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Window assembly facilitates observation of cryogenic liquids flowing through a smooth pipe at pressures up to several hundred pounds per square inch. This high-pressure cryogenic observation assembly which houses a thin wall glass pipe held within a steel retainer can accommodate fluids under a wide range of pressures and temperatures.
Direct numerical simulation (DNS) was used to study homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. There are many important reasons for studying the elliptic streamline flow. This flow contains the effects of both rotation and strain and is therefore similar to the mean flow in a vortex strained in the plane perpendicular to its axis. Such flows provide insight into the fundamental vortical interactions within turbulence. A strained vortex also occurs in airplane wakes, in which each wingtip vortex induces a strain field on the other. The strain field can affect the stability of these vortices and thereby their turbulent structure downstream. The ability to understand and predict the turbulent structure of the vortices is important to the wake hazard problem which is of major concern for the safety of commercial aircraft.
Direct numerical simulations are performed for the elliptic streamline flow, which is a homogeneous turbulent flow that combines the effects of solid body rotation and strain. Simulations are run over a range of parameters in order to determine the effect of changing rotation and strain separately. For early times the nonlinear cascade is suppressed, but then is re-established at later times. The growth rate of turbulent kinetic energy agrees at early times with the trends from linear theory, but at later times the flow seems to approach an asymptotic state that is independent of the ratio of mean flow rotation rate to strain rate. A comparison with standard Reynolds stress turbulence models is made. It is found that for strong rotation rates, the models predict decay of the turbulence, while the simulations show exponential growth. Close examination of the simulation results shows that they are affected by excessively low Reynolds numbers. Suggestions for reducing low Reynolds number effects in future simulations is given.
Hydrodynamic internal streamline flow analysis for turboprop inducer blades under cavitating and noncavitating conditions
Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.
A computer program (program LEE) has been developed to calculate the fully coupled solution of the radiating viscous stagnation streamline flow with strong blowing. The report describes the digital computer program, including FORTRAN IV listing, flow charts, instructions for the user, and a test case with input and output. Program LEE is available through COSMIC.
The direct simulation Monte Carlo (DSMC) method is applied to simulate one-dimensional flow along the stagnation streamline. The freestream conditions considered are those encountered by the nose region of the Space Shuttle Orbiter during the hypersonic reentry. The range of altitudes (75 to 92 km) considered in the present calculations covers continuum to the less rarefied portion of the transition flow regime. The calculations account for thermal as well as the chemical nonequilibrium effects. The attention is focused on the flow structure along the stagnation streamline for different specified shock locations at a given altitude. The effect of shock location on the stagnation-point gas composition and heat transfer is analyzed for specific altitude; consequently, these results are appropriate for hemispherical bodies with different nose radii. Finally, comparison is made between the present DSMC results and the viscous shock-layer calculations, which show good agreement at the lowest altitude.
Matrix of ink dots covers matte surface of polyester drafting film. Film placed against wind-tunnel wall. Layer of methyl salicylate (oil of wintergreen) sprayed over dotted area. Ink dot streaklines show several characteristics of flow, including primary saddle point of separations, primary horseshoe vortex and smaller vortex at cylinder/ endwall junction. Surface streamline flow visualization technique suitable for use in low-speed windtunnels or other low-speed gas flows.
In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.
In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.
Integral equations to calculate free streamline flow behind axisymmetric bodies at zero and small angles of attack
This paper describes a new surface-streamline flow-visualization technique that is suitable for use in low-speed wind tunnels or other low-speed gas flows. The technique provides a permanent record of ink traces that show surface-streamline direction and shape. The visualization of the endwall surface flow of the horseshoe-vortex system formed around the base of a cylinder by a separating turbulent boundary layer is used as an example. The results of the new technique are compared with those obtained from a conventional flow-visualization technique. Good agreement was found between the two, with the new technique appearing to give more-accurate surface streamlines.
Streamlines, contour lines, vector plots, and volume slices (cutting planes) are commonly used for flow visualization. These techniques are sometimes referred to as instantaneous flow visualization techniques because calculations are based on an instant of the flowfield in time. Although instantaneous flow visualization techniques are effective for depicting phenomena in steady flows,they sometimes do not adequately depict time-varying phenomena in unsteady flows. Streaklines and timelines are effective visualization techniques for depicting vortex shedding, vortex breakdown, and shock waves in unsteady flows. These techniques are examples of time-dependent flow visualization techniques, which are based on many instants of the flowfields in time. This paper describes the algorithms for computing streaklines and timelines. Using numerically simulated unsteady flows, streaklines and timelines are compared with streamlines, contour lines, and vector plots. It is shown that streaklines and timelines reveal vortex shedding and vortex breakdown more clearly than instantaneous flow visualization techniques.
The technique of tracing out a mean flow streamline with a three dimensional laser Doppler anemometer (LDA) is discussed with respect to cumulative, systematic errors that are inherent when the motion of the LDA test point is in the direction of the local measured velocity. Using simple potential flows that have variable curvature and inflection points to simulate an LDA experiment, a streamline tracing algorithm is developed that minimizes these errors. Also, the test point path remains close to the correct streamline even when simulated statistical measurement variations are included.
Homogeneous turbulent flows with various combinations of strain-rate, rotation rate and coriolis force capture some important aspects of more complex flows with streamline curvature and rotation. Presently, a situation is considered in which as a box of turbulence rotates, strain axes rotate with it. This is to be contrasted with the elliptic streamline flow in which the strain axes are fixed in an inertial frame. The elliptic flow is known to exhibit (inviscid) growth of turbulent energy and one might expect even more rapid growth with the strain-axes following the box. Instead, it is found that the sign of the Reynolds shear stress is reversed leading to a negative production term for turbulent energy. Partial understanding of the phenomenon is obtained from a consideration of the rotation of inertial waves relative to the strain axes as well as the "pressure-less" RDT argument put forward by Cambon etal. [J. Fluid Mech, 278, 175]. Some comparisons with the predictions of second-order closure models will be presented.
The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a dividing streamline separates air within the cat's eye from air outside.
Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.
Discontinuous flows and free streamline solutions for axisymmetric bodies at zero and small angles of attack