Large Eddy Simulation on Field of Film Cooling with Different Shaped Jet Holes

1、Large Eddy Simulation on Field of Film Cooling with Different Shaped Jet HolesZHANG LingInstitute for Energy and Power Engineering Northeast Dianli University,Jilin 132012, Jilin Province, Chinae-mail:ZWEN Guo-liang Institute for Energy and Power Engineering Northeast Dianli University,Jilin 132012,

2、 Jilin Province, Chinae-mail: AbstractLarge Eddy Simulation was performed to investigate the development process of vortices in different sections of a round-shaped hole and a cone-shaped hole with 30º under the condition of blowing rate M=1.0. The results show that the positive and negative vo

3、rtices in the centre plane and the two wings of the horseshoe vortices in the vertical profiles were shed off new vortices alternately and periodically, the time of shed off of cone-shaped holes was less than the round-shaped holes at the some profile, the acting of jet and cross-flow was more acuit

4、y in the near wall, so carried off more energy, then enhanced the film cooling effectiveness. The counter-rotating vortex plays an important effect on the fields of film cooling. The counter-rotating vortex pair (CVP) of the round-shaped hole is bigger than the cone-shaped holes and the position of

5、the round-shaped holes vortex center is higher than the cone-shaped holes in the same section. The cooling effectiveness of the round- shaped hole is inferior to the cone-shaped holes.Keywords- film coolingt; large eddy simulation; flow field; counter-rotating vortex pairI. IntroductionFilm cooling,

6、 as one of the primary cooling ways of the hot parts of aircraft engines, plays an important role in effectively reducing the turbine blade surface in the temperature and thermal stress. Cool air launch into the mainstream of the boundary layer then the low-temperature film formed on the surface, so

7、 that reduce effectively the thermal load of wall. At present, the film cooling research by domestic and abroad scholars is focused on experimental study and numerical simulation.Experimental investigation is essential to get the film cooling measurements on the surface, it can take various factors

8、effecting flow into account, with the results of objectivity and reliability. Eriksen et al 1 did research about heat transfer coefficient of three-dimensional film cooling of single hole and rows with the method of thermocouple temperature-measuring technology. Results showed that the heat transfer

9、 coefficient of film cooling holes in the downstream was significantly increased than no film. Nasir N and Ekkad S V et al 2,using the thermo-chromic liquid crystal thermometry, researched the heat transfer characteristic of film holes with compound angles, Results showed that compound angle film co

10、oling holes can increase the cooling effect of the downstream holes. Fric 3 and Smith et al4 using visualization technology measured the flow field structure, and the works further revealed the nature of transverse turbulent jet flow field.With the development of computer technology, numerical simul

11、ation has become one the most active research areas to study the flow and heat transfer of film cooling. At present, the turbulence models which are widely used to engineering simulation are two-equations turbulence models, turbulence model was used by Leylek and Zerkle 5 to predict the film cooling

12、 of discrete jet flow. The results showed that normal model with wall function method could describe dissymmetry complicated flow and the temperature distribution of jet flow area, but the calculations of vortexes strength and lateral cooling effects lacked precision. Bohn and Moritz 6 used B-L alge

13、braic model to do numerical calculation in film cooling efficiency of flat surface with interlaced rows, and primarily researched the form and evolvement of adiabatic wall temperature distribution and counter rotating renal vortexes at the downstream of different structure film holes. The calculatio

14、n time of B-L algebraic model is shorter than that of two-equations model, which is different from model. Some last articles indicated that it was satisfactory to use B-L algebraic model to analyze external flow. Large eddy simulation filtered N-S equations with the method of mathematics, and solved

15、 the movement activities of large scale vortexes explicitly. Sub-grid model was used to model small vortex, which enhanced the calculation accuracy on condition of complicated vortex structure and streamline curve detachment. Wegner 7 used LES to research the influences of jet-flows incline angles o

16、n flow distribution, Tyagi and Acharya 8 used LES to calculate the film cooling of square hole, Guo ting-ting used LES to calculate the film cooling of sector hole. The results verified the superiorities of LES on film cooling, showed that the film cooling research by LES had entered the practical s

17、tage.At present, the film cooling studies are focused on the flow and heat transfer characteristics of downstream flow field of circular nozzle. Goldstein et al 9 extend the circular nozzle into a ladder and found the cooling efficiency of single hole and drain holes are both significantly improved.

18、 To be able to select a more reasonable nozzle in practical engineering, in this paper, starting from the vorticity field, large eddy simulation was used to research the vorticity contours distribution characteristic and vorticity distribution changes with time in different sections of transverse tu

19、rbulent jet flow field of flat holes and 30 º fan-shaped holes, and the cooling effects of the two holes were compared and analyzed.II. Physical model and Numerical calculation methodA. Geometry Model and Gridding DivideIn this paper, the computational domain includes two parts: the jet tube an

20、d horizontal main flow channel, defining coordinate origin is the jet pipe axis and the intersection of the head pipe inner wall cylinder. Coordinate system shown in Figure 1, the inner diameter of cylindrical part of film hole is D=0.023m, the length of circular nozzle of film cooling holes is 6D,

21、is the expansion angle of fan-shaped film cooling holes, the length of fan-shaped part and cylindrical part are 2D and 4D. is the average speed of the main flow , is the average speed of the jet flow. In the calculation, selecting Cartesian right hand as the coordinates,-axis is the flow direction,-

22、axis is the spanwise direction,-axis is vertical direction, the average speed in three directions, respectively u, v, w.Fig.1 The models geometry and the coordinate system 2D4DDx0.2 m0.2 mzy0.45 m0.15 mUUjAccording to the characteristics of physical model, as jet nozzle and the underside of cross-fl

23、ow channel have interface, it is difficult to use a set of grid for computing. In this paper, dividing computational domain into some promoter regions, by transfering the interface information of each two parts to achieve coupling, grids are dense near the wall and in the mixing zone of the main flo

24、w and jet flow, the near wall distance of the first grid cell center near the wall meet the conditions of the law of the wall function.B. Numerical Computation Method and Boundary ConditionsIn this paper, Realizablemodel with wall function method of two layer model was adopted to calculate steady st

25、ate. The finite volume method was used to disperse common control equation. The physical quantities of control volume were obtained with the method of second-order upwind differences scheme. SIMPLEC algorithm was used to calculate the velocity-pressure coupling and the steady-state field was regarde

26、d as the initial value of LES calculation. The unchangeable outlet flow rate is the criterion to judge if it had reached quasi-steady-state. After the calculation close to the steady state, using Smagorinsky model of LES, the difference schema for time is second-order upwind differences hidden form.

27、 The calculation time step is 0.002s, the real time of calculation is 2s. Boundary conditions contain the boundary of inlet velocity, the boundary of outlet pressure and the boundary of no-slip wall. is the density of main flow, is the density of jet flow, which , blowing ratio =1.0, the velocity of

28、 main flow is 6.6 m/s, the normal gradient of all the physical quantities is 0.III. Results and DiscussionA. Verification of Calculation ResultFig.2 Cooling effectiveness on the centerline,M=1初始值t=0.10st=0.12s實驗值X/DThe distribution of the cooling efficiency in the bottom center line at blowing ratio

29、 M = 1.0 is showed as the Figure 2, and compared with the experimental values in the same conditions10. From the figure we can see, the initial value of steady state calculation with Realizablemodel and the cooling efficiency calculated by LES when t=0.10s, t=0.12s are coincident to the experiment v

30、alue, and it verified the reliability of calculation by LES. B. Vorticity Distribution of Symmetry PlaneFigure 3 is the vorticity contours distribution of the symmetry plane of circular holes and 30 º fan-shaped holes at different time when M=1, from the figure it can be seen that whatever circ

31、ular holes or fan-shaped holes the vortexes of symmetry plane form, develop and shed periodically. Taking the positive vortex for example, for circular holes, with the development of time, when t = 1.904s the vortex at the end of the main jet increase, when t=1.928s one vortex core forms two cores,

32、and break away from the main part, when t=1.936s a new vortex forms then move to the depth of main flow along the track of jet flow, and the vortex at the end of the main jet increase unceasingly. Downstream of thet=1.904sX/DZ/Dt=1.904sX/DZ/Dt=1.912X/DZ/Dt=1.912sX/DZ/Dt=1.920sX/DZ/Dt=1.920sX/DZ/Dt=1

33、.928sX/DZ/Dt=1.928sX/DZ/Dt=1.936sX/DZ/Dt=1.936X/DZ/Dt=1.968sX/DZ/Dt=1.968X/DZ/D round-shaped hole cone-shaped hole with 30ºFig.3 The contours of vorticity of the centreplaneat different times,M=1.0jet, positive vortex and reverse vortex move to downstream alternately, so it can be inferred: rev

34、erse vortex and positive vortex split into new vortexes alternately. The formation and shedding into a new vortex process of reverse vortex is the same to positive vortex, only the vortex value of reverse vortex is weak. When t=1.920s vortex value is from -470.9 to 1,393.14, which verify the conclus

35、ion.For fan-shaped hole, taking positive vortex for example, when t=1.904s the vortex at the end of the main jet increase, when t=1.920s one vortex core form two cores and the new vortex core break away from the main part gradually, when t=1.928s the new vortex shed completely from main jet and move

36、 to the depth of main flow along the track of jet flow, and the vortex at the end of the main jet increase again. Downstream of the jet, positive vortex and reverse vortex move to downstream alternately.t=1.968X/DZ/D From the figures it can be see, for circular hole, when t=1.904s, t=1.936s and t=1.

37、968s the figures of vorticity contours is similar, and it can be inferred that the vortex formation period of symmetry plane of circular hole is 0.032s. For fan-shaped hole, when t=1.904s and t=1.928s a new vortex increase gradually after a vortex shed from main jet, so it can be inferred that the p

38、eriod is 0.024s. So it can be seen the vortex of symmetry plane of fan-shaped hole shed fast and the period is short. So jet flow and main flow mix more sharply and the heat taken away increase with the mixing, thus the wall temperature is lower, and cooling efficiency is higher.C. Vorticity Distrib

39、ution of Vertical SectionWhen the horizontal main flow encountered in the obstacles of jet flow, the formation of the adverse pressure gradient within the wall boundary layer of the windward side of the jet nozzle upstream and the wall viscous make the flow separated, while the jet flow has entrainm

40、ent effect on the main flow, and making main flow in the boundary layer a vertical upward trend because of the entrainment. In the joint action of the two factors, horseshoe vortex formed in the jet nozzle upstream as the Figure 4 shown.Figure 4 is the vorticity contours of circular hole and fan-sha

41、ped hole at different time where M=1and Z/D=0.5, from the figure it can be seen for circular hole, the wings of horseshoe vortex is growing up from the moment of t=1.904s, the new eddy generated by reverse vortex has been broken away from the noumenon at the moment of t=1.944s, positive vortex didnt

42、 shed completely until the moment of t=1.952s, the wings of horseshoe vortex is growing up again, That is, the wings didnt break away from horseshoe vortex at the same. When t=1.904s and t=1.952s the vorticity contours is similar, so the period is 0.048s.For fan-shaped hole, from the figure it can b

43、e seen the formation and shedding of vortex are regular. With the development of time, when t=1.904s reverse vortex begin to increase gradually, and begin to shed when t=1.928s. When t=1.936s a new vortex increase gradually after a vortex shed t=1.928sX/DY/Dt=1.944sX/DY/Dt=1.920sX/DY/Dt=1.936sX/DY/D

44、t=1.952sX/DY/Dt=1.904sX/DY/Dt=1.904sX/DY/Dt=1.920sY/DX/Dt=1.928sY/DX/Dt=1.936sY/DX/Dt=1.944sY/DX/Dt=1.952sY/DX/Dround-shaped hole cone-shaped hole with 30ºFig.4 The contours of vorticitye at different times, Z/D=0.5,M=1.0from main jet, so the generation period of the reverse vortex is 0.032s. W

45、hen t=1.920s positive vortex begin to increase gradually, and begin to shed when t=1.944s. When t=1.952s a new vortex increase gradually after a vortex shed from main jet, so the generation period of the positive vortex is 0.032s too.Under the same conditions by comparing the vortex generation proce

46、ss where Z/D=0.5 can be seen that one period of circular hole is 0.048s and one period of fan-shaped hole is 0.032s. So comparing circular hole with 30ºfan-shaped hole, the vortex of fan-shaped hole shed fast and the period is short, it takes away more heat and cooling efficiency is higher.D. V

47、orticity Distribution of Longitudinal SectionFigure 5 is the vorticity isoline distribution of each longitudinal section of circular hole and fan-shaped hole. From the figure it can be seen: LES model was used to get a non-symmetric counter-rotating asymmetric shape vortex (CVP), CVP is the shear la

48、yer vortex formed on jet laterally mixed layer, it formed on near field and consist in the jet inside of far field and develop to downstream following the jet flow.For circular hole, when 0.5<X/D<2, the vorticity of CVP decay gradually, when X/D>3, the vorticity increase but no regular, Sep

49、arated vortex move up along the vertical direction , then enter into and mix with main jet to form reverse vortex pair within the main part, In addition, part of the wake vortex have been sucked into the jet inside. When X/D>5, CVP began to disappear gradually, main flow and jet flow mixed evenly

50、 For fan-shaped hole, when 1<X/D<2 the vorticity of CVP decay gradually, in other positions the vorticity increase but no regular, when X/D>4, CVP began to disappear gradually, it indicate that the vorticity field of fan-shaped hole is more unstable, leading to large energy losses near the

51、wall.The figure also shows that the CVP of circular hole is large than fan-shaped hole in the same cross-section, and the position of vortex core of circular hole is higher than fan-shaped hole. It indicate that at the same blowing ratio the cold air of circular hole spread obviously on both side wh

52、en move to downstream, its jet trajectory is far away from the wall, the strong CVP bring both side of the hot air into the center of cold air, so the cooling efficiency on the bottom is weaker than the fan-shaped hole.IV. ConclusionLES was used to simulate the changes of vorticity field with differ

53、ent time of circular hole and fan-shaped hole at the angle of 30º. Conclusion as followed:Y/DX/D=3Z/DY/DX/D=4Z/DY/DX/D=5Z/DX/D=0.5Z/DY/DX/D=1Z/DY/DX/D=2Z/DY/DX/D=0.5Z/DY/DX/D=1Z/DY/DX/D=2Z/DY/DX/D=3Z/DY/DX/D=4Z/DY/DX/D=5Z/DY/D round-shaped hole cone-shaped hole with 30ºFig.5 The contours o

54、f vorticity at different profiles. M=1.0,t=1.904 s1）The positive vortex, reverse vortex and the wings of horseshoe vortex of vertical section shed alternately and periodically, and form new vortexes.2）By comparing symmetry plane and vertical plane it can be found that: the vortex of fan-shaped hole

55、sheds faster than circular hole and the period is shorter. So jet flow and main flow mix more sharply and the heat taken away increase with the mixing, and cooling efficiency is higher.3）By comparing the vorticity isoline figures of flow cross-section at different time, the CVP of circular hole is large than fan-shape