1. DATA No. (FILE NAME) N1000002 2. KEY WORDS Natural Convection, Turbulent Boundary Layer, Reynolds Stress, Turbulent Heat Flux, Hot-Wire Measurement 3. DATA TAKERS AND ARTICLE TITLE a. T. Tsuji and Y. Nagano b. Dep. of Mech. Eng., Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya 466 c. Turbulence Measurements in a Natural Convection Boundary Layer along a Vertical Flat Plate d. Int. J. Heat Mass Transfer e. Vol. 31, No. 10, 2101-2111 (1988) 4. ABSTRACT OF EXPERIMENT A turbulent natural convection boundary layer, the structure of which still remains a matter of conjecture for want of reliable measurement, is investigated with the V-shaped hot-wire technique. The reliability of Reynolds stress and turbulent heat flux measurements is verified by the excellent agreement with the indirect measurements estimated by integrating momentum and thermal energy equations with measured mean velocity and mean temperature. Turbulent quantities clarified quantitatively in the present study indicate that the natural convection boundary layer has a unique turbulent structure rarely seen in other turbulent boundary layers. 5. INSTRUMENTATION The flat surface generating flow was a copper plate 4 m high, 1 m wide and 2 mm thick. Two V-shaped hot-wires in an X-array and a cold-wire were used to measure fluid velocity and temperature. The V-shaped hot-wire was constructed by symmetrically bending a 0.0031 mm dia. and 1.5 mm long tungsten wire at the center. The cold-wire of 0.0031 mm dia. and 3.5 mm long tungsten wire located upstream of the hot-wires for temperature compensation. 6. EXPERIMENTAL PARAMETERS *** Test conditions *** Comments x [m] 2.536 : Vertical location Tw[deg.] 60.63 : Wall temp. Ta[deg.] 15.29 : Ambient temp. Pa[Pa] 1.017E05 : Atom. pres. Grx 8.986E10 : Grashof no. Pr 0.710 : Prandtl no. Physical properties were evaluated at the film temperature (=(Tw+Ta)/2), except that the body expansion coefficient B was defined as 1/Ta. Ambient temperature increased at the rate of about 0.6 deg./m in the vertical direction. 7. MEASURED VARIABLES Eh - Eddy diffusivity for heat Em - Eddy diffusivity for momentum Prt - Turbulent Prandtl number T - Mean temperature t2 - Intensity of temperature fluctuation (rms value) U - Mean streamwise velocity u2 - Intensity of streamwise velocity fluctuation (rms value) ut - Streamwise turbulent heat flux uv - Reynolds stress V - Mean transverse velocity v2 - Intensity of transverse velocity fluctuation (rms value) vt - Transverse turbulent heat flux y - Distance normal to the flat plate 8. DATA Grx=8.986E+10, Tw=60.63 deg., Ta=15.29 deg., Pr=0.710 u*=0.07049 m/s (u*: Friction velocity) t*=2.866 deg. (t*: Friction temperature) N=1.6727E-05 m**2/s (N: Kinematic viscosity) y+=u*y/N, U+=U/u*, V+=V/u*, T+=(Tw-T)/t* In evaluating u* and t*, the wall shear stress Fw and the wall heat flux were estimated from the following experimental formulas (ref. [1]): Fw/(RUb**2)=0.684Grx**(1/11.9) Nux=0.120(GrxPr)**(1/3) where Nux is the Nusselt number, R is the density and Ub is the reference velocity defined as [gB(Tw-Ta)N]**(1/3). A dimensionless distance Z used to plot data in the article can be calculated from the following equation: Z=-(y/x)(Kf/Kw)Nux where Kf and Kw are thermal conductivities at film and wall temperature, respectively. a. Mean velocities and mean temperature y [mm] y+ U+ V+ T+ 1 1.11 4.680E+00 3.462E+00 4.058E-01 3.358E+00 2 1.31 5.520E+00 3.887E+00 3.623E-01 3.937E+00 3 1.51 6.360E+00 4.470E+00 3.257E-01 4.254E+00 4 1.81 7.630E+00 5.209E+00 2.565E-01 4.984E+00 5 2.11 8.890E+00 5.879E+00 1.737E-01 5.692E+00 6 2.41 1.016E+01 6.378E+00 6.321E-02 6.354E+00 7 2.81 1.184E+01 6.987E+00 -1.201E-02 6.944E+00 8 3.31 1.395E+01 7.592E+00 -6.459E-02 7.792E+00 9 3.81 1.606E+01 8.044E+00 -9.603E-02 8.418E+00 10 4.31 1.816E+01 8.367E+00 -1.147E-01 8.940E+00 11 4.81 2.027E+01 8.739E+00 -1.430E-01 9.369E+00 12 5.81 2.448E+01 8.905E+00 -1.831E-01 1.015E+01 13 6.81 2.870E+01 9.176E+00 -1.796E-01 1.042E+01 14 7.81 3.291E+01 9.529E+00 -2.071E-02 1.109E+01 15 8.81 3.713E+01 9.439E+00 -1.224E-01 1.129E+01 16 9.81 4.134E+01 9.704E+00 2.533E-01 1.157E+01 17 10.81 4.555E+01 9.650E+00 2.352E-01 1.188E+01 18 13.81 5.820E+01 9.328E+00 7.905E-02 1.243E+01 19 16.81 7.084E+01 9.080E+00 -1.273E-02 1.274E+01 20 20.81 8.770E+01 8.992E+00 9.488E-02 1.303E+01 21 25.81 1.088E+02 8.604E+00 1.932E-03 1.341E+01 22 30.81 1.298E+02 8.106E+00 -3.108E-01 1.369E+01 23 40.81 1.720E+02 7.828E+00 -2.485E-01 1.398E+01 24 50.81 2.141E+02 7.111E+00 -2.502E-01 1.428E+01 25 60.81 2.563E+02 6.772E+00 -1.608E-01 1.451E+01 26 70.81 2.984E+02 6.109E+00 -2.821E-01 1.468E+01 27 80.81 3.406E+02 5.676E+00 -2.849E-01 1.488E+01 28 100.81 4.248E+02 4.507E+00 -3.665E-01 1.523E+01 29 120.81 5.091E+02 3.236E+00 -4.262E-01 1.552E+01 30 140.81 5.934E+02 2.230E+00 -5.748E-01 1.570E+01 31 160.81 6.777E+02 1.736E+00 -6.631E-01 1.581E+01 32 180.81 7.620E+02 1.290E+00 -7.121E-01 1.587E+01 33 200.81 8.462E+02 1.058E+00 -7.161E-01 1.587E+01 b. Intensities of velocity and temperature fluctuations y [mm] y+ u2/u* v2/u* t2/t* 1 1.11 4.680E+00 8.133E-01 5.360E-01 1.383E+00 2 1.31 5.520E+00 8.642E-01 5.465E-01 1.586E+00 3 1.51 6.360E+00 1.002E+00 6.153E-01 1.752E+00 4 1.81 7.630E+00 1.099E+00 6.786E-01 1.926E+00 5 2.11 8.890E+00 1.248E+00 6.950E-01 2.183E+00 6 2.41 1.016E+01 1.342E+00 6.939E-01 2.367E+00 7 2.81 1.184E+01 1.366E+00 6.902E-01 2.466E+00 8 3.31 1.395E+01 1.449E+00 7.134E-01 2.515E+00 9 3.81 1.606E+01 1.554E+00 7.111E-01 2.586E+00 10 4.31 1.816E+01 1.563E+00 7.302E-01 2.626E+00 11 4.81 2.027E+01 1.601E+00 7.195E-01 2.552E+00 12 5.81 2.448E+01 1.737E+00 7.286E-01 2.538E+00 13 6.81 2.870E+01 1.740E+00 7.578E-01 2.431E+00 14 7.81 3.291E+01 1.803E+00 7.789E-01 2.338E+00 15 8.81 3.713E+01 1.806E+00 8.223E-01 2.288E+00 16 9.81 4.134E+01 1.850E+00 8.002E-01 2.195E+00 17 10.81 4.555E+01 1.884E+00 8.098E-01 2.085E+00 18 13.81 5.820E+01 1.929E+00 9.780E-01 1.874E+00 19 16.81 7.084E+01 1.878E+00 1.021E+00 1.726E+00 20 20.81 8.770E+01 1.950E+00 1.108E+00 1.537E+00 21 25.81 1.088E+02 1.965E+00 1.156E+00 1.372E+00 22 30.81 1.298E+02 2.003E+00 1.266E+00 1.215E+00 23 40.81 1.720E+02 2.072E+00 1.334E+00 1.052E+00 24 50.81 2.141E+02 2.105E+00 1.370E+00 9.256E-01 25 60.81 2.563E+02 2.106E+00 1.338E+00 8.372E-01 26 70.81 2.984E+02 2.053E+00 1.346E+00 7.440E-01 27 80.81 3.406E+02 1.995E+00 1.315E+00 6.930E-01 28 100.81 4.248E+02 1.970E+00 1.198E+00 5.745E-01 29 120.81 5.091E+02 1.712E+00 1.019E+00 4.825E-01 30 140.81 5.934E+02 1.525E+00 8.380E-01 4.249E-01 31 160.81 6.777E+02 1.138E+00 7.118E-01 4.027E-01 32 180.81 7.620E+02 8.293E-01 5.111E-01 3.633E-01 33 200.81 8.462E+02 6.063E-01 4.538E-01 2.480E-01 c. Reynolds stress and turbulent heat fluxes y [mm] y+ uv/u*u* ut/u*t* vt/u*t* 1 1.11 4.680E+00 4.222E-03 3.865E-02 -5.413E-04 2 1.31 5.520E+00 1.658E-02 6.854E-02 2.498E-02 3 1.51 6.360E+00 4.556E-02 2.690E-02 7.608E-02 4 1.81 7.630E+00 3.221E-02 -4.892E-02 1.409E-01 5 2.11 8.890E+00 3.853E-02 1.973E-01 3.006E-01 6 2.41 1.016E+01 2.752E-02 3.948E-01 3.571E-01 7 2.81 1.184E+01 4.617E-02 4.339E-01 4.296E-01 8 3.31 1.395E+01 6.782E-02 8.254E-01 5.282E-01 9 3.81 1.606E+01 1.215E-01 1.019E+00 5.599E-01 10 4.31 1.816E+01 1.252E-01 1.291E+00 6.565E-01 11 4.81 2.027E+01 1.534E-01 1.484E+00 6.783E-01 12 5.81 2.448E+01 2.398E-01 1.842E+00 7.350E-01 13 6.81 2.870E+01 2.594E-01 1.958E+00 7.273E-01 14 7.81 3.291E+01 3.610E-01 2.118E+00 7.518E-01 15 8.81 3.713E+01 4.045E-01 2.242E+00 8.003E-01 16 9.81 4.134E+01 4.719E-01 2.189E+00 8.026E-01 17 10.81 4.555E+01 5.408E-01 2.233E+00 7.879E-01 18 13.81 5.820E+01 7.210E-01 2.174E+00 8.104E-01 19 16.81 7.084E+01 8.331E-01 2.041E+00 8.237E-01 20 20.81 8.770E+01 9.170E-01 1.880E+00 7.937E-01 21 25.81 1.088E+02 1.089E+00 1.727E+00 7.841E-01 22 30.81 1.298E+02 1.319E+00 1.539E+00 7.426E-01 23 40.81 1.720E+02 1.458E+00 1.337E+00 6.853E-01 24 50.81 2.141E+02 1.558E+00 1.211E+00 6.176E-01 25 60.81 2.563E+02 1.557E+00 1.097E+00 5.713E-01 26 70.81 2.984E+02 1.543E+00 9.154E-01 4.873E-01 27 80.81 3.406E+02 1.490E+00 8.429E-01 4.650E-01 28 100.81 4.248E+02 1.320E+00 6.744E-01 3.226E-01 29 120.81 5.091E+02 8.400E-01 4.445E-01 2.062E-01 30 140.81 5.934E+02 7.263E-01 3.103E-01 1.307E-01 31 160.81 6.777E+02 3.458E-01 1.844E-01 1.041E-01 32 180.81 7.620E+02 2.065E-01 6.830E-02 3.342E-02 33 200.81 8.462E+02 1.137E-01 5.405E-03 1.165E-02 d. Eddy diffusivities for momentum and heat and turbulent Prandtl number y [mm] y+ Em/N Eh/N Prt 1 1.31 5.520E+00 -2.568E-02 4.050E-02 -6.340E-01 2 1.51 6.360E+00 -7.602E-02 1.300E-01 -5.848E-01 3 1.81 7.630E+00 -6.053E-02 2.619E-01 -2.311E-01 4 2.11 8.890E+00 -8.366E-02 6.206E-01 -1.348E-01 5 2.41 1.016E+01 -7.121E-02 8.285E-01 -8.594E-02 6 2.81 1.184E+01 -1.423E-01 1.146E+00 -1.243E-01 7 3.31 1.395E+01 -2.758E-01 1.603E+00 -1.721E-01 8 3.81 1.606E+01 -6.826E-01 1.909E+00 -3.576E-01 9 4.31 1.816E+01 -1.021E+00 2.550E+00 -4.004E-01 10 4.81 2.027E+01 -1.717E+00 3.108E+00 -5.524E-01 11 5.81 2.448E+01 -3.974E+00 4.583E+00 -8.672E-01 12 6.81 2.870E+01 -6.406E+00 5.748E+00 -1.115E+00 13 7.81 3.291E+01 -1.499E+01 7.493E+00 -2.000E+00 14 8.81 3.713E+01 -3.704E+01 1.069E+01 -3.464E+00 15 9.81 4.134E+01 -1.382E+02 1.413E+01 -9.776E+00 16 10.81 4.555E+01 1.562E+03 1.582E+01 9.876E+01 17 13.81 5.820E+01 7.288E+01 2.265E+01 3.218E+00 18 16.81 7.084E+01 5.865E+01 3.110E+01 1.886E+00 19 20.81 8.770E+01 5.767E+01 3.906E+01 1.476E+00 20 25.81 1.088E+02 6.763E+01 4.997E+01 1.353E+00 21 30.81 1.298E+02 8.230E+01 6.039E+01 1.363E+00 22 40.81 1.720E+02 9.476E+01 7.865E+01 1.205E+00 23 50.81 2.141E+02 1.055E+02 8.458E+01 1.248E+00 24 60.81 2.563E+02 1.114E+02 9.433E+01 1.181E+00 25 70.81 2.984E+02 1.108E+02 9.826E+01 1.128E+00 26 80.81 3.406E+02 1.210E+02 1.141E+02 1.060E+00 27 100.81 4.248E+02 1.136E+02 1.094E+02 1.039E+00 28 120.81 5.091E+02 8.357E+01 8.812E+01 9.483E-01 29 140.81 5.934E+02 7.694E+01 7.545E+01 1.020E+00 30 160.81 6.777E+02 5.009E+01 6.200E+01 8.080E-01 31 180.81 7.620E+02 3.466E+01 3.740E+01 9.266E-01 32 200.81 8.462E+02 2.748E+01 3.399E+01 8.084E-01 9. MEASUREMENT UNCERTAINTY The estimated uncertainties (95% coverage) at y =9.81 mm are as follows: