As you know, fluid forces may consist of one or more of the following components:

I. Pressure forces - acting normal to surfaces

II. Shear forces - acting tangentially to surfaces

III. Wave drag - due to compressible effects

IV. Induced drag - 'drag-due-to-lift'

I. Pressure forces can be calculated as follows:

1. FIND THE NORMAL - For parts comprised of 1D elements (e.g. bars), the function used to calculate the force, Force1D requires the Normal as input, so we'll need to use the Normal calculator function to calculate the normal vector field and name the variable 'Normal'. For parts with 2D elements (e.g. shells, plates, etc) the function used to calculate the force, Force, doesn't require a Normal vector, so we won't need to calculate this variable.

For 1D parts, the normal function attempts to make sure that you get consistent normals (in or out). It will not work if you have discontinous segments (such as a wing cross section and a flap in the same part). There is a possibility under these conditions that you get inward pointing normals on one portion and outward pointing normals on another. For 2D parts it is also possible

but unlikely that your elements may not have consistent normals.

For 1D parts, We highly recommend that after you compute 'Normal' you go ahead and create a vector arrow part using this variable to make sure it is oriented uniformly. For 2D parts, the vector arrow dialog also includes a variable for normal visualization that does not show up in the calculator: 'Surface Normal'. Use this variable for 2D parts to verify normal consistency.

If all of your 1D 'Normal' vectors or 2D 'Surface Normal' vectors are not consistent (either all inward or all outward), then you have a problem with your model and cannot continue.

For all parts, if all of your 'Normal' or 'Surface Normal' vectors are inward, then create a 'Normalneg' vector using the calculator which is -1*Normal and use it instead of 'Normal'.

2. CALCULATE THE PER ELEMENT FORCE

Important note:

If pressure is a nodal variable, then use NodeToElem to convert Nodal Pressure to Element Pressure before proceeding. Always use the Element Pressure to calculate a Force.

a. Use the 'Force' calculator function to

calculate the force vector using the per element pressure scalar on a 2-D part (e.g. shells, plates, etc) or

b. Use the 'Force1D'

calculator function to calculate on a 1D part (bars) using element pressure, and 'Normal'.

Possible reasons you will not get a force vector using Force1D:

The 1D part was structured (must have unstructured)

The part contains 2D or 3D elements - the part must contain only 1D elements

The part is not planar.

3. SUM THE FORCES.

Select your part or parts, and use StatMoment (option set to sum) and the element force [X], [Y], and [Z] scalar components to calculate the net force in the x, y, and z directions respectively.

4. LIFT & DRAG.

Once you have the force vector, the lift and drag can be resolved using the angle between the freestream velocity and the force vectors. The component of the force in the direction of the freestream velocity is drag, and the component normal to the freestream velocity is lift.

5. PRESSURE MOMENTS

You can calculate the MomentVector at every node on your part using Calculator 'MomentVector' function. This will enable you to visualize trends in the moment only at part node locations but cannot show the moment at any arbitrary point.

To calculate the moment about any arbitrary point,use the predefined calculator function 'Moment'. The location of the cursor tool is used to define the moment arm. The cursor tool may be placed at a precise (x,y,z) location using the transformation editor for tools.

A force vector is required. For pressure moments, use the same pressure force vector computed from integrating pressure * area in the normal direction (see above).

The [X], [Y] or [Z] component of the moment is computed based on the force vector, the position of the cursor tool and the component desired. The Moment function computes the sum of the cross product of the distance from the cursor to each of the force vectors.

The center of pressure is the location where the sum of the moments is zero. Finding this point requires some manual iteration. First calculate the MomentVector at every node to visualize the moment over the part. Using this insight, then place the cursor tool and calculate the Moment in the desired direction. Move the cursor around and recalculate the moment until it is sufficiently close to zero.

The steps from 1 to 3 have been implemented in a single User Defined Tool, that you can use to get directly from your pressure field to the net force. The tool follows the steps described above. It can be found in the User Defined Tools -> Analyze -> Net Force.

II. Shear forces calculation is a bit tedious as follows:

For shear forces, the shear stress at the surface must be computed using the gradient of the fluid velocity and the fluid's dynamic viscosity at the surface. Currently, a rather tedious procedure must be used to compute the fluid shear stress components on a model's surface:

a. in the fluid domain surrounding the surface, define vx, vy, vx, the velocity components, as three new scalars

b. using the Grad operator in the variable calculator, compute the gradient of each of these components in the fluid, resulting in new gradient vectors of these components, i.e. grad_vx, grad_vy, grad_vz

c. these gradients must be mapped from the fluid onto the surface. This is done either by using the Case Map feature in EnSight, or creating an isosurface (velocity = 0.) or a clip plane that corresponds to the surface of interest.

d. Compute the fluid shear stress components using the FluidShear function in the variable calculator and the mapped velocity gradients. A value for the fluid's dynamic viscosity must be provided. This may also be a scalar variable.

e. Create a fluid shear stress vector from these components using the MakeVect function in the variable calculator.

f. We need the tangential component of the fluid shear stress vector in order to integrate the shear stress forces and moments. The tangential component may be displayed by projecting this from the Feature Detail Editor (Vector Arrows)

g. Compute the tangential component of the shear stress. This is done using vector algebra. First, create a surface normal vector variable using the Normal function in the variable calculator. Next, dot this with the shear stress vector, and multiply this product by the surface normal vector. This produces the normal component of the shear stress vector. The tangential component is now computed by subtracting this normal component from the shear stress vector, or Vt = V - Vn, where V represents the shear stress vector.

h. We now use the tangential component of the surface shear stress, itself a vector, to compute a shear stress force vector, simple by multiplying the x/y/z components of the tangential component of the shear stress by the incremental surface area.

i. This force vector can then be summed using StatMoment (with option set to 0 to sum a variable across elements - see EnSight User Manual section 4.3 under Statistics Moments) to produce the shear stress components. (Note: udmf_sum used to be recommended here, but with 9.0 has been deprecated.It still exists, but StatMoment is threaded and multi-functional, where udmf_sum is not.)

Shear Moments

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Once the shear force vector has been computed, the Moment function in EnSight's variable calculator may be used to compute the components of the shear moment as for the pressure force contribution to moments.

III. Wave drag - To Be determined

IV. Drag due to lift is what we are trying to work out now.

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CEI plans to incorporate all of the above steps into a simple function in a future version of EnSight.

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