Improving performance estimation of a PCM-integrated solar chimney through reduced-order based data assimilation

TL;DR

This work presents a reduced-order data assimilation framework (ROM–DA) to improve outlet-velocity predictions in an inclined solar chimney that integrates phase-change material (PCM). It combines a high-fidelity CFD-derived reduced basis with a hybrid data-filling strategy to reconstruct time-varying temperature fields from sparse measurements, enabling near-real-time state estimation and digital-twin development. Validation with synthetic measurements shows temperature reconstruction errors below 10% for very sparse data and below 3% for denser sensor sets, while assimilating experimental data significantly enhances velocity predictions, reducing outlet RMS error by up to 55%. The approach demonstrates the feasibility of ROM–DA for multi-domain thermo-fluid systems with PCM, offering a practical route to improved design, monitoring, and control of solar-assisted HVAC configurations.

Abstract

This study evaluates a data assimilation framework based on reduced-order modeling (ROM-DA), complemented by a hybrid data-filling strategy, to reconstruct dynamic temperature fields in a phase-change-material (PCM) integrated solar chimney from limited temperature measurements. The goal is to enhance the estimation accuracy of the outlet airflow velocity. A regularized least-squares formulation is employed to estimate temperature distributions within an inclined solar chimney using RT-42 as the PCM. The methodology combines (i) a reduced-order model derived from high-fidelity finite-volume simulations of unsteady conjugate heat transfer with liquid-solid phase change and surface radiation, and (ii) three experimental datasets with 22, 135, and 203 measurement points. Missing data are reconstructed using a hybrid filling scheme based on boundary-layer and bicubic interpolations. The assimilated temperature fields are integrated into the thermally coupled forward solver to improve velocity predictions. Results show that the ROM-DA framework reconstructs the transient temperature fields in both the air and PCM domains with relative errors below 10 percent for sparse data and below 3 percent for expanded datasets. When applied to experimental measurements, the approach enhances the fidelity of temperature and velocity fields compared with the baseline model, reducing the outlet velocity RMS error by 20 percent. This represents the first application of a ROM-DA framework to a coupled multiphysics solar chimney with PCM integration, demonstrating its potential for near-real-time thermal state estimation and digital-twin development.

Figures (7)

• Figure 1: (a) Schematic representation of an inclined solar chimney. (b) Two-dimensional setup.
• Figure 2: (a) Snapshots of velocity magnitude and temperature in the airflow and PCM domains ($\Omega_f$ and $\Omega_p$) at three different time instants. (b) Local evolution of temperature and velocity at fixed points in $\Omega_f$ (top plot) and of temperature in $\Omega_p$ (middle plot), and of surface-averaged temperature and Nusselt numbers (bottom plot). Lines represent the forward numerical solution and symbols correspond to measurements from HUANG2024130154.
• Figure 3: Positions of the initial measurement set $\mathcal{S}_1$ (left) and the first expanded set $\mathcal{S}_2$ (right) in both the air and PCM domains.
• Figure 4: (a) Solution manifold of the forward dataset. Symbols are experimental data in fixed points at the surface of the PCM and at the outlet air gap, while the shaded regions represent maximum and minimum values of the forward dataset. (b) POD truncation error decay of each reduced basis ($\Phi_1$ and $\Phi_2$), and a-priori error bounds for each reduced basis and set of sensors.
• Figure 5: (a) Snapshots of the reconstructed temperature fields $T^*$ and of their absolute errors relative to the full-order solution (or ground through, $T_{GT}$), using sensor sets $\mathcal{S}_1$ and $\mathcal{S}_2$.(b) Relative reconstruction error over time for the test dataset comprising the 16 forward simulations and their mean error over time for each sensor set.