Use Dymos and OpenMDAO to simulate a pressurized bottle fluid expulsion - ode

Question

I am opening this new thread because I am looking for some to use Dymos, in order to simulate a dynamic system.
Indeed, I am trying to simulate a system which is composing of a pressurized bottle and a fluid inside. When t=0, the pressure is pushing the fluid through the bottle output, and as a result the pressure inside the bottle is decreasing. My aim is to simulate the behaviour of the pressure inside the bottle and the fluid volumic flow which is escaping from the bottle. If found an Dymos example whicih is very similar to what I am trying to do, but more simpler. https://openmdao.github.io/dymos/examples/water_rocket/water_rocket.html
To model my system, I am using two explicit components: the PressureRate, the VolumeFLowRate. Then I am defining the group component PressureModelODE to connect these two last components and their variables.
Here are these components:
class PressureRate(om.ExplicitComponent):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('p', shape=(nn,), desc='Pressure inside the nox bottle', units='Pa')
self.add_input('Vb', shape=(nn,), desc='Bottle volume', units='m**3')
self.add_input('Vl', shape=(nn,), desc='Liquid volume', units='m**3')
self.add_input('Vl_dot', shape=(nn,), desc='Liquid volume flow rate', units='m**3/s')
self.add_input('gamma', shape=(nn,), desc='Heat capacity ratio')
# Outputs
self.add_output('p_dot', val=np.ones(nn), desc='Pressure change rate', units='Pa/s')
self.declare_partials(of='*', wrt='*', method='fd')
def compute(self, inputs, outputs):
p = inputs['p']
Vb = inputs['Vb']
Vl = inputs['Vl']
Vl_dot = inputs['Vl_dot']
gamma = inputs['gamma']
outputs['p_dot'] = gamma * p/(Vb - Vl) * Vl_dot
class VolumeFlowRate(om.ExplicitComponent):
"""
A Dymos ODE for a damped harmonic oscillator.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
def setup(self):
# Inputs
self.add_input('p', desc='Pressure inside the nox_bottle', units='Pa')
self.add_input('pout', desc='Pressure outside the nox_bottle', units='Pa')
self.add_input('deltap', desc='Nox bottle pressure losses', units='Pa')
self.add_input('rhol', desc='Liquid density', units='kg/m**3')
self.add_input('Aout', desc='Output nox_bottle area', units='m**2')
# Outputs
self.add_output('Vl_dot', desc='Volume flow rate', units='m**3/s')
self.declare_partials(of='*', wrt='*', method='fd')
def compute(self, inputs, outputs):
p = inputs['p']
pout = inputs['pout']
deltap = inputs['deltap']
rhol = inputs['rhol']
Aout = inputs['Aout']
outputs['Vl_dot'] = Aout*np.sqrt(2/rhol*(p - pout - deltap))
class BottleModelODE(om.Group):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem('pressure_rate', subsys=PressureRate(num_nodes=nn),
promotes_inputs=['p', "Vb", "Vl", "Vl_dot", "gamma"], promotes_outputs=['p_dot'])
self.add_subsystem('volume_flow_rate', subsys=VolumeFlowRate(num_nodes=nn),
promotes_inputs=['p', "pout", 'deltap', 'rhol', "Aout"], promotes_outputs=['Vl_dot'])
self.connect('pressure_rate.p', 'volume_flow_rate.p')
self.connect('pressure_rate.Vl_dot', 'volume_flow_rate.Vl_dot')
Then to solve these equations and simulate my model, I build a program based on the oscillator example: https://openmdao.github.io/dymos/getting_started/intro_to_dymos/intro_segments.html
I am defining a phase called "explusion" by using the following function:
def expulsion_phase_fn(transcription: dm.transcriptions.pseudospectral.radau_pseudospectral.Radau, pamb: float):
phase = dm.Phase(ode_class=BottleModelODE, transcription=transcription)
phase.set_time_options(fix_initial=True, fix_duration=True)
phase.add_state('p', units='bar', rate_source='pressure_rate.p_dot',
targets=['pressure_rate.p', "volume_flow_rate.p"], fix_initial=True, fix_final=False, lower=pamb)
phase.add_state('Vl', units='m**3', rate_source='volume_flow_rate.Vl_dot', targets=['pressure_rate.Vl'],
fix_initial=True, fix_final=False, lower=0)
phase.add_parameter('Vb', targets=['pressure_rate.Vb'], units='m**3')
phase.add_parameter('gamma', targets=['pressure_rate.gamma'])
phase.add_parameter('rhol', targets=['volume_flow_rate.rhol'], units='kg/m**3')
phase.add_parameter('Aout', targets=['volume_flow_rate.Aout'], units='m**2')
phase.add_parameter('pout', targets=['volume_flow_rate.pout'], units="Pa")
phase.add_parameter('deltap', targets=['volume_flow_rate.deltap'], units="Pa")
return phase
Then, I am defining a trajectory with this function:
def trajectory(pamb: float):
transcript = dm.Radau(num_segments=50, solve_segments='forward')
traj = dm.Trajectory()
# Add phases to trajectory
expulsion_phase = traj.add_phase('expulsion',
expulsion_phase_fn(transcription=transcript, pamb=pamb))
return traj, expulsion_phase
And finally, I am setting the OpenMDAO problem, provide the initial values,... by doing the following lines, which are based on the Oscillator example:
def launch_compt():
# Set ambiant conditions
Tamb = 20 + 273.15
pamb = 100*10**3
deltap = 0
Vb = 5*10**-3
Aout = 10*10**-4
# Set NOX bottle properties up
bottle_params = {"Vb": 5*10**-3, "gamma": 1.4, "Aout": 3*10**-2, "rhol": 1000, "pout":
100*10**3, pinit": 300*10**3, "Vl": 1*10**-3}
# Instantiate an OpenMDAO Problem instance
prob = om.Problem(model=om.Group())
prob.driver = om.ScipyOptimizeDriver(optimizer='SLSQP')
# Instantiate a Dymos trjectory and add it to the Problem model
traj, phase = trajectory(pamb= 100*10*3)
phase.add_objective("time", loc="final")
# Setup the OpenMDAO problem
prob.model.add_subsystem("traj", traj)
prob.setup()
# Assign values to the times and states
prob.set_val('traj.explusion.t_initial', 0.0)
prob.set_val('traj.explusion.t_duration', 200.0)
prob.set_val('traj.explusion.states:p', bottle_params["pinit"])
prob.set_val('traj.explusion.states:Vl', bottle_params["Vl"])
prob.set_val('traj.explusion.parameters:Vb', bottle_params["Vb"])
prob.set_val('traj.explusion.parameters:gamma', bottle_params["gamma"])
prob.set_val('traj.explusion.parameters:rhol', bottle_params["rhol"])
prob.set_val('traj.explusion.parameters:Aout', bottle_params["Aout"])
prob.set_val('traj.explusion.parameters:pout', bottle_params["pout"])
prob.set_val('traj.explusion.parameters:deltap', bottle_params["deltap"])
prob.run_driver()
Unofortunately, that does not work I cannot understand why. It returns me that the parameter Vb (Bottle total volume) is not provided but I cannot understand why: it is provided when I am adding the parameters to the problem, like within the Oscillator example.
In that respect I am contacting, in the hope to find some help.
Thank in advance for any answer.
PS: Here is the error message that I get when I am trying to run the program:
raise ValueError(f'Invalid parameter in phase `{self.pathname}`.\n{str(e)}') from e
ValueError: Invalid parameter in phase `traj.phases.expulsion`.
Parameter `Vb` has invalid target(s).
No such ODE input: 'pressure_rate.Vb'.

Answer 1

The primary issue that you have asked about, related to the No such ODE input error, is cased by the way you coded your ODE and more specifically the way you promoted variables and then added the ODE to the phase.
For example, you promoted your input P then set the state target to pressure_rate.P. This is incorrect. When you promoted P that effectively moved the name address up to the top level of the ODE, so the name target is just P now. You can read more about promotion vs connection in the docs. You have this problem in most of your script, where you are not accounting for promotion when you set targets.
Unfortunately, this is not the only issue in your script. There are several more, and enough that I am not able to get things fully working.
Here are some other modest issues in rough order of importance:
The VolumeFlowRate component input and outputs are scalar, but seem to be intended to connect to the vector (of size num_nodes) variables of PressureRate. I suspect you meant to make them vector as well, but am not 100% sure
You have an execution order issue between PressureRate and VolumeRate. Pressure rate seems to need as an input Vl_dot, which comes from VolumeRate`, but you have added it first so it will run BEFORE the component providing its input value.
You had a typo in your set_val calls (explusion vs expulsion)
You did not have a deltap key in the parameter diction, but you did have a variable for it.
After fixing those, I could get the problem to start running but it did not converge or give an answer. You had solve_segments set to forward and had set 50 segments. Both of those seemed like bad settings to me, so I changed them to 3 segments, and removed the solve_segments option.
Then I was able to get the optimizer to take a few steps, but it errored with
Current function value: [200.]
Iterations: 6
Function evaluations: 12
Gradient evaluations: 2
Optimization FAILED.
Positive directional derivative for linesearch
Which indicated a problem with the derivatives. So I changed your setting for partial derivatives from fd to cs. That allowed it to iterate more, but still didn't converge. Without diving more into the physics of your problem I can't easily diagnose this further. I suspect you have some bad boundary conditions and probably bad initial guesses though.
Here is the modified script I came up with to at least get the optimizer iterating.
import numpy as np
import openmdao.api as om
import dymos as dm
class PressureRate(om.ExplicitComponent):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('p', shape=(nn,), desc='Pressure inside the nox bottle', units='Pa')
self.add_input('Vb', shape=(nn,), desc='Bottle volume', units='m**3')
self.add_input('Vl', shape=(nn,), desc='Liquid volume', units='m**3')
self.add_input('Vl_dot', shape=(nn,), desc='Liquid volume flow rate', units='m**3/s')
self.add_input('gamma', shape=(nn,), desc='Heat capacity ratio')
# Outputs
self.add_output('p_dot', val=np.ones(nn), desc='Pressure change rate', units='Pa/s')
self.declare_partials(of='*', wrt='*', method='cs')
def compute(self, inputs, outputs):
p = inputs['p']
Vb = inputs['Vb']
Vl = inputs['Vl']
Vl_dot = inputs['Vl_dot']
gamma = inputs['gamma']
outputs['p_dot'] = gamma * p/(Vb - Vl) * Vl_dot
class VolumeFlowRate(om.ExplicitComponent):
"""
A Dymos ODE for a damped harmonic oscillator.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('p', shape=(nn,), desc='Pressure inside the nox_bottle', units='Pa')
self.add_input('pout', shape=(nn,), desc='Pressure outside the nox_bottle', units='Pa')
self.add_input('deltap', shape=(nn,), desc='Nox bottle pressure losses', units='Pa')
self.add_input('rhol', shape=(nn,), desc='Liquid density', units='kg/m**3')
self.add_input('Aout', shape=(nn,), desc='Output nox_bottle area', units='m**2')
# Outputs
self.add_output('Vl_dot', shape=(nn,), desc='Volume flow rate', units='m**3/s')
self.declare_partials(of='*', wrt='*', method='cs')
def compute(self, inputs, outputs):
p = inputs['p']
pout = inputs['pout']
deltap = inputs['deltap']
rhol = inputs['rhol']
Aout = inputs['Aout']
outputs['Vl_dot'] = Aout*np.sqrt(2/rhol*(p - pout - deltap))
class BottleModelODE(om.Group):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem('volume_flow_rate', subsys=VolumeFlowRate(num_nodes=nn),
promotes_inputs=['p', "pout", 'deltap', 'rhol', "Aout"], promotes_outputs=['Vl_dot'])
self.add_subsystem('pressure_rate', subsys=PressureRate(num_nodes=nn),
promotes_inputs=['p', "Vb", "Vl", "Vl_dot", "gamma"], promotes_outputs=['p_dot'])
def expulsion_phase_fn(transcription: dm.transcriptions.pseudospectral.radau_pseudospectral.Radau, pamb: float):
phase = dm.Phase(ode_class=BottleModelODE, transcription=transcription)
phase.set_time_options(fix_initial=True, fix_duration=True)
phase.add_state('p', units='bar', rate_source='p_dot',
targets=['p'], fix_initial=True, fix_final=False, lower=pamb)
phase.add_state('Vl', units='m**3', rate_source='Vl_dot', targets=['Vl'],
fix_initial=True, fix_final=False, lower=0)
phase.add_parameter('Vb', targets=['Vb'], units='m**3')
phase.add_parameter('gamma', targets=['gamma'])
phase.add_parameter('rhol', targets=['rhol'], units='kg/m**3')
phase.add_parameter('Aout', targets=['Aout'], units='m**2')
phase.add_parameter('pout', targets=['pout'], units="Pa")
phase.add_parameter('deltap', targets=['deltap'], units="Pa")
return phase
def trajectory(pamb: float):
# transcript = dm.Radau(num_segments=50, solve_segments='forward')
transcript = dm.Radau(num_segments=3)
traj = dm.Trajectory()
# Add phases to trajectory
expulsion_phase = traj.add_phase('expulsion', expulsion_phase_fn(transcription=transcript, pamb=pamb))
return traj, expulsion_phase
if __name__ == "__main__":
# Set ambiant conditions
Tamb = 20 + 273.15
pamb = 100*10**3
deltap = 0
Vb = 5*10**-3
Aout = 10*10**-4
# Set NOX bottle properties up
bottle_params = {"Vb": 5*10**-3, "gamma": 1.4, "Aout": 3*10**-2, "rhol": 1000, "pout": 100*10**3, "pinit": 300*10**3, "Vl": 1*10**-3}
# Instantiate an OpenMDAO Problem instance
prob = om.Problem(model=om.Group())
prob.driver = om.ScipyOptimizeDriver(optimizer='SLSQP')
# Instantiate a Dymos trjectory and add it to the Problem model
traj, phase = trajectory(pamb=100*10*3)
phase.add_objective("time", loc="final")
# Setup the OpenMDAO problem
prob.model.add_subsystem("traj", traj)
prob.setup()
# Assign values to the times and states
prob.set_val('traj.expulsion.t_initial', 0.0)
prob.set_val('traj.expulsion.t_duration', 200.0)
prob.set_val('traj.expulsion.states:p', bottle_params["pinit"])
prob.set_val('traj.expulsion.states:Vl', bottle_params["Vl"])
prob.set_val('traj.expulsion.parameters:Vb', bottle_params["Vb"])
prob.set_val('traj.expulsion.parameters:gamma', bottle_params["gamma"])
prob.set_val('traj.expulsion.parameters:rhol', bottle_params["rhol"])
prob.set_val('traj.expulsion.parameters:Aout', bottle_params["Aout"])
prob.set_val('traj.expulsion.parameters:pout', bottle_params["pout"])
prob.set_val('traj.expulsion.parameters:deltap', deltap)
prob.run_driver()