Study of turbulent flow downstream from a linear source of heat

811 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
811
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Study of turbulent flow downstream from a linear source of heat

  1. 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME ENGINEERING AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 4 Issue 1 January- February (2013), pp. 08-21© IAEME: www.iaeme.com/ijmet.asp IJMETJournal Impact Factor (2012): 3.8071 (Calculated by GISI)www.jifactor.com ©IAEME STUDY OF TURBULENT FLOW DOWNSTREAM FROM A LINEAR SOURCE OF HEAT PLACED INSIDE THE CYLINDER WAKED. Tcheukam-Toko*1, B. S. Tagne-Kaptue2, A. Kuitche2, R. Mouangue1, P. Paranthoën3 1 Department of Energetic Engineering, IUT, University of Ngaoundere, P. O. Box 455 Ngaoundere, Cameroon2 Departments of Energetic and Electrical Engineering, ENSAI. P. O. Box 455 Ngaoundere, Cameroon. 3 CNRS UMR 6614 CORIA, University of Rouen, P. O. Box 12 – 76801 Saint-Etienne du Rouvray, France. * Corresponding author. Email: tcheukam_toko@yahoo.frABSTRACT A turbulent flow downstream from a linear source of heat placed inside the cylinderwake has been studied numerically in this paper. Special attention has been paid to thecylinder wake effect on the source of heat diffusion in downstream flow. The turbulent modelhas been applied a standard κ-ε two equations model and the two-dimensional ReynoldsAveraged Navier–Stokes (RANS) equations are discretized with the second order upwindscheme. The SIMPLE algorithm, which is developed using control volumes, is adopted as thenumerical procedure. Calculations were performed for a wide variation of the Reynoldsnumbers. The investigations reveal that with increasing Reynolds number, the instabilitiesappear in the wake zone, showing an oscillatory flow, also called von Karman Vortex Street.His geometry has an important influence on the thermal field and the diffusion process.Comparison of numerical results with the experimental data available in the literature issatisfactory.Keywords: Passive scalar, linear source of heat, Cylinder wake, Turbulent flow, CFD. 8
  2. 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEI. INTRODUCTION The dispersion of passive contaminant generated of locale fashion in a turbulent flow,is an important phenomenon funded in many problems of heat and mass transfer (Warhaft,[1]). His industrials applications are the dryer, the heat pump, the boilers, the airconditioning, the refreshes of electronics components, the reactor conception, etc... The termspassive and locale means respectively that the contaminant emitted does not modified thecharacteristics of main flow and the scale, at which the scalar is injected, is always very lowerthan the integral scale of turbulence. In many practices situations, these diffusionsphenomenon’s appeared in some complex turbulent flows which are perturbed by theobstacles and are characterized by the higher structures.Many studies carried out in turbulence during these last decade, have showed the existence ofcoherent structures inside the stress flows, even at the high Reynolds numbers. Veeravalli andWarhaft, [2], carried out a study of thermal dispersion from a line source in a shearlessturbulence mixing layer. They did not associate the instabilities phenomenon caused by theexistence of wake. Le Masson, [3], has worked on the control of Bénard Von-Karmaninstabilities downstream from a heated obstacle at low Reynolds number, but he does notdefined all the control parameters of instabilities. Brajon-Socolescu, [4], has carried out anumerical study on the Bénard Von-Karman instabilities behind a heated cylinder. Lecordierand al. [5], also, who have worked on the transition control downstream from a 2D obstacleusing a source of heat located inside his neared wake. These last two studies were limitedbecause of lack of critical Reynolds number. Weiss [6], has studied a passive scalar diffusioninside the neared obstacle wake. He demonstrated that the thermal field is strongly influencedby the geometry of Vortexes Street, but he worked only with one Reynolds number.Paranthoën and al. [7], have carried out a dynamic field experimental study of Bénard von-Karman Street downstream from a heated or not heated 2D obstacle. This study used onlyone Reynolds number. Many others recent studies were carried out by Champigny andSimoneau, [8], on the mixed convection around a wide vertical cylinder. They did not take inaccount, the wake effects on the thermal field dispersion and the choice of turbulence model.Aloui, [9], in the studies carried out on the flow control, does not take in account the choiceof parameters control and the source of heat. However, it is clear that few of these studieshave been dedicated on the influence of structures in the diffusion and transport phenomenon,with the exception of Crow and al. [10], who have worked on the solids particles dispersion.The number of studies carried out in this domain is not enough, however, it’s aroused manyinterest, because of his responsibility on the existence of counter-gradient zones in theseflows. In this case, the flux of passive contaminant has the same direction and the same waywith the mean temperature gradient (FuIachier and al. [11]; Sreenivasan and al. [12],Veeravalli and Warhaft, [2]). Corsin [13], has showed that it is not possible to model the heattransport with the linear model of gradient transport using a turbulent diffusivity.In order to explain the influence of structures on the thermal transfer phenomenon anddiffusion process, we have carried out a numerical study of turbulent flow downstream froma linear source of heat placed inside the cylinder wake, by using several Reynolds numbers.To lead well this study, we are going to analyze the temperature and velocity profilesrespectively inside the cylinder wake and downstream from the linear source of heat. Then,we will analyze the means temperature gaps profiles, the transversal flux of heat profiles, infunction of transversal gradient of mean temperature. We will end this analyze by doing thecomparison between the numerical and the experimental results. 9
  3. 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEII. MATERIAL AND METHODSII.1 Mathematical models usedThe continuity equation is given by the equation bellow:డఘ ሬԦ ൅ ݀݅‫ݒ‬൫ߩ ܸ ൯ ൌ 0 (1)డ௧The conservation equations of the average quantity of movement of Navier-Stockes known by thename RANS are for compressible fluid and Newtonian given by the formula bellow.డ ሺߩ‫ݑ‬௜ ሻ డ ൅ డ௫ ൫ߩ‫ݑ‬௜ ‫ݑ‬௝ ൯ ൌ െ డ௉ డ డ௨ డ௨ೕ ଶ డ௨ డ തതതതത ൅ డ௫ ൤ߤ ൬డ௫ ೔ ൅ డ௫ െ ଷ ߜ௜௝ డ௫೔ ൰൨ ൅ డ௫ ቀെߩ‫ݑ‬ప ‫ݑ‬ఫ ቁ ൅ ‫ܨ‬௜ (2) ′ ′డ௧ ᇣᇧೕ ᇧᇤᇧᇧᇥ ด డ௫೔ ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇥ ᇣᇧ ᇧᇤᇧ ᇧᇥ ೕ ೕ ೔ ೔ ೕᇧ ᇧ ௖௢௡௩௘௖௧௜௩௘ ௙௢௥௖௘௦ ௩௜௦௖௢௦௜௧௬ ௙௢௥௖௘௦ ௙௢௥௖௘௦ ୲୰ୟ୬ୱ୮୭୰୲ ௗ௨௘ ୲୭ ௚ୣ୬ୣ୰ୟ୲ୣୢ ୠ୷ ௣௥௘௦௦௜௢௡௦ ௧௨௥௕௨௟௘௡௖௘ തതതതതെߩ‫ݑ‬ప ‫ݑ‬ఫ are the components of the Reynolds stress. Its expression is bellow as given by the ′ ′Boussinesq J. (1897), hypothesis: തതതതത ′ ′ డ௨ డ௨ೕ ଶ డ௨െߩ‫ݑ‬ప ‫ݑ‬ఫ ൌ ߤ௧ ൬డ௫ ೔ ൅ డ௫ ൰ െ ଷ ൬ߩ݇ ൅ డ௫ ೔ ൰ ߜ௜௝ (3) ೕ ೔ ೕThe k- є turbulence models used by the software FLUENT [14] are: • the k-є standard model • the k-є RNG model • the k-є realisable model We are going to use the k-є realisable model to carry out calculations in the softwareFLUENT. The turbulence k-є realisable model proposed by Shih and al., [15], was proposed to makeup for the insufficiency of the other k-є models such as the k- є standard model, the k-є RNG model,etc..., by adopting a new formula for the turbulent viscosity while implicating a variable Cµ at theorigin (proposed by Reynolds) and a new equation for the disposed based on the dynamic equation ofthe vortices fluctuations. The equations of its transporting equations are: • The turbulent kinetic energy transport equation, which is given by the formula bellow. •ࣔ ࣔ ࣔ ࣆ ࣔ࢑ ሺ࣋࢑ሻ ൅ ࣔ࢞ ൫࣋࢑࢛࢐ ൯ ൌ ࣔ࢞ ൤ቀࣆ ൅ ࣌ ࢚ ቁ ࣔ࢞ ൨ ൅ ࡳ࢑ ൅ ࡳ࢈ െ ࣋ࢿ െ ࢅࡹ (4)࢚ࣔ ࢏ ࢏ ࢑ ࢐ • The transport equation of the dissipation rate of turbulent kinetic energy, which is given by the formula bellow.ࣔ ࣔ ࣔ ࣆ ࣔࢿ ࢿ૛ ࢿ ሺ࣋ࢿሻ ൅ ࣔ࢞ ൫࣋ࢿ࢛࢐ ൯ ൌ ࣔ࢞ ൤ቀࣆ ൅ ࣌ ࢚ ቁ ࣔ࢞ ൨ ൅ ࣋࡯૚ ࡿࢿ െ ࣋࡯૛ ࢑ା ൅ ࡯૚ࢿ ࢑ ࡯૜ࢿ (5)࢚ࣔ ࢐ ࢐ ࢿ ࢐ √࣏ࢿWhere: ఎ ௞ ‫ܥ‬ଵ ൌ ݉ܽ‫ ݔ‬ቂ0.43, ቃ, with, ߟ ൌ ܵ (6) ఎାହ ఌGk represent the turbulent kinetic energy due to the average gradient of velocity. Gb represent thegeneration of kinetic energy due to floating. YM represent the contribution of the fluctuatingdilatation. C2 and C1ε are the constants; σk and σε are the numbers of turbulent Prandtl relative to kand ε.The values of constants are represented on the table 1 below. Table 1: The constants of model C1ε ‫ܥ‬ଶ ߪ௞ ߪఌ 1.44 1.9 1.0 1.2 10
  4. 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEThe turbulent transport of heat is modelled by the usage of the analogy concepts of Reynolds to theturbulent transfer. The energy equation is given as:డ డ డ డ் ሺߩ‫ܧ‬ሻ ൅ ሾ‫ݑ‬௜ ሺߩ‫ܧ‬ ൅ ܲሻሿ ൌ డ௫ ൬݇௘௙௙ డ௫ ൅ ‫ݑ‬௜ ൫߬௜௝ ൯௘௙௙ ൰ ൅ ܵ௛ (7)డ௧ డ௫೔ ೕ ೕE is the total energy, its expression is: మ ௉ ௎೔‫ ܧ‬ൌ݄െఘ൅ ଶ (8)Keff, the coefficient of effective thermal conductivity and K, the coefficient of laminar thermalconductivity, expressed as: ஼೛ ఓ೟݇௘௙௙ ൌ ݇ ൅ (9) ௉௥೟൫߬௜௝ ൯௘௙௙ is the Tension Newtonian effective of vicious stress. Its expression is given by the formulabelow: డఓ డ௨ ଶ డ௨൫߬௜௝ ൯௘௙௙ ൌ ߤ௘௙௙ ൬ డ௫ ൅ డ௫ ೔ ൰ െ ଷ ߤ௘௙௙ డ௫೔ ߜ௜௝ ೕ (10) ೔ ೕ ೔II.2 Boundaries conditions We have based our study on the experimental study of Paranthoën and al. [16],carried out inside the air by choosing as first value of Reynolds number (Re = 15). Thefigure 1 bellow shows the configuration of that experiment. The Reynolds number isobtained from the following relation, Re = UD/ν, where D represented the cylinderdiameter, and U, the air longitudinal velocity. The value of Re, at which the vortexesstreet appears is 48, and it is considered as the critical Reynolds number (Rec ). Theelectric power by length unity (P/L), supply to linear source is about 10W/m, which iscorresponding to a temperature of 393K, higher than the temperature of the upstreamflow. For this threshold difference (Re - Rec), for this level of heating P/L, for thesepositions inside the vortexes street (Xs + = 7 ; Ys+ = 0), and for this ratio D/d = 100, thelinear source do not modified the instability as shown in Lecordier and al.[5], d is thelinear source of heat diameter. Figure 1: Experimental configuration of Paranthoën and al. [16].The calculation domain is a cobbled of length 300 mm, and of height 32 mm. On this domain,the linear source of heat is located at 14 mm behind the cylinder, at the same axis. Theprincipal flow is emitted longitudinally across a rectangular section of width 64 mm and ofheight 32 mm. The cylinder diameter is 2 mm, and the linear source of heat diameter is 0.02mm, which is well satisfied by the ratio D/d = 100. In this study, the sign “+” in quote, 11
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEindicates a normalised quantity. The heights are normalised by D and the temperature gapsare normalised by the reference temperature gap ∆Tref. The molecular effects being negligiblein front of the turbulence, the relationship ∆T/∆Tref can be assimilated to a concentration C,which will vary between 1 at emission and 0 at the infinity. ∆T is the difference between theinitial temperature of the principal flow and the temperature of the linear source of heat at aninstant t. The velocities are normalized by the sound velocity at 300K, when air is assimilatedas a perfect gas. This domain of calculation represented on figure 2 bellow, is meshed withthe Gambit program. It is a regular grid type with its cells in the quadrilateral form, with185,054 cells. The principal flow is introduced longitudinally through the left of the cylinder.Air comes out at 300 mm from the input. a) b) c) Figure 2: Mesh of calculation domain: a): Calculation domain, b): Zoom around the cylinder wake, c): Zoom around the linear source of heatWe have imposed the atmospheric pressure conditions at the output. The different values ofReynolds number applied at the input are: Re = 63, 126, 252, 504, 700 and 900. The wallcylinder temperature and the ambient temperature chosen are 300K.III. RESULTS AND DISCUSSIONIII.1 Dynamic field The figures 3a, 3b, 3c, 3d, 3e and 3f, represented the fields of dimensionless velocitiesiso-value, respectively for the following Reynolds number 63, 126, 252, 504, 700 and 900.For a low Reynolds number (Re = 63), we observe the formations of turbulent boundarieslayers around of cylinder. Inside the cylinder wake, the velocities remains weak and the flowis propagated progressively to the linear source of heat direction, located at the position X+ =7. This propagation has a spherical wave form which appear in upstream and downstream 12
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEfrom this linear source of heat. When the flow velocities increase (Re = 126), the vortexestables appears inside the cylinder wake and becomes slightly oscillatory in downstream fromthe linear source of heat, where the smalls vortexes street are beginning to appear.For the middle velocities (Re = 252, and Re = 504), the vortexes numbers are increasing, andthese small vortexes alternated are more than more periodicals. The vortexes tables areincreasing along the longitudinal axis, showing the formation of the Bénard von-Karmanvortex street. a) b) c) d) e) f) Figure 3: Dimensionless velocities iso-values. a) Re = 63, b): Re = 126, c): Re = 252, d): Re = 504, e): Re = 700, f): Re = 900.When the flow velocities are increased (Re = 700 and Re = 900), the coherent structures arebecoming more than more periodicals, because of the concave angle of the boundary layeraround the cylinder walls which decreases. For Re = 700, the periodical removing model ofvortex is changing. The wake symmetry is decreasing with a production of a secondary 13
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEperiodical removing of vortex. For Re = 900, the secondary periodical removing does notappear again inside the vortexes twins. For these two Reynolds numbers, there is a strongapparition of instabilities generating also an oscillatory flow which evolved as small alternatevortexes called Bénard Von-Karman Vortex Street. The thickness of these alternate vortexesis decreasing with their longitudinal propagation. We also noted a net adherence between thecylinder lateral wall and the fluid, because of low values of velocities (blue color zone, U+ =0.0625).The figures 4a and 4b represented the longitudinal variation of dimensionless velocities (U+),near the cylinder, respectively at the positions Y+ = -1, and Y+ = +1, for the differentReynolds number (Re = 63, 126, 252, 504, 700 and 900). We observed a strong augmentationof the velocity which decreased suddenly in the neared cylinder wake. This strong gradient ofvelocity approved the presence of turbulent boundaries layers around the cylinder. Theseprofiles show that the cylinder is an obstacle which generated the instabilities in the flowwhen the velocities are increasing. a) b) Figure 4: Dimensionless longitudinal velocity profiles : a) Y+ = -1.5, b) Y+ = +1.5.III.2 Thermal fieldThe figures 5a, 5b, 5c, 5d, 5e and 5f, represented the flow thermal field, principally the areaof the linear source of heat, for the different Reynolds numbers. When the Reynolds numberis increasing, the heat propagation is decreasing. The heat reached the position (X+, Y+) =(+9, ± 0.25), for Re = 63, while it’s reached a position less than (X+, Y+) = (+8, 0.02), for Re= 900. This give a difference of (∆X+, ∆Y+) = (+1, 0.23), on the thickness of the thermalfield. This strongly diminution shows the incapacity of thermal field to have more resistancewhen the flow becomes more than more turbulent. This means that the Reynolds numbersincreased the passive scalar dispersion in the turbulent flow (Tcheukam-Toko and al., [19]).The figures 6 bellow represented the longitudinal temperature profiles for different Reynoldsnumber at a certain positions around of cylinder. Theses profiles reveals the existence ofsymmetry between the temperatures evolutions with the origin axis Y+ = 0. For the lowReynolds number (Re < 504), the temperature of linear source of heat remains higher along alarge distance, then his value decreased from the position X+ = 16, where it’s not changing,and evolve longitudinally to his minima value. For the higher Reynolds numbers, thetemperature of linear source of heat remains weak and stays minima as from the position X+= 18, where it’s longitudinally evolve. This shows that the passive scalar total dispersion isdeveloping between the position X+ = 7 (linear source of heat position), and the position X+ =20 (from 40 mm of cylinder and from 26 mm of the linear source of heat). For the higherReynolds number, the longitudinal flow is predominating and the linear source of heatremains weak. 14
  8. 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME a) b) c) d) e) f) Figure 5: Dimensionless Temperature Iso-value. a) Re = 63, b): Re = 126, c): Re = 252, d): Re = 504, e): Re = 700, f): Re = 900. 15
  9. 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME a) b) c) d) Figure 6: Dimensionless longitudinal temperature profiles. a): Y+= -1, b) Y+= +1. c) Y+= -1.5, d) Y+= +1.5III.3 Comparison of numerical and experimental results To valid our results, we compared the dimensionless mean temperature gaps profiles( T+), and transversal velocity – temperature correlation profiles (<v’T’>+), with the experimentalresults.The figure 7 bellow, shows that the dimensionless mean temperature gaps profiles are inaccordance with the experimental result when Re = 63. These accordance are more important for∆X+ = 1. The figure 8 shows a similar accordance for the positions ∆X+ = 2, and ∆X+ = 4.The figure 9 shows that the comparison of transversal velocity – temperature correlation profiles(<v’T’>+), with experimental data, is also satisfactory. a) b) Figure 7: Comparison of dimensionless mean temperature gaps profiles numerical and experimental for Re = 63. a): at ∆X+ = 1, b): at ∆X+ = 16. 16
  10. 10. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME ) Figure 8: Comparison of dimensionless mean temperature gaps profiles. Numerical (multicolor) and Experimental (black) umerical Figure 9: Comparison of transversal velocity – temperature correlation profiles (<v’T’> +) for Re = 63: numerical (multi color) and experimental (black on white). :Figure 10: Comparison of transversal flux of heat profiles in function of transversal gradient of mean temperature. –v’+T’+ = f((dT/dY)+), at the position X+ = 9 17
  11. 11. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEThe Richardson number is very low for our all simulations Ri << 1. This means that, theforced convection predominated. Moreover, the dynamic perturbation and the gravity effectsare very low, because of linear source Reynolds number and Ri which are respectively lessthan 1 and 10-3, as approved by Lecordier and al., [5], and Godard and al., [17]. Thecalculated value of Peclet number confirmed that, the heat exchanges are only by convection(Pe >> 1), as in the studies carried out by par Husson, [18].Until present, the existence of counter-gradient zones was, observed in the heated flows,showing the dissymmetry of the velocity and temperature profiles, characterized by aminimum or a maximum (FuIachier and al. [11], Sreenivasan and al. [12], Veeravalli andWarhaft, [2]). The counter-gradient observed when the linear source is placed on thecentral line of the vortex street, shows that, the dissymmetry of the velocity and meantemperature profiles is not his necessary condition of existence. This last is depending atthe same time, of the fluctuations form v/u, of the location of the source of heat, and ofthe thickness of the linear source (Paranthoën and al., [16]). In these conditions, the heatemitted by the source of much localized fashion, undergo a preferential convection inthese two corresponding directions. These shows the presence of a maxima, observed onthe mean temperature profiles which has a symmetry position with the central line. Thiscould not be the same case if the prevision density of dynamic field parameters wereGaussian.The counter-gradient is coming out from a simply situation where the small dimensionsof heated fluid zones (relatively at velocity field scale), are carrying preferentially insome directions different to the principal flow. In this case, the heat flux createddownstream from a linear source and the mean temperature profiles are not stillcompatible with the transit by gradient. This variation can be dissymmetric as in theexperimental works carried out by Veeravalli & Warhaft, [2], or can be symmetry as inthis present numerical work. The necessary condition is that, this variation must bemaximal for one or many values different of zero at the position of air injection.VI. CONCLUSIONS These results reveal that, the stability of wake zone is influenced by the behavior ofthe physicals properties in function of temperature and of the geometry configurationconsidered. In fact, these show that, the thermal field is strongly influenced by the vortexstreet. The diffusion process seems to be in two phases connected to the filling time ofVortexes Street. Moreover, in this case where the mean temperature profiles is generated bythe thermal transfer; we could rather name these counter-gradient zones by “counter-fluxmean temperature profiles”. The different comparisons makes between the numerical andexperimental profiles are satisfactory, but the difference observed, is located at the maximallevel. In perspectives, it would be interesting to associate the heated air jets to this presentstudy, in order to analyze their influence on the stability of thermal and dynamic fields.ACKNOWLEDGEMENT The authors acknowledge the CORIA UMR 6614 CNRS University of Rouen-France,and The University of Ngaoundere, Cameroon. 18
  12. 12. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMENOMENCLATURESmall lettersx longitudinal coordinate (m)y vertical coordinates (m)Capital lettersD Cylinder diameter (m)d source of hat diameter (m)P Pressure (Pa)T Temperature (K)u,v velocities components (m/s)∆Tréf Temperature difference between heat source and the ambient domain (K)0x longitudinal axis0y vertical axisGreek symbolsν Kinetic viscosity of air (m2.s-1)ߤ Dynamic viscosity of air (Pa.s)ߝ Dissipation ratio of the turbulent kinetic energyK Turbulent kinetic energy (J.kg-1)ߩ Volume mass (m3.s-1)No Dimensional numbersRe Reynolds numberܲ‫ݎ‬௧ Turbulent Prandtl numberRes Reynolds number of the linear sourceGrs Grashof number of the heat linear sourceGr Grashof numberσk and σε Turbulent Prandtl number relative to k and ߝExponents, indices and specials characters+ Dimensionless values (with D for the lengths) and (with ∆Tréf for the Temperatures)Cp Thermal capacity at constant pressureߤ௧ Turbulent viscosity‫ܭ‬ Thermal conductivity‫ܭ‬௘௙௙ Effective thermal conductivity൫߬௜௝ ൯ Effective Newtonians tensor of viscous constraints ௘௙௙x relative to the longitudinal componenty relative to the vertical componenteff effectiveܵ௜௝ Stress ratio of mean Tensorߤ௧ Turbulent kinematic viscosity‫ܦ‬௧ Turbulent dynamic viscosityߥ௥௘௙ Referenciel turbulent dynamic viscosityσij Stress tensor 19
  13. 13. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEMEREFERENCES[1] Warhaft, Z., Passive scalars in turbulent flows. Annu. Rev. Fluid Mech., 32, 203. 2000.[2] Veeravalli, S., and Warhaft, Z., Thermal dispersion from a line source in a shearlessturbulence mixing layer, J. Fluid Mech., 216, 35-70. 1990.[3] Le Masson, S., Contrôle de linstabilité de Bénard Von Karman en aval dun obstaclechauffe à faible nombre de Reynolds, Thèse de Doctorat, Université de Rouen, Mont-Saint-Aignan, France. 1991.[4] Brajon-Socolescu, L., Etude numérique de linstabilité de Bénard Von Karman derrière uncylindre chauffé, Thèse de Doctorat, Université du Havre, Le Havre, France. 1996.[5] Lecordier, J-C., Weiss, F., Dumouchel F., et Paranthoën, P., Contrôle de la transition enaval dun obstacle 2D au moyen dune source de chaleur localisée dans son proche sillage,Congrès SFT 97, Toulouse, Ed. Elsevier, 237-242, 1997.[6] Weiss F., Diffusion dun scalaire passif dans le proche sillage dun obstacle, Thèse deDoctorat. U.M.R. 6614 CNRS Université de Rouen, 76821 Mont Saint-Aignan, France, 1999.[7] Paranthoën P., Dumouchel F. , Lecordier J. C., Caractéristiques du champ dynamique delallée de Bénard-Karman en aval dun obstacle bidimensionnel chauffé ou non , UMR CNRS6614, Université de Rouen, 76821 Mont Saint Aignan, France, Congrès de Thermique etenvironnement. 1996.[8] Champigny, J. and Simoneau, J-P., A LES-experiment comparison of mixed-convectionaround a large vertical cylinder, The 12th International Topical Meeting on Nuclear ReactorThermal Hydraulics, France. 2007.[9] Aloui, F., Etude de contrôle des écoulements, Thèse de Doctorat, Université de Toulouse,France, 2010.[10] Crow C.T., Chung J.N. and Troutt, T.R., Particle mixing in free shear flows, Prog.Energy Combust. Sci., 14, 171-194.1988.[11] FuIachier L., Keffer J., and Béguier, C., Production négative de fluctuations turbulentesde température dans le cas dun créneau de chaleur sépanouissant dans une zone de mélange,Comptes rendus Acad. Sciences, B 280, 519-522. 1975.[12] Sreenivasan K.R., Tavoularis S., and Corrsin S., Turbulent transport in passively heatedhomogeneous flows. Third Symposium on Turbulent Shear Flows, Davis. September 9-11.1981.[13] Corsin, S., Limitations of gradient transport models in random walks and in turbulence.Adv. Geophysics, 18A, 25-60. 1974.[14] Fluent 6.3.26, user manual, 2006.[15] Shih T. H., J. Zhu and J. A. Lumley, New Reynolds stress algebraic equation model,Comp. Meth. Appl. Mech. Eng. 125, 1, pp. 287– 302. 1995.[16] Paranthoën P., Godard G., Gonzalez M., Diffusion a contre -gradient en aval d’unesource linéaire de chaleur placée dans une allée de bénard von-karman, XVème CongrèsFrançais de Mécanique, 2001.[17] Godard, G., Diffusion de la chaleur en présence de structures cohérentes, Thèse deDoctorat, Université de Rouen, France. 2001.[18] Husson, S., Simulations des grandes échelles pour les écoulements turbulentsanisothermes. Thèse de Doctorat, Institut National des sciences Appliquées de Lyon (INSA),France, pp. 17-31. 2007.[19] Tcheukam-Toko D, Koueni-Toko, Mouangue R., and Paranthoën P., Modellind andexperimental validation of passive scalar diffusion. Journal of Engineering and appliedSciences, Vol. 7 (5), pp.364-371. 2012. 20
  14. 14. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, Jan - Feb (2013) © IAEME[20] Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation OfEnhancement Of Natural Convection Heat Transfer From Engine Cylinder With PermeableFins” International Journal of Mechanical Engineering & Technology (IJMET), Volume1,Issue1, 2010, pp. 238 - 247, Published by IAEME[21] Cherian Paul and Parvathy Venugopal, “Modelling Of Interfacial Heat TransferCoefficient And Experimental Verification For Gravity Die Casting Of Aluminium Alloys”International Journal of Mechanical Engineering & Technology (IJMET), Volume1, Issue1,2010, pp. 253 - 274, Published by IAEME[22] Kavitha T , Rajendran A , Durairajan A and Shanmugam A, “Heat TransferEnhancement Using Nano Fluids And Innovative Methods - An Overview” InternationalJournal of Mechanical Engineering & Technology (IJMET), Volume3, Issue 2, 2012,pp. 769 - 782, Published by IAEME[23] Er. Pardeep Kumar, Manoj Sain and Shweta Tripathi, “Enhancement Of Heat TransferUsing Wire Coil Insert In Tubes” International Journal of Mechanical Engineering &Technology (IJMET), Volume3, Issue 2, 2012, pp. 796 - 805, Published by IAEME[24] Sunil Jamra, Pravin Kumar Singh and Pankaj Dubey, “Experimental Analysis Of HeatTransfer Enhancementin Circular Double Tube Heat Exchanger Using Inserts” InternationalJournal of Mechanical Engineering & Technology (IJMET), Volume3, Issue 3, 2012,pp. 306 - 314, Published by IAEME[25] Manikandapirapu P.K, Srinivasa G.R, Sudhakar K.G and Madhu D., “ComparativeAnalysis Of Pressure Measurements In Ducted Axial Fan” International Journal ofMechanical Engineering & Technology (IJMET), Volume3, Issue 2, 2012, pp. 85 - 91,Published by IAEME[26] Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation OfEnhancement Of Natural Convection Heat Transfer From Engine Cylinder With PermeableFins” International Journal of Mechanical Engineering & Technology (IJMET), Volume1,Issue1, 2010, pp. 238 - 247, Published by IAEME 21

×