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119 lines
2.9 KiB
Plaintext
119 lines
2.9 KiB
Plaintext
---
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title: "Air Propulsion Simulation"
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description: |
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Simulating the performace of an air propulsion system as an alternative to solid rocket motors.
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author:
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- name: Anson Biggs
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url: https://ansonbiggs.com
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repository_url: https://gitlab.com/lander-team/air-prop-simulation
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date: 04-01-2021
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fig_width: 6
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fig_align: "center"
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output:
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distill::distill_article:
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self_contained: false
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categories:
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- Julia
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- Capstone
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---
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Boilerplate intro about why all of this was done
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```{r setup, include=FALSE}
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library(ggplot2)
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knitr::opts_chunk$set(echo = TRUE, results = 'hide')
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library(JuliaCall)
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julia_setup(JULIA_HOME = "/opt/julia-1.6.0/bin/")
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```
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```{julia, code_folding=TRUE}
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using Plots
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plotly()
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theme(:ggplot2); # In true R spirit
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using Unitful
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using DataFrames
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using Measurements
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using Measurements: value, uncertainty
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```
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This code is just the setup the setup, using values scraped from various parts of the world wide web.
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```{julia}
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# Tank https://www.amazon.com/Empire-Paintball-BASICS-Pressure-Compressed/dp/B07B6M48SR/
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V = (85 ± 5)u"inch^3"
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P0 = (4200.0 ± 300)u"psi"
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Wtank = (2.3 ± 0.2)u"lb"
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Pmax = (250 ± 50)u"psi" # Max Pressure that can come out the nozzle
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Wsolenoid = 1.5u"kg"
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# Params
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d_nozzle = ((1 // 18) ± 0.001)u"inch"
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a_nozzle = (pi / 4) * d_nozzle^2
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# Universal Stuff
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P_amb = (1 ± 0.2)u"atm"
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γ = 1.4 ± 0.05
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R = 287.05u"J/(kg * K)"
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T = (300 ± 20)u"K"
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```
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This is the actual simulation. Maybe throw some references in and explain some equations.
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The rocket equation is pretty sick:
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$$T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) $$
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And thats about all you need to get to the moon.
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```{julia}
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let
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t = 0.0u"s"
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P = P0 |> u"Pa"
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M = V * (P / (R * T)) |> u"kg"
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ts = 1u"ms"
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global df = DataFrame(Thrust=(0 ± 0)u"N", Pressure=P0, Time=0.0u"s", Mass=M)
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while M > 0.005u"kg"
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# while t < 30u"s"
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# Calculate what is leaving tank
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P = minimum([P, Pmax])
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ve = sqrt((2 * γ / (γ - 1)) * R * T * (1 - P_amb / P)^((γ - 1) / γ)) |> u"m/s"
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ρ = P / (R * T) |> u"kg/m^3"
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ṁ = ρ * a_nozzle * ve |> u"kg/s"
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Thrust = ṁ * ve + a_nozzle * (P - P_amb) |> u"N"
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# Calculate what is still in the tank
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M = M - ṁ * ts |> u"kg"
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P = (M * R * T) / V |> u"Pa"
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t = t + ts
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df_step = DataFrame(Thrust=Thrust, Pressure=P, Time=t, Mass=M)
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append!(df, df_step)
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end
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end
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```
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Heres the results plotted. Notice the massive error once the tank starts running low.
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```{julia, echo=FALSE, results='show'}
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thrust_values = df.Thrust .|> ustrip .|> value;
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thrust_uncertainties = df.Thrust .|> ustrip .|> uncertainty;
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out = DataFrame(Thrust=thrust_values, Uncertainty=thrust_uncertainties, Time=df.Time .|> u"s" .|> ustrip);
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plot(df.Time .|> ustrip, thrust_values,
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title="Thrust Over Time",
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ribbon=(thrust_uncertainties, thrust_uncertainties),
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fillalpha=.2,label="Thrust",
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xlabel="Time (s)",
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ylabel="Thrust (N)",
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)
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```
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Big conclusion about things.
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