Computation of Stiffness and Damping Derivatives of an Ogive in a Limiting Case of Mach Number and Specific Heat Ratio

This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.

Reconsideration on the role of the specific heat ratio in Arrhenius law applications

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy Ea can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio y and the gas constant R vary during chemical reaction processes. The varying y may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant γ assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable γ and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one- dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable γ and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.

Enhanced entropy generation and heat transfer characteristics of magnetic nano-encapsulated phase change materials in latent heat thermal energy storage systems

The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.

Effect of Y and Gd content on the microstructure and mechanical properties of Mg-Y-RE alloys

In the application of WE43,it is found that Y_(2)O_(3)inclusion formed in the process of casting seriously reduced the mechanical properties of the products.The reduction of the mechanical properties is even more distinct when it comes to the application in the thin walled complex-precision castings.In order to decrease the Y_(2)O_(3)inclusions,Gd element was used to replace part of the Y element in Mg-Y-RE series alloys.The effect of Y content(Mg-x Y-1Gd-2Nd-0.5Zn-0.5Zr)and Y/Gd ratio(Mg-x Y-(5-x)Gd-2Nd-0.5Zn-0.5Zr)on the microstructure and mechanical properties of Mg-Y-RE alloys were investigated in this paper.With decreasing Y content,the grain size of the alloys increased,both ultimate tensile strength(UTS)and yield strength(YS)of alloys decreased monotonically.Replacing part of Y content with Gd and keeping the total rare earth content unchanged,the low Y content Mg-2Y-3Gd-2Nd-0.5Zn-0.5Zr alloy showed the same mechanical properties as the high Y content Mg-4Y-1Gd-2Nd-0.5Zn-0.5Zr alloy at both room and elevated temperatures.After solution treatment at 525°C for 8 h and aging treatment at 225°C for 10 h,the UTS,YS and elongation(ε)of Mg-2Y-3Gd-2Nd-0.5Zn-0.5Zr alloy reached 281.7 MPa,198 MPa and 11.1%at room temperature,and 216.7 MPa,171.6 MPa and 16.1%at 250°C.The new low Y content Mg-2Y-2Nd-3Gd-0.5Zn-0.5Zr alloy is expected to replace the high Y content WE43 alloys,which can be used in the complex thin-walled parts of aviation products.

A LATTICE BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GAS

A new lattice Boltzmann model for compressible perfect gas is proposed. The numerical example shows that it can be used to simulate shock wave and contact discontinuity. The results are comparable with those obtained by traditional methods. The ratio of specific heats gamma may be chosen according to the requirement of problems.

AN APPROXIMATE ANALYTICAL SOLUTION OF THE CYLINDRICAL DETONATION WAVE GENERATED BY THE LINEAR EXPLOSION

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref. [1.].In this paper, when the ratio of specific heat by using the enlargement coordinate method, the first-order analytical solutions are obtained. The perturbation parameter is The correction of these solutions is checked at the end of this paper.

A Method for the Solution of the 2D-Oswatitsch Equations

Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressure coefficients and Mach number behind a strong shock. On this account, the principle is significant in the development process for hypersonic vehicles. Oswatitsch deduced a system of partial differential equations which describes hypersonic flow. These equations are the basic gasdynamic equations as well as Crocco’s theorem which are reduced for the case of very high Mach numbers, . Their numerical solution can not only result in simplified algorithms prospectively utilized to describe the flow around bodies flying mainly in the lower stratosphere with very high Mach numbers. It also offers a deeper understanding of similarity effects for hypersonic flows. In this paper, a solution method for Oswatisch’s equations for perfect gas, based on a 4-step Runge-Kutta-algorithm, is presented including a fast shock-fitting procedure. An analysis of numerical stability is followed by a detailed comparison of results for different Mach numbers and ratios of the specific heats.

Specific heat ratio effects of compressible Rayleigh—Taylor instability studied by discrete Boltzmann method

Rayleigh-Taylor(RT)instability widely exists in nature and engineering fields.How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value.At present,abundant results of RT instability have been obtained by traditional macroscopic methods.However,research on the thermodynamic non-equilibrium(TNE)effects in the process of system evolution is relatively scarce.In this paper,the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability.The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region.Firstly,as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region,the average TNE intensity first increases and then reduces,and it increases with the specific heat ratio decreasing;the specific heat ratio has the same effect on the global strength of the viscous stress tensor.Secondly,the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure.Thirdly,under the competition between the temperature gradients and the contact area of the two fluids,the average intensity of the non-equilibrium quantity related to the heat flux shows diversity,and the influence of the specific heat ratio is also quite remarkable.

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

Janus particle is a research hotspot due to its novelty and settlement in acid liquid during wastewater treatment.Heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion are numerically investigated based on immersed boundary lattice Boltzmann method.Chemical reaction heat ratio,Damkohler number,Peclet number,and particle number effects on temperature field,concentration field,Janus particle mass reduction,position,and velocity are investigated.The uniform particle has an equilibrium position of about 1/4 times the channel width for two corroded uniform particle settlement processes.The Janus particle horizontal position deviates from the uniform particle equilibrium position due to the force caused by nonuniform buoyancy and particle rotation.When the chemical reaction heat ratio is more than 1,the Janus particle horizontal position is closer to the channel centerline and has a positive deviation.However,the converse trend happens when the chemical reaction heat ratio is less than 1,and the Janus particle horizontal position has a negative deviation.The Janus particle horizontal position deviation magnitude increases with increasing Damkohler number and decreasing Peclet number.The horizontal position deviation phenomenon exists for the single corroded Janus particle and two corroded Janus particle settlement processes.