******************************************************************************** ******************************************************************************** ********** ********** ********** "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_BL007 2. KEY WORDS Natural Convection, Turbulent Boundary Layer, Reynolds Stress Turbulent Heat Flux 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. Estimation of Reynolds Stress and Turbulent Heat Flux in a Turbulent Natural Convection Boundary Layer d. Unpublished 4. ABSTRACT Turbulent quantities of velocity and temperature in a natural convection boundary layer along a vertical plate have been investigated with an anemometry technique (refs. [1] and [2]). The direct measurements of Reynolds stress and turbulent heat flux are verified by excellent agreement with the indirect measurements estimated by integrating momentum and thermal energy equations with measured mean velocity and mean temperature (ref. [2]). The indirect measurements of Reynolds stress and turbulent heat flux at Grashof numbers correspond- ing those shown in ref. [1] are presented. 5. INSTRUMENTATION The flat surface generating flow was a copper plate 4 m high, 1 m wide and 2 mm thick. A normal hot-wire and a cold-wire made of 0.0031 mm dia. tungsten were used to measure fluid velocity and temperature. 6. EXPERIMENTAL PARAMETERS *** Test conditions *** No. 1 No. 2 No. 3 No. 4 Comments x [m] 1.438 1.918 2.535 3.244 : Vertical location Tw [ßC] 60.01 60.05 59.97 60.42 : Wall temp. Ta [ßC] 16.36 16.86 16.69 16.51 : Ambient temp. Pa [Pa] 1.012E05 1.012E05 1.013E05 1.015E05 : Atom. pres. Grx 1.553E10 3.624E10 8.441E10 1.797E11 : Grashof no. Pr 0.710 0.710 0.710 0.710 : Prandtl no. Physical properties were evaluated at the film tempera- ture (=(Tw+Ta)/2), except that the body expansion coefficient B was defined as 1/(273.15+Ta). Ambient temperature increased nearly 2 ßC in the vertical direction from the leading to the trailing edges of the plate. 7. NOMENCLATURE Grx - Grashof number t* - Friction temperature u* - Friction velocity uv - Reynolds stress vt - Transverse turbulent heat flux y - Distance normal to the flat plate y+ - Dimensionless distance = u*y/N N - Kinematic viscosity 8. DATA NO. 1 Grx=1.553E10, Tw=60.01 deg.C, Ta=16.36 deg.C N=1.6831E-05 m**2/s, u*=0.06487 m/s, t*=2.961 deg.C Pr=0.710, y+=u*y/N y+ uv/u*u* vt/u*t* 1 5.505E-01 1.791E-02 -1.152E-03 2 7.865E-01 1.945E-02 -1.691E-03 3 1.180E+00 1.603E-02 -2.010E-03 4 1.573E+00 1.986E-02 -1.368E-03 5 1.966E+00 2.303E-02 -1.153E-04 6 2.360E+00 2.721E-02 1.790E-04 7 3.146E+00 4.358E-02 4.743E-03 8 3.933E+00 5.895E-02 2.448E-02 9 4.719E+00 6.169E-02 5.496E-02 10 5.505E+00 6.187E-02 8.949E-02 11 6.292E+00 6.455E-02 1.348E-01 12 7.079E+00 6.485E-02 1.887E-01 13 7.865E+00 8.984E-02 1.946E-01 14 9.342E+00 8.923E-02 2.877E-01 15 1.081E+01 8.907E-02 3.688E-01 16 1.226E+01 8.640E-02 4.264E-01 17 1.370E+01 8.771E-02 4.694E-01 18 1.513E+01 1.070E-01 5.014E-01 19 1.727E+01 1.614E-01 5.577E-01 20 1.939E+01 2.175E-01 6.165E-01 21 2.219E+01 2.857E-01 6.757E-01 22 2.567E+01 3.574E-01 7.179E-01 23 2.912E+01 4.273E-01 7.507E-01 24 3.254E+01 4.956E-01 7.825E-01 25 3.595E+01 5.561E-01 8.030E-01 26 4.270E+01 6.643E-01 8.096E-01 27 4.939E+01 7.588E-01 8.105E-01 28 5.603E+01 8.428E-01 8.076E-01 29 6.262E+01 9.179E-01 7.998E-01 30 6.917E+01 9.841E-01 7.900E-01 31 8.216E+01 1.094E+00 7.678E-01 32 9.503E+01 1.180E+00 7.452E-01 33 1.078E+02 1.247E+00 7.229E-01 34 1.205E+02 1.298E+00 6.978E-01 35 1.331E+02 1.335E+00 6.717E-01 36 1.456E+02 1.360E+00 6.445E-01 37 1.581E+02 1.375E+00 6.160E-01 38 1.705E+02 1.379E+00 5.878E-01 39 1.829E+02 1.374E+00 5.615E-01 40 1.952E+02 1.362E+00 5.347E-01 41 2.136E+02 1.331E+00 4.954E-01 42 2.318E+02 1.288E+00 4.578E-01 43 2.561E+02 1.207E+00 4.113E-01 44 2.862E+02 1.085E+00 3.587E-01 45 3.161E+02 9.539E-01 3.058E-01 46 3.459E+02 8.222E-01 2.583E-01 47 3.755E+02 6.822E-01 2.134E-01 48 4.050E+02 5.497E-01 1.734E-01 49 4.344E+02 4.187E-01 1.336E-01 50 4.636E+02 2.924E-01 1.043E-01 51 4.927E+02 1.681E-01 7.573E-02 52 5.507E+02 -5.224E-02 4.739E-02 NO. 2 Grx=3.624E10, Tw=60.05 deg.C, Ta=16.86 deg.C N=1.6857E-05 m**2/s, u*=0.06671 m/s, t*=2.841 deg.C Pr=0.710, y+=u*y/N y+ uv/u*u* vt/u*t* 1 6.085E-01 1.753E-02 -1.344E-03 2 8.692E-01 1.889E-02 -1.863E-03 3 1.304E+00 1.512E-02 -2.010E-03 4 1.738E+00 1.858E-02 -7.365E-04 5 2.173E+00 2.133E-02 7.460E-05 6 2.608E+00 2.506E-02 -1.860E-04 7 3.477E+00 4.040E-02 7.632E-03 8 4.346E+00 5.461E-02 3.179E-02 9 5.215E+00 5.606E-02 7.079E-02 10 6.085E+00 5.484E-02 1.153E-01 11 6.954E+00 5.608E-02 1.622E-01 12 7.823E+00 5.489E-02 2.126E-01 13 8.692E+00 5.431E-02 2.627E-01 14 1.043E+01 5.662E-02 3.640E-01 15 1.216E+01 6.077E-02 4.381E-01 16 1.389E+01 6.336E-02 4.834E-01 17 1.562E+01 6.989E-02 5.210E-01 18 1.735E+01 9.277E-02 5.634E-01 19 1.994E+01 1.498E-01 6.331E-01 20 2.254E+01 2.080E-01 6.818E-01 21 2.599E+01 2.789E-01 7.234E-01 22 3.031E+01 3.548E-01 7.631E-01 23 3.463E+01 4.282E-01 7.954E-01 24 3.895E+01 5.002E-01 8.158E-01 25 4.326E+01 5.653E-01 8.200E-01 26 5.188E+01 6.821E-01 8.214E-01 27 6.050E+01 7.848E-01 8.187E-01 28 6.912E+01 8.769E-01 8.101E-01 29 7.773E+01 9.594E-01 7.991E-01 30 8.634E+01 1.033E+00 7.866E-01 31 1.036E+02 1.155E+00 7.611E-01 32 1.208E+02 1.253E+00 7.349E-01 33 1.380E+02 1.331E+00 7.067E-01 34 1.552E+02 1.392E+00 6.773E-01 35 1.723E+02 1.437E+00 6.463E-01 36 1.895E+02 1.468E+00 6.143E-01 37 2.067E+02 1.487E+00 5.826E-01 38 2.239E+02 1.494E+00 5.520E-01 39 2.410E+02 1.491E+00 5.220E-01 40 2.582E+02 1.480E+00 4.924E-01 41 2.839E+02 1.450E+00 4.497E-01 42 3.097E+02 1.404E+00 4.100E-01 43 3.440E+02 1.320E+00 3.614E-01 44 3.869E+02 1.190E+00 3.008E-01 45 4.297E+02 1.046E+00 2.466E-01 46 4.726E+02 9.009E-01 1.961E-01 47 5.154E+02 7.446E-01 1.508E-01 48 5.582E+02 5.946E-01 1.089E-01 49 6.010E+02 4.468E-01 7.528E-02 50 6.438E+02 3.051E-01 4.452E-02 51 6.866E+02 1.664E-01 2.711E-02 52 7.722E+02 -6.965E-02 1.775E-02 No. 3 Grx=8.441E10, Tw=59.97 deg.C, Ta=16.69 deg.C N=1.6815E-05 m**2/s, u*=0.06929 m/s, t*=2.740 deg.C Pr=0.710, y+=u*y/N y+ uv/u*u* vt/u*t* 1 6.723E-01 1.715E-02 -1.505E-03 2 9.604E-01 1.832E-02 -2.003E-03 3 1.441E+00 1.421E-02 -2.010E-03 4 1.921E+00 1.728E-02 -5.576E-04 5 2.401E+00 1.962E-02 2.533E-04 6 2.881E+00 2.288E-02 9.054E-04 7 3.842E+00 3.718E-02 1.480E-02 8 4.802E+00 5.020E-02 4.308E-02 9 5.763E+00 5.035E-02 8.285E-02 10 6.723E+00 4.772E-02 1.338E-01 11 7.683E+00 4.745E-02 1.931E-01 12 8.644E+00 4.473E-02 2.499E-01 13 9.604E+00 2.647E-02 3.244E-01 14 1.160E+01 2.990E-02 4.161E-01 15 1.361E+01 3.602E-02 4.812E-01 16 1.563E+01 4.104E-02 5.282E-01 17 1.766E+01 4.990E-02 5.747E-01 18 1.970E+01 7.406E-02 6.229E-01 19 2.276E+01 1.340E-01 6.861E-01 20 2.585E+01 1.928E-01 7.286E-01 21 2.998E+01 2.651E-01 7.609E-01 22 3.517E+01 3.437E-01 7.955E-01 23 4.039E+01 4.201E-01 8.199E-01 24 4.563E+01 4.954E-01 8.294E-01 25 5.090E+01 5.638E-01 8.313E-01 26 6.148E+01 6.874E-01 8.302E-01 27 7.213E+01 7.967E-01 8.248E-01 28 8.283E+01 8.953E-01 8.149E-01 29 9.358E+01 9.844E-01 8.019E-01 30 1.044E+02 1.064E+00 7.883E-01 31 1.261E+02 1.198E+00 7.606E-01 32 1.479E+02 1.308E+00 7.332E-01 33 1.698E+02 1.398E+00 7.029E-01 34 1.919E+02 1.470E+00 6.709E-01 35 2.140E+02 1.525E+00 6.375E-01 36 2.363E+02 1.564E+00 6.039E-01 37 2.585E+02 1.590E+00 5.720E-01 38 2.809E+02 1.605E+00 5.401E-01 39 3.033E+02 1.609E+00 5.085E-01 40 3.258E+02 1.603E+00 4.777E-01 41 3.596E+02 1.580E+00 4.345E-01 42 3.935E+02 1.542E+00 3.947E-01 43 4.389E+02 1.466E+00 3.441E-01 44 4.959E+02 1.344E+00 2.828E-01 45 5.531E+02 1.205E+00 2.262E-01 46 6.105E+02 1.061E+00 1.773E-01 47 6.681E+02 9.039E-01 1.309E-01 48 7.259E+02 7.513E-01 9.253E-02 49 7.838E+02 5.996E-01 5.855E-02 50 8.419E+02 4.532E-01 3.307E-02 51 9.001E+02 3.118E-01 1.971E-02 52 1.017E+03 7.280E-02 9.035E-03 NO. 4 Grx=1.797E11, Tw=60.42 deg.C, Ta=16.51 deg.C N=1.6804E-05 m**2/s, u*=0.07182 m/s, t*=2.695 deg.C Pr=0.710, y+=u*y/N y+ uv/u*u* vt/u*t* 1 7.350E-01 1.681E-02 -1.533E-03 2 1.050E+00 1.782E-02 -2.003E-03 3 1.575E+00 1.340E-02 -1.845E-03 4 2.100E+00 1.612E-02 -4.074E-04 5 2.625E+00 1.807E-02 2.373E-04 6 3.150E+00 2.090E-02 1.822E-03 7 4.200E+00 3.424E-02 2.082E-02 8 5.250E+00 4.617E-02 5.644E-02 9 6.300E+00 4.513E-02 1.032E-01 10 7.350E+00 4.124E-02 1.577E-01 11 8.400E+00 3.966E-02 2.167E-01 12 9.450E+00 3.559E-02 2.739E-01 13 1.050E+01 6.009E-03 3.664E-01 14 1.274E+01 9.220E-03 4.588E-01 15 1.501E+01 1.569E-02 5.154E-01 16 1.729E+01 2.134E-02 5.640E-01 17 1.960E+01 3.080E-02 6.129E-01 18 2.192E+01 5.488E-02 6.643E-01 19 2.542E+01 1.101E-01 7.177E-01 20 2.896E+01 1.690E-01 7.478E-01 21 3.371E+01 2.412E-01 7.835E-01 22 3.970E+01 3.206E-01 8.171E-01 23 4.575E+01 3.985E-01 8.346E-01 24 5.184E+01 4.756E-01 8.372E-01 25 5.798E+01 5.459E-01 8.377E-01 26 7.036E+01 6.736E-01 8.370E-01 27 8.287E+01 7.880E-01 8.285E-01 28 9.549E+01 8.915E-01 8.169E-01 29 1.082E+02 9.853E-01 8.038E-01 30 1.210E+02 1.070E+00 7.902E-01 31 1.469E+02 1.214E+00 7.612E-01 32 1.730E+02 1.335E+00 7.318E-01 33 1.993E+02 1.435E+00 7.008E-01 34 2.259E+02 1.517E+00 6.677E-01 35 2.526E+02 1.581E+00 6.335E-01 36 2.795E+02 1.630E+00 5.994E-01 37 3.065E+02 1.665E+00 5.666E-01 38 3.337E+02 1.689E+00 5.343E-01 39 3.610E+02 1.701E+00 5.024E-01 40 3.885E+02 1.704E+00 4.714E-01 41 4.299E+02 1.694E+00 4.277E-01 42 4.714E+02 1.667E+00 3.875E-01 43 5.272E+02 1.606E+00 3.360E-01 44 5.975E+02 1.501E+00 2.746E-01 45 6.682E+02 1.377E+00 2.180E-01 46 7.393E+02 1.245E+00 1.694E-01 47 8.109E+02 1.099E+00 1.236E-01 48 8.828E+02 9.543E-01 8.566E-02 49 9.551E+02 8.079E-01 5.243E-02 50 1.028E+03 6.641E-01 2.621E-02 51 1.101E+03 5.234E-01 1.092E-02 52 1.247E+03 2.836E-01 -1.946E-03 53 1.395E+03 1.370E-01 -4.652E-03 9. GRAPH File name Contents NO1 REYNOLDS STRESS AND TURBULENT HEAT FLUX NO2 REYNOLDS STRESS AND TURBULENT HEAT FLUX NO3 REYNOLDS STRESS AND TURBULENT HEAT FLUX NO4 REYNOLDS STRESS AND TURBULENT HEAT FLUX 10. REFERENCES 1. T. Tsuji and Y. Nagano, Characteristics of a Turbulent Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 1723-1734 (1988). 2. T. Tsuji and Y. Nagano, Turbulent Measurements in a Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 2101-2111 (1988). 11. DISCUSSION