| 1 | """Collection of culvert routines for use with Culvert_flow in culvert_class |
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| 2 | |
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| 3 | Usage: |
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| 4 | |
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| 5 | |
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| 6 | |
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| 7 | """ |
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| 8 | |
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| 9 | #NOTE: |
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| 10 | # Inlet control: Delta_total_energy > inlet_specific_energy |
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| 11 | # Outlet control: Delta_total_energy < inlet_specific_energy |
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| 12 | # where total energy is (w + 0.5*v^2/g) and |
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| 13 | # specific energy is (h + 0.5*v^2/g) |
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| 14 | |
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| 15 | |
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| 16 | from math import pi, sqrt, sin, cos |
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| 17 | |
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| 18 | |
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| 19 | def boyd_generalised_culvert_model(inlet_depth, |
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| 20 | outlet_depth, |
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| 21 | inlet_specific_energy, |
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| 22 | delta_total_energy, |
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| 23 | g, |
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| 24 | culvert_length=0.0, |
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| 25 | culvert_width=0.0, |
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| 26 | culvert_height=0.0, |
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| 27 | culvert_type='box', |
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| 28 | manning=0.0, |
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| 29 | sum_loss=0.0, |
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| 30 | max_velocity=10.0, |
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| 31 | log_filename=None): |
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| 32 | |
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| 33 | """Boyd's generalisation of the US department of transportation culvert |
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| 34 | model |
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| 35 | |
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| 36 | The quantity of flow passing through a culvert is controlled by many factors |
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| 37 | It could be that the culvert is controlled by the inlet only, with it |
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| 38 | being unsubmerged this is effectively equivalent to the weir Equation |
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| 39 | Else the culvert could be controlled by the inlet, with it being |
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| 40 | submerged, this is effectively the Orifice Equation |
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| 41 | Else it may be controlled by down stream conditions where depending on |
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| 42 | the down stream depth, the momentum in the culvert etc. flow is controlled |
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| 43 | """ |
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| 44 | |
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| 45 | from anuga.utilities.system_tools import log_to_file |
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| 46 | from anuga.config import velocity_protection |
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| 47 | from anuga.utilities.numerical_tools import safe_acos as acos |
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| 48 | |
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| 49 | |
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| 50 | if inlet_depth > 0.1: #this value was 0.01: |
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| 51 | # Water has risen above inlet |
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| 52 | |
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| 53 | if log_filename is not None: |
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| 54 | s = 'Specific energy = %f m' % inlet_specific_energy |
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| 55 | log_to_file(log_filename, s) |
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| 56 | |
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| 57 | msg = 'Specific energy at inlet is negative' |
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| 58 | assert inlet_specific_energy >= 0.0, msg |
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| 59 | |
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| 60 | |
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| 61 | if culvert_type == 'circle': |
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| 62 | # Round culvert (use width as diameter) |
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| 63 | diameter = culvert_width |
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| 64 | |
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| 65 | # Calculate flows for inlet control |
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| 66 | Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*inlet_specific_energy**1.63 # Inlet Ctrl Inlet Unsubmerged |
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| 67 | Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*inlet_specific_energy**0.63 # Inlet Ctrl Inlet Submerged |
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| 68 | |
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| 69 | if log_filename is not None: |
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| 70 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' % (Q_inlet_unsubmerged, Q_inlet_submerged) |
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| 71 | log_to_file(log_filename, s) |
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| 72 | |
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| 73 | |
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| 74 | # FIXME(Ole): Are these functions really for inlet control? |
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| 75 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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| 76 | Q = Q_inlet_unsubmerged |
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| 77 | alpha = acos(1 - inlet_depth/diameter) |
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| 78 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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| 79 | outlet_culvert_depth = inlet_depth |
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| 80 | case = 'Inlet unsubmerged' |
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| 81 | else: |
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| 82 | Q = Q_inlet_submerged |
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| 83 | flow_area = (diameter/2)**2 * pi |
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| 84 | outlet_culvert_depth = diameter |
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| 85 | case = 'Inlet submerged' |
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| 86 | |
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| 87 | |
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| 88 | |
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| 89 | if delta_total_energy < inlet_specific_energy: |
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| 90 | # Calculate flows for outlet control |
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| 91 | |
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| 92 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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| 93 | if outlet_depth > diameter: # The Outlet is Submerged |
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| 94 | outlet_culvert_depth=diameter |
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| 95 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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| 96 | perimeter = diameter * pi |
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| 97 | case = 'Outlet submerged' |
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| 98 | elif outlet_depth==0.0: |
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| 99 | outlet_culvert_depth=inlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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| 100 | alpha = acos(1 - inlet_depth/diameter) |
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| 101 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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| 102 | perimeter = alpha*diameter |
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| 103 | |
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| 104 | case = 'Outlet depth is zero' |
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| 105 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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| 106 | outlet_culvert_depth=outlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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| 107 | alpha = acos(1 - outlet_depth/diameter) |
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| 108 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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| 109 | perimeter = alpha*diameter |
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| 110 | case = 'Outlet is open channel flow' |
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| 111 | |
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| 112 | hyd_rad = flow_area/perimeter |
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| 113 | |
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| 114 | if log_filename is not None: |
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| 115 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
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| 116 | log_to_file(log_filename, s) |
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| 117 | |
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| 118 | # Outlet control velocity using tail water |
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| 119 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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| 120 | Q_outlet_tailwater = flow_area * culvert_velocity |
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| 121 | |
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| 122 | if log_filename is not None: |
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| 123 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
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| 124 | log_to_file(log_filename, s) |
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| 125 | |
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| 126 | Q = min(Q, Q_outlet_tailwater) |
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| 127 | else: |
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| 128 | pass |
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| 129 | #FIXME(Ole): What about inlet control? |
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| 130 | |
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| 131 | |
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| 132 | else: |
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| 133 | # Box culvert (rectangle or square) |
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| 134 | |
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| 135 | # Calculate flows for inlet control |
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| 136 | height = culvert_height |
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| 137 | width = culvert_width |
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| 138 | |
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| 139 | Q_inlet_unsubmerged = 0.540*g**0.5*width*inlet_specific_energy**1.50 # Flow based on Inlet Ctrl Inlet Unsubmerged |
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| 140 | Q_inlet_submerged = 0.702*g**0.5*width*height**0.89*inlet_specific_energy**0.61 # Flow based on Inlet Ctrl Inlet Submerged |
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| 141 | |
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| 142 | if log_filename is not None: |
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| 143 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
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| 144 | log_to_file(log_filename, s) |
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| 145 | |
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| 146 | |
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| 147 | # FIXME(Ole): Are these functions really for inlet control? |
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| 148 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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| 149 | Q = Q_inlet_unsubmerged |
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| 150 | flow_area = width*inlet_depth |
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| 151 | outlet_culvert_depth = inlet_depth |
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| 152 | case = 'Inlet unsubmerged' |
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| 153 | else: |
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| 154 | Q = Q_inlet_submerged |
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| 155 | flow_area = width*height |
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| 156 | outlet_culvert_depth = height |
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| 157 | case = 'Inlet submerged' |
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| 158 | |
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| 159 | if delta_total_energy < inlet_specific_energy: |
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| 160 | # Calculate flows for outlet control |
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| 161 | |
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| 162 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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| 163 | if outlet_depth > height: # The Outlet is Submerged |
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| 164 | outlet_culvert_depth=height |
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| 165 | flow_area=width*height # Cross sectional area of flow in the culvert |
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| 166 | perimeter=2.0*(width+height) |
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| 167 | case = 'Outlet submerged' |
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| 168 | elif outlet_depth==0.0: |
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| 169 | outlet_culvert_depth=inlet_depth # For purpose of calculation assume the outlet depth = the inlet depth |
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| 170 | flow_area=width*inlet_depth |
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| 171 | perimeter=(width+2.0*inlet_depth) |
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| 172 | case = 'Outlet depth is zero' |
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| 173 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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| 174 | outlet_culvert_depth=outlet_depth |
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| 175 | flow_area=width*outlet_depth |
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| 176 | perimeter=(width+2.0*outlet_depth) |
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| 177 | case = 'Outlet is open channel flow' |
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| 178 | |
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| 179 | hyd_rad = flow_area/perimeter |
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| 180 | |
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| 181 | if log_filename is not None: |
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| 182 | s = 'hydraulic radius at outlet = %f' % hyd_rad |
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| 183 | log_to_file(log_filename, s) |
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| 184 | |
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| 185 | # Outlet control velocity using tail water |
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| 186 | culvert_velocity = sqrt(delta_total_energy/((sum_loss/2/g)+(manning**2*culvert_length)/hyd_rad**1.33333)) |
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| 187 | Q_outlet_tailwater = flow_area * culvert_velocity |
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| 188 | |
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| 189 | if log_filename is not None: |
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| 190 | s = 'Q_outlet_tailwater = %.6f' % Q_outlet_tailwater |
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| 191 | log_to_file(log_filename, s) |
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| 192 | Q = min(Q, Q_outlet_tailwater) |
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| 193 | else: |
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| 194 | pass |
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| 195 | #FIXME(Ole): What about inlet control? |
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| 196 | |
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| 197 | |
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| 198 | # Common code for circle and square geometries |
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| 199 | if log_filename is not None: |
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| 200 | log_to_file(log_filename, 'Case: "%s"' % case) |
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| 201 | |
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| 202 | if log_filename is not None: |
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| 203 | s = 'Flow Rate Control = %f' % Q |
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| 204 | log_to_file(log_filename, s) |
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| 205 | |
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| 206 | |
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| 207 | culv_froude=sqrt(Q**2*width/(g*flow_area**3)) |
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| 208 | |
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| 209 | if log_filename is not None: |
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| 210 | s = 'Froude in Culvert = %f' % culv_froude |
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| 211 | log_to_file(log_filename, s) |
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| 212 | |
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| 213 | # Determine momentum at the outlet |
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| 214 | barrel_velocity = Q/(flow_area + velocity_protection/flow_area) |
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| 215 | |
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| 216 | |
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| 217 | else: # inlet_depth < 0.01: |
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| 218 | Q = barrel_velocity = outlet_culvert_depth = 0.0 |
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| 219 | # Temporary flow limit |
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| 220 | if barrel_velocity > max_velocity: |
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| 221 | if log_filename is not None: |
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| 222 | s = 'Barrel velocity was reduced from = %f m/s to %f m/s' % (barrel_velocity, max_velocity) |
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| 223 | log_to_file(log_filename, s) |
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| 224 | |
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| 225 | barrel_velocity = max_velocity |
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| 226 | Q = flow_area * barrel_velocity |
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| 227 | |
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| 228 | |
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| 229 | |
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| 230 | |
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| 231 | return Q, barrel_velocity, outlet_culvert_depth |
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| 232 | |
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| 233 | |
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