Flow metering with swirl-cone throttling device and physics-informed neural networks: A comparative study of multi-differential pressure signal combinations

Abstract

Throttle-based multiphase flow measurement methods have been widely employed in industrial applications due to their simplicity and cost-effectiveness. Among these methods, the measurement accuracy significantly depends on the precise detection and utilization of differential pressure signals. To address the poor flow pattern adaptability of traditional methods and the limited generalization capability of empirical-formula-based approaches, this study proposes an innovative online gas-liquid two-phase flow measurement method. Specifically, we designed an integrated swirl-cone throttling device capable of simultaneously acquiring multi-point axial and radial differential pressures, while also reducing the impact of flow pattern variations on flow measurement. These differential pressure signals, combined with the gas-liquid density ratio, serve as input features for a feedforward neural network, enabling simultaneous predictions of total mass flow rate (M_TP) and quality (x_G). To further enhance the model's physical consistency and extrapolation capabilities, the throttling model equation was embedded as a physical constraint within the neural network's loss function during training. Comparative analyses of three differential pressure combination schemes demonstrate the significant impact of pressure signal selection on measurement accuracy. Among these, Differential Pressure Combination-C (DPC-C) exhibited optimal performance, with M_TP prediction errors predominantly within ±5 % (MAPE of 2.36 %) and x_G prediction errors mainly within ±10 % (MAPE of 4.08 %). The proposed method not only ensures high-precision, real-time measurement without markedly increasing pressure loss but also features compact structure, ease of deployment, and superior adaptability, making it particularly suitable for complex industrial operating environments.