Stagnation Point Flow and Heat Transfer Under Free-Stream Turbulence

Abstract

Public reporting burden for this collection of information is estinuted to awrage 1 hour per response, including the time for reviewing in maintaining the data needed, and completing and reviewing tWs ooHedion of infbrmatian. SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTKppi'oved fcv PMV.1 1 c rclsnsa, distribution unlikiiLoLl SUPPLEMENTARY NOTES 03914. ABSTRACT Stagnation point flow and heat transfer in the presence of free-stream turbulence is investigated through both numerical simulation and theoretical analysis. Large eddy simulations (LES) results for different free-stream turbulent intensity, length scale, and Mach number are reported. The Reynolds stress statistics and budgets are obtained and presented. The numerical results show good agreement with experimental measurements on elevated heat transfer coefficient, and reveals the characteristic vortical flow structures responsible for the observed heat transfer enhancement.The theoretical analysis shows that the vorticity amplification, and hence the heat transfer enhancement, increases with decreasing length scale and reaches a maximum value at about five times the boundary layer thickness. A new correlation for heat transfer enhancement which incorporates turbulence intensity, integral length scale and mean flow Reynolds number is derived and shown to reasonably collapse the recent experimental data. Abstract Stagnation point flow and heat transfer in the presence of free-stream turbulence is investigated through both numerical simulation and theoretical analysis. Large eddy simulations (LES), using fourth order finite difference in curvilinear coordinates and an efficient dual time linearized sub-iteration scheme, are performed to investigate free-stream turbulence impingement upon an elliptical leading edge and the resulting heat transfer enhancement. A new blending procedure is developed through which independent, statistically identical realizations of homogeneous isotropic turbulence are combined to provide realistic representations of free-stream turbulence.Results for diflTerent free-stream turbulent intensity, length scale, and Mach number are reported. Strong anisotropy of the turbulence due to the mean flow strain is observed as the stagnation point is approached. The Reynolds stress statistics and budgets are obtained and presented. These results are expected to provide unique data for turbulence modelling of strain dominated flows. The numerical results show good agreement with the experimental measurements on elevated heat transfer coefficient. It also reveals that small scale, intense vortical flow structures generated at the leading edge by vortex stretching induces significant changes in local thermal boundary layer, causing the observed heat transfer enhancement.In the theoretical study, the distortion of three dimensional unsteady disturbance in an incompressible Hiemenz boundary layer and its effect on the wall heat transfer is analyzed based on linear vortex dynamics. An asymptotic solution for disturbanc...

Stagnation-point flow under free-stream turbulence

“…The numerical method and validation problems for the present LES are described briefly in this section. For more details, see Xiong (2004).…”

“…The eddy coefficient C I for the subgrid normal stress is set to zero and the turbulence Prandtl number Pr t is set to unity. The eddy coefficient C for the subgrid shear stress is computed using the standard dynamic SGS model (see Xiong 2004 for details).…”

Computational Framework for Coupling Compressible and Low Mach Number Codes

“…The compressible code used in the present multicode solver was developed by Xiong [19]. Compressible Navier-Stokes equations written in primitive variables are solved numerically:…”

“…The resulting coefficient matrix can be inverted efficiently using the direct Gaussian elimination method. Further details of the numerical implementation of the compressible code can be found in [19].…”

“…The difference in normalization of pressure is taken into account in Method D is a Riemann invariant formulation in which Riemann invariants are formed from f lm ; u lm ; v lm ; w lm ; T lm g, and variables f c ; u c ; v c ; w c ; T c g are reconstructed from those Riemann invariants according to the procedure described, for example, in [19] Method E is a Riemann invariant formulation, but is calculated from the low Mach number pressure through the equation of state p lm =T lm and used instead of lm to form Riemann invariants as in method D.…”