A theoretical study on the unsteady aerothermodynamics for attached flow models
Tóm tắt
The principle of the unsteady aerothermodynamics was theoretically investigated for the attached flow. Firstly, two simplified models with analytic solutions to the N-S equations were selected for the research, namely the compressible unsteady flows on the infinite flat plate with both time-varying wall velocity and time-varying wall temperature boundary conditions. The unsteady temperature field and the unsteady wall heat flux (heat flow) were analytically solved for the second model. Then, the interaction characteristic of the unsteady temperature field and the unsteady velocity field in the simplified models and the effects of the interaction on the transient wall heat transfer were studied by these two analytic solutions. The unsteady heat flux, which is governed by the energy equation, is directly related to the unsteady compression work and viscous dissipation which originates from the velocity field governed by the momentum equation. The main parameters and their roles in how the unsteady velocity field affects the unsteady heat flux were discussed for the simplified models. Lastly, the similarity criteria of the unsteady aerothermodynamics were derived based on the compressible boundary layer equations. Along with the Strouhal number St
u
, the unsteadiness criterion of the velocity field, St
T
number, the unsteadiness criterion of the temperature field was proposed for the first time. Different from the traditional method used in unsteady aerodynamics which measures the flow unsteadiness only by the St
u
number, present results show that the flow unsteadiness in unsteady aerothermodynamics should be comprehensively estimated by comparing the relative magnitudes of the temperature field unsteadiness criterion St
T
number with the coefficients of other terms in the dimensionless energy equation.
Tài liệu tham khảo
Chapman G T. An overview of hypersonic aerothermodynamics. Commun Appl Numer M, 1988, 4: 319–325
Gnoffo P A, Weilmuenster K J, Hamilton H H, et al. Computational aerothermodynamic design issues for hypersonic vehicles. J Spacecr Rockets, 1999, 36: 21–43
Muylaert J, Kordulla W, Giordano D, et al. Aerothermodynamic analysis of space vehicle phenomena. Esa Bull-Eur Space, 2001, 105: 69–79
Longo J M A. Aerothermodynamics-a critical review at DLR. Aerosp Sci Technol, 2003, 7: 429–438
Weiland C, Longo J, Gülhan A, et al. Aerothermodynamics for reusable launch systems. Aerosp Sci Technol, 2004, 8: 101–110
Bertin J J, Cummings R M. Critical hypersonic aerothermodynamic phenomena. Annu Rev Fluid Mech, 2006, 38: 129–157
Bertin J J. Hypersonic Aerothermodynamics. Washington, DC: AIAA, 1994
Hirschel E H. Basics of Aerothermodynamics. Berlin: Springer-Verlag, 2005
Hirschel E H, Weiland C. Selected Aerothermodynamic Design Problems of Hypersonic Flight Vehicles. Berlin: Springer-Verlag, 2009
Stuart J T. Unsteady boundary layers// Rosenhead L. Laminar Boundary Layers. London: Oxford University Press, 1963
Telionis D P. Unsteady Viscous Flows. New York: Springer-Verlag, 1981
Moore F K. Unsteady Laminar Boundary-Layer Flow. Technical Report, NACA TN 2471, 1951
Ostrach S. Compressible Laminar Boundary Layer and Heat Transfer for Unsteady Motions of a Flat Plate. Technical Report, NACA TN 3569, 1955
Sparrow E M. Combined effects of unsteady flight velocity and surface temperature on heat transfer. J Jet Propul, 1958, 28: 403–405
Chen H, Bao L. Mechanism of unsteady aerodynamic heating with sudden change in surface temperature. Appl Math Mech, 2009, 30: 163–174
Illingworth C R. Unsteady laminar flow of gas near an infinite plate. Proc Camb Philol Soc, 1950, 46: 603–613
Pozzi A, Tognaccini R. On the thermal field in the impulsive Rayleigh flow. Phys Fluids, 2004, 16: 4539–4542
Ostrach S. Note on the Aerodynamic Heating of an Oscillating Surface. Technical Report, NACA TN 3146, 1954
Schlichting H. Boundary Layer Theory. 7th ed. New York: McGraw-Hill, 1979