Body of Revolution

Contents

The Body of Revolution (BOR) sweeps a single cross section once around the $X$ axis. In Flowthrough mode the section is set off from the axis, and the result is an open ring: a duct, a fan shroud, a ring wing or a short nacelle, with an airfoil for its wall. In Upper and Lower mode the axis runs along the section's chord, and the result is a closed, streamlined body whose radius follows the section's upper or lower surface.

The Gen, XForm, Mass and Sub tabs are described on their own pages.

Quick Start

A duct

1. Add a Body of Revolution. A new one is a torus: a circle of diameter 1 swept around a circle of diameter 2.
2. Place it with the XForm tab.
3. Choose an airfoil for the section on the XSec tab, and set its chord and T/C.
4. Set Diameter and Angle on the Design tab.

A streamlined body

1. Add a Body of Revolution and set Mode to Upper.
2. Place it with the XForm tab.
3. Choose a symmetric airfoil for the section on the XSec tab.
4. Set the chord to the body's length, and T/C to its diameter over its length.

Flowthrough

The section is laid with its chord along $X$, its leading edge at $X = 0$ and at a radius of half the Diameter, and its upper surface outward (Figure 1). Angle then turns the section about its leading edge; a positive angle turns its trailing edge toward the axis, so the ring narrows toward the back. The section is swept a full turn around the $X$ axis; its inner surface is the inside of the duct.

Figure 1. A Flowthrough BOR cut through its axis, above the axis: a NACA 4412 section, chord 1, Diameter 2, at Angle 0 (dashed) and 10 degrees.

Four areas are reported, each the area of a circle about the axis:

In Upper and Lower mode they are zero.

Figure 2 shows the radius behind each area. Once a positive Angle turns the trailing edge in far enough, the trailing edge is the point nearest the axis, and Amin equals Ae; on the section of Figure 1 that happens from an Angle of about 2 degrees.

Figure 2. The section of Figure 1 at Angle -5 degrees, cut through the axis above it, with the radii of the circles whose areas are A0, Ae and Amin: $A_0 = \pi r_0^2$, $A_e = \pi r_e^2$, $A_{min} = \pi r_{min}^2$. The dot is the point nearest the axis, on the inner surface.

A Flowthrough BOR is the quickest model of a round duct or nacelle: one airfoil, a diameter and an angle. It is always the open ring, though, and always round. When an analysis needs the nacelle closed at its lips or faces, a flowpath that cuts through the wing or fuselage it is buried in, or an inlet carried upstream to the edge of a CFD domain, or when the nacelle is not round, build it as a Stack from a nacelle preset (see Stack Presets) and choose its representation with the Engine Model.

Upper and Lower

In Upper mode the section's chord lies on the $X$ axis, leading edge at the origin, and its upper surface is swept around the axis, so the body's radius at each point along the chord is the height of the upper surface there. Lower does the same with the lower surface, measured below the chord. The result is closed at both ends, and as long as the chord (Figure 3). Diameter and Angle are not used, and are greyed.

The radius of the body is the section's thickness above (or below) its chord line, so a symmetric section of thickness ratio $t/c$ gives a body of diameter $t$ and length-to-diameter ratio $c/t$. Camber makes the Upper body fatter and the Lower body thinner.

Figure 3. The Upper (above) and Lower (below) bodies of a NACA 4412 section of chord 1, cut through their axis, with the section (dashed).

The Cross Section

The section may be any of the Cross Section Curves or Airfoils, and the Modify tab treats it as it treats a wing's airfoil (see Airfoils).

A new BOR's section is a circle of diameter 1. An airfoil chosen in its place keeps its width and height, so it starts with a chord of 1 and a T/C of 1: set the thickness straight away.

In every mode the BOR is a wing-type surface with the section as its airfoil, so analyses that reduce wings to thin lifting surfaces (DegenGeom, the VSPAERO vortex lattice) treat a Flowthrough BOR as a ring wing, and treat an Upper or Lower BOR as a lifting surface too, not as a body. Model a streamlined body that such an analysis should see as a body with a Fuselage or Stack or a Pod.

Tessellation

The Gen tab's Num_U sets the points around the axis, and Num_W the points around the section. LE Clustering and TE Clustering on the Design tab bunch the points around the section toward its leading and trailing edges (values below 1 bunch them). Cap Tess sets the points across the section's trailing edge when the Modify tab leaves it blunt.

Scripting

All are in the Design group. The section is changed with ChangeBORXSecShape and read with GetBORXSecShape; its parameters are in the BOR's XSecCurve group. ReadBORFileXSec, ReadBORFileAirfoil, SetBORXSecPnts, SetBORAirfoilPnts and the ...BORCST... calls set a section from a file, from points, or as a CST airfoil.