Patent Application: US-97501207-A

Abstract:
a system for cooling includes a surface to be cooled , at least one film - cooling hole within the surface for allowing a film cooling jet of coolant to reach the surface , each of the at least one film - cooling hole having a diameter and at least two spaced apart flow - aligned blockers positioned downstream of the at least one - film cooling hole , each of the flow - aligned blockers extending upwardly from the surface to assist in preventing hot - gas entrainment and increasing adiabatic effectiveness by confining coolant flow downstream of the at least one film - cooling hole between the blockers .

Description:
the present invention uses flow - aligned blockers to minimize the entrainment of hot gases by the crvs so that film - cooling effectiveness improves without unduly increasing surface heat transfer and pressure loss . since extended surfaces can increase surface heat transfer and this is undesirable on the hot - gas side , it is noted that the blockers can be constructed in the thermal - barrier coating ( tbc ) system by using the ceramic top coat , which has very low thermal conductivity ( private communication with bunker ( 2002 )). the objective of this study is twofold . the first is to assess the usefulness of the “ blocker ” concept in improving the adiabatic effectiveness of film - cooling jets , to examine the nature of the flow induced by the blockers , and to show how they minimize hot - gas entrainment . the second objective is to perform a parametric study to examine the effects of design parameters for a generic blocker . this study will be accomplished by using computational fluid dynamics ( cfd ) analysis that accounts for the three - dimensional nature of the flow and resolves the hot gas and film - cooling jet interactions above the plate as well as the flow in the plenum and in the film - cooling holes . to demonstrate the usefulness of flow - aligned blockers to improve film - cooling effectiveness , the problem of film - cooling of a flat plate from a row of inclined circular holes is studied . the problem selected is similar to the experimental study of kohli & amp ; bogard ( 1995 ) so that the meaningfulness of this computational study can be assessed by comparing the cfd predictions with the measurements . fig1 illustrates one embodiment of flow - aligned blockers . a system 10 is shown in fig1 , the system 10 may be associated with a gas turbine . a plate 12 is shown which has a hole 14 . downstream of the hole 14 are flow - aligned blockers 20 , 22 which are spaced apart by a spacing 24 . the flow - aligned blockers 20 , 22 have a height 26 . the flow - aligned blockers are positioned a distance 28 from the hole 14 in the surface 12 . coolant flows to the hole 14 through the tube 16 from a plenum 18 . for the problem studied , as shown in fig2 , the cooling jets emerge from a plenum through one row of circular holes . each hole has a diameter d of 12 . 7 mm , a length of 3 . 5d , and an inclination of 35 ° relative to the flat plate . the spacing between the centers of the film - cooling holes in the spanwise direction is 3d . since the film cooling is for a flat plate in which the cooling jet emerges from a row of inclined holes , the flow - aligned blockers are taken to be pairs of parallel ribs or fence - like protrusions from the flat plate with rectangular cross sections as shown in fig1 and 3 . these “ rectangular prism ” blockers are located 1d downstream of the film - cooling hole . each blocker has height b and thickness c , and separated by a distance a . three values of a , b , and c were examined , and they are as follows : 0 . 8d , d , and 1 . 2d for the spacing a ; 0 . 2d , 0 . 4d , and 0 . 6d for the height b ; and d / 20 , d / 10 /, and d / 5 for the thickness c . other dimensions that describe the geometry are given in fig1 to 3 . the operating conditions are as follows . the fluid for the main flow ( hot gas ) and coolant is air . the main flow above the flat plate has a freestream temperature t 8 of 298 k and a freestream velocity u 8 of 20 m / s along the x - direction . the flow in the boundary - layer is assumed to be turbulent from the leading edge of the flat plate . the coolant has a temperature t c of 188 k in the plenum . this gives a density ratio dr of 1 . 6 . when the average velocity in the film - cooling holes u c is 6 . 25 m / s , the mass flux or blowing ratio m is 0 . 5 . two other blowing ratios were also studied , 0 . 37 and 0 . 65 , by varying the velocity at the inflow of the plenum that feeds the film cooling holes . two types of boundary conditions were applied on the flat plate for the heat transfer study . when the film - cooling adiabatic effectiveness is sought , the flat plate is made adiabatic . when the surface heat transfer coefficient is sought , the flat plate is maintained at a constant wall temperature t w of 243k . all other walls , including the walls of the film - cooling holes and the plenum , are made adiabatic . the back pressure at the outflow boundary above the flat plate is maintained at the standard atmospheric pressure . for this problem , the computational domain is taken to be the region bounded by the solid lines shown in fig2 . as can be seen , periodicity is assumed in the spanwise direction so that only one film - cooling hole and one pair of blockers need to be examined . in addition , the “ upper channel wall ” ( i . e ., the wall without film - cooling holes ) was moved closer to the wall with the film - cooling holes . this was done to reduce the size of the computational domain and hence computational cost . the errors incurred by this are minimized by making the “ upper channel wall ” sufficiently far away and by making it inviscid ( i . e ., the velocity there can slip despite the viscous nature of the flow ) so that boundary layers will not form there . the problem just described was modeled by the ensemble - averaged continuity , momentum ( full compressible navier - stokes ), and energy equations for a thermally and calorically perfect gas . the effects of turbulence were modeled by using the two - equation realizable k - e model ( shih et al ., 1995 ). in all cases , the integration of all equations is to the wall ( i . e ., wall functions are not used ). solutions to the aforementioned governing equations were obtained by using version 6 . 1 . 18 of the fluent - uns code . the following algorithms in fluent were invoked . since only steady - state solutions were of interest , the simple algorithm was used . the fluxes at the cell faces representing advection were interpolated by using second - order upwind differences . the fluxes at the cell faces representing diffusion were interpolated by using second - order central differences . for all computations , iterations were continued until all residuals for all equations plateau to ensure convergence to steady - state has been reached . at convergence , the scaled residuals were always less than 10 − 6 for the continuity equation , less than 10 − 6 for the three components of the velocity , less than 10 − 8 for the energy equation and , and less than 10 − 5 for the turbulence quantities . accuracy of solutions is strongly dependent upon the quality of the grid system in minimizing grid - induced errors and in resolving the relevant flow physics . in this study , a grid sensitivity study was carried out to determine the appropriate grid . fig4 illustrates this study for the case without blockers , which involved three grids — the baseline grid with 2 . 291 million cells , a finer grid with 2 . 716 million cells ( adaptation 1 ), and a still finer grid with 5 . 252 million cells ( adaptation 2 ). for the two finer grids , the additional cells were all concentrated about the film - cooling hole and the hot gas / coolant jet interaction region , where the flow physics is most complicated . from this grid sensitivity study , the baseline grid was found to give essentially the same result for the centerline adiabatic effectiveness as those from adaptation 1 and 2 grids . the relative error in the “ average ” centerline adiabatic effectiveness is 0 . 4 % when comparing results from the baseline grid with those from the adaptation 2 grid . the grid systems used for this problem with and without blockers are shown in fig5 . when there are no blockers , the grid system used employ 2 . 291 million cells . when there are blockers , the grid systems used has cells that varied from 2 . 412 million to 2 . 478 million depending upon the height and thickness of each blocker . fig9 shows the equiangle skewness is almost closed to 0 . 1 and less than 0 . 6 in the histogram . for all grids used , the first grid point away from all viscous walls has a y + less than unity . fig1 shows y + values are less than unity at the first grid point from the wall . also , the first 5 grid points have y + values within five . the surface effectivenesses with h - refined grid are shown in fig1 . fig1 shows the computed surface effectiveness at 3d downstream of the exit hole and along the centerline , and the calculations for different grids match well . to assess the meaningfulness of this computational study , the grid - independent solutions generated for the problem of film - cooling over a flat plate were compared with the experimental data provided by kohli & amp ; bogard ( 1995 ) for l / d = 2 . 8 . at the leading edge of the film - cooling hole , the computations predicted a boundary - layer thickness of 0 . 14d , a shape factor of 1 . 49 , and a reynolds number based on the freestream velocity and momentum thickness of 1 , 492 . the corresponding measured values are 0 . 12d , 1 . 48 , and 1 , 100 , respectively . this comparison shows that the flow upstream of the film - cooling hole is predicted reasonably well . results for the predicted adiabatic effectiveness are shown in fig6 along with experimentally measured ones . from this figure , it can be seen that the centerline adiabatic effectiveness is over predicted and that the laterally averaged adiabatic effectiveness is under predicted . this indicates that the realizable k - e model over predicts normal spreading and under predicts lateral spreading of the cooling jet . despite this , the trends are predicted correctly . also , the qualitative features of the flow are captured by the computations . thus , though the predictions are not accurate quantitatively , they are good enough to discern differences in film - cooling designs . as will be shown , the proposed flow - aligned blockers do indeed greatly improve film - cooling adiabatic effectiveness without unduly increasing surface heat transfer or pressure rise . instead of showing this for one configuration , the results will be presented in the following order . first , a parametric study that uses the taguchi &# 39 ; s design of experiments ( taguchi , 1978 ) is described from which an “ optimal ” blocker design is identified . then , the nature of the flow field induced by blockers is given for this optimal design . here , optimal is used loosely since the blocker design considered is confined to be a rectangular prism . a parametric study via taguchi &# 39 ; s design of experiments for the rectangular - prism blockers shown in fig3 . the effects of the following three design parameters are sought : 0 . 8d , d , and 1 . 2d for the spacing between blockers a ; 0 . 2d , 0 . 4d , and 0 . 6d for the height of the blockers b ; and d / 20 , d / 10 /, and d / 5 for the thickness of the blockers c . if a full factorial study is to be performed ( i . e ., one parameter is varied at a time ) to assess the effects of the three parameters at the three levels , then a total of 3 3 or 27 simulations will be needed . to reduce the number of simulations needed , the taguchi fractional factorial ( taguchi , 1978 ; dehnad , 1990 ) is employed , where the number of simulations can be reduced to six . these six simulations are summarized in table 1 . the results of the simulations summarized in table 1 for the adiabatic effectiveness are given in fig7 to 8 . fig7 gives the average adiabatic effectiveness . from this figure , it can be seen that the averaged adiabatic effectiveness is highest when a = a2 = d , b = b3 = 0 . 6d , and c = c3 = d / 5 , which corresponds to run number 3 in table 1 . thus , for the range of the parameters studied , the optimal design has the pair of rectangular prism blockers to be spaced d apart and that each blocker should have a height of 0 . 6d and a thickness of d / 5 . fig7 also shows that d may indeed be near optimum for the spacing between the blockers . however , optimum values for the height and thickness of the blocker remain unclear since the effects of these two parameters remained monotonic in the range studied . it is anticipated that the optimal height is related to the blowing ratio , and the optimal thickness of each blocker is related to the spacing between film - cooling holes since there is a region between film - cooling holes that are unprotected by film cooling . thus , a true optimal design even for the simple configuration considered here requires further study . fig8 and 9 show the computed surface - adiabatic effectiveness . fig8 shows the centerline and the laterally averaged adiabatic effectiveness for all six runs in table 1 as a function of x / d . from this figure , it can readily be seen that all “ blockers ” investigated greatly improve laterally averaged adiabatic effectiveness . for the “ optimal ” case studied ( run 3 ), fig8 ( c ) shows the blockers to maintain the laterally averaged adiabatic effectiveness at nearly the highest levels from d to 15d downstream of the film - cooling hole . at 15d downstream of the film - cooling hole , blockers improved laterally averaged adiabatic effectiveness by about a factor of two , which is quite significant . fig9 shows the surface adiabatic effectiveness as a function of y / d at x / d = 3 . from this figure , it can be seen that though the blockers may cause parts of the flat plate from being inadequately cooled , this is not the case . in fact , with the blockers , the adiabatic effectiveness is improved in all regions . one reason is that a part of the film - cooling jet is split by the blocker . thus , fig8 and 12 show flow - aligned blockers to be useful in improving film cooling effectiveness . fig1 shows the predicted surface heat transfer coefficient on the flat plate without blockers and with the optimal blocker ( run 3 configuration ). the heat transfer coefficients were computed in three steps . first , simulations were performed with adiabatic walls to obtain the adiabatic surface temperature on the flat plate , t aw . next , computations were performed for the same configuration and operating conditions except the flat plate is maintained at a constant wall temperature t w of 243k to predict surface heat transfer per unit area , q w . then , the heat transfer coefficient h is computed by q w /( t w − t aw ). from fig1 , it can be seen that the blockers increase surface heat transfer slightly near its leading - edge , but reduces surface heat transfer downstream of the blockers . the slight increase in surface heat transfer at the leading edge of the blocker may not be significant since the adiabatic effectiveness is high there . the reduced surface heat transfer downstream of the blockers resulted from reduced temperature gradients that arose from less hot gas entrainment . the average heat transfer rate per unit area for the entire flat plate with and without rectangular - prism blockers is − 781 . 34 w / m 2 , and − 1094 . 70 w / m 2 , respectively . the average heat transfer coefficient with and without rectangular - prism blockers is 24 . 40 w / m 2 - k and 25 . 02 w / m 2 - k , respectively . thus , in general the blockers studies were found to reduce surface heat transfer instead of increasing them . this also means that the extended surface due to blockers may not be a concern . though surface heat transfer was not increased by the blockers , computed results show that there is non - negligible pressure rise . when there are no blockers , the average pressure drop from the inflow to the outflow boundary above the flat plate is 10 . 66 pa . when there are rectangular blockers , it increases to 16 . 07 pa . this represents an increase of 5 . 41 pa or 51 %, which is considerable . the magnitude of the average shear stress for the flat plate without blockers is 1 . 14 pa . the magnitude of the average shear stress for the case with blockers that include the shear stress on the flat plate and on the blockers is 0 . 95 pa . this indicates the rise in pressure loss from the blockers is due to pressure of the leading and trailing edges instead of from shear . thus , one way to reduce this pressure rise is to streamline the leading and the trailing edges . for example , instead of the flat leading and trailing faces as shown in fig1 and 3 , they can be rounded at the leading edge and pointed at the trailing edge , similar to that of an airfoil . with an “ optimal ” blocker design identified from the range of the design parameters investigated , this section examines how this blocker ( a = d , b = 0 . 6d , and c = d / 5 ) minimizes hot gas entrainment and thereby increase film - cooling adiabatic effectiveness . fig1 shows normalized temperature ( t 8 − t )/( t 8 − t c ) at two y - z planes , one located at x / d = 3 and one at x / d = 7 in which the blowing ratio is m = 0 . 5 with and without blockers . from this figure , it can be seen that the two blockers confine the cooling flow within it and prevents the entrainment of hot gases . by x / d = 7 , the coolant is fairly well mixed along the spanwise y direction so that the temperature variation is mostly along z . since the blockers are placed d downstream of the film - cooling - hole exit , the cooling flow also wraps around the “ outer ” sides of the blockers . thus , cooling extends beyond the blockers by as much as 0 . 2d beyond the blockers . this , of course , improved the film - cooling effectiveness outside of the blockers as shown in fig1 . to further examine the usefulness of this blocker , simulations were done with slightly lower and slightly higher blowing ratios for the same blocker geometry ( run 3 ). results of these simulations are shown in fig1 and 16 . in these two figures , it can be seen that even with a blowing ratio of m = 0 . 37 , laterally averaged adiabatic effectiveness is still quite respectable when there are blockers . with a lower blowing ratio , the cooling flow rate is less and so the wrap - around about the blockers is reduced . when the blowing ratio increases to m = 0 . 65 , the laterally averaged adiabatic effectiveness improves further . with higher blowing ratio , more of the coolant spills over and around the blockers . the present invention provides for “ flow - aligned blockers ” to increase the adiabatic effectiveness of film - cooling jets by minimizing hot - gas entrainment without unduly increasing surface heat transfer and pressure loss . numerical simulations based on the compressible navier - stokes equations were performed to investigate the usefulness of a blocker geometry that has a rectangular cross section . a parametric study based on the taguchi &# 39 ; s method was used to examine the effects of three parameters : spacing between blockers , height of blockers , and the thickness of each blocker . a limited study on the effects of blowing ratio was also carried out . results obtained show that the blockers studied are highly effective in preventing hot - gas entrainment and can increase adiabatic effectiveness significantly by confining the coolant flow between the blockers . for the blockers studied , the laterally averaged adiabatic effectiveness at 15d downstream of the film - cooling hole can be as high as that at 1d downstream . the blockers studied were found to increase surface heat transfer only slightly in the region about the leading edge of the blockers . downstream of the blockers , surface heat transfer was reduced . there is , however , some rise in pressure loss because of the flat leading and trailing edges , indicating a need for streamlining there . it is to be appreciated that although the embodiment described generally relate to use in a gas turbine , the present invention can be used in other appropriate applications . it is to be understood that the present invention contemplates numerous variations , including variations in the geometry of blockers , the position of the blockers , the type of hot gas , the type of coolant , the number of film - cooling holes , the arrangement of film - cooling holes whether in a row , pattern , or otherwise , variations in blowing ratio , and other variations . bunker , r . s . 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