{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

06%20Dimensional%20Analysis%20EGM%206812%20F11

# 06%20Dimensional%20Analysis%20EGM%206812%20F11 - EGM 6812...

This preview shows pages 1–4. Sign up to view the full content.

EGM 6812, F11, University of Florida, M. Sheplak 1/16 Section 6, Dimensional Analysis 6 Dimensional Analysis and Similarity Why? 1. Reduced number of experiments 2. Compact data representation 3. Solve problem fewer times 4. Lab prototype to full scale 5. If we non-dimensionalize the governing equations, we can “simplify” the equations by neglecting certain terms. Example Investigate drag on a sphere, with roughness (i.e. golf ball, high speed) , , , , , D D F F D u c   If we investigate 10 iterations of each parameter, we would have to conduct 6 10 experiments. Instead perform a non-dimensionalization. 6.1 Buckingham -theorem Answer- 2 2 Roughness Re , , 1 2 D D Ma C F uD u f c D u D Step 1. List all variables , , , , , D D F F D u c   7 n Step 2. Select the primary dimensions M,L,t 3 r Step 3. List dimensions of each parameter Parameter F D c u Dimension ML t 2 L L M L 3 M Lt L t L t Step 4. Select “r” repeating parameters (engineering judgment call!) Don’t choose: , , , D F c   non-repeaters

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EGM 6812, F11, University of Florida, M. Sheplak 2/16 Section 6, Dimensional Analysis “parameters that are physically interesting” Do choose , , u D } make sure that they cover mass, length, and time Step 5. Set up (n-r) groups 1 a b c D F u D   nondimensional choose a,b,c such that the s are nondimensional 2 4 ... d e f u D  When you do this you end up with drag force 1 2 2 2 2 area dynamic pressure drag coefficient D D D F F C u D u D   2 ratio of roughness to diameter D   3 1 Re uD   4 1 Ma c u 6.2 Flow Similarity How do we scale data from a wind-tunnel experiment to full-scale? Similarity!!! Geometric Similarity : Same shape between model and full scale Kinematic Similarity : velocity fields about a model and prototype must vary by no more than a constant. Kinematic similarity implies geometric similarity Dynamic Similarity : all forces on a model prototype must vary by no more than a constant scale factor. Dynamic similarity implies kinematic similarity and geometric similarity. To achieve dynamic similarity, we must match all the groups Example : 2 2 Re, , D D F C f Ma v D D For Dynamic similarity