get_tau_ave() -> averages the hydrodynamic profiles to get more accurate tau (matches fitted tau better)

Author: hmonroedd

examples/sparging_standard.py

@@ -56,9 +56,11 @@
     ]
 
     tau_pred = my_input.get_tau()
-    dt = (tau_pred * 0.02).to("s")  # gives 1% error on tau compared to fine mesh
+    dt = (tau_pred * 0.02).to(
+        "s"
+    )  # 2% of tau_pred gives 1% error on tau compared to fine mesh
     dx = my_input.dx_from_Pe(2)  # grid Pe = 2
-
+    my_input.K_s *= 1e-2
     print(f"dx={dx:~.2e}, dt={dt:~.2e}")
     t_start = time.perf_counter()
     output = my_simulation.solve(dt=dt, dx=dx, verbose=True)

src/sparging/correlations.py

@@ -350,7 +350,7 @@ def get_list(self, corr_type: CorrelationType) -> list[Correlation]:
     ),
     corr_type=CorrelationType.LIQUID_PHASE_DISPERSION,
     source="Deckwer 1974",
-    description="liquid phase axial dispersion coefficient, assumed equal to diffusivity of tritium in liquid FLiBe",
+    description="liquid phase axial dispersion coefficient",
     input_units=["m", PROFILE],
     output_units="m**2/s",
 )

src/sparging/inputs.py

@@ -172,6 +172,24 @@ def get_tau(self) -> pint.Quantity:
         """characteristic time of the sparger under the small partial pressure (SPP) approximation"""
         return (self.eps_l0 / (self.h_l0 * self.a_0)).to("seconds")
 
+    def get_tau_ave(self) -> pint.Quantity:
+        """characteristic time computed from a, h_l and eps_l profiles integrated
+        over the tank height, instead of evaluated at the bottom (z=0)."""
+        from scipy.integrate import quad
+
+        def eps_l_integrand(z_m: float) -> float:
+            return (1 - self.eps_g(z_m * ureg.m)).to("dimensionless").magnitude
+
+        def a_h_l_integrand(z_m: float) -> float:
+            z = z_m * ureg.m
+            return (self.a(z) * self.h_l(z)).to("1/s").magnitude
+
+        height_m = self.height.to("m").magnitude
+        int_eps_l = quad(eps_l_integrand, 0, height_m)[0] * ureg.m
+        int_a_h_l = quad(a_h_l_integrand, 0, height_m)[0] * ureg("m/s")
+
+        return (int_eps_l / int_a_h_l).to("seconds")
+
     def get_c_T2_SS(self) -> pint.Quantity:
         return (self.get_S_T() * 1 / (self.h_l0 * self.a_0)).to("molT2/m^3")
 

src/sparging/model.py

@@ -179,6 +179,7 @@ def _section_analytical_quantities(self, **_) -> dict:
         # each entry wrapped so one failing property doesn't kill the whole export
         candidates = {
             "tau_predicted": si.get_tau,
+            "tau_predicted_ave": si.get_tau_ave,
             "c_T2_steady_state": si.get_c_T2_SS,
             "Pi_number": si.get_Pi_number,
             "Bodenstein_number": si.get_Bo,

src/sparging/postprocess.py

@@ -152,8 +152,10 @@ def summarize_decay(
     (tau_fit, n0_fit), (tau_std, n0_std) = fit_exp(inv, times, t_0, t_end, "decay")
     tau_real = get_tau_real(inv, times, t_0)
     tau_pred = results.sim_input.get_tau()
+    tau_pred_ave = results.sim_input.get_tau_ave()
     residual = get_residual_fraction(inv, times, t_0, t_end)
     rel_error = ((tau_fit - tau_pred) / tau_pred).to("dimensionless")
+    ave_rel_error = ((tau_fit - tau_pred_ave) / tau_pred_ave).to("dimensionless")
 
     logger.info(
         f"tau_fitted={tau_fit.to('hour'):.3f}, tau_predicted={tau_pred.to('hour'):.3f}, "
@@ -164,10 +166,12 @@ def summarize_decay(
         "tau_fitted": tau_fit,
         "tau_fitted_std": tau_std,
         "tau_predicted": tau_pred,
+        "tau_predicted_ave": tau_pred_ave,
         "tau_real_1e": tau_real,
         "n0_fitted": n0_fit,
         "n0_fitted_std": n0_std,
         "residual_fraction": residual,
         "tau_rel_error": rel_error,
+        "tau_ave_rel_error": ave_rel_error,
         "fit_window": (t_0, t_end),
     }