Engineering topics

Mcdonald, H.

Publications and source records attributed to Mcdonald, H..

At least 37 records · Page 2

NASA NTRS1985

On hairpin vortices as model of wall turbulence structure

A model of the hairpin vortex has been constructed and used in two distinct but related approaches. The first approach is kinematic in nature in which a synthesis procedure using hairpin vortices to provide a quantitative link between mean flow quantities and the statistical quantities of near wall turbulence has become developed. The second approach is dynamic in nature, and the evolution of an incipient 'representative' hairpin vortex as well as the distortion of a background laminar boundary layer flow, in which the hairpin vortex is immersed, has been simulated by numerical solution of the unsteady, three-dimensional Navier-Stokes equations.

Liu, N.-S.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1984

Three-dimensional viscous flows with large secondary velocity

A new system of approximation equations is derived for three-dimensional steady viscous compressible flows in which a primary-flow direction is present, but in which both transverse velocity components can be large. Previous approaches which address simplification of the steady Navier-Stokes equations are discussed, and a new approach is proposed. The transverse velocity vector which corrects a given potential flow has been decomposed into potential and rotational components. It is found that the potential-velocity vector may be assumed small, whereas the rotational-velocity vector may be assumed small, whereas the rotational velocity vector and hence the composite secondary flow can be of order unity. This assumption leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach numbers. The resulting non-elliptic approximation equations can be solved as an initial/boundary-value problem. Computed results confirm the small scalar-potential approximation.

Briley, W. R.↗

NASA NTRS1984

Dynamic response of shock waves in transonic diffuser and supersonic inlet - An analysis with the Navier-Stokes equations and adaptive grid

An existing method which solves the multi-dimensional ensemble-averaged compressible time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique has been extended to include the shock-tracking adaptive grid systems. The numerical scheme for solving the governing equations is based on a linearized block implicit approach. The effects of grid-motion and grid-distribution on the calculated flow solutions have been studied in relative detail and this is carried out in the context of physically steady, shocked flows computed with non-stationary grids. Subsequently, the unsteady dynamics of the flows occurring in a supercritically operated transonic diffuser and a mixed compression supersonic inlet have been investigated with the adaptive grid systems by solving the Navier-Stokes equations.

Liu, N.-S.↗

NASA NTRS1983

Further development of a method for computing three-dimensional subsonic viscous flows in turbofan lobe mixers

Procedure for computing subsonic, turbulent flow in turbofan lobe mixers was extended to allow consideration of flow fields in which a swirl component of velocity may be present. Additional, an optional k-lambda turbulence model was added to the procedure. The method of specifying the initial flow field was also modified, allowing parametric specification or radial secondary flow velocities, and making it possible to consider initial flow fields which have significant inlet secondary flow vorticity. A series of example calculations was performed which demonstrate the various capabilities of the modified code. These calculations demonstrate the effects of initial secondary flows of various magnitudes, the effects of swirl, and the effects of turbulence model on the mixing process. The results of these calculations indicate that the initial secondary flows, presumed to be generated within the lobes, play a dominant role in the mixing process, and that the predicted results are relatively insensitive to the turbulence model used.

Lin, S. J.↗

NASA NTRS1983

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

Liu, N. S.↗

NASA NTRS1983

Numerical solution of the Navier-Stokes equations for compressible turbulent two/three dimensional flows in the terminal shock region of an inlet/diffuser

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique have been used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations have been carried out: (1) 2-D, steady, subsonic; (2) 2-D, steady, transonic with normal shock, (3) 2-D, steady, supersonic with terminal shock, (4) 2-D, transient process of shock development and (5) 3-D, steady, transonic with normal shock. The numerical results obtained for the 2-D and 3-D transonic shocked flows have been compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data. The predicted transient responses of the flow to externally applied impulsive disturbance are consistent with results obtained via asymptotic analysis.

Liu, N.-S.↗

NASA NTRS1982

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.

Weinberg, B. C.↗

NASA NTRS1982

Turbofan forced mixer-nozzle internal flowfield. Volume 3: A computer code for 3-D mixing in axisymmetric nozzles

A finite difference method is developed for making detailed predictions of three dimensional subsonic turbulent flow in turbofan lobe mixers. The governing equations are solved by a forward-marching solution procedure which corrects an inviscid potential flow solution for viscous and thermal effects, secondary flows, total pressure distortion and losses, internal flow blockage and pressure drop. Test calculations for a turbulent coaxial jet flow verify that the turbulence model performs satisfactorily for this relatively simple flow. Lobe mixer flows are presented for two geometries typical of current mixer design. These calculations included both hot and cold flow conditions, and both matched and mismatched Mach number and total pressure in the fan and turbine streams.

Kreskovsky, J. P.↗

NASA NTRS1982

Solution of three-dimensional time-dependent viscous flows

A procedure for solving three-dimensional, time-dependent turbulent flows is presented. The consistently split Linearized Block Implicit (LBI) scheme is used in conjunction with the QR Operator scheme to solve an approximate form of the Navier-Stokes equations in generalized nonorthogonal coordinates employing physical velocity components. Results of computations for both second order finite differences and the fourth order generalized Operator Compact Implicit (OCI) schemes are presented.

Weinberg, B. C.↗

NASA NTRS1981

A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

An approximate analysis is presented which is applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline. The primary flow direction is taken to coincide with the local direction of the duct centerline and is hence normal to transverse coordinate planes. The formulation utilizes vector components (velocity, vorticity, transport equations) defined in terms of local Cartesian directions aligned with the centerline tangent, although the governing equations themselves are expressed in general nonorthogonal coordinates. For curved centerlines, these vector quantities are redefined in new local Cartesian directions at each streamwise location. The use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation, and this provides for the aforementioned ease in using constructed coordinates.

Levy, R.↗

NASA NTRS1981

Prediction of laminar and turbulent primary and secondary flows in strongly curved ducts

The analysis is based on a primary secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial value problem in space using an implicit forward marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The solution procedure is effective even with the extreme local mesh resolution which is necessary to solve near wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compared very favorably with available analytical and experimental results. The overall method appears very promising as an economical procedure for making detailed predictions of viscous primary and secondary flows in highly curved passages.

Kreskovsky, J. P.↗

NASA NTRS1981

Analysis and computation of three-dimensional flow in strongly curved ducts

Numerical solutions are presented for three-dimensional laminar and turbulent flow in curved ducts of rectangular cross section and significant curvature. The analysis is based on a primary-secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial-value problem in space using an implicit forward-marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The present solution procedure is effective even with the extreme local mesh resolution which is necessary to resolve near-wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compare very favorably with available analytical and experimental results.

Kreskovsky, J. P.↗

NASA NTRS1980

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.

Weinberg, B. C.↗

NASA NTRS1980

A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

An approximate analysis, applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline, is presented for computation of three-dimensional subsonic flow in straight and curved diffusers. The formulation is intended to facilitate the use of constructed coordinates in circumstances where it is difficult to maintain smooth behavior in higher derivatives; the use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation. The analysis is applied to a particular family of duct and diffuser geometries having curved centerlines and superelliptic cross sections. Qualitative agreement with experimental measurements is observed with regard to streamwise vortices and distortion of the primary flow.

Levy, R.↗

NASA NTRS1980

Development of a three-dimensional supersonic inlet flow analysis

A method for computing three dimensional flow in supersonic inlets is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The governing equations are written in general orthogonal coordinates. These equations are modified in the subsonic region of the flow to prevent the phenomenon of branching. Results are presented for the two sample cases: a Mach number equals 2.5 flow in a square duct, and a Mach number equals 3.0 flow in a research jet engine inlet. In the latter case the computed results are compared with the experimental data. A users' manual is included.

Buggeln, R. C.↗

NASA NTRS1980

Computation of three-dimensional viscous supersonic flow in inlets

A new approach has been developed for the computation of the three-dimensional viscous supersonic flow with embedded subsonic regions adjacent to solid boundaries and is applied to a mixed-compression supersonic inlet typical of current designs. The approach uses a reduced form of the three-dimensional Navier-Stokes equations so that the resultant equations can be treated as an initial boundary value problem and thus be solved by non-iterative forward marching in space. The numerical procedure utilizes an efficient consistently-split linearized block implicit technique to solve the finite difference analogues to the set of governing partial differential equations.

Buggeln, R. C.↗

NASA NTRS1979

Solution of 3-dimensional time-dependent viscous flows. Part 1: Investigation of candidate algoriths

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow to aid in the design of helicopter rotors. Numerical algorithms are examined to determine their overall suitability for the efficient and routine solution of an appropriate system of partial differential equations. It is concluded that a consistently split time linearized block implicit scheme using either quintic B spline collocation or the generalized operator compact implicit approach to generate a fourth order accurate algorithm is particularly well suited for use on the present problem. High cell Reynolds number behavior leads to favoring the generalized operator compact implicit approach over the quintic B spline collocation method.

Weinberg, B. C.↗