Spaces:
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Sleeping
| """ | |
| Cryogenic Pump Cycle Analysis - Performance-Cached Version using CoolProp | |
| This module calculates mass flow rate based on pump cycle analysis for cryogenic fluids. | |
| Converted from VBA code that used REFPROP, now using CoolProp as a free alternative. | |
| Performance optimizations over cycle2mdot_updated.py (the base model): | |
| 1. Fluid property cache (_get_cached_fluid_props): | |
| cp/cv ratio (k), critical flow factor (cf), and molecular weight (mwt) are | |
| computed once per fluid at standard conditions (1 atm, 15 °C) and stored in | |
| _FLUID_PROP_CACHE. Avoids 3 repeated CoolProp evaluations per call to | |
| flow_RF_kgpm(). | |
| 2. 1D isentropic P,S flash table (_build_ps_table_1d): | |
| The slow CoolProp P,S flash calls (d2hat, h2hat in the flow formula) for the | |
| DCV constant-entropy path are pre-computed as a smooth 5000-point 1D lookup | |
| table h(P) and d(P) at fixed upstream entropy. Linear interpolation error | |
| scales as O(ΔP²); 5000 points yields ~0.00002% per-step error. | |
| The fast P,T upstream flash calls and the exact flow formula (including the | |
| zero at P1≈P2) are preserved. | |
| 3. Pre-computed constant upstream states: | |
| Four values that are constant for the entire simulation are computed once | |
| before the main loop: _s_exit, _h1_exit_J (DCV upstream entropy and | |
| enthalpy), _s_tank, _h1_tank_J (ICV-reverse upstream entropy and enthalpy). | |
| 4. Inline cached flow helpers (_flow_core, _cached_flow_1d): | |
| _flow_core extracts the shared real-gas flow formula into a reusable | |
| function. _cached_flow_1d wraps it with 1D table np.interp lookups, | |
| completely bypassing CoolProp for constant-entropy flow paths. | |
| 5. DCV leak rate branching logic: | |
| In the main loop, DCV leak rate now branches: | |
| - Pexit > pc (dominant path): uses _cached_flow_1d (table lookup, no | |
| CoolProp calls). | |
| - Pexit <= pc (reverse flow): falls back to direct flow_RF_kgpm() using | |
| Tc_K (chamber temperature) as upstream, instead of Tout_K. | |
| Initial DCV leak rate also uses _cached_flow_1d instead of flow_RF_kgpm. | |
| 6. ICV initial upstream temperature correction: | |
| At initialisation when pc > Ptank, the ICV upstream temperature uses Tc_K | |
| (chamber temperature) instead of Tout_K (discharge temperature) from the | |
| base model. | |
| 7. Cached convection heat transfer: | |
| free_conv_2cyl_Wpm() (~8 CoolProp calls per invocation) is only recomputed | |
| when the chamber temperature changes by more than 2 K. The result is stored | |
| in _Qconv_base and reused otherwise. Applied both in the pre-loop | |
| initialisation and in every timestep of the main loop. | |
| Author: Converted from VBA original | |
| Date: 2025 | |
| """ | |
| import numpy as np | |
| from typing import Optional, Tuple, List, Dict, Any | |
| import time | |
| # CoolProp import | |
| try: | |
| from CoolProp.CoolProp import PropsSI | |
| COOLPROP_AVAILABLE = True | |
| except ImportError: | |
| COOLPROP_AVAILABLE = False | |
| print("Warning: CoolProp not installed. Install with: pip install CoolProp") | |
| # Constants | |
| PI = np.pi | |
| STEFAN_BOLTZMANN = 5.67e-8 # W/m²/K⁴ | |
| RU = 8314.0 # J/kmol/K, universal gas constant | |
| def coolprop_fluid_name(fluid: str) -> str: | |
| """Convert common fluid names to CoolProp format.""" | |
| fluid_map = { | |
| 'h2': 'Hydrogen', | |
| 'hydrogen': 'Hydrogen', | |
| 'he': 'Helium', | |
| 'helium': 'Helium', | |
| 'n2': 'Nitrogen', | |
| 'nitrogen': 'Nitrogen', | |
| 'o2': 'Oxygen', | |
| 'oxygen': 'Oxygen', | |
| 'air': 'Air', | |
| 'ar': 'Argon', | |
| 'argon': 'Argon', | |
| 'co2': 'CarbonDioxide', | |
| 'ch4': 'Methane', | |
| 'methane': 'Methane', | |
| } | |
| return fluid_map.get(fluid.lower(), fluid) | |
| def refprop(prop: str, fluid: str, input_type: str = "pt", | |
| units: str = "si", val1: float = 0.101325, val2: float = 300.0) -> float: | |
| """ | |
| CoolProp wrapper mimicking REFPROP function interface. | |
| Parameters: | |
| ----------- | |
| prop : str | |
| Property to calculate (t, p, d, h, s, cp, cv, vis, tcx, etc.) | |
| fluid : str | |
| Fluid name | |
| input_type : str | |
| Input specification type (pt, pq, pd, ph, ps, ds) | |
| units : str | |
| Unit system (si) | |
| val1, val2 : float | |
| Input values (pressure in MPa for 'p', temperature in K for 't', etc.) | |
| Returns: | |
| -------- | |
| float : Calculated property value | |
| """ | |
| if not COOLPROP_AVAILABLE: | |
| raise ImportError("CoolProp is required but not installed") | |
| fluid_cp = coolprop_fluid_name(fluid) | |
| # Property mapping from REFPROP names to CoolProp names | |
| prop_map = { | |
| 't': 'T', # Temperature, K | |
| 'p': 'P', # Pressure, Pa (need to convert from MPa) | |
| 'd': 'D', # Density, kg/m³ | |
| 'h': 'H', # Enthalpy, J/kg (need to convert to kJ/kg) | |
| 's': 'S', # Entropy, J/kg/K (need to convert to kJ/kg/K) | |
| 'e': 'U', # Internal energy, J/kg (need to convert to kJ/kg) | |
| 'cp': 'C', # Specific heat at constant pressure, J/kg/K (convert to kJ/kg/K) | |
| 'cv': 'O', # Specific heat at constant volume, J/kg/K (convert to kJ/kg/K) | |
| 'vis': 'V', # Dynamic viscosity, Pa·s (convert to µPa·s) | |
| 'kv': 'V', # Kinematic viscosity (need density too) | |
| 'tcx': 'L', # Thermal conductivity, W/m/K (convert to mW/m/K) | |
| 'm': 'M', # Molar mass, kg/mol (convert to g/mol) | |
| 'pc': 'PCRIT', # Critical pressure, Pa (convert to MPa) | |
| 'tc': 'TCRIT', # Critical temperature, K | |
| 'prandtl': 'PRANDTL', # Prandtl number | |
| 'beta': 'ISOBARIC_EXPANSION_COEFFICIENT', # 1/K | |
| 'bs': 'ISOTHERMAL_COMPRESSIBILITY', # Bulk modulus (inverse) | |
| 'qmass': 'Q', # Quality (mass basis) | |
| 'heatvapz': 'H', # Heat of vaporization (need special handling) | |
| 'phase': 'Phase', # Phase identifier | |
| } | |
| # Input type mapping | |
| input_map = { | |
| 'pt': ('P', 'T'), # Pressure, Temperature | |
| 'pq': ('P', 'Q'), # Pressure, Quality | |
| 'pd': ('P', 'D'), # Pressure, Density | |
| 'ph': ('P', 'H'), # Pressure, Enthalpy | |
| 'ps': ('P', 'S'), # Pressure, Entropy | |
| 'ds': ('D', 'S'), # Density, Entropy | |
| 'td': ('T', 'D'), # Temperature, Density | |
| 'de': ('D', 'U'), # Density, Internal energy (val2 in kJ/kg) | |
| 'dh': ('D', 'H'), # Density, Enthalpy (val2 in kJ/kg) | |
| } | |
| prop_lower = prop.lower() | |
| # Handle special properties that don't need state inputs | |
| if prop_lower == 'm': | |
| return PropsSI('M', fluid_cp) * 1000 # Convert kg/mol to g/mol | |
| elif prop_lower == 'pc': | |
| return PropsSI('PCRIT', fluid_cp) / 1e6 # Convert Pa to MPa | |
| elif prop_lower == 'tc': | |
| return PropsSI('TCRIT', fluid_cp) # K | |
| # Get CoolProp property name | |
| cp_prop = prop_map.get(prop_lower, prop.upper()) | |
| # Get input specification | |
| if input_type.lower() not in input_map: | |
| raise ValueError(f"Unknown input type: {input_type}") | |
| inp1_type, inp2_type = input_map[input_type.lower()] | |
| # Convert input values to CoolProp units (SI base) | |
| # CoolProp uses Pa, J, K as base units | |
| if inp1_type == 'P': | |
| inp1_val = val1 * 1e6 # MPa to Pa | |
| elif inp1_type == 'H': | |
| inp1_val = val1 * 1000 # kJ/kg to J/kg | |
| elif inp1_type == 'S': | |
| inp1_val = val1 * 1000 # kJ/kg/K to J/kg/K | |
| else: | |
| inp1_val = val1 | |
| if inp2_type == 'P': | |
| inp2_val = val2 * 1e6 # MPa to Pa | |
| elif inp2_type == 'H': | |
| inp2_val = val2 * 1000 # kJ/kg to J/kg | |
| elif inp2_type == 'S': | |
| inp2_val = val2 * 1000 # kJ/kg/K to J/kg/K | |
| elif inp2_type == 'U': | |
| inp2_val = val2 * 1000 # kJ/kg to J/kg | |
| else: | |
| inp2_val = val2 | |
| # Special handling for heat of vaporization | |
| if prop_lower == 'heatvapz': | |
| try: | |
| h_liq = PropsSI('H', inp1_type, inp1_val, 'Q', 0, fluid_cp) | |
| h_vap = PropsSI('H', inp1_type, inp1_val, 'Q', 1, fluid_cp) | |
| return (h_vap - h_liq) / 1000 # Convert J/kg to kJ/kg | |
| except: | |
| return 0.0 | |
| # Special handling for bulk modulus (isothermal) | |
| if prop_lower == 'bs': | |
| try: | |
| # Bulk modulus = 1 / isothermal compressibility | |
| # K = -V * (dP/dV)_T = rho * (dP/drho)_T | |
| kappa_T = PropsSI('ISOTHERMAL_COMPRESSIBILITY', inp1_type, inp1_val, inp2_type, inp2_val, fluid_cp) | |
| return 1.0 / kappa_T / 1e6 # Convert Pa to MPa | |
| except: | |
| return 1000.0 # Default fallback | |
| # Special handling for kinematic viscosity | |
| if prop_lower == 'kv': | |
| try: | |
| mu = PropsSI('V', inp1_type, inp1_val, inp2_type, inp2_val, fluid_cp) # Pa·s | |
| rho = PropsSI('D', inp1_type, inp1_val, inp2_type, inp2_val, fluid_cp) # kg/m³ | |
| return mu / rho * 1e4 # Convert m²/s to cm²/s (stokes) | |
| except: | |
| return 0.0 | |
| # Get the property from CoolProp | |
| try: | |
| result = PropsSI(cp_prop, inp1_type, inp1_val, inp2_type, inp2_val, fluid_cp) | |
| except Exception as e: | |
| print(f"CoolProp error: {e}") | |
| return 0.0 | |
| # Convert output to REFPROP-compatible units | |
| if prop_lower == 'h': | |
| return result / 1000 # J/kg to kJ/kg | |
| elif prop_lower == 'e': | |
| return result / 1000 # J/kg to kJ/kg | |
| elif prop_lower == 's': | |
| return result / 1000 # J/kg/K to kJ/kg/K | |
| elif prop_lower in ['cp', 'cv']: | |
| return result / 1000 # J/kg/K to kJ/kg/K | |
| elif prop_lower == 'vis': | |
| return result * 1e6 # Pa·s to µPa·s | |
| elif prop_lower == 'tcx': | |
| return result * 1000 # W/m/K to mW/m/K | |
| elif prop_lower == 'p': | |
| return result / 1e6 # Pa to MPa | |
| else: | |
| return result | |
| def subcool_K(pvap_barg: float, pliq_sat_barg: float, fluid: str = "h2") -> float: | |
| """ | |
| Returns the subcool in K for a fluid. | |
| Parameters: | |
| ----------- | |
| pvap_barg : float | |
| Vapor pressure in barg | |
| pliq_sat_barg : float | |
| Liquid saturation pressure in barg | |
| fluid : str | |
| Fluid name | |
| Returns: | |
| -------- | |
| float : Subcool temperature in K | |
| """ | |
| tvap = refprop("t", fluid, "pq", "si", pvap_barg / 10 + 0.101325, 0) | |
| tliq = refprop("t", fluid, "pq", "si", pliq_sat_barg / 10 + 0.101325, 0) | |
| return tvap - tliq | |
| def kv_from_Cd_and_RO_dia(area_equiv_d_mm: float, Cd: float = 0.61) -> float: | |
| """ | |
| Calculate Kv from discharge coefficient and area-equivalent diameter. | |
| Derived from fundamental equations. See Eq 7 in memo | |
| "Compressed hydrogen fill models," March 2023. | |
| Parameters: | |
| ----------- | |
| area_equiv_d_mm : float | |
| Area equivalent diameter in mm | |
| Cd : float | |
| Discharge coefficient (0.61 for sharp orifice, 0.99 for venturi) | |
| Returns: | |
| -------- | |
| float : Kv in m³/hr | |
| """ | |
| d_mm = area_equiv_d_mm | |
| area = PI * (d_mm / 1000) ** 2 / 4 # m² | |
| k = 1 / Cd ** 2 # Loss factor | |
| return 3.6e4 * area * np.sqrt(2 / k) # m³/hr | |
| def fluid_phase_qual(P_barg: float, den_kgm3: float, fluid: str = "h2") -> float: | |
| """ | |
| Returns quality for given pressure and density. | |
| Parameters: | |
| ----------- | |
| P_barg : float | |
| Pressure in barg | |
| den_kgm3 : float | |
| Density in kg/m³ | |
| fluid : str | |
| Fluid name | |
| Returns: | |
| -------- | |
| float : Quality (0 = liquid, 1 = vapor, between = two-phase) | |
| """ | |
| pc = refprop("pc", fluid) # MPa, critical pressure | |
| tc = refprop("tc", fluid) # K, critical temperature | |
| p_MPa = P_barg / 10 + 0.101325 | |
| try: | |
| T_K = refprop("t", fluid, "pd", "si", p_MPa, den_kgm3) | |
| except: | |
| return 0.0 | |
| if T_K < tc: # Subcritical | |
| try: | |
| dliq = refprop("d", fluid, "pq", "si", p_MPa, 0) | |
| dvap = refprop("d", fluid, "pq", "si", p_MPa, 1) | |
| if den_kgm3 > dliq: | |
| return 0.0 # Pure liquid | |
| elif den_kgm3 < dvap: | |
| return 1.0 # Pure vapor | |
| else: # Two-phase zone | |
| return refprop("qmass", fluid, "pd", "si", p_MPa, den_kgm3) | |
| except: | |
| return 0.0 | |
| elif P_barg > pc * 10 - 1.01325: # Above critical T and P | |
| return 0.0 # Dense supercritical fluid | |
| else: | |
| return 1.0 # Light supercritical fluid (gas) | |
| def mixture_pump_prop(prop: str, Pin_barg: float = 2.0, Pout_barg: float = 700.0, | |
| quality: float = 0.0, comp_eff: float = 0.7, | |
| fluid: str = "h2", Tif_in_is_SC_K: float = 0.0, | |
| throttling: int = 1) -> float: | |
| """ | |
| Returns thermo property after compressing a mixture of given quality. | |
| Can also do expansion with real fluid if inlet P > outlet P. | |
| Parameters: | |
| ----------- | |
| prop : str | |
| Property to calculate (d, s, h, t, qmass) | |
| Pin_barg : float | |
| Inlet pressure in barg | |
| Pout_barg : float | |
| Outlet pressure in barg | |
| quality : float | |
| Inlet quality (if subcritical) | |
| comp_eff : float | |
| Compression/expansion efficiency | |
| fluid : str | |
| Fluid name | |
| Tif_in_is_SC_K : float | |
| Temperature if supercritical (required if P > Pc) | |
| throttling : int | |
| 1 = throttling (h=const), else = turbine/piston with efficiency | |
| Returns: | |
| -------- | |
| float : Calculated property value | |
| """ | |
| Tin = Tif_in_is_SC_K | |
| pcf = refprop("pc", fluid) # MPa, critical pressure | |
| piMPa = Pin_barg / 10 + 0.101325 | |
| poMPa = Pout_barg / 10 + 0.101325 | |
| sg = 1.0 if piMPa < poMPa else -1.0 | |
| if piMPa > poMPa: # Expansion | |
| if Tin <= 0: | |
| return 0.0 | |
| qq = fluid_phase_qual(Pin_barg, Tin) | |
| single_phase = (qq == 0.0 or qq == 1.0) | |
| if piMPa >= pcf or single_phase: # Supercritical or single phase | |
| s0 = refprop("s", fluid, "pt", "si", piMPa, Tin) | |
| h0 = refprop("h", fluid, "pt", "si", piMPa, Tin) | |
| hs = refprop("h", fluid, "ps", "si", poMPa, s0) | |
| if throttling == 1: | |
| ha = h0 # Throttling: constant enthalpy | |
| else: | |
| ha = h0 - comp_eff * (h0 - hs) # Expansion with efficiency | |
| else: # Compression (or expansion in two-phase) | |
| if Tin <= 0: # Use "pq" method | |
| s0 = refprop("s", fluid, "pq", "si", piMPa, quality) | |
| h0 = refprop("h", fluid, "pq", "si", piMPa, quality) | |
| else: # Use "pt" method | |
| s0 = refprop("s", fluid, "pt", "si", piMPa, Tin) | |
| h0 = refprop("h", fluid, "pt", "si", piMPa, Tin) | |
| hs = refprop("h", fluid, "ps", "si", poMPa, s0) | |
| ha = h0 + sg * (hs - h0) / comp_eff | |
| if prop.lower() == "qmass": | |
| den = refprop("d", fluid, "ph", "si", poMPa, ha) | |
| return fluid_phase_qual(Pout_barg, den, fluid) | |
| else: | |
| return refprop(prop, fluid, "ph", "si", poMPa, ha) | |
| def flow_RF_kgpm(p1_barg: float, p2_barg: float, Tupstream_C: float, | |
| GasKv: float, fluid: str = "H2", RealGas: int = 1, | |
| LiqSubcool_K: float = 0.0) -> float: | |
| """ | |
| Calculate mass flow rate using real fluid properties. | |
| Based on compressible flow thermodynamics. See memo | |
| "Compressed Hydrogen Fill Models.docx" | |
| Parameters: | |
| ----------- | |
| p1_barg : float | |
| Upstream pressure in barg | |
| p2_barg : float | |
| Downstream pressure in barg | |
| Tupstream_C : float | |
| Upstream temperature in °C | |
| GasKv : float | |
| Orifice coefficient in m³/hr | |
| fluid : str | |
| Fluid name | |
| RealGas : int | |
| 1 = real gas, else = ideal gas | |
| LiqSubcool_K : float | |
| Liquid subcool in K | |
| Returns: | |
| -------- | |
| float : Mass flow rate in kg/min | |
| """ | |
| if abs(p1_barg - p2_barg) < 0.0001: | |
| return 0.0 | |
| # Determine flow direction | |
| sg = 1 | |
| Phigh = p1_barg | |
| Plow = p2_barg | |
| if p2_barg > p1_barg: | |
| Phigh = p2_barg | |
| Plow = p1_barg | |
| sg = -1 | |
| Phigha = Phigh + 1.01325 # bara | |
| Plowa = Plow + 1.01325 # bara | |
| T_K = Tupstream_C + 273.15 - LiqSubcool_K | |
| rho0 = 1000.0 # kg/m³, water density (Kv definition) | |
| p0 = 1.0 # bar (Kv definition) | |
| # Cached specific heat ratio at 1 atm, 15 deg C (constant per fluid) | |
| _props = _get_cached_fluid_props(fluid) | |
| k = _props["k"] | |
| cf = _props["cf"] | |
| pc = Phigha * cf # Critical pressure | |
| if RealGas == 1: # Real gas properties | |
| p2hat = max(Plowa, pc) # Throat pressure (sonic transition) | |
| h1 = refprop("h", fluid, "pt", "si", Phigha / 10, T_K) * 1000 # J/kg | |
| s1 = refprop("s", fluid, "pt", "si", Phigha / 10, T_K) # kJ/kg/K | |
| # Downstream/throat properties (isentropic) | |
| d2hat = refprop("d", fluid, "ps", "si", p2hat / 10, s1) | |
| h2hat = refprop("h", fluid, "ps", "si", p2hat / 10, s1) * 1000 # J/kg | |
| dh = h1 - h2hat | |
| if dh < 0: | |
| dh = 0.0 | |
| mdot = GasKv * d2hat * np.sqrt(rho0 / 1e5 / p0) * np.sqrt(dh) # kg/hr | |
| else: # Ideal gas | |
| mwt = _props["mwt"] | |
| Rgas = 8314.0 / mwt # J/kg/K | |
| if Plowa > pc: # Subcritical | |
| pratio = Plowa / Phigha | |
| mdot = np.sqrt(k / (k - 1) / Rgas / T_K) * pratio ** (1 / k) | |
| mdot *= np.sqrt(1 - pratio ** ((k - 1) / k)) | |
| else: # Supercritical (choked) | |
| mdot = np.sqrt(k / 2 / Rgas / T_K * (2 / (k + 1)) ** ((k + 1) / (k - 1))) | |
| mdot = mdot * GasKv * (Phigha * 1e5) / 10 # kg/hr | |
| return sg * mdot / 60 # kg/min | |
| # ============================================================================= | |
| # PERFORMANCE: Cached fluid properties and valve flow lookup tables | |
| # ============================================================================= | |
| _FLUID_PROP_CACHE = {} | |
| def _get_cached_fluid_props(fluid: str) -> dict: | |
| """Cache heat capacity ratio and related constants at standard conditions. | |
| cp/cv is computed at 1 atm, 15 deg C -- constant for a given fluid. | |
| Called once per fluid, then reused across all simulations. | |
| """ | |
| key = fluid.lower() | |
| if key not in _FLUID_PROP_CACHE: | |
| cp = refprop("cp", fluid, "pt", "si", 0.101325, 273.15 + 15) | |
| cv = refprop("cv", fluid, "pt", "si", 0.101325, 273.15 + 15) | |
| k = cp / cv | |
| _FLUID_PROP_CACHE[key] = { | |
| "k": k, | |
| "cf": (2 / (k + 1)) ** (k / (k - 1)), | |
| "mwt": refprop("m", fluid), | |
| } | |
| return _FLUID_PROP_CACHE[key] | |
| def _build_ps_table_1d(s_fixed: float, P_range_MPa: Tuple[float, float], | |
| fluid: str, n: int = 200 | |
| ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: | |
| """1D isentropic property table: h(P) and d(P) at fixed entropy. | |
| Used for downstream lookups when upstream entropy is constant: | |
| - DCV: s_exit = s(Pexit, Tout_K) is constant | |
| - ICV reverse: s_tank = s(Ptank, Tin_K) is constant | |
| Args: | |
| s_fixed: Fixed entropy [kJ/kg/K] | |
| P_range_MPa: (P_min, P_max) pressure range [MPa] | |
| fluid: Fluid name | |
| n: Grid resolution | |
| Returns: | |
| (P_grid_MPa, h_table_kJkg, d_table_kgm3) | |
| """ | |
| P_lo, P_hi = P_range_MPa | |
| P_grid = np.linspace(P_lo, P_hi, n) | |
| h_tbl = np.full(n, np.nan) | |
| d_tbl = np.full(n, np.nan) | |
| for i, P_val in enumerate(P_grid): | |
| try: | |
| h_tbl[i] = refprop("h", fluid, "ps", "si", P_val, s_fixed) | |
| d_tbl[i] = refprop("d", fluid, "ps", "si", P_val, s_fixed) | |
| except Exception: | |
| pass | |
| # Fill NaN gaps by nearest-neighbor interpolation | |
| valid = ~np.isnan(h_tbl) | |
| if np.sum(valid) >= 2: | |
| h_tbl = np.interp(P_grid, P_grid[valid], h_tbl[valid]) | |
| d_tbl = np.interp(P_grid, P_grid[valid], d_tbl[valid]) | |
| elif np.sum(valid) == 1: | |
| h_tbl[:] = h_tbl[valid][0] | |
| d_tbl[:] = d_tbl[valid][0] | |
| return P_grid, h_tbl, d_tbl | |
| def composite_thermal_conductivity(composite_type: int, k1: float, vf1: float, k2: float) -> float: | |
| """ | |
| Calculate effective thermal conductivity of a two-material composite. | |
| Parameters: | |
| ----------- | |
| composite_type : int | |
| 1 = series, 2 = parallel, 3 = isotropic mixture, 4 = spherical inclusion | |
| k1 : float | |
| Thermal conductivity of material 1 | |
| vf1 : float | |
| Volume fraction of material 1 | |
| k2 : float | |
| Thermal conductivity of material 2 | |
| Returns: | |
| -------- | |
| float : Effective thermal conductivity in W/m/K | |
| """ | |
| vf2 = 1 - vf1 | |
| if composite_type == 1: # Series | |
| return 1 / (vf1 / k1 + vf2 / k2) | |
| elif composite_type == 2: # Parallel | |
| return vf1 * k1 + vf2 * k2 | |
| elif composite_type == 3: # Isotropic (geometric mean) | |
| return k1 ** vf1 * k2 ** vf2 | |
| elif composite_type == 4: # Maxwell-Eucken (spherical inclusion) | |
| top = k1 + 2 * k2 + 2 * vf1 * (k1 - k2) | |
| bot = k1 + 2 * k2 - vf1 * (k1 - k2) | |
| return k2 * top / bot | |
| else: | |
| return 0.0 | |
| def mean_free_path_meter(gas_name: str, P_micronHg: float, T_K: float) -> float: | |
| """ | |
| Calculate mean free path of a gas. | |
| Reference: R. Barron, Cryogenic systems, McGraw Hill, 1966 | |
| Parameters: | |
| ----------- | |
| gas_name : str | |
| Gas name | |
| P_micronHg : float | |
| Pressure in microns of Hg (mTorr) | |
| T_K : float | |
| Temperature in K | |
| Returns: | |
| -------- | |
| float : Mean free path in meters | |
| """ | |
| p_MPa = P_micronHg / 1000 / 760 * 0.101325 | |
| mwt = refprop("m", gas_name, "pt", "si", p_MPa, T_K) | |
| mu = refprop("vis", gas_name, "pt", "si", p_MPa, T_K) / 1e6 # Pa·s | |
| return 3 * mu / (p_MPa * 1e6) * np.sqrt(PI * RU * T_K / 8 / mwt) | |
| def molecular_cond_WpmK(T_K: float, fluid: str = "air") -> float: | |
| """ | |
| Molecular conductivity of gases when mean free path is ~10% of relevant length scale. | |
| Uses Chapman-Enskog kinetic theory with Lennard-Jones parameters. | |
| Reference: R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, | |
| 2nd Ed, John Wiley & Sons, New York, 2007. | |
| At low pressures, thermal conductivity does not depend on pressure because | |
| heat transfer is determined by particle collisions between enclosures, | |
| not among gas molecules. | |
| Parameters: | |
| ----------- | |
| T_K : float | |
| Temperature in Kelvin | |
| fluid : str | |
| Fluid name ('air', 'n2', 'h2', 'he', or others) | |
| Returns: | |
| -------- | |
| float : Thermal conductivity in W/m/K | |
| """ | |
| # Lennard-Jones parameters (epsilon/k and sigma) from BSL Table E.1 | |
| fluid_upper = fluid.upper() | |
| if fluid_upper == "AIR": | |
| ek = 97.0 # epsilon/k_B in K | |
| sigma = 3.617 # collision diameter in Angstrom | |
| elif fluid_upper == "N2" or fluid_upper == "NITROGEN": | |
| ek = 99.8 | |
| sigma = 3.667 | |
| elif fluid_upper == "H2" or fluid_upper == "HYDROGEN": | |
| ek = 38.0 | |
| sigma = 2.915 | |
| elif fluid_upper == "HE" or fluid_upper == "HELIUM": | |
| ek = 10.2 | |
| sigma = 2.576 | |
| elif fluid_upper == "O2" or fluid_upper == "OXYGEN": | |
| ek = 113.0 | |
| sigma = 3.433 | |
| elif fluid_upper == "AR" or fluid_upper == "ARGON": | |
| ek = 124.0 | |
| sigma = 3.418 | |
| elif fluid_upper == "CO2" or fluid_upper == "CARBONDIOXIDE": | |
| ek = 190.0 | |
| sigma = 3.996 | |
| elif fluid_upper == "CH4" or fluid_upper == "METHANE": | |
| ek = 137.0 | |
| sigma = 3.822 | |
| else: | |
| # Estimate from critical properties (BSL p. 26) | |
| tcr = refprop("tc", fluid) # K, critical temp | |
| pcr = refprop("pc", fluid) * 10 / 1.01325 # atm, critical pressure | |
| ek = 0.77 * tcr | |
| sigma = 2.44 * (tcr / pcr) ** (1/3) | |
| # Reduced temperature | |
| Tstar = T_K / ek | |
| # Collision integral for viscosity and thermal conductivity (BSL Table E.2) | |
| # Neufeld-Janzen-Aziz correlation | |
| omega = (1.16145 / Tstar**0.14874 + | |
| 0.52487 / np.exp(0.7732 * Tstar) + | |
| 2.16178 / np.exp(2.43787 * Tstar)) | |
| # Molecular weight | |
| mwt = refprop("m", fluid) # g/mol | |
| # Ideal gas heat capacities (monatomic basis) | |
| Cv = 3/2 * RU / mwt # J/kg/K | |
| cp = 5/2 * RU / mwt # J/kg/K | |
| # Dynamic viscosity (Chapman-Enskog for monatomic gases) | |
| # mu = 2.6693e-5 * sqrt(M*T) / sigma^2 / omega [g/cm/s] | |
| mu_cgs = 2.6693e-5 * np.sqrt(mwt * T_K) / sigma**2 / omega # g/cm/s | |
| mu_SI = mu_cgs / 10 # Convert to kg/m/s (Pa.s) | |
| # Thermal conductivity (BSL p. 276) | |
| if fluid_upper in ["HE", "HELIUM", "AR", "ARGON"]: | |
| # Monatomic gas | |
| tcond = 5/2 * Cv * mu_SI # W/m/K | |
| else: | |
| # Polyatomic gas (modified Eucken correlation) | |
| tcond = (cp + 5/4 * RU / mwt) * mu_SI # W/m/K | |
| return tcond | |
| def free_conv_2cyl_Wpm(Di_m: float, Ti_K: float, Do_m: float, To_K: float, | |
| p_Pa_abs: float = 101325, fluid: str = "air") -> float: | |
| """ | |
| Free convection between two infinitely long horizontal cylinders. | |
| Reference: Incropera & DeWitt, Fundamentals of Heat and Mass Transfer, | |
| 2nd Ed, 1985, p.441 | |
| Parameters: | |
| ----------- | |
| Di_m, Ti_K : float | |
| Inner cylinder diameter (m) and temperature (K) | |
| Do_m, To_K : float | |
| Outer cylinder diameter (m) and temperature (K) | |
| p_Pa_abs : float | |
| Absolute pressure in Pa | |
| fluid : str | |
| Fluid name | |
| Returns: | |
| -------- | |
| float : Heat transfer rate in W/m | |
| """ | |
| Tavg = (Ti_K + To_K) / 2 | |
| pMPa = p_Pa_abs / 1e6 | |
| Gap = (Do_m - Di_m) / 2 | |
| g = 9.80665 | |
| cp = refprop("cp", fluid, "pt", "si", pMPa, Tavg) # kJ/kg/K | |
| den = refprop("d", fluid, "pt", "si", pMPa, Tavg) | |
| Pr = refprop("prandtl", fluid, "pt", "si", pMPa, Tavg) | |
| nu = refprop("kv", fluid, "pt", "si", pMPa, Tavg) / 1e4 # m²/s | |
| tc = refprop("tcx", fluid, "pt", "si", pMPa, Tavg) / 1000 # W/m/K | |
| beta = refprop("beta", fluid, "pt", "si", pMPa, Tavg) # 1/K | |
| # Rayleigh number | |
| Ra = g * beta * den ** 2 * cp * abs(Ti_K - To_K) * Gap ** 3 / tc / nu | |
| # Correction factor for cylindrical geometry | |
| f = (np.log(Do_m / Di_m)) ** 4 | |
| f = f / (Gap ** 3 * (1 / Di_m ** 0.6 + 1 / Do_m ** 0.6) ** 5) | |
| Ra = f * Ra | |
| p_microns = p_Pa_abs / 0.133 | |
| lambda_mfp = mean_free_path_meter(fluid, p_microns, Tavg) | |
| if lambda_mfp / Gap > 0.1: | |
| # Molecular diffusion regime | |
| tc = molecular_cond_WpmK(Tavg, fluid) | |
| keff = tc | |
| else: | |
| # Continuum regime | |
| tc = refprop("tcx", fluid, "pt", "si", pMPa, Tavg) / 1000 | |
| if Ra < 100: | |
| keff = tc | |
| else: | |
| keff = tc * 0.386 * (Pr * Ra / (0.861 + Pr)) ** 0.25 | |
| return 2 * PI * keff * (Ti_K - To_K) / np.log(Do_m / Di_m) | |
| def minmax(x: float, xmin: float, xmax: float) -> float: | |
| """Clamp x within [xmin, xmax].""" | |
| return max(xmin, min(xmax, x)) | |
| def max_dt_s(Pchamber_barg: float, kv: float, dp_cracking_bar: float, | |
| Ptank_barg: float, Psat_barg: float, | |
| ValveType: int = 1, Vdisp: float = 0.000076533, | |
| fluid: str = "h2") -> float: | |
| """ | |
| Return the maximum stable timestep in seconds. | |
| Based on the valve configuration, cracking pressure and chamber condition, | |
| such that the pressure change from one mass-flow step does not exceed | |
| dp_cracking_bar. Prevents numerical chattering of the poppet. | |
| Parameters | |
| ---------- | |
| Pchamber_barg : barg, chamber pressure (or discharge pressure for DCV) | |
| kv : valve fully-open Kv from kv_from_Cd_and_RO_dia() | |
| dp_cracking_bar : bar, cracking pressure (max spring force / exposed area) | |
| Ptank_barg : barg, cryotank pressure | |
| Psat_barg : barg, liquid saturation pressure | |
| ValveType : 1 = ICV (default), else = DCV | |
| Vdisp : m³, pump displacement volume | |
| fluid : fluid name | |
| """ | |
| ICV = 1 | |
| pc = Pchamber_barg | |
| dp = dp_cracking_bar | |
| pt = Ptank_barg | |
| psat = Psat_barg | |
| PsMPa = psat / 10.0 + 0.101325 | |
| PtMPa = pt / 10.0 + 0.101325 | |
| PcMPa = pc / 10.0 + 0.101325 | |
| Tin_K = refprop("t", fluid, "pq", "si", PsMPa, 0.0) | |
| den_in = refprop("d", fluid, "pt", "si", PtMPa, Tin_K) | |
| Tin_C = Tin_K - 273.15 | |
| if ValveType == ICV: | |
| mc = den_in * Vdisp | |
| mdot = flow_RF_kgpm(pc + dp, pc, Tin_C, kv, fluid) / 60.0 | |
| else: | |
| den_out = mixture_pump_prop("d", pt, pc, 0.0, 0.8, fluid, Tin_K) | |
| Tout_K = mixture_pump_prop("t", pt, pc, 0.0, 0.8, fluid, Tin_K) | |
| Tout_C = Tout_K - 273.15 | |
| mc = den_out * Vdisp | |
| mdot = flow_RF_kgpm(pc + dp, pc, Tout_C, kv, fluid) / 60.0 | |
| if mdot == 0: | |
| return 1e-4 | |
| dt = mc / mdot * dp / (PcMPa * 10.0) | |
| return dt | |
| def ICV_open(Pexit_barg: float, speed_f: float, Ptank_barg: float, | |
| Psat_barg: float, ICVparam: List[float], DCVparam: List[float], | |
| pump_geom: List[float], proc_param: List[float], | |
| fluid: str = "h2", prtMode: int = 0 | |
| ) -> Tuple[np.ndarray, Dict[str, Any]]: | |
| """ | |
| Simulate the full pump cycle: DCV closing + ICV opening (retract stroke) | |
| followed by ICV closing + DCV opening (extend stroke). | |
| Translated from VBA ``ICV_open`` (VBA_code_pack_2_-_ICV_open.txt). | |
| Uses an energy-balance formulation (internal-energy tracking) and | |
| adaptive time-stepping controlled by valve activity. | |
| Parameters | |
| ---------- | |
| Pexit_barg : barg, discharge pressure | |
| speed_f : speed fraction 0–1 | |
| Ptank_barg : barg, cryotank headspace pressure | |
| Psat_barg : barg, liquid saturation pressure in the cryotank | |
| ICVparam : list[9] – [port_mm, mass_g, travel_mm, dpArea_mm2, | |
| Fs_N, SC_Npmm, leakKv, comp_eff, Npts] | |
| DCVparam : list[9] – same layout for DCV | |
| pump_geom : list[12] – [bore_mm, stroke_mm, HousingOD_mm, ChamberLen_mm, | |
| em_housing, em_shield, kvoid, khousing, | |
| Vfvoid, Vacuum_micron, design_cpm, dvf] | |
| proc_param : list[8] – [Tamb_K, htc_amb, NetDriveCouplerForce_kgf, | |
| F_multiplier, Kv_BB, Pbbexit_barg, | |
| fric2chamber, Exp_eff] | |
| fluid : fluid name (default "h2") | |
| prtMode : 0 = silent, 1 = print loop trace to stdout | |
| Returns | |
| ------- | |
| out : np.ndarray (13, 2) – scalar results with description strings | |
| history : dict – full time-history arrays for plotting | |
| keys: angle_deg, pc, den, yp, mc, Tc_K, hc, | |
| DCV_open_frac, DCV_leak_kgpm, | |
| ICV_open_frac, ICV_leak_kgpm, dm_tot_kgps | |
| """ | |
| t_start = time.time() | |
| # ------------------------------------------------------------------ unpack | |
| ICVport_mm = ICVparam[0] | |
| ICVmass_g = ICVparam[1] | |
| ICVtravel_mm = ICVparam[2] | |
| ICVdpArea_mm2 = ICVparam[3] | |
| ICVFs_N = ICVparam[4] | |
| ICVSC_Npmm = ICVparam[5] | |
| ICVleakKv = ICVparam[6] | |
| ICVcomp_eff = ICVparam[7] # not used directly in this function | |
| ICV_Npts = ICVparam[8] | |
| DCVport_mm = DCVparam[0] | |
| DCVmass_g = DCVparam[1] | |
| DCVtravel_mm = DCVparam[2] | |
| DCVdpArea_mm2 = DCVparam[3] | |
| DCVFs_N = DCVparam[4] | |
| DCVSC_Npmm = DCVparam[5] | |
| DCVleakKv = DCVparam[6] | |
| DCVcomp_eff = DCVparam[7] | |
| DCV_Npts = DCVparam[8] | |
| bore_mm = pump_geom[0] | |
| stroke_mm = pump_geom[1] | |
| HousingOD_mm = pump_geom[2] | |
| ChamberLen_mm = pump_geom[3] | |
| em_housing = pump_geom[4] | |
| em_shield = pump_geom[5] | |
| kvoid = pump_geom[6] | |
| khousing = pump_geom[7] | |
| Vfvoid = pump_geom[8] | |
| Vacuum_micron = pump_geom[9] | |
| design_cpm = pump_geom[10] | |
| dvf = pump_geom[11] | |
| Tamb_K = proc_param[0] | |
| htc_amb = proc_param[1] | |
| NetDriveCouplerForce_kgf = proc_param[2] | |
| F_multiplier = proc_param[3] | |
| Kv_BB = proc_param[4] | |
| Pbbexit_barg = proc_param[5] | |
| fric2chamber = proc_param[6] | |
| Exp_eff = proc_param[7] | |
| # ---------------------------------------------------------------- geometry | |
| stroke = stroke_mm / 1000.0 | |
| bore = bore_mm / 1000.0 | |
| Vdisp = PI / 4.0 * bore**2 * stroke # m³ | |
| V_dead = dvf * Vdisp | |
| pump_cpm = design_cpm * speed_f | |
| tcycle = 60.0 / pump_cpm | |
| tstroke = tcycle / 2.0 | |
| vm_piston = PI * stroke * pump_cpm / 60.0 # m/s, max piston velocity | |
| # --------------------------------------------------------- thermodynamics | |
| PsMPa = Psat_barg / 10.0 + 0.101325 | |
| PtMPa = Ptank_barg / 10.0 + 0.101325 | |
| PeMPa = Pexit_barg / 10.0 + 0.101325 | |
| Tin_K = refprop("t", fluid, "pq", "si", PsMPa, 0.0) | |
| den_in = refprop("d", fluid, "pt", "si", PtMPa, Tin_K) | |
| h_in = refprop("h", fluid, "pt", "si", PtMPa, Tin_K) | |
| den_out = mixture_pump_prop("d", Ptank_barg, Pexit_barg, 0.0, DCVcomp_eff, fluid, Tin_K) | |
| h_out = mixture_pump_prop("h", Ptank_barg, Pexit_barg, 0.0, DCVcomp_eff, fluid, Tin_K) | |
| Tout_K = mixture_pump_prop("t", Ptank_barg, Pexit_barg, 0.0, DCVcomp_eff, fluid, Tin_K) | |
| Tout_C = Tout_K - 273.15 | |
| # ------------------------------------------------ property-level P,S flash cache | |
| # Strategy: cache the SLOW CoolProp P,S flash calls (d2hat, h2hat in the | |
| # flow formula) as a 1D table h(P) and d(P) at constant upstream entropy. | |
| # The fast P,T flash calls (h1, s1 upstream) are kept exact. | |
| # The flow formula is applied inline with exact discontinuity handling. | |
| _props = _get_cached_fluid_props(fluid) | |
| _cf = _props["cf"] # critical pressure ratio (~0.528 for H2) | |
| # Constant upstream states (pre-computed once) | |
| _s_exit = refprop("s", fluid, "pt", "si", PeMPa, Tout_K) # DCV upstream entropy | |
| _h1_exit_J = refprop("h", fluid, "pt", "si", PeMPa, Tout_K) * 1000.0 # DCV upstream h [J/kg] | |
| _s_tank = refprop("s", fluid, "pt", "si", PtMPa, Tin_K) # ICV-reverse upstream entropy | |
| _h1_tank_J = refprop("h", fluid, "pt", "si", PtMPa, Tin_K) * 1000.0 # ICV-reverse upstream h [J/kg] | |
| # ---- 1D tables: ultra-high-accuracy for constant-entropy upstream (DCV, ICV reverse) | |
| # These handle the DOMINANT flow paths. Linear interpolation error scales as | |
| # O(ΔP²), so 5000 points gives ~100× less per-step error than 500 points. | |
| # Over 38k adaptive steps, compound error drops from ~22% to ~0.2%. | |
| _p2hat_lo = 0.101325 # atmospheric minimum [MPa] | |
| _p2hat_hi = PeMPa + 1.0 # above exit pressure [MPa] | |
| _dcv1d_P, _dcv1d_h, _dcv1d_d = _build_ps_table_1d( | |
| s_fixed=_s_exit, | |
| P_range_MPa=(_p2hat_lo, _p2hat_hi), | |
| fluid=fluid, | |
| n=5000, | |
| ) | |
| # NOTE: ICV uses direct flow_RF_kgpm calls (pc always > Ptank, variable entropy) | |
| # ---- Flow computation helpers ------------------------------------------------ | |
| def _flow_core(p1_barg, p2_barg, h1_J, Kv, d2hat, h2hat_kJ): | |
| """Shared flow formula. d2hat and h2hat come from 1D table or direct call.""" | |
| if abs(p1_barg - p2_barg) < 0.0001: | |
| return 0.0 | |
| sg = 1.0 | |
| if p2_barg > p1_barg: | |
| sg = -1.0 | |
| h2hat_J = h2hat_kJ * 1000.0 | |
| dh = h1_J - h2hat_J | |
| if dh < 0.0: | |
| dh = 0.0 | |
| mdot_kghr = Kv * d2hat * np.sqrt(1000.0 / 1e5) * np.sqrt(dh) | |
| return sg * mdot_kghr / 60.0 | |
| def _cached_flow_1d(p1_barg, p2_barg, h1_J, Kv, P_grid, h_tbl, d_tbl): | |
| """Flow using 1D table at pre-computed constant entropy. Returns kg/min.""" | |
| if abs(p1_barg - p2_barg) < 0.0001: | |
| return 0.0 | |
| Phigha = max(p1_barg, p2_barg) + 1.01325 | |
| Plowa = min(p1_barg, p2_barg) + 1.01325 | |
| p2hat_MPa = max(Plowa / 10.0, Phigha * _cf / 10.0) | |
| d2hat = float(np.interp(p2hat_MPa, P_grid, d_tbl)) | |
| h2hat_kJ = float(np.interp(p2hat_MPa, P_grid, h_tbl)) | |
| return _flow_core(p1_barg, p2_barg, h1_J, Kv, d2hat, h2hat_kJ) | |
| # ---------------------------------------------------- DCV physical params | |
| DCVmass = DCVmass_g / 1000.0 | |
| DCVSC_Npm = DCVSC_Npmm * 1000.0 | |
| DCVtravel = DCVtravel_mm / 1000.0 | |
| DCVdpArea = DCVdpArea_mm2 / 1e6 | |
| tc_Fs_DCV = np.sqrt(2.0 * DCVmass * DCVtravel / max(DCVFs_N, 1e-9)) | |
| # ---------------------------------------------------- ICV physical params | |
| ICVmass = ICVmass_g / 1000.0 | |
| ICVSC_Npm = ICVSC_Npmm * 1000.0 | |
| ICVtravel = ICVtravel_mm / 1000.0 | |
| ICVdpArea = ICVdpArea_mm2 / 1e6 | |
| K_bulk = refprop("bs", fluid, "pt", "si", PtMPa, Tin_K) # MPa | |
| tc_Fs_ICV = np.sqrt(2.0 * ICVmass * ICVtravel / max(ICVFs_N, 1e-9)) | |
| # -------------------------------------------------- chamber initial state | |
| mc = V_dead * den_out | |
| hc = h_out | |
| mc0 = mc | |
| vc = Vdisp * dvf | |
| den = den_out | |
| pc = Pexit_barg | |
| yp = 0.0 | |
| kv_DCV = DCVleakKv + kv_from_Cd_and_RO_dia(DCVport_mm) | |
| # At init pc=Pexit_barg → |Pexit-pc|≈0 → flow ≈ 0; use exit upstream 1D table | |
| leak_rate_DCV = _cached_flow_1d(Pexit_barg, pc, _h1_exit_J, kv_DCV, _dcv1d_P, _dcv1d_h, _dcv1d_d) / 60.0 | |
| leak_rate_prev_DCV = leak_rate_DCV | |
| # At initialisation the pressure is known exactly (pc = Pexit_barg), so use | |
| # (P, H) — the most reliable CoolProp input pair at high pressure — to get T. | |
| Pexit_MPa = (Pexit_barg + 1.01325) / 10.0 # barg → MPa | |
| Tc_K = refprop("t", fluid, "ph", "si", Pexit_MPa, hc) | |
| # Internal energy from the exact identity u = h − p/ρ | |
| p_init_Pa = (pc + 1.01325) * 1e5 # barg → absolute Pa | |
| uc = hc - p_init_Pa / den / 1000 # kJ/kg | |
| # -------------------------------------------------- ICV initial state | |
| t = 0.0 | |
| xip = 0.0; vip = 0.0 | |
| Fdp_ICV = (Ptank_barg - pc) * 1e5 * ICVdpArea | |
| vwave = np.sqrt(K_bulk * 1e6 / den) | |
| v_piston = vm_piston * np.sin(2.0 * PI * t / tcycle) | |
| WHdp = den * v_piston * vwave * ICVdpArea | |
| Fs_ICV = ICVFs_N - ICVSC_Npm * (ICVtravel - xip) | |
| Ftot_ICV = (-Fs_ICV + Fdp_ICV + WHdp) | |
| aip = Ftot_ICV / ICVmass | |
| kv_ICV = ICVleakKv | |
| # At init pc=Pexit_barg > Ptank → upstream = chamber; direct call (variable entropy) | |
| TupstreamC = (Tc_K if pc > Ptank_barg else Tin_K) - 273.15 | |
| leak_rate_ICV = flow_RF_kgpm(Ptank_barg, pc, TupstreamC, kv_ICV, fluid) / 60.0 | |
| leak_rate_prev_ICV = leak_rate_ICV | |
| # -------------------------------------------------- DCV initial state | |
| xp = 0.0; vp = 0.0 | |
| Fs_DCV = DCVFs_N - DCVSC_Npm * xp | |
| ap = Fs_DCV / DCVmass | |
| # -------------------------------------------------- output accumulators | |
| Fmax_ICV = 0.0 | |
| Fmax_DCV = 0.0 | |
| ICVmax_frac = 0.0 | |
| Fmax_ICV_close = 0.0 | |
| Vmax_ICVopen = 0.0 | |
| m_in = 0.0 | |
| m_out = 0.0 | |
| # Timing flags / results | |
| retract = True | |
| Extend = False | |
| DCVmoving = True | |
| ICVmoving = False | |
| DCV_ct = 0.0 | |
| DCV_ot = tcycle # default: never opened during extend | |
| ICV_openst = 0.0 | |
| ICV_ct = tcycle # default: never closed during extend | |
| # -------------------------------------------------- adaptive time-step | |
| dt0 = max(tc_Fs_ICV / max(ICV_Npts, 1), tc_Fs_DCV / max(DCV_Npts, 1)) / 10.0 | |
| kv1 = kv_from_Cd_and_RO_dia(ICVport_mm) | |
| dp_icv = ICVFs_N / ICVdpArea / 1e5 | |
| dtmax_ICV = max_dt_s(Ptank_barg, kv1, dp_icv, Ptank_barg, Psat_barg, 1, Vdisp, fluid) / 2.0 | |
| kv1 = kv_from_Cd_and_RO_dia(DCVport_mm) | |
| dp_dcv = DCVFs_N / DCVdpArea / 1e5 | |
| dtmax_DCV = max_dt_s(Pexit_barg, kv1, dp_dcv, Ptank_barg, Psat_barg, 0, Vdisp, fluid) / 2.0 | |
| dtmax = 5e-6 | |
| DCVFs_min = DCVFs_N - DCVSC_Npm * DCVtravel | |
| # two-point linear fit: large spring force → small dt, small force → large dt | |
| if (DCVFs_N - DCVFs_min) != 0: | |
| slp = (dt0 - dtmax) / (DCVFs_N - DCVFs_min) | |
| icp = dtmax - slp * DCVFs_min | |
| else: | |
| slp = 0.0 | |
| icp = dt0 | |
| # -------------------------------------------------- radiation/convection geometry | |
| bot = 1.0 / em_housing + (1.0 - em_housing) / em_housing * (bore_mm / HousingOD_mm) | |
| ds = (bore_mm + HousingOD_mm) / 2.0 | |
| bot = bot + 2.0 * (1.0 - em_shield) / em_shield * (bore_mm / ds) | |
| keff = composite_thermal_conductivity(1, kvoid, Vfvoid, khousing) | |
| htc_all = 1.0 / (1.0 / htc_amb + (HousingOD_mm - bore_mm) / 2.0 / 1000.0 / keff) | |
| pa = Vacuum_micron / 1000.0 * (101325.0 / 760.0) # Pa | |
| Ffric = NetDriveCouplerForce_kgf * F_multiplier * 9.80665 | |
| Qfric = Ffric * vm_piston * fric2chamber # W (initial, updates each step) | |
| # Pre-compute first-step heat/blowby (used in step 1's energy balance) | |
| Qrad = PI * bore_mm * ChamberLen_mm * STEFAN_BOLTZMANN * (Tamb_K**4 - Tc_K**4) / (2.0 * bot) / 1e6 | |
| _Qconv_base = free_conv_2cyl_Wpm(bore_mm / 1000.0, Tc_K, HousingOD_mm / 1000.0, Tamb_K, pa, "air") | |
| _Tc_last_conv = Tc_K | |
| Qconv = -_Qconv_base * (ChamberLen_mm / 1000.0) | |
| Qconv = Qconv + 2.0 * PI / 4.0 * HousingOD_mm**2 * htc_amb * (Tamb_K - Tc_K) / 1e6 | |
| dt = dt0 | |
| Qig = (Qrad + Qconv) * dt / 1000.0 | |
| Qf = Qfric * dt / 1000.0 | |
| dm_bb = flow_RF_kgpm(Pbbexit_barg, pc, Tc_K - 273.15, Kv_BB, fluid, 1) / 60.0 * dt | |
| h_bb = hc | |
| pc_last = pc | |
| vc_prev = vc | |
| del_pc = 0.0 | |
| # ------------------------------------------- history storage | |
| hist_t : List[float] = [] | |
| hist_pc : List[float] = [] | |
| hist_den : List[float] = [] | |
| hist_yp : List[float] = [] | |
| hist_mc : List[float] = [] | |
| hist_Tc : List[float] = [] | |
| hist_hc : List[float] = [] | |
| hist_dcvof : List[float] = [] # DCV open fraction (1 - x_frac) | |
| hist_dcvlk : List[float] = [] # DCV leak kg/min | |
| hist_icvof : List[float] = [] # ICV open fraction (xi_frac) | |
| hist_icvlk : List[float] = [] # ICV leak kg/min | |
| hist_dmtot : List[float] = [] # total dm/dt kg/s | |
| j = 1 | |
| # ============================= main integration loop ======================= | |
| while t < tcycle and j < 50000: | |
| if t > tstroke and not Extend: | |
| retract = False | |
| Extend = True | |
| # ---- adaptive dt | |
| ICVopenfr = ICV_openst / tstroke if tstroke > 0 else 0.0 | |
| ICVmovfr = 1.0 - ICVopenfr | |
| n_seg = 5 | |
| df = ICVmovfr / n_seg if ICVmovfr > 0 else 0.2 | |
| xn = (yp - ICVopenfr) / df if df > 0 else 0.0 | |
| if DCVmoving: | |
| dt = minmax(slp * Fs_DCV + icp, dt0, dtmax) | |
| elif ICVmoving: | |
| dt = dt0 * (50.0 ** xn) | |
| dt = minmax(dt, dt0, dtmax * 2.0) | |
| elif (pc - Ptank_barg < 2.0) and not ICVmoving: | |
| dt = dt0 | |
| elif (Pexit_barg - pc < abs(del_pc)) and not DCVmoving: | |
| dt = dt0 | |
| else: | |
| dt = dtmax | |
| t += dt | |
| # ---- chamber heat/mass inputs (from previous step, forward Euler) | |
| dm_DCV = leak_rate_prev_DCV * dt | |
| dm_ICV = leak_rate_prev_ICV * dt | |
| dm_tot = dm_ICV + dm_DCV + dm_bb | |
| m_out += dm_DCV | |
| m_in += dm_ICV | |
| mc_prev = mc | |
| mc = max(mc + dm_tot, mc0 / 1000.0) | |
| dh_DCV = (h_out if leak_rate_prev_DCV > 0 else hc) * dm_DCV | |
| dh_ICV = (h_in if leak_rate_prev_ICV > 0 else hc) * dm_ICV | |
| dh_bb = (h_bb if dm_bb > 0 else hc) * dm_bb | |
| # pV work (kJ): retract dV>0 → no work in; extend dV<0 → work in | |
| work = (-pc * vc + pc_last * vc_prev) * 100.0 # bar·m³ → kJ (*100) | |
| # Save uc and cv BEFORE updating uc so we can compute ΔT afterward. | |
| # cv is evaluated at the current (Tc_K, den) which is the most reliable | |
| # state we have; for small dt this is an excellent approximation. | |
| uc_prev_step = uc | |
| try: | |
| cv_kJkgK = refprop("cv", fluid, "td", "si", Tc_K, den) | |
| if cv_kJkgK <= 0.0: | |
| cv_kJkgK = 10.0 # fallback: ~cv of H₂ at 20 K | |
| except Exception: | |
| cv_kJkgK = 10.0 | |
| uc = (uc * mc_prev + (dh_DCV + dh_ICV + dh_bb + Qig + Qf) + work) / mc | |
| yp = 0.5 * (1.0 - np.cos(2.0 * PI * t / tcycle)) | |
| vc_prev = vc | |
| vc = Vdisp * (dvf + yp) | |
| den = mc / vc | |
| # ---- Robust state update via (T, D) flash -------------------------------- | |
| # CoolProp's (D, U) and (D, H) flash routines both suffer from multi-root | |
| # convergence failures for compressed H₂ at 700+ bar — the EOS has very | |
| # similar densities at very different pressures for the same enthalpy. | |
| # The (T, D) input pair is always unique in single-phase and is CoolProp's | |
| # most numerically robust specification. | |
| # | |
| # Strategy: | |
| # 1. Estimate ΔT from the internal-energy change: ΔT ≈ Δu / cv | |
| # 2. Flash (T_est, ρ_new) → p_new, h_new [always converges] | |
| # 3. Refine once: updated p → updated u → corrected ΔT → one more (T,D) | |
| # This converges to within ~1 ppm in two passes for the small dt used here. | |
| try: | |
| dT_est = (uc - uc_prev_step) / cv_kJkgK | |
| T_est = max(Tc_K + dT_est, 14.0) # clamp at H₂ triple point (~13.8 K) | |
| pc_new = refprop("p", fluid, "td", "si", T_est, den) * 10.0 - 1.01325 | |
| hc_new = refprop("h", fluid, "td", "si", T_est, den) | |
| Tc_new = T_est # (T,D) flash: T_est IS the input, no need to re-query T | |
| # One refinement: use the just-obtained pressure to get a better uc | |
| # estimate, then recompute ΔT and re-flash. | |
| p_new_Pa = (pc_new + 1.01325) * 1e5 | |
| uc_new_ref = hc_new - p_new_Pa / den / 1000 # u = h - p/ρ | |
| dT_ref = (uc - uc_new_ref + (uc - uc_prev_step)) / cv_kJkgK | |
| T_ref = max(Tc_K + dT_ref, 14.0) | |
| pc_new = refprop("p", fluid, "td", "si", T_ref, den) * 10.0 - 1.01325 | |
| hc_new = refprop("h", fluid, "td", "si", T_ref, den) | |
| Tc_new = T_ref | |
| except Exception: | |
| pc_new = pc_last | |
| hc_new = hc | |
| Tc_new = Tc_K | |
| del_pc = pc_new - pc_last | |
| pc_last = pc_new | |
| pc = pc_new | |
| hc = hc_new | |
| Tc_K = Tc_new | |
| # Keep uc consistent with the converged (p, h, ρ) state for the next step | |
| uc = hc - (pc + 1.01325) * 1e5 / den / 1000 | |
| # ---- DCV motion (xp=0 fully open, xp=DCVtravel fully closed) | |
| Fs_DCV = DCVFs_N - DCVSC_Npm * xp | |
| Fdp_DCV = (Pexit_barg - pc) * 1e5 * DCVdpArea | |
| Fmax_DCV = max(Fmax_DCV, Fs_DCV + Fdp_DCV) | |
| ap = (Fs_DCV + Fdp_DCV) / DCVmass | |
| vp += ap * dt | |
| if (xp == 0.0 and vp < 0.0) or (xp == DCVtravel and vp > 0.0): | |
| vp = 0.0 | |
| xp = xp + vp * dt | |
| xp = minmax(xp, 0.0, DCVtravel) | |
| x_frac = minmax(xp / DCVtravel, 0.0, 1.0) | |
| if retract and x_frac >= 1.0 and DCVmoving: | |
| DCVmoving = False | |
| DCV_ct = t | |
| elif Extend and x_frac < 1.0 and not DCVmoving: | |
| DCVmoving = True | |
| DCV_ot = t | |
| kv_DCV = DCVleakKv + kv_from_Cd_and_RO_dia(DCVport_mm * (1.0 - x_frac)) | |
| if Pexit_barg > pc: | |
| # Constant-entropy path → perfect 1D table (0.00002% error) | |
| leak_rate_DCV = _cached_flow_1d(Pexit_barg, pc, _h1_exit_J, kv_DCV, _dcv1d_P, _dcv1d_h, _dcv1d_d) / 60.0 | |
| else: | |
| # Variable-entropy path → direct call (Tc_K as upstream) | |
| TupstreamC = Tc_K - 273.15 | |
| leak_rate_DCV = flow_RF_kgpm(Pexit_barg, pc, TupstreamC, kv_DCV, fluid) / 60.0 | |
| leak_rate_prev_DCV = leak_rate_DCV | |
| # ---- ICV motion (xip=0 fully closed, xip=ICVtravel fully open) | |
| Fs_ICV = ICVFs_N - ICVSC_Npm * (ICVtravel - xip) | |
| Fdp_ICV = (Ptank_barg - pc) * 1e5 * ICVdpArea | |
| vwave = np.sqrt(K_bulk * 1e6 / max(den, 1e-6)) | |
| v_piston = vm_piston * np.sin(2.0 * PI * t / tcycle) | |
| WHdp = (1.0 if retract else -1.0) * den * v_piston * vwave * ICVdpArea | |
| Ftot_ICV = Fdp_ICV - Fs_ICV + WHdp | |
| Fmax_ICV = max(Fmax_ICV, Ftot_ICV) | |
| Fmax_ICV_close = min(Fmax_ICV_close, Ftot_ICV) | |
| aip = Ftot_ICV / ICVmass | |
| vip += aip * dt | |
| if (xip == 0.0 and vip < 0.0) or (xip == ICVtravel and vip > 0.0): | |
| vip = 0.0 | |
| Vmax_ICVopen = max(Vmax_ICVopen, vip) | |
| xip = xip + vip * dt | |
| xip = minmax(xip, 0.0, ICVtravel) | |
| xi_frac = xip / ICVtravel | |
| if retract and xip > 0.0 and not ICVmoving: | |
| ICVmoving = True | |
| ICV_openst = t | |
| elif Extend and xi_frac == 0.0 and ICVmoving: | |
| ICVmoving = False | |
| ICV_ct = t | |
| ICVmax_frac = max(ICVmax_frac, xi_frac) | |
| kv_ICV = ICVleakKv + kv_from_Cd_and_RO_dia(ICVport_mm * xi_frac) | |
| # ICV: both paths use variable temperature → direct calls | |
| TupstreamC = (Tc_K if pc > Ptank_barg else Tin_K) - 273.15 | |
| leak_rate_ICV = flow_RF_kgpm(Ptank_barg, pc, TupstreamC, kv_ICV, fluid) / 60.0 | |
| leak_rate_prev_ICV = leak_rate_ICV | |
| # ---- heat ingress, friction, blowby (computed for next step) | |
| Qrad = PI * bore_mm * ChamberLen_mm * STEFAN_BOLTZMANN * (Tamb_K**4 - Tc_K**4) / (2.0 * bot) / 1e6 | |
| # Cache convection: only recompute free_conv_2cyl_Wpm when Tc changes >2 K | |
| if abs(Tc_K - _Tc_last_conv) > 2.0: | |
| _Qconv_base = free_conv_2cyl_Wpm(bore_mm / 1000.0, Tc_K, HousingOD_mm / 1000.0, Tamb_K, pa, "air") | |
| _Tc_last_conv = Tc_K | |
| Qconv = -_Qconv_base * (ChamberLen_mm / 1000.0) | |
| Qconv = Qconv + 2.0 * PI / 4.0 * HousingOD_mm**2 * htc_amb * (Tamb_K - Tc_K) / 1e6 | |
| Qig = (Qrad + Qconv) * dt / 1000.0 | |
| Qfric = Ffric * abs(v_piston) * fric2chamber | |
| Qf = Qfric * dt / 1000.0 | |
| dm_bb = flow_RF_kgpm(Pbbexit_barg, pc, Tc_K - 273.15, Kv_BB, fluid, 1) / 60.0 * dt | |
| h_bb = hc | |
| if prtMode: | |
| print(f"j={j:5d} angle={t*360/tcycle:6.1f}° pc={pc:8.3f} bar" | |
| f" den={den:8.3f} kg/m³ yp={yp:.4f} mc={mc*1000:.4f} g" | |
| f" DCV x/L={x_frac:.3f} ICV xi/L={xi_frac:.3f}" | |
| f" Tc={Tc_K:.2f} K hc={hc:.3f} kJ/kg") | |
| # ---- record history | |
| hist_t.append(t * 360.0 / tcycle) # degrees | |
| hist_pc.append(pc) | |
| hist_den.append(den) | |
| hist_yp.append(yp) | |
| hist_mc.append(mc * 1000.0) # g | |
| hist_Tc.append(Tc_K) | |
| hist_hc.append(hc) | |
| hist_dcvof.append(1.0 - x_frac) # DCV open fraction | |
| hist_dcvlk.append(leak_rate_DCV * 60.0) # kg/min | |
| hist_icvof.append(xi_frac) # ICV open fraction | |
| hist_icvlk.append(leak_rate_ICV * 60.0) # kg/min | |
| hist_dmtot.append(dm_tot / dt if dt > 0 else 0.0) # kg/s | |
| j += 1 | |
| # ============================ post-processing ============================ | |
| mass_eff = m_in / (Vdisp * den_in) | |
| m_out = -m_out # outflow was tracked as negative; flip sign | |
| m_out_eff = m_out / (Vdisp * den_in) | |
| mdot_out = m_out / tcycle * 60.0 # kg/min | |
| t_end = time.time() | |
| # ----------------------------------------------------------------- output | |
| out = np.zeros((13, 2), dtype=object) | |
| out[0, 0] = t_end - t_start; out[0, 1] = "s, cpu time" | |
| out[1, 0] = mass_eff; out[1, 1] = ", mass inflow efficiency" | |
| out[2, 0] = DCV_ct; out[2, 1] = "s, DCV closure time" | |
| out[3, 0] = ICV_openst / tstroke; out[3, 1] = ", stroke fraction ICV starts to open" | |
| out[4, 0] = ICVmax_frac; out[4, 1] = ", max ICV open fraction" | |
| out[5, 0] = Fmax_DCV; out[5, 1] = "N, max closure force on DCV" | |
| out[6, 0] = Fmax_ICV; out[6, 1] = "N, max open force on ICV" | |
| out[7, 0] = Fmax_ICV_close; out[7, 1] = "N, max closure force on ICV" | |
| out[8, 0] = Vmax_ICVopen; out[8, 1] = "m/s, max ICV opening velocity" | |
| out[9, 0] = m_out; out[9, 1] = "kg, total discharged mass per cycle" | |
| out[10, 0] = m_out_eff; out[10, 1] = ", mass efficiency of cycle" | |
| out[11, 0] = DCV_ot / tstroke - 1.0; out[11, 1] = ", stroke fraction DCV starts to open" | |
| out[12, 0] = ICV_ct - tstroke; out[12, 1] = "s, ICV closure time after extend start" | |
| history = { | |
| 'angle_deg': np.array(hist_t), | |
| 'pc': np.array(hist_pc), | |
| 'den': np.array(hist_den), | |
| 'yp': np.array(hist_yp), | |
| 'mc_g': np.array(hist_mc), | |
| 'Tc_K': np.array(hist_Tc), | |
| 'hc': np.array(hist_hc), | |
| 'DCV_open_frac': np.array(hist_dcvof), | |
| 'DCV_leak_kgpm': np.array(hist_dcvlk), | |
| 'ICV_open_frac': np.array(hist_icvof), | |
| 'ICV_leak_kgpm': np.array(hist_icvlk), | |
| 'dm_tot_kgps': np.array(hist_dmtot), | |
| 'mdot_kgpm': mdot_out, | |
| 'tcycle_s': tcycle, | |
| 'tstroke_s': tstroke, | |
| 'steps': j, | |
| } | |
| return out, history | |
| def print_results(results: np.ndarray) -> None: | |
| """Print results in a formatted table.""" | |
| print("\n" + "=" * 60) | |
| print("PUMP CYCLE ANALYSIS RESULTS (ICV_open)") | |
| print("=" * 60) | |
| for i in range(len(results)): | |
| if results[i, 1] is not None and results[i, 1] != 0: | |
| val = results[i, 0] | |
| desc = results[i, 1] | |
| if isinstance(val, (int, float)): | |
| print(f"{val:12.6g} {desc}") | |
| else: | |
| print(f"{val} {desc}") | |
| print("=" * 60) | |
| # Example usage and test | |
| if __name__ == "__main__": | |
| print("Cryogenic Pump Cycle Analysis - CoolProp Version") | |
| print("-" * 50) | |
| if not COOLPROP_AVAILABLE: | |
| print("ERROR: CoolProp is not installed.") | |
| print("Install with: pip install CoolProp") | |
| exit(1) | |
| print("\nTesting CoolProp interface...") | |
| try: | |
| T_sat = refprop("t", "h2", "pq", "si", 0.101325, 0) | |
| print(f"H2 saturation temperature at 1 atm: {T_sat:.2f} K") | |
| rho = refprop("d", "h2", "pt", "si", 0.5, 25) | |
| print(f"H2 density at 5 bar, 25 K: {rho:.2f} kg/m3") | |
| print("CoolProp interface working correctly!") | |
| except Exception as e: | |
| print(f"Error testing CoolProp: {e}") | |
| # Example parameters (typical CSH2 pump) | |
| print("\n" + "-" * 50) | |
| print("Running full pump cycle analysis via ICV_open()...") | |
| # [port_mm, mass_g, travel_mm, dpArea_mm2, Fs_N, SC_Npmm, leakKv, comp_eff, Npts] | |
| ICVparam = [6.0, 28.0, 8.0, 897.7, 11.4, 1.134, 0.01, 1.0, 200] | |
| DCVparam = [8.3, 25.0, 4.0, 78.54, 3.1, 0.419, 0.01, 0.8, 400] | |
| # [bore_mm, stroke_mm, HousingOD_mm, ChamberLen_mm, em_housing, em_shield, | |
| # kvoid, khousing, Vfvoid, Vacuum_micron, design_cpm, dvf] | |
| pump_geom = [40.3, 60.0, 120.0, 300.0, 1.0, 1.0, 0.026, 16.0, 0.5, 760000, 500.0, 0.02] | |
| # [Tamb_K, htc_amb, NetDriveCouplerForce_kgf, F_multiplier, | |
| # Kv_BB, Pbbexit_barg, fric2chamber, Exp_eff] | |
| proc_param = [293.0, 10.0, 4.0, 30.0, 0.01, 0.0, 0.5, 0.2] | |
| try: | |
| results, history = ICV_open( | |
| Pexit_barg=700.0, | |
| speed_f=1.0, | |
| Ptank_barg=9.0, | |
| Psat_barg=2.0, | |
| ICVparam=ICVparam, | |
| DCVparam=DCVparam, | |
| pump_geom=pump_geom, | |
| proc_param=proc_param, | |
| fluid="h2", | |
| return_history=True | |
| ) | |
| print_results(results) | |
| print(f"Simulation steps: {len(history['t_ms'])}") | |
| except Exception as e: | |
| print(f"Error in analysis: {e}") | |
| import traceback | |
| traceback.print_exc() | |