Results for “Steady flows” — Page 18

NASA NTRS1978

Advanced panel-type influence coefficient methods applied to unsteady three dimensional potential flows

A panel method for solving unsteady, subsonic wind-body-tail flow problems is formulated and partially verified. The method is applicable to general aircraft configurations consisting of arbitrary arrangements of wings, bodies, tails, and nacelles. The wake may be located arbitrarily and the unsteady, transverse component of vorticity in the wake may be assigned any covection velocity. The wake in the unsteady flow problem, therefore, can be given the location and convection velocity of the wake produced by a steady flow which is the mean flow of the unsteady flow problem. The panel method has been used as a basis for expanding the unsteady kernel function in a power series to obtain panel influence coefficients which can be integrated in closed form.

Dusto, A. R.↗

NASA NTRS1985

Application of Runge Kutta time marching scheme for the computation of transonic flows in turbomachines

Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The present study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions, and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in the solution procedure.

Subramanian, S. V.↗

NASA NTRS1987

Application of Runge Kutta time marching scheme for the computation of transonic flows in turbomachines

Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in solution procedures.

Subramanian, S. V.↗

NASA NTRS1989

The secondary flow and its stability for natural convection in a tall vertical enclosure

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air and the time-periodic flow of oil are investigated, and descriptions of these flows using both physical and spectral approaches are presented. The time dependence of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The three-dimensional linear stabiltiy of the multicellular air flow is parametrically studied. The domain of stable two-dimensional cellular motion is found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550.

Chait, Arnon↗

NASA NTRS1989

Simple models of fluid flow at the core surface derived from geomagnetic field models

The fluid flow at the core surface is determined for a given model of temporal magnetic field variation, assuming steady flow and adopting the frozen-flux approximation. Evidence is presented for ageostrophic flow in the form of flow across the geographical equator. A simple pattern of the large-scale toroidal part of the flow is found. The pattern is nearly symmetric about the equator. Changes in the flow pattern are obtained from flow maps covering 5-year intervals beginning in 1915.

Bloxham, Jeremy↗

NASA NTRS1990

Prediction of steady and unsteady asymmetric vortical flows around cones

Steady and unsteady, supersonic asymmetric vortical flows and their passive control around circular and noncircular cones are considered in this paper. These problems are formulated by using the unsteady, compressible, single and double, thin-layer. Navier-Stokes equations. The equations are solved by using an implicit, upwind, flux-difference splitting, finite-volume scheme, either in a pseudotime stepping or in an accurate-time stepping. An implicit, approximately-factored, central-difference finite-volume scheme has also been used to validate some applications of the upwind scheme. Steady asymmetric vortical flows have been predicted by using random and controlled disturbances for circular and noncircular cones. Unsteady asymmetric vortex-shedding flows have also been predicted, for the first time, using time-accurate solutions, for circular and noncircular cones. Control of flow asymmetry have been demonstrated computationally, for the first time, by inserting a vertical fin the leeward plane of geometric symmetry.

Kandil, Osama A.↗

NASA NTRS1988

Calculation of unsteady Euler flows in turbomachinery using the linearized Euler equations

The model used by the present unsteady cascade flow calculation method is based on the linearized unsteady Euler equations and accounts for blade loading and geometry, shock motion, and wake motion. The steady flow that must be determined prior to the unsteady flow is ascertained by means of a Newton iteration procedure. A noteworthy feature of the procedure is the use of shock-fitting to determine steady and unsteady shock positions; the use of the Euler equations in conjunction with the Rankine-Hugoniot shock-jump conditions is found to directly model the generation of entropy and vorticity at shocks. Results are presented for both channel and cascade flows.

Hall, Kenneth C.↗

NASA NTRS1989

Viscous flow in simple curved gaps. I - An asymptotic theory. II - Viscous stress and shape function

The present asymptotic theory for generalized incompressible two-dimensional steady flow in curved channels has been constructed in the limit when gas thickness approaches zero with its lateral dimensions fixed; successive asymptotic solution terms are analytically generated by quadratures. In the second part of this work, the curvature of the gap treated is arbitrary. It is established that each term in the series solution of velocity and pressure is the product of a scale factor and a universal shape functions. Various interaction modes between the volume rate-of-flow, curvature, and its variations, are identified and quantitatively characterized.

Fan, D.-N.↗

NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1987

Numerical simulation of transonic propeller flow using a 3-dimensional small disturbance code employing novel helical coordinates

The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.

Snyder, Aaron↗

NASA NTRS1987

Numerical simulation of transonic propeller flow using a three-dimensional small disturbance code employing novel helical coordinates

The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.

Snyder, Aaron↗

NASA NTRS1953

The similarity law for hypersonic flow and requirements for dynamic similarity of related bodies in free flight

The similarity law for nonsteady, inviscid, hypersonic flow about slender three-dimensional shapes is derived. Conclusions drawn are shown to be valid for rotational flow. Requirements for dynamic similarity of related shapes in free flight are obtained. The law is examined for steady flow about related three-dimensional shapes. Results of an experimental investigation of the pressures acting on two inclined cones are found to check the law as it applies to bodies of revolution.

Hamaker, Frank M↗

NASA NTRS1973

Propagation of plane waves in flow through a variable area duct

Duct geometry is an important factor that influences the transmission of sound in a duct. Nonconstant area produces variations in steady flow quantities through the duct, which can cause reflections of acoustic disturbances and the creation of standing wave patterns, and which can attenuate and disperse propagating waves. To study the problem, a second-order-accurate numerical method has been developed. The method of characteristics is used to solve the acoustic equations with the assumption of quasi-one-dimensional flow in the duct. Numerical results are presented over a broad range of frequencies. Low-frequency results are compared with approximate solutions for compact nozzles and high-frequency calculations are compared with results from the short-wave theory. The numerical results are also compared with an analytical solution of the acoustic equations for exponential horn sections with zero mean flow to further establish the validity of the numerical method.

King, L. S.↗

NASA NTRS1976

Effects of high subsonic flow on sound propagation in a variable-area duct

The propagation of sound in a converging-diverging duct containing a quasi-one-dimensional steady flow with a high subsonic throat Mach number was studied. The behavior of linearized acoustic theory at the throat of the duct was shown to be singular. This singularity implies that linearized acoustic theory is invalid. The explicit singular behavior was determined and used to sketch the development (by the method of matched asymptotic expansions) of a nonlinear theory for sound propagation in a sonic throat region.

Callegari, A. J.↗

NASA NTRS1986

An exact energy corollary for homentropic flow

An exact conservation equation is developed which generalizes the familiar acoustic energy equation. The new relation is valid for arbitrary homentropic disturbances to a homentropic steady flow. It is suggested by a derivation of the acoustic energy equation by means of a regular perturbation expansion of the general energy equation for an ideal compressible fluid. A perturbation energy density and flux are defined and are identified as the exact physical quantities whose leading order representations are the usual acoustic energy density and flux.

Myers, M. K.↗

NASA NTRS2000

Computational Aeroacoustic Analysis of Slat Trailing-Edge Flow

An acoustic analysis based on the Ffowcs Williams and Hawkings equation was performed for a high-lift system. As input, the acoustic analysis used un- steady flow data obtained from a highly resolved, time-dependent, Reynolds-averaged Navier-Stokes calculation. The analysis strongly suggests that vor- tex shedding from the trailing edge of the slat results in a high-amplitude, high-frequency acoustic signal, similar to that which was observed in a correspond- ing experimental study of the high-lift system.

Singer, Bart A.↗

NASA NTRS2003

Numerical Modeling of Thermofluid Transients During Chilldown of Cryogenic Transfer Lines

The chilldown of fluid transfer lines is an important part of using cryogenic systems such as those found in both ground and space based applications. The chilldown process is a complex combination of both thermal and fluid transient phenomena. A cryogenic liquid flows through a transfer line that is initially at a much higher temperature than the cryogen. Transient heat transfer processes between the liquid and transfer line cause vaporization of the liquid, and this phase change can cause transient pressure and flow surges in the liquid. As the transfer line is cooled, these effects diminish until the liquid reaches a steady flow condition in the chilled transfer line. If these transient phenomena are not properly accounted for in the design process of a cryogenic system, it can lead to damage or failure of system components during operation. For such cases, analytical modeling is desirable for ensuring that a cryogenic system transfer line design is adequate for handling the effects of a chilldown process. The purpose of this paper is to present the results of a numerical model developed using Generalized Fluid System Simulation Program (GFSSP)'s new fluid transient capability in combination with its previously developed thermal transient capability to predict pressure and flow surge in cryogenic transfer lines during a chilldown process. An experiment performed by the National Bureau of Standards (NBS) in 1966 has been chosen as the baseline comparison case for this work. NBS s experimental set-up consisted of a 10.59 cubic foot supply dewar, an inlet valve, and a 200 foot long, in Outside Diameter (OD) vacuum jacketed copper transfer line that exhausted to atmosphere. Three different inlet valves, an in-port ball valve, a 1-in-port globe valve and a 1-in-port gate valve, were used in NBS's experiments. Experiments were performed using both liquid hydrogen and liquid nitrogen as the fluids. The proposed paper will include detailed comparisons of GFSSP's predictions with NBS's experimental results.

Majumdar, Alok↗