Abstract
Measurements of mean velocity and temperature, and of surface heat flux, have been made in a turbulent boundary layer on a heated convex surface of modest curvature (δ/R ∼0.01). The results show surprisingly large curvature effects on heat transfer: at the end of the curved plate the Stanton number fell by 18% of the predicted flat plate value; the corresponding fall in the skin friction coefficient was 10%.
Profile measurements of temperature and velocity were obtained well into the viscous sublayer.
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Abbreviations
- c f :
-
skin friction coefficient, [Eq. (4)]
- c p :
-
static pressure coefficient, \(2(p - {{p}_{{ref}}})/\rho U_{{pw}}^{2}\), specific heat
- \(\dot{q}\prime \prime\) :
-
heat flux
- R :
-
radius of curvature of plate
- s :
-
distance measured along curved wall
- T :
-
temperature
- T + :
-
dimensionless temperature [Eq. (6)]
- U :
-
velocity
- U + :
-
dimensionless velocity U/μτ
- uτ:
-
friction velocity, \(\sqrt {{{{\tau }_{w}}/\rho }}\)
- y :
-
distance measured normal to the wall
- y + :
-
dimensionless distance, yuτ/υ
- Δ2 :
-
enthalpy thickness, [Eq. (2)]
- δ2 :
-
momentum thickness, [Eq. (1)]
- δ:
-
boundary layer thickness
- ρ:
-
density
- τ:
-
shear stress
- υ:
-
kinematic viscosity
- p:
-
potential flow
- w:
-
wall
- ∞:
-
free stream
References
Bradshaw, P.: Effect of streamwise curvature on turbulent flows. AGARDograph 169 (1973)
Smits, A. J., Young, S. T. B., Bradshaw, P.: The effect of short regions of high surface curvature on turbulent boundary layers. J. Fluid Mech. 94, 209 (1979)
Gillis, J.C., Johnston, J.P.: “Experiments on the Turbulent Boundary Layer over Convex Walls and its Recovery to Flat-Wall Conditions. In Turbulent Shear Flows II ed. by L.J.S. Bradbury, F. Durst, B.E. Launder, F.W. Schmidt, J.H. Whitelaw (Springer, Berlin, Heidelberg, New York 1980) pp. 116–128
Hoffmann, P.H., Bradshaw, P.: “Turbulent Boundary Layers on Surfaces of Mild Longitudinal Curvature”. Imperial Coll. Aero. Rpt. 78-104 (1978)
Ramaprian, B. R., Shivaprasad, B. G.: The structure of turbulent boundary layers along mildly curved surfaces. J. Fluid Mech. 85, 273 (1978)
Gibson, M.M., Verriopoulos, CA., Vlachos, N.S.: “Measurements in the Turbulent Boundary Layer on a Convex Wall”, Int. Symp. on Applications of Fluid Mechanics and Heat Transfer to Energy and Environmental Problems, Patras, Greece (1981)
Thomann, H.: Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer. J. Fluid Mech., 33, 283 (1968)
Mayle, R.E., Blair, M.F., Kopper, F.C.: Turbulent boundary layer heat transfer on curved surfaces. ASME J. Heat Transfer 101, 521 (1979)
Bradshaw, P.: The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177 (1969)
Businger, J. A., Wyngaard, J. C, Izumi, Y., Bradley, E. F.: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181 (1971)
Gibson, M.M.: An algebraic stress and heat flux model for turbulent shear flow with streamline curvature. Int. J. Heat Mass Transfer 21, 1609 (1978)
Simon, T.W., Moffat, R.J.: “Heat Transfer Through Turbulent Boundary Layers — the Effects of Introduction of and Recovery from Convex Curvature”. ASME paper 79-WA/GT-10 (1979)
Gillis, J.C., Johnston, J.P., Kays, W.M., Moffat, R.J.: “Turbulent Boundary Layer on a Convex Curved Surface”. Rpt. No. HMT-31, Thermosciences Div., Mech. Eng. Dept., Stanford University (1980)
Gibson, M. M., Launder, B. E.: Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86, 491 (1978)
So, R.M.C.: “The Effects of Streamline Curvature on Reynolds Analogy”. ASME paper 77-WA/FE-17 (1977)
So, R. M.C.: Heat transfer modelling for turbulent shear flows. Z. Angew. Math. Phys. 32, 541 (1981)
Oka, S., Kostic, Z.: Influence of wall proximity on hot wire velocity measurements. DISA Inf. 13, 29 (1972)
Blackwell, B. F., Moffat, R. J.: Design and construction of a low-velocity boundary-layer temperature probe. ASME J. Heat Transfer 97, 313 (1975)
Hishida, M., Nagano, Y., Nakamura, Y.: Temperature distribution in the turbulent boundary layer in a circular pipe. Bull. JSME 21, 157, 1175 (1978)
Kays, W.M., Crawford, M.E.: Convective Heat and Mass Transfer (McGraw-Hill, New York 1980)
Coles, D.: The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191 (1956)
Kader, B. A., Yaglom, A. M.: Heat and mass transfer laws for fully turbulent wall flows. Int. J. Heat Mass Transfer 15, 2329 (1972)
Simon, T.W., Moffat, R.J.: “Turbulent Boundary Layer Heat Transfer Experiments: a Separate Effects Study on a Convexly Curved Wall”. ASME paper 81-HT-78 (1981)
Simon, T.W., Moffat, R.J., Johnston, J.P., Kays, W.M.: “Turbulent Boundary Layer Heat Transfer Experiments: Convex Curvature Effects Including Introduction and Recovery”, Rpt. No. HMT-32, Thermosciences Div., Mech. Eng. Dept., Stanford University (1980)
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Gibson, M.M., Verriopoulos, C.A., Nagano, Y. (1982). Measurements in the Heated Turbulent Boundary Layer on a Mildly Curved Convex Surface. In: Bradbury, L.J.S., Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95410-8_8
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DOI: https://doi.org/10.1007/978-3-642-95410-8_8
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