import os import sys import numpy as np #importing pressure conversion function current = os.path.dirname(os.path.realpath(__file__)) parent = os.path.dirname(current) sys.path.append(parent) from functions.pressure_conversion import pressure_conversion class Druckrohrleitung_class: # units # make sure that units and display units are the same # units are used to label graphs and disp units are used to have a bearable format when using pythons print() 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' # DONT CHANGE needed for pressure conversion time_unit = 's' velocity_unit = r'$\mathrm{m}/\mathrm{s}$' # for flux and pressure propagation volume_unit = r'$\mathrm{m}^3$' acceleration_unit_disp = 'm/s²' angle_unit_disp = 'rad' area_unit_disp = 'm²' density_unit_disp = 'kg/m³' flux_unit_disp = 'm³/s' length_unit_disp = 'm' # pressure_unit_disp will be set within the __init__() method time_unit_disp = 's' velocity_unit_disp = 'm/s' # for flux and pressure propagation volume_unit_disp = 'm³' g = 9.81 # m/s² gravitational acceleration # init def __init__(self,total_length,diameter,pipeline_head,number_segments,Darcy_friction_factor,pw_vel,timestep,pressure_unit_disp,rho=1000): """ Creates a reservoir with given attributes in this order: \n Pipeline length [m] \n Pipeline diameter [m] \n Pipeline head [m] \n Number of pipeline segments [1] \n Darcy friction factor [1] \n Pressure wave velocity [m/s] \n Simulation timestep [s] \n Pressure unit for displaying [string] \n Density of the liquid [kg/m³] \n """ self.length = total_length # total length of the pipeline self.dia = diameter # diameter of the pipeline self.head = pipeline_head # hydraulic head of the pipeline self.n_seg = number_segments # number of segments for the method of characteristics self.f_D = Darcy_friction_factor # = Rohrreibungszahl oder flow coefficient self.c = pw_vel # propagation velocity of pressure wave self.dt = timestep self.density = rho # density of the liquid in the pipeline # derivatives of input attributes self.angle = np.arcsin(self.head/self.length) # angle of the pipeline self.A = (diameter/2)**2*np.pi # crossectional area of the pipeline self.dx = total_length/number_segments # length of each segment self.x_vec = np.arange(0,(number_segments+1),1)*self.dx # vector giving the distance from each node to the start of the pipeline self.h_vec = np.arange(0,(number_segments+1),1)*self.head/self.n_seg # vector giving the height difference from each node to the start of the pipeline self.pressure_unit_disp = pressure_unit_disp # pressure unit for displaying # setter - set attributes def set_initial_pressure(self,pressure,display_warning=True): # initialize the pressure distribution in the pipeline if display_warning == True: print('You are setting the pressure distribution in the pipeline manually. \n \ This is not an intended use of this method. \n \ Refer to the set_steady_state() method instead.') # make sure the vector has the right size if np.size(pressure) == 1: p0 = np.full_like(self.x_vec,pressure) elif np.size(pressure) == np.size(self.x_vec): p0 = pressure else: raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.x_vec)) #initialize the vectors in which the old and new pressures are stored for the method of characteristics self.p_old = p0.copy() self.p = p0.copy() self.p0 = p0.copy() # initialize the vectors in which the minimal and maximal value of the pressure at each node are stores self.p_min = p0.copy() self.p_max = p0.copy() def set_initial_flow_velocity(self,velocity, display_warning=True): # initialize the velocity distribution in the pipeline if display_warning == True: print('You are setting the velocity distribution in the pipeline manually. \n \ This is not an intended use of this method. \n \ Refer to the set_steady_state() method instead.') # make sure the vector has the right size if np.size(velocity) == 1: v0 = np.full_like(self.x_vec,velocity) elif np.size(velocity) == np.size(self.x_vec): v0 = velocity else: raise Exception('Unable to assign initial velocity. Input has to be of size 1 or' + np.size(self.x_vec)) #initialize the vectors in which the old and new velocities are stored for the method of characteristics self.v_old = v0.copy() self.v = v0.copy() # initialize the vectors in which the minimal and maximal value of the velocity at each node are stores self.v_min = v0.copy() self.v_max = 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 v_boundary_tur = v_turbine # at new timestep p_boundary_res = p_reservoir # at new timestep # calculate the missing boundary conditions 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 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 # write boundary conditions to the velocity/pressure vectors of the next timestep self.v[0] = v_boundary_res self.v[-1] = v_boundary_tur self.p[0] = p_boundary_res self.p[-1] = p_boundary_tur def set_steady_state(self,ss_flux,ss_pressure_res): # 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_like(self.x_vec,ss_flux/self.A) # the static pressure is given by static state pressure of the reservoir, corrected for the hydraulic head of the pipe and friction losses ss_pressure = ss_pressure_res+(self.density*self.g*self.h_vec)-(self.f_D*self.x_vec/self.dia*self.density/2*ss_v0**2) # set the initial conditions self.set_initial_flow_velocity(ss_v0,display_warning=False) self.set_initial_pressure(ss_pressure,display_warning=False) # getter - return attributes 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_disp} {new_line}" f"Diameter = {self.dia:<10} {self.length_unit_disp} {new_line}" f"Hydraulic head = {self.head:<10} {self.length_unit_disp} {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_disp} {new_line}" f"Pipeline angle = {round(self.angle,3):<10} {self.angle_unit_disp} {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_disp} {new_line}" f"Pressure wave vel. = {self.c:<10} {self.velocity_unit_disp} {new_line}" f"Simulation timestep = {self.dt:<10} {self.time_unit_disp} {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,disp_flag=False): # disp_flag if one wants to directly plot the return of this method if disp_flag == True: # convert to pressure unit disp return pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_disp) elif disp_flag == False: # stay in Pa return self.p def get_current_velocity_distribution(self): return self.v def get_current_flux_distribution(self): return self.v*self.A def get_lowest_pressure_per_node(self,disp_flag=False): if disp_flag == True: # convert to pressure unit disp return pressure_conversion(self.p_min,self.pressure_unit,self.pressure_unit_disp) elif disp_flag == False: # stay in Pa return self.p_min def get_highest_pressure_per_node(self,disp_flag=False): if disp_flag == True: # convert to pressure unit disp return pressure_conversion(self.p_max,self.pressure_unit,self.pressure_unit_disp) elif disp_flag == False: # stay in Pa return self.p_max def get_lowest_velocity_per_node(self): return self.v_min def get_highest_velocity_per_node(self): return self.v_max def get_lowest_flux_per_node(self): return self.v_min*self.A def get_highest_flux_per_node(self): return self.v_max*self.A def get_initial_pressure_distribution(self,disp_flag=False): # disp_flag if one wants to directly plot the return of this method if disp_flag == True: # convert to pressure unit disp return pressure_conversion(self.p0,self.pressure_unit,self.pressure_unit_disp) elif disp_flag == False: # stay in Pa return self.p0 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 # constants for cleaner formula 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 diameter 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]) # update overall min and max values for pressure and velocity per node self.p_min = np.minimum(self.p_min,self.p) self.p_max = np.maximum(self.p_max,self.p) self.v_min = np.minimum(self.v_min,self.v) self.v_max = np.maximum(self.v_max,self.v) # 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() def timestep_characteristic_method_vectorized(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 # constants for cleaner formula 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 diameter g = self.g # graviational acceleration alpha = self.angle # pipeline angle # Vectorized loop self.v[1:-1] = 0.5*(self.v_old[2:]+self.v_old[:-2])-0.5/(rho*c)*(self.p_old[2:]-self.p_old[:-2]) \ +dt*g*np.sin(alpha)-f_D*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]+np.abs(self.v_old[:-2])*self.v_old[:-2]) self.p[1:-1] = 0.5*(self.p_old[2:]+self.p_old[:-2])-0.5*rho*c*(self.v_old[2:]-self.v_old[:-2]) \ +f_D*rho*c*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]-np.abs(self.v_old[:-2])*self.v_old[:-2]) # update overall min and max values for pressure and velocity per node self.p_min = np.minimum(self.p_min,self.p) self.p_max = np.maximum(self.p_max,self.p) self.v_min = np.minimum(self.v_min,self.v) self.v_max = np.maximum(self.v_max,self.v) # 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()