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At least 1,765 records · Page 98

The relation between temporal and spatial stability in three-dimensional flows

An analysis is presented of the nonparallel spatial or temporal stability of three-dimensional incompressible, isothermal boundary-layer flows taking into account the transverse velocity component as well as the axial and crossflow variations of the mean flow. The method of multiple scales is used to derive partial differential equations that describe the axial and crossflow variations of the disturbance amplitude, phase and wavenumbers. This equation is used to derive the expressions that relate the temporal and spatial instabilities. These relations are functions of the complex group velocities. Moreover, this equation is used to derive the expression that relates the spatial amplification in any direction to a calculated amplification in any other direction. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.

Nayfeh, A. H.↗

Unsteady separated boundary layer in a transonic diffuser flow with self-excited oscillations

A numerical investigation of two-dimensional unsteady boundary layer in a transonic diffuser flow with self-excited oscillations and strong flow separation by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equations with two-equations turbulence model is described. Three different meshes with constant streamwise mesh distribution and varying vertical mesh distribution were used. Results obtained indicate that a refinement of mesh studied here has minimal effect on the mean boundary layer flow but significantly increases the amplitude of oscillation of all flow variables. Comparisons of unsteady wall pressure, velocity profile, terminal shock, and separation pocket among computations and with experiment are presented.

Hsieh, T.↗

Computation of the Space Shuttle solid rocket booster nozzle start-up transient flow

The first NASA Space Shuttle flight (STS-1) produced an overpressure wave that exceeded preflight predictions by as much as 5 to 1. This second overpressure wave occurred just after the solid rocket booster (SRB) igniter wave. To understand this overpressure phenomenon, a numerical simulation effort was undertaken. Both the SRB static firing test and STS-1 geometries were studied for two-dimensional, inviscid and viscous flow. The inviscid calculations did not produce significant second overpressure waves. However, the viscous calculations did produce second overpressure waves that qualitatively agree with experiment. These overpressure waves were present in both the static firing test and STS-1 geometries. This second overpressure wave is generated by the motion of the boundary layer separation point and the subsequent radial motion of the exhaust jet during the start-up of the SRB nozzle flow. The presence of the mobile launch platform exhaust hole wale amplifies this wave, but does not appear to be the source of any additional overpressure waves. The lack of good quantitative agreement between theory and experiment indicates that other overpressure sources, not accounted for by this simulation, may be present.

Cline, M. C.↗

Approximate and exact numerical computation of supersonic flow over an airfoil

The computation of inviscid supersonic flow over a two-dimensional airfoil is considered. There are two main nonlinear approaches which lead to approximate solutions. Small-amplitude theory gives valid solutions provided the airfoil thickness is not too great and the Mach number is not too high. The second type of approximation, shock expansion theory, employs the fact that even for flows with strong shocks the effect of the down-running characteristics remains small. This leads to an analytic solution at the airfoil. It is pointed out that the approximate solution is accurate enough for many cases of interest. The numerical method furnishes a rapid correction to the solution in those cases where it is not. The characteristic-streamline coordinate system is useful both for the computation of the approximate solution and the corrections, and is also convenient for displaying and interpreting the results.

Lewis, T. S.↗

Numerical analysis of pulse facility transient flow through a supersonic combustion model

The supersonic high enthalpy flow from a shock tunnel facility flowing through a two-dimensional duct simulating a combustor has been computed for two test conditions for both steady and transient inflow. The nominal test conditions had stagnation enthalpies of 4.3 and 12.1 MJ/kg, with corresponding flight Mach numbers of 9 and 16, respectively. A full Navier-Stokes code (SPARK) was used to compute the flow development and the mixing of a hydrogen jet injected from the base of a central strut. Results of the calculations are presented and compared with wall pressure data. Additional comparisons of the transient and steady inflow results are presented to assess the effect of transient flow on the data. This paper presents a status of the progress in applying CFD codes to analyze the transient flow from a pulse facility.

Rogers, R. Clayton↗

Rearward-facing steps in laminar supersonic flows with and without suction

An experimental investigation of heat-transfer and pressure distributions within regions of laminar separated flows produced by two-dimensional rearward-facing steps has been carried out at freestream Mach numbers of around 4 in the range of step height-to-boundary layer thickness varying from 0.1 to 2.4. With no suction from the separated area, the ratio of the maximum post-step heat transfer to the attached-flow values was less than unity. The maximum heating-rate region was located far downstream of the reattachment plate stagnation point. Mass suction from the separated area increased the local heating rates, this effect was however relatively weak for purely laminar flow conditions and the competing effect of the step height clearly predominated. At step heights comparable with boundary-layer thickness, even removing the entire approaching boundary layer was not sufficient to raise the post-step heating rates above the flat-plate values.

Jakubowski, A. K.↗

Numerical simulation of a ramjet inlet flowfield in response to large amplitude combustor pressure oscillation

The unsteady flow of a two-dimensional ramjet inlet is studied numerically by solving the Navier-Stokes equation with a two-equation turbulence model. Unsteadiness is introduced by prescribing the pressure disturbance at the inlet exit plane. The case with a sinusoidal exit plane pressure fluctuation of 20 percent of the steady exit pressure is considered. The resulting flow field exhibits a complicated interaction between the terminal shock, separation pockets and core flow. The exit plane properties feature a non-linear response to the imposed sinusoidal pressure variation.

Hsieh, T.↗

Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle

Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects. The expression for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instances it is important to have a single expression representing the whole flow. Recently Von Karman and Tsien constructed more general types of stream functions, but only by replacing the true pressure density relation by the linear pressure-specific volume relation so that their method is essential limited to flows the maximum Mach number of which is not too large. In a companion report the author derived a new formula for stream functions based on the true pressure density relation. It is not subject to the limitations of the Chaplygin method. In the present report this formula is employed to construct two-dimensional subsonic compressible fluid flows around a body similar in shape to a given symmetric obstacle. The methods described in the report are illustrated by numerical examples.

FLOW, COMPRESSIBLE-MEASUREMENT↗

The Effect of Two-Dimensional Forcing on Self-Similar Turbulent Plane Wakes

Three direct numerical simulations of time-evolving turbulent plane wakes with velocity deficit Reynolds numbers of about 2,000 have been simulated using a spectral numerical method with up to 600 x 260 x 160 modes. The initial conditions for the simulations are generated from direct numerical simulations of a turbulent boundary layer (momentum thickness Reynolds number of 670), and varying amounts of additional two- dimensional, forcing. In order to preserve the self-similar flow evolution, the forcing is implemented by multiplying all the two-dimensional modes in the initial condition by a constant factor. In the "natural" case no additional forcing is used; in the "forced" and "heavily forced" cases this factor is 5 and 20, respectively. The wake spreading rate Is increased by factors of 1.7 and 7.1 for the two forced cases. The Reynolds stresses are also increased by a similar or even larger factor. These results indicate that the plane wake is much more sensitive to initial forcing than the plane mixing layer. As in the plane mixing layer, two-dimensional forcing promotes more organized large-scale vortical flow structures and these structures axe sometimes separated by "braid regions" containing streamwise "rib" vortices, unlike in the unforced wake.

Rogers, M. M.↗

Particle flow in blade passages of turbomachinery with application to laser-Doppler velocimetry

A theoretical analysis was conducted of the dynamic behavior of micron size particles entrained in gas flow on the two-dimensional blade-to-blade surface of a circular stationary cascade of turbine stator blades. The particle velocity lag and angular deviation relative to the gas was determined as a function of particle diameter and mass density. Particles size and density were varied over ranges selected to correspond to typical laser-Doppler velocimeter (LDV) flow field mapping applications. It was found that velocity lag and angular deviation increased whenever particle size or mass density increased, and that particle tracking was more sensitive to a change in particle diameter than to a change in mass density. Results indicated that LDV applications employing 1 gm/cc tracer particles with diameters greater than approximately 1 micron, or 0.5 micron diameter particles with mass densities greater than 4 gm/cc would experience velocity and angular deviations generally greater than 2 percent and 1 degree, respectively.

Maxwell, B. R.↗

Theoretical prediction of interference loading on aircraft stores. Part 1: Subsonic speeds

A method is developed for theoretically predicting the loading on pylon-mounted stores in subsonic compressible flow. Linear theory is used, without two-dimensional or slender body assumptions, to predict the flow field produced by the aircraft wing, nose, inlet, and pylons. The interference loading is integrated over the store length by considering the local crossflow, its axial and radial derivatives, and buoyancy. Store moment calculations under an F-4 aircraft at Mach 8 are compared to wind tunnel data. The method is computerized, and program user information is included.

Danfernandes, F.↗

Computation of nonequilibrium three-dimensional inviscid flow over blunt-nosed bodies flying at supersonic speeds

A computer code based on the method of characteristics is described and applied to the study of two- and three-dimensional chemical nonequilibrium flow over sharp and blunt-nosed bodies. Nonequilibrium flow over a wedge is used to show the approach to equilibrium flow, and to demonstrate the nature of the reaction zone behind the bow shock wave. The structure and development of a blunt-body entropy layer in nonequilibrium flow is examined for a blunt cone at zero incidence. Three-dimensional computations for the space shuttle body at 30 deg angle of attack are presented. A nondimensional scaling parameter, the Damkoehler number, which is the ratio of flow time to chemical reaction time, is calculated and its significance discussed.

Rakich, J. V.↗

Nonlinear instability of the accretion line

The instability of the flow along the accretion line in the two-dimensional Bondi-Hoyle-Lyttleton type accretion flow is studied. By means of numerical simulations, the nonlinear regime of the instability is explored, thus extending a previous work that dealt with the linear regime using the WKB approximation. In contrast to the behavior in the linear regime, in the nonlinear regime the radial and tangential modes are coupled. The radial instability, which manifests itself as large density and velocity variations on short distances, grows far beyond the linear regime. The tangential instability, on the other hand, stays in the linear regime and is dominant by long-wavelength perturbations. This results from both the influence of the radial instability and the incoming material (the material accreted onto the accretion line).

Soker, Noam↗

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a $\mathbb{Z}$ 2 -symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $\overline{g}$, and is expected to have a critical point at a tuned value ${\overline{g}}_{\ast }$ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the $\mathbb{Z}$ 2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $\overline{g}$ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C -function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Detonation propagation for shock-driven, subsonic and supersonic confiner flow

In this work, we study the compressible flow dynamics of two-dimensional, steady detonation wave propagation in a high explosive (HE) confined by aluminium (Al) or stainless steel (SS), outside of which is an air layer. We examine how the thickness of the confinement affects the subsonic detonation driving zone structure (DDZ) and the detonation speed (D 0 ), demonstrating a strong dependence on whether the oblique shock-driven flow in the confiner is supersonic, as for SS, or subsonic, as for Al. A characteristic path analysis is used to examine the information flow from the material boundaries through the supersonic flow regions in both the HE and confiner that can impact the sonic surfaces bounding the subsonic flow regions. It is shown that the nature of gas-dynamic wave reflection off the SS–air or Al–air boundary can significantly influence the DDZ and D 0 .

54 ENVIRONMENTAL SCIENCES↗

Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.

Warsi, Z. U. A.↗

Optical measurements of fluctuating temperatures in a supersonic turbulent flow using one- and two-photon, laser-induced fluorescence

A laser-induced fluorescence technique was developed that provides a practical means of nonintrusively measuring the instantaneous temperatures in low-temperature turbulent flows. The capabilities of the method are reviewed, and its application to a simple, two-dimensional, turbulent boundary-layer flow at Mach 2 is reported. Measurements of the average temperature distribution through the boundary layer and the magnitudes of temperature fluctuations about their average values are presented.

Gross, K. P.↗

Optical measurements of fluctuating temperatures in a supersonic turbulent flow using one- and two-photon, laser-induced fluorescence

A laser-induced fluorescence technique has been developed that provides a practical means of nonintrusively measuring the instantaneous temperatures in low-temperature turbulent flows. The capabilities of the method are reviewed, and its application to a simple, two-dimensional, turbulent boundary-layer flow at Mach 2 is reported. Measurements of the average temperature distribution through the boundary layer and the magnitudes of temperature fluctuations about their average values are presented.

Gross, K. P.↗