Computational Mechanics Research and Support for Aerodynamics ...
Computational Mechanics Research and Support for Aerodynamics ... Computational Mechanics Research and Support for Aerodynamics ...
0 0 0 1 0 0 B 0 = E -1 0 0 1 0 1 0 T 0 0 1 1 0 0 B 1 = E -1 [ 0 0 0] T 3.2.1.2. Conversion of wind velocity to wind pressure The conversion of wind velocity to wind pressure is necessary because the wind is described in terms of velocity and in the finite element analysis the velocities are attached to the nodes and pressure is applied to elements. The loading on elements would provide more accurate results compared to the node loading. The pressure due to wind velocity can be computed using the following conversion: Where, P = Pressure (N/m 2 ) C = Drag coefficient D = Density of air (1.25 Kg/m 3 ) V = Speed of air (m/s) The drag coefficient is a dimensionless quantity and it depends upon the surface area under the influence of attacking wind. The drag coefficients for flat and cylindrical body are approximated as follows: Drag coefficient for flat surface = 1 Drag coefficient for cylindrical surface = 0.67. 3.2.1.3. Development with the FEM After understanding the spring-damper system in LS-DYNA, it was necessary to study the motion of a node on a surface. To perform the analysis, a flat surface was created with two beam element and two massless nodes attached to it (Figure 3.13). These nodes were given a velocity and constraint so as to follow the beam element from start to end. TRACC/TFHRC Y1Q3 Page 58
̈ With the success to the above analysis, a spring element was attached to the nodes and a block was mounted on it (Figure 3.14). To verify the proper behavior of the spring, an initial displacement was given and it produced the appropriate result. After verifying the behavior with the above model, the task was to give an appropriate loading to the vertical face of block in order to understand the effects of wind pressure (Figure 3.15). Two types of wind pressure were given to the block, a constant load and a sine load. The properties of the model are: Mass = 5.88 Kg, Stiffness = 60 N/mm, Length of spring = 50 mm, Amplitude = 0.01, Frequency = 100 Hz, Forcing function = Amplitude*SIN(2*3.14*Frequency*TIME) Figure 3.16 shows the graph of horizontal displacement of the block with the application of sinusoidal wave as a forcing function. Theoretically, the equation of motion of the block with vertical springs and horizontal sine forcing function (Figure 3.15) is given by: √ (3.6) Where, m = Mass of the block, k = Stiffness of spring, l = original length, x = Displacement from static equilibrium position F 0 = Forcing function (sine wave) 3.2.1.4. Ford F-800 truck development A Ford F-800 truck model (Figure 3.17) was taken from the National Crash Analysis Center (NCAC) website [2]. The raw file contained a FEM model of the truck with six rigid walls attached to each tire and forward velocity. This model was studied and modified according to the requirements of the TRACC/TFHRC Y1Q3 Page 59
- Page 11 and 12: List of Tables Table 2.1: Boundary
- Page 13 and 14: experiments at TFHRC continued. A m
- Page 15 and 16: 2. Computational Fluid Dynamics for
- Page 17 and 18: ( ) ( ) (2.8) where A 0, A 1, and n
- Page 19 and 20: efine the rate function to improve
- Page 21 and 22: The objective of this work is to de
- Page 23 and 24: 2.3.2. Mesh Refinement Study As det
- Page 25 and 26: Table 2.2: Details of the various m
- Page 27 and 28: indicating the surface averaged vel
- Page 29 and 30: Figure 2.13: Line probes created at
- Page 31 and 32: In Figure 2.15 the velocity and the
- Page 33 and 34: Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5
- Page 35 and 36: Figure 2.20: Dimensional details of
- Page 37 and 38: Figure 2.22: Velocity distribution
- Page 39 and 40: Figure 2.25: CFD velocity contour p
- Page 41 and 42: Figure 2.27: CFD velocity contour p
- Page 43 and 44: Conclusions for Comparison with Exp
- Page 45 and 46: 3.1.1.1. Approach To date, an initi
- Page 47 and 48: Figure 3.4: Sampling domain [3] A c
- Page 49 and 50: present. In addition during the sum
- Page 51 and 52: For each level, the figures below s
- Page 53 and 54: 0.0 sec 0.5 sec 1.0 sec 1.5 sec 2.0
- Page 55 and 56: 0.5 sec 1.0 sec 1.5 sec 2.0 sec 3.0
- Page 57 and 58: 0.5 sec 1.0 sec 1.5 sec 2.0 sec 3.0
- Page 59 and 60: 3.2.1. Vehicle Stability under High
- Page 61: ̇ = steer angle These equations co
- Page 65 and 66: command. This requires the creation
- Page 67 and 68: Figure 3.17: FEM Model of a Ford F-
- Page 69 and 70: 3) Chen, F. and Chen, S., “Assess
- Page 71 and 72: 75 50 25 Force (N) 0 -25 -50 -75 -1
- Page 73 and 74: while the passive system has fixed
- Page 75 and 76: the controllable EMSA. Simulations
- Page 77 and 78: 4. Build a shell container with the
- Page 79 and 80: Figure 3.32 Comparison of the initi
0 0 0 1 0 0<br />
B 0 = E -1 0 0 1 0 1 0 T<br />
0 0 1 1 0 0<br />
B 1 = E -1 [ 0 0 0] T<br />
3.2.1.2. Conversion of wind velocity to wind pressure<br />
The conversion of wind velocity to wind pressure is necessary because the wind is described in terms of<br />
velocity <strong>and</strong> in the finite element analysis the velocities are attached to the nodes <strong>and</strong> pressure is<br />
applied to elements. The loading on elements would provide more accurate results compared to the<br />
node loading.<br />
The pressure due to wind velocity can be computed using the following conversion:<br />
Where,<br />
P = Pressure (N/m 2 )<br />
C = Drag coefficient<br />
D = Density of air (1.25 Kg/m 3 )<br />
V = Speed of air (m/s)<br />
The drag coefficient is a dimensionless quantity <strong>and</strong> it depends upon the surface area under the<br />
influence of attacking wind. The drag coefficients <strong>for</strong> flat <strong>and</strong> cylindrical body are approximated as<br />
follows:<br />
Drag coefficient <strong>for</strong> flat surface = 1<br />
Drag coefficient <strong>for</strong> cylindrical surface = 0.67.<br />
3.2.1.3. Development with the FEM<br />
After underst<strong>and</strong>ing the spring-damper system in LS-DYNA, it was necessary to study the motion of a<br />
node on a surface. To per<strong>for</strong>m the analysis, a flat surface was created with two beam element <strong>and</strong> two<br />
massless nodes attached to it (Figure 3.13). These nodes were given a velocity <strong>and</strong> constraint so as to<br />
follow the beam element from start to end.<br />
TRACC/TFHRC Y1Q3 Page 58
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