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NASA NTRS1989

A PBL-radiation model for application to regional numerical weather prediction

Often in the short-range limited-area numerical weather prediction (NWP) of extratropical weather systems the effects of planetary boundary layer (PBL) processes are considered secondarily important. However, it may not be the case for the regional NWP of mesoscale convective systems over the arid and semi-arid highlands of the southwestern and south-central United States in late spring and summer. Over these dry regions, the PBL can grow quite high up into the lower middle troposphere (600 mb) due to very effective solar heating and hence a vigorous air-land thermal interaction can occur. The interaction representing a major heat source for regional dynamical systems can not be ignored. A one-dimensional PBL-radiation model was developed. The model PBL consists of a constant-flux surface layer superposed with a well-mixed (Ekman) layer. The vertical eddy mixing coefficients for heat and momentum in the surface layer are determined according to the surface similarity theory, while their vertical profiles in the Ekman layer are specified with a cubic polynomial. Prognostic equations are used for predicting the height of the nonneutral PBL. The atmospheric radiation is parameterized to define the surface heat source/sink for the growth and decay of the PBL. A series of real-data numerical experiments has been carried out to obtain a physical understanding how the model performs under various atmospheric and surface conditions. This one-dimensional model will eventually be incorporated into a mesoscale prediction system. The ultimate goal of this research is to improve the NWP of mesoscale convective storms over land.

Chang, Chia-Bo↗

NASA NTRS1990

Thermal radiation characteristics of nonisothermal cylindrical enclosures using a numerical ray tracing technique

Analysis of energy emitted from simple or complex cavity designs can lead to intricate solutions due to nonuniform radiosity and irradiation within a cavity. A numerical ray tracing technique was applied to simulate radiation propagating within and from various cavity designs. To obtain the energy balance relationships between isothermal and nonisothermal cavity surfaces and space, the computer code NEVADA was utilized for its statistical technique applied to numerical ray tracing. The analysis method was validated by comparing results with known theoretical and limiting solutions, and the electrical resistance network method. In general, for nonisothermal cavities the performance (apparent emissivity) is a function of cylinder length-to-diameter ratio, surface emissivity, and cylinder surface temperatures. The extent of nonisothermal conditions in a cylindrical cavity significantly affects the overall cavity performance. Results are presented over a wide range of parametric variables for use as a possible design reference.

Baumeister, Joseph F.↗

NASA NTRS1989

Numerical algorithms for computations of feedback laws arising in control of flexible systems

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Lasiecka, Irena↗

NASA NTRS1989

Numerical solution of large Lyapunov equations

A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.

Saad, Youcef↗

NASA NTRS1989

The implementation of the graphics of program EAGLE: A numerical grid generation code on NASA Langley SNS computer system

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.

Houston, Johnny L.↗

NASA NTRS1990

Numerical investigation of laminar-turbulent transition in a flat plate wake

Lamina-turbulent transition of high-deficit flat plate wakes is investigated by direct numerical simulations using the complete Navier Stokes equations. The simulations are based on a spatial model so that both the base flow and the disturbance flow can develop in the downstream direction. The Navier Stokes equations are used in a vorticity-velocity form and are solved using a combination of finite difference and spectral approximations. Fourier series are used in the spanwise direction. Second-order finite-differences are used to approximate the spatial derivatives in the streamwise and transverse directions. For the temporal discretion, a combination of ADI, Crank-Nicolson, and Adams-Bashforth methods is employed. The discretized velocity equations are solved using fast Helmholtz solvers. Code validation is accomplished by comparison of the numerical results to both linear stability and to experiments. Calculations of two- and/or three-dimensional sinuous and mode disturbances in the wake of flat plate are undertaken. For calculations of two-dimensional disturbances, the wake is forced at an amplitude level so that nonlinear disturbance development may be observed. In addition, the forcing amplitude is varied in order to determine its effect on the disturbance behavior. To investigate the onset of three-dimensionality, the wake is forced with a small-amplitude three-dimensional disturbance and a larger amplitude two-dimensional disturbance. The two-dimensional forcing amplitude is varied in order to determine its influence on the three-dimensional flow field.

Fasel, Hermann F.↗

NASA NTRS1990

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Chen, C. P.↗

NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗

NASA NTRS1990

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗

NASA NTRS1989

Theoretical and numerical study of a three-dimensional turbulent boundary layer

A boundary layer created on an infinite flat plate by a time-dependent freestream velocity vector whose magnitude is independent of time but whose direction changes at a constant angular velocity is theoretically studied using Reynolds-number scaling laws and numerical simulations performed over a range of Reynolds numbers. Results obtained with a higher-order version of existing theories of the Ekman layer are shown to agree well with the numerical results at three Reynolds numbers. The present results can be extrapolated to the case of high Reynolds numbers. The Reynolds-averaged equations reduce to a one-dimensional steady problem, making possible the easy and accurate testing of turbulence models.

Spalart, Philippe R.↗

NASA NTRS1989

Explosive east coast cyclogenesis - Numerical experimentation and model-based diagnostics

Numerical experimentation of explosive east-coast cyclogenesis is performed using the Florida State University Global Spectral Model (FSUGSM). The three cases examined here are the Presidents' Day storm of February 18-19, 1979 and the North Atlantic and Pacific bombs of January 18-20, 1979 which formed off the east coasts of the United States and Japan, respectively. The use of a global model provides a framework for studying the phenomena on the 3-5 day time scale. The forecast verifications of the numerical experiments indicate that the FSUGSM was able to adequately predict the phase, intensity, and synoptic-scale structure. These results justify the use of model data for diagnostic studies of the bomb. The model data are used to quantify the role of the adiabatic and diabatic forcing in the explosive cyclogenetic process, using surface pressure tendency to gage development.

Manobianco, John↗

NASA NTRS1990

A study of numerical methods for hyperbolic conservation laws with stiff source terms

In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

Leveque, R. J.↗

NASA NTRS1990

Vortical flows over delta wings and numerical prediction of vortex breakdown

Navier-Stokes solutions of subsonic vortical flow over a 75 deg sweep delta wing with a sharp leading edge are presented. The sensitivity of the solution to the numerical scheme is examined using both a partially upwind scheme and a scheme with central differencing in all directions. At moderate angles of attack, no vortex breakdown is observed, whereas the higher angle-of-attack cases exhibit breakdown. The effect of numerical grid density is investigated, and solutions that are obtained with various grid densities are compared with experimental data. An embedded grid approach is implemented to enable higher resolution in selected isolated flow regions, such as the leeward-side surface, the leading-edge vortical flow, and the vortex breakdown region.

Ekaterinaris, J. A.↗

NASA NTRS1990

Numerical simulation of the incompressible internal flow through a tilting disk valve

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady and unsteady flow calculations are performed by solving the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Chang, I-Dee↗

NASA NTRS1989

Numerical analysis of natural convection in liquid droplets by phase change

A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.

Duh, J. C.↗

NASA NTRS1990

Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils

A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.

Scott, James R.↗

NASA NTRS1990

Numerical simulation of an F-16A at angle of attack

The transonic flowfield around an F-16A fighter configuration at a moderate incidence angle is simulated by solving the Navier-Stokes equations on a single-block grid. The numerical solution matches experimental freestream conditions with a mach number of 0.85, 16 degrees angle of attack, and a characteristic Reynolds number of 12.75 million. MacCormack's explicit algorithm is used in conjuction with a local time step and consecutive mesh refinement procedure to accelerate numerical convergence. The Baldwin-Lomax algebraic model provides turbulent closure. Computed surface pressure distributions and the aircraft lift coefficient compare favorably with wind tunnel data. The drag coefficient in the simulation overpredicts the experimental value by 8 percent.

Huband, G. W.↗

NASA NTRS1989

Basic numerical methods

Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.

Steger, Joseph L.↗