Turbine Design and Application, Volume 1
Review of turbine technology including thermodynamics, compressible fluid mechanics, fundamental turbine concepts, and velocity diagram design
Arthur J. Glassman↗
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The three-dimensional steady radial expansion of a viscous gas from a sonic source into a vacuum.
The three-dimensional steady radial expansion of a viscous, heat-conducting, compressible fluid from a spherical sonic source into a vacuum is analyzed using the Navier-Stokes equations as a basis. It is assumed that the model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Limiting forms for the flow variable solutions are studied for the Reynolds number based on the sonic source conditions, going to infinity and the Newtonian parameter both fixed and going to zero. For the case of the viscosity-temperature exponent between .5 and 1, it is shown that the velocity as well as the pressure approach zero as the radial distance goes to infinity. The formulations of the distinct regions that span the domain extending from the sonic source to the vacuum are presented.
Bush, W. B.↗
Calculation of sonic boom signatures by bicharacteristic methods.
An improved method is described for correcting the zeroth order (free stream) characteristics to obtain a uniformly valid first order solution to the exact equations of motion for a compressible fluid. The method is based on constructing first order bicharacteristic lines from the system of ordinary differential equations belonging to the exact equation for the characteristic surface. Calculated sonic boom signatures are compared with experiments conducted at Langley Research Center on a cone-cylinder at Mach numbers 2.96, 3.83, and 4.63. Theory and experiment agree well over the entire Mach number range.
Davis, S. S.↗
Quasi-one-dimensional compressible flow across face seals and narrow slots. 2: Computer program
A computer program is presented for compressible fluid flow with friction across face seals and through narrow slots. The computer program carries out a quasi-one-dimensional flow analysis which is valid for laminar and turbulent flows under both subsonic and choked flow conditions for parallel surfaces. The program is written in FORTRAN IV. The input and output variables are in either the International System of Units (SI) or the U.S. customary system.
Zuk, J.↗
The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables
The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.
Rubesin, M. W.↗
Computer program for quasi-one-dimensional compressible flow with area change and friction - Application to gas film seals
A computer program is presented for compressible fluid flow with friction and area change. The program carries out a quasi-one-dimensional flow analysis which is valid for laminar and turbulent flows under both subsonic and choked flow conditions. The program was written to be applied to gas film seals. The area-change analysis should prove useful for choked flow conditions with small mean thickness, as well as for face seals where radial area change is significant. The program is written in FORTRAN 4.
Zuk, J.↗
Compressible flow computer program for gas film seals
Computer program, AREAX, calculates properties of compressible fluid flow with friction and area change. Program carries out quasi-one-dimensional flow analysis which is valid for laminar and turbulent flows under both subsonic and choked flow conditions. Program was written to be applied to gas film seals.
Zuk, J.↗
Study of multilayered insulation pipe penetration. Thermal acoustic oscillation
Tests were conducted to determine the net heat leak to a source of liquid nitrogen caused by a metal penetration through the blanket of multilayer insulation. The conditions under which the tests were conducted are described. A graph of the theoretical and experimental temperature distribution is developed for comparison. The variables involved in the computer program to process the data are defined. A study was conducted to develop analytical methods for predicting the effect and magnitudes of thermoacoustic oscillations on the penetration heat leak to cryogens. The oscillations develop as a result of large thermal gradients imposed on a compressible fluid. The predominant amplitudes and frequencies of the thermal acoustic oscillations were investigated.
Lovin, J. K.↗
Dynamic heave-pitch analysis of air cushion landing systems
A program to develop analytical tools for evaluating the dynamic performance of Air Cushion Landing Systems (ACLS) is described. The heave (vertical) motion of the ACLS was analyzed, and the analysis was extended to cover coupled heave-pitch motions. The mathematical models developed are based on a fundamental analysis of the body dynamics and fluid mechanics of the aircraft-cushion-runway interaction. The air source characteristics, flow losses in the feeding ducts, trunk and cushion, the effects of fluid compressibility, and dynamic trunk deflections, including ground contact are considered. A computer program, based on the heave-pitch analysis, was developed to simulate the dynamic behavior of an ACLS during landing impact and taxi over an irregular runway. The program outputs include ACLS motions, loadings, pressures, and flows as a function of time. To illustrate program use, three basic types of simulations were carried out. The results provide an initial indication of ACLS performance during (1) a static drop, (2) landing impact, and (3) taxi over a runway irregularity.
Captain, K. M.↗
COMOC: Three dimensional boundary region variant, programmer's manual
The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.
Orzechowski, J. A.↗
Nonlinear initial-boundary value solutions by the finite element method
The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.
Baker, A. J.↗
Stellar convection theory. I - The anelastic modal equations
Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.
Latour, J.↗
Heating of the solar chromosphere and corona. I - Generalized inhomogeneous wave equation for magnetoacoustic motions
The generalized inhomogeneous wave equation that governs magnetoacoustic, vortical, and thermal motions in compressible fluids and that is applicable to the problem of heating of the solar chromosphere and corona is obtained. The effects of kinematic and bulk viscosity, heat conduction, Joule dissipation, and magnetic diffusivity are included. Under the usual assumptions, the generalized wave equation reduces to the well-known equations of Lighthill, Kulsrud, Phillips, and others. The major problems encountered in applying Lighthill's (1952) mechanism to sound generation in turbulent media are reviewed for both the subsonic and supersonic cases.
Anand, S. P. S.↗
Actuator device for artificial leg
An actuator device is described for moving an artificial leg of a person having a prosthesis replacing an entire leg and hip joint. The device includes a first articulated hip joint assembly carried by the natural leg and a second articulated hip joint assembly carried by the prosthesis whereby energy from the movement of the natural leg is transferred by a compressible fluid from the first hip joint assembly to the second hip joint assembly for moving the artificial leg.
Burch, J. L.↗
Numerical solution for supersonic flow near the trailing edge of a flat plate
In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates that the asymptotic triple deck theory for supersonic trailing edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.
Degani, D.↗
Dynamics of liquid films and thin jets
The theory of liquid films and thin jets as one- and two-dimensional continuums is examined. The equations of motion have led to solutions for the characteristic speeds of wave propagation for the parameters characterizing the shape. The formal analogy with a compressible fluid indicates the possibility of shock wave generation in films and jets and the formal analogy to the theory of threads and membranes leads to the discovery of some new dynamic effects. The theory is illustrated by examples.
Zak, M.↗
Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
Miles, J. H.↗
Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one-dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
Miles, J. H.↗