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