********************************************************************* ********************************************************************* ******** ******** ******** "Establishment of ******** ******** the Direct Numerical Simulation Data Bases of ******** ******** Turbulent Transport Phenomena" ******** ******** ******** ******** Co-operative Research ******** ******** No. 02302043 ******** ******** ******** ******** Supported by the Ministry of Education, ******** ******** Science and Culture ******** ******** ******** ******** 1990 - 1992 ******** ******** ******** ******** ******** ******** ******** ******** N. Kasagi (Organizer) ******** ******** K. Horiuchi, Y. Miyake, T. Miyauchi, Y. Nagano ******** ******** ******** ********************************************************************* ********************************************************************* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++ << CAUTION >> ++++++++ ++++++++ ++++++++ ++++++++ All rights are reserved by the computors 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: ++++++++ ++++++++ ++++++++ ++++++++ N. Kasagi ++++++++ ++++++++ Department of Mechanical Engineering ++++++++ ++++++++ The University of Tokyo ++++++++ ++++++++ Bunkyo-ku, Tokyo 113 ++++++++ ++++++++ Japan. ++++++++ ++++++++ ++++++++ ++++++++ December 1990 ++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ============ this data base begins from this line =================== Test case: Homogeneous Isotropic Flow with Passive Scalar Diffusion Code number: IS____UT.HM1 Date of Release: March 20, 1991 Computors: T. Miyauchi, M. Tanahashi and T. Ishizu Department of Mechanical Engineering Science Tokyo Institute of Technology Meguro-ku, Tokyo 152 Nomenclature: E: spectral distribution of kinetic energy; cm**3/s**2, E(k) = 2 x pai x k**2 x ui(k) x conjg(ui(k)) (i=1,2,3) repeated summation is used for i Ene: kinetic energy per unit mass (space averaged); cm**2/s**2, Ens: enstrophy; 1/s**2 Et: spectral distribution of scalar fluctuation; cmK**2, Et(k) = 2 x pai x k**2 x dT(k) x conjg(dT(k)) dT = fluctuation from mean temperature : spatialy averaged value of variable f Fi: flatness factor of ui Fdi: flatness factor of i-derivative of ui Int: mean square value of temperature fluctuation; K**2 k: absolute value of wave number; 1/cm L: reference length = 2 x pai(fundamental wave length); cm Lu: integral scale of u1 in x1-derection; cm, Lu = the integral of R11 from zero to pai Lt: integral scale of T in x1-direction; cm, Lt = the integral of Rtt from zero to pai Ramdu: Taylor micro scale for u1; cm Ramdt: Taylor micro scale for T; cm Re_ramd:micro scale Reynolds number U*Ramdu/Ve Rtt: two-point auto-correlation coefficient of scalar fluctuation Rtt = / Rij: two-point correlation coefficient of ui and uj Rij = /sqrt()/sqrt() Rut: two-point correlation coefficient of u1 and T Rut = /sqrt()/sqrt() Si: skewness factor of ui Sdi: skewness factor of i-th derivative of ui tau: lag in x1-direction; cm T: temprature; K TS: time step; s, 1TS=0.005 ui: velocity in xi-direction; cm/s U: reference velocity = root mean square velocity fluctuation at initial stage; cm/s Ve: kinematic viscosity; cm**2/s 1. Description of Flow Field The flow field simulated is homogeneous isotropic turbulence with temperature diffusion. Temperature fluctuation is not so large so that temperature can be assumed to be a passive scalar. We simulated two cases with Prandtl numbers of 0.20 and 0.71. 2. Numerical Method Governing Equation: time dependent Navier Stokes equation (rotational form) and energy conservation equation. Discretization method:spectral method = 64 x 64 x 64 Fourier modes in the x1-,x2-,x3-direction. Aliasing treatment:nonlinear term is computed in physical space by using padding method. Time integration:second order Adams-Bashforth scheme for the nonlinear term, Backward-Euler scheme for the pressure term, and Crank-Nicolson scheme for the viscous and diffusion terms. Size of computational box:(2 x pai) x (2 x pai) x (2 x pai) Initial spectral distribution: E(k)=0.038 x k**4 x exp(-0.14 x k**2) Et(k)=0.40 x k**2 x exp(-0.10 x k**2) Error in continuity equation = Max{abs(div u)}: less than 1.0E-15 Computer:HITAC-S820/80 at the Computer Center of the University of Tokyo 3. Flow condition Re = U*L/Ve =309 4. Numerical data of Velocity Field 4.1 Kinetic Energy per Unit Mass TS Ene(TS) 0 1.22052E-1 100 1.05959E-1 200 9.10524E-2 300 7.75190E-2 400 6.58436E-2 500 5.60734E-2 600 4.80062E-2 4.2 3-D Energy Spectrum TS=0 k E(k) 1.41421 1.00360E-1 2.00000 3.10754E-1 3.00000 8.31843E-1 4.00000 9.14860E-1 5.00000 6.44100E-1 6.00000 3.23011E-1 7.00000 9.38450E-2 8.06225 1.85709E-2 TS=200 k E(k) 1.00000 5.55352E-4 2.00000 2.40827E-1 3.00000 7.06399E-1 4.00000 4.35846E-1 5.00000 2.82298E-1 6.00000 1.74570E-1 7.00000 1.25323E-1 8.00000 5.20969E-3 9.00000 6.37578E-2 10.0000 1.13119E-2 15.0000 2.32024E-3 20.0000 2.74516E-2 25.0000 1.44430E-5 30.0000 1.20502E-6 35.0000 2.74168E-7 40.1249 2.04499E-8 45.0222 1.05743E-9 TS=400 k E(k) 1.00000 1.93256E-3 2.00000 1.78107E-1 3.00000 5.10856E-1 4.00000 7.11306E-2 5.00000 2.05873E-1 6.00000 1.01789E-1 7.00000 1.54639E-1 8.00000 3.47021E-3 9.00000 5.38501E-2 10.0000 9.67449E-3 15.0000 2.98650E-3 20.0000 4.92136E-5 25.0000 1.81891E-5 30.0000 1.54466E-6 35.0000 2.12039E-7 40.1249 2.19996E-8 45.0555 1.44693E-9 TS=600 k E(k) 1.00000 3.46109E-3 2.00000 1.29655E-1 3.00000 3.61931E-1 4.00000 1.71386E-2 5.00000 1.49187E-1 6.00000 6.01920E-2 7.00000 9.58069E-2 8.00000 3.81687E-3 9.00000 3.20410E-2 10.0000 5.81278E-3 15.0000 1.72995E-3 20.0000 1.88906E-5 25.0000 6.13948E-6 30.0000 3.91979E-7 35.0000 4.12451E-8 40.1249 3.64087E-9 42.7317 1.09891E-9 4.3 Two-point Velocity Correlations (x1-direction) 4.3.1 Two-point Auto-correlation of u1 TS=0 tau R11(tau) 0.00000 1.00000 3.92699E-1 8.01477E-1 7.85396E-1 4.16887E-1 1.17809 1.42585E-1 1.57079 2.34320E-2 1.96349 -1.39152E-2 2.35619 -1.12421E-2 2.74889 1.01116E-2 3.04341 2.15049E-2 TS=200 tau R11(tau) 0.00000 1.00000 3.92699E-1 7.82555E-1 7.85396E-1 3.98984E-1 1.17809 1.22451E-1 1.57079 -4.69710E-3 1.96349 -3.47308E-2 2.35619 -3.68531E-2 2.74889 -3.75797E-2 3.04341 -3.68706E-2 TS=400 tau R11(tau) 0.00000 1.00000 3.92699E-1 7.77175E-1 7.85396E-1 4.09594E-1 1.17809 1.53880E-1 1.57079 2.83990E-2 1.96349 -1.87648E-2 2.35619 -4.80518E-2 2.74889 -7.61841E-2 3.04341 -8.72665E-2 TS=600 tau R11(tau) 0.00000 1.00000 3.92699E-1 7.96694E-1 7.85396E-1 4.58991E-1 1.17809 2.21358E-1 1.57079 9.09038E-2 1.96349 1.67314E-2 2.35619 -3.34679E-2 2.74889 -6.46255E-2 3.04341 -7.46684E-2 4.3.2 Two-point Cross-correlation of u1 and u2 TS=0 tau R12(tau) 0.00000 -2.52921E-3 3.92699E-1 1.36380E-2 7.85396E-1 1.95040E-2 1.17809 -7.93034E-3 1.57079 -3.07035E-2 1.96349 -2.27267E-2 2.35619 -1.34261E-2 2.74889 -2.45913E-2 3.04341 -4.06192E-2 TS=200 tau R12(tau) 0.00000 -9.15311E-3 3.92699E-1 -1.66495E-3 7.85396E-1 -1.16247E-2 1.17809 -3.88549E-2 1.57079 -6.18614E-2 1.96349 -6.62977E-2 2.35619 -6.43712E-2 2.74889 -6.87116E-2 3.04341 -7.34356E-2 TS=400 tau R12(tau) 0.00000 4.86372E-3 3.92699E-1 1.88666E-3 7.85396E-1 -9.99898E-3 1.17809 -9.54547E-3 1.57079 -1.45949E-2 1.96349 -3.48256E-2 2.35619 -4.74712E-2 2.74889 -4.52225E-2 3.04341 -4.54916E-2 TS=600 tau R12(tau) 0.00000 1.57828E-2 3.92699E-1 -7.63564E-4 7.85396E-1 -3.18279E-3 1.17809 2.74346E-2 1.57079 3.79977E-2 1.96349 1.39818E-2 2.35619 -1.67513E-2 2.74889 -2.57774E-2 3.04341 -2.45575E-2 4.4 Enstrophy TS Ens(TS) 0 1.72438 100 1.53886 200 1.43236 300 1.26384 400 1.06958 500 8.87075E-1 600 7.30283E-1 4.5 Flatness of u1 TS F1(TS) 0 3.22735 100 3.17413 200 3.09192 300 3.06572 400 3.07073 500 3.06446 600 3.03757 4.6 Flatness of x1 derivative of u1 TS Fd1(TS) 0 3.00407 100 3.21584 200 3.63375 300 3.86776 400 3.90112 500 3.81612 600 3.71646 4.7 Skewness of u1 TS S1(TS) 0 9.22152E-2 100 9.05295E-2 200 7.62247E-2 300 5.84252E-2 400 4.57007E-2 500 4.52819E-2 600 5.52007E-2 4.8 Skewness of x1 derivative of u1 TS Sd1(TS) 0 1.24398E-2 100 -3.71311E-1 200 -5.11329E-1 300 -5.42004E-1 400 -5.48522E-1 500 -5.45802E-1 600 -5.37426E-1 4.9 Taylor Micro Scale of u1 TS Ramdu 0 5.89143E-1 100 5.78069E-1 200 5.48347E-1 300 5.33189E-1 400 5.33179E-1 500 5.43749E-1 600 5.55990E-1 4.10 Micro Scale Reynolds Number TS Re_ramda 0 29.1078 100 26.6111 200 23.4000 300 20.9942 400 19.3484 500 18.2092 600 17.3492 4.11 Integral Scale of u1 TS Lu 0 7.70470E-1 100 7.46703E-1 200 6.90412E-1 300 6.70576E-1 400 6.96117E-1 500 7.44976E-1 600 8.00514E-1 5. Numerical data of Scalar Field 5.1 Averaged Intensity of Scalar fluctuation 5.1.1 Prandtl Nnmber = 0.20 TS Int(TS) 0 3.02647E-1 100 1.88012E-1 200 1.25224E-1 300 8.70439E-2 400 6.23675E-2 500 4.57898E-2 600 3.43929E-2 5.1.2 Prandtl Number = 0.71 TS Int(TS) 0 3.02647E-1 100 2.59492E-1 200 2.16989E-1 300 1.77294E-1 400 1.43593E-1 500 1.16202E-1 600 9.44040E-2 5.2 Spectrum of fluctuation 5.2.1 Prandtl Nnmber = 0.20 TS=0 k Et(k) 1.41421 4.02415E-1 2.00000 6.70266E-1 3.00000 9.92101E-1 4.00000 7.48541E-1 5.00000 5.38204E-1 6.00000 2.72123E-1 7.00000 8.73092E-2 7.81024 3.59780E-2 TS=200 k Et(k) 1.00000 1.05466E-3 2.00000 3.36166E-1 3.00000 3.67973E-1 4.00000 6.25681E-2 5.00000 6.43270E-2 6.00000 2.94095E-2 7.00000 2.19399E-2 8.00000 5.00320E-4 9.00000 8.67487E-3 10.0000 9.70602E-4 15.0000 6.25349E-5 20.0000 1.95121E-7 25.0000 2.32717E-8 30.0000 1.23606E-9 31.0644 1.19609E-9 TS=400 k Et(k) 1.00000 2.55930E-3 2.00000 1.44344E-1 3.00000 1.44038E-1 4.00000 1.13994E-2 5.00000 1.51787E-2 6.00000 5.00846E-3 7.00000 8.01863E-3 8.00000 4.40039E-4 9.00000 2.17536E-3 10.0000 4.03067E-4 15.0000 1.64498E-5 20.0000 4.98806E-8 25.0000 4.28694E-9 28.4604 1.20757E-9 TS=600 k Et(k) 1.00000 3.38334E-3 2.00000 6.41323E-2 3.00000 5.92391E-2 4.00000 2.47813E-3 5.00000 9.64493E-3 6.00000 2.90652E-3 7.00000 2.23367E-3 8.00000 1.82921E-4 9.00000 7.40450E-4 10.0000 1.20997E-4 15.0000 3.92064E-6 20.0000 1.22954E-8 25.0000 1.06088E-9 26.2488 1.23265E-9 5.2.2 Prandtl Number = 0.71 TS=0 k Et(k) 1.41421 4.02415E-1 2.00000 6.70266E-1 3.00000 9.92101E-1 4.00000 7.48541E-1 5.00000 5.38204E-1 6.00000 2.72123E-1 7.00000 8.73092E-2 7.81024 3.59780E-2 TS=200 k Et(k) 1.00000 1.29962E-3 2.00000 4.39541E-1 3.00000 6.68757E-1 4.00000 1.78571E-1 5.00000 2.47688E-1 6.00000 1.62595E-1 7.00000 1.52707E-1 8.00000 2.84070E-3 9.00000 1.21958E-1 10.0000 2.15648E-2 15.0000 5.25002E-3 20.0249 6.66627E-4 25.0000 3.16783E-5 30.0000 1.91073E-6 35.0000 3.52409E-7 40.1249 2.62925E-8 45.0222 1.06691E-9 45.4972 1.07276E-9 TS=400 k Et(k) 1.00000 3.63503E-3 2.00000 2.30373E-1 3.00000 4.05406E-1 4.00000 5.89957E-2 5.00000 9.92578E-2 6.00000 4.18847E-2 7.00000 1.35679E-1 8.00000 1.25409E-2 9.00000 7.35297E-2 10.0000 1.78520E-2 15.0000 4.28378E-3 20.0249 6.60598E-4 25.0000 1.95621E-5 30.0000 1.92381E-6 35.0000 1.98541E-7 40.1249 1.09693E-8 43.7035 1.20398E-9 TS=600 k Et(k) 1.00000 5.30288E-3 2.00000 1.18290E-1 3.00000 2.31282E-1 4.00000 1.85658E-2 5.00000 8.56520E-2 6.00000 3.71559E-2 7.00000 6.90075E-2 8.00000 4.60320E-3 9.00000 4.70612E-2 10.0000 9.06811E-3 15.0000 2.33428E-3 20.0249 2.38316E-4 25.0000 9.34227E-6 30.0000 4.70629E-7 35.0000 3.57281E-8 40.1249 4.17494E-9 42.7317 1.11619E-9 5.3 Two-point Scalar Correlation (x1-direction) 5.3.1 Two-point Auto-correlation of T 5.3.1.1 Prandtl Nnmber = 0.20 TS=0 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 7.65198E-1 7.85396E-1 3.80563E-1 1.17809 1.96080E-1 1.57079 1.29589E-1 1.96349 3.49275E-2 2.35619 -4.35902E-2 2.74889 -2.45681E-2 3.04341 7.40358E-3 TS=200 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 8.42460E-1 7.85396E-1 5.47156E-1 1.17809 3.06791E-1 1.57079 1.36871E-1 1.96349 5.10942E-3 2.35619 -9.71935E-2 2.74889 -1.62158E-1 3.04341 -1.82194E-1 TS=400 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 8.64442E-1 7.85396E-1 5.92639E-1 1.17809 3.41050E-1 1.57079 1.37506E-1 1.96349 -3.38250E-2 2.35619 -1.80986E-2 2.74889 -2.89195E-1 3.04341 -3.27239E-1 TS=600 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 8.75289E-1 7.85396E-1 6.12474E-1 1.17809 3.49222E-1 1.57079 1.18035E-1 1.96349 -8.43321E-2 2.35619 -2.53471E-2 2.74889 -3.74504E-1 3.04341 -4.17435E-1 5.3.1.2 Prandtl Number = 0.71 TS=0 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 7.65198E-1 7.85396E-1 3.80563E-1 1.17809 1.96080E-1 1.57079 1.29589E-1 1.96349 3.49275E-2 2.35619 -4.35902E-2 2.74889 -2.45681E-2 3.04341 7.40358E-3 TS=200 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 7.41081E-1 7.85396E-1 4.01289E-1 1.17809 2.12377E-1 1.57079 1.02886E-1 1.96349 1.18153E-2 2.35619 -6.33214E-2 2.74889 -1.08048E-1 3.04341 -1.16941E-1 TS=400 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 7.23875E-1 7.85396E-1 3.89504E-1 1.17809 2.03907E-1 1.57079 8.73791E-2 1.96349 -9.34931E-3 2.35619 -1.04056E-2 2.74889 -1.84025E-1 3.04341 -2.12603E-1 TS=600 tau Rtt(tau) 0.00000 1.00000 3.92699E-1 7.11879E-1 7.85396E-1 3.61104E-1 1.17809 1.74932E-1 1.57079 5.64651E-2 1.96349 -4.39034E-2 2.35619 -1.39069E-1 2.74889 -2.26159E-1 3.04341 -2.66649E-1 5.3.2 Two-point Cross-correlation of u1 and T 5.3.2.1 Prandtl Number = 0.20 TS=0 tau Rut(tau) 0.00000 -1.44586E-2 3.92699E-1 -6.11074E-3 7.85396E-1 -1.33807E-2 1.17809 -4.25926E-2 1.57079 -6.47857E-2 1.96349 -5.59928E-2 2.35619 -3.87882E-2 2.74889 -4.49668E-2 3.04341 -6.26223E-2 TS=200 tau Rut(tau) 0.00000 -1.04887E-3 3.92699E-1 8.77347E-4 7.85396E-1 -1.04764E-2 1.17809 -3.60806E-2 1.57079 -6.03131E-2 1.96349 -7.15026E-2 2.35619 -7.54783E-2 2.74889 -8.10526E-2 3.04341 -8.68597E-2 TS=400 tau Rut(tau) 0.00000 1.92512E-2 3.92699E-1 1.03815E-2 7.85396E-1 -2.50776E-3 1.17809 -8.33401E-3 1.57079 -1.85051E-2 1.96349 -4.12017E-2 2.35619 -6.19532E-2 2.74889 -7.13868E-2 3.04341 -7.65273E-2 TS=600 tau Rut(tau) 0.00000 2.80603E-2 3.92699E-1 1.27637E-2 7.85396E-1 7.49954E-3 1.17809 1.89814E-2 1.57079 1.81352E-2 1.96349 -6.40816E-3 2.35619 -3.68489E-2 2.74889 -5.48986E-2 3.04341 -6.30438E-2 5.3.2.2 Prandtl Number = 0.71 TS=0 tau Rut(tau) 0.00000 -1.44586E-2 3.92699E-1 -6.11074E-3 7.85396E-1 -1.33807E-2 1.17809 -4.25926E-2 1.57079 -6.47857E-2 1.96349 -5.59928E-2 2.35619 -3.87882E-2 2.74889 -4.49668E-2 3.04341 -6.26223E-2 TS=200 tau Rut(tau) 0.00000 -9.15311E-3 3.92699E-1 -1.66495E-3 7.85396E-1 -1.16247E-2 1.17809 -3.88549E-2 1.57079 -6.18614E-2 1.96349 -6.62977E-2 2.35619 -6.43712E-2 2.74889 -6.87116E-2 3.04341 -7.34356E-2 TS=400 tau Rut(tau) 0.00000 4.86372E-3 3.92699E-1 1.88666E-3 7.85396E-1 -9.99898E-3 1.17809 -9.54547E-3 1.57079 -1.45949E-2 1.96349 -3.48256E-2 2.35619 -4.74712E-2 2.74889 -4.52225E-2 3.04341 -4.54916E-2 TS=600 tau Rut(tau) 0.00000 1.57828E-2 3.92699E-1 -7.63564E-4 7.85396E-1 -3.18279E-3 1.17809 2.74346E-2 1.57079 3.79977E-2 1.96349 1.39818E-2 2.35619 -1.67513E-2 2.74889 -2.57774E-2 3.04341 -2.45575E-2 5.4 Taylor Micro Scale of T 5.4.1 Prandtl Number = 0.20 TS Ramdt 0 5.30994E-1 100 6.01636E-1 200 6.25611E-1 300 6.89005E-1 400 7.10113E-1 500 7.27146E-1 600 7.45882E-1 5.4.1 Prandtl Number = 0.71 TS Ramdt 0 5.30994E-1 100 5.09580E-1 200 4.71441E-1 300 4.56420E-1 400 4.49209E-1 500 4.44183E-1 600 4.43962E-1 5.5 Integral Scale of T 5.5.1 Prandtl Number = 0.20 TS Lt 0 7.63122E-1 100 8.24965E-1 200 8.19134E-1 300 7.85126E-1 400 7.37302E-1 500 6.89601E-1 600 6.48297E-1 5.5.1 Prandtl Number = 0.71 TS Lt 0 7.63122E-1 100 7.58729E-1 200 7.19570E-1 300 6.79317E-1 400 6.28680E-1 500 5.78482E-1 600 5.36436E-1 6. References 6.1 Miyauchi T. and Ishizu T., "Direct Numerical Simulation of Homogeneous Isotropic Turbulence. - Decay of passive scalar fluctuation", Prepr. of Jpn. Soc. Mech. Eng. No.914-2, pp. 166-168, (Kansaishibu Dai66ki Teijisoukai), (1991). (EOF)