Perfect Gas Model Research Articles

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.

Comparison among unstructured TVD, ENO and UNO schemes in two- and three-dimensions

This study focuses on unstructured TVD, ENO and UNO schemes applied to solve the Euler equations in two- and three-dimensions. They are implemented on a finite volume context and cell centered data base. The algorithms of Yee, Warming and Harten 1982; Harten; Yee and Kutler; Yee Warming and Harten 1985; Yee; Yee and Harten; Harten and Osher; Yang 1990, Hughson and Beran; Yang 1991; and Yang and Hsu are implemented to solve such system of equations in two- and three-dimensions. All schemes are flux difference splitting and good resolution is expected. This study deals with calorically perfect gas model and in so on the cold gas formulation has been employed. Two problems are studied, namely: the transonic convergent-divergent symmetrical nozzle, and the supersonic ramp. A spatially variable time step is implemented to accelerate the convergence process. The results highlights the excellent performance of the Yang 1990 TVD scheme, yielding an excellent pressure distribution at the two-dimensional nozzle wall, whereas the Harten and Osher scheme yields accurate values to the angle of the oblique shock wave and the best wall pressure distributions in the two-dimensional ramp problem. On the other hand, the excellent performance of the Harten scheme in the three-dimensional nozzle problem, yielding an excellent pressure distribution at the nozzle wall, and the Yee and Harten scheme yielding an accurate value to the angle of the oblique shock wave and the best wall pressure distribution in the three-dimensional ramp problem are of good quality.

Effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider under different angles of attack

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.

Supersonic steady aerodynamics of a cylinder with a fluid flare

Basing upon the ideal inviscid perfect gas model the aerodynamic characteristics and the gasdynamic function distributions over the surface of a cylinder in a steady supersonic three-dimensional flow are studied in the absence and the presence of combined intense air injection from the flat-ended nose and the lateral surface of the body into the shock layer. The purpose of the study is to investigate the influence of gas injection from different regions of the cylinder surface on supersonic flow past the cylinder at different angles of attack.

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.

Prediction of Chemical Nonequilibrium Flow Structure at Different Free-Stream Knudsen Numbers

AbstractA numerical study is conducted to investigate the effects of the inflow Knudsen number (Kn) on hypersonic chemical nonequilibrium rarefied flows using the unstructured direct simulation Monte-Carlo (DSMC) method, and an empirical formula for fast prediction of flow-field structure for different values of Kn is proposed and verified. First, the flow around a vertical plate is analyzed at a free-stream velocity of 7,500 m/s using a perfect-gas model with inflow Kn values ranging from 0.035 to 13.36. Through analysis of the flow-field characteristics with varying Kn values, a linear expansion law of flow-field versus the square root of Kn is discovered and an empirical formula based on least-squares fitting is developed for fast prediction of the flow structure at different values of Kn. Further, the effects of chemical nonequilibrium on hypersonic rarefied flow-field structure are investigated to verify the applicability of the empirical formula. Finally, cases of the cylinder flow are simulated in...

Simple, stable and reliable modeling of gas properties of organic working fluids in aerodynamic designs of turbomachinery for ORC and VCC

A simple, stable and reliable modeling of the real gas nature of the working fluid is required for the aerodesigns of the turbine in the Organic Rankine Cycle and of the compressor in the Vapor Compression Cycle. Although many modern Computational Fluid Dynamics tools are capable of incorporating real gas models, simulations with such a gas model tend to be more time-consuming than those with a perfect gas model and even can be unstable due to the simulation near the saturation boundary. Thus a perfect gas approximation is still an attractive option to stably and swiftly conduct a design simulation. In this paper, an effective method of the CFD simulation with a perfect gas approximation is discussed. A method of representing the performance of the centrifugal compressor or the radial-inflow turbine by means of each set of non-dimensional performance parameters and translating the fictitious perfect gas result to the actual real gas performance is presented.

Stagnation pressure effect on the supersonic flow parameters with application for air in nozzles

ABSTRACTWhen the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas doesn't stay perfect. Its state equation changes and it becomes a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation. The aim of this work is to determine the effect of stagnation pressure on the thermodynamic, physical and geometrical supersonic flow parameters in order to find a general form for real gas. With the assumptions that Berthelot's state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The design parameters of the supersonic nozzle-like thrust coefficient depend directly on the stagnation parameters of the combustion chamber. The application made for air. A computation of error was made in this case to give a limit of the perfect gas model compared to the real gas model.

Effective high-order solver with thermally perfect gas model for hypersonic heating prediction

Effective high-order solver based on the model of thermally perfect gas has been developed for hypersonic heat transfer computation. The technique of polynomial curve fit coupling to thermodynamics equation is suggested to establish the current model and particular attention has been paid to the design of proper numerical flux for thermally perfect gas. We present procedures that unify five-order WENO (Weighted Essentially Non-Oscillatory) scheme in the existing second-order finite volume framework and a line-implicit method that improves the computational efficiency without increasing memory consumption. A variety of hypersonic viscous flows are performed to examine the capability of the resulted high order thermally perfect gas solver. Numerical results demonstrate its superior performance compared to low-order calorically perfect gas method and indicate its potential application to hypersonic heating predictions for real-life problem.

AN EMPIRICAL METHOD FOR FAST PREDICTION OF RAREFIED FLOW FIELD AROUND A VERTICAL PLATE

Numerical study is conducted to investigate the effects of free-stream Knudsen (Kn) number on rarefied flow field around a vertical plate employing an unstructured DSMC method, and an empirical method for fast prediction of flow-field structure at different Kn numbers in a given inflow velocity is proposed. First, the flow at a velocity 7500m/s is simulated using a perfect-gas model with free-stream Kn changing from 0.035 to 13.36. The flow-field characteristics in these cases with varying Kn numbers are analyzed and a linear-expansion phenomenon as a function of the square of Kn is discovered. An empirical method is proposed for fast flow-field prediction at different Kn based on the least-square-fitting method. Further, the effects of chemical reactions on flow field are investigated to verify the applicability of the empirical method in the real gas conditions. Three of the cases in perfect-gas flow are simulated again by introducing five-species air chemical module. The flow properties with and without chemical reactions are compared. In the end, the variation of chemical-reaction flow field as a function of Kn is analyzed and it is shown that the empirical method are also suitable when considering chemical reactions.

Supersonic flow past a cylinder with a fluid flare

The aerodynamic parameters and the pressure distribution over the surface of a cylinder in a steady axisymmetric supersonic flow is studied within the framework of the inviscid perfect gas model in the absence and the presence of combined intense air injection fromthe flat face and the lateral surface into the shock layer. The purpose of the study is to investigate the effect of gas blowing from different regions of the cylindrical surface on the supersonic axisymmetric flow past the body.

Influence of the External Force on the Vortex–Source Combination Crisis

This paper considers the force stagnation of a supersonic vortex–source combination flowing out into a vacuum, leading to a decrease in the radial Mach number to unity and stationary flow choking. The similarity parameters influencing the crisis are analyzed. It has been shown that the ″force″ crisis (choking) is also possible for the vortexsink combination flowing out of a submerged space. The formulation of the thermal crisis problem is generalized to the case of a given external force per unit mass and in a unit volume. Comparison has been made between certain characteristics of the crisis due to the applied external force in the absence of power supply/removal and the characteristics of the crisis due to the heat input in the absence of external force. The investigation has been carried out from the viewpoint of the perfect gas model.

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.

Three-Dimensional Supersonic Minimum Length Nozzle Design at High Temperature for Arbitrary Exit Cross Section

The scope of this work was to perform a new three-dimensional MLN shape design of supersonic nozzles with an arbitrary exit cross section. The shape design is done by making a transition from the axisymmetrical nozzle using the streamline definition in space. The study is made at high temperature, however, less than the dissociation temperature. Studying asymmetric nozzles is very important for the improvement in the axisymmetric nozzles efficiency, higher Mach number, mass and thrust coefficient. Three cases are considered in order to find a three-dimensional nozzle shape with equal mass, the same exit Mach number and the same throat area compared with the axisymmetric geometry. The difference between the perfect gas model and our high-temperature model is presented. Calculation can be performed for any selected 3D nozzle exit cross section. Hence, an infinite number of nozzle shapes are available, depending on the selected exit Mach number, stagnation temperature or exit cross-sectional shape. The application is for air.

Sound Generation by Taylor and Scully Vortexes and the Blade of the Varying Cross Section

A problem of the blade vortex interaction noise (BVI) generation has been solved for incoming flux and Taylor, Scully vortexes. Solution for this problem is a closed system of the aeroacoustical equations, which is based on perfect compressible gas model. A behavior of the generated noise has been studied for the different flow velocities and blade thicknesses. Results of the calculations show existence of the two frank regions of the sound existence on the blade shape. The first of it is more resistant for the parameters changing. The second one is a flow region of the instability. These two regions interaction forms far field acoustical pressure distribution. In particular, it has been found that noise characteristics depend on incoming flow velocity and its maximal level depends on blade’s cross section thickness. A sound pressure distribution for Scully vortex is smoother than for Taylor vortex. A frequency distribution of the harmonics level in the noise spectrum has showed low-frequency character of the generated noise. Moreover, at the frequency 700 Hz a local level maximum is seen, which is not present for vortex absence in flow. This fact says about some BVI-energy redistribution in the flux for the higher frequencies generation.

Supersonic axisymmetric flow past a blunt cone executing longitudinal low-frequency oscillations

The aerodynamic parameters of an oscillating cone in unsteady axisymmetric supersonic flow are investigated on the basis of the inviscid perfect gas model both in the absence and in the presence of strong air injection from its flat end into the shock layer.

Thermal Crisis of the Vorticity Source at a Constant Pressure

The thermal crisis of the vorticity source at a given energy input at a constant pressure has been investigated from the viewpoint of a perfect gas model and Euler equations. The energy release rates given per unit mass or unit volume of the gas with vorticity source outflow into a vacuum and a submerged space have been considered. The features of analytical solutions for the gas-dynamic parameters in various regimes and for different variants of the vorticity source with energy input, including heat removal, have been investigated. The boundaries of the region of energy input at a constant pressure have been determined.

The Effect of Gas Models on Compressor Efficiency Including Uncertainty

Since isentropic efficiency is widely used in evaluating the performance of compressors, it is essential to accurately calculate this parameter from experimental measurements. Quantifying realistic bounds of uncertainty in experimental measurements are necessary to make meaningful comparisons to computational fluid dynamics simulations. This paper explores how the gas model utilized for air can impact not only the efficiency calculated in an experiment, but also the uncertainty associated with that calculation. In this paper, three different gas models are utilized: the perfect gas model, the ideal gas model, and the real gas model. A commonly employed assumption in calculating compressor efficiency is the perfect gas assumption, in which the specific heat, is treated as a constant and is independent of temperature and pressure. Results show significant differences in both calculated efficiency and the resulting uncertainty in efficiency between the perfect gas model and the real gas model. The calculated compressor efficiency from the perfect gas model is overestimated, while the resulting uncertainties from the perfect gas model are underestimated. The ideal gas model agrees well with the real gas model, however. Including the effect of uncertainty in gas properties results in very large uncertainties in isentropic efficiency, on the order of ten points, for low pressure ratio machines.

Partition Function of the Model of Perfect Gas of Clusters for Interacting Fluids

The last paper of A. Fronczak presents a new, combinatorial approach to the model of perfect gas of clusters of interacting fluids. In the paper the enumerative properties and combinatorial meaning of Bell polynomials have been used to reveal some properties of systems described by grand canonical ensemble . In this paper, an exact proof of one of the important assertions from the work mentioned above is given. The assertion states that for the system in which one can distinguish k non interacting clusters the canonical partition function is given by Bell polynomial of the derivatives of the grand-thermodynamic potential with respect to the fugacity. Some possible applications of the considered theorem are presented.

Numerical study of unsteady starting characteristics of a hypersonic inlet

The impulse and self starting characteristics of a mixed-compression hypersonic inlet designed at Mach number of 6.5 are studied by applying the unsteady computational fluid dynamics (CFD) method. The full Navier–Stokes equations are solved with the assumption of viscous perfect gas model, and the shear-stress transport (SST) k–ω two-equation Reynolds averaged Navier–Stokes (RANS) model is used for turbulence modeling. Results indicate that during impulse starting, the flow field is divided into three zones with different aerodynamic parameters by primary shock and upstream-facing shock. The separation bubble on the shoulder of ramp undergoes a generating, growing, swallowing and disappearing process in sequence. But a separation bubble at the entrance of inlet exists until the freestream velocity is accelerated to the starting Mach number during self starting. The mass flux distribution of flow field is non-uniform because of the interaction between shock and boundary layer, so that the mass flow rate at throat is unsteady during impulse starting. The duration of impulse starting process increases almost linearly with the decrease of freestream Mach number but rises abruptly when the freestream Mach number approaches the starting Mach number. The accelerating performance of booster almost has no influence on the self starting ability of hypersonic inlet.