Skip navigation links
(Wind-US Documentation Home Page) (Wind-US User's Guide) (GMAN User's Guide) (MADCAP User's Guide) (CFPOST User's Guide) (Wind-US Utilities) (Common File User's Guide) (Wind-US Installation Guide) (Wind-US Developer's Reference) (Guidelines Documents)

(Introduction) (Tutorial) (Geometry and Flow Physics Modeling) (Numerical Modeling) (Boundary Conditions) (Convergence Monitoring) (Files) (Scripts) (Parallel Processing) (Keyword Reference) (Test Options)



REL-ROT-ZONE - Relative rotating zones (block)

Structured Grids

REL-ROT-ZONE
   ZONE iz1 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \
        [SUBSET I range J range K range]
   ZONE iz2 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \
        [SUBSET I range J range K range]
   ROTATING-ZONE AVERAGE [ABOUT] {X | Y | Z} \
        [AREA | MIXED-OUT] [GILES] [AXIAL | RADIAL]
ENDRRZ

For structured grids, the REL-ROT-ZONE keyword block, along with the ROTATE keyword, may be used to specify that one zone is rotating relative to another zone. This "relative rotating zone" capability is intended to simulate rotating devices such as compressor fans.

The ROTATE keyword is used to specify which zone(s) are rotating, plus the center of rotation and rotation rate. The REL-ROT-ZONE keyword block specifies the location of the interface between the two zones, and how flow conditions are to be transferred between zones. Note that each pair of relative rotating zones must appear in its own REL-ROT-ZONE block.

Zones sharing an interface may have different circumferential extents. Thus, when modeling a turbomachinery component like a compressor, only one blade per stage is required. Multiple zones and zonal interfaces may be used to cover the radial extent of the stage-to-stage interface, but a single zone must be used in the circumferential direction. The interface between zones must correspond to a surface of revolution, and grid lines in the circumferential direction must be at a constant radius relative to the rotation axis. The rotation axis must correspond to a coordinate axis.

As noted above, this capability is intended to simulate rotating devices such as compressor fans. A typical configuration would be an upstream non-rotating zone covering the full 360° cross-section, and a rotating downstream zone (or zones, if multiple zones are used in the radial direction) with a circumferential extent of 360°/N corresponding to a single blade. Periodic boundary conditions would be set at the circumferential boundaries in the rotating zone(s), using GMAN's rotational coupling mode.

The coupling of the downstream face of the non-rotating zone to the upstream face of the rotating zone would also be done using GMAN's rotational coupling mode, repeated N - 1 times. This will couple all the points except for that portion of the face that corresponds to the downstream zone in its non-rotated position. These remaining points are then coupled using ordinary (i.e., non-rotated) coupling mode. [In Wind-US, non-zero rotation angles trigger the use of a rotationally periodic boundary condition. Since this is not what is wanted between two relative rotating zones, this "non-rotated" coupling should be done last, so that zero rotation angles are written into the common grid (.cgd) file.]

The elements of the REL-ROT-ZONE keyword block are defined as follows:

REL-ROT-ZONE

Defines the beginning of the relative rotating zone block.

ZONE iz1 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \
     [SUBSET I range J range K range]
ZONE iz2 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \
     [SUBSET I range J range K range]

These two lines define the interface between the two zones. The relevant zones are given by the values of iz1 and iz2, and the relevant boundaries within zones iz1 and iz2 are specified via the BOUNDARY keyword parameter.

    iz1   Zone to which increments will be added when passing information to iz2
iz2 Zone receiving positive increments, increments will be subtracted when passing information back to zone iz1

The SUBSET parameter may be used to specify that the change in properties occurs only over a portion of the zone boundary. Otherwise, it is assumed that the change occurs over the entire boundary. The range parameters define the part of the zone boundary over which the change occurs, and take one of the following forms:

    index1 index2   Starting and ending indices in the specified direction. LAST may be used for the last index.
ALL Equivalent to 1 LAST.

The starting and ending indices for the appropriate I, J, or K parameter (depending on the boundary specified) must be the same, and correspond to that boundary.

ROTATING-ZONE AVERAGE [ABOUT] {X | Y | Z} \
     [AREA | MIXED-OUT] [GILES] [AXIAL | RADIAL]

When the relative-rotating-zone capability is used, flow conditions at each radial grid point are circumferentially averaged before sending them to the adjacent coupled zone. This averaging-plane approach permits the communication of the bulk fluid properties between zones, while maintaining radial distributions and the efficiency of local time stepping. The ROTATING-ZONE AVERAGE keyword defines the circumferential direction used for the averaging.

Note that since it is currently assumed that the axis of rotation aligns with one of the Cartesian coordinate axes, the circumferential direction specified with ROTATING-ZONE AVERAGE must be consistent with the rotation rate specified with with the ROTATE keyword.

Since flow properties are related nonlinearly, the average properties may not satisfy all characteristics of the original system (i.e., information is lost through the averaging process). The averaging scheme used will dictate which properties are preserved. Two averaging methods are available for use.

    AREA   Area averaging uses simple area-weighted integrations of the flow properties. It does not guarantee conservation of mass, momentum, or energy, but may be more stable for certain applications. This is the default setting.
MIXED-OUT Mixed-out averaging uses a stream-thrust flux-average to conserve mass, momentum, and energy. The averaged values formally represent the uniform flow that would exist far downstream..

The GILES option activates a non-reflecting boundary treatment at the rotor-stator interface to reduce problems caused by coupling of averaged data from the "other" zone.

The AXIAL or RADIAL option may be used to specify whether the REL-ROT-ZONE interface is oriented axially or radially. The default is AXIAL.

ENDRRZ

Defines the end of the relative rotating zone block.

Example

The following figure shows a four-zone configuration. Zone 1 is non-rotating, and zones 2, 3, and 4 are rotating about the x-axis at 1680 radians/sec in the counter-clockwise direction. The figure shows the grid from the side in a θ-constant plane, and at the interface plane between the non-rotating and rotating zones, looking downstream. In both views, only every other grid point is shown.

Four-zone grid from the side. Zone 1 is upstream 75% of duct; zones 2 to 4 are downstream 25%, stacked vertically from centerline

Four-zone grid at the interface plane, looking downstream

The non-rotating zone 1 covers the full 360° cross section, but the rotating zones 2-4 cover just 36°. As noted previously, zones sharing an interface may have different circumferential extents. This particular configuration is similar to one that might be used to model a single blade from a compressor blade row with 10 blades.

The indices i, j, and k are in the axial, radial, and circumferential directions, respectively. The table below summarizes the number of points used in each zone.

Zone imax jmax kmax
1 49 43 61
2 17 19 11
3 17 17 11
4 17 17 11

For this configuration, the zone coupling was done in GMAN as described below. In this discussion, the "boundary zone" is the one containing grid points for which a boundary condition is being set. GMAN is used to set the connectivity between points in the boundary zone to points in the "source zone". The source zone is specified using GMAN's "SEL OTHER BND" menu choice.

Note that some users have reported difficulty inputting values to the GMAN prompts when the caps-lock and/or num-lock keys are active. Also note that GMAN only allows periodic coupling of an entire boundary surface, not a subset of that boundary. Certain grid topologies, such as C-grids and O-grids, may need to be split into multiple zones.

Here is the procedure for specifying the zone coupling with GMAN:

  1. Load the grid file.
       file relrotzone.cgd
    
  2. Switch to graphics mode.
       switch
    
  3. Make sure that the boundary condition is "undefined" for zone 1 IMAX and zones 2,3,4 I1.
    1. Set zone 1 IMAX to "undefined".
      • Select TOP.
        • Select BOUNDARY COND.
          • Select PICK ZONE/BNDY.
            • Pick zone 1 IMAX.
          • Select MODIFY BNDY.
            • Select CHANGE ALL.
              • Select UNDEFINED.
      • Select TOP.
        • Select YES-UPDATE FILE.
    2. Set zone 2 I1 to "undefined" using the previous step.
    3. Set zone 3 I1 to "undefined" using the previous step.
    4. Set zone 4 I1 to "undefined" using the previous step.
  4. Manually couple the zone 1 K1 (θ=0°) and KMAX (θ=360°) planes using ordinary coupling. Ordinary coupling is used, because the points physically overlap each other.
    1. Manually couple zone 1 K1 to KMAX.
      • Select TOP.
        • Select BOUNDARY COND.
          • Select PICK ZONE/BNDY.
            • Pick zone 1 K1.
          • Select MODIFY BNDY.
            • Select COUPLE.
              • Select SEL OTHER BND.
                • Pick zone 1 KMAX.
              • Select COUPLE (not CONNECT).
                • You should be notified that "2107 undefined points were changed." This corresponds to IMAX*JMAX=49*43.
      • Select TOP.
        • Select YES-UPDATE FILE.
      Zone 1 K1 is now coupled to KMAX, but KMAX is still undefined.
      Need to manually couple in the opposite direction next.
    2. Manually couple zone 1 KMAX to K1 by following the previous step but switching K1 and KMAX. You should again find that "2107 undefined points were changed."
  5. Manually couple zone 2 K1 and KMAX as rotated periodic boundaries. Periodic coupling is used, because the boundary surfaces must be rotated to align. Again this is a two step process.
    1. Manually couple zone 2 K1 to KMAX.
      • Select TOP.
        • Select BOUNDARY COND.
          • Select PICK ZONE/BNDY.
            • Pick zone 2 K1.
          • Select MODIFY BNDY.
            • Select COUPLE.
              • Select SEL OTHER BND.
                • Pick zone 2 KMAX.
              • Select SET COUP MODE.
                • Select CONNECT MODE. At the prompt, enter the following values:
                    1 (rotation mode)
                     0.0 0.0 0.0 (rotation center)
                    36.0 0.0 0.0 (rotation angles)
                  
              • Select CONNECT (not COUPLE).
                • You should be notified that "323 undefined points were changed." This corresponds to IMAX*JMAX=17*19.
      • Select TOP.
        • Select YES-UPDATE FILE.
    2. Manually couple zone 2 KMAX to K1 by following the previous step but switching K1 and KMAX, and using a rotation angle of -36 degrees. You should again find that "323 undefined points were changed."
  6. Repeat the previous step for zones 3 and 4. You should find that:
    • IMAX*JMAX=17*17="289 undefined points were changed in zone 3."
    • IMAX*JMAX=17*17="289 undefined points were changed in zone 4."
  7. Because the outer circumference of zones 1 and 4 is discretely represented by different polygons, some points may not get properly coupled unless the containment tolerance in increased. To estimate how large the containment tolerance must be, consider that the distance from the midpoint of a polygon face to the outer radius (R) is given by:
       dR = R * ( 1 - cos(  / 2 ) )
    
    where is the circumferential angle represented by the largest polygon face in the two zones. For this example,
       dR = 2.0 * ( 1 - cos( 12° / 2 ) ) = 0.01096 ≈ 0.011
    
    This value will be used for the containment tolerance in the steps below.
  8. Change the view to be along the x-axis. This will make it easier to visualize your progress during the following steps.
    • Select VIEWING from the top right of the screen.
      • Select AXIAL VIEWS.
        • Select -X AXIS.
  9. Couple zone 1 IMAX to zone 2 I1, using rotational coupling mode repeatedly. This procedure is very similar to specifying periodic coupling, but the coupling is only done in one direction. Then finish by coupling the zones in the non-rotated position.
    1. For the first rotation,
      • Select TOP.
        • Select BOUNDARY COND.
          • Select PICK ZONE/BNDY.
            • Pick zone 1 IMAX.
          • Select MODIFY BNDY.
            • Select COUPLE.
              • Select SEL OTHER BND.
                • Pick zone 2 I1.
              • Select SET TOLERANCE.
                • Select CONTAINMENT TOL. At the prompt, enter the following value:
                     0.011
                  
                  Once set, this value should remain in effect for all subsequent operations.
              • Select SET COUP MODE.
                • Select CONNECT MODE. At the prompt, enter the following values:
                    1 (rotation mode)
                     0.0 0.0 0.0 (rotation center)
                    36.0 0.0 0.0 (rotation angles)
                  
              • Select CONNECT (not COUPLE).
                • "205 undefined points were changed, 2418 points could not be changed." Note that k=8 radial gridlines plus the remaining centerline points is 8*19+(61-8) = 205.
              • Select IDENTIFY PNTS.
                • Pick zone 2 I1.
                  You should be able to see which points were connected.
        • Select BOUNDARY COND.
          • Select YES-UPDATE FILE.
    2. For the second rotation,
      • TOP should still be selected.
        • BOUNDARY COND should still be selected.
          • Select PICK ZONE/BNDY.
            • Pick zone 1 IMAX, if not already selected.
          • Select MODIFY BNDY.
            • Select COUPLE.
              • Select SEL OTHER BND.
                • Pick zone 2 I1, if not already selected.
              • Select SET COUP MODE.
                • Select CONNECT MODE. At the prompt, enter the following values:
                    1 (rotation mode)
                     0.0 0.0 0.0 (rotation center)
                    72.0 0.0 0.0 (rotation angles)
                  
              • Select CONNECT (not COUPLE).
                • "108 undefined points were changed, 2310 points could not be changed." Note that k=6 radial gridlines omitting the previously coupled centerline points is 6*(19-1) = 108.
                • Also note that the screen view should automatically update to include the newly connected points.
        • Select BOUNDARY COND.
          • Select YES-UPDATE FILE.
    3. Repeat the previous step for rotation angles of: 108, 144, 180, 216, 252, 288, and 324. For each of these, you should be notified that "108 undefined points were changed."
    4. Couple zone 1 IMAX to zone 2 I1 in its non-rotated position using regular coupling. Note that if you attempt to "connect" the zones using 0 degree rotation, you will be told to use "couple" instead.
      • TOP should still be selected.
        • BOUNDARY COND should still be selected.
          • Select PICK ZONE/BNDY.
            • Pick zone 1 IMAX, if not already selected.
          • Select MODIFY BNDY.
            • Select COUPLE.
              • Select SEL OTHER BND.
                • Pick zone 2 I1, if not already selected.
              • Select COUPLE (not CONNECT).
                • You should be notified that "90 undefined points were changed." This corresponds to k=5 radial gridlines with j=18 points each.
                • The full 360 degrees should now be coupled.
        • Select BOUNDARY COND.
          • Select YES-UPDATE FILE.
  10. Repeat the previous step twice, coupling zone 1 IMAX to I1 in zones 3 and 4.
    • For zone 3,
      1. "128 undefined points were changed." This corresponds to k=8 radial gridlines with only j=16 points each, because the zone 1 points along the the inner radius of zone 3 were previously coupled to zone 2.
      2. "96 undefined points were changed." This corresponds to k=6 radial gridlines with j=16 points each.
      3. "96 undefined points were changed." This corresponds to k=6 radial gridlines with j=16 points each.
      4. "80 undefined points were changed." This corresponds to k=5 radial gridlines with j=16 points each, because the gridline at θ=360° was coupled in step (a).
    • For zone 4,
      1. "64 undefined points were changed." This corresponds to k=8 radial gridlines with j=8 points each, because the zone 1 points along the inner radius (j=1) of zone 4 were previously coupled to zone 3.
      2. "48 undefined points were changed." This corresponds to k=6 radial gridlines with j=8 points each.
      3. "48 undefined points were changed." This corresponds to k=6 radial gridlines with j=8 points each.
      4. "40 undefined points were changed." This corresponds to k=5 radial gridlines with j=8 points each, because the gridline at θ=360° was coupled in step (a).
  11. Couple zone 2 I1 to zone 1 IMAX
    • Select TOP.
      • Select YES-UPDATE FILE, if asked.
      • Select BOUNDARY COND.
        • Select PICK ZONE/BNDY.
          • Pick zone 2 I1.
        • Select MODIFY BNDY.
          • Select COUPLE.
            • Select SEL OTHER BND.
              • Pick zone 1 IMAX.
            • Select COUPLE (not CONNECT).
              • You should be notified that JMAX*KMAX=19*11="209 undefined points were changed."
      • Select BOUNDARY COND.
        • Select YES-UPDATE FILE.
  12. Repeat the previous step twice, coupling zone 3 and zone 4 I1 to zone 1 IMAX.
    • For zone 3, JMAX*KMAX=17*11="187 undefined points were changed."
    • For zone 4, JMAX*KMAX=17*11="187 undefined points were changed."
  13. Run "auto-couple" to generate connectivity between zones 2,3,4.
    • Select TOP.
      • Select YES-UPDATE FILE, if asked.
      • Select BOUNDARY COND.
        • Does not matter which zone/surface is currently selected.
        • Select AUTO COUPLE.
          • Select RUN AUTO COUP.
      • Select BOUNDARY COND.
        • Select YES-UPDATE FILE.
  14. At this point, all of the coupled boundaries should be set. To check, examine the boundary condition report.
    • Select TOP.
      • Select LIST.
        • Select LIST OPTIONS.
          • Select BNDY CND REPT.
            • Examine the results in the terminal window.
  15. Proceed with setting the remaining boundaries along the inflow, outflow, centerline, and casing surfaces.
  16. Set the grid units to feet, inches, etc., as desired.

The steps above can also be accomplished with the following GMAN script.

   file relrotzone.cgd
   ZONE 1
     BOUNDARY IMAX
       UNDEFINED
       UPDATE
   ZONE 2
     BOUNDARY I1
       UNDEFINED
       UPDATE
   ZONE 3
     BOUNDARY I1
       UNDEFINED
       UPDATE
   ZONE 4
     BOUNDARY I1
       UNDEFINED
       UPDATE
   ZONE 1
     BOUNDARY K1
       COUPLED TO ZONE 1 BOUNDARY KMAX
       UPDATE
     BOUNDARY KMAX
       COUPLED TO ZONE 1 BOUNDARY K1
       UPDATE
   ZONE 2
     BOUNDARY K1
       CONNECTED TO ZONE 2 BOUNDARY KMAX ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       UPDATE
     BOUNDARY KMAX
       CONNECTED TO ZONE 2 BOUNDARY K1   ROTATION CENTER 0. 0. 0. ANGLES -36. 0. 0.
       UPDATE
   ZONE 3
     BOUNDARY K1
       CONNECTED TO ZONE 3 BOUNDARY KMAX ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       UPDATE
     BOUNDARY KMAX
       CONNECTED TO ZONE 3 BOUNDARY K1   ROTATION CENTER 0. 0. 0. ANGLES -36. 0. 0.
       UPDATE
   ZONE 4
     BOUNDARY K1
       CONNECTED TO ZONE 4 BOUNDARY KMAX ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       UPDATE
     BOUNDARY KMAX
       CONNECTED TO ZONE 4 BOUNDARY K1   ROTATION CENTER 0. 0. 0. ANGLES -36. 0. 0.
       UPDATE
   ZONE 1
     BOUNDARY IMAX
       CONTAINMENT TOLERANCE 0.011
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  72. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 108. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 144. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 180. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 216. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 252. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 288. 0. 0.
       CONNECTED TO ZONE 2 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 324. 0. 0.
       COUPLED TO ZONE 2 BOUNDARY I1
       UPDATE
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  72. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 108. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 144. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 180. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 216. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 252. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 288. 0. 0.
       CONNECTED TO ZONE 3 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 324. 0. 0.
       COUPLED TO ZONE 3 BOUNDARY I1
       UPDATE
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  36. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES  72. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 108. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 144. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 180. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 216. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 252. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 288. 0. 0.
       CONNECTED TO ZONE 4 BOUNDARY I1 ROTATION CENTER 0. 0. 0. ANGLES 324. 0. 0.
       COUPLED TO ZONE 4 BOUNDARY I1
       UPDATE
   ZONE 2
     BOUNDARY I1
       COUPLED TO ZONE 1 BOUNDARY IMAX
       UPDATE
   ZONE 3
     BOUNDARY I1
       COUPLED TO ZONE 1 BOUNDARY IMAX
       UPDATE
   ZONE 4
     BOUNDARY I1
       COUPLED TO ZONE 1 BOUNDARY IMAX
       UPDATE
   LIST BOUNDARY CONDITION REPORT
   ZONE 3
    AUTOMATIC COUPLE FACE ZONE ALL
   LIST BOUNDARY CONDITION REPORT

The relevant keyword input in the input data (.dat) file would be

   ROTATE 0.0 0.0 0.0 -1680.0 0.0 0.0 ZONE 2:4

   REL-ROT-ZONE
      ZONE 1 BOUNDARY IMAX SUBSET I LAST LAST J  1   19 K ALL
      ZONE 2 BOUNDARY I1
      ROTATING-ZONE AVERAGE ABOUT X AREA AXIAL
   ENDRRZ
   REL-ROT-ZONE
      ZONE 1 BOUNDARY IMAX SUBSET I LAST LAST J 20   35 K ALL
      ZONE 3 BOUNDARY I1
      ROTATING-ZONE AVERAGE ABOUT X AREA AXIAL
   ENDRRZ
   REL-ROT-ZONE
      ZONE 1 BOUNDARY IMAX SUBSET I LAST LAST J 36 LAST K ALL
      ZONE 4 BOUNDARY I1
      ROTATING-ZONE AVERAGE ABOUT X AREA AXIAL
   ENDRRZ
See Also: ROTATE


Last updated 1 Apr 2016