Low thrust viscous nozzle flow fields prediction

An existing Navier-Stokes code (PARC2D) was used to compute the nozzle flow field. Grids were generated by the interactive grid generator codes TBGG and GENIE. All computations were made on the NASA/MSFC CRAY X-MP computer. Comparisons were made between the computations and MSFC in-house wall pressure measurements for CO2 flow through a conical nozzle having an area ratio of 40. Satisfactory agreements exist between the computations and measurements for different stagnation pressures of 29.4, 14.7, and 7.4 psia, at stagnation temperature of 1060 R. However, agreements did not match precisely near the nozzle exit. Several reasons for the lack of agreement are possible. The computational code assumes a constant gas gamma, whereas the gamma i.e. the specific heat ratio for CO2 varied from 1.22 in the plenum chamber to 1.38 at the nozzle exit. The computations also assumes adiabatic and no-slip walls. Both assumptions may not be correct. Finally, it is possible that condensation occurs during the nozzle expansion at the low stagnation pressure. The next phase of the work will incorporate variable gamma and slip wall boundary conditions in the computational code and develop a more accurate computer code

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated

Modeling of Non-Spherical Droplet Dynamics

A two-dimensional time-dependent computer code based on the modified Arbitrary Lagrangian Eulerian (ALE) technique, has been developed to simulate non-spherical droplet dynamics and evaporation under convective flows at real rocket combustion chamber conditions. The equations of mass, momentum, energy and species are simultaneously solved for both liquid and gas phases with an accurate dynamic interface tracking. The jump boundary conditions across the deforming droplet surface are obtained by applying the integral forms of conservation of mass, momentum, and energy. At each time step, the interface geometry and flow properties at the droplet surface are implicitly solved by satisfying the interface boundary conditions. A Lagrangian technique was developed to track the arbitrarily moving interface between the liquid droplet and the external gas. An elliptic grid generator is adopted to dynamically reconstruct grids both inside and outside the droplet surface. This code has been used to study droplet oscillation, droplet deformation/breakup, nonspherical droplet evaporation in both low and high pressure convective flows. This presentation briefly describes the numerical algorithm for modeling of the nonspherical droplet dynamics and demonstrates the representative simulation results of nonspherical droplet evaporation at low and high pressure convective flows. Potential applications of this code to rocket combustor design and performance predictions are discussed

Exhausted Plume Flow Field Prediction Near the Afterbody of Hypersonic Flight Vehicles in High Altitudes

A two-dimensional computer code to solve the Burnett equations has been developed which computes the flow interaction between an exhausted plume and hypersonic external flow near the afterbody of a flight vehicle. This Burnett-2D code extends the capability of Navier-Stokes solver (RPLUS2D code) to include high-order Burnett source terms and slip-wall conditions for velocity and temperature. Higher-order Burnett viscous stress and heat flux terms are discretized using central-differencing and treated as source terms. Blocking logic is adopted in order to overcome the difficulty of grid generation. The computation of exhaust plume flow field is divided into two steps. In the first step, the thruster nozzle exit conditions are computed which generates inflow conditions in the base area near the afterbody. Results demonstrated that at high altitudes, the computations of nozzle exit conditions must include the effects of base flow since significant expansion exists in the base region. In the second step, Burnett equations were solved for exhaust plume flow field near the afterbody. The free stream conditions are set at an altitude equal to 80km and the Mach number is equal to 5.0. The preliminary results show that the plume expansion, as altitude increases, will eventually cause upstream flow separation