C t ti l domai

    Boundary conditions assi ned to t e computational domain are shown in Fi 5.1. The

    values to the di erent parameters are taken directly from the experimental data of

    (Prabhu and Katti .

    1) Velocity inlet ( avg. velocity = 20 m/s)

    2) Pressure outlet: atmospheric pressure

    3) Wall: heat flux 5000 W;thickness: 0.06 mm; wall material: Steel

    4) Reynolds number (Re) = 20000

    5) Fluid: Air

    Properties of air at 300 k:

    i) Density = 1.225 kg/m3

    ii) Specific heat CP = 1006.43 J/kg-K

    iii) Thermal conductivity = 0.0242 W/m-k

    iv) Viscosity = 1.7894 X 10-5 kg/m-s

    Velocity Inlet (d= 15 mm)

    Pressure OutletPressure Outlet

    Wall (160mm)

    z

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    Grid

    A picture of grid used for computationalis shown in Fig. 4.3. This grid is based on the

    grid independence study. Itis refined till y+ value atthe wallis reduces to less than 5.Successive ratio used in grid is 1.05.

    Figure 4:3 Grid considered in the present study

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    Chapter 5. Results and DiscussionGrid Independence Study

    This study was carried out using three different mesh si es. Experimental data shows

    that Nusselt number values increases first and then reduces continuously from peak

    Nusselt number point to the wall of nozzle. The same trend was obtained using the

    fine mesh with y+ value ofthe grid point equalto 4.0. The simulation was carried out

    using the standard k- model with enhanced wall function approach. According to the

    theory for the temperature law of the wall y+ value at the first grid point should be

    less than 13.2. Therefore accordingly mesh size was reduced so that y+

    reaches up to

    4.0. A further refinementin mesh did not change the results.

    Figure 5:1 Grid independence study

    0

    50

    00

    50

    200

    250

    300

    0 05

    5 2 2

    5

    Nu

    r/d

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    Comparison between Standard k- and RNG k- models

    Fig. 5.2 shows that results depend on turbulence model used. The predictions using

    the standard k-

    model are in good agreement with experimental results than those bythe RNG k- model. One reason forthis conflictis assumption made in formulation of

    these models. In standard k- model formulation is done with assumption that flow is

    fully turbulent in other way in RNG k- ,low Re flow is the assumption. Maximum

    percentage deviation for Standard k- modelis 11.95 %, while forRNG k- modelit

    is 20.65 %

    Figure 5:2 Comparisons of results using the RNG and standard k- models.

    0

    0

    100

    1

    0

    200

    2

    0

    300

    0 0!

    1 1!

    2 2!

    r/d

    Nu

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    E ect of detached rib

    As we see in last section, Standard k- method gives much better results than RNG

    k- method. So for further analysis we are going to use standard k- turbulence model.And we tried to keep y+ value less than 5.

    In this section, effect of detached rib is examined. In following graph, Nusselt

    number is compared in both the cases. It is found that in the case of detached rib,

    Nussult numberincreases in nozzle region ( r/d = 0 to 0.5 mm). So we can definitely

    say that, detached ribs are much effective to increase heattransfer from flat plate.

    Following results are obtained forthe-

    1) z/d =0.5 (distance of nozzle from plate)

    2) w/d= e/d= 0.23 (width and height of rib)

    3) c/d = 0.067 (clearance from the flat surface)

    4) r1/d = 0.5 (distance of first rib from axis of nozzle)

    5) p/e = 4.0 (pitch ofthe rib)

    Figure 5:3 Effect of detached rib on Nusselt number

    0

    50

    100

    150

    200

    250

    300

    0.000 0.500 1.000 1.500 2.000 2.500

    Smooth plate

    Plate with rib

    r/d

    Nu

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    If we analyse above graph, Peak nusselt numberis achieved atjust behind the

    first detached ri b from the centre of the nozzle. The reasons that mentioned in

    literature, due to turbulence, and minimum clearance, flow trying to escape from the

    space available. Because ofthis, wake region is createdjust behind the first rib. This

    wake region is responsible for highly turbulent flow and resulting into high heat

    transfer and hence high Nusselt number.

    Effect ofturbulentlength scale (l)and turbulentintensity

    Turbulent length scale and turbulent intensity are the main parameter of turbulence.

    These parameters have direct impact on turbulent kinetic energy and its dissipation

    rate. Hence, it has measure influence on heattransfer. Following results are obtainedforthe dimensions as mentioned in previous section.

    1) Turbulentintensity:It is given by the ratio of square root of mean fluctuations to the mean

    velocity. i.e. The intensity is directly be the measure ofturbulence. More the

    intensity more will be the turbulence and hence the heat transfers from the

    surface.

    Figure 5:4 Effect ofturbulentintensity on Nusselt number

    0

    50

    100

    150

    200

    250

    300

    0.000 0.500 1.000 1.500 2.000 2.500

    Turbulent intensity = 4.7 %

    Turbulent intensity= 8 %

    turbulent intensity = 10 %

    "

    'uI

    U

    !

    Nu

    r/d

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    From graph, it is clear that, as turbulent intensity increases, peak Nusselt

    number increases. Hence our objective is to increase turbulent intensity i.e.

    Fluctuations in the flow.

    2) Turbulentlength scale ( l) :-Turbulent length scale is inversely proportional to energy dissipation rate.

    Hence more the turbulentlength scale minimum is the turbulent kinetic energy

    dissipation rate. Energy dissipation rate has direct impact on heat transfer.

    Hence more is dissipation rate more is the heattransfer.

    Hence from graph, Peak Nusselt number is larger for length scale

    1.05mm than lenth scale 4.2 mm and 5.6 mm.

    Figure 5:5 Effect ofturbulentlength scale on Nusselt number

    0

    50

    100

    150

    200

    250

    300

    0.000 0.500 1.000 1.500 2.000 2.500

    Turbulent length scale, l= 1.05 mm

    Turbulent length scale, l= 4.2 mm

    Turbulent length scale, l=5.6 mm

    Nu

    r/d

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    Effect ofrib clearance (c)

    Following graph clearly shows that, for rib clearance (c) 1.0 mm, Nusselt number

    reaches to 247.3. which is larger than for clearance of 0.5, 1.5 and 2.0 mm. Thisvalues are obtained by Standard k- method, keeping y+ value around 3.8 i.e. less

    than 5. At stagnation point, as clearance increases, Nusselt numbertends to increases,

    but away from nozzle it shows less values. Allthe curves in the graph has maximum

    percentage deviation from experimental results is less than 15%.

    Figure 5:6 Effect of rib clearance ( c/d ) on heattransfer

    0

    #0

    100

    1#

    0

    200

    2$ 0

    300

    0.000 0.500 1.000 1.500 2.000 2.500

    rib clearence c= 0.5mm

    rib clearence c= 1 mm

    rib clearence c=1.5 mm

    rib clearence c = 2.0 mm

    r/d

    Nu

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    Chapter 6.

    Conclusions and Future Scope

    The following conclusions may be drawn based on the results obtained thus far

    1) The problem of air impingement can be modeled with standard k- model

    with a good agreement between experimental and computational results.

    2) Sufficiently low values of y+

    can be obtained by successive mesh refinement

    using successive ratio 1.05 and interval size 0.09. y+ value should be less than

    5 for enhanced wall treatment.

    3) Turbulent intensity and turbulent length scale are the parameter of turbulence

    and have influence on Nussul number i.e. heat transfer through flat plate

    4) Distance, at which ribs are placed, has impact on heat transfer. For clearance

    of 1 mm (c/d = 0.067) will give more heat transfer than any other clearance.

    In future the effect of rib on the heat transfer by air impingement will be studied. The

    effect of parameter under considerations is

    1) Nozzle to plate distance (z/d)

    2) Height of the rib (e/d)

    3) Width of the rib (w/d)

    4) Distance of first rib from axis of nozzle.

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    References

    1. C. J. Hoogendoorn, 1977. The effect of turbulence on heat transfer at a

    stagnation point. Int. J. Heat Mass Transfer, Vol. 20, pp. 1333-1338.

    2. C. Sak, R. Liu, D.S.-K. Ting, G. W. Rankin, 2007, Role of turbulent length

    scale and turbulent intensity on forced convection from a heated horizontal

    circular cylinder, Experimental thermal and fluid sciences, vol. 31, pp. 279-

    289.

    3. FLUENT Inc., Fluent 6.3 Documentation, http://www.fluent.com, 2006.

    4. Gardon, R., Akfirat, C., 1965. The role of turbulence in determining the heat

    transfer characteristics of impinging jet. Int. J. Heat Mass Transfer Vol. 8, pp.

    12611272.

    5. Gao, N., Sun, H., Ewing, D., 2003. Heat transfer to impinging round jets with

    triangular tabs. Int. J. of Heat Mass Transfer Vol.46, pp.25572569.

    6. Gau, C., Lee, I.C., 2000. Flow and impingement cooling heat transfer along

    triangular rib-roughened walls. Int. J. Heat Mass Transfer Vol.43, pp. 4405

    4418.7. Hansen, L.G., Webb, B.W., 1993. Air jet impingement heat transfer from

    modified surfaces. Int. J. Heat Mass Transfer Vol.36, pp. 989997.

    8. Katti V.V., Prabhu, S.V., 2008. Experimental study and theoretical analysis of

    local heat transfer distribution between smooth flat surface and impinging air

    jet from a circular straight pipe nozzle. Int. J. Heat Mass Transfer Vol.51, pp.

    4480-4495

    9. Katti V.V., Prabhu, S.V., 2008 Heat transfer enhancement on a flat surface

    with axisymmetric detached ribs by normal impingement of circular air jet Int.

    J. Heat Mass Transfer. Vol. 29, pp. 1279-1294

    10.K Kanokjaruvijit and R F Martinez-Botas, 2004, An experimental

    investigation of the heat transfer due to multiple jets impinging normally on a

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    dimpled surface. J. Mechanical Engineering Science. Vol. 218 Part C,

    pp.1337-1347.

    11.Manabendra Pathak, Anupam Dewan, Anoop K. Dass, 2006, Computational

    prediction of a slightly heated turbulent rectangular jet discharged into a

    narrow channel crossflow using two different turbulence models, Int. J. Heat

    Mass Transfer. Vol. 49, pp.3914-3928

    12. S. Sugawara, T. Sato, H. Komatsu and H. Osaka, 1988. Effect of free stream

    turbulence on the flat plate heat transfer, Int. J. Heat Mass Transfer, Vol. 31,

    pp. 5-12.

    13.Yuling Shi, M. B. Ray and A. S. Mujumdar, 2002, Computational study of

    impingement heat transfer under a turbulent slot jet, Ind. Eng. Chem. Vol. 41,

    pp. 4643-4651.