Equation of Tainter Gate implementation after Bollrich2019

OpenHPL/Examples/Gate.mo

@@ -0,0 +1,94 @@
+within OpenHPL.Examples;
+model Gate "Usage of the tainter gate"
+  extends Modelica.Icons.Example;
+  inner Data data(SteadyState = true, Vdot_0 = 75) annotation (
+    Placement(transformation(extent = {{-100, 80}, {-80, 100}})));
+  Modelica.Blocks.Sources.Ramp gateOpening(
+    height=0,
+    duration=1000,
+    offset=1,
+    startTime=500) annotation (Placement(transformation(extent={{-90,-10},{-70,10}})));
+  Waterway.Reservoir upstream(
+    h_0=5,
+    constantLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(extent={{-40,38},{-20,58}})));
+  Waterway.Reservoir downstream(
+    h_0=4,
+    constantLevel=false,
+    useLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=180,
+        origin={30,48})));
+  Waterway.Gate_HR gate_HR(W=16.5, T=5.6) annotation (Placement(transformation(extent={{-10,38},{10,58}})));
+  Modelica.Blocks.Sources.Ramp level(
+    height=4.89,
+    duration=1000,
+    offset=0.01,
+    startTime=500)                            annotation (Placement(transformation(extent={{80,38},{60,58}})));
+  Waterway.Reservoir upstream1(
+    h_0=5,
+    constantLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(extent={{-40,-10},{-20,10}})));
+  Waterway.Reservoir downstream1(
+    h_0=4,
+    constantLevel=false,
+    useLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=180,
+        origin={32,0})));
+  Waterway.Gate gate(
+    sluice=false,
+    b=16.5,
+    r=8.5,
+    h_h=5.6) annotation (Placement(transformation(extent={{-8,-10},{12,10}})));
+  Modelica.Blocks.Sources.Ramp level1(
+    height=4.89,
+    duration=1000,
+    offset=0.01,
+    startTime=500)                            annotation (Placement(transformation(extent={{82,-10},{62,10}})));
+  Waterway.Reservoir upstream2(
+    h_0=5,
+    constantLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(extent={{-40,-50},{-20,-30}})));
+  Waterway.Reservoir downstream2(
+    h_0=4,
+    constantLevel=false,
+    useLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=180,
+        origin={30,-40})));
+  Waterway.Gate gate_sluice(
+    sluice=true,
+    b=16.5,
+    r=8.5,
+    h_h=5.6) annotation (Placement(transformation(extent={{-10,-50},{10,-30}})));
+  Modelica.Blocks.Sources.Ramp level2(
+    height=4.89,
+    duration=1000,
+    offset=0.01,
+    startTime=500)                            annotation (Placement(transformation(extent={{80,-50},{60,-30}})));
+equation
+  connect(upstream.o, gate_HR.i) annotation (Line(points={{-20,48},{-10,48}}, color={0,128,255}));
+  connect(gate_HR.o, downstream.o) annotation (Line(points={{10,48},{20,48}}, color={0,128,255}));
+  connect(gateOpening.y, gate_HR.B) annotation (Line(points={{-69,0},{-44,0},{-44,70},{0,70},{0,60}}, color={0,0,127}));
+  connect(level.y, downstream.level) annotation (Line(points={{59,48},{50,48},{50,54},{42,54}},   color={0,0,127}));
+  connect(upstream1.o, gate.i) annotation (Line(points={{-20,0},{-8,0}}, color={0,128,255}));
+  connect(gate.o, downstream1.o) annotation (Line(points={{12,0},{22,0}}, color={0,128,255}));
+  connect(level1.y, downstream1.level) annotation (Line(points={{61,0},{52,0},{52,6},{44,6}}, color={0,0,127}));
+  connect(gateOpening.y, gate.a) annotation (Line(points={{-69,0},{-44,0},{-44,22},{2,22},{2,12}}, color={0,0,127}));
+  connect(upstream2.o, gate_sluice.i) annotation (Line(points={{-20,-40},{-10,-40}}, color={0,128,255}));
+  connect(gate_sluice.o, downstream2.o) annotation (Line(points={{10,-40},{20,-40}}, color={0,128,255}));
+  connect(level2.y, downstream2.level) annotation (Line(points={{59,-40},{50,-40},{50,-34},{42,-34}}, color={0,0,127}));
+  connect(gateOpening.y, gate_sluice.a) annotation (Line(points={{-69,0},{-44,0},{-44,-18},{0,-18},{0,-28}}, color={0,0,127}));
+  annotation (
+    experiment(StopTime=2000, Interval=0.4));
+end Gate;

OpenHPL/Examples/TainterGate3.mo

@@ -0,0 +1,42 @@
+within OpenHPL.Examples;
+model TainterGate3 "Usage of the tainter gate"
+  extends Modelica.Icons.Example;
+  inner Data data(SteadyState = true, Vdot_0 = 75) annotation (
+    Placement(transformation(extent = {{-100, 80}, {-80, 100}})));
+  Modelica.Blocks.Sources.Ramp gateOpening(
+    height=0,
+    duration=1000,
+    offset=0.4,
+    startTime=500) annotation (Placement(transformation(extent={{-40,30},{-20,50}})));
+  Waterway.Reservoir upstream(
+    h_0=5.6,
+    constantLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(extent={{-40,-20},{-20,0}})));
+  Waterway.Reservoir downstream(
+    h_0=2.8,
+    constantLevel=false,
+    useLevel=true,
+    L=10,
+    W=10) annotation (Placement(transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=180,
+        origin={30,-10})));
+  Waterway.Gate tainterGate3_1(
+    sluice=true,
+    r=8.5,
+    h_h=5.55,
+    b=5.9) annotation (Placement(transformation(extent={{-10,-20},{10,0}})));
+  Modelica.Blocks.Sources.Ramp downstream_level(
+    height=4,
+    duration=1000,
+    offset=0,
+    startTime=500) annotation (Placement(transformation(extent={{80,-20},{60,0}})));
+equation
+  connect(upstream.o, tainterGate3_1.i) annotation (Line(points={{-20,-10},{-10,-10}}, color={0,128,255}));
+  connect(tainterGate3_1.o, downstream.o) annotation (Line(points={{10,-10},{20,-10}}, color={0,128,255}));
+  connect(tainterGate3_1.a, gateOpening.y) annotation (Line(points={{0,2},{-2,2},{-2,42},{-19,42},{-19,40}}, color={0,0,127}));
+  connect(downstream.level, downstream_level.y) annotation (Line(points={{42,-4},{54,-4},{54,-10},{59,-10}}, color={0,0,127}));
+  annotation (
+    experiment(StopTime=2000, Interval=0.4));
+end TainterGate3;

OpenHPL/Examples/package.order

@@ -7,5 +7,6 @@ DetailedGen
 DetailedGenFrancis
 PowerSystemSimple
 VolumeFlowSource
-TainterGate
+Gate
 WithOpenIPSL
+TainterGate3

OpenHPL/Icons/TainterGate.mo → OpenHPL/Icons/Gate.mo

@@ -1,12 +1,30 @@
 within OpenHPL.Icons;
-partial class TainterGate "Icon of a tainter gate"
+partial class Gate "Icons for the gate"
   annotation (Icon(graphics={
         Rectangle(
-          extent={{-100,-2},{-46,-72}},
+          extent={{-46,-60},{100,-72}},
+          lineColor={28,108,200},
+          fillColor={28,108,200},
+          fillPattern=FillPattern.Solid),
+        Rectangle(
+          visible = sluice,
+          extent={{-46,0},{-4,-60}},
+          lineColor={28,108,200},
+          fillColor={28,108,200},
+          fillPattern=FillPattern.Solid),
+          Rectangle(
+          visible = sluice,
+          extent={{-4,20},{4,-60}},
+          lineColor={0,0,0},
+          fillColor={175,175,175},
+          fillPattern=FillPattern.Solid),
+        Rectangle(
+          extent={{-100,0},{-46,-72}},
           lineColor={28,108,200},
           fillColor={28,108,200},
           fillPattern=FillPattern.Solid),
         Ellipse(
+          visible = not sluice,
           extent={{-60,140},{220,-140}},
           lineColor={135,135,135},
           startAngle=155,
@@ -18,11 +36,6 @@ partial class TainterGate "Icon of a tainter gate"
           lineColor={0,0,0},
           fillColor={215,215,215},
           fillPattern=FillPattern.Forward),
-        Rectangle(
-          extent={{-46,-60},{100,-72}},
-          lineColor={28,108,200},
-          fillColor={28,108,200},
-          fillPattern=FillPattern.Solid),
         Rectangle(extent={{-100,100},{100,-100}}, lineColor={0,0,0}),
                      Text(
           lineColor={28,108,200},
@@ -38,4 +51,4 @@ partial class TainterGate "Icon of a tainter gate"
           points={{0,-6},{0,100}},
           color={0,0,0},
           pattern=LinePattern.Dash)}));
-end TainterGate;
+end Gate;

OpenHPL/Icons/package.order

@@ -7,11 +7,11 @@ Surge
 Fitting
 DraftTube
 OpenChannel
+Gate
 ElectroMech
 Turbine
 Generator
 Pylon
 RunOff
 Method
 Governor
-TainterGate

OpenHPL/Waterway/TainterGate3.mo → OpenHPL/Waterway/Gate.mo

@@ -1,39 +1,54 @@
 within OpenHPL.Waterway;
-model TainterGate3 "Model of a tainter gate based on [Bollrich2019]"
+model Gate "Model of a sluice or tainter gate based on [Bollrich2019]"
   outer Data data "Using standard class with system parameters";
-  extends Icons.TainterGate;
+  extends Icons.Gate;
   extends OpenHPL.Interfaces.ContactPort;
-
-//   parameter SI.Height b_max "Maxium opening of the gate";
-//   parameter SI.Height b_min = 0 "Minimum opening of the gate";
-  parameter SI.Length r "Radius of the gate arm";
-  parameter SI.Height a "Height of the hinge above gate bottom";
-  parameter SI.Height b "Width of the gate";
-  parameter Real Cc_[3] = {1,2,3} "Polinomial factors of contraction coefficient Cc {linear,quadratic,cube}";
-  SI.Height h_i "Inlet water level";
-  SI.Height h_o "Outlet water level";
-  Real alpha = h_o/(Cc*u);
-  Real beta = h_i/h_o;
-  Real gamma = (h_o/(Cc*u))^2 - (h_o/h_i)^2 "Loss factor";
-  Real psi = (1/beta)^2 - 1 + (gamma^2*(beta-1))/(psi_x1 + psi_x2) "Head-loss parameter";
-  Real psi_ = (1/beta)^2 - 1 + (gamma^2*(beta-1))/(psi_x1 - psi_x2) "Neg Head-loss parameter";
-  Real psi_x1 = gamma*beta-2*(alpha-1);
-  Real psi_x2 =  sqrt((2*(alpha-1)-gamma*beta)^2 - gamma^2*(beta^2-1));
-
-  SI.Angle theta = C.pi/2 - asin((a-u)/r) "Flow angle of the gate";
-  Real Cc = Cc_[3]*theta^3 + Cc_[2]*theta^2 + Cc_[1]*theta + 1.002282138151680 "Contraction coefficient";
-  SI.VolumeFlowRate Vdot,Vdot_gamma "Volume flow rate through the gate";
-
-    Modelica.Blocks.Interfaces.RealInput u "Opening of the gate [m]" annotation (Placement(transformation(
+  import Modelica.Units.Conversions.to_deg;
+  parameter Boolean sluice=false "if true, gate is of type sluice gate, otherwise it is a radial/tainter gate type" annotation (Dialog(group="Type"), choices(checkBox=true));
+  parameter SI.Height b "Width of the gate" annotation (Dialog(group="Common"));
+  parameter SI.Length r "Radius of the gate arm" annotation (Dialog(enable=not sluice, group="Radial/Tainter"));
+  parameter SI.Height h_h "Height of the hinge above gate bottom" annotation (Dialog(group="Radial/Tainter", enable=not sluice));
+  SI.Height h_0 "Inlet water level";
+  SI.Height h_2 "Outlet water level";
+  SI.Height h_2_limit "Limit of free flow";
+  SI.Area A = a*b "Area of the physical gate opening";
+  SI.VolumeFlowRate Vdot "Volume flow rate through the gate";
+  Real mu_A "Discharge coefficient";
+  Real psi "Contraction coefficient";
+  //Real psi90 "Contraction coefficient for vertical gate";
+  Real chi "Back-up coefficient";
+  SI.Angle alpha = C.pi/2 - asin((h_h-a)/r) "Edge angle of the gate";
+    Real x,y,z;
+    Real h0_a = h_0/a;
+    Real h2_a = h_2/a;
+  Modelica.Blocks.Interfaces.RealInput a "Opening of the gate [m]" annotation (Placement(transformation(
           extent={{-20,-20},{20,20}},
           rotation=270,
           origin={0,120})));
 equation
-  Vdot = b*h_o * sqrt((2*data.g*max(0,(h_i - h_o)))/(psi + 1 - (h_o/h_i)^2)) "Calculated flow";
-  Vdot_gamma = b*h_o * sqrt((2*data.g*max(0,(h_i - h_o)))/(gamma + 1 - (h_o/h_i)^2)) "Calculated flow";
+  mu_A = psi/sqrt(1+psi*a/h_0);
+  if sluice then
+    psi = 1 / (1+ 0.64 * sqrt(1-(a/h_0)^2));
+  else
+    psi = 1.3 - 0.8 * sqrt(1 - ((to_deg(alpha)-205)/220)^2) "Normally only valid for a/h_0 --> 0";
+  end if;
+      x = (1-2*psi*a/h_0*(1-psi*a/max(C.small,h_2)))^2;
+    y = x+z-1;
+    z = (h_2/h_0)^2;
+
+  h_2_limit = a*psi/2*(sqrt(1+16/(psi*(1+psi*a/h_0)) * (h_0/a))-1);
+
+  if h_2 >= h_2_limit then
+    chi = sqrt((1+psi*a/h_0) * ((1-2*psi*a/h_0 * (1-psi*a/h_2))-
+          sqrt((1-2*psi*a/h_0*(1-psi*a/max(C.small,h_2)))^2 + (h_2/h_0)^2 - 1))) "Backed-up flow";
+  else
+    chi = 1 "Free flow";
+  end if;
+
+  Vdot = chi * mu_A * A * sqrt(2*data.g*h_0) "Volume flow rate through the gate";
   mdot = Vdot * data.rho "Mass flow rate through the gate";
-  i.p = h_i * data.g * data.rho + data.p_a "Inlet water pressure";
-  o.p = h_o * data.g * data.rho + data.p_a "Outlet water pressure";
+  i.p = h_0 * data.g * data.rho + data.p_a "Inlet water pressure";
+  o.p = h_2 * data.g * data.rho + data.p_a "Outlet water pressure";
   annotation (Documentation(info="<html>
 <h4>Implementation</h4>
 <p>
@@ -85,9 +100,9 @@ $$Q_A = \\chi \\cdot \\mu_A \\cdot A \\cdot \\sqrt{2g\\cdot h_0} \\tag{8.29} $$
 
 With 
 <dl>
-<dd>Back-up factor</dd>
+<dd>Back-up coefficient</dd>
 <dt> $$ \\chi = \\sqrt{
-	      \\left(
+              \\left(
                    1 + \\frac{\\psi\\cdot a}{h_0} 
                  \\right) \\cdot 
                  \\left\\{ 
@@ -105,8 +120,8 @@ With
                          \\right)
                        \\right]^2
                        +
-	           \\left(
-                   	\\frac{h_2}{h_0}
+                   \\left(
+                           \\frac{h_2}{h_0}
                       \\right)^2
                       - 1
                      } 
@@ -123,4 +138,4 @@ $$ \\frac{h_2^*}{a} = \\frac{\\psi}{2} \\cdot \\left( \\sqrt{ 1 + \\frac{16}{\\p
 So when \\(\\frac{h_2}{a} \\geq \\frac{h_2^*}{a}\\) then we have back-up flow.
 </p>
 </html>"));
-end TainterGate3;
+end Gate;

OpenHPL/Waterway/TainterGate.mo → OpenHPL/Waterway/Gate_HR.mo

@@ -1,7 +1,7 @@
 within OpenHPL.Waterway;
-model TainterGate "Model of a tainter gate (HEC-RAS)"
+model Gate_HR "Model of a tainter gate (HEC-RAS)"
   outer Data data "Using standard class with system parameters";
-  extends Icons.TainterGate;
+  extends Icons.Gate;
   extends OpenHPL.Interfaces.ContactPort;
 
   parameter SI.Height W "Width of the gated spillway"
@@ -84,4 +84,4 @@ $$Q = C_{dx} A \\sqrt{2gH} \\tag{3}$$
 The use of <code>Cdx</code> is different to the implementaion as done in HEC-RAS. This was done in order to have a smoother transition from the partially to fully submerged region.
 </p>
 </html>"));
-end TainterGate;
+end Gate_HR;