[Paper Review] A fluid flow model for the pressure loss through perforated plates

Shuai Li, Lars Davidson+1 more|arXiv (Cornell University)|Apr 23, 2023

Fluid Dynamics and Turbulent Flows4 citations

TL;DR

This paper proposes a novel, mathematically simple fluid flow model for predicting pressure loss through perforated plates across laminar and turbulent flows. Based on experimental data from the EU H2020 INVENTOR project and validated against numerical simulations and experiments, the model outperforms existing models in accuracy while maintaining simplicity, and is successfully implemented in RANS simulations with excellent agreement.

ABSTRACT

A fluid flow through a perforated plate is a common problem in a wide variety of practical applications in thermal, mechanical, chemical, civil, nuclear, ocean and aerospace engineering. In this paper, we proposed a novel fluid flow model for the pressure loss through plates with circular perforations in both laminar and turbulent flows. The design of this model is based on the recent measurements conducted at ONERA in the framework of the on-going European Union H2020 INVENTOR project, as well as an existing model for laminar flows. The new model is then validated against existing numerical simulations in the laminar regime and experiments in the turbulent regime. Overall, the predictions given by the new model agree well with the numerical simulations and experiments, and are superior to other models in the literature. This is significant, considering that the present model is much simpler than these previous models. To demonstrate the application of the new model in numerical simulations, two-dimensional channel flows are simulated using Reynolds-averaged Navier-Stokes (RANS) equations with the new model as a pressure-drop source term added to the momentum equations. Results show that the RANS predictions agree very well with the present model predictions.

Motivation & Objective

• To develop a unified, mathematically simple model for pressure loss through perforated plates applicable across laminar and turbulent flow regimes.
• To improve predictive accuracy over existing models, which are either overly complex or limited to specific flow regimes.
• To leverage recent experimental data from the EU H2020 INVENTOR project to inform and validate the model.
• To enable accurate and efficient implementation in Reynolds-averaged Navier–Stokes (RANS) simulations for engineering applications.
• To establish practical applicability limits in terms of porosity (ε) and thickness ratio (δ/D) based on experimental constraints.

Proposed method

• The model is derived from a combination of recent experimental measurements from the ONERA wind-tunnel campaign within the INVENTOR project and an existing laminar flow model by Bae & Kim (2020).
• It employs a modified Darcy-Forchheimer formulation to represent pressure loss as a function of porosity (ε), thickness-to-diameter ratio (δ/D), and flow velocity.
• The model incorporates a correction factor f that adjusts for flow regime transitions and geometric effects, ensuring consistency across laminar and turbulent conditions.
• The model is validated against numerical simulations in the laminar regime and experimental data in the turbulent regime, showing strong agreement.
• The model is implemented as a source term in the momentum equations of RANS simulations to assess its predictive capability in channel flow configurations.
• A minimum of four computational cells in the streamwise direction is recommended to accurately resolve the flow through the perforated plate in simulations.

Experimental results

Research questions

• RQ1 Can a unified, simple model accurately predict pressure loss across both laminar and turbulent flows through perforated plates?
• RQ2 How does the proposed model compare in accuracy to existing empirical and numerical models across varying porosities and thickness ratios?
• RQ3 To what extent can the model be reliably implemented in RANS simulations for engineering flow predictions?
• RQ4 What are the practical limits of applicability in terms of porosity (ε) and thickness ratio (δ/D) for the model?
• RQ5 Does the model capture the transition in pressure loss behavior between laminar and turbulent regimes, particularly the reversal in trends with plate thickness?

Key findings

• The proposed model shows excellent agreement with both numerical simulations in the laminar regime and experimental data in the turbulent regime.
• The model outperforms existing models in the literature in terms of predictive accuracy while maintaining a significantly simpler mathematical form.
• RANS simulations using the model as a pressure-drop source term show very good agreement with the model’s own predictions, validating its robustness in CFD applications.
• The model is applicable for porosities in the range 0.3 ≤ ε ≤ 0.7 and thickness ratios 0.2 < δ/D < 1.0, with performance degrading outside these bounds.
• The model correctly captures the reversal in pressure loss trends with plate thickness: thicker plates increase losses in laminar flow, while thinner plates increase losses in turbulent flow.
• The model’s simplicity and high accuracy make it a strong candidate for use in design optimization of heat exchangers, noise abatement systems, and flow conditioning devices.