Method of Determining Initial Tangents of Contours of Flow Variables Behind a Curved, Axially Symmetric Shock Wave
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A critical flow experiment was performed with fluid nitrogen in a converging-diverging nozzle at stagnation conditions from 87.5 to 234 K and pressures to 9.3 MN/sq m, with particular emphasis on the thermodynamic critical region. The nozzle throat conditions ranged from two-phase to near critical to gaseous. Proximity of the fluid in the nozzle to the critical point has a significant influence on the critical flow rate and pressure ratio curves. The flow rate exhibits an inflection and the pressure ratio shows a sharp peak when stagnation conditions are near the transposed critical point. The critical flow data are compared with equilibrium and nonequilibrium theories, and conditions are defined for which various methods of prediction remain valid.
In this investigation, two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative indication of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa-epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa-esilon model predictions are included.
A curved wall tunnel was designed, and an equilibrium turbulent boundary layer was set up on the straight section preceding the curved test section. Turbulent boundary layer flows with uniform and adverse pressure distributions along convex and concave walls were investigated. Hot-wire measurements along the convex surface indicated that turbulent mixing between fluid layers was very much reduced. However, the law of the wall held and the skin friction, thus determined, correlated well with other measurements. Hot-wire measurements along the concave test wall revealed a system of longitudinal vortices inside the boundary layer and confirmed that concave curvature enhances mixing. A self-consistent set of turbulent boundary layer equations for flows along curved surfaces was derived together with a modified eddy viscosity. Solution of these equations together with the modified eddy viscosity gave results that correlated well with the present data on flows along the convex surface with arbitrary pressure distribution. However, it could only be used to predict the mean characteristics of the flow along concave walls because of the existence of the system of longitudinal vortices inside the boundary layer.
Curved porous wall gas core reactor flow distribution experiment
The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier-Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40-0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m + 1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.
A theoretical method for evaluating the stability characteristics and the amplitude and the frequency of pulsation of ram-jet engines without heat addition is presented herein. Experimental verification of the theoretical results are included where data were available. Theory and experiment show that the pulsation amplitude of a high mass-flow-ratio diffuser having no cone surface flow separation increases with decreasing mass flow. The theoretical trends for changes in amplitude, frequency, and mean-pressure recovery with changes in plenum-chamber volume were experimentally confirmed. For perforated convergent-divergent-type diffusers, a stability hysteresis loop was predicted on the pressure-recovery mass-flow-ratio curve. At a given mean mass-flow ratio, the higher.value of mean pressure recovery corresponded to oscillatory flow in the diffuser while the lower branch was stable. This hysteresis has been observed experimentally. The theory indicates that for a ram-jet engine of given diameter, the amplitude of pulsation of a supersonic diffuser is increased by decreasing the relative size of the plenum chamber with respect to the diffuser volume down to a critical value at which oscillations cease. In the region of these critical values, the stable mass-flow range of the diffuser may be increased either by decreasing the combustion chamber volume or by increasing the length of the diffuser.
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An exact turbulence dissipation equation in the generalized relative system is presented. Simplified forms of the equation are obtained for computational purposes in the high Reynolds number approximation. Modeling of the rotation term is proposed. Modeling of the other higher-order terms is also presented in a generalized system using the tensor invariance technique. An estimate of the angular velocity is provided for the rotation term to be included in the turbulence dissipation equation. The associated significant curvature terms for turbomachinery flows are also identified.
Heat transfer and hydrodynamic boundary layer measurements were made in a turbulent boundary layer on a convex surface with 13 rows of injection. Both full- and partial-coverage cases were tested for three blowing ratios: 0.2, 0.4, and 0.6. Heat transfer results are discussed in terms of Stanton number with injection air temperature equal to wall temperature. In the blown region, for both m (blowing ratio) = 0.2 and 0.4, the local response of the boundary layer is dominated by curvature, and m = 0.4 shows higher cooling effects than m = 0.2 or 0.6, as expected, based on flat-plate results. Hydrodynamic measurements with a triple-hot-wire suggest the existence of two streamwise lanes. Lanes containing injection holes are highly affected by injection and show a definite streamwise evolution. Lanes which do not contain holes are not affected much by injection and show little change in the streamwise direction.
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The stability curves for traveling disturbances in rotating-disk flow are computed using the sixth-order system of incompressible linear stability equations. The neutral curve has two minima for disturbances with positive frequencies as found earlier by Malik (1986) for stationary disturbances. The upper branch minimum occurs at omega = -2.9, R = 283.6 while the lower branch minimum occurs at omega = 7.9, R = 64.46, where R is Reynolds number. There exists a critical angle of approximately -35.34 deg below which all the waves are linearly damped.
The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.
Force convection heat transfer characteristics of cryogenic hydrogen flowing turbulently at high heat fluxes
For papers presented in this volume provide an overview of the latest developments in experimental measurements and analytical and numerical predictions of three-dimensional flows in fluid machinery. Topics discussed include three-dimensional cascade testing of turbine nozzles at high exit Mach number; the use of a secondary flow computation in the compressor design process; an experimental investigation of static propeller flow field; and calculation of three-dimensional boundary layers on rotating turbine blades. Papers are also presented on a three-dimensional solution method for turbomachinery analysis; analysis of rotational inviscid flows in curved passages; and a mathematical model for the analysis of fluid flow in a scroll.
Gas core reactor curved porous walls geometry tested with clear and smoky air injection, noting mass flow ratio in reactor cavity
Compact, lightweight instruments have been developed for measuring small flows of helium and/or detecting helium leaks in solenoid valves when the valves are nominally closed. These instruments do not impede the flows when the valves are nominally open. They can be integrated into newly fabricated valves or retrofitted to previously fabricated valves. Each instrument includes an upstream and a downstream thermistor separated by a heater, plus associated analog and digital heater-control, signal- conditioning, and data-processing circuits. The thermistors and heater are off-the-shelf surface mount components mounted on a circuit board in the flow path. The operation of the instrument is based on a well-established thermal mass-flow-measurement technique: Convection by the flow that one seeks to measure gives rise to transfer of heat from the heater to the downstream thermistor. The temperature difference measured by the thermistors is directly related to the rate of flow. The calibration curve from temperature gradient to helium flow is closely approximated via fifth-order polynomial. A microprocessor that is part of the electronic circuitry implements the calibration curve to compute the flow rate from the thermistor readings.
A method for computing three-dimensional turbulent subsonic flow in curved ducts is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The derivation is coordinate invariant, and the resulting equations are expressed in terms of tensors. General tube-like coordinates were developed for a general class of geometries applicable to many internal flow problems. The coordinates are then particularized to pipes having superelliptic cross sections whose shape can vary continuously between a circle and a near rectangle. The analysis is applied to a series of relevant aerodynamic problems including transition from nearly square to round pipes and flow through a pipe with an S-shaped bend.