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 | # NEW DEFINED CULVERT FLOW---- Flow from INLET 1 ------> INLET 2 (Outlet) |
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10 | # |
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11 | # The First Attempt has a Simple Horizontal Circle as a Hole on the Bed |
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12 | # Flow Is Removed at a Rate of INFLOW |
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13 | # Downstream there is a similar Circular Hole on the Bed where INFLOW effectively Surcharges |
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14 | # |
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15 | # This SHould be changed to a Vertical Opening Both BOX and Circular |
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16 | # There will be several Culvert Routines such as: |
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17 | # CULVERT_Boyd_Channel |
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18 | # CULVERT_Orifice_and_Weir |
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19 | # CULVERT_Simple_FLOOR |
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20 | # CULVERT_Simple_WALL |
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21 | # CULVERT_Eqn_Floor |
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22 | # CULVERT_Eqn_Wall |
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23 | # CULVERT_Tab_Floor |
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24 | # CULVERT_Tab_Wall |
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25 | # BRIDGES..... |
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26 | # NOTE NEED TO DEVELOP CONCEPT 1D Model for Linked Pipe System !!!! |
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27 | |
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28 | # COULD USE EPA SWMM Model !!!! |
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29 | |
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30 | |
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31 | from math import pi, sqrt, sin, cos |
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32 | |
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33 | |
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34 | def boyd_generalised_culvert_model(culvert, inlet, outlet, delta_Et, g): |
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35 | |
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36 | """Boyd's generalisation of the US department of transportation culvert model |
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37 | # == The quantity of flow passing through a culvert is controlled by many factors |
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38 | # == It could be that the culvert is controled by the inlet only, with it being Un submerged 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 Submerged, this is effectively the Orifice Equation |
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40 | # == Else it may be controlled by Down stream conditions where depending on the down stream depth, the momentum in the culvert etc. flow is controlled |
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41 | """ |
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42 | |
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43 | from anuga.utilities.system_tools import log_to_file |
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44 | from anuga.config import velocity_protection |
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45 | from anuga.utilities.numerical_tools import safe_acos as acos |
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46 | |
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47 | |
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48 | Q_outlet_tailwater = 0.0 |
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49 | inlet.rate = 0.0 |
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50 | outlet.rate = 0.0 |
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51 | Q_inlet_unsubmerged = 0.0 |
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52 | Q_inlet_submerged = 0.0 |
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53 | Q_outlet_critical_depth = 0.0 |
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54 | |
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55 | log_filename = culvert.log_filename |
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56 | |
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57 | manning = culvert.manning |
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58 | sum_loss = culvert.sum_loss |
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59 | length = culvert.length |
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60 | |
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61 | if inlet.depth_trigger >= 0.01 and inlet.depth >= 0.01: |
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62 | # Calculate driving energy |
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63 | E = inlet.specific_energy |
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64 | |
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65 | s = 'Driving energy = %f m' %E |
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66 | log_to_file(log_filename, s) |
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67 | |
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68 | msg = 'Driving energy is negative' |
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69 | assert E >= 0.0, msg |
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70 | |
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71 | |
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72 | # Water has risen above inlet |
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73 | if culvert.culvert_type == 'circle': |
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74 | # Round culvert |
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75 | |
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76 | # Calculate flows for inlet control |
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77 | diameter = culvert.diameter |
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78 | |
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79 | Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*E**1.63 # Inlet Ctrl Inlet Unsubmerged |
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80 | Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*E**0.63 # Inlet Ctrl Inlet Submerged |
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81 | |
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82 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
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83 | log_to_file(log_filename, s) |
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84 | |
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85 | case = '' |
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86 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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87 | Q = Q_inlet_unsubmerged |
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88 | |
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89 | alpha = acos(1 - inlet.depth/diameter) |
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90 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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91 | outlet_culvert_depth = inlet.depth |
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92 | width = diameter*sin(alpha) |
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93 | #perimeter = alpha*diameter |
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94 | case = 'Inlet unsubmerged' |
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95 | else: |
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96 | Q = Q_inlet_submerged |
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97 | flow_area = (diameter/2)**2 * pi |
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98 | outlet_culvert_depth = diameter |
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99 | width = diameter |
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100 | #perimeter = diameter |
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101 | case = 'Inlet submerged' |
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102 | |
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103 | |
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104 | |
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105 | if delta_Et < E: |
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106 | # Calculate flows for outlet control |
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107 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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108 | |
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109 | if outlet.depth > diameter: # The Outlet is Submerged |
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110 | outlet_culvert_depth=diameter |
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111 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
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112 | perimeter = diameter * pi |
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113 | width = diameter |
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114 | case = 'Outlet submerged' |
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115 | elif outlet.depth==0.0: |
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116 | outlet_culvert_depth=inlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
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117 | alpha = acos(1 - inlet.depth/diameter) |
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118 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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119 | perimeter = alpha*diameter |
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120 | width = diameter*sin(alpha) |
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121 | |
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122 | case = 'Outlet depth is zero' |
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123 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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124 | outlet_culvert_depth=outlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
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125 | alpha = acos(1 - outlet.depth/diameter) |
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126 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
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127 | perimeter = alpha*diameter |
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128 | width = diameter*sin(alpha) |
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129 | case = 'Outlet is open channel flow' |
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130 | |
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131 | hyd_rad = flow_area/perimeter |
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132 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
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133 | log_to_file(log_filename, s) |
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134 | |
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135 | # Outlet control velocity using tail water |
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136 | culvert_velocity = sqrt(delta_Et/((sum_loss/2*g)+(manning**2*length)/hyd_rad**1.33333)) |
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137 | Q_outlet_tailwater = flow_area * culvert_velocity |
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138 | |
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139 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
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140 | log_to_file(log_filename, s) |
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141 | Q = min(Q, Q_outlet_tailwater) |
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142 | |
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143 | |
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144 | |
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145 | else: |
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146 | # Box culvert (rectangle or square) |
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147 | |
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148 | # Calculate flows for inlet control |
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149 | height = culvert.height |
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150 | width = culvert.width |
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151 | |
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152 | Q_inlet_unsubmerged = 0.540*g**0.5*width*E**1.50 # Flow based on Inlet Ctrl Inlet Unsubmerged |
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153 | Q_inlet_submerged = 0.702*g**0.5*width*height**0.89*E**0.61 # Flow based on Inlet Ctrl Inlet Submerged |
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154 | |
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155 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
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156 | log_to_file(log_filename, s) |
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157 | |
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158 | case = '' |
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159 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
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160 | Q = Q_inlet_unsubmerged |
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161 | flow_area = width*inlet.depth |
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162 | outlet_culvert_depth = inlet.depth |
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163 | #perimeter=(width+2.0*inlet.depth) |
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164 | case = 'Inlet unsubmerged' |
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165 | else: |
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166 | Q = Q_inlet_submerged |
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167 | flow_area = width*height |
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168 | outlet_culvert_depth = height |
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169 | #perimeter=2.0*(width+height) |
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170 | case = 'Inlet submerged' |
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171 | |
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172 | if delta_Et < E: |
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173 | # Calculate flows for outlet control |
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174 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
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175 | |
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176 | if outlet.depth > height: # The Outlet is Submerged |
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177 | outlet_culvert_depth=height |
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178 | flow_area=width*height # Cross sectional area of flow in the culvert |
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179 | perimeter=2.0*(width+height) |
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180 | case = 'Outlet submerged' |
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181 | elif outlet.depth==0.0: |
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182 | outlet_culvert_depth=inlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
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183 | flow_area=width*inlet.depth |
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184 | perimeter=(width+2.0*inlet.depth) |
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185 | case = 'Outlet depth is zero' |
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186 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
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187 | outlet_culvert_depth=outlet.depth |
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188 | flow_area=width*outlet.depth |
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189 | perimeter=(width+2.0*outlet.depth) |
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190 | case = 'Outlet is open channel flow' |
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191 | |
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192 | hyd_rad = flow_area/perimeter |
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193 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
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194 | log_to_file(log_filename, s) |
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195 | |
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196 | # Outlet control velocity using tail water |
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197 | culvert_velocity = sqrt(delta_Et/((sum_loss/2*g)+(manning**2*length)/hyd_rad**1.33333)) |
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198 | Q_outlet_tailwater = flow_area * culvert_velocity |
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199 | |
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200 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
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201 | log_to_file(log_filename, s) |
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202 | Q = min(Q, Q_outlet_tailwater) |
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203 | |
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204 | |
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205 | # Common code for circle and square geometries |
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206 | log_to_file(log_filename, 'Case: "%s"' %case) |
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207 | flow_rate_control=Q |
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208 | |
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209 | s = 'Flow Rate Control = %f' %flow_rate_control |
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210 | log_to_file(log_filename, s) |
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211 | |
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212 | inlet.rate = -flow_rate_control |
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213 | outlet.rate = flow_rate_control |
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214 | |
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215 | culv_froude=sqrt(flow_rate_control**2*width/(g*flow_area**3)) |
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216 | s = 'Froude in Culvert = %f' %culv_froude |
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217 | log_to_file(log_filename, s) |
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218 | |
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219 | # Determine momentum at the outlet |
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220 | barrel_velocity = Q/(flow_area + velocity_protection/flow_area) |
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221 | |
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222 | |
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223 | else: #inlet.depth < 0.01: |
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224 | Q = barrel_velocity = outlet_culvert_depth = 0.0 |
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225 | |
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226 | return Q, barrel_velocity, outlet_culvert_depth |
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227 | |
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228 | |
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