******************************************************************************** ******************************************************************************** ********** ********** ********** "Data-Base on Turbulent Heat Transfer" ********** ********** ********** ********** Supported by the Ministry of Education, ********** ********** Science and Culture ********** ********** ********** ********** 1991 ********** ********** ********** ********** ********** ********** ********** ********** Y. Nagano (Organizer) ********** ********** ********** ********** N. Kasagi, T. Ota, H. Fujita, H. Yoshida, M. Kumada ********** ********** ********** ******************************************************************************** ******************************************************************************** ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++ << NOTICE >> ++++++++++ ++++++++++ ++++++++++ ++++++++++ All rights are reserved by the presenters of each ++++++++++ ++++++++++ data base. No part of the data described herein ++++++++++ ++++++++++ may be represented or otherwise used in any form ++++++++++ ++++++++++ without fully referring to this data base and ++++++++++ ++++++++++ the literature cited at the end of the data base. ++++++++++ ++++++++++ The original data base will be revised without ++++++++++ ++++++++++ notice, whenever necessary. Future revisions ++++++++++ ++++++++++ will be notified to those who register by writing ++++++++++ ++++++++++ to Research Organizer: ++++++++++ ++++++++++ ++++++++++ ++++++++++ Y. Nagano ++++++++++ ++++++++++ Department of Mechanical Engineering ++++++++++ ++++++++++ Nagoya Institute of Technology ++++++++++ ++++++++++ Gokiso-cho, Showa-ku, Nagoya 466 ++++++++++ ++++++++++ Japan. ++++++++++ ++++++++++ ++++++++++ ++++++++++ March 1992 ++++++++++ ++++++++++ ++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1. DATA No. (FILE NAME) NW_BL006 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, Y. Nagano, and M. Tagawa b. Dep. of Mech. Eng., Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya 466 c. Thermally Driven Turbulent Boundary Layer d. 8th Symposium on Turbulent Shear Flows Technical University of Munich e. Vol. 2, 24.3.1-24.3.6 (1991) 4. ABSTRACT OF EXPERIMENT Velocity and temperature measurements have been conducted to investigate the structure and heat transport of a turbulent natural convection boundary layer along a vertical plate. The results presented include important knowledge of the spanwise velocity fluctuation, which is indispensable to the examination of the turbulent kinetic energy budget and the construction of a turbulence model for turbulent buoyant flows. The turbulence structure is discussed on the basis of a spectral analysis of velocity and temperature fluctuations and a conditional sampling for Reynolds shear stress and turbulent heat fluxes. 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] 2.538 : Vertical location Tw[deg.] 60.00 : Wall temp. Ta[deg.] 18.60 : Ambient temp. Pa[Pa] 1.016E05 : Atom. pres. Grx 7.985E10 : 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/(273.15+Ta). Ambient temperature increased at the rate of about 0.6 deg./m in the vertical direction. 7. MEASURED VARIABLES 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 uw - Reynolds stress W - Mean spanwise velocity w2 - Intensity of spanwise velocity fluctuation (rms value) wt - Spanwise turbulent heat flux y - Distance normal to the flat plate 8. DATA Grx=7.985E+10, Tw=60.00 deg., Ta=18.60 deg., Pr=0.710 u*=0.06801 m/s (u*: Friction velocity) t*=2.630 deg. (t*: Friction temperature) N=1.6881E-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. Mean velocities and mean temperature y [mm] y+ U+ W+ T+ 1 1.21 4.900E+00 3.669E+00 -3.000E-02 3.309E+00 2 1.31 5.300E+00 4.022E+00 -3.500E-02 3.384E+00 3 1.41 5.700E+00 4.204E+00 -3.300E-02 3.691E+00 4 1.51 6.100E+00 4.489E+00 -4.000E-03 3.887E+00 5 1.61 6.500E+00 4.727E+00 -2.000E-02 4.144E+00 6 1.81 7.300E+00 5.155E+00 2.000E-02 4.675E+00 7 2.01 8.100E+00 5.385E+00 -1.100E-02 5.089E+00 8 2.21 8.900E+00 5.752E+00 -1.300E-02 5.499E+00 9 2.41 9.700E+00 6.199E+00 -1.800E-02 5.820E+00 10 2.61 1.050E+01 6.513E+00 1.600E-02 6.147E+00 11 3.11 1.250E+01 7.108E+00 4.400E-02 7.165E+00 12 3.61 1.450E+01 7.732E+00 3.700E-02 7.802E+00 13 4.11 1.660E+01 8.035E+00 4.700E-02 8.545E+00 14 4.61 1.860E+01 8.402E+00 -3.100E-02 8.842E+00 15 5.61 2.260E+01 8.846E+00 1.000E-03 9.664E+00 16 6.61 2.660E+01 9.268E+00 6.000E-03 1.021E+01 17 7.61 3.070E+01 9.431E+00 -2.000E-03 1.060E+01 18 8.61 3.470E+01 9.468E+00 1.300E-02 1.102E+01 19 9.61 3.870E+01 9.485E+00 1.600E-02 1.132E+01 20 10.61 4.280E+01 9.603E+00 -5.000E-03 1.147E+01 21 13.61 5.480E+01 9.397E+00 -5.000E-03 1.212E+01 22 16.61 6.690E+01 9.237E+00 -1.800E-02 1.241E+01 23 20.61 8.300E+01 8.939E+00 -6.000E-03 1.285E+01 24 25.61 1.032E+02 8.773E+00 -4.000E-03 1.312E+01 25 30.61 1.233E+02 8.303E+00 4.400E-02 1.344E+01 26 40.61 1.636E+02 7.741E+00 1.300E-02 1.377E+01 27 50.61 2.039E+02 7.306E+00 -2.500E-02 1.406E+01 28 60.61 2.442E+02 6.394E+00 -1.000E-02 1.435E+01 29 70.61 2.845E+02 6.084E+00 2.100E-02 1.450E+01 30 80.61 3.248E+02 5.424E+00 1.500E-02 1.467E+01 31 100.61 4.053E+02 4.318E+00 1.100E-02 1.493E+01 32 120.61 4.859E+02 3.389E+00 -2.200E-02 1.517E+01 33 140.61 5.665E+02 2.438E+00 -5.000E-02 1.523E+01 34 160.61 6.471E+02 1.925E+00 -4.800E-02 1.536E+01 35 180.61 7.276E+02 1.510E+00 -3.600E-02 1.539E+01 36 200.61 8.082E+02 1.258E+00 1.600E-02 1.537E+01 b. Intensities of velocity and temperature fluctuations y [mm] y+ u2/u* w2/u* t2/t* 1 1.21 4.900E+00 7.420E-01 5.600E-01 1.451E+00 2 1.31 5.300E+00 8.240E-01 5.810E-01 1.485E+00 3 1.41 5.700E+00 8.900E-01 6.030E-01 1.580E+00 4 1.51 6.100E+00 9.480E-01 6.990E-01 1.643E+00 5 1.61 6.500E+00 1.009E+00 7.140E-01 1.768E+00 6 1.81 7.300E+00 1.142E+00 7.840E-01 1.918E+00 7 2.01 8.100E+00 1.245E+00 9.390E-01 2.082E+00 8 2.21 8.900E+00 1.283E+00 1.018E+00 2.179E+00 9 2.41 9.700E+00 1.342E+00 1.054E+00 2.283E+00 10 2.61 1.050E+01 1.407E+00 1.110E+00 2.276E+00 11 3.11 1.250E+01 1.487E+00 1.196E+00 2.450E+00 12 3.61 1.450E+01 1.585E+00 1.285E+00 2.485E+00 13 4.11 1.660E+01 1.669E+00 1.374E+00 2.555E+00 14 4.61 1.860E+01 1.692E+00 1.471E+00 2.546E+00 15 5.61 2.260E+01 1.770E+00 1.507E+00 2.527E+00 16 6.61 2.660E+01 1.766E+00 1.504E+00 2.438E+00 17 7.61 3.070E+01 1.756E+00 1.472E+00 2.350E+00 18 8.61 3.470E+01 1.817E+00 1.511E+00 2.230E+00 19 9.61 3.870E+01 1.832E+00 1.507E+00 2.157E+00 20 10.61 4.280E+01 1.822E+00 1.528E+00 2.093E+00 21 13.61 5.480E+01 1.878E+00 1.513E+00 1.876E+00 22 16.61 6.690E+01 1.882E+00 1.521E+00 1.706E+00 23 20.61 8.300E+01 1.942E+00 1.540E+00 1.527E+00 24 25.61 1.032E+02 1.968E+00 1.568E+00 1.374E+00 25 30.61 1.233E+02 1.987E+00 1.612E+00 1.205E+00 26 40.61 1.636E+02 2.073E+00 1.637E+00 1.056E+00 27 50.61 2.039E+02 2.005E+00 1.582E+00 8.970E-01 28 60.61 2.442E+02 1.987E+00 1.557E+00 8.080E-01 29 70.61 2.845E+02 1.981E+00 1.517E+00 7.160E-01 30 80.61 3.248E+02 1.926E+00 1.450E+00 6.750E-01 31 100.61 4.053E+02 1.759E+00 1.227E+00 5.640E-01 32 120.61 4.859E+02 1.676E+00 9.440E-01 4.700E-01 33 140.61 5.665E+02 1.368E+00 7.400E-01 4.610E-01 34 160.61 6.471E+02 1.119E+00 6.430E-01 4.280E-01 35 180.61 7.276E+02 8.810E-01 5.590E-01 4.290E-01 36 200.61 8.082E+02 7.200E-01 5.040E-01 3.950E-01 c. Reynolds stress and turbulent heat fluxes y [mm] y+ uw/u*u* ut/u*t* wt/u*t* 1 1.21 4.900E+00 -1.800E-02 8.000E-03 6.400E-02 2 1.31 5.300E+00 1.000E-03 -9.600E-02 5.200E-02 3 1.41 5.700E+00 -4.000E-03 -4.300E-02 5.200E-02 4 1.51 6.100E+00 5.000E-03 -7.600E-02 6.500E-02 5 1.61 6.500E+00 -2.000E-03 -1.750E-01 2.500E-02 6 1.81 7.300E+00 8.000E-03 -5.000E-02 2.600E-02 7 2.01 8.100E+00 6.400E-02 -4.100E-02 -4.100E-02 8 2.21 8.900E+00 6.000E-02 -2.400E-02 3.300E-02 9 2.41 9.700E+00 8.400E-02 -2.800E-02 5.000E-02 10 2.61 1.050E+01 5.400E-02 0.000E+00 8.700E-02 11 3.11 1.250E+01 2.100E-02 3.360E-01 1.000E-03 12 3.61 1.450E+01 3.000E-02 5.830E-01 7.600E-02 13 4.11 1.660E+01 -4.000E-03 9.780E-01 3.200E-02 14 4.61 1.860E+01 4.000E-02 1.087E+00 4.500E-02 15 5.61 2.260E+01 3.500E-02 1.557E+00 4.000E-03 16 6.61 2.660E+01 -3.200E-02 1.618E+00 4.700E-02 17 7.61 3.070E+01 3.100E-02 1.751E+00 8.700E-02 18 8.61 3.470E+01 3.500E-02 1.971E+00 2.500E-02 19 9.61 3.870E+01 3.600E-02 1.981E+00 -1.500E-02 20 10.61 4.280E+01 2.000E-02 1.972E+00 -6.000E-03 21 13.61 5.480E+01 8.000E-02 2.012E+00 -8.000E-02 22 16.61 6.690E+01 6.100E-02 1.849E+00 7.500E-02 23 20.61 8.300E+01 1.000E-02 1.816E+00 4.000E-03 24 25.61 1.032E+02 6.000E-02 1.663E+00 1.600E-02 25 30.61 1.233E+02 -4.900E-02 1.426E+00 -2.000E-02 26 40.61 1.636E+02 2.900E-02 1.323E+00 -8.000E-03 27 50.61 2.039E+02 1.300E-02 1.075E+00 -3.100E-02 28 60.61 2.442E+02 2.600E-02 9.280E-01 1.000E-03 29 70.61 2.845E+02 0.000E+00 8.190E-01 -6.000E-03 30 80.61 3.248E+02 -1.200E-02 7.360E-01 -1.600E-02 31 100.61 4.053E+02 -1.900E-02 5.060E-01 1.400E-02 32 120.61 4.859E+02 2.900E-02 4.130E-01 -7.000E-03 33 140.61 5.665E+02 4.100E-02 2.250E-01 9.000E-03 34 160.61 6.471E+02 6.200E-02 1.370E-01 1.300E-02 35 180.61 7.276E+02 1.600E-02 4.200E-02 1.000E-02 36 200.61 8.082E+02 -4.900E-02 -5.000E-03 -2.000E-03 9. MEASUREMENT UNCERTAINTY The estimated uncertainties (95% coverage) at y=9.61 mm are as follows: y+ = -+ 0.13 U+ = -+ 0.14 W+ = -+ 0.24 T+ = -+ 0.13 u2/u* = -+ 0.04 w2/u* = -+ 0.03 t2/t* = -+ 0.05 uw/u*u*= -+ 0.08 ut/u*t*= -+ 0.07 wt/u*t*= -+ 0.05 10. GRAPH File name Contents U2W2T2 INTENSITY OF VELOCITY AND TEMPERATURE FLUCTUATIONS UWT MEAN VELOCITIES AND MEAN TEMPERATURE UWUTWT REYNOLDS STRESS AND TURBULENT HEAT FLUXES 11. REFERENCES 1. T. Tsuji and Y. Nagano, Characteristics of a Turblent Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 1723-1734 (1988). 2. T. Tsuji and Y. Nagano, Turbulence Measurements in a Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 2101-2111 (1988). 12. DISCUSSION