Effective Specific Heat Ratio Research Articles

A diffuse-interface method for reducing spurious pressure oscillations in multicomponent transcritical flow simulations

Spurious pressure oscillations are a numerical instability that is commonly observed in multiphase and multicomponent flow problems near the critical point. A diffuse-interface model has been created to simulate transcritical mixing in multispecies and multiphase systems where spurious pressure oscillations pose a serious challenge in achieving convergence. To reduce the spurious pressure oscillations, three methods have been proposed and implemented in the present paper: (1) artificially thickening the interface between different species, (2) reconstruction of the primitive variables in the characteristics space, and (3) developing a hybrid method (HY) that switches between quasi-conservative (QC) double-flux (DF) and the classical fully-conservative numerical procedures based on the changes in the effective specific heat ratio and the effective reference internal energy. The cases considered include (1) a transcritical shock tube problem between nitrogen and n-dodecane, (2) a near-critical shock-droplet interaction, and (3) the transcritical Spray A benchmark case of Engine Combustion Network (ECN) that represents the injection of n-dodecane into a high-pressure and high-temperature nitrogen environment. Characteristic-wise reconstruction of the primitive variables in our proposed fully-conservative method tends to reduce the spurious pressure oscillations compared to primitive-wise reconstruction including the reconstruction of the speed of sound. The HY model is found to effectively reduce the magnitude of the spurious pressure oscillations, the loss of energy conservation, and provides more accurate results for all tested cases. The artificial thickening of the interface between different species is found to reduce spurious pressure oscillations and reduce energy conservation loss when used in conjunction with a QC method (HY or DF).

Near-sonic pure steam flow with real-gas effects and non-equilibrium and homogeneous condensation around thin airfoils

A small-disturbance asymptotic model is derived to describe the complex nature of a pure water vapour flow with non-equilibrium and homogeneous condensation around a thin airfoil operating at transonic speed and small angle of attack. The van der Waals equation of state provides real-gas relationships among the thermodynamic properties of water vapour. Classical nucleation and droplet growth theory is used to model the condensation process. The similarity parameters which determine the flow and condensation physics are identified. The flow may be described by a nonlinear and non-homogeneous partial differential equation coupled with a set of four ordinary differential equations to model the condensation process. The model problem is used to study the effects of independent variation of the upstream flow and thermodynamic conditions, airfoil geometry and angle of attack on the pressure and condensate mass fraction distributions along the airfoil surfaces and the consequent effect on the wave drag and lift coefficients. Increasing the upstream temperature at fixed values of upstream supersaturation ratio and Mach number results in increased condensation and higher wave drag coefficient. Increasing the upstream supersaturation ratio at fixed values of upstream temperature and Mach number also results in increased condensation and the wave drag coefficient increases nonlinearly. In addition, the effects of varying airfoil geometry with a fixed thickness ratio and chord on flow properties and condensation region are studied. The computed results confirm the similarity law of Zierep & Lin (Forsch. Ing. Wes. A, vol. 33 (6), 1967, pp. 169–172), relating the onset condensation Mach number to upstream stagnation relative humidity, when an effective specific heat ratio is used. The small-disturbance model is a useful tool to analyse the physics of high-speed condensing steam flows around airfoils operating at high pressures and temperatures.

The effect of cosmic ray acceleration on supernova blast wave dynamics

Non-relativistic shocks accelerate ions to highly relativistic energies provided that the orientation of the magnetic field is closely aligned with the shock normal (quasi-parallel shock configuration). In contrast, quasi-perpendicular shocks do not efficiently accelerate ions. We model this obliquity-dependent acceleration process in a spherically expanding blast wave setup with the moving-mesh code {\sc arepo} for different magnetic field morphologies, ranging from homogeneous to turbulent configurations. A Sedov-Taylor explosion in a homogeneous magnetic field generates an oblate ellipsoidal shock surface due to the slower propagating blast wave in the direction of the magnetic field. This is because of the efficient cosmic ray (CR) production in the quasi-parallel polar cap regions, which softens the equation of state and increases the compressibility of the post-shock gas. We find that the solution remains self-similar because the ellipticity of the propagating blast wave stays constant in time. This enables us to derive an effective ratio of specific heats for a composite of thermal gas and CRs as a function of the maximum acceleration efficiency. We finally discuss the behavior of supernova remnants expanding into a turbulent magnetic field with varying coherence lengths. For a maximum CR acceleration efficiency of about 15 per cent at quasi-parallel shocks (as suggested by kinetic plasma simulations), we find an average efficiency of about 5 per cent, independent of the assumed magnetic coherence length.

Potential for the Vishniac instability in ionizing shock waves propagating into cold gases

The Vishniac instability was posited as an instability that could affect supernova remnants in their late stage of evolution when subject to strong radiative cooling, which can drive the effective ratio of specific heats below 1.3. The potential importance of this instability to these astrophysical objects has motivated a number of laser-driven laboratory studies. However, the Vishniac instability is essentially a dynamical instability that should operate independently of whatever physical processes happen to reduce the ratio of specific heats. In this paper, we examine the possibility that ionization and molecular dissociation processes can achieve this, and we show that this is possible for a certain range of shock wave Mach numbers for ionizing/dissociating shock waves propagating into cold atomic and molecular gases.

Sensitivity analysis of geometric parameters upon the aerothermodynamic performances of Mars entry vehicle

Aerothermodynamic environment predictions play an important role in the heatshield design of Mars entry vehicle. This article investigates and presents the influences of geometric parameters of the heatshield on its aerothermodynamic performances. The three-dimensional coupled implicit compressible Reynolds Averaged Navier–Stokes (RANS) equations and perfect gas model with the specified effective specific heat ratio have been applied to numerically simulate the flow fields around the vehicle. Menter’s shear stress transport (SST) turbulence model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates are demonstrated and analyzed in detail. Furthermore, a non-intrusive polynomial chaos (NIPC) method with Latin hypercube sampling (LHS) is utilized to establish the functional relationship between the aerothermodynamics and geometric parameters. In addition, Sobol indices as global sensitivity metrics have been introduced to investigate the relative contribution of each geometric parameter. The results show that for the maximum heat flux, the value of the cone angle (αc) with a high index is the top contributor to the both laminar and turbulent flow state, thus the geometric parameter αc should be considered firstly in the material design process of thermal protection system. Moreover, in the most region of MSL heatshield, cone angle (αc) also became the major influence factor. However, in a relatively small region, aerothermodynamics exhibits a great sensitivity to the change of nose radius (Rn). In all regions of heatshield, the parameter of shoulder radius (Rs) is always at a low level of Sobol index.

Laminar and turbulent heating predictions for mars entry vehicles

Laminar and turbulent heating rates play an important role in the design of Mars entry vehicles. Two distinct gas models, thermochemical non-equilibrium (real gas) model and perfect gas model with specified effective specific heat ratio, are utilized to investigate the aerothermodynamics of Mars entry vehicle named Mars Science Laboratory (MSL). Menter shear stress transport (SST) turbulent model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates of the two gas models are compared and analyzed in detail. The laminar heating rates predicted by the two gas models are nearly the same at forebody of the vehicle, while the turbulent heating environments predicted by the real gas model are severer than the perfect gas model. The difference of specific heat ratio between the two gas models not only induces the flow structure's discrepancy but also increases the heating rates at afterbody of the vehicle obviously. Simple correlations for turbulent heating augmentation in terms of laminar momentum thickness Reynolds number, which can be employed as engineering level design and analysis tools, are also developed from numerical results. At the time of peak heat flux on the +3σ heat load trajectory, the maximum value of momentum thickness Reynolds number at the MSL's forebody is about 500, and the maximum value of turbulent augmentation factor (turbulent heating rates divided by laminar heating rates) is 5 for perfect gas model and 8 for real gas model.

Effects of Approximation and Close-Fitting Technique of Corona Model on Neon Soft X-Ray Emission in 3-kJ Plasma Focus

In plasma focus (PF), the thermodynamic parameters such as ion fraction $\alpha $ , effective ionic charge number $Z_{\rm eff}$ , and effective specific heat ratio $\gamma $ at different temperatures may be calculated by corona model (CM). In the Lee model code, the neon $Z_{\rm eff}$ and $\gamma $ are stored in subroutines using convenient tables and polynomials derived from the CM (we call this approach approximated CM). In this paper, the thermodynamic parameters of the CM are close fitted to the data, thus replacing the approximate CM data with a more accurate close-fitting CM (CFCM). The comparisons of the Lee model code using the approximated CM and CFCM subroutines are conducted, with the main emphasis on optimum neon soft X-ray (SXR) emission and their properties. The suitable focus pinch temperature window of 200–500 eV is applied to generate the optimum neon SXR yield ( $Y_{\rm sxr}$ ). The optimum neon $Y_{\rm sxr}$ is found to be 3.19 and 3.49 J at the optimum pressure $P_{0}=3.1$ torr with approximated CM and CFCM subroutines, respectively. A high optimum value of SXR yield is obtained using CFCM subroutines in the Lee model, which is nearer to the experimental value compared with the approximated CM subroutines. The use of CFCM in the Lee model contributes to better estimation for further numerical experiment studies and gives confidence that the model is sufficiently realistic in describing the PF dynamics and SXR emission.

Static Instability of Martian Entering Vehicles at Small Angle of Attack

Martian atmosphere which is quite different from Earth atmosphere brings a new challenge for computational fluid dynamics in aerodynamic prediction of Mars entry vehicles. Three-dimensional Navier-Stokes equations with high temperature gas model and perfect gas model have been solved by a parallel code, aiming at entry process of Mars Pathfinder. Aerodynamic characteristics has been calculated and analyzed, discussion about mechanism of static instability at small angle of attack found in simulation has been carried out. The results shows that good agreement is achieved among the numerical results, the reference values and the flight data of Viking, which validates the physical chemical models and the numerical methods applied in this paper. Prediction and comparison of aerodynamic characteristics of MPF prove results of high temperature gas model are close to LAURA code. Perfect gas model with effective specific heat ratio is capable of computing the lift and drag coefficients. At 2 degree angle of attack, MPF exhibits static instability along the trajectory, which perfect gas model failed to catch on. It is concluded that sonic line shifting around the shoulder in windward and subsonic region changing in leeward, result in different transportation processes of pressure from the expansion zone behind the shoulder to upstream, which is the main reason of occurrence of static instability.

Hypersonic static aerodynamics for Mars science laboratory entry capsule

The Mars Science Laboratory (MSL) entry capsule has been designed as a lifting entry for sufficient deceleration and precise landing performance. This paper presents the static aerodynamics analysis of the MSL capsule in the hypersonic entry process for exploration mission to Mars. Hypersonic static coefficients were derived from fully three-dimensional computational fluid dynamics solutions with a specified effective specific heat ratio on a typical trajectory state. Aerodynamic performance analysis ascertains the trim characteristics and static stability of the capsule with respect to the center of gravity (CG) location. Analysis results obtained show that CG location determines the trim characteristics and the static stability, and certain CG radial and axial shift alters the lifting entry performance, so that proper aerodynamic configuration and inner equipment layout is needed for CG adjustment to satisfy the static aerodynamics requirements.

Numerical Experiments in Plasma Focus Operated in Various Gases

We adapted the Lee Model code as a branch version RADPF5.15K to gases of special interest to us, namely, nitrogen and oxygen and applied numerical experiments specifically to our AECS PF-1 and AECS PF-2. We also generalized the numerical experiments to other machines and other gases to look at scaling laws and to explore recently uncovered insights and concepts. The required thermodynamic data of nitrogen, oxygen, neon, and argon gases (ion fraction, the effective ionic charge number, the effective specific heat ratio) were calculated, the X-ray emission properties of plasmas were studied, and suitable temperature range (window) for generating H- and He-like ions (therefore soft X-ray emissions) of different species of plasmas were found. The code is applied to characterize the AECS-PF-1 and AECS-PF-2, and for optimizing the nitrogen, oxygen, neon, and argon SXR yields. In numerical experiments we show that it is useful to reduce static inductance <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm L}_{0}$</tex></formula> to a range of 15–25 nH; but not any smaller. These yields at diverse wavelength ranges are large enough to be of interest for applications. Scaling laws for argon and nitrogen SXR were found. Model parameters are determined by fitting computed with measured current waveforms in neon for INTI PF and in argon for the AECS PF-2. Radiative cooling effects are studied indicating that radiative collapse may be observed for heavy noble gases (Ar, Kr, Xe) for pinch currents even below 100 kA. The creation of the consequential extreme conditions of density and pulsed power is of interest for research and applications.

Relations estimated at shock discontinuities excited by coronal mass ejections

An analysis of SOHO/LASCO C3 data shows that there are discontinuities in the radial profiles of the plasma density within limited regions in front of each of ten coronal mass ejections, which represent shocks. The shock velocities in various events reach V ≈ 800–2500 km/s. A comparison of the dependence of the AlfvenicMach numberM A on the shock strength ρ 2/ρ 1 detected at distancesR > 10R⊙ from the center of the Sun with calculations carried out using ideal magnetic hydrodynamics shows that the effective ratio of specific heats γ describing processes inside the shock front varies from 2 to 5/3 (ρ 1 and ρ 2 are the densities in front of and behind the shock, and R⊙ is the solar radius). This corresponds to an effective number of degrees of freedom between two and three. A similar dependenceMA(ρ 2 /ρ 1) was found for near-Earth bow shocks and interplanetary collisionless shocks. These features support the hypothesis that the studied discontinuities preceding coronal mass ejections are collisionless shocks.

Inclusion of Turbulence in Solar Modeling

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer of the sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass, and the effective ratio of specific heats due to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g. pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in 3D simulations, and produces a p-mode frequency correction an order of magnitude better than the first method.

Hot spot ignition: the Newtonian limit

One-dimensional initiation of gaseous detonations is analysed for a confined domain in which there is a prescribed thermal gradient. For this type of non-uniformity, the high-temperature regions lead to local hot spots that preferentially promote ignition. Spatio-temporal development of the hot spots, which generate complex structures within the induction domain, is governed by Clarke9s equation. In this paper, the ignition onset is studied through a combination of high activation energy asymptotics and the Newtonian limit γ → 1, where γ is an effective specific heat ratio. Examination of the hot spot behaviour reveals the existence of a region that is exponentially thin with respect to γ → 1, and it is in this region that a reaction front is born. The front is associated with a spatially evolving logarithmic singularity that corresponds to the local ignition time. Although the front decelerates rapidly as it crosses the exponentially thin zone away from the initiating hot spot, its speed remains supersonic. Explicit results for the flow field and for the singularity path are obtained; they agree well with full numerical calculations.

Computational flow predictions for hypersonic drag devices

The effectiveness of two types of hypersonic decelerators are computationally examined: mechanically deployable flares and inflatable ballutes. CFD is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The surface pressure coefficients, the drag, and the extent of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5 in order to assure that the SRM will splash down in the Pacific Ocean. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.

Free-flight trim-angle predictions for the aeroassist flight experiment

The aerodynamic coefficients and trim angle for an aerobrake at Mach numbers of 9.2 and 11.8 were found using a combination of experiment and computation. Free-flight tests were performed at NASA Ames Research Center's Hypervelocity Free-Flight Aerodynamic Facility, and the forebody pressure distribution was calculated using a three-dimensional Navier-Stokes code with an effective specific heat ratio. The computed drag, lift, and moments were used to prescribe the number of terms in the aerodynamic coefficient expansions and to specify values of the higher-order terms, and the experimental aerodynamic coefficients and trim angle were extracted from the experimental data. The experimental and computed aerodynamic coefficients and trim angles were in good agreement. The trim angle obtained from the free-flight tests, 14.7 deg, differed from the design trim angle, 17 deg, and from the Langley wind-tunnel results, 12 deg in air and 17 deg in CF4. These differences are attributable to real-gas effects.

Characterization of supersonic beams by time-of-flight technique

Time-of-flight technique has been used to characterize supersonic beams of polyatomic molecules in terms of translational and vibrational temperatures, various velocity parameters and speed ratio. Collision effectiveness and effective specific heat ratio of polyatomic gases pertinent to jet expansion have also been determined and interpreted.

Pitot pressure and heat-transfer measurements in hydrazine thruster plumes

Pitot pressure and heat-transfer measurements have been made in plumes of 0.5-N (conical nozzle), 2-N, and 5-N (contoured nozzles) monopropellant hydrazine thrusters. The main objectives are to check the DFVLR simple plume model and to determine reliable model input values for real thrusters. The methods used for the heattransfer measurements (applying a sphere probe), the recovery temperature determination, and the evaluation of the plume quantities relevant for plume impingement calculations are outlined. The Pitot pressure measurements showed the existence of shock disturbances in the near plume flowfield of the contoured nozzles. Stagnation temperatures between 900 and 1350 K were deduced from the measured recovery temperatures. The corresponding molecular weight range was found to be between 11 and 14.5 and the most reasonable mean effective ratio of specific heats to be K = 1.4 ±0.03 for the expansion from the stagnation chamber to the continuum plume flow. This value is proposed for simple plume model calculations. The model heat-transfer results agree well with the experiments.

Relaxation in pure and seeded supersonic jets of SF6

Abstract Nozzle expansion of pure SF 6 and SF 6 seeded in carrier gases e.g. Ar, He and N 2 , is used to study relaxation of the various degrees of freedom. The diode laser absorption spectrum of the Q branch of the ν 3 mode of SF 6 is used to derive the rotational temperature ( T rot ). Time-of-flight studies determine the translational temperature ( T tg ) while the vibrational temperature ( T vib ) is estimated from the energy balance equation. Rotational and translational temperatures follow each other closely while the vibrational temperature lags behind considerably. The effective specific heat ratio (γ) and the collisional effectiveness parameter ( e ) for SF 6 are determined from these measurements. Seeded-beam data prove argon to be a better refrigerant than He or N 2 . Cooling in seeded beams at moderate stagnation pressures is not substantially enhanced even at very high dilution.

Shock Waves in Dusty Gas with Radiation Effects

The jump conditions across a three dimensional curved shock in dusty gas with radiation have been derived. The general Rankine-Hugoniot relations for a three dimensional curved shock in dusty gas with radiation are investigated. These relations differ considerably from those without radiation effects. The most important parameter is the ratio of radiation pressure to the pressure of the mixture (gas+dust), ie the radiation pressure number Rp. The successive approximations have been used for different cases depending upon the value of radiation pressure number. In certain cases, the result. may be expressed in terms of an effective ratio of specific heats and an effective dusty gas pressure. A general method of solution is given and some numerical results are obtained.

Radius Ratios of Argon Pinches

According to a new theory based on energy balance, the radius ratio Yp/Yo of a constant-current plasma pinch depends only on the value of the effective specific heat ratio y of the pinched plasma. In this paper the value of y for argon is computed as a function of temperature. From these values the constant-current pinch ratios are computed. The results show argon pinch ratios of about o� 08 from (2-4) x 106 K, rising to 0�18 at 1�1 x 107 K and to O� 27 at 108 K. There is good agreement between this theory and an Imperial College measurement of Y o/ro ~ 0 �17 for a constant-current argon pinch at an estimated temperature of 1 keY.