Make Cylinder jet actuation zero-net-mass-flux

docs/docs/api/firedrake/envs/cylinder/flow.md

@@ -87,3 +87,6 @@ Velocity vector for boundary condition
 Blowing/suction actuation on the cylinder wall, following Rabault, et al (2018)
 https://arxiv.org/abs/1808.07664
 
+The two jets act as a zero-net-mass-flux pair: a positive control blows
+through the upper jet and sucks through the lower jet with equal flow rate.
+

docs/docs/examples/firedrake/cylinder.md

@@ -20,7 +20,7 @@ All scripts live in [`examples/firedrake/advanced/cylinder/`](https://github.com
 
 Two independent actuation mechanisms are available:
 
-- **Jet blowing/suction** ([`Cylinder`](../../api/firedrake/envs/cylinder/flow)): two 10° tangential jets at ±90° from the stagnation point — used by `solve-steady.py`, `unsteady.py`, `step_input.py`, and `pressure-probes.py`.
+- **Jet blowing/suction** ([`Cylinder`](../../api/firedrake/envs/cylinder/flow)): two 10° jets at ±90° from the stagnation point with zero net mass flux — used by `solve-steady.py`, `unsteady.py`, `step_input.py`, and `pressure-probes.py`.
 - **Rotary control** ([`RotaryCylinder`](../../api/firedrake/envs/cylinder/flow)): a prescribed tangential surface velocity — used by `run-transient.py`, `pd-control.py`, `pd-phase-sweep.py`, and `lti_system.py`.
 
 Both mechanisms are capable of suppressing vortex shedding, but they operate through different physical mechanisms and are suited to different control design approaches.

hydrogym/firedrake/envs/cylinder/flow.py

@@ -194,6 +194,9 @@ def cyl_velocity_field(self):
 
         Blowing/suction actuation on the cylinder wall, following Rabault, et al (2018)
         https://arxiv.org/abs/1808.07664
+
+        The two jets act as a zero-net-mass-flux pair: a positive control blows
+        through the upper jet and sucks through the lower jet with equal flow rate.
         """
 
         # Set up tangential boundaries to cylinder
@@ -217,5 +220,5 @@ def cyl_velocity_field(self):
             0.0,
         )
 
-        # Normal velocity (blowing/suction) at the cylinder wall
-        return ufl.as_tensor((self.x, self.y)) * (A_up + A_lo)
+        # Normal velocity at the cylinder wall (blowing on top, suction on bottom)
+        return ufl.as_tensor((self.x, self.y)) * (A_up - A_lo)

test/test_cyl.py

@@ -24,6 +24,18 @@ def test_steady(tol=1e-3):
     assert abs(CD - 1.2840) < tol  # Re = 100
 
 
+def test_jet_zero_net_mass_flux(tol=1e-8):
+    flow = hgym.Cylinder(mesh="medium")
+
+    # Volume flux from the cylinder wall into the fluid for unit actuation
+    flux = fd.dot(flow.cyl_velocity_field, -flow.n)
+    upper_flux = fd.assemble(fd.conditional(flow.y > 0, flux, 0.0) * fd.ds(flow.CYLINDER))
+    lower_flux = fd.assemble(fd.conditional(flow.y < 0, flux, 0.0) * fd.ds(flow.CYLINDER))
+
+    assert upper_flux > 0  # Blowing through the upper jet
+    assert abs(upper_flux + lower_flux) < tol * abs(upper_flux)
+
+
 def test_steady_rotation(tol=1e-3):
     Tf = 4.0
     dt = 0.1