A Spring-Mass-Damper Model Based on Separated Phase Flow Mode for Pulsating Heat Pipe with Adjustive-Structured Channels

Research Overview

This study develops a new spring-mass-damper model based on a separated phase flow mode to describe the oscillating behavior of vapor–liquid slug flow in pulsating heat pipes (PHPs). Conventional models often approximate the frictional resistance of two-phase flow as single-phase flow, which cannot adequately reflect the real pressure loss of slug flow. By incorporating separated two-phase pressure loss and liquid-film evaporation, this study evaluates the thermal performance of a newly proposed pulsating heat pipe with adjustive-structured channels (ASCPHP).

Graphical Abstract

Figure: One-page summary of the background, spring-mass-damper model, adjustive-structured channel PHP, model validation, main results, and potential applications.

Background and Objective

Pulsating heat pipes (PHPs) are compact and efficient passive phase-change cooling devices. Inside a PHP, vapor slugs and liquid slugs are alternately formed and oscillate due to the pressure difference between the evaporating and condensing sections, thereby transporting heat.

However, the vapor–liquid two-phase flow inside a PHP is highly complex and often chaotic, making performance prediction and structural optimization difficult. This study aims to establish a more realistic model based on separated phase flow and to evaluate the heat transfer enhancement potential of adjustive-structured channels.

Key Features of This Study

Separated phase flow model: Realistic two-phase pressure loss of slug flow is introduced into the damping term.
Spring-mass-damper model: Liquid slugs are represented as masses, vapor slugs as springs, and frictional resistance as dampers.
Liquid-film evaporation model: Film thickness, evaporation mass, and heat transfer coefficient are related to oscillation behavior.
ASCPHP structure: An expanding evaporator section and contracting condenser section are proposed to improve thermal performance.

Proposed Method and Working Mechanism

1. Dynamic modeling of vapor–liquid slugs

Adjacent liquid slugs are treated as masses, while the vapor slug between them is treated as a spring. The pressure difference caused by the temperature difference between the evaporator and condenser drives the reciprocating motion.

2. Pressure loss evaluation with separated phase flow

Instead of using a single-phase approximation, the proposed model evaluates frictional pressure loss based on the separated two-phase flow model, which better represents real slug flow in PHPs.

3. Heat transfer enhancement by adjustive-structured channels

The evaporator section expands to promote vapor discharge and liquid-film evaporation, while the condenser section contracts to enhance condensation heat transfer. This structure promotes more stable and directional oscillation.

Main Findings

Model validationComparison with literature data showed that 80% of the data fall within a ±20% error band.

Optimum filling ratioA filling ratio of around 50% is recommended for the proposed ASCPHP.

Oscillation amplitudeAt 50% filling ratio, the oscillation amplitude reaches about 0.12 m.

Effect of temperature differenceA larger temperature difference between the evaporator and condenser increases oscillation amplitude and promotes heat and mass transfer through the liquid film.

Effect of saturated temperatureWhen the saturated temperature increases from 293 K to 373 K, the oscillation amplitude decreases by about 24%.

Comparison with structured PHPsThe oscillating velocity of ASCPHP is 7.3% higher than that of a Tesla-valve PHP, 10.8% higher than that of a check-valve PHP, and 17.0% higher than that of an equal-diameter PHP.

Future Prospects

The proposed separated-phase-flow-based spring-mass-damper model can more realistically reflect vapor–liquid slug flow in pulsating heat pipes. Therefore, it is useful for predicting oscillation characteristics and optimizing PHP channel structures.

Future work can extend the model to different working fluids, filling ratios, orientations, heat-load conditions, and channel geometries. Further comparison with experimental results will help establish more practical design guidelines for adjustive-structured channel PHPs.

This approach is particularly promising for compact systems where high heat transport performance must be achieved within a limited space, such as electronics cooling and advanced thermal management systems.

Potential Applications

The results can support the design of compact and high-performance passive cooling devices.

Compact electronics cooling High-heat-flux devices Space thermal control Passive thermal management Thin heat transport devices

Summary

This study proposed a separated-phase-flow-based spring-mass-damper model to evaluate vapor–liquid slug oscillation in pulsating heat pipes more realistically.

The ASCPHP concept showed higher oscillating velocity and promising heat transfer enhancement compared with other structured PHPs.

          Conclusion：
          The proposed model is an effective design tool for optimizing pulsating heat pipes by considering real two-phase slug flow and liquid-film evaporation.
        