Merge pull request #1599 from paulromano/energy-dep-fixes

Two fixes for energy deposition calculations

docs/source/methods/energy_deposition.rst

@@ -12,19 +12,18 @@ is deposited for a specific reaction is referred to as
 "heating numbers" and can be computed using a program like NJOY with the
 ``heatr`` module.
 
-These heating rate is the product of reaction-specific coefficients and
-a reaction cross section
+The heating rate is the product of reaction-specific coefficients and a reaction
+cross section
 
 .. math::
 
     H(E) = \phi(E)\sum_i\rho_i\sum_rk_{i, r}(E),
 
-and has units energy per time, typically eV / s.
-Here, :math:`k_{i, r}` are the KERMA (Kinetic Energy Release in Materials)
-[Mack97]_ coefficients for reaction :math:`r` of isotope :math:`i`.
-The KERMA coefficients have units energy :math:`\times` cross-section, e.g.
-eV-barn, and can be used much like a reaction cross section for the purpose
-of tallying energy deposition.
+and has units energy per time, typically eV/s. Here, :math:`k_{i, r}` are the
+KERMA (Kinetic Energy Release in Materials) [Mack97]_ coefficients for reaction
+:math:`r` of isotope :math:`i`. The KERMA coefficients have units of energy
+:math:`\times` cross-section (e.g., eV-barn) and can be used much like a reaction
+cross section for the purpose of tallying energy deposition.
 
 KERMA coefficients can be computed using the energy-balance method with
 a nuclear data processing code like NJOY, which performs the following
@@ -56,11 +55,11 @@ broken up into the following categories:
 - :math:`E_{\beta}` - energy of released :math:`\beta` particles
 - :math:`E_{\nu}` - energy of neutrinos
 
-These components are defined in MF=1,MT=458 data in a standard ENDF/B-6 formatted
-file. All these quantities may depend upon incident neutron energy,
-but this dependence is not shown to make the following demonstrations cleaner.
-As neutrinos scarcely interact with matter, the recoverable energy from
-fission is defined as
+These components are defined in MF=1, MT=458 data in a standard ENDF-6 formatted
+file. All these quantities may depend upon incident neutron energy, but this
+dependence is not shown to make the following demonstrations cleaner. As
+neutrinos scarcely interact with matter, the recoverable energy from fission is
+defined as
 
 .. math::
 

docs/source/publications.rst

@@ -149,6 +149,16 @@ Geometry and Visualization
 Miscellaneous
 -------------
 
+- Shikhar Kumar, Benoit Forget, and Kord Smith, "`Stationarity Diagnostic using
+  Functional Expansion Tallies
+  <https://doi.org/10.1016/j.anucene.2020.107388>`_", *Ann. Nucl. Energy*,
+  **143**, 107388 (2020).
+
+- T. Eade, B. Colling, J. Naish, L. W. Packer, and A. Valentine, "`Shutdown dose
+  rate benchmarking using modern particle transport codes
+  <https://doi.org/10.1088/1741-4326/ab8181>`_, *Nucl. Fusion*, **60**, 056024
+  (2020).
+
 - Jiankai Yu, Qiudong Wang, Ding She, and Benoit Forget, "Modelling of the
   HTR-PM Pebble-bed Reactor using OpenMC", *Trans. Am. Nucl. Soc.*, **122**,
   643-646 (2020).

include/openmc/nuclide.h

@@ -82,6 +82,10 @@ public:
   std::unique_ptr<Function1D> total_nu_; //!< Total neutron yield
   std::unique_ptr<Function1D> fission_q_prompt_; //!< Prompt fission energy release
   std::unique_ptr<Function1D> fission_q_recov_; //!< Recoverable fission energy release
+  std::unique_ptr<Function1D> prompt_photons_; //!< Prompt photon energy release
+  std::unique_ptr<Function1D> delayed_photons_; //!< Delayed photon energy release
+  std::unique_ptr<Function1D> fragments_; //!< Fission fragment energy release
+  std::unique_ptr<Function1D> betas_; //!< Delayed beta energy release
 
   // Resonance scattering information
   bool resonant_ {false};

include/openmc/particle.h

@@ -212,10 +212,11 @@ public:
   //
   //! stores the current phase space attributes of the particle in the
   //! secondary bank and increments the number of sites in the secondary bank.
+  //! \param wgt Weight of the secondary particle
   //! \param u Direction of the secondary particle
   //! \param E Energy of the secondary particle in [eV]
   //! \param type Particle type
-  void create_secondary(Direction u, double E, Type type);
+  void create_secondary(double wgt, Direction u, double E, Type type);
 
   //! initialize from a source site
   //

include/openmc/photon.h

@@ -120,8 +120,8 @@ namespace data {
 extern xt::xtensor<double, 1> compton_profile_pz; //! Compton profile momentum grid
 
 //! Photon interaction data for each element
-extern std::vector<std::unique_ptr<PhotonInteraction>> elements;
 extern std::unordered_map<std::string, int> element_map;
+extern std::vector<std::unique_ptr<PhotonInteraction>> elements;
 
 } // namespace data
 

src/bremsstrahlung.cpp

@@ -108,7 +108,7 @@ void thick_target_bremsstrahlung(Particle& p, double* E_lost)
 
     if (w > settings::energy_cutoff[photon]) {
       // Create secondary photon
-      p.create_secondary(p.u(), w, Particle::Type::photon);
+      p.create_secondary(p.wgt_, p.u(), w, Particle::Type::photon);
       *E_lost += w;
     }
   }

src/distribution_energy.cpp

@@ -224,13 +224,11 @@ double ContinuousTabular::sample(double E, uint64_t* seed) const
 
   double E_l_k = distribution_[l].e_out[k];
   double p_l_k = distribution_[l].p[k];
-  double E_out;
+  double E_out = E_l_k;
   if (distribution_[l].interpolation == Interpolation::histogram) {
     // Histogram interpolation
     if (p_l_k > 0.0 && k >= n_discrete) {
       E_out = E_l_k + (r1 - c_k)/p_l_k;
-    } else {
-      E_out = E_l_k;
     }
 
   } else if (distribution_[l].interpolation == Interpolation::lin_lin) {
@@ -238,12 +236,14 @@ double ContinuousTabular::sample(double E, uint64_t* seed) const
     double E_l_k1 = distribution_[l].e_out[k+1];
     double p_l_k1 = distribution_[l].p[k+1];
 
-    double frac = (p_l_k1 - p_l_k)/(E_l_k1 - E_l_k);
-    if (frac == 0.0) {
-      E_out = E_l_k + (r1 - c_k)/p_l_k;
-    } else {
-      E_out = E_l_k + (std::sqrt(std::max(0.0, p_l_k*p_l_k +
-                       2.0*frac*(r1 - c_k))) - p_l_k)/frac;
+    if (E_l_k != E_l_k1) {
+      double frac = (p_l_k1 - p_l_k)/(E_l_k1 - E_l_k);
+      if (frac == 0.0) {
+        E_out = E_l_k + (r1 - c_k)/p_l_k;
+      } else {
+        E_out = E_l_k + (std::sqrt(std::max(0.0, p_l_k*p_l_k +
+                        2.0*frac*(r1 - c_k))) - p_l_k)/frac;
+      }
     }
   } else {
     throw std::runtime_error{"Unexpected interpolation for continuous energy "

src/nuclide.cpp

@@ -262,21 +262,24 @@ Nuclide::Nuclide(hid_t group, const std::vector<double>& temperature)
   }
 
   // Read fission energy release data if present
-  std::unique_ptr<Function1D> prompt_photons;
-  std::unique_ptr<Function1D> delayed_photons;
   if (object_exists(group, "fission_energy_release")) {
     hid_t fer_group = open_group(group, "fission_energy_release");
     fission_q_prompt_ = read_function(fer_group, "q_prompt");
     fission_q_recov_ = read_function(fer_group, "q_recoverable");
 
+    // Read fission fragment and delayed beta energy release. This is needed for
+    // energy normalization in k-eigenvalue calculations
+    fragments_ = read_function(fer_group, "fragments");
+    betas_ = read_function(fer_group, "betas");
+
     // We need prompt/delayed photon energy release for scaling fission photon
     // production
-    prompt_photons = read_function(fer_group, "prompt_photons");
-    delayed_photons = read_function(fer_group, "delayed_photons");
+    prompt_photons_ = read_function(fer_group, "prompt_photons");
+    delayed_photons_ = read_function(fer_group, "delayed_photons");
     close_group(fer_group);
   }
 
-  this->create_derived(prompt_photons.get(), delayed_photons.get());
+  this->create_derived(prompt_photons_.get(), delayed_photons_.get());
 }
 
 Nuclide::~Nuclide()

src/particle.cpp

@@ -84,13 +84,13 @@ Particle::clear()
 }
 
 void
-Particle::create_secondary(Direction u, double E, Type type)
+Particle::create_secondary(double wgt, Direction u, double E, Type type)
 {
   secondary_bank_.emplace_back();
 
   auto& bank {secondary_bank_.back()};
   bank.particle = type;
-  bank.wgt = wgt_;
+  bank.wgt = wgt;
   bank.r = this->r();
   bank.u = u;
   bank.E = settings::run_CE ? E : g_;

src/photon.cpp

@@ -27,8 +27,8 @@ namespace data {
 
 xt::xtensor<double, 1> compton_profile_pz;
 
-std::vector<std::unique_ptr<PhotonInteraction>> elements;
 std::unordered_map<std::string, int> element_map;
+std::vector<std::unique_ptr<PhotonInteraction>> elements;
 
 } // namespace data
 
@@ -669,7 +669,7 @@ void PhotonInteraction::atomic_relaxation(const ElectronSubshell& shell, Particl
     u.y = std::sqrt(1.0 - mu*mu)*std::cos(phi);
     u.z = std::sqrt(1.0 - mu*mu)*std::sin(phi);
     double E = shell.binding_energy;
-    p.create_secondary(u, E, Particle::Type::photon);
+    p.create_secondary(p.wgt_, u, E, Particle::Type::photon);
     return;
   }
 
@@ -701,7 +701,7 @@ void PhotonInteraction::atomic_relaxation(const ElectronSubshell& shell, Particl
     // Non-radiative transition -- Auger/Coster-Kronig effect
 
     // Create auger electron
-    p.create_secondary(u, E, Particle::Type::electron);
+    p.create_secondary(p.wgt_, u, E, Particle::Type::electron);
 
     // Fill hole left by emitted auger electron
     int i_hole = shell_map_.at(secondary);
@@ -711,7 +711,7 @@ void PhotonInteraction::atomic_relaxation(const ElectronSubshell& shell, Particl
     // Radiative transition -- get X-ray energy
 
     // Create fluorescent photon
-    p.create_secondary(u, E, Particle::Type::photon);
+    p.create_secondary(p.wgt_, u, E, Particle::Type::photon);
   }
 
   // Fill hole created by electron transitioning to the photoelectron hole

src/physics.cpp

@@ -4,6 +4,7 @@
 #include "openmc/bremsstrahlung.h"
 #include "openmc/constants.h"
 #include "openmc/eigenvalue.h"
+#include "openmc/endf.h"
 #include "openmc/error.h"
 #include "openmc/material.h"
 #include "openmc/math_functions.h"
@@ -302,7 +303,7 @@ void sample_photon_reaction(Particle& p)
       double mu_electron = (alpha - alpha_out*mu)
         / std::sqrt(alpha*alpha + alpha_out*alpha_out - 2.0*alpha*alpha_out*mu);
       Direction u = rotate_angle(p.u(), mu_electron, &phi, p.current_seed());
-      p.create_secondary(u, E_electron, Particle::Type::electron);
+      p.create_secondary(p.wgt_, u, E_electron, Particle::Type::electron);
     }
 
     // TODO: Compton subshell data does not match atomic relaxation data
@@ -363,7 +364,7 @@ void sample_photon_reaction(Particle& p)
         u.z = std::sqrt(1.0 - mu*mu)*std::sin(phi);
 
         // Create secondary electron
-        p.create_secondary(u, E_electron, Particle::Type::electron);
+        p.create_secondary(p.wgt_, u, E_electron, Particle::Type::electron);
 
         // Allow electrons to fill orbital and produce auger electrons
         // and fluorescent photons
@@ -388,11 +389,11 @@ void sample_photon_reaction(Particle& p)
 
     // Create secondary electron
     Direction u = rotate_angle(p.u(), mu_electron, nullptr, p.current_seed());
-    p.create_secondary(u, E_electron, Particle::Type::electron);
+    p.create_secondary(p.wgt_, u, E_electron, Particle::Type::electron);
 
     // Create secondary positron
     u = rotate_angle(p.u(), mu_positron, nullptr, p.current_seed());
-    p.create_secondary(u, E_positron, Particle::Type::positron);
+    p.create_secondary(p.wgt_, u, E_positron, Particle::Type::positron);
 
     p.event_ = TallyEvent::ABSORB;
     p.event_mt_ = PAIR_PROD;
@@ -433,8 +434,8 @@ void sample_positron_reaction(Particle& p)
   u.z = std::sqrt(1.0 - mu*mu)*std::sin(phi);
 
   // Create annihilation photon pair traveling in opposite directions
-  p.create_secondary(u, MASS_ELECTRON_EV, Particle::Type::photon);
-  p.create_secondary(-u, MASS_ELECTRON_EV, Particle::Type::photon);
+  p.create_secondary(p.wgt_, u, MASS_ELECTRON_EV, Particle::Type::photon);
+  p.create_secondary(p.wgt_, -u, MASS_ELECTRON_EV, Particle::Type::photon);
 
   p.E_ = 0.0;
   p.alive_ = false;
@@ -567,8 +568,21 @@ void sample_photon_product(int i_nuclide, Particle& p, int* i_rx, int* i_product
 
     for (int j = 0; j < rx->products_.size(); ++j) {
       if (rx->products_[j].particle_ == Particle::Type::photon) {
+        // For fission, artificially increase the photon yield to account
+        // for delayed photons
+        double f = 1.0;
+        if (settings::delayed_photon_scaling) {
+          if (is_fission(rx->mt_)) {
+            if (nuc->prompt_photons_ && nuc->delayed_photons_) {
+              double energy_prompt = (*nuc->prompt_photons_)(p.E_);
+              double energy_delayed = (*nuc->delayed_photons_)(p.E_);
+              f = (energy_prompt + energy_delayed)/(energy_prompt);
+            }
+          }
+        }
+
         // add to cumulative probability
-        prob += (*rx->products_[j].yield_)(p.E_) * xs;
+        prob += f * (*rx->products_[j].yield_)(p.E_) * xs;
 
         *i_rx = i;
         *i_product = j;
@@ -1126,7 +1140,7 @@ void inelastic_scatter(const Nuclide& nuc, const Reaction& rx, Particle& p)
   if (std::floor(yield) == yield) {
     // If yield is integral, create exactly that many secondary particles
     for (int i = 0; i < static_cast<int>(std::round(yield)) - 1; ++i) {
-      p.create_secondary(p.u(), p.E_, Particle::Type::neutron);
+      p.create_secondary(p.wgt_, p.u(), p.E_, Particle::Type::neutron);
     }
   } else {
     // Otherwise, change weight of particle based on yield
@@ -1137,7 +1151,7 @@ void inelastic_scatter(const Nuclide& nuc, const Reaction& rx, Particle& p)
 void sample_secondary_photons(Particle& p, int i_nuclide)
 {
   // Sample the number of photons produced
-  double y_t =  p.neutron_xs_[i_nuclide].photon_prod /
+  double y_t = p.neutron_xs_[i_nuclide].photon_prod /
     p.neutron_xs_[i_nuclide].total;
   int y = static_cast<int>(y_t);
   if (prn(p.current_seed()) <= y_t - y) ++y;
@@ -1158,8 +1172,21 @@ void sample_secondary_photons(Particle& p, int i_nuclide)
     // Sample the new direction
     Direction u = rotate_angle(p.u(), mu, nullptr, p.current_seed());
 
+    // In a k-eigenvalue simulation, it's necessary to provide higher weight to
+    // secondary photons from non-fission reactions to properly balance energy
+    // release and deposition. See D. P. Griesheimer, S. J. Douglass, and M. H.
+    // Stedry, "Self-consistent energy normalization for quasistatic reactor
+    // calculations", Proc. PHYSOR, Cambridge, UK, Mar 29-Apr 2, 2020.
+    double wgt;
+    if (settings::run_mode == RunMode::EIGENVALUE && !is_fission(rx->mt_)) {
+      wgt = simulation::keff * p.wgt_;
+    } else {
+      wgt = p.wgt_;
+    }
+
     // Create the secondary photon
-    p.create_secondary(u, E, Particle::Type::photon);
+    p.create_secondary(wgt, u, E, Particle::Type::photon);
+
   }
 }
 

src/tallies/tally_scoring.cpp

@@ -259,9 +259,27 @@ double get_nuclide_neutron_heating(const Particle& p, const Nuclide& nuc,
   auto i_grid = p.neutron_xs_[i_nuclide].index_grid;
   if (i_grid < xs.threshold) return 0.0;
 
+  // Determine total kerma
   auto f = p.neutron_xs_[i_nuclide].interp_factor;
-  return (1.0 - f) * xs.value[i_grid-xs.threshold]
+  double kerma = (1.0 - f) * xs.value[i_grid-xs.threshold]
     + f * xs.value[i_grid-xs.threshold+1];
+
+  if (settings::run_mode == RunMode::EIGENVALUE) {
+    // Determine kerma for fission as (EFR + EB)*sigma_f
+    double kerma_fission = nuc.fragments_ ?
+      ((*nuc.fragments_)(p.E_last_) + (*nuc.betas_)(p.E_last_))
+      *p.neutron_xs_[i_nuclide].fission : 0.0;
+
+    // Determine non-fission kerma as difference
+    double kerma_non_fission = kerma - kerma_fission;
+
+    // Re-weight non-fission kerma by keff to properly balance energy release
+    // and deposition. See D. P. Griesheimer, S. J. Douglass, and M. H. Stedry,
+    // "Self-consistent energy normalization for quasistatic reactor
+    // calculations", Proc. PHYSOR, Cambridge, UK, Mar 29-Apr 2, 2020.
+    kerma = simulation::keff * kerma_non_fission + kerma_fission;
+  }
+  return kerma;
 }
 
 //! Helper function to obtain neutron heating [eV]
@@ -452,6 +470,51 @@ score_fission_eout(Particle& p, int i_tally, int i_score, int score_bin)
   p.filter_matches_[i_eout_filt].bins_[i_bin] = bin_energyout;
 }
 
+double get_nuclide_xs(const Particle& p, int i_nuclide, int score_bin) {
+  const auto& nuc {*data::nuclides[i_nuclide]};
+
+  // Get reaction object, or return 0 if reaction is not present
+  auto m = nuc.reaction_index_[score_bin];
+  if (m == C_NONE) return 0.0;
+  const auto& rxn {*nuc.reactions_[m]};
+
+  auto i_temp = p.neutron_xs_[i_nuclide].index_temp;
+  if (i_temp >= 0) { // Can be false due to multipole
+    // Get index on energy grid and interpolation factor
+    auto i_grid = p.neutron_xs_[i_nuclide].index_grid;
+    auto f = p.neutron_xs_[i_nuclide].interp_factor;
+
+    // Calculate interpolated cross section
+    const auto& xs {rxn.xs_[i_temp]};
+    double value;
+    if (i_grid >= xs.threshold) {
+      value = ((1.0 - f) * xs.value[i_grid-xs.threshold]
+        + f * xs.value[i_grid-xs.threshold+1]);
+    } else {
+      value = 0.0;
+    }
+
+    if (settings::run_mode == RunMode::EIGENVALUE && score_bin == HEATING_LOCAL) {
+      // Determine kerma for fission as (EFR + EGP + EGD + EB)*sigma_f
+      double kerma_fission = nuc.fragments_ ?
+        ((*nuc.fragments_)(p.E_last_) + (*nuc.betas_)(p.E_last_) +
+         (*nuc.prompt_photons_)(p.E_last_) + (*nuc.delayed_photons_)(p.E_last_))
+        * p.neutron_xs_[i_nuclide].fission : 0.0;
+
+      // Determine non-fission kerma as difference
+      double kerma_non_fission = value - kerma_fission;
+
+      // Re-weight non-fission kerma by keff to properly balance energy release
+      // and deposition. See D. P. Griesheimer, S. J. Douglass, and M. H. Stedry,
+      // "Self-consistent energy normalization for quasistatic reactor
+      // calculations", Proc. PHYSOR, Cambridge, UK, Mar 29-Apr 2, 2020.
+      value = simulation::keff * kerma_non_fission + kerma_fission;
+    }
+    return value;
+  }
+  return 0.0;
+}
+
 //! Update tally results for continuous-energy tallies with any estimator.
 //
 //! For analog tallies, the flux estimate depends on the score type so the flux
@@ -1252,40 +1315,13 @@ score_general_ce(Particle& p, int i_tally, int start_index, int filter_index,
           + std::to_string(tally.id_));
         score = 0.;
         if (i_nuclide >= 0) {
-          const auto& nuc {*data::nuclides[i_nuclide]};
-          auto m = nuc.reaction_index_[score_bin];
-          if (m == C_NONE) continue;
-          const auto& rxn {*nuc.reactions_[m]};
-          auto i_temp = p.neutron_xs_[i_nuclide].index_temp;
-          if (i_temp >= 0) { // Can be false due to multipole
-            auto i_grid = p.neutron_xs_[i_nuclide].index_grid;
-            auto f = p.neutron_xs_[i_nuclide].interp_factor;
-            const auto& xs {rxn.xs_[i_temp]};
-            if (i_grid >= xs.threshold) {
-              score = ((1.0 - f) * xs.value[i_grid-xs.threshold]
-                + f * xs.value[i_grid-xs.threshold+1]) * atom_density * flux;
-            }
-          }
+          score = get_nuclide_xs(p, i_nuclide, score_bin) * atom_density * flux;
         } else if (p.material_ != MATERIAL_VOID) {
           const Material& material {*model::materials[p.material_]};
           for (auto i = 0; i < material.nuclide_.size(); ++i) {
             auto j_nuclide = material.nuclide_[i];
             auto atom_density = material.atom_density_(i);
-            const auto& nuc {*data::nuclides[j_nuclide]};
-            auto m = nuc.reaction_index_[score_bin];
-            if (m == C_NONE) continue;
-            const auto& rxn {*nuc.reactions_[m]};
-            auto i_temp = p.neutron_xs_[j_nuclide].index_temp;
-            if (i_temp >= 0) { // Can be false due to multipole
-              auto i_grid = p.neutron_xs_[j_nuclide].index_grid;
-              auto f = p.neutron_xs_[j_nuclide].interp_factor;
-              const auto& xs {rxn.xs_[i_temp]};
-              if (i_grid >= xs.threshold) {
-                score += ((1.0 - f) * xs.value[i_grid-xs.threshold]
-                  + f * xs.value[i_grid-xs.threshold+1]) * atom_density
-                  * flux;
-              }
-            }
+            score += get_nuclide_xs(p, j_nuclide, score_bin) * atom_density * flux;
           }
         }
       }

tests/regression_tests/photon_production_fission/results_true.dat

@@ -20,50 +20,50 @@ tally 1:
 tally 2:
 2.602512E+00
 2.258176E+00
-4.394176E+08
-6.437709E+16
+4.185969E+08
+5.842526E+16
 0.000000E+00
 0.000000E+00
 2.602512E+00
 2.258176E+00
-4.394176E+08
-6.437709E+16
+4.185969E+08
+5.842526E+16
 0.000000E+00
 0.000000E+00
 0.000000E+00
 0.000000E+00
-2.921131E+06
-2.853657E+12
+2.366791E+06
+1.872101E+12
 0.000000E+00
 0.000000E+00
 0.000000E+00
 0.000000E+00
-2.921131E+06
-2.853657E+12
+2.366791E+06
+1.872101E+12
 0.000000E+00
 0.000000E+00
 tally 3:
 2.663535E+00
 2.364845E+00
-4.394176E+08
-6.437709E+16
+4.185969E+08
+5.842526E+16
 0.000000E+00
 0.000000E+00
 2.663535E+00
 2.364845E+00
-4.394176E+08
-6.437709E+16
+4.185969E+08
+5.842526E+16
 0.000000E+00
 0.000000E+00
 0.000000E+00
 0.000000E+00
-2.780823E+06
-2.586737E+12
+2.185301E+06
+1.596625E+12
 0.000000E+00
 0.000000E+00
 0.000000E+00
 0.000000E+00
-2.921131E+06
-2.853657E+12
+2.366791E+06
+1.872101E+12
 0.000000E+00
 0.000000E+00

tests/regression_tests/tallies/results_true.dat

@@ -1 +1 @@
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