MODAL DISCONTINUOUS GALERKIN METHOD FOR SHOCK WAVE STRUCTURES

The discontinuous Galerkin(DG)finite element method has been popular as a numerical technique for solving the conservation laws.In the present study,in order to investigate the shock wave structures in highly thermal nonequilibrium,an explicit modal cell-based DG scheme is developed for solving the conservation laws in conjunction with nonlinear coupled constitutive relations(NCCR).Convergent iterative methods for solving algebraic constitutive relations are also implemented in the DG scheme.It is shown that the new scheme works well for all Mach numbers,for example,Ma=15.

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 highorder 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.

Effect of chemical reactivity on the detonation initiation in shock accelerated flow in a confined space

The interactions of a spherical flame with an incident shock wave and its reflected shock wave in a confined space were investigated using the three-dimensional reactive Navier-Stokes equations, with emphasis placed on the effect of chemical reactivity of mixture on the flame distortion and detonation initiation after the passage of the reflected shock wave. It is shown that the spatio-temporal characteristics of detonation initiation depend highly on the chemi- cal reactivity of the mixture. When the chemical reactivity enhances, the flame can be severely distorted to form a reactive shock bifurcation structure with detonations initiating at different three-dimensional spatial locations. Moreover, the detonation initiation would occur earlier in a mixture of more enhanced reactivity. The results reveal that the detona- tions arise from hot spots in the unburned region which are initiated by the shock-detonation-transition mechanism.

Molecular dynamics simulations of microscopicstructure of ultra strong shock waves in dense helium

Hydrodynamic properties and structure of strong shock waves in classical dense helium are simulated using non-equilibrium molecular dynamics methods. The shock speed in the simulation reaches 100 km/s and the Mach number is over 250, which are close to the parameters of shock waves in the implosion process of inertial confinement fusion. The simulations show that the high-Mach-number shock waves in dense media have notable differences from weak shock waves or those in dilute gases. These results will provide useful information on the implosion process, especially the structure of strong shock wave front, which remains an open question in hydrodynamic simulations.

NATURE OF THE SURFACE HEAT TRANSFER FLUCTUATION IN A HYPERSONIC SEPARATED TURBULENT FLOW

This paper presents the results of an experimental study of the unsteady nature of a hypersonic sepa- rated turbulent flow.The nominal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5x10^7/m.The separated flow was generated using finite span forward facing steps.An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make mul- ti-channel measurements of the fluctuating surface heat trtansfer within the separated flow.Conditional sampling ana- lysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness.The compression waves con- verge into a single leading shock beyond the boundary layer.The shock structure is unsteady and undergoes large-scale motion in the streamwise direction.The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave.There exists a wide band of frequency of oscillations of the shock system.Most of the frequencies are in the range of 1-3 kHz.The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave.This inter mittent phenomenon is considered as the consequence of the large-scale shock system oscillations.Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed.

Aerodynamic design of transonic fan/compressor by 3D viscous RNS combined with genetic algorithms

This paper presents an aerodynamic design of a small transonic fan by 3D viscous RNS solver combined with genetic algorithms.The aerodynamic design system based on the 3D viscous RNS solver reduces the dependency on the design experience for designers.Furthermore the optimum with genetic algorithms is an effective method for improving the transonic fan performance as a part of the design system.The design result showed that the transonic fan designed by this method reaches the design requirement even with more efficiency value.

Evolution of wall flow structure and measurement of shear stress issuing from supersonic jet with extended shelf

This paper reports an experimental study on the supersonic jet surface flow structure visualization and shear stress field measurement issuing from a rectangular nozzle with extended shelf. The evolution of the near-field surface flow structures with an increased Nozzle Pressure Ratio(NPR) is successfully captured by the surface oil flow, infrared detection technology, and the Shear-Sensitive Liquid Crystal Coating(SSLCC) technique. Results reveal that under smaller NPR, the wall flow structure is similar to that of a jet without the extended shelf i.e., clean jets,and this is caused by insufficient effect on the boundary layer. However, at higher amplitudes of NPR, there exists a significant effect of the boundary layer, as a near triangular separation forms on the trailing edge of the Mach stem due to the adverse pressure gradient, which is visualized for the very first time in this paper. Furthermore, the vector field of shear stress is measured quantitatively by SSLCC technique. Results shows that the magnitude of shear stress heightened with NPR increasing, and the directions of shear stress changes across the shock wave and expansion fans. In addition, surface streamlines measured by SSLCC is significantly consistent with the streamlines visualized using the oil flow technique.

The response of stromatolites to seismic shocks: Tomboliths from the Palaeoproterozoic Chaibasa Formation,E India: Discussion and liquefaction basics

This discussion of a paper by Van Loon et al.（2016）, published in the Journal of Palaeogeography（2016, 5（4）, 381e390）, is aimed at illustrating that there are fundamental deficiencies, which include（1）incomplete etymological reasoning for proposing a new genetic term ＂tomboliths＂ for stromatolitic bioclasts in the Palaeoproterozoic Chaibasa Formation, eastern India,（2） omission of empirical data in documenting depositional facies using sedimentological logs,（3） misapplication of the stratigraphic concept of ＂angular unconformity＂,（4） failure to consider the multifarious origins of earthquakes, and（5） a dated view on the basic tenets of process sedimentology and triggering mechanisms of liquefaction that are the basis for forming soft-sediment deformation structures（SSDS）. As a consequence, their conclusions are unconvincing.

The Dynamic Impact of Structural Oil Price Shocks on the Macroeconomy

In this paper,we apply the structural vector autoregression(SVAR)model to decompose the international oil price shock into oil supply shocks,aggregate demand shocks and oil-specific demand shocks,and then use the DCC-GARCH model to analyse the dynamic correlations between these three kinds of oil price shocks and the macroeconomic variables of several oil importing and exporting countries.To quantify the intensity of the effect of oil shocks on these variables,we propose a measure,conditional expectation(Co E),to capture the percent change of the economic variable under oil price shocks relative to the median state.The time-varying copula model is employed to estimate the proposed measure through time.The empirical results show that,for instance,the impacts of oil price shocks on macroeconomic variables are different in different periods,showing the time-varying characteristics.Additionally,the impacts of oil price shocks on macroeconomic variables show great differences and some similarities among different countries.Finally,we give some policy suggestions for these countries,in particular for China’s special results.

Design of hypersonic wavecatcher intake at Mach 12 with rectangular-to-elliptical shape transition

Wavecatcher(inward-turning)intake flows,at design Mach 12,are investigated numerically,to display the effect of wall temperature on flow structures and intake performance.Hypersonic experiments on shock wave/boundary layer interaction are used to validate the Spalart-Allmaras turbulence model for reproducing the features of hypersonic flow.Simulations of hypersonic intake flow are performed at different wall temperatures,including isothermal T_(w)Z 300 K,T_(w)Z 1000 K,T_(w)Z 2000 K,and the adiabatic case.The shock structures,impinging shock positions,surface streamlines,and the development of internal streamwise vortices are discussed.The mass-averaged performance of intake flow shows that,when the wall temperature changes from T_(w)Z 300 K to adiabatic,the mass capture coefficient decreases from 0.991 to 0.933,the total pressure recovery decreases from 0.200 to 0.083,while exit section Mach number decreases from 4.478 to 3.514.The results suggest that the osculating design method of wavecatcher intake design can successfully be extended to Mach 12,while capturing all airflow at isothermal wall conditions.

Steady-state solution of traffic flow on a simple road network

The steady-state traffic flow on a simply circled road network is analytically studied using the Lighthill-Witham-Richards(LWR)model.The network is typically composed of a diverging and a merging junction together with three connected road sections.At the diverging junction,traffic flow is assigned to satisfy the user-equilibrium condition.At the merging junction,queuing or shock structures due to the bottleneck effect is taken into account.We indicate that the solution depends on the total number of vehicles on the road network,and that the bottleneck effect gives rise to not only capacity drop but inefficient utilization of the two road sections upstream the merging junction.To further validate the derived steady-state solution,a first-order Godunov scheme of the LWR model is adopted for simulation of traffic flow in each road section and the demand-supply concept is applied to provide boundary values at the junctions for the scheme.By varying the total number of vehicles from zero to the maximum,the simulation shows that a randomly distributed state of traffic flow is bound to evolve into a steady state,which is completely in agreement with the analytical solution.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo(DSMC)method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows,data-driven nonlinear constitutive relations(DNCR)are proposed first through the machine learning method.Based on the training data from both Navier-Stokes(NS)solver and unified gas kinetic scheme(UGKS)solver,the map between responses of stress tensors and heat flux and feature vectors is established after the training phase.Through the obtained off-line training model,new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux.Finally,conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR,NS,UGKS,DSMC and experimental results.The improvement of the predictive capability of the coarsegraining model could make the DNCR method to be an effective tool in the rarefied gas community,especially for hypersonic engineering applications.

Words of the Editor-in-Chief——Academic discussion is an effective measure to promote scientific development

Van Loon et al.＇s paper ＂The response of stromatolites to seismic shocks： Tomboliths from the Palaeoproterozoic Chaibasa Formation, E India＂ with a new term ＂tomboliths＂ and original viewpoints should be published, but some contents need to be discussed. Shanmugam＇s paper ＂The response of stromatolites to seismic shocks： Tomboliths from the Palaeoproterozoic Chaibasa Formation, E India： Discussion and liquefaction basics＂ pointed out some queries and problems about Van Loon et al.＇s paper. It is an academic discussion paper and should be published as well. However, some main problems, such as the new term＂tomboliths＂ and its origin of seismic shocks, ＂whether stromatolites or tomboliths are soft-sediment deformation structures or not＂, etc., also need to be discussed. Academic discussion is an effective measure to promote scientific development. The more thorough academic discussions are carried out regarding academic problems, the more scientific facts and truths will become clear. All participants in this discussion are contributors. It is active to carry out the policy of ＂A hundred flowers blossom and a hundred schools of thought contend＂ by our Journal of Palaeogeography.