Predicting thermal instability in a closed loop pulsating heat pipe system

Mathematical models for a closed loop pulsating heat pipe (CLPHP) with multiple liquid slugs and vapor plugs are presented in this study. The model considers the effect of thermal instability in different sections of a CLPHP at different operational conditions. Based on a neural network, an approach of nonlinear autoregressive moving average model with exogenous inputs (NARMAX) can be applied to the thermal instability of CLPHP. This study approximates the nonlinear behavior of CLPHP with a linear approximation method that can establish the relationship among the response temperature differences between evaporator, adiabatic, and condenser sections. A multi-input single-output (MISO) strategy is adopted in this study to approximate nonlinear behavior of CLPHP. The predicted results show that the effect of the three sections to vapor condensation could be precisely distinguished; meanwhile, thermal performance of CLPHP would be predicted. The development of nonlinear identification technique will be helpful to optimize and understand the heat transfer performance of thermal instability in the different designs of CLPHP.     

Convective instability of a vertical thermal boundary layer in a differentially heated cavity

The convective instability of a vertical thermal boundary layer adjacent to the sidewall of a water-filled differentially heated cavity over a range of Rayleigh numbers (5 × 10⁷–3.44 × 10⁹) is investigated using direct stability analysis. The results show that the dominant frequency of the convective instability changes as perturbations travel downstream due to the presence of the horizontal boundaries, which is different from that of the vertical thermal boundary layer adjacent to an infinite or semi-infinite thermal wall. The features of the convective instability of the vertical thermal boundary layer adjacent to the sidewall are described, and the dependence of the dominant frequency on the Rayleigh number is obtained. Furthermore, the dependence of the flow rate and heat transfer through the cavity on the Rayleigh number is quantified by numerical results.     

Buoyancy driven convection in a particle-fluid mixture layer heated from below

An analytical study of thermal instability in a horizontal fluid layer with suspended particles is reported. A linear stability analysis for an initially motionless suspension confined between horizontal isothermal solid surfaces and subject to density driven mechanism is presented. By accounting for the possibility of fluid-particle thermal interaction, calculations predict instability for heating from below. Response is strongly dependent on the volume fraction of the particles, the heat loading and the particle aspect ratio.     

Thermal instability of a power-law fluid-saturated porous layer with an internal heat source and vertical throughflow

The thermal instability of internally heated convection in a porous medium saturated by a power-law (PL) fluid is studied. The governing dimensionless equations are solved using the normal mode approach, which leads to an eigenvalue problem for the linear stability theory. The neutral curves are obtained for different prescribed values of the other physical parameters. The effect of the PL index, internal heat source parameter, and Peclet number on the onset of instability was analyzed. Furthermore, an analytical solution is obtained for the regime of small wave numbers by using asymptotic analysis.     

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study.     

The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media

In this paper we use the parallel-flow approximation to determine the criterion for the onset of instability in the form of travelling waves in a horizontal thermal boundary layer in porous media. We find that waves grow beyond a nondimensional distance of 28.90 from the leading edge, a result which shows, somewhat surprisingly, that waves are to be preferred over vortices, which have been found to grow beyond 33.47 from the leading edge [1]. We discuss very briefly the implications of our analysis for the use of the parallel flow approximation in the determination of stability criteria for thermal boundary layers.     

Thermal instability in a plane channel with internal heating and horizontal Poiseuille throughflow

The effect of a basic Poiseuille throughflow on the thermal instability of a horizontal fluid layer bounded by two plane parallel walls is studied. An unstable thermal stratification is studied, entirely due to a uniform internal heat generation in the fluid, whereas the thermal boundary conditions do not impress any temperature difference across the fluid layer. Two cases are investigated: a symmetric case where both boundaries are perfectly conducting; a non-symmetric case where the lower boundary is adiabatic and the upper boundary is perfectly conducting. A linear stability analysis is carried out and the eigenvalue problem is solved numerically for arbitrary oblique rolls, and by a symbolic weighted residual method in the special case of longitudinal rolls. The main result is that the basic Poiseuille flow does not influence the thermoconvective instability at the onset of the least stable modes, i.e. the longitudinal rolls. Thus, the critical conditions are just the same as for a fluid at rest in the basic state. Although the focus is on the thermoconvective instability, it is proved that, even in the presence of the internal heat generation, Squire’s theorem holds for the hydrodynamic instability of the plane Poiseuille flow.     

Onset of Marangoni instability of a two-component evaporating droplet

The temperature and solute concentration reductions across a thin boundary layer near the free surface of an evaporating droplet may induce cellular flow motion in the droplet because of Marangoni instability. The present study is aimed at investigating theoretically the onset of Marangoni instability due to the evaporation of a two-component evaporating droplet.

With the quasi-steady approximation which means that the surrounding gas motion is asymptotically steady, the size change of the droplet is negligible, and the temperature and concentration distributions of the droplet are temporarily frozen at each specified instant of interest, the onset condition for Marangoni instability is obtained through the linear stability analysis.

By assuming the surface tension is a monotonically decreasing function of both temperature and concentration of the higher-volatility substance, the thermocapillary and diffuso-capillary effects augment each other. Therefore, the theoretical analysis predicts a linear relation, with a negative slope, between the onset thermal Marangoni number, Ma_T, and the onset solute Marangoni number, Ma_S. Moreover, when liquid Lewis number Le_l>1, the critical wave number, l_c, may possess different values depending on the variation of the thermocapillary effect and diffuso-capillary effect. In addition, Le_l has a stronger effect on the critical solute Marangoni number Ma_S,C, than on the critical thermal Marangoni number Ma_T,C. That is, as Le_l decreases, Ma_T,C decreases mildly while Ma_S,C increases drastically.     

Hydrodynamics and heat transfer prior to onset of nucleate boiling in a rectangular microchannel heat sink

The conjugate heat transfer of flow boiling in a rectangular microchannel heat sink (MCHS) was modelled numerically to investigate the hydrodynamics and thermal responses of flow prior to the onset of nucleate boiling (ONB). Local hydrodynamics and thermal conditions leading to ONB are analysed numerically for different heat flux. The flow patterns of different modes of microconvection and mixed convective flows including the circulating flow, wavy flow and seeping flow were demonstrated and discussed. The numerical study proposes the mechanism leading to the first bubble nucleation which cover the initiation of fluid instability until the ONB. This work provides better understanding of the superheat induced flow instability and the progressive fluid convection under transient heating.     

Flame dynamics of a meso-scale heat recirculating combustor

The dynamics of premixed propane–air flame in a meso-scale ceramic combustor has been examined here. The flame characteristics in the combustor were examined by measuring the acoustic emissions and preheat temperatures together with high-speed cinematography. For the small-scale combustor, the volume to surface area ratio is small and hence the walls have significant effect on the global flame structure, flame location and flame dynamics. In addition to the flame–wall thermal coupling there is a coupling between flame and acoustics in the case of confined flames. Flame–wall thermal interactions lead to low frequency flame fluctuations (∼100 Hz) depending upon the thermal response of the wall. However, the flame–acoustic interactions can result in a wide range of flame fluctuations ranging from few hundred Hz to few kHz. Wall temperature distribution is one of the factors that control the amount of reactant preheating which in turn effects the location of flame stabilization. Acoustic emission signals and high-speed flame imaging confirmed that for the present case flame–acoustic interactions have more significant effect on flame dynamics. Based on the acoustic emissions, five different flame regimes have been identified; whistling/harmonic mode, rich instability mode, lean instability mode, silent mode and pulsating flame mode.     

The effect of the various system stresses on the integrity of a cracked piping system

The paper describes the analysis of a simple model which allows for the effect of the various stresses: weight, thermal, pressure and earthquake, to be incorporated within a stability analysis for a cracked piping system. The instability criterion is derived on the basis of the tearing modulus concept, and it is clearly shown that the instability condition is independent of the various types of loading but depends solely on the interplay between the properties of the cracked section, i.e. the material's crack growth resistance, and the elastic flexibility of the piping system.     

高压下氢气-乙醇球形膨胀火焰的层流燃烧速度和火焰不稳定性研究

在初始温度为400 K、不同的初始压力（0.1 MPa、0.4 MPa）、氢气比例（70%、80%）和当量比（0.7～1.4）条件下进行氢气-乙醇预混燃烧实验,使用高速纹影技术记录火焰传播图像。对氢气-乙醇球形膨胀火焰中的层流燃烧速度（LBV）进行实验研究,发现LBV随着氢气比例的增加而增加,压力升高却有着负影响。对火焰发展不同阶段的火焰形貌进行了研究。当火焰表面的大裂纹分裂出现小裂纹并且导致新细胞再生时,火焰变得不稳定。通过热膨胀比、火焰厚度和刘易斯数等参数考察了流体动力学效应和热扩散效应对火焰固有不稳定性的影响。结果表明,流体动力不稳定性随着压力的增加而增加,热扩散不稳定性对压力变化的敏感性较低。此外,增加氢气比例或初始压力会导致火焰更早遭受不稳定。     

Observation of preferred instability modes in a mechanically excited thermal plume using Schlieren visualizations

An experimental study of the instability modes of a laminar axisymmetric thermal plume under symmetrical controlled disturbances of varicose type was carried out. The Schlieren technique was used to investigate the considered flow. The range of excitation frequencies over which the studied plume became unstable was determined. The size of the corresponding induced large-scale structures was analyzed in function of the disturbance frequency. The results obtained throughout this work confirmed the ability of a plume to behave like a frequencies filter.     

The onset of instability in a horizontal fluid layer due to a step change in temperature

The onset of instability in a fluid layer which is subjected to a sudden change in surface temperature is analysed by a modified version of the frozen time hypothesis. The assumption that for large Prandtl number the temperature disturbances are confined to the effective thermal depth leads to a considerable simplification in the formulation of the stability problem. The effect of the Rayleigh number on the onset time is discussed and clearly explained. The relation between the Rayleigh number and the wavenumber predicted here agrees remarkably well with the extant amplification theory.     

Linear analysis of an aerothermal instability occurring in diffusion-controlled premixed catalytic combustion

The onset of the unstable temperature distribution which may appear in plane axisymmetric catalytic burner is studied. The instability mechanism is assumed to be related with the temperature dependence of the viscosity, thus with the pressure drop in the porous combustor, governed by Darcy’s law. An area e.g., of lower temperature (dark zone) characterised by a smaller value of the kinetic viscosity gives rise to a locally increased gas flow mass velocity, the pressure drop remaining constant over the burner cross-section. The locally increased mass velocity produces an enhanced cooling of the area, whereby heat conduction from the hotter surrounding area tends to restore a homogeneous temperature distribution. A linear analysis of this thermal instability mechanism is carried out and yields a simple analytic solution for the state of neutral stability.     

Onset of convective stability in a fluid-saturated porous layer subjected to time-dependent heating

A theoretical analysis of thermal instability driven by buoyancy forces in transient temperature fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy's law is used to explain characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the principle of exchange of stabilities, the stability analysis is performed on the basis of the linear amplification theory. The result predicts the critical condition of onset of buoyancy-driven convection, which is governed by the Darcy-Rayleigh number. The present stability criteria predict the experimental data quite well.     

The onset of vortex instability in laminar forced convection flow through a horizontal porous channel

The onset of convective instability in a fluid-saturated porous layer between the two horizontal plates heated isothermally from below has been analyzed theoretically by using propagation theory. In the analysis the thermal dispersion coefficient is assumed to be proportional to the streamwise velocity. The results show that both inertia and thermal dispersion stabilize the system.     

Thermal performance of integral bypass diode solar cell modules

Without appropriate protection, solar cell arrays can be vulnerable to thermal instability because of mismatched cell characteristics caused by effects such as cell cracking or partial shading of the array. The normal method of protecting against such thermal instability in both small and large arrays is to include bypass diodes across groups of series-connected cells. Experimental results are described for the thermal performance of a novel approach whereby bypass diodes are integrated into the solar cell structure during cell fabrication. The main conclusion is that the present integral bypass diode approach automatically protects against thermal instability in both small and large arrays without the need for any other protective measures. This is in addition to the improved tolerance of the array output power to partial shading.     

Hydrodynamic and diffusion effects on the stability of spherically expanding flames

We examine the stability of an outwardly propagating spherical flame accounting for both hydrodynamic and thermodiffusive effects. For Lewis numbers less than a critical value Le¹ < 1, disturbances of the flame front grow during the initial phase of propagation, i.e., when the radius is comparable to the flame thickness. However, for Le > Le¹, the flame, which is stable to thermodiffusive effects, becomes unstable only after a critical size is reached. This instability is hydrodynamic in nature and is caused by the thermal expansion of the gas. In this study we provide an expression for the determination of the critical size, or a critical Peclet number, which depends on the thermal expansion coefficient and on the Lewis number. The explicit dependence on all the relevant physicochemical parameters enables us to compare our results with experimental data.     

Mono‐diffusive Hadley‐Prats flow in a horizontal porous layer subject to variable gravity and internal heat generation

Analysis of internal heated and gravity effect on the onset of Hadley‐Prats flow in a horizontal porous layer with inclined temperature gradients is investigated using the linear and nonlinear instability analysis. The transformed eigenvalue problem is evaluated numerically to find the eigenvalue, which is treated as a vertical thermal Rayleigh number (R_z). It is evaluated by applying shooting and Runge‐Kutta method. Also, the critical R_z is investigated for different parameters governing the flow. A theoretical study is made to understand the influence of gravity field on the mechanism of mono‐diffusive instability of Hadley‐Prats convection in a fluid saturated horizontal porous layer. Nonlinear stability is evaluated by using energy functional. The comparison between linear and nonlinear instability results are presented and it is noted that linear theory of instability may not be useful to capture the complete picture of stability and instabilities may arise before one attains the linear stability threshold. This subcritical instability region is identified between the linear and energy thresholds in the parameter space of the problem considered.