Nonuniform Initial Temperature Research Articles

Unified Picture on Temperature Dependence of Lithium Dendrite Growth via Phase-Field Simulation

Lithium dendrite growth due to uneven electrodeposition may penetrate the separator and solid electrolyte, causing inner short circuit and potential thermal runaway. Despite great electrochemical phase-field simulation efforts devoted to exploring the dendrite growth mechanism under the temperature field, no unified picture has emerged. For example, it remains open how to understand the promotion, inhibition, and dual effects of increased temperature on dendrite growth when using different electrolyte types. Here, by comprehensively considering the temperature-dependent Li + diffusion coefficient, electrochemical reaction coefficient, and initial temperature distribution in phase-field model, we propose that the activation–energy ratio, defined as the ratio of electrochemical reaction activation energy to electrolyte Li + diffusion activation energy, can be used to quantify the effect of temperature on dendrite morphology. Specifically, we establish a mechanism diagram correlating the activation–energy ratio, uniform initial temperature, and maximum dendrite height, which unifies the seemingly contradictory simulation results. Furthermore, results based on nonuniform initial temperature distribution indicate that a positive temperature gradient along the discharging current facilitates uniform Li + deposition and local hotspot should be avoided. These findings provide valuable insights into the temperature-dependent Li dendrite growth and contribute to the practical application of Li metal batteries.

Multi-regime reaction front and detonation initiation by temperature inhomogeneity

Auto-ignition, reaction front propagation, and detonation development are foundational events in combustion, and are relevant to the occurrence of engine knock. It is generally understood that different auto-ignition modes can be initiated by non-uniform initial temperatures, manifesting the transition from supersonic to subsonic combustion modes with increasing temperature gradients. In this work, we have investigated the auto-ignition and reaction front propagation of syngas/air mixtures initiated by wide-ranging temperature gradients, in both spherical and planar coordinates, and have identified a universal detonation response diagram with multiple, non-monotonic boundaries of auto-ignition modes under engine-relevant conditions. Specifically, it is shown that with increasing gradient steepness, in addition to the conventional three regimes of supersonic auto-ignition deflagration, detonation development, and subsonic auto-ignition deflagration, the reaction front propagation speed would first decrease dramatically and then increase, hence inducing additional detonation regimes. Consequently, two detonation peninsulas are identified, with the first corresponding to the well-established Bradley detonation peninsula and the second manifesting a broader detonation regime. Both detonation peninsulas depend on the hotspot size and they can connect together when the hotspot radius becomes sufficiently large. The transient auto-ignition processes and chemical-gas dynamic interactions agree with the typical characteristics of various auto-ignition modes. Finally, auto-ignition modes are summarized in the detonation diagram, in which the Bradley detonation peninsula is well reproduced and the new detonation peninsula is quantitatively determined. The present study demonstrates that auto-ignition modes are significantly affected by the non-monotonic behavior of reaction front propagation, and the use of actual propagation speed is necessary for steeper temperature gradients in order to determine more accurate dimensionless parameters.

Method of solving nonlinear nonstationary thermal conductivity problems for half-space

The technique of temperature fields determination in a half-space taking into account thermal radiation, temperature dependence of thermophysical characteristics, densities of surface and volumetric heat sources with non-uniform initial temperature distribution is suggested. Using Kirchhoff transform, Green's function, generalized functions and linear splines, heat conduction problems were reduced to solving a recurrent nonlinear algebraic equation with respect to values in the nodes of the spline of the Kirchhoff variable on the bounding surface. The results of numerical researches are provided. Cite as: B. V. Protsiuk, “Method of solving nonlinear nonstationary thermal conductivity problems for half-space,” Prykl. Probl. Mekh. Mat. , Issue 18, 93–101 (2020) (in Ukrainian), https://doi.org/10.15407/apmm2020.18.93-101

Spontaneous initiation and development of hydrogen–oxygen detonation with ozone sensitization

This work studies numerically the spontaneous initiation and sustenance of a detonation wave from a hot spot with a nonuniform initial temperature embedded within an H2O2 mixture with and without O3 addition. For the case with either no or just a small amount of O3 addition, a weak reaction wave is auto-ignited at the hot spot, accelerates and then transitions to a pulsating detonation, which propagates along the temperature gradient and quenches as it runs into the cold fresh mixture. However, with increasing O3 addition, the possibility of sustenance of a developing detonation within the gradient is significantly enhanced as it enters the cold mixture. Furthermore, the reduced induction time by O3 addition leads to earlier appearance of the spontaneous reaction wave and detonation formation in the cold mixture, demonstrating that quenching of the detonation is largely related to the instability property of the mixture because the shortened induction time reduces substantially the instability. It is also noted that, for 5%O3 addition, a low-temperature flame produced by the O3 reactions is present in front of the spontaneous reaction wave, inducing a local pressure wave, which facilitates spontaneous initiation and sustains the detonation entering the cold mixture. Moreover, O3 addition renders the critical temperature to induce the minimum spontaneous wave speed higher than the crossover temperature, while they are very close for the case without O3.

Simulation of high-pressure gas breakdown under conditions of spatially non-uniform initial ionization and temperature

The paper presents the results of numerical simulation of the extended atmospheric pressure discharge in configuration of the tip-to-plane diode. The simulation is based on a hydrodynamic model of a discharge plasma in a pure O2 medium at low average electric field strengths ~ 10 kV·cm−1. It was investigated how initial conditions, such as the presence of a weakly ionized plasma channel or a given temperature profile on the discharge axis, influence on the formation of a discharge structure at the initiation stage.

The uncertainty of laminar burning velocity of premixed H2-air flame induced by the non-uniform initial temperature field inside the constant-volume combustion vessel

The initial temperature distribution of the combustible mixture has a significant effect on the measurement accuracy of the laminar burning velocity using the outwardly propagating spherical flame method. In the present study, the initial temperature fields inside the constant-volume combustion vessel were obtained by different arrangement methods of heater. Further, the effects of the non-uniformity of initial temperature field on the propagation processes of two-dimensional premixed H2-air laminar flames were numerically studied. The results show that when the initial temperature field inside the vessel heated by heating tapes reaches a stable state, the temperature of H2-air mixture tends to descend first and then rise along the gravity direction, which indicates that the non-uniformity of the temperature field increases with the actual delivered power. Compared with the uniform initial temperature field, the maximum relative deviation of laminar burning velocity of H2-air mixture obtained in the non-uniform initial temperature field is 7% when the vessel is heated by heating tapes under the power of 669 W. However, the non-uniformity of the initial temperature field of the H2-air mixture in the vessel obviously decreases and the maximum relative deviation of laminar burning velocity is only 2% when a simulated evenly arranged heater is employed to heat the vessel. Consequently, it is quite necessary to evaluate the non-uniformity of the initial temperature field inside the constant-volume combustion vessel before using the outwardly propagating spherical flame method to determine the laminar burning velocity.

Rayleigh-Taylor turbulence with singular nonuniform initial conditions

We perform direct numerical simulations of three dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood number; the long-time growth is still self-similar, but not anymore proportional to $t^2$ and depends on the singularity exponent $c$ of the initial profile $\Delta T \propto z^c$. We show that the universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.

Extension of a viscous thread with temperature-dependent viscosity and surface tension

We consider the evolution of a long and thin vertically aligned axisymmetric viscous thread that is composed of an incompressible fluid. The thread is attached to a solid wall at its upper end, experiences gravity and is pulled at its lower end by a fixed force. As the thread evolves, it experiences either heating or cooling by its environment. The heating affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We develop a framework that can deal with threads that have arbitrary initial shape, are non-uniformly preheated and experience spatially non-uniform heating or cooling from the environment during the pulling process. When inertia is completely neglected and the temperature of the environment is spatially uniform, we obtain analytic solutions for an arbitrary initial shape and temperature profile. In addition, we determine the criteria for whether the cross-section of a given fluid element will ever become zero and hence determine the minimum stretching force that is required for pinching. We further show that the dynamics can be quite subtle and leads to surprising behaviour, such as non-monotonic behaviour in time and space. We also consider the effects of non-zero Reynolds number. If the temperature of the environment is spatially uniform, we show that the dynamics is subtly influenced by inertia and that the location at which the thread will pinch is selected by a competition between three distinct mechanisms. In particular, for a thread with initially uniform radius and a spatially uniform environment but with a non-uniform initial temperature profile, pinching can occur either at the hottest point, at the points near large thermal gradients or at the pulled end, depending on the Reynolds number. Finally, we show that similar results can be obtained for a thread with initially uniform radius and uniform temperature profile but exposed to a spatially non-uniform environment.

Film cooling sensitivity of laidback fanshape holes to variations in exit configuration and mainstream turbulence intensity

Experimental measurements and numerical simulations have been performed to investigate the sensitivity of film cooling of laidback fanshape hole to the variations in hole exit configuration and mainstream turbulence intensity. The measurements are conducted on a flat plate model with low-speed, incompressible mainstream. Film cooling performances of two laidback fanshape hole configurations are measured under four blowing ratios using transient liquid crystal measurement technique which can process the nonuniform initial wall temperature. Hole exit corner shape is changed from sharp corner to round corner to simulate the effect of real manufacturing and/or deposition on the exit configuration of ideal laidback fanshape hole. The lateral film coverage as well as the film cooling effectiveness of laidback fanshape hole with round corner exit are reduced due to the smaller lateral expansion caused by round corner shape, especially under low turbulence condition. Large mainstream turbulence intensity can enhance the lateral diffusion of film jets which is beneficial to film cooing of laidback fanshape hole with round corner under larger blowing ratios. For the heat transfer coefficient distributions of the two film hole configurations, variation in film hole exit configuration has very small influence on both the spatial features and the averaged values under the same mainstream turbulence conditions. However, the variation in mainstream turbulence intensity has notable influences on the heat transfer coefficient distributions for both film hole configurations, because the enhancement effect of film jets on heat transfer and the strength of counter-rotating vortex pair are different between high and low mainstream turbulence conditions. The discharge coefficients of laidback fanshape hole configurations are not sensitive to the variations in hole exit configuration and mainstream turbulence intensity under the same blowing ratio.

Effects of the non-uniform initial environment and the guide field on the plasmoid instability

Effects of non-uniform initial mass density and temperature on the plasmoid instability are studied via 2.5-dimensional resistive magnetohydrodynamic (MHD) simulations. Our results indicate that the development of the plasmoid instability is apparently prevented when the initial plasma density at the center of the current sheet is higher than that in the upstream region. As a result, the higher the plasma density at the center and the lower the plasma β in the upstream region, the higher the critical Lundquist number needed for triggering secondary instabilities. When β=0.2, the critical Lundquist number is higher than 104. For the same Lundquist number, the magnetic reconnection rate is lower for the lower plasma β case. Oppositely, when the initial mass density is uniform and the Lundquist number is low, the magnetic reconnection rate turns out to be higher for the lower plasma β case. For the high Lundquist number case (>104) with uniform initial mass density, the magnetic reconnection is not affected by the initial plasma β and the temperature distribution. Our results indicate that the guide field has a limited impact on the plasmoid instability in resistive MHD.

Investigation on the influence of nonuniform initial temperature on the transient heat transfer measurement of film cooling

Numerical and experimental investigations on the influence of nonuniform initial temperature on the transient heat transfer measurements are presented in this paper. The case of film cooling is investigated. When the initial wall temperature is nonuniform, the results of heat transfer coefficient and film cooling effectiveness, which are calculated by the equations derived with constant initial temperature, could deviate from the true values badly, especially in the condition of short test duration. Using initial wall temperature which is higher than the real values causes the results of heat transfer coefficient and film cooling effectiveness lower than the true values. And lower initial wall temperature produces higher results of heat transfer coefficient and film cooling effectiveness. However, when the initial temperature distribution in the region where conduction plays more influence on the wall surface temperature than the convection is well fitted by the cubic polynomial, accurate results can be obtained by the new equation which is derived from 1-D unsteady conduction model with nonuniform initial wall temperature. Some suggestions are also introduced to reduce the influence of nonuniform initial temperature when the initial temperature distribution is difficult to obtain and the equation derived from constant initial temperature has to be employed.

Film Cooling Performance of Converging-Slot Holes With Different Exit-Entry Area Ratios

Film cooling performances of two kinds of converging-slot-hole (console) with different exit-entry area ratios have been measured using a new transient liquid crystal measurement technique, which can process the nonuniform initial wall temperature. Four momentum ratios are tested. The film cooling effectiveness distribution features are similar for the two consoles under all the momentum ratios. Consoles with smaller exit-entry area ratio produce higher cooling effectiveness. And the laterally averaged cooling effectiveness results show that the best momentum ratio for both consoles’ film cooling effectiveness distribution is around 2. For both consoles, the heat transfer in the midspan region is stronger than that in the hole centerline region in the upstream but gradually becomes weaker as flowing downstream. With the momentum ratio increasing, the normalized heat transfer coefficient h∕h0 of both consoles increases. In the upstream, the heat transfer coefficient of console with small exit-entry area ratio is higher. But in the downstream, the jets’ turbulence and the couple vortices play notable elevating effect on the heat transfer coefficient for large exit-entry area ratio case, especially under small momentum ratios. Consoles with smaller exit-entry area ratio provide better thermal protection because of higher cooling effectiveness. And the distributions of heat flux ratio are similar with those of cooling effectiveness because the influence of η on q∕q0 is larger. For the consoles, smaller exit-entry area ratios produce lower discharge coefficients when the pressure variation caused by the hole shape is regarded as flow resistance.

Critical Slow Dynamics of Detonation in a Gas with Non-Uniform Initial Temperature and Composition: A Large-Activation-Energy Analysis

We study the dynamic conditions of existence of the self-sustained detonation regime in gases with non-uniform initial temperature and dilution in the case where the gradients of initial state are parallel to the propagation direction. We analyze the slow dynamics of the detonation supposing that the initial variations have the same order of smallness as the unsteadiness and curvature of the leading shock of the detonation front. We obtain a hyperbolic evolution law for the detonation shock front as a solution to an eigenvalue problem solved in the asymptotic limit of large activation energies for which the induction time of the chemical decomposition process is considered much larger than the heat-release time. We study the effect of the shock dynamics of this self-sustained detonation front on the induction time and we integrate the evolution law for some examples of distinct or combined, dispersive or localized, initial variations in the temperature and diluent mass fraction. We show the existence of a bifurcation set of initial conditions that separates the self-sustained detonations that will continuously achieve the CJ regime from those whose dynamics eventually fail to initiate the chemical decomposition because the dynamic induction length becomes too long. We find that the characteristic critical lengths associated with the initial or boundary conditions are larger than the reference CJ characteristic chemical length by several orders of magnitude, a well-established experimental feature of gaseous detonations. We identify subcritical and supercritical limits which, respectively, give necessary and sufficient conditions for detonation. Below the subcritical limit, the combustion front cannot be coupled to the shock front because the volumetric expansion rate behind the shock is too large. Above the supercritical limit, the relaxation from an overdriven detonation regime to the self-sustained regime is a continuous process, without decoupling and recoupling of the combustion and shock fronts. We interpret the critical domain between these limits as the parametric zone in which experiments show successive decouplings and transverse recouplings of the combustion and shock fronts before the final self-sustained CJ regime.

Experimental research on the thermal performance of converging slot holes with different divergence angles

Thermal performances of two kinds of converging slot-hole ( console) with different divergence angles have been measured using transient liquid crystal measurement technique which can process the nonuniform initial wall temperature. Four momentum ratios are tested. Consoles with different divergence angles produce different cooling effectiveness distributions in the upstream region. However, the cooling effectiveness distributions of the two consoles are similar in the downstream. The laterally averaged cooling effectiveness results show that the differences between the two consoles are very small and the best momentum ratio for both consoles’ cooling effectiveness distribution is around two. With the momentum ratio increasing, the normalized heat transfer coefficient h/ h 0 of both consoles increases, but the h/ h 0 value of small divergence case is higher and becomes progressively higher than that of large divergence case. Moreover, the effect of the couple vortices on the heat transfer coefficient distributions is more significant for the large divergence case. Both consoles provide the surface a certain degree of thermal protection, especially in the upstream region. The distributions of heat flux ratio q/ q 0 are similar with those of η because the influence of η on q/ q 0 is much larger than that of h/ h 0 on q/ q 0.

Unsteady conjugate laminar heat transfer of a rotating non-uniformly heated disk: Application to the transient experimental technique

Presented in the paper are the results of an investigation of 2D heat conduction effects on the transient heat transfer of a rotating disk heated up to a non-uniform initial temperature and suddenly subjected to unsteady cooling by still air. A self-similar solution of the transient laminar convective heat transfer confirmed that the heat transfer coefficient rapidly becomes time-independent and equal to its value at steady-state conditions. An analytical solution of the unsteady two-dimensional heat conduction inside a disk made of Plexiglas ® confirmed that the known infinite-slab approach can still be used as a transient technique for determining heat transfer coefficients. Use of the regular heat transfer regime theory for the same purpose can be recommended only for the cases with the moderate initial temperature non-uniformity.

Finite element analysis of thermal stresses in ceramic/metal gradient thermal barrier coatings

This paper studied the thermal stresses of ceramic/metal gradient thermal barrier coating which combines the conceptions of ceramic thermal barrier coating (TBC) and functionally gradient material (FGM). Thermal stresses and residual thermal stresses were calculated by an ANSYS finite element analysis software. Negative thermal expansion coefficient method was proposed and element birth and death method was applied to analyze the residual thermal stresses which have non-uniform initial temperature field. The numerical results show a good agreement with the analytical results and the experimental results.

An analytical model of a matrix heat exchanger with longitudinal heat conduction in the matrix in application for the exchanger dynamics research

The paper presents an analytical method for the solution of the problem of a fixed matrix heat exchanger with axial heat conduction within the matrix. The small parameter method and Laplace transform have been applied. A general solution has been obtained for the unsteady state in the form of function series, using single and double convolutions of functions, as well as a particular solution for both the uniform and non-uniform initial temperature of the matrix and for an arbitrary function of the fluid temperature at the inlet. Particular solutions have been used in the study of the matrix dynamics in determining dynamic characteristics for the standard input signals in the form of: Dirac δ pulse, Heaviside function and the function of sinusoidal variable temperature of the fluid at the inlet. The results obtained both illustrate and enable the assessment of the effect of axial heat conduction in the matrix on the dynamic properties of the heat exchanger.

A Transient Infrared Thermography Method for Simultaneous Film Cooling Effectiveness and Heat Transfer Coefficient Measurements From a Single Test

In film cooling situations, there is a need to determine both local adiabatic wall temperature and heat transfer coefficient to fully assess the local heat flux into the surface. Typical film cooling situations are termed three temperature problems where the complex interaction between the jets and mainstream dictates the surface temperature. The coolant temperature is much cooler than the mainstream resulting in a mixed temperature in the film region downstream of injection. An infrared thermography technique using a transient surface temperature acquisition is described which determines both the heat transfer coefficient and film effectiveness (nondimensional adiabatic wall temperature) from a single test. Hot mainstream and cooler air injected through discrete holes are imposed suddenly on an ambient temperature surface and the wall temperature response is captured using infrared thermography. The wall temperature and the known mainstream and coolant temperatures are used to determine the two unknowns (the heat transfer coefficient and film effectiveness) at every point on the test surface. The advantage of this technique over existing techniques is the ability to obtain the information using a single transient test. Transient liquid crystal techniques have been one of the standard techniques for determining h and η for turbine film cooling for several years. Liquid crystal techniques do not account for nonuniform initial model temperatures while the transient IR technique measures the entire initial model distribution. The transient liquid crystal technique is very sensitive to the angle of illumination and view while the IR technique is not. The IR technique is more robust in being able to take measurements over a wider temperature range which improves the accuracy of h and η. The IR requires less intensive calibration than liquid crystal techniques. Results are presented for film cooling downstream of a single hole on a turbine blade leading edge model.

Investigation of Thermal Resonance in Solution of a Two-Dimensional Singularly Perturbed Boundary-Value Problem of Nonstationary Heat Conduction with Nonlinear Boundary Conditions of the Stefan–Boltzmann Type

Data of the analytical-numerical parametric investigation of a singularly perturbed temperature field in the boundary layer of the side of a rectangle on which nonlinear boundary conditions of the Stefan–Boltzmann type are specified have been given. It has been established that a nonuniform initial temperature distribution of the Gaussian type causes the appearance of “discontinuous traveling thermal waves” in the corresponding boundary layer. A set of parameters for which the “discontinuous traveling thermal waves,” being superimposed, lead to a local nonlinear enhancement of the thermal field has been found. This effect can be considered as “thermal resonance.”

TWO-DIMENSIONAL UNSTEADY THERMAL STRESS ANALYSIS BY TRIPLE-RECIPROCITY BOUNDARY ELEMENT METHOD

If the initial temperature is assumed to be constant, a domain integral is not required for the solution of unsteady thermal stress problems without heat generaton using the boundary element method (BEM). However, under heat generation or nonuniform initial temperature distribution, the domain integral is necesary. In this report it is shown that the problem of unsteady heat conduction with heat generation and nonuniform initial temperature can be approximately solved without using the domain integral by the triple-reciprocity BEM. In this method, the distributions of heat generation and nonuniform initial temperature are interpolated using integral equations.