1 | """Collection of culvert routines for use with Culvert_flow in culvert_class |
---|
2 | |
---|
3 | Usage: |
---|
4 | |
---|
5 | |
---|
6 | |
---|
7 | """ |
---|
8 | |
---|
9 | # NEW DEFINED CULVERT FLOW---- Flow from INLET 1 ------> INLET 2 (Outlet) |
---|
10 | # |
---|
11 | # The First Attempt has a Simple Horizontal Circle as a Hole on the Bed |
---|
12 | # Flow Is Removed at a Rate of INFLOW |
---|
13 | # Downstream there is a similar Circular Hole on the Bed where INFLOW effectively Surcharges |
---|
14 | # |
---|
15 | # This SHould be changed to a Vertical Opening Both BOX and Circular |
---|
16 | # There will be several Culvert Routines such as: |
---|
17 | # CULVERT_Boyd_Channel |
---|
18 | # CULVERT_Orifice_and_Weir |
---|
19 | # CULVERT_Simple_FLOOR |
---|
20 | # CULVERT_Simple_WALL |
---|
21 | # CULVERT_Eqn_Floor |
---|
22 | # CULVERT_Eqn_Wall |
---|
23 | # CULVERT_Tab_Floor |
---|
24 | # CULVERT_Tab_Wall |
---|
25 | # BRIDGES..... |
---|
26 | # NOTE NEED TO DEVELOP CONCEPT 1D Model for Linked Pipe System !!!! |
---|
27 | |
---|
28 | # COULD USE EPA SWMM Model !!!! |
---|
29 | |
---|
30 | |
---|
31 | from math import pi, sqrt, sin, cos |
---|
32 | |
---|
33 | |
---|
34 | def boyd_generalised_culvert_model(culvert, inlet, outlet, delta_Et, g): |
---|
35 | |
---|
36 | """Boyd's generalisation of the US department of transportation culvert model |
---|
37 | # == The quantity of flow passing through a culvert is controlled by many factors |
---|
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 |
---|
39 | # == Else the culvert could be controlled by the inlet, with it being Submerged, this is effectively the Orifice Equation |
---|
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 |
---|
41 | """ |
---|
42 | |
---|
43 | from anuga.utilities.system_tools import log_to_file |
---|
44 | from anuga.config import velocity_protection |
---|
45 | from anuga.utilities.numerical_tools import safe_acos as acos |
---|
46 | |
---|
47 | |
---|
48 | Q_outlet_tailwater = 0.0 |
---|
49 | inlet.rate = 0.0 |
---|
50 | outlet.rate = 0.0 |
---|
51 | Q_inlet_unsubmerged = 0.0 |
---|
52 | Q_inlet_submerged = 0.0 |
---|
53 | Q_outlet_critical_depth = 0.0 |
---|
54 | |
---|
55 | log_filename = culvert.log_filename |
---|
56 | |
---|
57 | manning = culvert.manning |
---|
58 | sum_loss = culvert.sum_loss |
---|
59 | length = culvert.length |
---|
60 | |
---|
61 | if inlet.depth_trigger >= 0.01 and inlet.depth >= 0.01: |
---|
62 | # Calculate driving energy |
---|
63 | E = inlet.total_energy |
---|
64 | |
---|
65 | s = 'Driving energy = %f m' %E |
---|
66 | log_to_file(log_filename, s) |
---|
67 | |
---|
68 | msg = 'Driving energy is negative' |
---|
69 | assert E >= 0.0, msg |
---|
70 | |
---|
71 | |
---|
72 | # Water has risen above inlet |
---|
73 | if culvert.culvert_type == 'circle': |
---|
74 | # Round culvert |
---|
75 | |
---|
76 | # Calculate flows for inlet control |
---|
77 | diameter = culvert.diameter |
---|
78 | |
---|
79 | Q_inlet_unsubmerged = 0.421*g**0.5*diameter**0.87*E**1.63 # Inlet Ctrl Inlet Unsubmerged |
---|
80 | Q_inlet_submerged = 0.530*g**0.5*diameter**1.87*E**0.63 # Inlet Ctrl Inlet Submerged |
---|
81 | |
---|
82 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
---|
83 | log_to_file(log_filename, s) |
---|
84 | |
---|
85 | case = '' |
---|
86 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
---|
87 | Q = Q_inlet_unsubmerged |
---|
88 | |
---|
89 | alpha = acos(1 - inlet.depth/diameter) |
---|
90 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
---|
91 | outlet_culvert_depth = inlet.depth |
---|
92 | width = diameter*sin(alpha) |
---|
93 | #perimeter = alpha*diameter |
---|
94 | case = 'Inlet unsubmerged' |
---|
95 | else: |
---|
96 | Q = Q_inlet_submerged |
---|
97 | flow_area = (diameter/2)**2 * pi |
---|
98 | outlet_culvert_depth = diameter |
---|
99 | width = diameter |
---|
100 | #perimeter = diameter |
---|
101 | case = 'Inlet submerged' |
---|
102 | |
---|
103 | |
---|
104 | |
---|
105 | if delta_Et < E: |
---|
106 | # Calculate flows for outlet control |
---|
107 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
---|
108 | |
---|
109 | if outlet.depth > diameter: # The Outlet is Submerged |
---|
110 | outlet_culvert_depth=diameter |
---|
111 | flow_area = (diameter/2)**2 * pi # Cross sectional area of flow in the culvert |
---|
112 | perimeter = diameter * pi |
---|
113 | width = diameter |
---|
114 | case = 'Outlet submerged' |
---|
115 | elif outlet.depth==0.0: |
---|
116 | outlet_culvert_depth=inlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
---|
117 | alpha = acos(1 - inlet.depth/diameter) |
---|
118 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
---|
119 | perimeter = alpha*diameter |
---|
120 | width = diameter*sin(alpha) |
---|
121 | |
---|
122 | case = 'Outlet depth is zero' |
---|
123 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
---|
124 | outlet_culvert_depth=outlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
---|
125 | alpha = acos(1 - outlet.depth/diameter) |
---|
126 | flow_area = diameter**2 * (alpha - sin(alpha)*cos(alpha)) |
---|
127 | perimeter = alpha*diameter |
---|
128 | width = diameter*sin(alpha) |
---|
129 | case = 'Outlet is open channel flow' |
---|
130 | |
---|
131 | hyd_rad = flow_area/perimeter |
---|
132 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
---|
133 | log_to_file(log_filename, s) |
---|
134 | |
---|
135 | # Outlet control velocity using tail water |
---|
136 | culvert_velocity = sqrt(delta_Et/((sum_loss/2*g)+(manning**2*length)/hyd_rad**1.33333)) |
---|
137 | Q_outlet_tailwater = flow_area * culvert_velocity |
---|
138 | |
---|
139 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
---|
140 | log_to_file(log_filename, s) |
---|
141 | Q = min(Q, Q_outlet_tailwater) |
---|
142 | |
---|
143 | |
---|
144 | |
---|
145 | else: |
---|
146 | # Box culvert (rectangle or square) |
---|
147 | |
---|
148 | # Calculate flows for inlet control |
---|
149 | height = culvert.height |
---|
150 | width = culvert.width |
---|
151 | |
---|
152 | Q_inlet_unsubmerged = 0.540*g**0.5*width*E**1.50 # Flow based on Inlet Ctrl Inlet Unsubmerged |
---|
153 | Q_inlet_submerged = 0.702*g**0.5*width*height**0.89*E**0.61 # Flow based on Inlet Ctrl Inlet Submerged |
---|
154 | |
---|
155 | s = 'Q_inlet_unsubmerged = %.6f, Q_inlet_submerged = %.6f' %(Q_inlet_unsubmerged, Q_inlet_submerged) |
---|
156 | log_to_file(log_filename, s) |
---|
157 | |
---|
158 | case = '' |
---|
159 | if Q_inlet_unsubmerged < Q_inlet_submerged: |
---|
160 | Q = Q_inlet_unsubmerged |
---|
161 | flow_area = width*inlet.depth |
---|
162 | outlet_culvert_depth = inlet.depth |
---|
163 | #perimeter=(width+2.0*inlet.depth) |
---|
164 | case = 'Inlet unsubmerged' |
---|
165 | else: |
---|
166 | Q = Q_inlet_submerged |
---|
167 | flow_area = width*height |
---|
168 | outlet_culvert_depth = height |
---|
169 | #perimeter=2.0*(width+height) |
---|
170 | case = 'Inlet submerged' |
---|
171 | |
---|
172 | if delta_Et < E: |
---|
173 | # Calculate flows for outlet control |
---|
174 | # Determine the depth at the outlet relative to the depth of flow in the Culvert |
---|
175 | |
---|
176 | if outlet.depth > height: # The Outlet is Submerged |
---|
177 | outlet_culvert_depth=height |
---|
178 | flow_area=width*height # Cross sectional area of flow in the culvert |
---|
179 | perimeter=2.0*(width+height) |
---|
180 | case = 'Outlet submerged' |
---|
181 | elif outlet.depth==0.0: |
---|
182 | outlet_culvert_depth=inlet.depth # For purpose of calculation assume the outlet depth = the inlet depth |
---|
183 | flow_area=width*inlet.depth |
---|
184 | perimeter=(width+2.0*inlet.depth) |
---|
185 | case = 'Outlet depth is zero' |
---|
186 | else: # Here really should use the Culvert Slope to calculate Actual Culvert Depth & Velocity |
---|
187 | outlet_culvert_depth=outlet.depth |
---|
188 | flow_area=width*outlet.depth |
---|
189 | perimeter=(width+2.0*outlet.depth) |
---|
190 | case = 'Outlet is open channel flow' |
---|
191 | |
---|
192 | hyd_rad = flow_area/perimeter |
---|
193 | s = 'hydraulic radius at outlet = %f' %hyd_rad |
---|
194 | log_to_file(log_filename, s) |
---|
195 | |
---|
196 | # Outlet control velocity using tail water |
---|
197 | culvert_velocity = sqrt(delta_Et/((sum_loss/2*g)+(manning**2*length)/hyd_rad**1.33333)) |
---|
198 | Q_outlet_tailwater = flow_area * culvert_velocity |
---|
199 | |
---|
200 | s = 'Q_outlet_tailwater = %.6f' %Q_outlet_tailwater |
---|
201 | log_to_file(log_filename, s) |
---|
202 | Q = min(Q, Q_outlet_tailwater) |
---|
203 | |
---|
204 | |
---|
205 | # Common code for circle and square geometries |
---|
206 | log_to_file(log_filename, 'Case: "%s"' %case) |
---|
207 | flow_rate_control=Q |
---|
208 | |
---|
209 | s = 'Flow Rate Control = %f' %flow_rate_control |
---|
210 | log_to_file(log_filename, s) |
---|
211 | |
---|
212 | inlet.rate = -flow_rate_control |
---|
213 | outlet.rate = flow_rate_control |
---|
214 | |
---|
215 | culv_froude=sqrt(flow_rate_control**2*width/(g*flow_area**3)) |
---|
216 | s = 'Froude in Culvert = %f' %culv_froude |
---|
217 | log_to_file(log_filename, s) |
---|
218 | |
---|
219 | # Determine momentum at the outlet |
---|
220 | barrel_velocity = Q/(flow_area + velocity_protection/flow_area) |
---|
221 | |
---|
222 | |
---|
223 | else: #inlet.depth < 0.01: |
---|
224 | Q = barrel_velocity = outlet_culvert_depth = 0.0 |
---|
225 | |
---|
226 | return Q, barrel_velocity, outlet_culvert_depth |
---|
227 | |
---|
228 | |
---|