Experiments

The F_UNCLE project currently does not use any true experimental data

Gun

class F_UNCLE.Experiments.GunModel.Gun(name=u'Gun Toy Computational Experiment', *args, **kwargs)

A toy physics model representing a gun type experiment

The problem integrates the differential equation for a mass being accelerated down the barrel of a gun by an the expanding products- of-detonation of a high explosive. The gun has finite dimensions and the integration lasts beyond when the projectile exits the gun.

Units

This model is based on the CGS units system

Diagram

variables defining the gun experiment

Options

Name	Type	Def	Min	Max	Units	Description
X_i	(float)	0.4	0.0	None	cm	Initial position of projectile
x_f	(float)	3.0	0.0	None	cm	Final/muzzle position of projectile
m	(float)	500.0	0.0	None	g	Mass of projectile
mass_he	(float)	4	0.0	None	g	The initial mass of high explosives used to drive the projectile
area	(float)	1.0	0.0	None	cm**2	Projectile cross section
sigma	(float)	1.0e0	0.0	None	??	Variance attributed to v measurements
t_min	(float)	1.0e-6	0.0	None	sec	Range of times for t2v spline
t_max	(float)	1.0e-2	0.0	None	sec	Range of times for t2v spline
n_t	(int)	250	0	None	‘’	Number of times for t2v spline

Attributes

Inherited from ::pyclass::pyStruc

Methods

__init__(name=u'Gun Toy Computational Experiment', *args, **kwargs)

Instantiate the Experiment object

Parameters:None – Keyword Arguments:  name (str) – A name. (Default = ‘Gun Toy Computational Experiment’)

_fit_t2v(vel, time)

Fits a cubic spline to the velocity-time history

This allows simulations and experiments to be compared at the experimental time-stamps

Parameters:

• vel (np.ndarray) – Velocity history
• time (np.ndarray) – Time history

Returns:

Spline of vel = f(time)

Return type:

(Spline)

_get_force(eos, posn)

Calculates the force on the projectile

The force is the pressure of the HE gas acting on the projectile. The pressure is given by the EOS model

Parameters:

• eos (Isentrope) – The equation of state model
• posn (float) – The scalar position

Returns:

The force in dyes

Return type:

(float)

_on_call(eos, **kwargs)

Performs the simulation / experiment using the internal EOS

Parameters:

• eos (Isentrope) – The equation of state model
• **kwargs – Arbitrary keyword arguments.

Returns:

Length 3, elements are:

0. (np.ndarray): Time, the independent variable

1. (tuple): length 2 for the two dependent variables

   0. (np.ndarray): Velocity history of the simulation
   1. (np.ndarray): Position history of the simulation

2. (Spline): A spline representing the velocity-time history

Return type:

(tuple)

_on_check_models(models)

Checks that the model is valid

Parameters:model (Isentrope) – A new EOS model Returns:A copy of self with the new eos model Return type:(GunModel)

_on_str(*args, **kwargs)

Print method of the gun model

Parameters:

• *args – Variable length argument list.
• **kwargs – Arbitrary keyword arguments.

Returns:

A string representing the object

Return type:

(str)

_shoot(eos)

Run a simulation and return the results: t, [x,v]

Solves the ODE

\[F(x,v,t) = \frac{d}{dt} (x, v)\]

Parameters:eos (Isentrope) – The equation of state model Returns:Length 2 elements are:

0. (np.ndarray): time vector
1. (list): elements are:

   0. (np.ndarray): position
   1. (np.ndarray): velocity

Return type:(tuple)

compare(simdata1, simdata2)

Compares a set of experimental data to the model

Error is dep less the model_data

See F_UNCLE.Utils.Experiment.Experiment.compare()

get_sigma(models)

Returns the co-variance matrix

see F_UNCLE.Utils.Experiment.Experiment.get_sigma()

plot(axes=None, fig=None, level=0, data=None, linestyles=[u'-k', u'-r'], labels=[u'Model', u'Error'], *args, **kwargs)

Plots the gun experiment

Overloads F_UNCLE.Utils.Struc.Struc.plot()

Plot Levels

0. The velocity-time history
1. The position-time history
2. The velocity-position history
3. A 4 subplot figure with levels 1-3 as well as the EOS plotted

Parameters:

• axes (plt.Axes) – Axes object on which to plot, if None, creates new figure
• fig (str) – A Figure object on which to plot, used for level3 plot
• linestyles (list) – A list of strings for linestyles 0. Data ‘-k’ 1. Error ‘-r’
• labels (list) – A list of strings for labels 0. ‘Model’ 1. ‘Error’
• level (int) – A tag for which kind of plot should be generated
• data (dict) – A list of other data to be plotted for comparison

Returns:

A figure

Return type:

(plt.figure)

shape()

Returns the degrees of freedom of the model

see F_UNCLE.Utils.Experiment.Experiment.shape()

Stick

class F_UNCLE.Experiments.Stick.Stick(name=u'Rate Stick Computational Experiment', *args, **kwargs)

A toy physics model representing a rate stick TO DO

• Update the __call__ method to not use hardcoded sensor positions

Units

Units are based on CGS system

Diagram

The assumed geometry of the rate stick

Attributes

eos

Isentrope – The products-of-detonation equation of state

Methods

__init__(name=u'Rate Stick Computational Experiment', *args, **kwargs)

Instantiate the Experiment object

Keyword Arguments:  name (str) – A name. (Default = “Rate Stick Computational Experiment”)

_on_call(eos)

Performs the rate stick experiment

Parameters:eos (Isentrope) – A valid EOS model Returns:Length 3. Elements are

0. (np.ndarray): The independent variable, the n sensor positions
1. (list): The dependent variables, elements are:
   0. (np.ndarray): The arrival n times at each sensor
   1. (list): The lables
2. (dict): The other solution data - ‘mean_fn’(Function): A function returning shock arrival

   time as a function of position

   • ‘vel_CJ’(float): The detonation velocity
   • ‘vol_CJ’(float): The specific volume at the_CJ point
   • ‘pres_CJ’(float): The pressure at the_CJ point
   • ‘Rayl_fn’(Function): A Rayleigh line function, see below

Return type:(tuple)

Rayleigh Line Function

p = ray(v, vel, vol0, eos)

Args:

• v(np.ndarray): The specific volume
• vel(float): Detonation velocity
• vol_0(float): Specific volume ahead of the shock
• eos(Isentrope): An equation of state model

Return:

• p(float): The pressure along the Rayleigh line at v

_on_check_models(models)

Checks that the model is valid

Parameters:model (dict) – A dictionary of models Returns:A copy of self with the new eos model Return type:(GunModel)

_on_str(*args, **kwargs)

Print method of the gun model. Called by Struct.__str__

Parameters:

• *args – Variable length argument list.
• **kwargs – Arbitrary keyword arguments.

Returns:

A string representing the object

Return type:

(str)

compare(simdata1, simdata2)

Compares the model instance to other data

The error is the difference in arrival times, dep less data.

see F_UNCLE.Utils.Experiment.Experiment.compare()

get_sigma(models)

Returns the variance matrix

variance is

\[\Sigma_i = \sigma_t^2 + \frac{\sigma_x^2}{V_{CJ}}\]

Where

• \(\sigma_t\) is the error in time measurements
• \(\sigma_x\) is the error in sensor position
• \(V_{CJ}\) is the detonation velocity

see F_UNCLE.Utils.Experiment.Experiment.get_sigma()

plot(models, axes=None, fig=None, data=None, level=1, linestyles=[u'-k', u':k', u'ok', u'+k'], labels=[u'Fit EOS', u'Rayleigh Line', u'($v_o$, $p_o$)', u'Inital point'], vrange=None)

Plots the EOS and Rayleigh line

Plots the critical Rayleigh line corresponding to the detonation velocity tangent to the EOS.

Parameters:

models (dict) – Dict of models

Keyword Arguments:  

• axes (plt.Axes) – The Axes on which to plot
• fig (plt.Figure) – The figure on which to plot ignored
• data (list) – The output from a call to Stick
• level (int) – Specifies what to plot

1. Plots the EOS with the Raylight line intersecting the CJ point

2. Plots the output from a simulation

   linestyles(list): Format strings for the trends, entries as follow

0. Stlye for the best fit EOS OR The data trend

   1. Style for the Rayleigh line
   2. Style for the CJ point
   3. Style for the initial condiations

   labels(list): Strings for the legend

0. ‘Fit EOS’ (Change to Data for level 2 plot)

   1. ‘Rayleigh line’
   2. ‘v_o, p_o’
   3. ‘Initial point’

   vrange(tuple): Range of volumes to plot

see F_UNCLE.Utils.Struc.Struc.plot()

shape()

Returns the shape of the object

see F_UNCLE.Utils.Experiment.Experiment.shape()

Sphere

class F_UNCLE.Experiments.Sphere.Sphere(name=u'Sphere compuational experiment', *args, **kwargs)

A toy physics model representing an expanding plastic sphere driven by HE

const

dict – A dictionary of conversion factors

__init__(name=u'Sphere compuational experiment', *args, **kwargs)

Instantiate the Experiment object

Keyword Arguments:  name (str) – A name. (Default = ‘Sphere computational experiment’)

_on_call(eos, strength)

Solves the sphere problem

Parameters:

• eos (Isentrope) – The Equation of strength model
• strength (Ptw) – The material strength model

Returns:

[0] - times [1](list): Data at each timestep

[0] - velocity of the case [1] - radius of the case [2] - case thickness [3] - specific volume of gasses within case [4] - pressure of gasses within case [5] - stress in the case [6] - strain in the case

Return type:

(tuple)

_on_check_models(models)

Checks that the model is valid

Parameters:model (Isentrope) – A new EOS model Returns:A copy of self with the new eos model Return type:(GunModel)

_on_str(*args, **kwargs)

Print method of the gun model

Parameters:

• *args – Variable length argument list.
• **kwargs – Arbitrary keyword arguments.

Returns:

A string representing the object

Return type:

(str)

compare(data1, data2)

Compares a set of experimental data to the model

Error is data2 less the data1

See F_UNCLE.Utils.Experiment.Experiment.compare()

plot(data, axes=None, fig=None, linestyles=[u'-k'], labels=[])

Plots the object

Parameters:

data (tuple) – The output from a call to a Sphere object

Keyword Arguments:  

• axes (plt.Axes) – The axes on which to plot Ignored
• fig (plt.Figure) – The figure on which to plot
• linestyles (list) – Strings for the linestyles
• labels (list) – Strings for the labels

Returns:

A reference to the figure containing the plot

Return type:

(plt.Figure)

shape(*args, **kwargs)

Gives the length of the independent variable vector

see F_UNCLE.Utils.Experiment.Experiment.shape()

update(model=None, strength=None)

Update the analysis with a new EOS model

Parameters:model (Isentrope) – A new EOS model Returns:A copy of self with the new eos model Return type:(GunModel)

Cylinder

Note

Cylinder has not been implemented yet