Numerical Analysis of Steady Smoldering of Biomass Rods

Understanding the steady mechanism of biomass smoldering plays a great role in the utilization of smoldering technology.In this study numerical analysis of steady smoldering of biomass rods was performed.A two-dimensional(2D)steady model taking into account both char oxidation and pyrolysis was developed on the basis of a calculated propagation velocity according to empirical correlation.The model was validated against the smoldering experiment of biomass rods under natural conditions,and the maximum error was smaller than 31%.Parameter sensitivity analysis found that propagation velocity decreases significantly while oxidation area and pyrolysis zone increase significantly with the increasing diameter of rod fuel.

POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION

In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.

A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

Fourier neural operator with boundary conditions for efficient prediction of steady airfoil flows

An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator(FNO),which is a new framework of neural networks.Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO,which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions.The proposed approach runs several orders of magnitude faster than the traditional numerical methods.The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach.Furthermore,the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids,thereby improving the accuracy in the near-wall region.There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.

A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

STEADY HEAT TRANSFER ANALYSIS AND PARAMETER OPTIMIZATION FOR MULTILAYER THERMAL INSULATIONS

The energy equilibrium equation and discrete ordinate methods are combined to establish the one-dimensional steady heat transfer mathematical model of multi-layer thermal insulations （MTIs） in metallic thermal protection systems. The inverse problem of heat transfer is solved by the genetic algorithm and data from the steady heat transfer experiment of fibrous thermal insulations. The density radiation attenuation coefficient, the albedo of fibrous thermal insulations and the surface emissivity of reflective screens are optimized. Finally, the one-dimensional steady heat transfer model of MTIs with optimized thermal physical parameters is verified by experimental data of the effective MTI conductivity.

REVIEW OF THE GREEN＇S FUNCTION METHOD FOR STEADY ＆UNSTEADY，SUBSONIC，TRANSONIC ＆SUPERSONIC AERODYNAMICS AROUND COMPLEX CONFIGURATIONS

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NUMERICAL INVESTIGATION OF UNSTEADY DROPLET COMBUSTION PROCESS IN HOT QUIESCENT AIR ENVIRONMENTS (HQAE)

A mathematical model has been presented for describing single droplet unsteady processes of vaporization, ignition and combustion in a hot quiescent air environment. The arbitrary Lagrangian Eulerian numerical method, incorporated with an effective adaptive mesh method, is applied. From the obtained time space distributions of gas temperature and species densities, the characteristics of droplet ignition and combustion process are clarified. It is also demonstrated that, due to the strong damping of the high temperature flame region around the droplet, the ambient conditions have little effects on the properties of the drop's surface; and that, due to the unsteady prediction of droplet heating time being much less than the corresponding quasi steady prediction under burning condition, the differences between unsteady and quasi steady results are much greater than those under pure vaporization.

THE STEADY/PULSATILE FLOW AND MACROMOLECULAR TRANSPORT IN T-BIFURCATION BLOOD VESSELS

A numerical analysis of the steady and pulsatile, macromolecular(such as low density lipopotein (LDL), Albumin) transport in T-bifurcation was proposed. The influence of Reynolds number and mass flow ratio etc. parameters on the velocity field and mass transport were calculated. The computational results predict that the blood flow factors affect the macromolecular distribution and the transport across the wall, it shows that hemodynamic play an important role in the process of atherosclerosis. The LDL and Albumin concentration on the wall varies most greatly in flow bifurcation area where the wall shear stress varies greatly at the branching vessel and the atherosclerosis often appears there.

List流上梯度Steady Solitons的位势函数

利用比较定理,研究了List流上梯度Steady Solitons的位势函数下确界的退化率,并得到了如下结论:如果位势函数是有界的,则梯度Steady Solitons一定是平凡的;梯度Steady Solitons的广义数量曲率不具有一致正下界.

Multiple steady state phenomenon in martensitic transformation

Based on the basic facts that the martensitic transformation is a physical phenomenon which occurs in non equilibrium conditions and there exists the feedback mechanism in the martensitic transformation, the dynamical processes of the isothermal and athermal martensitic transformations were analyzed by using nonlinear theory and a bifurcation theory model was established. It is shown that a multiple steady state phenomenon can take place as austenite is cooled, and the transitions of the steady state temperature between the branches of stable steady states can be considered the transformation from austenite to martensite. This model can estimate the starting temperature of the martensitic transformation and explain some experimental features of the martensitic transformation such as the effects of cooling rate, fluctuation and austenitic grain size on the martensitic transformation. [

A Simple Strategy for Capturing the Unstable Steady Solution of an Unsteady Flow

A simple strategy for capturing unstable steady solution is proposed in this paper. By enlarging the real time step, the unstable high frequency modes of the unsteady flow can be effectively suppressed because of the damping action on the real time level. The steady component will not be changed during real time marching. When the unsteady flow solution converges to a steady state, the partial derivatives of real time in unsteady governing equations will disappear automatically. The steady solution is the exacted unstable steady solution. The method is validated by the laminar flow past a circular cylinder and a transonic buffet of NACA0012 airfoil. This approach can acquire high-precision unstable steady solutions quickly and effectively without reducing the spatial discretization accuracy. This work provides the basis for unstable flow modeling and analysis.

Numerical simulation on trapping efficiency of steady filtration process in diesel particulate filter and its experimental verification

Taking wall-flow diesel particulate filter(DPF) as the research objective and separately assuming its filtering wall to be composed of numerous spherical or cylindrical elements, two different mathematical models of steady filtration for wall-flow diesel particulate filter were developed and verified by experiments as well as numerically solved. Furthermore, the effects of the macroand micro-structural parameters of filtering wall and exhaust-flow characteristic parameters on trapping efficiency were also analyzed and researched. The results show that: 1) The two developed mathematical models are consistent with the prediction of variation of particulate size; the influence of various factors on the steady trapping efficiency is exactly the same. Compared to model 2, model 1 is more suitable for describing the steady filtration process of wall-flow diesel particulate filter; 2)The major influencing factors on steady trapping efficiency of wall-flow diesel particulate filter are the macro-and micro-structural parameters of filtering wall; and the secondary influencing factors are the exhaust-flow characteristic parameters and macro-structural parameters of filter; 3)The steady trapping efficiency will be improved by increasing filter body volume, pore density as well as wall thickness and by decreasing exhaust-flow, but effects will be weakened when particulate size exceeds a certain critical value; 4) The steady trapping efficiency will be significantly improved by increasing exhaust-flow temperature and filtering wall thickness, but effects will be also weakened when particulate size exceeds a certain critical value; 5) The steady trapping efficiency will approximately linearly increase with reducing porosity, micropore aperture and pore width.

A new coupled map car-following model considering drivers' steady desired speed

Based on the pioneering work of Konishi et al., in consideration of the influence of drivers＇ steady desired speed ef/ect on the traffic flow, we develop a new coupled map car-following model in the real world. By use of the control theory, the stability condition of our model is derived. The validity of the present theoretical scheme is verified via numerical simulation, confirming the correctness of our theoretical analysis.

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.

A Calculation of Steady Pressure Drop and an Analysis of HT-7U CICC

Under the condition of steady state, the pressure drop of coolant is mainly caused by friction along the cable. In the CICC (cable-in-conduit-conductor), helium flow within the conductor consists of two parallel interconnected tubes. The velocity distribution has some differece between the central channel and conductor space. The region of Reynolds number is from 103 to 106. This paper describes the calculation of pressure drop of HT-7U CICC at various mass flows. It is assumed that the coolant flows in two parallel, rough tubes during the calculation.

Using the surface panel method to predict the steady performance of ducted propellers

A new numerical method was developed for predicting the steady hydrodynamic performance of ducted propellers. A potential based surface panel method was applied both to the duct and the propeller, and the interaction between them was solved by an induced velocity potential iterative method. Compared with the induced velocity iterative method, the method presented can save programming and calculating time. Numerical results for a JD simplified ducted propeller series showed that the method presented is effective for predicting the steady hydrodynamic performance of ducted propellers.

Existence for positive steady states of an eco-epidemiological model

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.

Analysis of steady heat conduction for 3D axisymmetric functionally graded circular plate

The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation （ODE） in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.

Rheological behavior of semi-solid 7075 aluminum alloy at steady state

The further application of semi-solid processing lies in the in-depth fundamental study like rheological behavior. In this research, the apparent viscosity of the semi-solid slurry of 7075 alloy was measured using a Couette type viscometer. The effects of solid fraction and shearing rate on the apparent viscosity of this alloy were investigated under different processing conditions. It can be seen that the apparent viscosity increases with an increase in the solid fraction from 10% to 50% （temperature 620 ℃ to 630 ℃） at steady state. When the solid fraction was fixed, the apparent viscosity can be decreased by altering the shearing rate from 61.235 s-1 to 489.88 s-1 at steady state. An empirical equation that shows the effects of solid fraction and shearing rate on the apparent viscosity is fitted： ηα = [0.871 - 0.00849. γ0.74924]. exp（3.7311, fs） . The microstructure of quenched samples was examined to understand the alloy＇s rheological behavior.