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NASA NTRS1992

Recent advances in numerical simulation and control of asymmetric flows around slender bodies

The problems of asymmetric flow around slender bodies and its control are formulated using the unsteady, compressible, thin-layer or full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. The problem is numerically simulated for both locally-conical and three-dimensional flows. The numerical applications include studies of the effects of relative incidence, Mach number and Reynolds number on the flow asymmetry. For the control of flow asymmetry, the numerical simulation cover passive and active control methods. For the passive control, the effectiveness of vertical fins placed in the leeward plane of geometric symmetry and side strakes with different orientations is studied. For the active control, the effectiveness of normal and tangential flow injection and surface heating and a combination of these methods is studied.

Kandil, Osama A.↗

NASA NTRS1992

Numerical Modeling of a Vortex Stabilized Arcjet

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Pawlas, Gary E.↗

NASA NTRS1992

Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods

Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.

Yang, Yii-Ching↗

NASA NTRS1993

Structure of confined laminar spray diffusion flames: Numerical investigation

The structure of confined laminar spray diffusion flames is investigated numerically by solving the gas-phase conservation equations for mass species, continuity, momentum, and energy and the liquid-phase equations for droplet position, velocity, size, and temperature. A one-step global reaction scheme along with six equilibrium reactions are employed to model the flame chemistry. Monodisperse as well as polydisperse sprays are considered. The numerical results demonstrate that liquid spray flames substantially differ from gaseous flames in their structure, i.e., temperature, concentration, and velocity fields, shape, and dimensions under the same conditions. Spray flames are predicted to be taller and narrower than their counterpart gaseous ones and their shapes are almost cylindrical. This is in agreement with experimental observations. The numerical computations also show that the use of the equilibrium reactions with the one-step reaction scheme decreases the flame temperature compared to the one-step reaction scheme without the equilibrium reactions and more importantly increases the surface area of the flame zone due to a phenomenon termed 'equilibrium broadening.' The spray flames also possess a finite thickness with minimal overlap of the fuel and oxygen species. A case for which a fuel-mixture consisting of 20 to 80 percent gas-liquid by mass is introduced into the combustor is also investigated and compared with predictions using only gaseous or liquid fuel.

Mawid, M. A.↗

NASA NTRS1993

A numerical study of confined turbulent jets

A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

Zhu, J.↗

NASA NTRS1992

Numerical simulations of high-speed flows about waveriders with sharp leading edges

A procedure is developed for the numerical simulation of stagnation-free inviscid supersonic and hypersonic flows about waveriders with sharp leading edges. The numerical approach involves the development of a specialized grid generator (named HYGRID), an algebraic solution-adaptive grid scheme, and a modified flow solving method. A comparison of the results obtained for several waverider geometries with exact solutions, other numerical solutions, and experimental results demonstrated the ability of the new procedure to produce stagnation-free Euler solutions about sharp-edged configurations and to describe the physics of the flow in these regions.

Jones, Kevin D.↗

NASA NTRS1992

Direct numerical simulations of a spatially developing plane wake

In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Maekawa, Hiroshi↗

NASA NTRS1993

Numerical model for the Programmable Multirole Furnace (PMZF)

The present account of the Programmable Multizone Furnace numerical model uses various examples to illustrate the ways in which the model serves as an optimization, test, prediction, and visualization tool; a numerical PID-control algorithm obtains the desired sample temperature distributions and allows the model to solve an inverse heat transfer problem where the desired sample temperature profile is the input and the required heater power distribution is the output of numerical simulations. Parametric studies show how the total power consumption of the furnace is affected by such design variables as the conductivity.

Kassemi, M.↗

NASA NTRS1993

Numerical modeling of wall-injected scramjet experiments

A wall-injected, hydrogen-fueled scramjet is modeled numerically using a parabolic Navier-Stokes computer code with a k-epsilon turbulence model and finite-rate chemistry. The numerical results are compared to experimental scramjet data taken in a shock tunnel and are found to be in reasonable agreement. Under the conditions studied, the numerical results show that combustion in the scramjet is mainly mixing limited.

Brescianini, C. P.↗

NASA NTRS1992

Comparison of numerical oblique detonation solutions with an asymptotic benchmark

In order to have confidence in a numerical method, the verification of its reproduction of known benchmark analytic solutions for simple model problems is of great importance. Attention is presently given to a novel benchmarking procedure for numerical models of high speed, reactive 2D flows. The procedure is illustrated by comparing asymptotic and numerical solutions for oblique detonations in which an attached oblique shock is followed by an exothermic reaction with a thick reaction zone.

Grismer, Matthew J.↗

NASA NTRS1991

Ground-based PIV and numerical flow visualization results from the Surface Tension Driven Convection Experiment

The Surface Tension Driven Convection Experiment (STDCE) is a Space Transportation System flight experiment to study both transient and steady thermocapillary fluid flows aboard the United States Microgravity Laboratory-1 (USML-1) Spacelab mission planned for June, 1992. One of the components of data collected during the experiment is a video record of the flow field. This qualitative data is then quantified using an all electric, two dimensional Particle Image Velocimetry (PIV) technique called Particle Displacement Tracking (PDT), which uses a simple space domain particle tracking algorithm. Results using the ground based STDCE hardware, with a radiant flux heating mode, and the PDT system are compared to numerical solutions obtained by solving the axisymmetric Navier Stokes equations with a deformable free surface. The PDT technique is successful in producing a velocity vector field and corresponding stream function from the raw video data which satisfactorily represents the physical flow. A numerical program is used to compute the velocity field and corresponding stream function under identical conditions. Both the PDT system and numerical results were compared to a streak photograph, used as a benchmark, with good correlation.

Pline, Alexander D.↗

NASA NTRS1993

A numerical study of wave propagation in a confined mixing layer by eigenfunction expansions

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained.

Hu, Fang Q.↗

NASA NTRS1991

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Cerro, J. A.↗

NASA NTRS1993

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Felici, Helene M.↗

NASA NTRS1993

High resolution numerical simulation of the linearized Euler equations in conservation law form

A linearized Euler solver based on a high resolution numerical scheme is presented. The approach is to linearize the flux vector as opposed to carrying through the complete linearization analysis with the dependent variable vector written as a sum of the mean and the perturbed flow. This allows the linearized equations to be maintained in conservation law form. The linearized equations are used to compute unsteady flows in turbomachinery blade rows arising due to blade vibrations. Numerical solutions are compared to theoretical results (where available) and to numerical solutions of the nonlinear Euler equations.

Sreenivas, Kidambi↗

NASA NTRS1993

Numerical simulation of upstream disturbance on flows around a slender body

Numerical solutions of the thin-layer approximation of the compressible Navier-Stokes equations have been obtained for flows around an ogive-cylinder body with and without a small fixed disturbance placed upstream of the body tip. Locating the disturbance at positions in the flow field upstream of the tip provokes the same range of behavior of the asymmetric flow that was numerically produced earlier by use of a geometrical disturbance on the body tip. Results remain consistent with the presence of a convective instability mechanism, and demonstrate the potential for a precise mapping of the body's receptivity to fixed disturbances in the flow field. Numerical solutions were also obtained for the flow-field responses to impulsive upstream disturbances to determine whether there is a growing response to an asymmetric impulsive disturbance that is consistent with presence of a convective instability mechanism. Results for surface pressure are interpreted with the aid of a mathematical model. The model suggests that the observed growth of surface pressure gradient with time and distance along a ray in response to an asymmetnc impulsive disturbance is in accord with the solution of a Ginzberg-Landau equation, with distinguishing features of the solution being consistent with the convective instability mode of behavior.

Degani, David↗

NASA NTRS1993

Analysis of direct numerical simulation data of a Mach 4.5 transitional boundary-layer flow

This paper describes the creation, by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations, of a high-quality data set that represents the laminar-turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang (1992), and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along a hollow cylinder is simulated numerically. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy 'budgets' are constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production and dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure-dilatation term is of the same order of magnitude as the compressible dissipation rate.

Dinavahi, Surya P. G.↗

NASA NTRS1992

Numerical predictions in acoustics

Computational Aeroacoustics (CAA) involves the calculation of the sound produced by a flow as well as the underlying flowfield itself from first principles. This paper describes the numerical challenges of CAA and recent research efforts to overcome these challenges. In addition, it includes the benefits of CAA in removing restrictions of linearity, single frequency, constant parameters, low Mach numbers, etc. found in standard acoustic analyses as well as means for evaluating the validity of these numerical approaches. Finally, numerous applications of CAA to both classical as well as modern problems of concern to the aerospace industry are presented.

Hardin, Jay C.↗