The numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation (k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.
ChimaR. V.Explicit multigrid algorithm for quasi three dimensional viscous flows in turbomachinery. J. Propulsion and Power, 1987, 3(5), 1556–1563.
2.
HahC.Numerical study of three-dimensional flow and heat transfer near the endwall of a turbine blade row. AIAA paper 89-1689, 1989.
3.
BoyleR. J.Navier-Stokes analysis of turbine blade heat transfer. J. Turbomachinery, 1991, 113, 392–403.
4.
AmeriA. A.SockolM. P.GorlaR. S. R.Navier-Stokes analysis of turbomachinery blade external heat transfer. J. Propulsion and Power, 1992, 8(2), 374–381.
5.
KunzR. F.LakshminarayanaB.Three-dimensional Navier-Stokes computation of turbomachinery flows using an explicit numerical procedure and a coupled k-ε turbulence model. J. Turbomachinery, 1992, 114, 627–642.
6.
AmeriA. A.ArnoneA.Prediction of turbine blade passage heat transfer using a zonal and a two-equation turbulence model. ASME paper 94-GT-122, 1994.
7.
AmeriA. A.ArnoneA.Transitional modeling effects on turbine rotor blade heat transfer predictions. J. Turbo-machinery, 1996, 118, 307–313.
8.
SarkarS.Three-dimensional Euler and Navier-Stokes analysis of a transonic turbine cascade. In Proceedings of Seventh Asian Congress on Fluid Mechanics, IIT Madras, India, 1997, pp. 717–720.
9.
KoiroM.LakshminarayanaB.Simulation and validation of Mach number effects on secondary flow in a transonic cascade using a multigrid, k-ε solver. J. Turbo-machinery, 1998, 120, 285–297.
10.
BaldwinB. S.LomaxH.Thin layer approximation and algebraic model for separated turbulent flows. AIAA paper 78-257, 1978.
11.
BoyleR. J.GielP.Three-dimensional Navier-Stokes heat transfer predictions for turbine blade rows. AIAA paper 92-3068, 1992.
12.
SarkarS.BasuD.DasK.Prediction of transitional flow and heat transfer over transonic turbine cascades. In 34th National Heat Transfer Conference, 2000, paper NHTC2000-12045.
13.
BoyleR. J.SimonF. F.Mach number effects on turbine blade transition length prediction. J. Turbomachinery, 1999, 121, 691–702.
14.
JonesW. P.LaunderB. E.The prediction of laminar-isation with a two-equation model of turbulence. Int. J. Heat Mass Transfer, 1972, 15, 301–314.
15.
JonesW. P.LaunderB. E.The calculation of low Reynolds number phenomena with a two equation model of turbulence. Int. J. Heat Mass Transfer, 1973, 16, 1119–1130.
16.
SchmidtR. C.PatankarS. V.Simulating boundary layer transition with low-Reynolds number k-ε turbulence models: Part 1–an evaluation of prediction characteristics. J. Turbomachinery, 1991, 113, 10–17.
17.
LuoJ.LakshminarayanaB.Numerical simulation of turbine blade boundary layer and heat transfer and assessment of turbulent models. J. Turbomachinery, 1997, 119, 794–801.
18.
AmeriA. A.ArnoneA.Navier-Stokes heat transfer predictions using two-equation turbulence clousers. AIAA paper 92-3067, 1992.
19.
ChimaR. V.Application of k-w turbulence model to quasi-three-dimensional turbomachinery flows. J. Propulsion and Power, 1996, 12(6), 1176–1179.
20.
ChienK.Prediction of channel and boundary-layer flows with a low-Reynolds number turbulence model. Am. Inst. Aeronaut. Astronaut. J., 1982, 20, 33–38.
21.
JamesonA.SchmidtW.TurkelE.Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA paper 81-1259, 1981.
22.
DeiwertG. S.Numerical simulation of high Reynolds number transonic flows. Am. Inst. Aeronaut. Astronaut. J., 1975, 13(10), 1354–1359.
23.
SarkarS.DasK.BasuD.Two-dimensional Navier-Stokes analysis of an internally cooled turbine blade. Proc. Instn Mech. Engrs, Part A, Journal of Power and Energy, 2000, 214(A6), 585–598.
24.
MartinelliL.Calculations of viscous flows with a multigrid method. PhD dissertation, MAE Department, Princeton University, 1987.
25.
BrandtA.Multilevel adaptive computations in fluid dynamics. AIAA paper 79-1455, 1979.
26.
NiR. H.A multiple grid scheme for solving the Euler equations. Am. Inst. Aeronaut. Astronaut. J., 1982, 20(11), 1565–1571.
27.
JamesonA.Transonic flow calculations. MAE Report 1651, MAE Department, Princeton University, 1983.
28.
ChimaR. V.JohnsonG. M.Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm. Am. Inst. Aeronaut. Astronaut. J., 1985, 23 (1), 23–32.
29.
ArnoneA.SwansonR. C.A Navier-Stokes solver for turbomachineryapplications. J. Turbomachinery, 1993, 115, 305–313.
30.
ArnoneA.LiouM. S.PovinelliL. A.Multigrid calculation of three-dimensional viscous cascade flows. Am. Inst. Aeronaut. Astronaut. J. Propulsion and Power, 1993, 9 (4), 605–614.
31.
GranvilleP. S.Baldwin-Lomax factors for turbulent boundary layers in pressure gradients. Am. Inst. Aeronaut. Astronaut. J., 1987, 25, 1624–1627.
32.
MayleR. E.The role of laminar-turbulent transition in gas turbine engines. J. Turbomachinery, 1991, 113, 509–537.
33.
WhiteF. M.Viscous Flow Theory, 2nd edition, 1991 (McGraw-Hill, New York).
34.
Abu-GhannamB. J.ShawR.Natural transition of boundary layers–the effects of turbulence, pressure gradient, and flow history. J. Mech. Engng Sci., 1980, 22, 213–228.
35.
WaskiewiczJ. D.ShangJ. S.HankeyW. L.Numerical simulation of near wakes utilizing a relaxation turbulence model. Am. Inst. Aeronaut. Astronaut. J., 1980, 18 (12), 1440–1445.
36.
HyltonL. D.MihelcM. S.TurnerE. R.NealyD. A.YorkR. E.Analytical and experimental evaluation of heat transfer distribution over the surface of turbine vanes. NASA CR-168015, 1983.
37.
PatelV. C.RodiW.ScheuererG.Turbulence models for near-wall and low-Reynolds-number flows. Am. Inst. Aeronaut. Astronaut. J., 1985, 23 (9), 1308–1319.
38.
ArtsT.Lambert de RouvroitM.Aero-thermal performance of a two-dimensional highly loaded transonic turbine nozzle guide vane: A test case for inviscid and viscous flow computations. J. Turbomachinery, 1992, 114, 147–154.
39.
NicholsonH.ForestA. E.OldfieldM. L. G.SchultzD. L.Heat transfer optimized turbine rotor blades–an experimental study using transient techniques. J. Engng for Gas Turbines and Power, 1984, 106, 173–182.
