SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A geometrical interpretation of the grouping and variation rate terms of Reynolds stresses in compressible turbulent flow is presented. Examples of applications of the method are also given.
Effects of fluid mass flow rate and exit orifice diameter on radial static pressure distribution in compressible vortex flow field
The objectives of this research are to employ direct numerical simulation (DNS) to study the phenomenon of mixing (or lack thereof) in compressible free shear flows and to suggest new means of enhancing mixing in such flows. The shear flow configurations under investigation are those of parallel mixing layers and planar jets under both non-reacting and reacting nonpremixed conditions. During the three-years of this research program, several important issues regarding mixing and chemical reactions in compressible shear flows were investigated.
The two-dimensional symmetrical potential flow of compressible fluid past a circular cylinder placed in the center line of a straight tunnel is analyzed in second approximation according to the Jansen-Rayleigh method. The departure of the profile from the exact circular shape can be kept to the same magnitude as for the incompressible flow. The velocities in the narrowest section of the tunnel wall and at the profile edge are discussed in detail.
An algebraic skin friction law is derived for adiabatic, compressible, equilibrium, turbulent boundary layer flow. An outer solution in terms of the Clauser defect stream function is matched to an inner empirical expression composed of compressible laws of the wall and wake. The modified Crocco temperature-velocity relationship and the Clauser eddy viscousity model are used in the outer solution. The skin friction law pertains for all pressure gradients in the incompressible through supersonic range and for small pressure gradients in the hypersonic range. Excellent comparisons with experiment are obtained in the appropriate parameter ranges. The application to numerical computation is discussed.
A finite-difference program is described for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain the factors of arbitrary Reynolds number, free-stream Mach number, free-stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile.
The potential function for flow, with circulation, of a compressible fluid about a circular cylinder is obtained in series form including terms of the orders of m(4) where m is the Mach number of the free stream. The resulting equations are used to obtain pressure coefficients as a function of Mach number at a point on the surface of the cylinder for different values of circulation. The coefficients derived are compared with the Glauert-Prandtl and Karman-Tsien approximations which are functions of the pressure coefficients of an incompressible fluid. For the cases considered, the values of the pressure coefficients computed from the theory were found to be somewhere between the two approximations, the first underestimating and the second overestimating it.
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.
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.
The effect of an aperture on an impinging plane wave in a duct is extended to the case where the duct carries a compressible mean flow. The effect of the mean flow is to induce the closing mechanical impedance to have a significant resistive component in addition to the reactive component due to the 'attached mass' effect. The effect of the reactive load on the aperture is shown to be especially important for large contraction ratios. Of special interest is the acoustic particle velocity at the exit plane of the aperture. This is the 'piston velocity' that drives the spherical acoustic waves in the far field. The effect of aperture geometry on the piston velocity is established, and a criterion for minimum acoustic radiation is presented. An experimental arrangement for measuring the piston velocity with a hot-wire anemometer is described.
Although much progress has already been made in solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A method for solving these equations has been devised that: (1) is second-order accurate in space and time; (2) is unconditionally stable; (3) preserves conservation form; (4) requires no block or scalar tridiagonal inversions; (5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs); (6) is more efficient than present methods; and (7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 300,000 to 3 x 10 to the 7th and at CFL numbers as high as 1000 are compared with theory and experiment.
A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.
Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.
High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.
This report presents a treatment of the effects of the tunnel walls on the flow velocity and direction in a compressible medium at subsonic speed by an approximate method. Calculations are given for the rotationally symmetric and two- dimensionl problems of the flow past bodies, as well for the downwash effect in the tunnel with circular cross section.
Relaxation turbulence eddy viscosity models are incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensional compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of relaxation process are studied, and several relaxation models are tested and compared. Good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96, and Reynolds number of 10,000,000, with wedge angle of 25 deg. However, the application of the relaxation models to hypersonic flow at Mach number 8.66 and Reynolds number of 22,000,000, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.
A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.
The structure of the separated flow region over a 20 degree compression corner at a free-stream Mach number of 2.84 is investigated computationally using a Reynolds averaged Navier Stokes (R.A.N.S.) solver and kappa-epsilon model. At this Mach number and ramp angle, a steady-state recirculation region of order delta(sub o) is observed, with onset of a 'plateau' in the wall pressure distribution near the corner. At lower ramp angles, separation is negligible, while at an angle of 24 degrees, separation regions of length 2 delta(sub o) are expected. Of interest here is the response of the mathematical model to inclusion of the pressure dilatation term for turbulent kinetic energy. Compared with the experimental data of Smits and Muck (1987), steady-state computations show improvement when the pressure dilatation term is included. Unsteady computations, using both unforced and then forced inlet conditions, did not predict the oscillatory motion of the separation bubble as observed in laboratory experiments. An analysis of the separation bubble oscillation and the turbulent boundary layer (T.B.L.) frequencies for this flow suggests that the bubble oscillations are of nearly the same order as the turbulent frequencies, and therefore difficult for the model to separate and resolve.