Instability Boundary Research Articles

Influence of radiation on the stability of MHD micropolar fluid in a vertical channel

The objective of the present article is to explore the stability of micropolar fluid flow in a vertical channel in the presence of thermal radiation and a transverse magnetic field. The generalized eigenvalue problem is numerically solved by utilizing the Chebyshev spectral collocation method, which is obtained from the perturbed state using the normal mode technique. The numerical data were compared with previously published results for particular cases. The critical modified Grashof number (Grc′) and the associated wave numbers (αc) are calculated and displayed graphically for different values of the parameters. It is noticed that the boundaries of instability may be increased or decreased with the flow governing parameters because of the presence of a magnetic field and thermal radiation.

Parametric instability analysis of rotors under anisotropic boundary conditions

Ensuring rotor stability is a major concern in engineering, as instabilities can lead to catastrophic failures. Existing literature shows that anisotropic boundary conditions significantly affect the parametric instability characteristics of rotors under periodical axial loads. However, there is little literature systematically analyzing the formation mechanism of parametric resonance under these boundary conditions or providing a detailed classification of the parametric instability regions. Therefore, this paper presents a comprehensive parametric instability analysis of a rotor subjected to periodic axial loads under anisotropic boundary conditions. A novel approach based on the multiple scales method is proposed to address anisotropy in the boundary conditions. Using this approach, the analytical boundaries of the parametric instability regions are derived, and a proof regarding the absence of certain parametric resonances is presented. These analytical solutions are validated by numerical results obtained from the discrete transition matrix method, which form the basis for systematically investigating the effects of anisotropy in direct or cross-coupling stiffness/damping coefficients on the rotor instability. The key scientific contributions of this work include: Deriving analytical instability boundaries, providing a more efficient alternative to purely numerical methods while maintaining high accuracy; Demonstrating the absence of parametric resonance of difference type under both isotropic or anisotropic boundary conditions; Discovering that anisotropy in stiffness coefficients can induce self-interaction within a given forward or backward whirl mode, as well as interaction between two forward or two backward whirl modes, leading to additional instability regions; Reducing anisotropy in direct damping coefficients may increase critical dynamic load coefficients, potentially enhancing rotor safety; If the cross-coupling stiffness coefficients exceed the threshold for triggering intrinsic instability, the rotor may become unstable in all operating conditions. All these findings offer insights into the stability management of rotors under various operating conditions and provide valuable guidance for designing and operating safer, more efficient rotor systems.

К оценке геодинамической устойчивости геосфер Земли

The Earth, as a system, is characterized by certain average state parameters (density, temperature). These parameters cannot but depend on similar states of internal geospheres (subsystems), which follow the unified law of increasing entropy of the cooling Earth from the center in the direction of the Earth's radius. As a model for assessing the dynamic stability of the Earth's internal geospheres relative to each other, the principle of the golden proportion (golden section) was used with the given parameters of density, temperature, power of the geospheres to the extreme ratios of their states at points (0.618; 1.618; 2.618), which determine the conditions for the stable dynamic equilibrium of the compared parameters of geospheres. And if these relations satisfied the known theoretical, model, geophysical data, then the conclusion was made that the geospheres in the compared parameter relations were in a state close to a stable dynamic equilibrium of the exchange of matter and energy between them. Otherwise, it was recognized that the compared geospheres of the Earth were in a state of either unstable dynamic equilibrium with an assessment of the level of this deviation from the golden numbers, or the known values of the density and temperature of the geospheres, as well as their structure, should be subject to clarification. Average model estimates of the parameters of the Earth's internal geospheres reach a stable dynamic equilibrium at a level of deviation from the golden numbers of up to 2.72 %. This allows estimating the model duration of the modern geological activity of the Earth for another 124 million years until the formation of a new state of the existing continents. The instability of the dynamic equilibrium of density and temperature of matter is established at the boundaries: continental and oceanic crust; oceanic crust and Golitsin layer; at the boundary between the outer part of the Earth's core and the lower mantle; inside the Earth's core at the level of identified transition zones in the four-layer core model. The presence of spheres with a high core density from 16.05 to 26.45 g/cm3 suggests the stratification of its central part into essentially gold and platinoid. The presence of instability boundaries in the dynamic state of geospheres is in good agreement with the concept of plate tectonics and with the depths of plume origin. It can be assumed that the relative equilibrium of the internal structure of the Earth will continue for about 124 million years until the beginning of the formation of a new Pangea Proxima, which, according to Cristofor Scotese, will arise in 200 million years.

Dynamics of axially moving spinning microbeams composed of tri-directional graded porous materials with axisymmetric cross-sections and piezoelectric layers in complex fields

The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.

A nonlinear disturbance observer for sliding mode control of surge in centrifugal compressors via TCV actuator

Surge is a form of dynamic instability created as an unstable pattern in the flow of fluid and can severely affect centrifugal compressor performance by causing fluctuations in flow and pressure parameters. Due to the heavy and costly damage that the surge may cause in various industrial processes such as petrochemical plants, it is necessary to design an appropriate control system to reduce the effect of this phenomenon. The problem of active surge control of a centrifugal compressor using the throttle control valve (TCV) in the presence of compressor parametric uncertainties as well as large demands on upstream and downstream loads is investigated in this work. The control objective was to design a robust control system that can stabilize the compressor over a wide operating range without knowing the upper bound for the uncertainties and load demand. The controller should also react quickly by generating a smooth control signal without saturating the control input. These objectives are achieved by designing a sliding mode controller along with a nonlinear disturbance observer. The performance of the proposed disturbance observer-based controller is evaluated under various operational and load conditions and the results are compared against fuzzy type 1, conventional sliding mode, and wavelet-based neural network robust adaptive controllers. The results show that the proposed method can tolerate large disturbances without any knowledge on the upper bound of the incident disturbance, both on the downstream pressure and upstream mass flow which is highly desirable in practice. The comparative study proves the efficacy of the proposed method using various performance measures. The study also confirms the superior robust performance and stability of the proposed method in front of matched and mismatched disturbances as well as model uncertainties especially close to the instability boundary. Although choosing a TCV actuator has made the control system design easier, the sensitivity of the control valve to flow coefficient and zero calibration under different operating ranges of the compression system is studied carefully and some recommendations for the users are provided.

Influence of heat flux profile on two-phase flow instability in parallel channels of helical coil once-through steam generator

To enhance the heat transfer capability, the helical coil once-through steam generator (HCOTSG) has been widely utilized in the small modular reactor (SMR). There are hundreds of parallel helical channels in the HCOTSG, and the coolant undergoes the phase change from subcooled liquid to superheated vapor in the helical tube. The flow oscillation between parallel channels may be triggered during the phase change. In present study, the two-phase flow instability is investigated with different heat flux profiles under many operating conditions. The thermal–hydraulic model for parallel channels of HCOTSG is established based on our previous work, while the local heat transfer phenomenon such as subcooled boiling, critical heat flux, and wall conduction are considered in detail. The heat flux profile along the tube is ascertained by the steady-state analysis of HCOTSG under different operating conditions and applied to the outside surface of the helical channel. The heat flux value is increased step by step to trigger the out-of-phase oscillation between parallel helical channels. The thermal–hydraulic model and analysis method are validated against experimental results. The characteristics of flow instability in the helical channel are also analyzed. It is observed that the delay effect causing the flow instability is more obvious if the void fraction exceeds 0.7 in the starting stage. Then the boundary of flow instability is compared under different heat flux profiles for various operating conditions of HCOTSG. The results suggest that the distribution of heat flux in the two-phase region plays a more significant role in the occurrence of flow instability in the parallel helical channel system. The thermal–hydraulic characteristics during flow instability are governed by the combined effects of void propagation and delayed feedback in the system. In conclusion, the thermal–hydraulic condition of HCOTSG undergoes the unstable region to achieve the normal operating point, which can be avoided by adjusting the operating parameters.

The nonlinear instability of transverse vibration behavior of functionally graded materials sandwich rectangular plates of under a harmonic loading and subsonic flow

This work is devoted to studying the combined action of periodic in-plane load and tangential subsonic flow on the nonlinear mechanism of the out-plane deformation of the functionally graded composite plate. Three distribution functions are proposed to investigate the distribution of the transverse shear strains and stresses across the thickness of the plates. By using Hamilton’s variational principle, the equations governing the plate instability boundaries are formulated. A nonlinear differential equation describing the first mode of the plate dynamic instability behavior by employing Galerkin’s method. The method of multiple time scales is used to obtain a periodic one-mode solution, which directly leads to the solvability condition. The different resonance cases for the interaction between the frequency of out- plane deformation and the external forces are discussed to discover the extent of the sandwich functionally graded material (FGM) rectangular plate resistance in the presence of external influences. Various bifurcation diagrams for different cases of resonance are obtained versus the basic parameters. In view of this study, we could get a deeper look at the complexity of frequency components in resonance responses of the sandwich FGM rectangular plate. The results could provide some suggestions for the sandwich plate’s vibration reduction design or fault diagnosis field or design fault diagnosis.

Computational Study on Compressor-Combustor Interactions for Improved Matching of a Micro Gas Turbine

ABSTRACT Understanding complex aerodynamics/combustion interactions across major components of aeroengines, including the compressor, combustor and turbine is demanded for the improved performance of advanced propulsion systems. This study employs high-fidelity CFD simulations to investigate the coupled compressor-combustor interactions for the improved performance of a micro gas turbine. In the prototype configuration, the deficient compressor/combustor matching causes insufficient air/fuel mixing and delayed combustion inside the combustor chamber. By reducing the flow area of the compressor and redistributing the air holes on the combustor chamber, a stable united recirculation structure is formed to promote air/fuel mixing and efficient combustion, achieving a over 50% decrease in OTDF and RTDF at the combustor exit and a total 20% decrease of pressure loss in the entire engine through-flow. Compared with the single-component combustor simulation, the coupled compressor-combustor results exhibit stronger turbulence mixing, increased temperature uniformity inside the combustor chamber. Compared with the single-component compressor simulation, the compressor in the multi-component simulation shows the reduced flow angle and Mach number at the compressor outlet, leading to increased stall critical angles and delayed flow separation at the compressor diffuser and vanes. This demonstrates that the added combustor endues the compressor with an expanded operating range and a lower mass-flow rate instability boundary. This work implies that 3D multi-component CFD simulation is necessary to understand the aerodynamic and combustion interactions and improve the multi-component matching in gas turbine engines.

Numerical study of triggered thermoacoustic instability driven by linear and nonlinear combustion response in a solid rocket motor

Thermoacoustic instability (TAI) has consistently presented challenges to the development of solid rocket motors (SRMs), making the prediction of TAI critically important. Most existing TAI predictions rely on linear instability theory, which is inadequate for predicting certain nonlinear TAI, such as triggered TAI. To address this challenge, this study has constructed the nonlinear response model for the burning rate, known as the nonlinear pressure-coupled response function (PCR). The nonlinear PCR is capable of considering the effects of both frequency and amplitude of pressure oscillations. By integrating the PCR into the computational fluid dynamics framework, this study successfully replicated the nonlinear triggered TAI. When exclusively employing the linear PCR, the model demonstrates typical multi-order resonant modes, and the stability map exhibits either persistent stability or persistent instability, contingent upon the distribution of the linear PCR function. However, by incorporating the nonlinear PCR, this study effectively reproduces nonlinear pulse-triggered instability. This instability arises only when the pulse intensity surpasses the threshold value due to SRM damping. The nonlinear response framework allows for the identification of the instability boundary, facilitating a more comprehensive assessment of SRM performance. This study fills a critical gap in predicting triggered TAI in SRMs, providing insights into nonlinear TAI mechanisms.

Experimental study on voltage instability of proton exchange membrane fuel cell: Types and boundaries

ABSTRACT This paper presents an experimental study on the voltage instability in proton exchange membrane fuel cells operating at high current densities, which is important for improving their reliability and durability. Based on experimental findings regarding transparent fuel cells, a method is proposed to identify different types of voltage instability via statistical results of linear changing rate and oscillation amplitude. The types and boundaries of voltage instability are elucidated while evaluating the impact of cathode relative humidity and flow rate on voltage instability. The findings reveal that (1) the voltage instability is greatly influenced by the cathode-side relative humidity and flow rate, (2) there are three typical types of voltage instability: voltage decline, voltage oscillation, and both, and (3) voltage decline occurs at low cathode humidity, while voltage oscillation becomes more severe at large cathode humidity and low flow rate; (4) Reduction of water content in the membrane leads to voltage decline, while an increase in water content in the catalyst layer, gas diffusion layer, and channels leads to voltage oscillation. A full-condition map diagram demonstrating voltage instability during high current density conditions is presented. The method for creating this map for voltage instability will be employed to enhance fuel cell performance.

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.

Global nonlinear stability of bidispersive porous convection with throughflow and depth-dependent viscosity

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation.

Fractional Mathieu Differential Equations in Dynamic Stability of Piles

Piles are commonly used in Civil and Mechanical Engineering to provide support to superstructures and to transmit loads to deeper ground layers. During earthquakes, pile instability can result in the collapse of the entire structure. In this paper, the pile is modeled as a column surrounded by Winkler soil foundations with fractional damping. Investigation of the axially loaded pile leads to a fractional Mathieu differential equation of motion. The Bolotin method, employing harmonic balance, is proposed to obtain the approximate instability boundaries of the pile in the stability diagrams. A practical example is presented to conduct a parametric study on pile instability concerning the fractional order. The study observes parametric resonance in the first order, representing the principal instability region, which requires special attention to maintain stability. Furthermore, increasing the fractional damping order leads to a higher critical dynamic load and a slight reduction in the critical frequency ratio in each instability region. Higher-order instability regions exhibit greater sensitivity to changes in the fractional order. These results provided insights into the stability of piles under earthquake conditions.

Flow-induced oscillations of pitching swept wings: stability boundary, vortex dynamics and force partitioning

We study experimentally the aeroelastic instability boundaries and three-dimensional vortex dynamics of pitching swept wings, with the sweep angle ranging from 0 $^\circ$ to 25 $^\circ$ . The structural dynamics of the wings are simulated using a cyber-physical control system. With a constant flow speed, a prescribed high inertia and a small structural damping, we show that the system undergoes a subcritical Hopf bifurcation to large-amplitude limit-cycle oscillations (LCOs) for all the sweep angles. The onset of LCOs depends largely on the static characteristics of the wing. The saddle-node point is found to change non-monotonically with the sweep angle, which we attribute to the non-monotonic power transfer between the ambient fluid and the elastic mount. An optimal sweep angle is observed to enhance the power extraction performance and thus promote LCOs and destabilize the aeroelastic system. The frequency response of the system reveals a structural-hydrodynamic oscillation mode for wings with relatively high sweep angles. Force, moment and three-dimensional flow structures measured using multi-layer stereoscopic particle image velocimetry are analysed to explain the differences in power extraction for different swept wings. Finally, we employ a physics-based force and moment partitioning method to correlate quantitatively the three-dimensional vortex dynamics with the resultant unsteady aerodynamic moment.

Prediction Method for Instability Boundaries of Self-Excited Oscillation Combustion in a Model Combustor

ABSTRACT This paper presents a method for predicting the stability boundaries of a model combustion chamber using a data-driven approach based on the n-τ model. The n-τ model is derived using a combination of quasi-Monte Carlo sampling and a low-order thermoacoustic network model (LOTANM), and its optimization is established based on experimental data of self-excited oscillating combustion. The objective function is defined as a function of the growth rate, the difference between the corresponding eigenfrequency and the experimental self-excited oscillating combustion frequencies. The critical operating condition boundaries of the model combustion chamber are successfully predicted using the LOTANM, and the results conform with the experimental results. Importantly, while the proposed method reduces the required number of reproducible experiments and eliminates the need for high-power speakers, the linear n-τ model has an inherent limitation in capturing the spectrum of nonlinear behaviors that may arise in the oscillating combustion processes. Overall, the proposed approach represents a practical and effective tool for predicting the stabilities in the testing phases of aeroengine engineering.

Coevolution of Rock Slope Instability Damage and Resonance Frequencies From Distinct‐Element Modeling

AbstractAmbient vibration measurements can detect resonance frequency changes related to rock slope instability damage or boundary condition changes during progressive failure. However, the impact of slope kinematics on resonance changes and the expected form and sensitivity of frequency evolution during destabilization require clarification to improve the implementation of this technique across diverse settings. Since instrumented rock slope failures are rare, numerical modeling is needed to study the anticipated spectral response from in situ monitoring. We used 2D distinct‐element modeling to evaluate the sensitivity and evolution of rock slope resonance behavior for slab toppling, flexural toppling, and planar sliding instabilities during progressive failure. Model simulations revealed that fundamental resonance frequency decreases between 20% and 60% with changes correlated with increasing length of open joints. Changes to higher‐order frequencies associated with landslide sub‐volumes were also detectable for cases with multiple fracture networks. Resonance behavior was most pronounced for failures dominated by steeply dipping open tension cracks, that is, flexural and slab toppling. Additionally, amplification patterns across the slope varied for the flexural toppling and sliding cases, providing potential new information with which to characterize landslide failure mechanisms using ambient vibration array measurements. Our results demonstrate landslide characteristics well‐suited for in situ ambient resonance monitoring and provide new data describing the anticipated changes in resonance frequencies during progressive rock slope failure.

The role of local thermal non-equilibrium on the instability analysis in the presence of variable gravity field with throughflow

The influence of variable gravity on the stability analysis has been investigated in a horizontal porous region with throughflow under a local thermal non-equilibrium (LTNE) situation. Flow inside the porous region is considered to be followed by the Darcy model. Also, the linear varying gravity field with height and nonlinear (parabolic, cubic, and exponential) changing gravity field depth have been considered to address the investigation. The obtained eigenvalue problem for the perturbed state is solved via bvp4c technique in MATLAB. Finally, we investigated the convective boundaries of the system due to the governing parameters, such as gravity variation parameter (λ), porosity-modified conductivity ratio (γ), interphase heat transfer parameter (H), and throughflow parameter (Q). The outcomes assure that the interphase heat transfer parameter has a significant impact on the breakdown of the convection inside of its intermediate range, while the local thermal equilibrium (LTE) state occurred when H converges both the limiting cases, i.e. H→0 and H→∞. It has also been observed that the gravity variation parameter and throughflow parameter have a stabilizing effect, whereas the porosity-modified conductivity ratio destabilizes the flow. Further, it is distinguished that the instability boundaries are unchanged by H when γ≥10. In addition, the flow field is more delayed for exponential changing gravity field, whereas more advanced for cubic varying gravity field.

A semi-analytical and semi-numerical method for solving plasma instability of nonuniform two-dimensional electron gas

The plasma instability of two-dimensional electron gas (2DEG) is a crucial physical mechanism for generating terahertz radiation in field-effect transistors, especially in high electron mobility transistors (HEMTs). In this paper, we have proposed a new semi-analytical and semi-numerical method to deal with oscillation problems of any nonuniform 2DEG plasma, especially considering the steady-state distribution, which can be calculated and analyzed more quickly than only using numerical calculation. By constructing a wave equation, using the auxiliary function and Wentzel–Kramers–Brillouin approximation method, the wave vector of the plasma wave is obtained. On this basis, combined with the Dyakonov–Shur instability's boundary conditions, the oscillation frequency, the wave amplitude increment, and their correction caused by the nonuniformity can be obtained by numerical calculation. Furthermore, the analytical solution is obtained under reasonable approximate conditions for the linear distribution of electron concentration. It is proved that the electron concentration gradient in the channel will not only attenuate the wave increment but also decrease the plasmonic frequency in the case of linear distribution. Moreover, we get the reasons for the above conclusions through theoretical derivation. We also investigate the effects of various device parameters on attenuation, such as gate length, electron mobility, and voltage, which may explain the difference between the actual and theoretical values in HEMTs and provide new guidance for device design.

Diffusion mechanisms of convective instability in liquid and gas mixtures

AbstractA review of publications on stability of mechanical equilibrium of multicomponent mixtures in gases and liquids under non‐isothermal and isothermal conditions is given. Studies where diffusion in binary and multicomponent mixtures led to the occurrence of instability of mechanical equilibrium of the system have been analyzed. The main attention is paid to the description of approaches predicting the areas where there are increasing convective disturbances, as well as the determination of the spectrum of thermophysical parameters where the contribution of convection to heat and mass transfer is negligible. At the same time, the problems determining the role of diffusion, thermodiffusion, and double diffusion mechanisms in the separation of mixture components at the boundary of convective instability were given priority in the description. The results of investigations related to the study of the evolution of flows arising due to instability at the initial stage of mixing were also discussed.

An improved frequency-domain model for the supercritical flow instability analysis in vertical tubes

In a supercritical water reactor, the density wave oscillation (DWO) may occur due to the dramatic changes in the density of the working fluid in the pseudo-critical region. Based on the frequency-domain method, this study proposes an improved model to study DWO. First, the latest partition method is used in this study. Second, in the derivation of the transfer function in the light fluid region, the density change of the fluid is considered. Moreover, the different states of the outlet fluid are handled differently. We use the Nyquist criterion to determine the flow stability and obtain the boundary heat flux (BHF) of different working conditions. After model verification, it is proved that the model accuracy is improved. We analyze the influence of pressure, inlet enthalpy, mass flow rate, inlet throttling coefficient, and tube parameter on the instability boundary. At a certain inlet enthalpy, a minimum BHF of flow instability exists.