Real gas effects on thermally choked ram accelerator performance

Operation of the thermally choked propulsive mode provides a high level of acceleration at velocities below the Chapman-Jouguet detonation speed. A one-dimensional modeling of this process has been elaborated which takes into account the real gas effects and yields results that are in good agreement with experimental data at this velocity and acceleration. It also provides an estimate for the pressure level at the thermal choking point that is assumed to occur in the region where the pressure rapidly drops and the oscillatory character of the signal abruptly smoothes out. A fairly good agreement between experimental data and those derived from the one-dimensional modeling based on the ideal gas equation of state was observed. The effects of increasing the initial pressure, however, suggest that a real gas equation of state should be used. The present paper is aimed at providing experimental data on the thermal choking pressure. These values are compared to calculations based on real gas equations of state, i.e. Boltzmann and Percus-Yevick. The thermal choke point pressure in many high-pressure experiments is much lower than the calculated values which brings into question the validity of the criteria for identifying the choke point and/or the accuracy of the pressure measurements under these conditions.

The problem of a one-dimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed the practical notion of how Guderley-like flows might be generated. One candidate is a constant velocity, converging “cylindrical or spherical piston,” giving rise to a converging shock wave in the spirit of its classical, planar counterpart. A limitation of pre-existing analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is of course necessary for the direct comparison with the classical Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility in describing a wide variety of physical phenomena and, in particular, the shock compression of solid materials. This work is thus intended to provide an extension of previous work to a nonideal EOS. The stiff gas EOS is chosen as a logical starting point due to not only its close resemblance to the ideal gas law but also its relevance to the shock compression of various liquid and solid materials. Using this choice of EOS, the solution of a 1D planar piston problem is constructed and subsequently used as the lowest order term in a quasi-self-similar series expansion intended to capture both curvilinear and nonideal EOS effects. The solution associated with this procedure provides correction terms to the 1D planar solution so that the expected accelerating shock trajectory and nontrivially varying state variable profiles can be obtained. This solution is further examined in the limit as the converging shock wave approaches the 1D curvilinear origin. Given the stiff gas EOS is not otherwise expected to admit a Guderley-like solution when coupled to the inviscid Euler equations, this work thus provides the semianalytical limiting behavior of a flow that cannot be otherwise captured using self-similar analysis.

An experimental investigation of ram accelerator operational characteristics at fill pressures up to 20 MPa has been carried out in the 38-mm-bore test facility at the University of Washington. The minimum requirements for successfully starting titanium alloy projectiles at an entrance velocity of 1250 m/s and maintaining ram accelerator operation for 4 meters in 20 MPa propellant were determined. Velocity gains greater than 1000 m/s were achieved and average accelerations of 46,000 g with 118 gm projectiles were attained. An overview of the experimental results leading up to the successful conclusion of this phase of the ram accelerator research program is presented.

From the classical kinetic theory of gases we know the equation of state of the ideal gas, βp = n (see Chap. 1). For real gases, the interaction forces between the molecules lead to corrections to the ideal gas equation of state. We mention the classical theory by van der Waals and the systematic expansions with respect to density, called virial expansions.

view Abstract Citations (12) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Vortex funnels in accretion flows Scott, H. A. ; Lovelace, R. V. E. Abstract A study is carried out of the axisymmetric gravitational accretion of a perfect fluid with angular momentum. Flows are calculated with the aid of two coordinate expansions of the poloidal velocity potential. By way of example, the generalization of spherically symmetric inflow is presented in detail. The flows possess empty vortex cores that become cylindrical far from the accreting object with a width proportional to the fluid's angular momentum. In the study, the flow is assumed to be nonrelativistic, inviscid, isentropic, and axially symmetric. An ideal gas equation of state is adopted, and the self-gravity of the gas is neglected. The poloidal flow is assumed to be irrotational and the velocity of the fluid is assumed to approach zero at large distances from the accreting object. Publication: The Astrophysical Journal Pub Date: January 1982 DOI: 10.1086/159599 Bibcode: 1982ApJ...252..765S Keywords: Angular Momentum; Axisymmetric Flow; Gravitational Effects; Ideal Gas; Stellar Mass Accretion; Vortices; Axial Flow; Equations Of State; Flow Equations; Flow Velocity; Inviscid Flow; Isentropic Processes; Potential Flow; Astrophysics full text sources ADS |

By taking carbon dioxide and hydrogen as lubricating gas, respectively, this paper presents an analysis on the pressure characteristics and temperature distribution of spiral groove dry gas seal which influenced by real gas effect under choked flow condition. Numerical results show that the deviation between real gas and ideal gas, which expressed by the deviation degree between compressibility factor Z and 1, is the main reason for real gas effect affecting sealing performance. Compared with ideal gas model, real gas effect raises exit pressure, opening force, leakage rate, Mach number in dam region, and temperature for carbon dioxide ( Z < 1), while it decreases those characteristics for hydrogen ( Z > 1) under the same operating conditions. In addition, choked flow effect increases opening force and reduces leakage rate and temperature-drop between entrance and exit of sealing clearance. Meanwhile, it may cause an unstable behavior for the seal.

Real gas effect on steady planar detonation and uncertainty quantification

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments by means of the irreducible tensorial Hermite polynomials.

An efficient procedure for evaluating the thermodynamic and transport properties of real fluids was presented. Block-structured adaptive mesh refinement was used to construct the equations of state look-up table, which provides uniform accuracy over a selected thermodynamic plane with fewer grids. An overlapping uniform index domain was developed to provide fast search capability. Properties can be evaluated by bilinear, bicubic, and biquintic interpolation to achieve different levels of function continuity and thermodynamic consistency. Reconstruction discontinuity may appear across the interface of unequally sized blocks, but the level of discontinuity decreases when reconstruction is based on structured grids on each block. The effectiveness and efficiency of the method was demonstrated by comparing the storage, data retrieval, and computational fluid dynamics samples. The storage requirement decreases by 20 to 80% compared to the table constructed with uniform mesh. The overlapping uniform index domain is 14 to 19% faster than the tree data-structure in computational fluid dynamics calculations with the table of 0.1% accuracy. When reconstructed property is within 0.1% of the exact value, the degree of discontinuity is small enough to obtain a convergent solution in computational fluid dynamics cases. An equation of state table look-up method is as efficient as ideal gas equations of state and two orders of magnitude faster than the complex thermodynamic database.

There is currently a great amount of interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index of n = 3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms—a finite-volume “grid” code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code are chosen to match as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. We also present comparisons of simulations calculated from two different energy equations: in one series, we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations, an atmosphere forms around the accretor, which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.

Computational fluid dynamics (CFD) solutions of the full Navier-Stokes equations along with finite-rate chemical kinetics, are used to numerically simulate the reacting in-bore flowfield for a 120mm ram accelerator projectile propulsion system. Various unsteady flow phenomena are investigated, including projectile starting, obturator discard, and high-velocity unstarting. These simulations illustrate the importance of obturator discard dynamics in achieving a successful starting of the ram acceleration process. However, once started, high projectile velocities can induce an unstart if the combustion wave precedes the projectile under certain conditions. In addition, a CFD code validation case is presented for low pressure, steady flow, hydrogen/oxygen combustion around a wedge as compared to Schlieren/PLIF data from Stanford. Introduction Experimental testing and gasdynamic modeling of the ram acceleration technique for in-bore projectile propulsion has been investigated at the U.S. Army Research Laboratory (ARL) under the Hybrid Inbore RAM (HIRAM) propulsion program. This research program seeks to provide a highly efficient method of achieving hypervelocity (> 3 km/s) projectile gun-launch for use in high speed impact testing applications. The ARL ram accelerator system used a 120-mm (bore diameter) tube which was modeled after the 38-mm system at the University of Washington. Numerical solutions of the Navier-Stokes equations have been obtained at the ARL via computational fluid dynamics (CFD) codes for non-reacting and reacting, two-and three-dimensional flows. These codes are being used to investigate the complex gas dynamic physics of ram accelerator projectile propulsion. A variety of CFD techniques have been brought to bear on this problem, including models for chemically frozen (non-reacting) gas, finite-rate global and multiple step chemical kinetics, and equilibrium chemical processes. Accurate numerical simulation of hydrocarbon-based reacting flow creates a very great demand on computational resources since the number of intermediate species and the number of kinetic steps for typical hydrocarbon fuels are prohibitively large. Global reaction mechanisms based on up to thirty-two steps have therefore been investigated for use in preliminary design studies. Within several hours on supercomputers, viscous and chemically reacting gas dynamic simulations are used to assess the influence of projectile velocity, tube fill pressure and mixture composition, and projectile geometry on species consumption, tube wall pressure and projectile thrust. These studies are being used to seek optimum performance for the 120-mm ram accelerator with minimal gun firings. In particular, significant advances in CFD * Aerospace Engineer, Ballistics &; Weapons Concepts Division. Associate Fellow AIAA. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. • modeling for ram acceleration have been made at the ARE. Recently, ARL CFD models have been modified to simulate the unsteady coupling between the launch gun and the ram accelerator. In the Army experimental gun, projectile transition from the conventional (solid propellant) launcher to the accelerator was made through a transition/vent section. This section decouples the launch gun movement from the accelerator and vents combustion gases from the conventional launcher. Redesign of the ram accelerator for Navy applications has required that the ram accelerator operate without the vent section. The removal of the vent section requires that the CFD code be linked to an interior ballistics (IB) simulation of the launch gun in order to supply the pressure behind the obturator. The IB code must be able to adjust to the pressure on the forward face of the obturator, supplied from the CFD code simulating ram combustion. Simulation of ventless ram acceleration has been accomplished. Reacting Flow Model The chemically reacting hypervelocity flow field around a body is numerically simulated using a computer code based on computational fluid dynamics. The ARL-NSRG2 code solves the 2D/axisymmetric, unsteady, real-gas Navier-Stokes equations including equations for chemical kinetics and diffusion. These partial differential equations are cast in conservation form and converted to algebraic equations using a finite-volume formulation. The conservation law form of the equations assures that the end states of regions of discontinuity (e.g., shocks, flames and deflagrations) are physically correct even when smeared over a few computational cells. Solution takes place on a mesh of nodes distributed in a zonal fashion around the projectile and throughout the flow field such that sharp geometric corners and other details are accurately represented. The Navier-Stokes equations for 2D/axisymmetric reacting and unsteady flow are written in the following conservation form with variables nondimensionalized in a conventional fashion. dU dF_ dG_ fat

Numerical simulation of real gas flows in natural gas supersonic separation processing

An experimental travel-time curve for the plane shock produced in air at room temperature and atmospheric pressure by a detonation wave from solid explosive is analyzed by a graphical procedure based on the method of characteristics [R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves (Interscience Publishers, Inc., New York), Chap. II]. From the observed velocity and attenuation of the shock, profiles of pressure, density, particle velocity, temperature, entropy, and sound velocity have been calculated at fixed times. The calculation is based on the Rankine-Hugoniot jump conditions, the conservation laws for particle-isentropic flow, and the equilibrium equation of state as computed by Gilmore and by Hilsenrath and Beckett. The effects of relaxation and radiation are neglected. The results are compared with those obtained assuming an ideal gas equation of state with γ = 1.4. Preliminary results show that pressure, density, and particle velocity decrease with distance behind the shock as expected, but that temperature, sound velocity, and entropy increase behind the shock. A qualitative argument is presented which indicates that this last result may be expected for sufficiently nonuniform shock waves. [This work supported in part by Office of Chief of Ordnance, U. S. Army.]

Implications of a viscosity bound on black hole accretion

We present the accretion of collisional dark matter on a supermassive black hole seed. The analysis is based on the numerical solution of the fully coupled system of Einstein-Euler equations for spherically symmetric flow, where the dark matter is modeled as a perfect fluid that obeys an ideal gas equation of state. As the black hole actually grows, the accretion rate of dark matter corresponds to the black hole apparent horizon growth rate. We analyse cases with infall velocity as high as $0.5c$ and an environment density of $100M_{\odot}/\mathrm{pc}^3$, which are rather extreme conditions. Being the radial flux the maximum accretion case, our results show that the accretion of an ideal gas, eventually collisional dark matter, does not contribute significantly to SMBH masses. This result favors models predicting SMBHs were formed already with supermasses. We show that despite the fact that we are solving the full general relativistic system, for the parameter space studied our results are surprisingly similar to those obtained using the Bondi formula, which somehow certifies its use as a good approximation of a fully evolving space-time with spherical symmetry at short scales at least for dark matter densities. Additionally, we study the density profile of the gas and find that the presence of SMBHs redistributes the gas near the event horizon with a cuspy profile, whereas beyond a small fraction of a parsec it is not-cuspy anymore.