CFD Utilities Files

HEMISPHERES_OF_SIGHT Description:

  HEMISPHERES_OF_SIGHT is a variant of CONES_OF_SIGHT, itself an adaptation
  of LINES_OF_SIGHT, q.v.  Originally, it worked with structured discretiz-
  ations of lines of latitude and longitude, and retained the functionality
  of LINES_OF_SIGHT if the lat/long steps were specified as zero.  However,
  such discretizations produce clustering of the lines of site towards the
  north pole of each hemisphere.  Therefore, this version triangulates the
  underlying unit hemisphere (or rather one quadrant of it) to produce more
  uniform (but not perfectly uniform) spacing of the lines associated with
  one target body point.  The option to treat more than one body point at a
  time has been retained, but generating only the primary line(s) of sight
  is no longer an option - use LINES_OF_SIGHT for those.

  Note that a full 3D volume grid, not half the volume, is all that makes
  sense here, so be sure to reflect the half grid likely used for the
  associated flow solution, unless the target points are all on the (y = 0)
  symmetry plane, in which case the y < 0 half of the output hemisphere
  data is suppressed.  This volume grid is assumed to contain a single
  layer of grid blocks with k in the body normal direction, as is typical
  for hypersonic flow over atmospheric entry vehicles.  Ox points down-
  stream, y is positive on the starboard side, and Oz is "up."

Further details:

  For radiative heat flux calculations on an atmospheric entry vehicle, at
  a specified body surface point, the "right" answer should account for all
  possible viewing directions.  For a typical convex body, this means a
  full hemisphere of lines of sight at each body point, not just the line
  of sight normal to the body at each point as used with the tangent-slab
  approximation in a typical radiation solver.  Here, the solver is expected
  to provide a value of radiance (W.sr^-1.m^-2) for each hemisphere line
  (vastly more expensive for even moderate discretizations), and a companion
  utility will integrate those values with respect to solid angle subtended
  at the body point to produce a truer estimate of radiative heat flux
  (W.m^-2).

  The primary line of sight is taken to be normal to the k = 1 surface at
  the indicated target point.  It extends to the outer grid boundary with a
  point distribution derived from (but not necessarily the same as) that of
  the nearest local radial grid line.  The secondary lines have the same
  relative distribution as the primary line.  All discretized lines are
  saved in PLOT3D multiblock form (one line of sight per block) compatible
  with the earlier FLOW_INTERP, which can perform the flow interpolations
  and tabulations that are normally what are really desired for application
  to hypersonic flows, in this case for radiation calculations involving
  full angular integration.

  The hemisphere discretization is determined by the prompted-for number of
  points (ne) along a great circle from pole to equator (and along a 4th
  of the equator) defining a certain triangulation.  A quarter of the
  underlying unit hemisphere discretization is produced by slices parallel
  to the equator through the uniform arc points, starting from near the
  north pole.  The rest of the hemisphere is obtained by geometric trans-
  formations.  Common edge points are presently NOT suppressed:  they will
  be needed for eventual quadratures with respect to solid angle.

  For the ne edge points specified, the number of node points on a quarter
  hemisphere is ne*(ne + 1)/2, and the number of triangular elements is
  (ne - 1)**2.  The primary line (along the surface normal through the
  body point) is line number 1 in the <ID>.<bp #>.lines.g output file(s).

  The triangulated surfaces, before and after the intersections-with-outer-
  grid-boundary calculations, are output as multizone triangulations for
  visualization with Tecplot.

Strategy:

  o  Read the entire volume grid and extract the inner and outer boundaries
     as multiblock surface grids.

  o  For all body points (expected to be one, but more are allowed for)
     defining (primary) lines of sight, search the inner boundary and save
     the relevant patch number, cell indices, and fractional interpolation
     coefficients (which are already in hand if surface grid indices are
     input instead of coordinates).

  o  Build a [new?] search tree from the outer boundary, for the inter-
     section calculations.

  o  Construct a triangulation of a quadrant of a unit hemisphere, as
     indicated by the input number of edge points, ne.

  o  For each inner surface target point:

     > Construct a two-point line normal to the wall with length that of
       a local radial grid line.  This should be at least as long as the
       straight line distance to the outer boundary.

     > This line determines the transformations to be applied to the
       discretized unit hemisphere quadrant.

     > For each line defined by the two or four transformed quadrants,
       intersect the line with the outer boundary and impose the indicated
       point distribution.

     > Save all lines of sight in multiblock form, with each block sized
       1 x 1 x npts, where npts is the prompted-for number.

Input body point format (read to EOF):

     Either                                      or

     n   i   j                                   x   y   z
    [n   i   j                                  [x   y   z
     n   i   j                                   x   y   z
     :   :   :]                                  :   :   :]

     where n = block number and k = 1 is implied.

     Presence or absence of a decimal point in line 1 determines whether
     indices or coordinates are being entered.

Outputs:

  For each target body point:

      (a) Discretized hemisphere (or half-hemisphere if all target points
          are on the symmetry plane), tangent to the body at the body pts.
          for visualization purposes (<ID>.<BP #>.hemi.dat):

          Tecplot triangulation (1 hemisphere quadrant/zone; 2|4 zones)

      (b) The topologically similar triangulated surface resulting from
          intersecting this hemisphere with the roughly-uniformly-spaced
          lines of sight, also for visualization purposes
          (<ID>.<BP #>.boundary.dat):

          Similar Tecplot triangulation

      (c) Lines of sight in PLOT3D multiblock form, 1 line per block,
          all blocks 1 x 1 x npts, where npts is prompted for, ASCII
          (<ID>.<BP #>.lines.g):

          nnodes x nquadrants
          1 1 npts
          1 1 npts
            : : :

History:

  10/07/05  D.A.Saunders  Initial design of LINES_OF_SIGHT.
  11/22/05    "     "     Expanded the range of t for INTSEC6 to 2, not 1.1;
                          Added the option to read a structured surface grid
                          rather than a list of indices or coordinates.
  03/06/06    "     "     Added the cone angle option.
  03/07/06    "     "     Renamed it as CONES_OF_SIGHT.
  03/08/06    "     "     HEMISPHERES_OF_SIGHT variant, using discretized
                          latitude and longitude.
  03/20/06    "     "     Users requested separate delta lat/long angles.
  03/27/06    "     "     Move origin of longitude from xy plane to xz;
                          suppress half a hemisphere if ytarget = 0.
  03/29/06    "     "     Specify multiples of the first and last grid
                          spacings, and allow the # points to vary from nk.
  03/30/06    "     "     Reversed the storage of latitudes to go from 90 to
                          zero, and output one line-per-block form with no
                          replication at the "north pole."
  02/01/14    "     "     All variants of the ADT routines have been merged
                          into a module (generic build & search calls).
  02/12/14    "     "     The search range for secondary-line intersections
                          has been raised from 0.5 L : 10 L to 0.5 L : 30 L
                          where L is the length of the initial primary line
                          that is rotated to all the secondary positions.
  02/21/14    "     "     A body point on the aft-body of a sphere-cone
                          showed that 0.5 L is too large.  Use 0.1 L now.
  03/17/14 -  "     "     Replaced latitude/longitude discretization with
  03/24/14                triangulation of a unit hemisphere quadrant and
                          transformations of that, to obtain roughly uniform
                          solid-angle spacing of the lines of sight defined
                          by the primary line and its hemisphere for each
                          target body point.
  03/26/14    "     "     Realized that the underlying unit hemisphere
                          quadrant needs to be rotated about its original
                          Oz axis to be properly axisymmetric, because the
                          triangulation is done with constant-z slices, not
                          constant-x (which in retrospect would have been
                          preferable).
  03/31/14    "     "     The last fix happily means the primary line is
                          now the first line, not nnodes - (ne - 1).
  01/26/15    "     "     An aft body point near the shoulder for MSL
                          with a longer wake needed a larger search range
                          for some of the intersections:  double the
                          default range for aft body points.
                          Also: element type needs to be TRIANGLE for all
                          zones of output triangulations, now that the
                          triangulation_io package handles volume grids too.

Author:  David Saunders, ELORET/NASA Ames Research Center, Moffett Field, CA
         Now with ERC, Inc. at  NASA ARC.