Monthly Archives: July 2013

Addendum to nose cone heating: stagnation temperature

It’s useful to calculate the stagnation temperature of the air. It gives an upper bound to the temperature that the nose could reach.

Altitude (m) Velocity (m/s) Temp (K) Pressure (Pa) Mach number Stagnation temp (K)
827 344 282.8 91777 1.02 341.7
2022 532 275.0 79278 1.60 415.9
8056 360 235.8 35312 1.17 300.3
9955 780 223.4 26619 2.60 526.2
11750 1112 216.7 20108 3.77 831.9
13703 1445 216.7 14771 4.90 1255.6

Going near Mach 5 at 13km: quite toasty.

Solidworks Simulation of near hypersonic nose cone

Richard asked if I could do some simulation of the nose cone heating of the Double Sugar Shot rocket. It’s quite a big nose cone, nearly a meter long by 169mm diameter (~3ft by 6.65″). I modeled it in Solidworks, then ran it in Solidworks Simulation. With my current computer, it takes a few days for it to complete a run, then a few days more to get time to check the results and re-run it if anything was off. Following is the final results of one run.

I was given a few points with altitude, velocity, temperature, pressure, and density. I calculated dynamic pressure.

Altitude (m) Velocity (m/s) Temp (K) Pressure (Pa) Density (kg/m^3) Dynamic pressure (Pa) Mach number
827 344 282.8 91777 1.131 66898 1.02
2022 532 275.0 79278 1.004 142116 1.60
8056 360 235.8 35312 0.522 33808 1.17
9955 780 223.4 26619 0.415 126247 2.60
11750 1112 216.7 20108 0.323 199903 3.77
13703 1445 216.7 14771 0.238 247967 4.90

The last point had the highest dynamic pressure (also known as “max Q”) for the data points given, so I ran it in the simulation as it may have the most interesting results. That point is 1445 m/s at 13703 m MSL. For the simulation input I used air as the fluid at the density at that altitude; 14771 Pa and 216.65 K. I set the surface roughness to 6.35 micrometer, which should be appropriate for a finish equivalent to smooth paint.

Here’s a video of one result, followed by charts of others. Click to embiggen.

The mesh:Image

 

Gas density:Image

 

Pressure:Image

 

Temperature:Image

 

Velocity:Image

 

The shockwave coming off the cone is prominent in all the plots, and raked back at a severe angle due to the high velocity. The temperature is relatively low, aside from a small warm area just downstream of the nose.

Here the analysis wasn’t set to deal with conduction in solids, so it’s impossible to give temperatures for the solid part, just for the gas touching the part. It does bound the maximum temperature the part could reach, which is a reasonable design point, but it isn’t as interesting as having a plot of the actual expected part temperatures.

To analyze the heat going into the nose cone its material properties must be defined. These include:

  • Density
  • Specific heat (possibly at multiple temperatures)
  • Conductivity type (Isotropic, Unidirectional, Asymmetrical/Biaxial, or Orthotropic)
  • Thermal conductivity (which can also vary with temp and can be multiple, if not isotropic)
  • Melting temperature (the glass transition temperature of the resin would be a good analog for a composite nose cone)

The thickness of the nose cone would also need to be known, especially if it varies at different positions.

For the next analysis I will shorten the length of the straight tube to just a few inches, close the end so that the flow inside isn’t taking calculation cycles, and possibly change the size of the bounding box to remove the volume downstream of the nose.

A full simulation can also be done with time dependent variables. The velocity, temperature, and pressure can all be varied with time to get an idea of the total heating over the flight. However that analysis would probably take weeks for the computer to run. It’d be interesting to try, though.

Image

Colorful fluid drawing of a cone traveling hypersonically

Colorful fluid drawing of a cone traveling hypersonically

Running an experiment with some very basic geometry to see the capabilities of Solidworks Flow Simulation in analyzing a shape traveling mach 5+.

The cone is 4 inches tall and 2 inches wide at the base, to roughly simulate the tip of a rocket nose cone at a severe Max-Q. Fluid is air at STP.