Executive Summary

SimV1 represents the benchmark reference for all AURA-MFP multi-fidelity simulations. This module implements full-physics modeling of photovoltaic thermal behavior using Monte Carlo photon transport coupled with high-resolution Navier-Stokes computational fluid dynamics (CFD). The goal for SimV1 is to achieve temperature prediction accuracy of RMSE < 1.0 K when validated against the Sandia National Laboratories PVMC dataset, to establish it as the "gold standard" for subsequent fidelity approximations.

Physical Modeling Framework

Radiative Transport: Monte Carlo BTE

The cornerstone of SimV1 is the solution to the Boltzmann Transport Equation (BTE) for photon intensity using stochastic Monte Carlo methods. The spectral radiance $I(\mathbf{r}, \boldsymbol{\Omega}, \lambda, t)$ satisfies:

$$ \frac{1}{c}\frac{\partial I}{\partial t} + \boldsymbol{\Omega} \cdot \nabla I + (\sigma_a + \sigma_s) I = \sigma_s \int_{4\pi} p(\boldsymbol{\Omega}' \rightarrow \boldsymbol{\Omega}) I(\mathbf{r}, \boldsymbol{\Omega}', \lambda, t) \, d\Omega' + S(\mathbf{r}, \lambda, t) $$

where:

• $I(\mathbf{r}, \boldsymbol{\Omega}, \lambda, t)$ is the spectral intensity $[\text{W m}^{-2} \text{ sr}^{-1} \mu\text{m}^{-1}]$
• $\sigma_a(\lambda)$ is the absorption coefficient $[\text{m}^{-1}]$
• $\sigma_s(\lambda)$ is the scattering coefficient $[\text{m}^{-1}]$
• $p(\boldsymbol{\Omega}' \rightarrow \boldsymbol{\Omega})$ is the scattering phase function
• $S(\mathbf{r}, \lambda, t)$ is the emission source term

Spectral Resolution

SimV1 employs 120 wavelength bins spanning the solar spectrum ($\lambda \in [280, 4000]$ nm) with adaptive bin widths:

$$ \Delta\lambda_i = \lambda_{\min} \cdot \left(1.02\right)^{i-1}, \quad i = 1, 2, \ldots, 120 $$

Conjugate Heat Transfer Interface

The fluid-solid coupling at the PV panel surface $\Gamma$ requires simultaneous satisfaction of thermal equilibrium and heat flux continuity:

$$ \begin{cases} T_{\text{fluid}}\big|_{\Gamma} = T_{\text{solid}}\big|_{\Gamma} = T_{\Gamma} & \text{(Temperature continuity)} \\[8pt] -k_{\text{solid}} \frac{\partial T_{\text{solid}}}{\partial n}\bigg|_{\Gamma} = -k_{\text{fluid}} \frac{\partial T_{\text{fluid}}}{\partial n}\bigg|_{\Gamma} & \text{(Heat flux continuity)} \end{cases} $$

SimV1 implements a Dirichlet-Neumann partitioned coupling scheme with Aitken dynamic relaxation to ensure stability during rapid solar flux transients ($dG/dt > 100$ W m$^{-2}$ s$^{-1}$).

High-Resolution Computational Fluid Dynamics

Navier-Stokes Equations with Buoyancy

The atmospheric boundary layer dynamics are governed by the incompressible Navier-Stokes equations with Boussinesq approximation:

$$ \begin{aligned} \nabla \cdot \mathbf{u} &= 0 \\[8pt] \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u} &= -\frac{1}{\rho_0}\nabla p + \nu \nabla^2 \mathbf{u} + \beta g (T - T_\infty) \hat{\mathbf{z}} \end{aligned} $$

where $\beta = -\frac{1}{\rho}\frac{\partial \rho}{\partial T}\bigg|_p$ is the thermal expansion coefficient ($\beta \approx 3.43 \times 10^{-3}$ K$^{-1}$ at 300 K for air).

Large Eddy Simulation (LES)

SimV1 employs dynamic Smagorinsky-Lilly LES on a $100 \times 100 \times 10$ Cartesian grid with characteristic spacing $\Delta x = \Delta y = 2$ mm, $\Delta z = 5$ mm. The subgrid-scale (SGS) stress tensor is modeled as:

$$ \tau_{ij}^{\text{SGS}} = -2 \nu_t S_{ij}, \quad \nu_t = (C_s \Delta)^2 |\overline{S}| $$

where the Smagorinsky constant $C_s$ is computed dynamically via Germano's identity to prevent excessive dissipation in transitional regions (typical range: $C_s \in [0.1, 0.23]$).

Current-Voltage Characteristics

Shockley-Queisser Single-Diode Model

SimV1 attempts to predict electrical performance using the modified diode equation with series ($R_s$) and shunt ($R_{sh}$) resistances:

$$ I = I_L - I_0 \left[\exp\left(\frac{V + IR_s}{n_{\text{id}} V_T}\right) - 1\right] - \frac{V + IR_s}{R_{sh}} $$

where:

• $I_L = \int_{280}^{1100} \Phi(\lambda) \eta_{\text{IQE}}(\lambda) \, d\lambda$ is the photogenerated current
• $I_0 = I_{0,\text{ref}} \left(\frac{T}{T_{\text{ref}}}\right)^3 \exp\left[-\frac{E_g}{k_B}\left(\frac{1}{T} - \frac{1}{T_{\text{ref}}}\right)\right]$ is the dark saturation current
• $V_T = k_B T / q$ is the thermal voltage
• $n_{\text{id}} \approx 1.3$ is the ideality factor for polycrystalline silicon

Temperature Coefficient

The open-circuit voltage degrades linearly with temperature:

$$ \frac{dV_{oc}}{dT} = \frac{V_{oc}}{T} - \frac{E_g}{qT} + \frac{k_B}{q} \ln\left(\frac{I_{sc}}{I_0}\right) \cdot \frac{1}{T} $$

For typical c-Si modules, this yields $\beta_{V_{oc}} \approx -0.35\%$ per °C, consistent with manufacturer datasheets.

Validation Results

Sandia PVMC Benchmark

SimV1 will be validated against outdoor measurements from the Photovoltaic Module Characterization (PVMC) facility in Albuquerque, New Mexico (1619 m elevation, 35.05°N, 106.54°W).

Test Conditions:

• Incident irradiance: $G = 1100 \pm 50$ W m$^{-2}$ (pyranometer-measured)
• Ambient temperature: $T_\infty = 298.15 \pm 2$ K
• Wind speed: $u_\infty = 1.0 \pm 0.5$ m s$^{-1}$
• Relative humidity: RH $= 12 \pm 5\%$

References

1. King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic Array Performance Model. Sandia National Laboratories, SAND2004-3535.
2. Howell, J. R., Menguc, M. P., & Siegel, R. (1998). Thermal Radiation Heat Transfer (7th ed.). CRC Press.
3. Modest, M. F. (2013). Radiative Heat Transfer (3rd ed.). Academic Press.
4. Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing.