초고온가스로(VHTR) TRISO 삼중피복 핵연료 SiC 인장 과압 파괴 & 1,000Hz 0-Alloc C# 핵분열 생성물 방출 방어 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Nuclear.TrisoFuel
{
    /// 

    /// TRISO 피복 입자 SiC 층 과압 인장 응력 및 와이블 파손율 평가 엔진 (0-Alloc C#)
    /// 
    public ref struct TrisoFuelRuptureEngine
    {
        private const double GasConstantR = 8.314462618; // J/(mol*K)
        private const double WeibullModulusM = 8.0;      // SiC 와이블 계수
        private const double CharacteristicStrengthMPa = 850.0; // 특성 인장강도

        private readonly double _sicInnerRadiusUm;      // SiC 내경 (~310 um)
        private readonly double _sicOuterRadiusUm;      // SiC 외경 (~345 um)
        private readonly double _bufferFreeVolumeM3;    // 버퍼 공극 체적
        private readonly double _dt;

        private double _internalFissionGasPressurePa;   // 내부 가스압
        private double _sicHoopStressMPa;               // SiC 원주 인장 응력
        private double _cumulativeFailureProbability;   // 파손 확률

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public TrisoFuelRuptureEngine(
            double sicInnerRadiusUm = 310.0,
            double sicOuterRadiusUm = 345.0,
            double bufferPorosity = 0.5,
            double dt = 0.001)
        {
            _sicInnerRadiusUm = sicInnerRadiusUm;
            _sicOuterRadiusUm = sicOuterRadiusUm;
            _dt = dt;

            // 버퍼 다공성 공극 체적 근사: V_free = (4/3)*pi*(R_buf^3 - R_ker^3) * porosity
            double rBufM = 310e-6;
            double rKerM = 250e-6;
            _bufferFreeVolumeM3 = (4.0 / 3.0) * Math.PI * (Math.Pow(rBufM, 3.0) - Math.Pow(rKerM, 3.0)) * bufferPorosity;
            _internalFissionGasPressurePa = 0.0;
            _sicHoopStressMPa = 0.0;
            _cumulativeFailureProbability = 1e-9;
        }

        /// 

        /// 핵연료 연소도(FIMA %) 및 커널 중심 온도(K)로부터 기체 압력과 SiC 응력을 평가 (1,000Hz)
        /// 
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void UpdateFuelStep(
            double burnupFimaPercent,
            double fuelTemperatureKelvin,
            double externalCoolantPressureMPa,
            out double internalPressureMPa,
            out double hoopStressMPa,
            out double failureProbability,
            out bool isSiCRuptureAlert)
        {
            // 핵분열 기체 생성 몰수: n_gas ~ FIMA * moles_U * yield (Xe+Kr yield ~ 0.3, CO yield ~ 0.4)
            double molesFissionGas = (burnupFimaPercent * 0.01) * 3.5e-8 * 0.7;

            // 이상기체 상태방정식 내부 압력: P_int = n * R * T / V_free
            _internalFissionGasPressurePa = (molesFissionGas * GasConstantR * fuelTemperatureKelvin) / Math.Max(_bufferFreeVolumeM3, 1e-18);
            internalPressureMPa = _internalFissionGasPressurePa * 1e-6;

            // 구형 두꺼운 실린더 라메 응력 공식
            double rIn3 = Math.Pow(_sicInnerRadiusUm, 3.0);
            double rOut3 = Math.Pow(_sicOuterRadiusUm, 3.0);
            double pInt = internalPressureMPa;
            double pExt = externalCoolantPressureMPa;

            double numerator = (pInt * (2.0 * rIn3 + rOut3)) - (3.0 * pExt * rOut3);
            double denominator = 2.0 * (rOut3 - rIn3);
            _sicHoopStressMPa = numerator / Math.Max(denominator, 1e-3);

            // IPyC 조사 수축에 의한 압축 완화 응력 (~ -150 MPa)
            double irradiationReliefMPa = Math.Min(180.0, burnupFimaPercent * 15.0);
            double effectiveTensileStressMPa = Math.Max(0.0, _sicHoopStressMPa - irradiationReliefMPa);

            // 와이블 누적 파괴 확률
            double stressRatio = effectiveTensileStressMPa / CharacteristicStrengthMPa;
            _cumulativeFailureProbability = 1.0 - Math.Exp(-Math.Log(2.0) * Math.Pow(stressRatio, WeibullModulusM));

            // 안전 한계치 (파손 확률 10^-4 초과 시 조기 방출 경보)
            isSiCRuptureAlert = _cumulativeFailureProbability > 1e-4;

            hoopStressMPa = effectiveTensileStressMPa;
            failureProbability = _cumulativeFailureProbability;
        }

        public double SicHoopStressMPa => _sicHoopStressMPa;
        public double CumulativeFailureProbability => _cumulativeFailureProbability;
    }
}