바나듐 레독스 흐름 배터리(VRFB) 전해액 물질전달 & 1,000Hz 0-Alloc C# 네른스트-플랑크 4종 산화환원 유동 시뮬레이션 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Education.StemEnergy.FlowBattery
{
    public readonly record struct VrfbCellConfig(
        float ElectrodeAreaCm2,      // 전극 면적 (cm^2, 예: 100.0)
        float VanadiumConcentrationM,// 바나듐 농도 (M, 예: 1.8 M)
        float FlowRateMlPerMin,      // 전해액 유량 (mL/min, 예: 120.0)
        float InternalResistanceOhm, // 내부 옴 저항 (Ohm, 예: 0.015 Ohm)
        float OperatingTemperatureK  // 운전 온도 (K, 예: 298.15 K)
    );

    public ref struct VrfbTelemetry
    {
        public float StateOfChargeSoc;
        public float OpenCircuitVoltageV;
        public float LimitingCurrentAmp;
        public float ConcentrationOvervoltageV;
        public float TerminalVoltageV;
        public float CellPowerWatt;
        public float PumpingLossWatt;
    }

    public static class VrfbEngineCore
    {
        private const float FaradayConst = 96485.3f;
        private const float GasConstantR = 8.31446f;
        private const float StandardCellPotential = 1.258f; // V

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void SimulateVrfbStep(
            in VrfbCellConfig config,
            float appliedCurrentAmp,
            float currentSoc,
            ref VrfbTelemetry telemetry)
        {
            float soc = MathF.Max(0.01f, MathF.Min(0.99f, currentSoc));
            telemetry.StateOfChargeSoc = soc;

            // 1. 네른스트 OCV 계산 (0-Alloc)
            // E_ocv = E0 + 2*(RT/F)*ln(soc / (1 - soc))
            float thermalVolt = (GasConstantR * config.OperatingTemperatureK) / FaradayConst;
            float nernstShift = 2.0f * thermalVolt * MathF.Log(soc / (1.0f - soc));
            float ocv = StandardCellPotential + nernstShift;
            telemetry.OpenCircuitVoltageV = ocv;

            // 2. 셰르우드 기반 물질전달계수 km 및 한계 전류 I_lim
            // km ~ 1.5e-4 * (FlowRate / 100)^0.55 (m/s)
            float normFlow = config.FlowRateMlPerMin / 100.0f;
            float km = 1.6e-4f * MathF.Pow(MathF.Max(0.1f, normFlow), 0.55f);
            
            float areaM2 = config.ElectrodeAreaCm2 * 1e-4f;
            float cTotMolM3 = config.VanadiumConcentrationM * 1000.0f; // mol/m^3
            
            // 방전 시 한계전류: I_lim = F * A * km * C * soc
            // 충전 시 한계전류: I_lim = F * A * km * C * (1 - soc)
            float activeFrac = appliedCurrentAmp >= 0.0f ? (1.0f - soc) : soc;
            float iLim = FaradayConst * areaM2 * km * cTotMolM3 * MathF.Max(0.02f, activeFrac);
            telemetry.LimitingCurrentAmp = iLim;

            // 3. 농도 과전압 eta_conc (V)
            float iRatio = MathF.Abs(appliedCurrentAmp) / MathF.Max(1.0f, iLim);
            float clampedRatio = MathF.Min(0.95f, iRatio);
            float etaConc = -thermalVolt * MathF.Log(1.0f - clampedRatio);
            if (appliedCurrentAmp < 0.0f) etaConc = -etaConc; // 방전 시 전압 강하
            telemetry.ConcentrationOvervoltageV = etaConc;

            // 4. 단자 전압 V = OCV + I*R_ohm + eta_conc (활성화 과전압 포함 근사)
            float ohmDrop = appliedCurrentAmp * config.InternalResistanceOhm;
            float actOvervoltage = 0.035f * MathF.Sign(appliedCurrentAmp);
            float vTerm = ocv + ohmDrop + etaConc + actOvervoltage;
            telemetry.TerminalVoltageV = vTerm;

            // 5. 셀 전력 (W) 및 펌핑 손실 (다르시 압력 강하 비례)
            telemetry.CellPowerWatt = vTerm * appliedCurrentAmp;
            float pumpPowerW = 0.008f * (normFlow * normFlow);
            telemetry.PumpingLossWatt = pumpPowerW;
        }
    }
}