Tarek Bengherbia

Equations of state for 1-D modelling of ram accelerator thrust in thermally choked propulsion mode

A one-dimentional performance analysis code has been developed at eh Laboratoire de Combustion et de Detonique to predict the thrust in the thermally choked ram accelerator propulsion mode. This code includes the real gas effect in steady calculations and incorporates the following equations of state: ideal gas, Boltzman, Percus-Yevick (PY) and Becker-Kistiakowsky-Wilson (BKW). The code was validated against key experimental data from representative experiments at the University of Washngton 38-mm-bore facility. The predicted thrust and valicity agree well with experimental measurements. The present paper provides details about the algorithm of the calculation in the thermally choked propulsion mode.

Improved One-Dimensional Unsteady Modeling of Thermally Choked Ram Accelerator in Subdetonative Velocity Regime

The subdetonative propulsion mode using thermal choking has been studied with a one-dimensional (1D) real gas model that included projectile acceleration. Numerical results from a control volume analysis that accounted for unsteady flow effects established that the thrust coefficient versus Mach number profile was lower than that obtained with a quasi-steady model. This deviation correlates with experimental results obtained in a 38-mm-bore ram accelerator at 5.15 MPa fill pressure. Theoretical calculations were initially carried out with the assumption that the combustion process thermally choked the flow about one projectile length behind the projectile base. Thus the control volume length used in this 1D modeling was twice the projectile length, which is consistent with experimental observations at velocities corresponding to Mach number less than 3.5. Yet the choice of the length of the combustion zone and thus the control volume length remains a key issue in the unsteady modeling of the ram accelerator. The present paper provides a refinement of the unsteady one-dimensional model in which the effect of control volume length on the thrust coefficient and the projectile acceleration were investigated. For this purpose the control volume length determined from computational fluid dynamics (CFD) as a function of projectile Mach number was applied. The CFD modeling utilized the Reynolds-averaged Navier-Stokes (RANS) equations to numerically simulate the reacting flow in the ram accelerator. The shear-stress transport turbulence and the eddy dissipation combustion models were used along with a detailed chemical kinetic mechanism with six species and five-step reactions to account for the influence of turbulence and rate of heat release on the length of the combustion zone. These CFD computational results provided Mach number dependent estimates for the control volume length that were implemented in the 1D modeling. Results from the proposed improved 1D unsteady modeling were compared and validated with ram accelerator experimental data with significant improvements in terms of the predicted thrust dependence on Mach number.

Numerical Investigation of Thermally Choked Ram Accelerator in Sub-Detonative Regime

Numerical investigations of thermally choked ram accelerator in sub-detonative regime have been carried out. The simulation solves axis-symmetric compressible Navier-Stokes equations and includes modern turbulent combustion models. The experimental operating characteristics of a four-finned projectile in a 38-mm-diameter tube loaded with premixed propellant gas of methane/oxygen/nitrogen at a fill pressure and temperature of 5.15 MPa and 300 K, respectively, are considered. Simulations for projectile Mach numbers of 2.98, 3.05, 3.21, 3.41, 3.6, 4.36, and 5.01 were carried out. The shear-stress transport turbulence model and the eddy dissipation turbulent combustion model are used to simulate the turbulent reactive flow around the projectile. Complex chemical reaction mechanisms have been modeled with one-step, two-step and five-step simplified global reaction models. Not surprisingly, the non-dimensional pressure distributions from the simulation using the fivestep reaction model are in better agreement with the experimental measurements than those from the one-step and two-step models. The simulations reveal some key features of the shock system around the projectile, which are important in determining the characteristics of the thermally choked propulsive mode. These findings are useful in understanding the characteristics of supersonic turbulent combustion processes in the ram accelerator.

Thrust Prediction in Thermally Choked Ram Accelerator

Computational fluid dynamics solutions of the Reynolds-averaged Navier-Stokes equations have been used to numerically simulate the reacting flow in the ram accelerator mass-driver concept. The shear-stress transport turbulence model and the eddy dissipation combustion model are also used including a detailed chemical kinetic mechanism with six species and five-step reactions. Simulations for a series of incoming Mach numbers were carried out to investigate the details of the flow field in the thermally choked combustion regime. It was found that the predicted thrust-velocity characteristics agreed well with those obtained from the one-dimensional modeling computation and the experimental measurements. The present study provides some useful results such as the influence of Mach number on length of ram accelerator combustion zone at velocities approaching the Chapman-Jouguet detonation speed.

Equations of state implementation for 1-D modelling of performance in ram accelerator thermally choked propulsion mode

This paper presents advancement on one–dimensional (1–D) unsteady modelling of a ram accelerator (RAMAC) in the sub–detonative velocity regime by including real–gas equations of state (EoS) in order to account for the compressibility effects of the combustion products. Several equations of state based on generalised empirical and theoretical considerations are incorporated into a 1–D computer code TARAM. The objective of this work is to provide the best available formulations in order to improve the unsteady 1–D model and make the TARAM code a useful tool to predict the performance of the RAMAC in the sub–detonative velocity regime, without having to resort to more complicated 2–D or 3–D computational schemes. The calculations are validated against experimental data from 38–mm and 90–mm–bore facilities and good agreements have been achieved. Yet, the results demonstrate the need for further CFD studies involving the scale effect.

One-Dimensional Modeling of Thermally Choked Ram Accelerator Based on CFD Simulations

In order to improve one-dimensional unsteady modeling of ram accelerator thrust performance, computational fluid dynamics solutions of Reynoldsaveraged Navier-Stokes equations have been used to investigate the reacting flow field of a projectile accelerated in the sub-detonative velocity regime. Both shearstress transport turbulence and eddy dissipation combustion models were used, including a detailed chemical kinetic mechanism with six species and five-step reactions. Simulations for a series of incoming Mach numbers were performed to estimate the length within which the combustion reactions were completed. This in-depth calculation of the flow field allowed implementing the unsteady 1D modeling with an accurate Mach number dependent heat release zone length. A significantly better agreement of the predicted thrust-Mach number behavior with experimental data was observed.

Effects of Mach number on the combustion zone length for a RAMAC configuration at sub-detonative mode

Computational investigation of Mach number effects on the combustion zone length in supersonic flow over a ram accelerator has been carried out to provide valuable data for an on-going theoretical study of the same problem. It is found that the combustion zone length is inversely proportional to the Mach number with a significant reduction of about 33% at Mach 3.5 and about 44% at Mach 4, respectively, while comparing to the combustion zone length at Mach 2.5. This correlation provides some useful guidelines to define the control volume box in corresponding theoretical study.