Mech. Engg. Dept., Stanford University STANFORD CA 94305-3030 Collaborative Testing of Turbulence Models DATA LIBRARY 1. INTRODUCTION This library of experimental data and simulation results for turbulent flows was compiled for the project on Collaborative Testing of Turbulence Models funded by AFOSR, Army Research Office, NASA and ONR (see J. Fluids Engg vol. 116, p. 243, 1996), and is available as images of 1.44MB 3-1/2 in. MS-DOS diskettes. It falls into three parts:-- (i) the six disks, D1-D6, distributed to modelers taking part in the Collaboration (containing many more cases than were actually used) - in this JFE Data Bank (ii) seven disks, R1-R7 containing further selected, but mainly unedited, cases from the bank of undistributed data - in this JFE Data Bank (iii) the remainder of the data, "as-is" - available on request, at a cost of about US$10 per disk, from P. Bradshaw at the Stanford address above. The three parts are described in order in Sections 2 to 4. Section 5 is a set of informal notes on data which are not in the library but may be available from the originators. The text material in the J. Fluids Engg Data Bank is a - hopefully self-contained - description of the data. It includes or excerpts some documents issued to Collaborators, but much of the project material (e.g. graphs of results submitted by the Collaborators) exists only as paper copies, in the full "Proceedings" of the project (Stanford Univ. ME Dept Rept MD-73: total 650 pages) which is available from Bradshaw (price US$80 including handling and shipping): the Proceedings of the 1980-81 meeting (reprinted: 3 volumes, 1500 pages) are available at US$200. 2. DISTRIBUTED TEST CASES (Disks 1 to 6) 2.1 Disk contents and format The basis for the test cases was the data library for the 1980-81 AFOSR-IFP-Stanford Conference on Complex Turbulent Flows. Comparatively few of the 1980-81 cases were used: some of the newer test cases were almost direct replacements for 1980-81 data. Appendix A is a complete list of the 80-81 test cases. The data were compiled in packed format by Brian Cantwell; all values are given as integers, "intval", in the range 0 to 10000, with maximum and minimum values in separate `files', so the real value is "(min)+(intval)*(max- min)/10000". The data were transcribed from tape to disk by Prof. G.M. Lilley of Southampton University. The data on disks 1-3 differ from the original tape only in that each case occupies only one disk file: the beginnings and ends of the original tape files, counting serially from "file 1" in the first test case, are marked in the disk file. Note that internal references to `file' numbers start from no. 1 in each test case. For most purposes users can ignore the tape file numbers. File F0112 (Hinze) as originally distributed had two spurious (repeated) lines after the end of tape-file 33: these should be ignored. We distributed the 80-81 data unaltered (on Disk 1 for incompressible flow and Disks 2 and 3 for compressible flow) and in full except for five very long files. These exceptions are 0411 (circular cylinder), 0441 (stalled airfoil), 0511 (wing-body junction), 0512 (curved duct) and 8602 (shock/BL interaction): they can be furnished on request. All files have the same names as the 80-81 cases, with prefix "F", e.g. F0141 for 80-81 case 0141, Samuel/Joubert boundary layer. For the 80-81 cases actually used in the Collaboration, we distributed unpacked and annotated data: these files are mostly on disk 4 onward, and have suffix "A": for example, unpacked and interpolated data for 80-81 case 0141 are on file F0141A. File 8501A (Disk 3) contains Papamoschou and Roshko's data for the spreading rate of compressible mixing layers, to replace the "Langley" correlation in 80-81 case 8501 (though it must be pointed out that the older correlation still has its adherents and that convective Mach number, the independent variable in F8501A, is not quite a unique parameter for two-stream mixing layers). The updated files for F0251 are in Directory NLR3D on Disk D6. Some of the 80-81 cases were ignored in favor of more recent data sets for similar configurations. These and other new cases are in the format supplied by the originators, but with some editing to produce reasonable uniformity. Since 1981 it has become much easier to edit data files and we did not think it advisable to use Cantwell's format, which is easily read by machines but not by humans. The new test cases are labeled by the names of the originators (test cases actually used in the Collaboration were given code numbers, listed in Appendix B for the record). In Disks 1 to 5 each test case is contained in one file. The more extensive complex-flow data on Disk 6 and in Disks R1 to R4 are in separate directories for each case: Disk R5 contains only one case. For the new test cases, starting with Disk 4, the effort available allowed us, at most, to edit the data files so that a given line contains either alphabetic information (titles, etc) or numerical values, but not both. That is, modellers will merely have to edit out, or arrange their data-reading programs to ignore, lines that begin with alpha characters, and then use free-format reads for numerical data. We assume that all modelers are able to read free format numbers separated by spaces, e.g. 1729 2.71828 6.6E-23 ........ For the shorter data files such as correlations, which are more likely to be edited and plotted than read into the prediction program directly, we inserted a "%" sign as the first character of every alphabetic line (this is the "comment" character in TeX: modellers who prefer another "ignore this line" sign should be able to edit the "%" sign into something else). For longer files, we inserted a standard "skip then read" line before each cluster of alphabetic lines followed by data lines, as in the following example.......... 3 5 .... (2I3) [skip three lines, then read five lines] In the second century of the Christian era, the Empire of Rome comprehended the fairest part of the earth, and the most civilised portion of mankind. 4004 8008 8080 8086 80286 1 2 [another skip/read pair] 94.305 30.30 ................The modeller's program must be set up to read the two numbers on the "skip/read" line (NS, NR), then read NS lines into a dummy string, then read NR lines, then read the next skip/read pair. Disk 5 contains selected test cases from the latest in the series of AGARDograph reviews of compressible flow data initiated by Hans Fernholz and John Finley, AGARDograph 315 "A survey of measurements and measuring techniques in rapidly distorted compressible turbulent boundary layers" by H.H. Fernholz, P.J. Finley, J.P. Dussauge and A.J. Smits. The disk files are in the same format as the samples in the AGARDograph except that the double quote used for exponentiation has been replaced by the standard "E". The present organizers have added a few lower-case comments but made no other changes: in particular we have NOT inserted "skip then read" values. File names look similar to 80-81 compressible cases but are distinct. The internal notation should be obvious, but note that "Pitot" pressure is the total pressure downstream of a normal shock. The full data set is available from NASA Sci. and Tech. Info. Ctr., phone (301) 621-0204, or from the AGARD National Centers listed on p. 1-3 of AGARDograph 315. 2.2 Test cases actually used Sections 2.2.1 and 2.2.2 are condensed versions of the descriptions and instructions for the simpler flows sent to Collaborators: for more detail see file CASE15.TXT, but note that section numbers do not correspond with those above. 2.2.1 Simulation results for simple flows A major breakthrough since 1980-81 is the availability of simulation data, potentially including all possible turbulence statistics. Data for the NASA Ames simulations of a constant-pressure boundary layer (Spalart, J. Fluid Mech. 187, 61) and a 2D duct ("channel") flow (Kim, Moin and Moser, e.g. J. Fluid Mech. 194, 15) are together in file SIMUL1.DAT on disk 4. These are nominally easy test cases, but provide a check on individual terms in turbulence models which cannot be measured directly and are especially useful for testing near-wall ("low Reynolds number") models. The Spalart boundary layer starts at an Retheta of only 300, and initial conditions in a computation may obscure results. One way of allowing initial conditions to decay is to start at Retheta = 300 (or the lowest Reynolds number at which the model allows turbulence to survive) and march forward, increasing the viscosity at each step so that Retheta remains constant, until the results cease to change: then fix the viscosity and run on to Retheta = 600 and 1400. Complex-flow simulations are discussed in Section 2.2.4. 2.2.2 Experimental data for simple incompressible flows Of the cases in the Stanford 80-81 data library, the Samuel- Joubert boundary layer in increasing adverse pressure gradient (case 0141) tests the ability to handle rapidly- growing flows, which can defeat transport equations for length scale (or time scale or dissipation). The homogeneous turbulence test cases (0371-0376) of the 80-81 meeting are replaced by fewer and more recent data, except for the classical Comte-Bellot/Corrsin results (0371) for decay of isotropic turbulence. File PENVEN.DAT on Disk 4 contains data on response to plane strain and TAVOU.DAT on disk 4 contains homogeneous shear data (the latter data include microscale measurements from which dissipation can be deduced, but the answers proved to be not very accurate and it is suggested that initial dissipation rate be deduced from initial decay rate). In the Collaboration, free shear layer predictions were compared with consensus growth rates, and the only new free- shear-layer data set, the circular jet of Panchapakesan and Lumley (PANCH.DAT on Disk 4) was not used explicitly. The backward-facing step with inclined top wall was a "predictive" test case in 80-81, the measurements being reported by Driver and Seegmiller (AIAA J. 23, 163, 1985). The BAKSTP files on Disk 4 contain these and the same authors' data for a parallel top wall (the latter being a replacement for 80-81 test case 0420). 2.2.3 Simple compressible flows The main compressible test cases were adiabatic and cold- wall constant-pressure flows up to M = 8 (80-81 test cases 8101, 8201, approximately): most of the prediction methods produced results close to those of the Van Driest II skin- friction formula, and the predicted Reynolds-analogy factor St/(cf/2) did not vary significantly with wall temperature. Detailed comparisons with flat-plate data were not made. The mixing layer, case 8501 (new data in file F8501A), is the only flow which undoubtedly suffers from compressibility effects at non-hypersonic Mach numbers. None of the methods presented at the 1981 Stanford meeting could predict these effects, except by inserting arbitrary Mach-number-dependent coefficients. This happened again in the present Collaboration, with the difference that M-dependent terms with some physical basis are now the subject of active research. Two cautions should be issued: different workers use different definitions of mixing layer thickness, and doubts have been expressed about the use of "convection Mach number" to collapse data from two-stream mixing layers. The only case of a boundary layer in distributed adverse pressure gradient that was actually used was that of Fernando and Smits, starting at M=2.65 (AGARDograph 315, case 8601, and J. Fluid Mech. 211, 285, 1990). Mean-flow data are in file 8601 on disk 5, with turbulence data in 8601T). A genuine boundary layer calculation using the measured wall pressure should be adequate, at least for skin friction determination. The skin friction coefficient in this flow happens to remain nearly constant but this is a coincidental balancing of pressure-gradient and Mach number effects: this is not a trivial test case. 2.2.4 Complex (incompressible) flows Disk 6 contains incompressible complex flows, including computationally-simple 3-D and time-dependent flows. We give the full running instructions issued to the Collaborators, since the initial and boundary conditions in some of these flows need care. The data directories are as follows:-- \SPALASK Two-dimensional sink-flow boundary layer simulation. \ALVING Two-dimensional boundary layer in and downstream of a convex bend (stabilizing curvature: replaces 80- 81 case group 0230). \JOHNSON Two-dimensional boundary layer in a concave bend (destabilizing curvature: replaces 80- 81 case group 0230). \CASTRO Two-dimensional stably-curved mixing layer (80-81 case 0331, edited). \LAUNDER Normally-impinging jet from a circular nozzle. \MORSE Single-stream swirling jet in still air (80-81 case 0340, not used). \NLR3D "Infinite" 35 deg. swept "wing" (80-81 case 0251, not used). \SPALA3D Pseudo-Ekman 3D boundary layer simulation. \JENSEN One-dimensional time-periodic boundary layer. All of these test cases are degenerate numerically, compared to fully-3D steady flow or 2D time-dependent flow, but they pose most of the modelling difficulties that appear in general flows, without posing the full numerical difficulties. Except for the simulations, dissipation data are not available. For the initial profiles, assume (dissipation) = (production), except for the swirling jet (see below). 2.2.5 Running instructions for complex flows \SPALASK. Calculate two-dimensional sink-flow boundary layers (boundary-layer edge velocity inversely proportional to distance from sink) for the conditions of the three simulations by Spalart (J. Fluid Mech. 172, 307, 1986). The pressure-gradient parameter K=(nu/Ue2)dUe/dx defines the flow. Note that (1/K) = Ue(x0 - x)/nu , where x0 is sink position. Values of K for the three cases are 1.5x10-6, 2.5x10-6 and 2.75x10-6, in files SINK_K.150, SINK_K.250 and SINK_K.275 respectively. These flows are close to reverse transition, and Spalart's simulation at K = 3.0x10-6 reverted to laminar flow. Therefore these are good test cases for near-wall models (shear stress gradient expressed in wall variables is large and negative). Simulation data are made dimensionless by wall variables and are exactly self-similar. Other nondimensionalizations are deducible as needed, given the value of U+ at the boundary layer edge, Ue+: for example delta+ = delta/[(x0 -x)KUe+]. For the three cases, the simulations give Ue+ = 20.015, 19.577, and 19.418. Start by using the simulation data as initial conditions (the latter should of course be immaterial), and march until the results regain self-similarity or are obviously indicating reverse transition. Note that the tabulated "dissipation" in the budget for twice the turbulent kinetic energy is twice the rate of dissipation of turbulent energy! If possible, try other values of pressure-gradient parameter K, inside or outside the given range, to bracket your model's reverse-transition value of K. Plot cf, equal to 2/(Ue+)2, against x u0 / nu, where u0 is initial value of friction velocity, until similarity is regained or until (x0 - x) has halved, whichever distance is larger. Plot predicted similarity profiles against both y+ and ln y+, for U, -uv, and the highest-order quantities your model predicts (e.g. dissipation, pressure-strain term). Put simulation profiles on same graphs (use velocity-pressure-gradient term for pressure-strain data, provisionally: this implies neglect of transport by pressure fluctuations). If possible, "dissipation" should be true viscous dissipation of turbulent energy, nu(dui/dxj + dui/dxi)2/2, not the modified dissipation used in some turbulence models for convenience near the wall. \ALVING. Calculate a two-dimensional boundary layer in and downstream of a convex bend (stabilizing curvature: Alving, Smits and Watmuff, J. Fluid Mech. vol. 211, p. 529, 1990; see also A.E. Alving, PhD thesis, Princeton University, 1988). There is a full description of the experiment in README.TXT and dimensions, pressure coefficients, etc. in file INFO.DAT. The files have been left in exactly the (admirable) form prepared by Dr Alving. Note that no measurements were made within the bend, and that no turbulence measurements were reported at station 2, just downstream of the bend. Also note that static-pressure variations through the boundary layer were ignored, so that velocities evaluated from pitot traverses are actually the so-called "potential velocity", Up, derived from Bernoulli's equation using the total pressure at height y and the static pressure at the wall. The velocity made using the external-stream total pressure and the wall static pressure is called the "potential wall velocity", Upw. A calculation using the boundary-layer approximation with the surface pressure as input will - ideally - yield the potential velocity. Start the calculation at station 1, s = - 0.646m, and continue to station 9, s = 2.100m. Take the surface pressure coefficient from file CP1.DAT, noting that "Y" is the streamwise distance s. Interpolated pressure coefficients at the probe tip positions are in INFO.DAT. Unfortunately details of the contoured concave wall shape and of the quantity of suction applied to it are not available either in the journal paper or the thesis, making Navier-Stokes calculations difficult. Plot the experimental and calculated skin-friction coefficient against s (in meters). Plot experimental and calculated shear-stress profiles in the form -uv / Uref2 against y (in meters) for each measured s- station excluding station 2, and include the wall values, utau2/Uref2. Use a separate graph for each station. \JOHNSON. Calculate a two-dimensional boundary layer in a concave bend (destabilizing curvature: Johnson and Johnston, Rept MD-53, Mech Engg Dept, Stanford University, 1989). There is a full description of the experiment in file INDEX.TXT. Note that only the case with No turbulence grid is considered here, with data in the files whose names have an "N" as the second character, but grid data are also on the disk. The distance x is the arc length along the concave test surface measured from the start of curvature (represented by s in Alving's experiment). This experiment was done with an LDV in a low-speed water flow (with the bend in the horizontal plane) and no pressure measurements were made: as in Alving's experiment the walls were contoured to maintain constant pressure in and upstream of the bend but in this case the channel width is given as a function of x, in file xdata.dat. This file also contains some station data including the potential wall velocity Upw (as defined for Case 5.2). Start the calculation at station FN, x = - 56cm, and continue to station CN60, x = 142cm, after 60 deg. of turning. Note that the Reynolds number based on momentum thickness at station FN is only 1450. Plot the experimental and calculated skin-friction coefficient (based on Upw) against x (in cm). Plot experimental and calculated shear- stress profiles in the form -uv / Upw2 against y (in cm) for each measured x-station, and include the wall values, cf/2: use a separate graph for each station. Note that if Upw is really constant this is compatible with the plots against Uref requested for case 5.2. \CASTRO. Calculate the two-dimensional stably-curved mixing layer of Castro and Bradshaw (J. Fluid Mech. 73, 265, 1976). Data in 1980-81 format are in F0331 on Disk 1, but the Disk 6 files have been completely reformatted into the same general style as the new test cases. The radial pressure gradient is large enough that thin-shear-layer calculations which neglect it are likely to give poor results. The data file includes the shape of a "reference streamline" within the irrotational core of the flow, and this is the most reliable choice for the inner boundary of a Navier-Stokes calculation. Conditions at "infinity" should not be critical, except that any constraint on entrainment through that boundary may lead to partial recirculation of the mixing layer, which should exit smoothly through the downstream end of the domain of integration (the "top" in the experiment). Start with a thin turbulent boundary layer at the nozzle exit, adjusting if necessary to obtain best agreement at the first measurement station. The upper boundary in a Navier- Stokes solution should be chosen well downstream of the last measurement station. Plot the maximum shear stress as a function of downstream distance and compare with the measurements. \LAUNDER. Calculate the normally-impinging jet from a circular nozzle two diameters above the impingement plate, with fully developed pipe flow at exit, at a Reynolds number of 23000 based on nozzle diameter and bulk-average velocity (Cooper, D.; Jackson, D.C.; Launder, B.E.; Liao, G.X., Impinging jet studies for turbulence model assessment. Part 1 - Flow-field experiments, UMIST Mech Engg Dept TFD/92/5, 1992). If possible calculate heat transfer for a small temperature difference in air for the same conditions (Baugn and Shimizu, J. Heat Transfer 111, 1096, 1989), assuming uniform temperature at the pipe exit. This is a more complicated axisymmetric equivalent of the Castro flow. For initial conditions, use your own calculation of turbulent pipe flow at bulk-average Reynolds number of 23000 and report cf or the pipe-flow friction factor. The nozzle lip thickness is 1/32 of the diameter. For the first calculation, assume atmospheric pressure over the whole of the exit plane and the cylindrical (or other) boundary at large distance from the jet axis. Assume that the exit plane is entirely an inflow boundary, with zero or negligibly small turbulence quantities everywhere outside the nozzle. Assume that the cylindrical boundary is entirely an outflow boundary, with zero radial gradient of (radius times variable) for all quantities, or take the boundary far enough away that "zero gradient of variable" is adequate. The real flow might have some inflow through the upper part of the cylindrical boundary. If this gives trouble, do further calculations, with your choice of boundary conditions for the nozzle lip and the outer boundaries, but still using your pipe-flow prediction to give total pressure at the nozzle exit. Plot the maximum resultant mean velocity against radial distance, and compare with data. If calculating heat transfer, plot Nusselt number (it is difficult to define a meaningful Stanton number). \MORSE. Calculate a single-stream swirling jet in still air, swirl number S = 0.4. This is the case of A.P. Morse (PhD thesis, London University, 1980: most accessible relevance is Gibson & Younis, Phys. Fluids 29, 38, 1986). The data, and a draft of the following instructions, were kindly supplied by Dr Younis. Data for max. axial and tangential velocity components (Umax and Wmax), and half-radius r1/2 (where U=0.5Umax) are tabulated against x/D in file MORSE0.DAT (Wmax and r1/2 are given only at radial traverse stations). Profile data for x/D=0.5 (starting position), 1.0, 2.0, 4.0, 6.0 and 10.0 are in files MORSE1.DAT to MORSE6.DAT, and include all mean velocity components and all Reynolds stresses. Reynolds number Uexit d / nu = 56000. Start at x/D=0.5. If needed, evaluate initial dissipation profile from inversion of the k, eps. formula for (x-r)- plane shear stress, as dissipation = cmu k2 (dU/dr)/(-uv), with cmu = 0.09. This is probably better than assuming (production) = (dissipation), but modelers are welcome to try the latter or other assumption, after trying the k, eps. derivation. For calculations by boundary layer methods, integrate the reduced radial momentum equation, dp/dr = - p W2/r and use upstream values to evaluate dp/dx (at x/D = 0.5, assume dp/dx = 0). Plot maximum circumferential mean velocity as a function of x and compare with data. \NLR3D. Calculate the "infinite" swept "wing" of van den Berg et al. (J. Fluid Mech. 70, 127, 1975). Data in 1980-81 format are in F0251 on Disk 1, reformatted data on Disk 6. The normal pressure gradient is significant in the downstream region near separation, and Dr van den Berg has supplied a suggested pressure distribution along a line in the external stream, for use as the outer boundary condition in a Navier-Stokes calculation. In an N-S calculation, the streamwise pressure gradient should be relaxed at a short distance downstream of the last measurement station, to reattach the flow and ensure that the downstream boundary is an outflow boundary. Start a Navier-Stokes calculation with a thin turbulent boundary layer at the leading edge, adjusting if necessary to match the boundary layer at the first measurement station. In a boundary-layer calculation, use data at the first measurement station directly, and continue to the last measurement station or to separation, whichever comes first. Plot surface shear stress and wall flow angle (measured with respect to the x (tunnel) axis, not the local external stream) at each measurement station, and compare with data. \SPALA3D. Calculate the pseudo-Ekman 3D boundary layer of Spalart (J. Fluid Mech. 205, 319, 1989). The variables are functions of y (vertical) and time t, but not of the horizontal coordinates x and z. Because of this simplicity, a program capable of computing steady flow over infinite swept wings (z coordinate along generators and d[ ]/dz=0) could be adapted: Ud[ ]/x becomes d[ ]/dt; Vd[ ]/dy and Wd[ ]/dz are zero - for different reasons - and the program can be stepped in time instead of marching in x. As for the self-similar sink flow, the initial conditions are immaterial and can therefore legally be taken straight from the data. Step in time until the periodic amplitude of one component of skin friction becomes constant again, indicating self-similarity. Report the peak-to-peak amplitude of skin friction coefficient. \JENSEN. Calculate the one-dimensional time-periodic boundary layer of Jensen, Sumer and Fredsoe (J. Fluid Mech. 206, 265, 1989: only case 10 has been included here). Ensemble (phase) averages can be used in place of simple Reynolds averages. The convection term D/Dt reduces to partial d/dt, all spatial-derivative contributions being zero: thus a 2-D steady boundary-layer code can be easily adapted by equating Ud/dx to d/dt (U=constant=1 in that term) and imposing V=0, which follows from dU/dx=0. Start at t=0 with the experimental data for a suitable phase angle, and, using the measured, approximately-sinusoidal free-stream velocity as the outer boundary condition, march in time until the computed solution becomes periodic (same peak-to-peak amplitude in successive periods). Navier-Stokes codes should of course be run time-accurate, at least in the later stages of the calculation. Plot surface shear stress (normalized by the maximum free-stream dynamic pressure) as a function of phase angle and compare with the data. 3. SELECTION OF "UNUSED" DATA This is not to be regarded as a definitive selection, but a set which happened to interest a particular expert. The names of the directories on Disks R1 to R7 are based on the names of the data originators, generally in alphabetical order. Because of the backup procedure used some data sets are split between two disks. Ahmed isothermal dump combustor with swirl (FAVALORO, S.C. et al., An experimental and computational investigation of isothermal swirling flow in an axisymmetric dump combustor, AIAA-89-0620) Anderson and Eaton 3D flow in wedge-plate junction (ANDERSON, S.D.; EATON, J.K., Reynolds stress development in pressure-driven three-dimensional boundary layers, J.Fluid Mech. 202, 263, 1989) Antonia wake with T fluctuations (ANTONIA, R.A.; BROWNE, L.W.B., Anisotropy of the temperature dissipation in a turbulent wake, J. Fluid Mech. 163, 393, 1986) Anwer curved pipe flow (ANWER, M.; SO, R.M.C.; LAI, Y.G., Perturbation by and recovery from bend curvature of a fully developed turbulent pipe flow, Phys. Fluids A1, 1387, 1989.) Brereton unsteady boundary layer (Stanford rept TF-29 and Cornell TSF 5, plus free-stream vel from TF-18: BRERETON, G.J.; REYNOLDS, W.C.; JAYARAMAN, R., Response of a turbulent boundary layer to sinusoidal free-stream unsteadiness, J. Fluid Mech. 221, 131, 1990. Choi square-section duct, 180 deg bend, Re = 56, 690 (CHOI, Y.D.; MOON, C.; YANG, S.H., Measurememnt of turbulent flow characteristics of square duct with a 180o bend by hot wire anemometer, Proc. of Int. Sympo. on Engg Turb, Modeling and Meas., Dubrovnik 1990, and Trans Korea Soc. Mech Engrs 12, 900, 1988). Davis transition duct (NASA TM 105210 [with data supplement] and DAVIS, D.O.; GESSNER, F.B., Experimental investigation of turbulent flow through a circular-to-rectangular transition duct, AIAA J. 30, 367, 1992). Devenport and Simpson wing/body junction with separation (DEVENPORT, W.J.; SIMPSON, R.L., Time-dependent and time- averaged turbulence structure near the nose of a wing-body junction, J. Fluid Mech. 210, 23, 1990). Kegelman and Roos delta wing (KEGELMAN, J.T.; ROOS, F.W., The flowfields of bursting vortices over moderately swept delta wings, AIAA-90-0599, 1990). Two 1.2MB disks (R5A and R5B) or one 1.44 MB disk (R5). Nagano natural-convection boundary layer (TSUJI, T.; NAGANO, Y., Characteristics of a turbulent natural convection boundary layer along a vertical flat plate, Int. J. Heat and Mass Transf. 31, 1723, 1988). Nakabayashi Couette flow with fixed wavy wall (NAKABAYASHI, K.; KITOH, O.; IWATA, H., Turbulent Couette type flow with an alternating pressure gradient, Presented at 8th Symposium on Turbulent Shear Flows, Munich, poster no. I-13, 1991). Nakayama airfoil BL and wake (NAKAYAMA, A., Curvature and pressure-gradient effects on a small-defect wake, J.Fluid Mech. 175, 215, 1987) Pauley and Eaton vortices in boundary layer (Stanford rept. MD-51 and PAULEY, W.R.; EATON, J.K., Boundary layer turbulence structure in the presence of embedded streamwise vortex pairs, 7th Sympo. on Turbulent Shear Flows, Stanford Univ., 1989). Szczepura pipe expansion (axi. backstep: SZCZEPURA, R.T., Flow characteristics of an axisymmetric sudden pipe expansion, British Central Elec. Gen. Board repts TPRD/B/0702/N85 and /0703/R86, 1986). Tavoularis homogeneous curved flow (HOLLOWAY, A.G.L.; TAVOULARIS, S., The effects of curvature on sheared turbulence, J. Fluid Mech. 237, 569, 1992). Zierke and Deutsch transitional cascade blade (NASA CR 185118, 1989). 4. OTHER DATA AVAILABLE ON DISK (mainly unedited) Bremhorst pulsed jet Brown cylinder-cone shock-BL interaction (NASA Ames) Coleman and Stollery M = 9 ramp (JFM 56, 741, 1972) Delville/Lemay/Bonnet boundary layer with LEBUs Dengel & Fernholz boundary layer near separation (Turbulent Shear Flows 7, paper 1.4, 1989) Driver spinning body (AIAA J. 25, 35, 1987) Driver axi. separation and reattachment (presented at Am. Phys. Soc. meeting, Nov. 89) Fujita square duct with two opposite rough walls, rectangular duct with one rough wall. Harvey hypersonic cone (mean profiles) Hastings/Wadcock stalled airfoil - 80-81 flow 0440 Hoffmann ship stern (Hamburg Inst. fur Schiffbau Ber. 290, 1976: see Larsson, SSPA-ITTC Workshop on Ship BLs 1980, SSPA pub. 90) Kawamura (i) reverse transition in strongly heated pipe flow (known inlet conditions but heat transfer measurements only) Karnik & Tavoularis diffusion from line source (J. Fluid Mech. 202, 233, 1989) Knight M=3 fin (AIAA 86-0343) Settles hypersonic fin shock/BL interaction SSPA, Gothenburg HSVA2 ship stern 5. DATA VOLUNTEERED (OR RECOMMENDED) but not available in machine-readable form from the organizers: all enquiries should go to to the originators. Bandyopadhyay TBL on smooth-to-rough wall (JFM 180, 231, 1987) Bandyopadhyay TBL on axi. bodies with various longitudinal curvature (AIAA J. 27, 274, 1989) Brune (i) 4-element high-lift airfoil (AIAA-83-0566) (ii)Pot - wake/plate interaction (NLR-TR 79063L, 1979) Castro (i) Johnson and Hancock impinging axi. jet (axi. equvalent of 0331, above; Turbulent Shear Flows 7, paper 28- 5) (ii) Castro and Hacque normal plate and splitter (JFM 179, 439, 1987) Chung (i) curved square-section duct with sheared and unsheared entry profiles (ii) swirling jets (iii) wall jet on convex surface Cimbala 2D momentumless wake (Turbulent Shear Flows 7, paper 6.1) Coantic (i)Beguier - mixing layer and wake mixing with heat transfer (ii) Elena - supersonic boundary layer on strongly heated wall (iii) Chauve - coaxial heated jet mixing in diffuser Comte-Bellot wall-pressure fluctuations statistics in 2D and 3D boundary layers Dang simulations (i) homogeneous turbulence with strain or rotation, including scalar transport (ii) plane, curved or diverging channel flows Durst orifice plate (Turbulent Shear Flows 7, paper 10.4) Fernholz 3D flow over 2D normal plate - Jaroch and Fernholz J. Fluid Mech. 205, 523, 1989) Fujita (i) rectangular duct with one rough wall (Exptl. Thermo. and Fluid Sci. 2, 72, 1989) (ii) heat transfer in square duct with two rough facing walls (Chem. Engg. Comm. 74, 95, 1988) Hanjalic (i) pulsating flow (Karlsruhe TSF) (ii) Deardorff buoyant flow Marasli plane wake (JFM 168, 31 - including x-wire rake traces) Miyake channel simulation with pseudo-wavy wall (represented by suction/injection) Pollard 3D wall jet (see 0264) Savill curved wake (IUTAM Complex Flow Sympo., Marseille) Simpson (i) separating diffuser flow (addition to 0431); (ii) unsteady versions of (i); (iv) Meier-like ellipsoid Squire transonic shock/BL interaction - interferometer density maps Van den Berg (i) GARTEUR (European collab.) swept wing - not available at end 1996 (iii) NLR airfoil with flap Vogel and Eaton heat transfer behind backstep (presented at TSF 5, Cornell 1985 - plus velocity field from Adams and Johnston, Expts. in Fluids 6, 400 and 493, 1988) Wood axi. diffuser with swirl. APPENDIX A 1980-81 TEST CASES This list is reproduced form the 1981 data tape. Details of publication, etc. are given in the individual data files: case numbers in CTTM are the 80-81 numbers prefixed by an "F" (and followed by an "A" if the data have been reformatted or otherwise upgraded). For full details of the 1980-81 cases see the Proceedings, "The 1980-81 AFOSR-HTTM- Stanford Conference on Complex Turbulent Flows" (S.J. Kline, B.J. Cantwell and G.M. Lilley, eds.), Mech. Engg Dept., Stanford University, 1981: reprinted 1994. AFOSR-STANFORD LIBRARY OF EVALUATED TURBULENCE DATA - INDEX TO THE TAPE CASE NUMBER TITLE 0111 PO, J.K., LUND, E.G., & GESSNER, F.B.; DEVELOPING FLOW IN A SQUARE DUCT. (SECONDARY FLOW OF THE SECOND KIND) 0112 HINZE, J.O.; SECONDARY CURRENTS IN THE TURBULENT FLOW THROUGH A STRAIGHT CONDUIT. 0141 SAMUEL, A.E. & JOUBERT, P.N.; INCREASINGLY ADVERSE PRESSURE GRADIENT FLOW. 0142 & 0143 POZZORINI, R.; SIX-DEGREE CONICAL DIFFUSER FLOW, LOW AND HIGH CORE TURBULENCE. 0211 BRADSHAW, P., HANCOCK, P.E.; EFFECT OF FREE STREAM TURBULENCE. 0231 & 0232 HOFFMANN, P.H. & BRADSHAW, P.; TURBULENT BOUNDARY LAYERS ON SURFACES OF MILD LONGITUDINAL CURVATURE. 0233 GILLIS, J.C., JOHNSTON, J.P.; TURBULENT BOUNDARY LAYER ON A CONVEX, CURVED SURFACE. 0234 HUNT, I.A. & JOUBERT, P.N.; EFFECTS OF SMALL STREAMLINE CURVATURE ON TURBULENT DUCT FLOW. 0235 SMITS, A.J., YOUNG, S.T.B. & BRADSHAW, P.; THE EFFECTS OF SHORT REGIONS OF HIGH SURFACE CURVATURE ON TURBULENT BOUNDARY LAYERS. (CONVEX 30 DEGREES) 0241 ANDERSEN, P.S., KAYS, W.M. & MOFFAT, R.J.; ZERO PRESSURE GRADIENT CONSTANT INJECTION. 0242 ANDERSEN, P.S., KAYS, W.M. & MOFFAT, R.J.; ADVERSE PRESSURE GRADIENT WITH CONSTANT SUCTION. 0244 FAVRE, A., DUMAS, R., VEROLLET, E. AND COANTIC, M.; ZERO PRESSURE GRADIENT WITH CONSTANT SUCTION. 0251 NLR INFINITE SWEPT WING EXPERIMENT. 0252 PART-ROTATING CYLINDER EXPERIMENT. (BISSONNETTE & MELLOR) 0253 CYLINDER ON A FLAT TEST PLATE. (DECHOW & FELSCH) 0254 PART-ROTATING CYLINDER. (LOHMANN) 0261, 0263, 0264TURBULENT WALL JET DATA COLLECTED FROM VARIOUS SOURCES. 0311 PLANAR MIXING LAYER DEVELOPING FROM TURBULENT WALL BOUNDARY LAYERS. 0331 CASTRO, I.P. & BRADSHAW, P.; THE TURBULENCE STRUCTURE OF A HIGHLY CURVED MIXING LAYER. 0361 CHEVRAY, R.; THE TURBULENT WAKE OF A BODY OF REVOLUTION. 0370 (0371, HOMOGENOUS TURBULENT FLOWS. 0372, 0373, 0374, 0375, 0376) 0381 & 0382 ANDREOPOULOS, J. & BRADSHAW, P.; MEASUREMENTS OF INTERACTING TURBULENT SHEAR LAYERS IN THE NEAR WAKE OF AN AIRFOIL. 0411 CANTWELL, B.J. & COLES, D.; A FLYING HOT WIRE STUDY OF THE TURBULENT NEAR WAKE OF A CIRCULAR CYLINDER AT A REYNOLDS NUMBER OF 140000. 0421 KIM, J., KLINE, S.J. & JOHNSTON, J.P.; FLOW OVER A BACKWARD FACING STEP. 0431 CHEW, Y.T., SIMPSON, R.L. & SHIVAPRASAD, B.G.; SEPARATING ADVERSE PRESSURE GRADIENT FLOW. 0441 WADCOCK, A.J. & COLES, D.E.; FLYING-HOT WIRE STUDY OF TWO-DIMENSIONAL TURBULENT SEPARATION OF AN NACA 4412 AIRFOIL AT MAXIMUM LIFT. 0471 VISWANATH, P.R., CLEARY, T.W., SEEGMILLER, H.L. & HORSTMAN, C.C.; TRAILING-EDGE FLOWS AT HIGH REYNOLDS NUMBER. 0511 SHABAKA, I.M.M.A; TURBULENT FLOW IN AN IDEALIZED WING-BODY JUNCTION. 0512 HUMPHREY, J.A.C.; TURBULENT FLOW IN A CURVED DUCT OF SQUARE CROSS-SECTION. 0612 WIEGHARDT, K.; ON THE TURBULENT FRICTION LAYER FOR RISING PRESSURE. 8301 THOMAS, G.D.; FAVORABLE PRESSURE GRADIENT AT SUPERSONIC SPEEDS WITH INJECTION. 8401 PEAKE, D.J., BRAKMANN, G. & ROMESKIE, J.M.; BOUNDARY LAYER IN ADVERSE PRESSURE GRADIENT. 8402 LEWIS, J.E., GRAN, R.L. & KUBOTA, T.; BOUNDARY LAYER IN ADVERSE PRESSURE GRADIENT. 8403 KUSSOY, M.I., HORSTMAN, C.C. & ACHARYA, M.; PRESSURE GRADIENT AND REYNOLDS NUMBER EFFECTS ON COMPRESSIBLE TURBULENT BOUNDARY LAYERS IN SUPER- SONIC FLOW. 8411 ZWARTS, F.J.; BOUNDARY LAYER IN ADVERSE PRESSURE GRADIENT. 8501 COMPRESSIBILITY EFFECTS ON FREE SHEAR LAYERS. (BRADSHAW) 8601 MATEER, G.C., BOSH, A. & VIEGAS, J.; NORMAL SHOCK-WAVE/TURBULENT BOUNDARY-LAYER INTERACTION AT TRANSONIC SPEEDS. 8602 KOOI, J.W.; INFLUENCE OF FREE STREAM MACH NUMBER ON TRANSONIC SHOCK-WAVE BOUNDARY LAYER INTERACTION. 8611 BACHALO, W.D. & JOHNSON,D.A.; TRANSONIC TURBULENT BOUNDARY LAYER SEPARATION ON AN AXISYMMETRIC BUMP. 8612 DELERY, J. & LE DUIZET; TRANSONIC FLOW OVER 2-DIMENSIONAL BUMP, M = 1.37. 8621 COOK, P.H., MCDONALD, M.A. & FIRMIN, M.C.P.; AEROFOIL RAE 2822 - PRESSURE DISTRIBUTION AND BOUNDARY LAYER AND WAKE MEASUREMENTS. 8623 SPAID, F.W. & STIVERS, L.S.; SUPERCRITICAL AIRFOIL BOUNDARY LAYER MEASUREMENTS. 8631 SETTLES, G.S., FITZPATRICK, T.J. & BOGDONOFF, S.M.; ATTACHED AND SEPARATED COMPRESSION CORNER FLOW FIELDS IN HIGH REYNOLDS NUMBER SUPERSONIC FLOW. 8632 DUSSAUGE, J. & GAVIGLIO, J.; TURBULENT BOUNDARY-LAYER /EXPANSION INTERACTION AT SUPERSONIC SPEED. 8641 SETTLES, G.S., BACA, B.K., WILLIAMS, D.R. & BOGDONOFF, S.M.; REATTACHING PLANAR FREE SHEAR LAYER. (SUPERSONIC) 8651 HORSTMAN, C.C. & KUSSOY, M.I.; HYPERSONIC SHOCK WAVE TURBULENT BOUNDARY LAYER INTERACTION-WITH AND WITHOUT SEPARATION. 8661 PEAKE, D.J.; THREE DIMENSIONAL SWEPT SHOCK/TURBULENT BOUNDARY LAYER INTERACTION. 8663 KUSSOY, M.I., VIEGAS, J.R. & HORSTMAN, C.C.; INVESTIGATION OF 3-D SHOCK SEPARATED TURBULENT BOUNDARY LAYER. 8671 POINTED AXISYMMETRIC BODIES AT ANGLE OF ATTACK -SUPERSONIC. (RAINBIRD) 8691 MCDEVITT, J.B., SEEGMILLER, H.L. & OKUNO, H.L.; NON-LIFTING TRANSONIC AIRFOIL, SHOCK-SEPARATED FLOW. (Hard copies of this document distributed from Stanford contain the more detailed list of test cases reproduced from vol. 1, pp. 624-632 of the 1980-81 Proceedings). Appendix B SUMMARY OF DATA ACTUALLY USED (Disks 1 to 6) Note that identification numbers refer to the class of flow (incompressible/compressible/complex) and not the disk number. Entry test cases: flat plate skin friction and heat transfer at momentum-thickness Reynolds number of 10000: (i) M=0 adiabatic (ii) M=0 heat transfer with small temperature difference (iii) M=0 heat transfer with Tw/Te=6 (iv) M=5 adiabatic. August 1990 test cases (canonical flows and backstep) (a) Incompressible flows (disks 1, 4) 3.1 Boundary layer in increasing adverse pressure gradient - 80-81 case 0141, Samuel and Joubert 3.2.1 Boundary layer simulation - Spalart 3.2.2 Duct simulation - Kim, Moin and Moser 3.3.1 Homogeneous turbulence, unstrained - 80-81 case 0371 3.3.2 Homogeneous turbulence, strained - Le Penven et al. 3.3.1 Homogeneous turbulence, sheared - Tavoularis & Karnik 3.4.1 Round jet in still air ) 3.4.2 Plane jet in still air )Data correlations 3.4.3 Plane mixing layer in still air ) 3.5.1 Backward-facing step in duct with 6 deg. expansion angle - Driver and Seegmiller 3.5.2 Backward-facing step in duct with parallel top wall (b) Compressible flows 4.1.1 Skin friction on an adiabatic wall at M = 2, 3 and 8 4.1.2 Skin friction and heat transfer at M=5, for Tw/Taw = 0.2, 0.4, 0.6 and 0.8. 4.2 Compressible mixing layer (plot spreading rate against Mc) 4.3.1 Boundary layer of Fernando and Smits (disk 5). August 1991 test cases - incompressible complex flows (disk 6) 5.1 Two-dimensional sink-flow boundary layer simulation - Spalart 5.2 Two-dimensional boundary layer in and downstream of a convex bend (stabilizing curvature) - Alving 5.3 Two-dimensional boundary layer in a concave bend (destabilizing curvature) - Johnson 5.4 Two-dimensional stably-curved mixing layer - Castro. 5.5 Normally-impinging jet from a circular nozzle - Cooper 5.6 Single-stream swirling jet in still air - Morse 5.7 "Infinite" 35 deg. swept "wing" - Van den Berg 5.8 Pseudo-Ekman 3D boundary layer simulation - Coleman 5.9 One-dimensional time-periodic boundary layer - Jensen APPENDIX C DISK DIRECTORIES Disk 1: 80-81 incompressible data (0411, 0441, 0511, 0512 absent) DIR8081 1323 03-08-90 12:20p INDEX 14336 05-09-85 2:58a F0612 36736 05-24-85 1:51a F0111 82688 05-09-85 3:51a F0112 17920 05-09-85 4:11a F0141 62720 05-09-85 6:42a F0142 124948 01-01-80 12:22a F0211 7168 05-10-85 1:56a F0231 39936 01-01-80 3:40a F0233 57600 05-10-85 3:19a F0234 69120 05-10-85 3:59a F0235 36992 05-10-85 4:43a F0241 14720 05-10-85 5:05a F0242 23936 05-10-85 1:53a F0244 19968 05-13-85 5:31a F0251 42880 05-13-85 6:40a F0252 26496 05-13-85 7:15a F0253 40064 05-13-85 8:17a F0254 27520 05-14-85 7:06a F0261 26752 05-14-85 7:44a F0311 11008 05-15-85 1:32a F0331 73126 02-06-90 2:14p F0361 84304 01-01-80 12:44a F0370 24448 05-15-85 1:42a F0381 62208 05-15-85 3:39a F0421 37376 06-12-85 2:26a F0431 57088 06-12-85 3:07a F0471 61312 05-23-85 2:27a README 1 1231 03-08-90 12:19p PPLOT DOC 16665 03-20-90 10:36a 30 file(s) 1202589 bytes 6144 bytes free Disk 2: 80-81 compressible data, part 1 (8602 absent) F8301 16000 05-24-85 2:59a F8401 18688 05-24-85 5:37a F8402 32768 05-28-85 1:23a F8403 228288 01-01-80 2:33a F8411 15616 05-29-85 3:00a F8501 5888 05-29-85 1:23a F8601 61440 05-29-85 2:48a F8611 27136 06-06-85 1:30a F8612 91392 06-06-85 2:24a F8621 237062 01-01-80 3:22a F8623 189666 01-01-80 3:29a F8631 222958 01-01-80 3:33a F8632 61952 06-07-85 3:43a DIR8081 2 749 03-08-90 1:20p README 2 351 03-08-90 1:19p 15 file(s) 1209954 bytes 1024 bytes free Disk 3: 80-81 compressible data, part 2 F8641 38144 06-07-85 4:09a F8651 194258 01-01-80 3:41a F8661 14592 06-08-85 1:16a F8663 196882 01-01-80 3:47a F8671 65792 01-11-85 1:51a F8691 26752 01-11-85 2:08a README 3 364 03-08-90 1:22p DIR8081 3 503 04-09-90 11:05a F8501A 1835 04-09-90 10:54a 9 file(s) 539122 bytes 672768 bytes free Disk 4: new incompressible cases, part 1 F0141A 45204 04-05-90 4:21p SIMUL1 DAT 215974 03-06-90 12:36p PENVEN DAT 2873 04-04-90 4:04a SIMUL1 FOR 597 03-06-90 12:30p TAVOU DAT 2351 04-05-90 5:43p PANCH DAT 112590 04-06-90 12:49p BAKSTP1 DAT 110848 04-06-90 10:15a BAKSTP3 DAT 73895 04-06-90 10:18a BAKSTP2 DAT 18960 04-06-90 10:25a BAKSTP FOR 709 02-16-90 4:14p DIR 4 508 04-09-90 11:08a DIR1-5 4537 04-09-90 11:16a 12 file(s) 589046 bytes 621056 bytes free Disk 5: new compressible cases (AG-315) 8701-S7T 5692 04-04-90 1:37a 8601 73949 04-04-90 1:41a CONTENTS 10325 04-04-90 2:23a 7904-S1 73669 04-04-90 1:09a 8602-A 42485 04-04-90 1:15a 7904-S2 125036 04-04-90 1:08a 7904-S3 119548 04-04-90 1:10a 7904-S4 191665 04-04-90 1:10a 7904-S5 56855 04-04-90 1:11a 8602-B 47938 04-04-90 1:16a 8603 57590 04-04-90 1:16a 8601T 18179 04-04-90 1:26a 8602T 3261 04-04-90 1:28a 8603T 16197 04-04-90 1:29a 8701-S1T 42482 04-04-90 1:30a 8701-S2T 10750 04-04-90 1:31a 8701-S3T 25408 04-04-90 1:31a 8701-S4T 15009 04-04-90 1:32a 8701-S5T 16831 04-04-90 1:32a 8701-S6T 14511 04-04-90 1:32a DIR315 5 918 04-09-90 11:10a 21 file(s) 968298 bytes 211456 bytes free Disk 6: new incompressible cases, part 2 SPALASK 06-12-90 1:53p SPALA3D 11-02-90 2:52p ALVING 11-02-90 2:53p JOHNSON 11-02-90 2:59p JENSEN 12-14-90 4:08p LAUNDER 01-03-91 8:50a NLR3D 01-03-91 1:39p MORSE 06-12-90 1:51p CASTRO 01-03-91 5:20p 9 file(s) 0 bytes 631296 bytes free Disk R1: Selection of unused data, part 1 AHMED 04-01-93 4:11p ANDER 04-01-93 4:13p ANTON 04-01-93 4:16p ANWER 04-01-93 4:17p BRERE 04-01-93 4:20p CONTENT 1229 04-01-93 5:32p 6 file(s) 1229 bytes 185344 bytes free Disk R2: Selection of unused data, part 2 CHOI 04-01-93 4:26p DEVEN 04-01-93 4:30p BRERE 04-01-93 4:23p 3 file(s) 0 bytes 212992 bytes free Disk R3: Selection of unused data, part 3 DEVEN 04-01-93 4:39p NAGANO 04-01-93 5:11p NAKAB 04-01-93 5:14p NAKAY 04-01-93 5:15p 4 file(s) 0 bytes 86528 bytes free Disk R4: Selection of unused data, part 4 PAULEY 04-01-93 5:17p SZCZE 04-01-93 5:23p TAVOUK 04-01-93 5:24p ZIERKE 04-01-93 5:27p 4 file(s) 0 bytes 325632 bytes free Disk R5: Selection of unused data, part 5. Kegelman and Roos delta-wing data in PLOT3D "XYZ" and "Q" file format. (Split on to two disks, R5A and R5B, in 5-1/4" 1.2MB format.) QA733 FMT 527202 04-02-93 9:52a QP733 FMT 296202 04-02-93 9:52a XA733 FMT 316284 04-02-93 9:52a XP733 FMT 177684 04-02-93 9:52a VORTICIT COM 326 04-02-93 9:53a TPLOSS COM 256 04-02-93 9:53a 6 file(s) 1317954 bytes 138240 bytes free Disk R6: Selection of unused data, part 6 Volume in drive A has no label Directory of A:\ DAVTRAN 11-12-93 6:19p 1 file(s) 0 bytes 187904 bytes free Disk R7: Selection of unused data, part 7 Volume in drive A has no label Directory of A:\ DAVTRAN 11-12-93 6:31p 1 file(s) 0 bytes 625664 bytes free Price list, August 1994 (includes US or overseas surface mail) (i) Disks 1-6 (including 1980-81 data)..............US$60 (ii) Disks R1-R7 (selected data not on 1-6)..........US$60 A 24-page description of the data library, with the running instructions given to the Collaborators, is included. 3-1/2" MS-DOS disks will be sent if no other format is requested. (iii) The "Proceedings" of the project (newsletters and other documentation, including selected results (total 650 pages).........US$80 (iv) Proceedings of the 1980-81 meeting (reprinted:3 volumes, 1500 pages)....................US$200 These charges are for single orders, for which handling costs are necessarily high. No copyright is claimed - feel free to copy disks and text for yourself or others. Either invoice with delivery or payment with order is acceptable. Payment should be in US dollars unless otherwise arranged. Make checks payable to "Stanford University" and send to Prof. P. Bradshaw, Mech. Engg. Dept., Stanford University, STANFORD CA 94305-3030, USA