Method for Calculating Effects of Dissociation on Flow Variables in the Relaxation Zone Behind Normal Shock Waves
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Evans, John, S↗
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Vibrational relaxation of diatomic molecules in solids at low temperatures
The application of a hemiquantal method to the specific problem of the vibrational relaxation of a diatomic molecule embedded in a one dimensional lattice is presented. The vectorization of a CYBER 205 algorithm which integrates the 1,000 to 10,000 simultaneous hemiquantal differential equations is examined with comments on optimization. Results of the simulations are briefly discussed.
Halcomb, L. L.↗
Three dimensional hypersonic flow simulations with the CSCM implicit upwind Navier-Stokes method
The Bardina and Lombard (1985) three-dimensional CSCM Navier-Stokes method is presently extended to the simulation of complex hypersonic reentry vehicle external flows at angle of attack. The robust stability of the method derives from the combination of conservative implicit upwind flux difference splitting with a three-dimensional diagonally-dominant approximate factorization and relaxation scheme and characteristic-based implicit boundary approximations. The method's efficiency derives from an implicit symmetric Gauss-Seidel 'method of planes' relaxation scheme with alternating directional space marching sweeps along the flow coordinate direction.
Bardina, Jorge↗
Heat of segregation of single substitutional impurities
The method of Bozzolo, Ferrante and Smith (BFS) is applied for the calculation of the heat of segregation of single substitutional impurities in fcc metals. A simple equation for predicting the heat of segregation is derived for the rigid case (no atomic relaxations). The results of including atomic relaxation using a Monte Carlo method are also presented and the results compared with a number of experimental and theoretical results.
Bozzolo, Guillermo↗
A novel technique for response function determination of shear sensitive cholesteric liquid crystals for boundary layer investigations
A description of the design and setup of an experimental technique for measurement of the response function in shear sensitive liquid crystals has been reported. Utilizing the selective reflection characteristics of cholesteric liquid crystals, the method is capable of measuring the delay, rise, and relaxation times in response to a given dynamic shear stress as a function of the wavelength of the incident light. Application of a step input shear stress results in a liquid crystal time response that can be described as consisting of an initial delay, a shear induced helix deformation, and a relaxation to the initial state through diffusion processes. The method has been used for quantitative calibration of a shear sensitive liquid crystal by observing the peak in reflected light intensity, at a given wavelength, as a function of the shear stress.
Parmar, D. S.↗
Numerical modeling of a vortex stabilized arcjet thruster
A numerical method to solve the equations governing a vortex stabilized arcjet thruster is being developed. The model will allow the effects of swirling flow and geometry on arcjet thruster performance to be determined. The propellant flow equations, i.e., the axisymmetric, thin layer, Navier-Stokes equations, are solved using a Gauss-Siedel line-relaxation procedure. An implicit FTCS method is used to solve the electromagnetic field equations. A grid generation scheme was developed for an arbitrary arcjet geometry. The model will allow the radial and axial components of velocity and current distributions to be determined from a region upstream of the cathode, through the constrictor, to the exit plane of the nozzle.
Keith, Theo G., Jr.↗
An elliptic representation of coupled boundary layers and inviscid core for computation of separated internal flows
This report presents a viscous-inviscid calculation method for the prediction of turbulent incompressible flows in diffusers with small regions of stall. Integral turbulent boundary layer equations (BLE) are used to provide boundary conditions for a finite difference representation of the inviscid core. The BLE are applied at the floating displacement-thickness line, resulting in a simulataneous set of nonlinear block tridiagonal equations which are solved iteratively using a sucessive line-relaxation technique. Results of the method have been applied to calculate the performance of a variety of asymmetric stalled diffusers.
Ghose, S.↗
A spectral multidomain method for the solution of hyperbolic systems
A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.
Kopriva, D.↗
A new method for predicting response in complex linear systems. II
The paper describes convergence and response studies in the low frequency range of complex systems, particularly with low values of damping of different distributions, and reports on the modification of the relaxation procedure required under these conditions. A new method is presented for response estimation in complex lumped parameter linear systems under random or deterministic steady state excitation. The essence of the method is the use of relaxation procedures with a suitable error function to find the estimated response; natural frequencies and normal modes are not computed. For a 45 degree of freedom system, and two relaxation procedures, convergence studies and frequency response estimates were performed. The low frequency studies are considered in the framework of earlier studies (Kayser and Bogdanoff, 1975) involving the mid to high frequency range.
Bogdanoff, J. L.↗
Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness
The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.
Liu, Chaoqun↗
A minimal residual method for transonic potential flows
For transonic flow calculations, a combination of the successive line over-relaxation (SLOR) and the preconditioned conjugate gradient (CG) method has been suggested by Wong and Hafez (1981). This paper studies the method of minimal residual (MR) which avoids a combined iteration. This method is closely related to the CG method, may be regarded as a first-order gradient method, and is applicable to symmetric and nonsymmetric matrices. The problem is formulated as a nonlinear mixed elliptic-hyperbolic partial differential equation which includes an artificial viscosity and a switching function which is zero in subsonic regions and nonzero in supersonic regions. Alternatives to the SLOR method which provide faster convergence rates are introduced. The preconditioned MR algorithm is developed, and transonic potential flows around NACA 0012 airfoil are calculated for different Mach numbers and angles of attack. Preliminary results are presented, demonstrating that the MR algorithm requires no parameter estimation and rapidly converges for subsonic flows.
Wong, Y. S.↗
Transient ion cyclotron resonance method for studying ion-molecule collision and charge- transfer rates- N2/plus/ and CH4/plus/
Ion-molecule collision charge transfer and momentum transfer relaxation rates, using ion cyclotron resonance heterodyning method
Dunbar, R. C.↗
Convergence acceleration and shock fitting for transonic aerodynamics computations
Two problems in computational fluid dynamics are studied in the context of transonic small-disturbance theory - namely, (1) how to speed up the convergence for currently available iterative procedures, and (2) how a shock-fitting method may be adapted to existing relaxation procedures with minimal alterations in computer programming and storage requirements. The paper contributes to a clarification of error analyses for sequence transformations based on the power method (including also the nonlinear transforms of Aitken, Shanks, and Wilkinson), and to developing a cyclic iterative procedure applying the transformations. Examples testing the procedure for a model Dirichlet problem and for a transonic airfoil problem show that savings in computer time by a factor of three to five are generally possible, depending on accuracy requirements and the particular iterative procedure used.-
Hafez, M. M.↗
Generation and development of a viscous vortex ring.
The vorticity transport and definition of vorticity equations are derived for an axisymmetric incompressible viscous vortex ring. The coupled system is solved numerically by the Peaceman-Rachford method and the method of successive over-relaxation. Instantaneous streaklines, velocity vector fields, vorticity contours, and streamline patterns offer a detailed picture of vortex ring generation. Results compare well with experimental observations of the behavior of viscous vortex rings. The radius, trajectory, and velocity of the ring are calculated and employed to predict the propagation velocity of the vortex ring using the vortex models of Helmholtz and Hill.
Whitehead, K. D.↗
The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules
Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.
Cheremisin, F. G.↗
A simple method for studying slow crack growth.
A simple, inexpensive method for studying slow crack growth is described. The method entails measurements of load relaxation at constant displacement using a double torsion specimen. It is demonstrated that the data generated using this technique are in excellent agreement with data obtained using the more complex conventional techniques, for a range of materials - steel, titanium, glass, aluminum oxide, PMMA. These encouraging initial results suggest that additional and more detailed studies using this test procedure are merited.
Williams, D. P.↗
Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements
The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.
Liu, C.↗
Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations
The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.
Thomas, J. L.↗