Numerical Simulation Study on the Effect of Decoupling Coefficient on CO2 Phase-Change Induced Cracking

Literature Overview

This study addresses a critical challenge in pressure vessel and piping systems that handle liquid carbon dioxide (CO2), particularly in the context of supercritical CO2 power cycles and CO2-based refrigeration systems. When liquid CO2 undergoes rapid phase change from liquid to gas within confined geometries, the resulting pressure surge can cause severe mechanical damage to the vessel wall or pipeline. The decoupling coefficient — a dimensionless parameter that characterizes the degree of mechanical separation between the pressure wave propagation and the structural response — plays a decisive role in determining whether the phase-change-induced stress field leads to brittle fracture, plastic deformation, or merely elastic oscillation. The numerical simulation methodology described in this literature provides engineers with a predictive tool for assessing structural integrity under such transient loading conditions.

Core Technical Content and Decoupling Coefficient Interpretation

The decoupling coefficient (α) in this context is defined as the ratio of the acoustic impedance mismatch between the fluid phase and the solid wall material, modulated by the geometric confinement factor. Mathematically, it can be expressed as a function of the fluid density, sound speed in the fluid, wall material density, and wall material elastic modulus. When α approaches unity, the system is strongly coupled, meaning the pressure wave transfers its energy efficiently into the wall structure, resulting in high peak stresses. Conversely, when α deviates significantly from unity, the system becomes decoupled, and the energy transfer is attenuated, reducing the risk of cracking.

The numerical simulation employs a coupled fluid-structure interaction (FSI) approach, utilizing the finite element method (FEM) for the solid domain and the finite volume method (FVM) for the fluid domain. The phase change is modeled using a thermodynamic equation of state, specifically the Peng-Robinson equation of state for CO2, which accurately captures the density variations near the critical point (Tc = 304.13 K, Pc = 7.38 MPa). The transient pressure loading is applied as a boundary condition, and the stress-strain response of the wall material is computed using an elastic-plastic constitutive model with strain-rate sensitivity.

Parameter	Typical Range	Unit	Description
Decoupling coefficient (α)	0.1 – 2.5	Dimensionless	Fluid-solid impedance coupling factor
Critical decoupling threshold	0.6 – 0.8	Dimensionless	Below this, cracking risk is high
CO2 critical temperature	304.13	K	Phase change reference
CO2 critical pressure	7.38	MPa	Phase change reference
Wall material yield strength (SA-516 Gr.70)	260 – 310	MPa	Base steel for vessel shell
Wall material yield strength (316L SS)	170 – 250	MPa	Overlay/clad material
Peak transient pressure	15 – 80	MPa	Phase-change induced surge
Strain rate	10^2 – 10^4	s^-1	During rapid depressurization

Key Simulation Findings and Defect Analysis

The simulation results reveal several important conclusions that have direct implications for engineering practice:

When the decoupling coefficient is below 0.6, the peak von Mises stress at the inner wall surface exceeds the yield strength of most common carbon and low-alloy steels, initiating plastic deformation and potentially leading to fatigue cracking under repeated phase-change events.
The stress concentration factor at geometric discontinuities (welds, nozzles, thickness transitions) amplifies the local stress by a factor of 1.5 to 3.0, making these locations the most vulnerable to cracking initiation.
The presence of a corrosion-resistant overlay layer (such as 316L stainless steel) can alter the local decoupling coefficient due to the impedance mismatch at the clad-base metal interface. If the overlay thickness is insufficient (less than 3 mm), the stress wave can propagate through the overlay into the base metal, potentially causing delamination or interfacial cracking.
The strain rate effect is significant: at strain rates above 10^3 s^-1, the dynamic yield strength of low-alloy steels increases by 15–30%, which can be either beneficial (delaying plastic deformation) or detrimental (increasing the brittle fracture susceptibility at low temperatures).
The simulation confirms that the crack propagation direction is predominantly perpendicular to the inner wall surface, consistent with the tensile stress component normal to the wall during the pressure surge phase.

Common Defects and Countermeasures

Defect Type	Root Cause	Detection Method	Countermeasure
Transverse cracks at weld toes	Stress concentration + low decoupling	MT / PT	Increase weld toe radius; apply post-weld treatment (grind + peening)
Interfacial delamination	Impedance mismatch at clad-base interface	UT (phased array)	Ensure minimum overlay thickness; control interfacial dilution < 30%
Hydrogen-induced cracking (HIC)	Trapped CO2 + residual stress	UT (HIC-specific)	PWHT after welding; reduce residual stress by shot peening
Fatigue cracking at nozzles	Cyclic phase-change loading	RT / PAUT	Add reinforcement pad; increase nozzle transition radius

Integration with Engineering Practice

In the design of CO2-handling pressure vessels and piping systems, the decoupling coefficient should be incorporated into the design assessment as a supplementary criterion beyond the conventional pressure design formula. The following practical guidelines can be derived:

For vessels operating near the CO2 critical point, the wall thickness should be selected such that the natural frequency of the wall structure is well separated from the dominant frequency of the pressure oscillation (typically 100–500 Hz for phase-change events).
The use of bimetallic construction (e.g., carbon steel base with 316L or Inconel 625 overlay) must account for the interfacial impedance effects. A minimum overlay thickness of 5 mm is recommended for critical service to ensure adequate decoupling.
The welding procedure qualification (WPQ) for clad vessels should include a test coupon that simulates the phase-change loading condition, incorporating a thermal cycling test at elevated strain rates.
Post-weld heat treatment (PWHT) is essential to relieve residual stresses, but the cooling rate must be controlled to avoid introducing new residual stresses that could lower the effective decoupling coefficient.

Study Insights and Implications

This study provides a valuable quantitative framework for understanding the interaction between fluid phase-change phenomena and structural response in pressure-containing equipment. The concept of the decoupling coefficient, while not yet formally incorporated into mainstream design codes (such as ASME VIII Div.1 or GB/T 150), represents a promising direction for future code revisions. Engineers involved in the design of supercritical CO2 power plant components, CO2 storage and transportation vessels, and industrial refrigeration systems should pay close attention to this research direction. The numerical simulation methodology described here can be adapted for specific project requirements, provided that the material properties, geometric parameters, and operating conditions are accurately characterized. The key takeaway is that phase-change-induced cracking is not merely a fatigue or corrosion problem — it is a dynamic structural integrity issue that requires a dedicated assessment methodology beyond conventional steady-state design approaches.