Influence of leading-edge lateral injection angles on the film coolingeffectiveness of a gas turbine blade

Abbes Azzi, Bassam Ali Jubran

Abstract Typical film-cooling configuration of a sym-metrical turbine blade leading edge is investigated using athree-dimensional finite volume method and a multi-blocktechnique. The computational domain includes the curvedblade surface as well as the coolant regions and the ple-num. The turbulence is approximated by a two layer k–emodel. The computations have been performed using theTLV two-layer and the TLVA models. However, the utili-zation of the TLV and TLVA models has not improved theprediction of the lateral averaged film cooling effectivenessof gas turbine blades when compared with those obtainedusing wall function strategy.

The general features of film cooling such as jet blow-off,high turbulence intensity in the shear layer, and secondaryrotating vortices are captured in the present study. Com-parison between predicted and experimental results indi-cates that the trends of the thermal field are well predictedin most cases. In the second part of this study, the influ-ence of lateral injection angle on lateral averaged adiabaticfilm cooling effectiveness is investigated by varying thelateral injection angle around the experimental value (b =25�, 30�, 35� and 60� spanwise to the blade surface). It wasfound that the best coverage and consequently, the maxi-mum film cooling effectiveness are provided by the mostextremely inclined injection angle, which is 25� in thisinvestigation.

Keywords Film cooling, Leading edge injection,Navier-Stokes equations, Two-layer k–e turbulence model

1IntroductionThe stagnation region near the leading edge of a gas tur-bine blade is highly exposed to the hot free stream gases

and it is considered to be the most critical part in the bladewhere advanced stagnation cooling techniques such asshowerhead film cooling injections are applied. Compar-ing to the flat plate injection, the stagnation film cooling ismore complex due to additional effects of thin boundarylayer, high acceleration, and nearly opposite coolantdirection to the main stream. In order to understand thecomplex phenomenon related to leading edge film cooling,Salcudean et al. [1] conducted an experimental investiga-tion using the UCB model, which is a flat-sided with acircular leading edge and four laterally inclined rows offilm cooling orifices positioned symmetrically around thestagnation line.

The experimental blade model, UBC reported bySalcudean et al. [1] had a semicircular leading edgediameter of 17 mm, spanwise top and bottom lengths of1.2 m (between fences), and an overall chordwise lengthof 2.3 m. Coolant was injected through four rows oforifices inclined at 30� to a spanwise line on the cylin-drical leading edge. These four rows of orifices werelocated symmetrically at ±150 and ±440 with respect tothe stagnation line. Each injection tube had a diameter dof 12.7 mm and each row had orifices whose spanwisespacing was 4 d.

With the same objective, Azzi and Abidat [2] con-ducted a numerical simulation on a nearly identicalconfiguration to that used by Salcudean et al. [1]. Nev-ertheless, the holes were simply perpendicular to theblade surface and the rows were positioned at ±22.5� and±67.5� instead ±15� and ±44� spanwise to the bladesurface. The study was conducted to investigate theinfluence of injection hole position and blowing ratios onfilm cooling of the blade. It was found that while at lowblowing ratio case (M = 0.52), the film cooling effec-tiveness was reasonably predicted, the prediction was notwell for the high blowing ratio case (M = 0.97) dueprobably to the use of wall function when applying wallboundary conditions. It was found out from our previousexperience in predicting film cooling from variousinjection configurations [3–5], that a good numericalprediction must resolve the near wall region where mostimportant phenomenon occur and at the same time donot use bridging techniques like the wall function, spe-cially for high blowing ratio cases. That is why in thepresent study more sophisticated near wall techniques areused and the computational domain is extended to in-clude the plenum supply. The position and the angle ofthe injection holes are also modified to match exactly theexperimental work of Salcudean et al. [1]. The rows are

Heat and Mass Transfer 40 (2004) 501–508

DOI 10.1007/s00231-003-0457-5

501

Received: 3 June 2002Published online: 31 July 2003� Springer-Verlag 2003

A. AzziUniversite des Sciences et de la Technologie d’Oran,Faculte de Mecanique, Departement de Genie-Maritime,B.P. 1505 El’mnaouar, Oran, Algerie

B. Ali Jubran (&)Sultan Qaboos University,Department of Mechanical and Industrial Engineering,P.O. Box 33, Muscate, Sultante of OmanE-mail: bassamj@squ.edu.om

positioned at ± 15� and ±44� to the stagnation line, andthe lateral injection is fixed at 30�. In the second partof the present paper an investigation is conducted tostudy the lateral angle injection influence on film coolingeffectiveness of the blade. The lateral injection anglestested are 25�, 30�, 35� and 60� respectively.

The notable features of the present study are:

– Fully coupled and elliptic computation of flow inplenum, film-holes, and cross-stream region of astagnation film-cooling situation.

– Exact representation of inclined, round film-holegeometry and plenum.

– Multi-block structured strategy, which reduces signifi-cantly the core memory needed for the computationsand gives more freedom in the generation of the grids.

– A second-order accurate bounded scheme for convec-tive terms, which allows grid independence for rela-tively small numbers of nodes.

– Near wall turbulence modelling using a two-layermodel based on DNS data.

2The three-dimensional Navier-Stokes modelThe mathematical model is composed by the steady-state,three-dimensional, incompressible Reynolds AveragedNavier Stokes (RANS) Equations, the Energy Equation anda modified version of the k–e turbulence model (Azzi andLakehal [5]).

2.1The two-layer DNS-based k–e turbulence model (TLV)The two-layer approach represents an intermediate mod-eling strategy between wall functions and pure low-Renumber models. It consists of resolving the viscosity-affected regions close to walls with a one-equation model,while the outer core flow is treated with the standard k–emodel. In the outer core flow, the isotropic eddy viscosityis proportional to the turbulent kinetic energy k and a timescale (k/e)

mt ¼ Clk2=e ð1Þ

Where, e represents the rate of dissipation of k, and Cl

stands for a model constant. The distributions of k and eare determined from the conventional model transportequations, and standard values of constants. In the one-equation model, the eddy viscosity is made proportional toa velocity scale determined by resolving the k-equation,and a length scale ll prescribed algebraically. The dissi-pation rate e is related to the same velocity scale and adissipation length scale le, also prescribed algebraically.Such models have the advantage of requiring considerablyfewer grid points in the viscous sublayer than any purelow-Re scheme, and are, therefore, more suitable forcomplex situations involving more than one wall. Also,because of the fixed length-scale distribution near the wall,these models have been found to give better predictionsfor adverse pressure gradient boundary layers than purek–e models.

The present version of the two-layer model is in essencea re-formulation of the so-called ð�vv2Þvelocity-scale-based

model (TLV) of Rodi et al. [6], in the sense that k1/2 is nowre-incorporated as a velocity scale to conform to the TLKmodel, instead of

ffiffiffiffiffi

�vv2p

whereas ll and le are re-scaled onthe basis of the same (Direct Numerical Simulation) DNSdata of Kim et al. [7]

lt ¼ qClk1=2ll; e ¼ k3=2=le ð2Þ

ll ¼ jyC�3=4l fl; le ¼

jC�3=4l y

2þ 17:29= RyjC�3=4l fl

� � ð3Þ

where j = 0.42 and Cl = 0.082. The near-wall dampingfunction fl is determined by the following DNS-basedrelation:

fl ¼1

32

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0:116� R2y þ Ry

q

; Ry ¼ffiffiffi

kp

yn=m ð4Þ

The outer and the near-wall model are matched at thelocation where viscous effects become negligible i.e., fl �0.9. More details can be found in the previous paper(Azzi and Lakehal 2002), where the model is tested andcompared to other models for calculating the fully tur-bulent channel flow and found to provide the best resultscomparing to DNS data. The so-called TLVA model,which is a DNS-Based anisotropic one-equation model, isalso tested in the present investigation (Azzi and Lakehal[5]).

2.2Numerical procedureThe numerical procedure used to calculate the test case isbased on a finite-volume approach for implicitly solvingthe incompressible averaged Navier-Stokes equations onmulti-block arbitrary non-orthogonal grids, employing acell-centered grid arrangement. The momentum-interpolation technique of Rhie and Chow [8] is used toprevent pressure-field oscillations and the pressure-velocity coupling is achieved using the SIMPLECalgorithm of Van Doormal and Raithby [9]. The resultingsystem of the algebraic difference equations is solved usingthe Strongly Implicit Procedure (SIP) of Stone [10]. Theconvection fluxes are approximated by a second-order

Fig. 1. Computational domain and boundary conditions

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bounded scheme, namely the MUSCL (MonotonicUpstream Scheme for Conservation Laws) of van Leer(Leonard [11]).

2.3Boundary conditionsFigure 1 shows the computational domain used in thisstudy, which reproduces the exact test facility of thebenchmarking-experimental case including the plenum,film-holes, and the cross-stream region.

The mass flux ratio which is defined as (M = qcUc/q¥U¥) was matched with the experimental values (0.52and 0.97 respectively), where the density ratio is kept equalto unity.

Boundary conditions are prescribed at all boundaries ofthe computational domain. The inlet position of themainstream is located at a distance 20 d from the leadingedge where all the dependent variables are prescribed tomatch the experimental values. The mainstream flowvelocity is taken as U¥ = 10 m/s. The turbulence intensityis assigned a value of 2% and the turbulence dissipation iscalculated based on a turbulent viscosity equal 20 timesthe laminar viscosity. No-slip, adiabatic boundaries andk = 0 were used on all wall surfaces.

The stagnation line at the bottom of the main flowregion is treated as symmetry plane and periodicconditions are used on the boundaries in the spanwisedirection. The top boundary is located 25 d from thestagnation line and assumed as symmetry plane. Theoutflow boundary is located at a distance 30 d downstreamfrom semi-cylindrical leading edge where a zero-gradientis imposed for all dependent variables.

Fig. 2. Close-up of the computational grid (b = 30�) (a) Measuredvalues, Salcudean et al. [1]. (b) Computed contours

Fig. 3. Contours of film cooling effectiveness for (b = 30�) at the blade surface

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2.4Grid meshThe quality of a computational solution is strongly linkedto the quality of the grid mesh. So a highly orthogonal-ized, nonuniform, multi-block fine grid mesh was gen-erated with grid nodes considerably refined in the near-wall region and in the inlet and the exit hole vicinity. Thenormalized y+ values at the near wall node are kept al-ways smaller than 1.0, and care is taken so that thestretching factors are kept close to unity. Figure 2 showsa close picture of the grid near the leading edge, which iscomposed by a total of 220440 grid nodes disposed on aglobal array 167 · 60 · 22 nodes in x, y, and z directions.The grid generated is composed of five blocks, which arethe domain over the blade, two half-injection tubes infirst row, the injection tube in the second row and theplenum. The multi-block grid method used in this study

reduces significantly the number of inactive nodes andallow the combination of C and H grids for differentregions.

3Results and discussion

3.1(a) Validation (M = 0.52 and M = 0.97, b = 30�)Figure 3(a) shows the measured film cooling effectivenesscontours on the blade surface for M = 0.52 and M = 0.97for lateral injection (b = 30�) [1], while Figure 3(b) showsthe present predicted contours. The agreement betweenthe measured and the computed contours is good, andnearly of the same shapes and magnitudes especially forlow blowing ratio. Physically, it can be seen that theblowing ratio M = 0.52 provides a good coverage of the

Fig. 4. Lateral averaged adia-batic film cooling effectiveness,b = 30�. (a) (xy-plane) throughthe centerline of first row (15�).(b) (xy-plane) through thecenterline of second row (44�)

Fig. 5. Local effectiveness at the streamwise planes, (M = 0.52 and M = 0.97, beta = 30�). (a) (xy-plane) through the centerline of firstrow (15�). (b) (xy-plane) through the centerline of second row (44�)

504

blade surface, since the coolant from the first row of ori-fices spread between the cooling orifices of the second row.A similar observation was made in the experiments ofSalcudean et al. [1]. From physical point of view when

using the high blowing ratio, the coolant from the first rowof orifices is recovering the orifices of the second rowwhile a large region of the blade surface is leaved withoutprotection.

Fig. 6. Turbulence intensity in percent at the streamwise planes, (b = 30�). (a) (xy-plane) through the centerline of first row (15�). (b)(xy-plane) through the centerline of second row (44�)

Fig. 7. Velocity field at the streamwiseplanes, (b = 30�). (a) b = 25� (b) b = 35�(c) b = 60�

505

Figure 4 shows the lateral averaged adiabatic filmcooling effectiveness compared with measurements valuesof Salcudean et al. [1] for the low blowing ratio M = 0.52and M = 0.97. The x-axis presents the curve distance fromthe stagnation line and the y-axis presents the laterallyaveraged film cooling effectiveness. We can see that for thetwo cases there is a heavy over prediction while the trendis satisfactory reproduced. It is clear from the figure, that

the coolant injection is responsible for the formation of aturbulent boundary layer, which relaminarize after theinjection positions. It is worth pinting out that the resultfor the high blowing ratio is not as pronounced as it wasfound when applying the wall function strategy (result notpresented here). Results with the TLVA model are alsocompared in the same figure and seems to be not veryhelpful in the present case as it was for the flat plate filmcooling (Azzi and Lakehal [5]). This behavior was nearlyexpected because previous tests of such correction appliedwith wall function strategy (Theodoridis et al. [12]) had nobeneficial effect on the suction side with concave walls.

Figure 5(a) presents the predicted film cooling effec-tiveness in the xy-plane through the centerline of theinjection orifice at the first row for M = 0.52 and M = 0.97while the effectiveness at the second row is presented onthe Figure 5(b). It can be seen that for M = 0.52 the coolantis more attached to the wall and does not penetrate intothe mainstream flow. That is why a low mass flow ratioproduces higher film cooling effectiveness than highblowing ratio where the coolant penetrates deeply into themainstream flow. Figures 6(a and b) present turbulenceintensity in similar ways, while Figures 7(a and b) showthe flow field. It can be seen that the turbulence is mainlyproduced into the injection tube itself and downstream ofthe orifices. The plenum-hole interactions are clearlyshown by the velocity profiles and as expected the influ-ence of this perturbation is maintained until the injectionpoint on the blade. This demonstrates why it is importantto include the plenum in the computational domain,especially for small L/D ratios. This recommendation waspreviously established by Leylek and Zerkle [13]. Allphysical phenomenon’s cited by Salcudean et al. [1] suchas the dependency of the hole behavior on the pressurefield is reproduced by the present numerical prediction.For example, the first row of coolant at ±15�, which islocated in a high-pressure region, cannot go deeply intothe main flow and the flow temperature in a small interiorregion near the hole is higher than the coolant tempera-ture. While the second row at ±44�, which is situated in alow-pressure region does not show these imperfections. Itis clear from the detailed velocity vectors (Figure 7) that

Fig. 8. Predicted film cooling effectiveness contours near theleading edge for M = 0.97 at various lateral injection

Fig. 9. Lateral averaged adiabatic film cooling effectiveness(M = 0.97)

506

the coolant jets from the second row have differentbehaviour than that from the first row. It can be concludedthat in showerhead injections, low blowing ratios are verydangerous and are susceptible to produce hot spots spe-cially if the coolant is injected into different pressure fieldregions from the same plenum chamber.

3.2(b) Lateral injection angle influenceFigures 8 shows the predicted film cooling effectivenesscontours near the leading edge for M = 0.97 and lateralinjection angles of 25�, 35�, and 60� respectively. It can beseen that the best coverage of the blade surface is providedby 25� lateral injection. For the nearly perpendicular case(b = 60�), large unprotected zone exists between theinjection rows, while for 25� injection case the coolantfrom the first row of orifices spreads between the coolingorifices of the second row. This is confirmed by Figure 9where we can see that 25� case provide the best lateralaveraged adiabatic film cooling effectiveness.

The lateral injection angle has a similar effect of thatof blowing ratio, where it can be seen that for the samerow, increasing the lateral injection angle results in morecoolant jet lift-off and hence, less film cooling effectiveness.It is clear that the lateral injection angle has more influenceon the second row than on the first row. This is probablydue to the pressure field, which is more intense near thestagnation line than in the vicinity of the second row.

The film cooling effectiveness contours in planes whichare perpendicular to the blade surface and situated at thedownstream leading edge of the second injection row arepresented in Figure 10. The contour shape shows that onlyone secondary vortex flow exists at spanwise plane whilefor the nearly perpendicular injection angle two counterrotating vortices are present. The improvement effect ofthe lateral injection is clearly presented by the effective-ness contours on the first panel.

4ConclusionsNumerical predictions have been carried out to investigatethe three-dimensional film cooling velocity field and adi-abatic film cooling effectiveness near the leading edge of asymmetrical gas turbine blade. Computed results werepresented in the form of adiabatic effectiveness contourson the blade surface and compared with experimentalmeasurements. Furthermore, predicted film cooling resultsin the streamwise and spanwise planes were also pre-sented. The present predicted results show good qualita-tive and quantitative agreement with experimentalmeasurements. Effects of the lateral injection angles on thelateral film cooling effectiveness were also investigated.It was found that the lateral injection allows the destruc-tion of the typical two counter rotating vortices thatpresent in streamwise injection and has more influence onthe second row, which is in low pressure region, than onthe first row near the stagnation line. It was also estab-lished that the best coverage is provided by a smallinjection angle of 25� to the stagnation line. Physicalaspects of the film cooling coverage were also discussed atthe centerline plane through the first and second injectionrows. Both the TLV and TLVA models still overpredict thelateral averaged film cooling effectiveness of gas turbineblades with almost negligible improvement over that whenwall function strategy is used.

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