Flow and sound fields of low-Reynolds-number temporal jets at Mach numbers from 0.3 to 2

Pressure distribution of supercritical airfoil at flight Reynolds number could not be fully simulated except in cryogenic wind tunnel such as NTF (National Transonic Facility) and ETW (European Transonic Wind tunnel), which is costly and time resuming. This paper aimed to explore an engineering extrapolation to flight Reynolds number from low Reynolds number wind tunnel data for supercritical airfoil pressure distribution. However, the extrapolation method requiring plenty of data was investigated based on the CFD results for the reason of low cost and short period. Flows over a typical supercritical airfoil were numerically simulated by solving the two dimensional Navier-Stokes equations, with applications of ROE scheme spatial discretization and LU-SGS time march. Influence of computational grids convergence and turbulent models were investigated during the process of simulation. The supercritical airfoil pressure distribution were obtained with Reynolds numbers varied from 3.0×106to 30×106per airfoil chord, angles of attack from 0 degree to 6 degree and Mach numbers from 0.74 to 0.8. Simulated results indicated that weak shock existed on the upper surface of supercritical airfoil at cruise condition, that the shock location, shock strength and trailing edge pressure were dependent of Reynolds number, attack angles and Mach numbers. A similar parameter describing the Reynolds number effects factors was obtained by analyzing the relationship of shock wave location, shock front pressure and trailing edge pressure. Based on the similar parameter, airfoil pressure distribution at Reynolds number 30×106was obtained by extrapolation. It was shown that extrapolated result compared well with simulated result at Reynolds number 30×106, implying that the engineering method was at least promising applying to the extrapolation of low Reynolds number wind tunnel data.

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Numerical and experimental investigation of tip leakage flow and heat transfer using idealised rotor-tip models at transonic conditions

The Aeronautical Journal ◽

10.1017/s0001924000011453 ◽

2009 ◽

Vol 113 (1141) ◽

pp. 165-175 ◽

Cited By ~ 2

Author(s):

S. K. Krishnababu ◽

H. P. Hodson ◽

W. N. Dawes ◽

P. J. Newton ◽

G. D. Lock

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Nusselt Number ◽

Discharge Coefficient ◽

Fluid Dynamic ◽

Low Reynolds Number ◽

Analytical Models ◽

Tip Leakage Flow ◽

Mach Numbers ◽

Low Reynolds

Abstract The effect of tip geometry on discharge coefficient and heat transfer is investigated both experimentally and numerically using idealised models of an unshrouded rotor blade. A flat tip was compared with two squealer-type geometries (a cavity and suction-side squealer) under the transonic conditions expected in the gas turbine engine. Heat transfer measurements were performed using a transient liquid crystal technique while a duplicate test section was used for measuring the pressure field. Computations were carried out using an unstructured, fully compressible, three-dimensional RANS (Reynolds averaged Navier Stokes) solver. Initial computations performed using a low Reynolds number k-ε model demonstrated the inability of the model to predict the Nusselt number with reasonable accuracy. Further computations performed using a low Reynolds number k-ω model improved the predictions dramatically. The computed discharge coefficient and the average Nusselt number over the blade tip agreed well with the experiments. Three upstream-total to exit-static pressure ratios were used to create a range of engine-representative Mach numbers. Both experimental and numerical studies at the lower pressure ratio of 1·3 (exit Mach number ~ 0·65) established the cavity geometry as the best performer from an aerodynamic perspective by reducing the discharge through the tip. However, from the heat transfer perspective, both the peak Nusselt number and the average heat transfer to the tip were higher than the flat tip. At the higher pressure ratios of 1·85 and 2·27 (corresponding to exit Mach numbers ~ 0·98 and 1·12) the discharge coefficient and heat transfer to the tip increases. This paper explores the fluid dynamics associated with these flows and shows that the highest heat transfer is caused by reattachment and flow impingement. The fluid dynamic computations provide insight into the experimental measurements and were successfully compared with simple analytical models.

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