Continuum Formulation for Non-Equilibrium Shock Structure Calculation

Are extensions to continuum formulations for solving fluid dynamic problems in the transition-to-rarefied regimes viable alternatives to particle methods? It is well known that for increasingly rarefied flow fields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier-Stokes equations. The inclusion of higher-order terms, such as Burnett or high-order moment equations, could improve the predictive capabilities of such continuum formulations, but there has been limited success in the shock structure calculations, especially for the high Mach number case. Here, after reformulating the viscosity and heat conduction coefficients appropriate for the rarefied flow regime, we will show that the Navier-Stokes-type continuum formulation may still be properly used. The equations with generalization of the dissipative coefficients based on the closed solution of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation, are solved using the gas-kinetic numerical scheme. This paper concentrates on the non-equilibrium shock structure calculations for both monatomic and diatomic gases. The Landau-Teller-Jeans relaxation model for the rotational energy is used to evaluate the quantitative difference between the translational and rotational temperatures inside the shock layer. Variations of shear stress, heat flux, temperatures, and densities in the internal structure of the shock waves are compared with, (a) existing theoretical solutions of the Boltzmann solution, (b) existing numerical predictions of the direct simulation Monte Carlo (DSMC) method, and (c) available experimental measurements. The present continuum formulation for calculating the shock structures for monatomic and diatomic gases in the Mach number range of 1.2 to 12.9 is found to be satisfactory.     

A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes

In this paper, a gas-kinetic unified algorithm (GKUA) is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes. Based on the ellipsoidal statistical model with rotational energy excitation, the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function. By constructing the corresponding conservative discrete velocity ordinate method for this model, the conservative properties during the collision procedure are preserved at the discrete level by the numerical method, decreasing the computational storage and time. Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly. Applying the new GKUA, some numerical examples are simulated, including the Sod Riemann problem, homogeneous flow rotational relaxation, normal shock structure, Fourier and Couette flows, supersonic flows past a circular cylinder, and hypersonic flow around a plate placed normally. The results obtained by the analytic, experimental, direct simulation Monte Carlo method, and other measurements in references are compared with the GKUA results, which are in good agreement, demonstrating the high accuracy of the present algorithm. Especially, some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.     

Extended Thermodynamic Approach for Non-Equilibrium Gas Flow

Gases in microfluidic structures or devices are often in a non-equilibrium state. The conventional thermodynamic models for fluids and heat transfer break down and the Navier-Stokes-Fourier equations are no longer accurate or valid. In this paper, the extended thermodynamic approach is employed to study the rarefied gas flow in microstructures, including the heat transfer between a parallel channel and pressure-driven Poiseuille flows through a parallel microchannel and circular microtube. The gas flow characteristics are studied and it is shown that the heat transfer in the non-equilibrium state no longer obeys the Fourier gradient transport law. In addition, the bimodal distribution of streamwise and spanwise velocity and temperature through a long circular microtube is captured for the first time.     

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases

With discretized particle velocity space, a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case [J. Comput. Phys., vol. 229 (2010), pp. 7747-7764]. For the kinetic equation, to extend a one-dimensional scheme to multidimensional flow is not so straightforward. The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional, rather than axially symmetric, in velocity space. In this paper, a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented. Instead of particle-based modeling for the rarefied flow, such as the direct simulation Monte Carlo (DSMC) method, the philosophical principal underlying the current study is a partial-differential-equation (PDE)-based modeling. Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different, the gas evolution in a discretized space is modeled with the help of kinetic equation, instead of directly solving the partial differential equation. Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface, the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions. In comparison with the DSMC and Navier-Stokes flow solvers, the current method is much more efficient than DSMC in low speed transition and continuum flow regimes, and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes. As a result, the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation. This paper will extensively evaluate the performance of the unified scheme from free molecule to continuum NS solutions, and from low speed micro-flow to high speed non-equilibrium aerodynamics. The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations, and the scheme provides an important tool in the study of non-equilibrium flow.     

A Multiple Temperature Kinetic Model and Its Application to Near Continuum Flows

In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)]. Based on this model, the stress strain relationship in the Navier-Stokes (NS) equations is replaced by the translational temperature relaxation terms. The kinetic model has been successfully used in both continuum and near continuum flow computations. In this paper, we will further validate the multiple translational temperature kinetic model to flow problems in multiple dimensions. First, a generalized boundary condition incorporating the physics of Knudsen layer will be introduced into the model. Second, the direct particle collision with the wall will be considered as well for the further modification of particle collision time, subsequently a new effective viscosity coefficient will be defined. In order to apply the kinetic model to near continuum flow computations, the gas-kinetic scheme will be constructed. The first example is the pressure-driven Poiseuille flow at Knudsen number 0.1, where the anomalous phenomena between the results of the NS equations and the Direct Simulation Monte Carlo (DSMC) method will be resolved through the multiple temperature model. The so-called Burnett-order effects can be captured as well by algebraic temperature relaxation terms. Another test case is the force-driven Poiseuille flow at various Knudsen numbers. With the effective viscosity approach and the generalized second-order slip boundary condition, the Knudsen minimum can be accurately obtained. The current study indicates that it is useful to use multiple temperature concept to model the non-equilibrium state in near continuum flow limit. In the continuum flow regime, the multiple temperature model will automatically recover the single temperature NS equations due to the efficient energy exchange in different directions.     

An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems

In this paper, a diffuse-interface immersed boundary method (IBM) is proposed to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin) in thermal flow problems. The novel IBM is implemented combining with the lattice Boltzmann method (LBM). The present algorithm enforces the three types of thermal boundary conditions at the boundary points. Concretely speaking, the IBM for the Dirichlet boundary condition is implemented using an iterative method, and its main feature is to accurately satisfy the given temperature on the boundary. The Neumann and Robin boundary conditions are implemented in IBM by distributing the jump of the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained by applying the jump interface conditions in the normal and tangential directions. A simple analysis of the computational accuracy of IBM is developed. The analysis indicates that the Taylor-Green vortices problem which was used in many previous studies is not an appropriate accuracy test example. The capacity of the present thermal immersed boundary method is validated using four numerical experiments: (1) Natural convection in a cavity with a circular cylinder in the center; (2) Flows over a heated cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation of a single isothermal cold particle in a vertical channel. The numerical results show good agreements with the data in the previous literatures.     

Vlasov-Fokker-Planck Simulations for High-Power Laser-Plasma Interactions

A review is presented on our recent Vlasov-Fokker-Planck (VFP) simulation code development and applications for high-power laser-plasma interactions. Numerical schemes are described for solving the kinetic VFP equation with both electron-electron and electron-ion collisions in one-spatial and two-velocity (1D2V) coordinates. They are based on the positive and flux conservation method and the finite volume method, and these two methods can insure the particle number conservation. Our simulation code can deal with problems in high-power laser/beam-plasma interactions, where highly non-Maxwellian electron distribution functions usually develop and the widely-used perturbation theories with the weak anisotropy assumption of the electron distribution function are no longer in point. We present some new results on three typical problems: firstly the plasma current generation in strong direct current electric fields beyond Spitzer-Härm's transport theory, secondly the inverse bremsstrahlung absorption at high laser intensity beyond Langdon's theory, and thirdly the heat transport with steep temperature and/or density gradients in laser-produced plasma. Finally, numerical parameters, performance, the particle number conservation, and the energy conservation in these simulations are provided.     

Heat shock protein expression and injury optimization for laser therapy design

BACKGROUND AND OBJECTIVES: Hyperthermia can induce heat shock protein (HSP) expression in tumor regions where non-lethal temperature elevation occurs, enhancing cell viability and resistance to chemotherapy and radiation treatments typically employed in conjunction with thermal therapy. However, HSP expression control has not been incorporated into current thermal therapy design. Treatment planning models based on achieving the desired post-therapy HSP expression and injury distribution in the tumor and healthy surrounding tissue can enable design of more effective thermal therapies that maximize tumor destruction and minimize healthy tissue injury. STUDY DESIGN/MATERIALS AND METHODS: An optimization algorithm for prostate cancer laser therapy design was integrated into a previously developed treatment planning model, permitting prediction and optimization of the spatial and temporal temperature, HSP expression, and injury distributions in the prostate. This optimization method is based on dosimetry guidelines developed from measured HSP expression kinetics and injury data for normal and cancerous prostate cells and tumors exposed to hyperthermia. RESULTS: The optimization model determines laser parameters (wavelength, power, pulse duration, fiber position, and number of fibers) necessary to satisfy prescribed HSP expression and injury distributions in tumor and healthy tissue. Optimization based on achieving desired injury and HSP expression distributions within the tumor and normal tissue permits more effective tumor destruction and diminished injury to healthy tissue compared to temperature driven optimization strategies. CONCLUSIONS: Utilization of the treatment planning optimization model can permit more effective tumor destruction by mitigating tumor recurrence and resistance to chemotherapy and radiation arising from HSP expression and insufficient injury.     

谷氨酰胺诱导热休克蛋白在感染性休克中的作用

热休克蛋白(heatshockproteins,HSPs)为一组高度保守的蛋白质,因其独特的生物学特性及功能,在生物体内广泛参与了多种复杂的功能活动,人们将其生物活性比喻为“瑞士军刀”[1]。已有研究证明HSPs对感染性休克动物具有保护作用,但是诱导热休克蛋白产生的因素多数对机体有害,体内外实验研究发现Gln能诱导动物的热休克反应,特异性增强起主要保护作用的HSP72和HSP27的表达,从而改善感染性休克动物的生存率。本文对应用Gln诱导体内HSPs表达,从而提高机体对感染性休克的防御作用及可能机制作一综述。1谷氨酰胺对热休克蛋白表达的影响Gln是…     

Temperature measurement

The terms heat and temperature are two distinct but closely related concepts. The core difference between heat and temperature is that heat deals with thermal energy, whereas temperature is more concerned with molecular kinetic energy. As a substance is cooled, it loses thermal energy. Eventually it will reach a temperature at which it no longer possesses any thermal or kinetic energy and so it can no longer be cooled; this temperature is absolute zero. Another unique temperature concept is the triple point of a substance; the temperature at which a substance exists simultaneously and in perfect equilibrium in a solid, liquid and gaseous phase. The triple point is unique for every substance; for water, it reaches its triple point at 0.01 °C at a pressure of 0.006 atmospheres. Temperature may be measured using the Celsius, Fahrenheit and Kelvin scales. Many clinical thermometers are designed to display the output in a digital format to enable easier monitoring as well as recording. Non-electrical thermometers are still in use today. Thermoregulation in the anaesthetized patient is achieved by the understanding of the mechanisms of heat loss, as well as the use of thermometers, warming and cooling devices.     

Assessment of Heat Flux Prediction Capabilities of Residual Distribution Method: Application to Atmospheric Entry Problems

In the present contribution we evaluate the heat flux prediction capabilities of second-order accurate Residual Distribution (RD ) methods in the context of atmospheric (re-)entry problems around blunt bodies. Our departing point is the computation of subsonic air flows (with air modeled either as an inert ideal gas or as chemically reacting and possibly out of thermal equilibrium gas mixture) around probe-like geometries, as those typically employed into high enthalpy wind tunnels. We confirm the agreement between the solutions obtained with the RD method and the solutions computed with other Finite Volume (FV ) based codes.However, a straightforward application of the same numerical technique to hypersonic cases involving strong shocks exhibits severe deficiencies even on a geometry as simple as a 2D cylinder. In an attempt to mitigate this problem, we derive new variants of RD schemes. A comparison of these alternative strategies against established ones allows us to derive a diagnose for the shortcomings observed in the traditional RD schemes.     

Grown-in Defects of InSb Crystals: Models and Computation

In this paper, we present a model for grown-in point defects inside indium antimonide crystals grown by the Czochralski (CZ) technique. Our model is similar to the ones used for silicon crystal, which includes the Fickian diffusion and a recombination mechanism. This type of models is used for the first time to analyze grown-in point defects in indium antimonide crystals. The temperature solution and the advance of the melt-crystal interface, which determines the time-dependent domain of the model, are based on a recently derived perturbation model. We propose a finite difference method which takes into account the moving interface. We study the effect of thermal flux on the point defect patterns during and at the end of the growth process. Our results show that the concentration of excessive point defects is positively correlated to the heat flux in the system.     

热刺激介导兔关节软骨细胞凋亡的实验研究

目的研究体外培养的兔关节软骨细胞对热刺激的反应。方法取兔关节软骨细胞在37℃培养24 h,然后在48℃的水浴箱中孵育10 min,之后在37℃培养箱中培养2周;热刺激后,用tunel检测法分别检测第0.5 h、1 h、3h、和5 h关节软骨细胞凋亡的情况;用电子显微镜分析证实软骨骨细胞在形态学上凋亡的特性;用免疫组化染色法显示caspase-3活性随细胞凋亡增加的改变。结果形态学和生物化学上的证据提示48℃热刺激10 min导致体外关节软骨细胞凋亡加速。结论这项研究显示热刺激是软骨细凋亡的因素,并为选择杀死骨关节恶性肿瘤细胞、最小限度损伤关节软骨细胞提供了基础温度指导。     

Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations

Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form where are any consistent approximations to the pressure and the mass flux. This scheme thus leaves most terms in the numerical flux unspecified and various authors have used simple averaging. Here we enforce approximate or exact entropy consistency which leads to a unique choice of all the terms in the numerical fluxes. As a consequence, a novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed. These fluxes are centered and some dissipation has to be added if shocks are present or if the mesh is coarse. We construct scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy condition. Secondly, we use entropy-variable based matrix dissipation flux which leads to kinetic energy and entropy stable schemes. These schemes are shown to be free of entropy violating solutions unlike the original Roe scheme. For hypersonic flows a blended scheme is proposed which gives carbuncle free solutions for blunt body flows. Numerical results for Euler and Navier-Stokes equations are presented to demonstrate the performance of the different schemes.     

Conductive heat exchange with a gel-coated circulating water mattress

The use of forced-air warming is associated with costs for the disposable blankets. As an alternative method, we studied heat transfer with a reusable gel-coated circulating water mattress placed under the back in eight healthy volunteers. Heat flux was measured with six calibrated heat flux transducers. Additionally, mattress temperature, skin temperature, and core temperature were measured. Water temperature was set to 25 degrees C, 30 degrees C, 35 degrees C, and 41 degrees C. Heat transfer was calculated by multiplying heat flux by contact area. Mattress temperature, skin temperature, and heat flux were used to determine the heat exchange coefficient for conduction. Heat flux and water temperature were related by the following equation: heat flux = 10.3 x water temperature - 374 (r(2) = 0.98). The heat exchange coefficient for conduction was 121 W . m(-2) . degrees C(-1). The maximal heat transfer with the gel-coated circulating water mattress was 18.4 +/- 3.3 W. Because of the small effect on the heat balance of the body, a gel-coated circulating water mattress placed only on the back cannot replace a forced-air warming system.     

Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT)

Thermal analyses of biological tissues exposed to microwaves were studied by using thermal wave model of bio-heat transfer (TWMBT). As a model, skin stratified as three layers with various thermal physical properties were simulated and thermal wave model of bio-heat transfer equations were solved by using finite difference method. Finally, the thermal variations were simulated in the cross section of the model. Comparative studies on the traditional Pennes' equations and thermal wave model of bio-heat transfer were performed and evaluated. Furthermore, temperature variations in the skin exposed to microwave were predicted depending on blood perfusion rate, thermal conductivity, frequency and power density of microwave, and exposure time. Thermal wave model of bio-heat transfer gives lower heat rise predictions than that of Pennes' equation, initially. When it approaches to steady state, it overlaps with the Pennes' equation.     

Successful Thermal Management of a Totally Implantable Ventricular Assist System

Abstract: Thermal management of the implantable ventricular assist system (VAS) is important not only from the pathophysiological point of view but also from the standpoint of system endurance. The heat distribution within the Baylor VAS was measured using different motor housing materials and environmental conditions. The temperature of the circulating water in the mock loop was set at 37° and 42°C. A polycarbonate motor housing was not a suitable material because of the high temperature development in the actuation system. An anodized aluminum housing demonstrated excellent heat conductivity. The surface temperature of this motor housing was 41.6°C when immersed in circulating water at 42°C. Heat conduction from the motor to the circulating blood revealed an effective thermal path. In the worst case, the heat flux of the motor to the circulating blood revealed an effective thermal path. In the worst case, the heat flux of the motor housing was calculated to be less than 0.062 W/cm²—an acceptable level for the surrounding tissues.