184 lines
10 KiB
Python
184 lines
10 KiB
Python
import numpy as np
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class Druckrohrleitung_class:
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# units
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acceleration_unit = r'$\mathrm{m}/\mathrm{s}^2$'
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angle_unit = 'rad'
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area_unit = r'$\mathrm{m}^2$'
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density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
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flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
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length_unit = 'm'
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pressure_unit = 'Pa'
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time_unit = 's'
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velocity_unit = r'$\mathrm{m}/\mathrm{s}$' # for flux and pressure propagation
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volume_unit = r'$\mathrm{m}^3$'
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acceleration_unit_print = 'm/s²'
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angle_unit_print = 'rad'
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area_unit_print = 'm²'
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density_unit_print = 'kg/m³'
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flux_unit_print = 'm³/s'
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length_unit_print = 'm'
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time_unit_print = 's'
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velocity_unit_print = 'm/s' # for flux and pressure propagation
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volume_unit_print = 'm³'
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# init
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def __init__(self,total_length,diameter,number_segments,pipeline_angle,Darcy_friction_factor,rho=1000,g=9.81):
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self.length = total_length # total length of the pipeline
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self.dia = diameter # diameter of the pipeline
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self.n_seg = number_segments # number of segments for the method of characteristics
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self.angle = pipeline_angle # angle of the pipeline
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self.f_D = Darcy_friction_factor # = Rohrreibungszahl oder flow coefficient
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self.density = rho # density of the liquid in the pipeline
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self.g = g # gravitational acceleration
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self.A = (diameter/2)**2*np.pi
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self.dx = total_length/number_segments # length of each segment
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self.l_vec = np.arange(0,(number_segments+1),1)*self.dx # vector giving the distance from each node to the start of the pipeline
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# initialize for get_info method
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self.c = '--'
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self.dt = '--'
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# setter
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def set_pressure_propagation_velocity(self,c):
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self.c = c # propagation velocity of the pressure wave
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self.dt = self.dx/c # timestep derived from c, demanded by the method of characteristics
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def set_number_of_timesteps(self,number_timesteps):
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self.nt = number_timesteps # number of timesteps
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if self.c == '--':
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raise Exception('Please set the pressure propagation velocity before setting the number of timesteps.')
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else:
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self.t_vec = np.arange(0,self.nt*self.dt,self.dt)
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def set_initial_pressure(self,pressure):
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# initialize the pressure distribution in the pipeline
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if np.size(pressure) == 1:
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self.p0 = np.full_like(self.l_vec,pressure)
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elif np.size(pressure) == np.size(self.l_vec):
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self.p0 = pressure
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else:
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raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.l_vec))
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#initialize the vectors in which the old and new pressures are stored for the method of characteristics
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self.p_old = self.p0.copy()
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self.p = self.p0.copy()
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def set_initial_flow_velocity(self,velocity):
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# initialize the velocity distribution in the pipeline
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if np.size(velocity) == 1:
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self.v0 = np.full_like(self.l_vec,velocity)
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elif np.size(velocity) == np.size(self.l_vec):
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self.v0 = velocity
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else:
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raise Exception('Unable to assign initial velocity. Input has to be of size 1 or' + np.size(self.l_vec))
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#initialize the vectors in which the old and new velocities are stored for the method of characteristics
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self.v_old = self.v0.copy()
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self.v = self.v0.copy()
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def set_boundary_conditions_next_timestep(self,p_reservoir,v_turbine):
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# derived from the method of characteristics, one can set the boundary conditions for the pressures and flow velocities at the reservoir and the turbine
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# the boundary velocity at the turbine is specified by the flux through the turbine or an external boundary condition
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# the pressure at the turbine will be calculated using the forward characteristic
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# the boundary pressure at the reservoir is specified by the level in the reservoir of an external boundary condition
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# the velocity at the reservoir will be calculated using the backward characteristic
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# constants for a cleaner formula
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rho = self.density
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c = self.c
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f_D = self.f_D
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dt = self.dt
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D = self.dia
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g = self.g
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alpha = self.angle
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p_old_tur = self.p_old[-2] # @ second to last node (the one before the turbine)
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v_old_tur = self.v_old[-2] # @ second to last node (the one before the turbine)
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p_old_res = self.p_old[1] # @ second node (the one after the reservoir)
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v_old_res = self.v_old[1] # @ second node (the one after the reservoir)
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# set the boundary conditions derived from reservoir and turbine
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v_boundary_tur = v_turbine # at new timestep
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p_boundary_res = p_reservoir # at new timestep
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# calculate the missing boundary conditions
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v_boundary_res = v_old_res+1/(rho*c)*(p_boundary_res-p_old_res)+dt*g*np.sin(alpha)-f_D*dt/(2*D)*abs(v_old_res)*v_old_res
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p_boundary_tur = p_old_tur-rho*c*(v_boundary_tur-v_old_tur)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v_old_tur)*v_old_tur
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# write boundary conditions to the velocity/pressure vectors of the next timestep
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self.v[0] = v_boundary_res
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self.v[-1] = v_boundary_tur
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self.p[0] = p_boundary_res
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self.p[-1] = p_boundary_tur
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def set_steady_state(self,ss_flux,ss_level_reservoir,pl_vec,h_vec):
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# set the pressure and velocity distributions, that allow a constant flow of water from the (steady-state) reservoir to the (steady-state) turbine
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# the flow velocity is given by the constant flow through the pipe
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ss_v0 = np.full(self.n_seg+1,ss_flux/self.A)
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# the static pressure is given by the hydrostatic pressure, corrected for friction losses and dynamic pressure
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ss_pressure = self.density*self.g*(ss_level_reservoir+h_vec)-ss_v0**2*self.density/2-(self.f_D*pl_vec/self.dia*self.density/2*ss_v0**2)
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self.set_initial_flow_velocity(ss_v0)
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self.set_initial_pressure(ss_pressure)
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# getter
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def get_info(self):
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new_line = '\n'
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angle_deg = round(self.angle/np.pi*180,3)
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# :<10 pads the self.value to be 10 characters wide
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print_str = (f"The pipeline has the following attributes: {new_line}"
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f"----------------------------- {new_line}"
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f"Length = {self.length:<10} {self.length_unit_print} {new_line}"
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f"Diameter = {self.dia:<10} {self.length_unit_print} {new_line}"
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f"Number of segments = {self.n_seg:<10} {new_line}"
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f"Number of nodes = {self.n_seg+1:<10} {new_line}"
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f"Length per segments = {self.dx:<10} {self.length_unit_print} {new_line}"
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f"Pipeline angle = {round(self.angle,3):<10} {self.angle_unit_print} {new_line}"
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f"Pipeline angle = {angle_deg}° {new_line}"
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f"Darcy friction factor = {self.f_D:<10} {new_line}"
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f"Density of liquid = {self.density:<10} {self.density_unit_print} {new_line}"
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f"Pressure wave vel. = {self.c:<10} {self.velocity_unit_print} {new_line}"
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f"Simulation timestep = {self.dt:<10} {self.time_unit_print} {new_line}"
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f"Number of timesteps = {self.nt:<10} {new_line}"
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f"Total simulation time = {self.nt*self.dt:<10} {self.time_unit_print} {new_line}"
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f"----------------------------- {new_line}"
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f"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object")
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print(print_str)
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def get_current_pressure_distribution(self):
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return self.p
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def get_current_velocity_distribution(self):
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return self.v
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def timestep_characteristic_method(self):
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# use the method of characteristics to calculate the pressure and velocities at all nodes except the boundary ones
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# they are set with the .set_boundary_conditions_next_timestep() method beforehand
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nn = self.n_seg+1 # number of nodes
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rho = self.density # density of liquid
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c = self.c # pressure propagation velocity
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f_D = self.f_D # Darcy friction coefficient
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dt = self.dt # timestep
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D = self.dia # pipeline diametet
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g = self.g # graviational acceleration
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alpha = self.angle # pipeline angle
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# Vectorize this loop?
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for i in range(1,nn-1):
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self.v[i] = 0.5*(self.v_old[i+1]+self.v_old[i-1])-0.5/(rho*c)*(self.p_old[i+1]-self.p_old[i-1]) \
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+dt*g*np.sin(alpha)-f_D*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]+abs(self.v_old[i-1])*self.v_old[i-1])
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self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1]) - 0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \
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+f_D*rho*c*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]-abs(self.v_old[i-1])*self.v_old[i-1])
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# prepare for next call
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# use .copy() to write data to another memory location and avoid the usual python reference pointer
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# else one can overwrite data by accidient and change two variables at once without noticing
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self.p_old = self.p.copy()
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self.v_old = self.v.copy()
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