JANNAF Handbook: Rocket Exhaust Plume Technology: Fluid Dynamic Flow Models - Chapter 2
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Classical free-streamline flow over a polygonal obstacle
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.
Elcrat, A. R.↗
Instability in Rotating Machinery
The proceedings contain 45 papers on a wide range of subjects including flow generated instabilities in fluid flow machines, cracked shaft detection, case histories of instability phenomena in compressors, turbines, and pumps, vibration control in turbomachinery (including antiswirl techniques), and the simulation and estimation of destabilizing forces in rotating machines. The symposium was held to serve as an update on the understanding and control of rotating machinery instability problems.
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Instability in hydraulic machines demonstration rig
In fluid flow machines, the working fluid involved in rotative motion due to shaft rotation significantly modifies the rotor synchronous response. This can result in the rotor maintaining the high vibration amplitude that occurs at resonance over an extended rotative speed range. The phase changes in this range are typically very small. The fluid may also create rotor instability, i.e., subsynchronous self-excited vibrations, when the rotative speed is sufficiently high. This rotor instability is often related and increases with higher rotor unbalance (Opposite to other types of instability such as oil whirl/whip, internal friction, etc.). The rotor rig demonstrates typical dynamic behavior of hydraulic machines. At lower speeds the effect of amplitude/phase mentioned above is noticeable; at higher speeds the subsynchronous instability occurs.
Muszynska, A.↗
Classical free-streamline flow over a polygonal obstacle
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.
Elcrat, A. R.↗
GASCan 2 payload integration
This project, conducted in cooperation with the NASA Advanced Space Design Program, is part of an ongoing effort to place an experiment package into space. The goal of this project is to build and test flight-ready hardware that can be launched from the Space Shuttle. Get Away Special Canister 2 (GASCan 2) consists of three separate experiments. The Ionospheric Properties and Propagation Experiment (IPPE) determines effects of the ionosphere on radio wave propagation. The Microgravity Ignition experiment (MGI) tests the effects of combustion in a microgravity environment. The Rotational Fluid Flow experiment (RFF) examines fluid behavior under varying levels of gravity. This year the following tasks were completed: design of the IPPE antenna, X- and J-cell battery boxes, J-cell battery box enclosure, and structural bumpers; construction of the MGI canisters, MGI mounting brackets, IPPE antenna, and battery boxes; and the selection of the RFF's operating fluid and the analysis of the fluid behavior under microgravity test conditions.
Cody, Dennis J.↗
SRM Internal Flow Tests and Computational Fluid Dynamic Analysis: Cold Flow Analyses and CFD Analysis Capability Development - Volume 4
An evaluation of the effect of model inlet air temperature drift during a test run was performed to aid in the decision on the need for and/or the schedule for including heaters in the SRMAFTE. The Sverdrup acceptance test data was used to determine the drift in air temperature during runs over the entire range of delivered flow rates and pressures. The effect of this temperature drift on the model Reynolds number was also calculated. It was concluded from this study that a 2% change in absolute temperature during a test run could be adequately accounted for by the data analysis program. A handout package of these results was prepared and presented to ED35 management.
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Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions
As shown by NASA resources dedicated to measuring residual gravity (SAMS and OARE systems), g-jitter is a critical issue affecting space experiments on solidification processing of materials. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. We have so far completed asymptotic analyses based on the analytical solutions for g-jitter driven flow and magnetic field damping effects for a simple one-dimensional parallel plate configuration, and developed both 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without presence of an applied magnetic field. Numerical models have been checked with the analytical solutions and have been applied to simulate the convective flows and mass transfer using both synthetic g-jitter functions and the g-jitter data taken from space flight. Some useful findings have been obtained from the analyses and the modeling results. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow approximately oscillates at the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes numerical simulations and ground-based measurements. Both 2-D and 3-D numerical simulations are being continued to obtain further information on g-jitter driven flows and magnetic field effects. A physical model for ground-based measurements is completed and some measurements of the oscillating convection are being taken on the physical model. The comparison of the measurements with numerical simulations is in progress. Additional work planned in the project will also involve extending the 2-D numerical model to include the solidification phenomena with the presence of both g-jitter and magnetic fields.
Li, Ben Q.↗
Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions
As shown in space flight experiments, g-jitter is a critical issue affecting solidification processing of materials in microgravity. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. Analytical solutions and 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without the presence of an applied magnetic field have been developed and extensive analyses were carried out. A physical model was also constructed and PIV measurements compared reasonably well with predictions from numerical models. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow oscillates at approximately the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes developing numerical models for solidification phenomena with the presence of both g-jitter and magnetic fields and developing a ground-based physical model to verify numerical predictions.
Li, Ben Q.↗
Exploring Inflated Pahohoe Lava Flow Morphologies and the Effects of Cooling Using a New Simulation Approach
Pahoehoe lavas are recognized as an important landform on Earth, Mars and Io. Observations of such flows on Earth (e.g., Figure 1) indicate that the emplacement process is dominated by random effects. Existing models for lobate a`a lava flows that assume viscous fluid flow on an inclined plane are not appropriate for dealing with the numerous random factors present in pahoehoe emplacement. Thus, interpretation of emplacement conditions for pahoehoe lava flows on Mars requires fundamentally different models. A new model that implements a simulation approach has recently been developed that allows exploration of a variety of key influences on pahoehoe lobe emplacement (e.g., source shape, confinement, slope). One important factor that has an impact on the final topographic shape and morphology of a pahoehoe lobe is the volumetric flow rate of lava, where cooling of lava on the lobe surface influences the likelihood of subsequent breakouts.
PAHOHOE LAVA↗
Thermocapillary Flow in Fluid Smectic Bubbles in Microgravity
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Eric Minor↗
Soliton solutions and their stability for the flow of relativistic fluids through channels
The flow of a perfect relativistic fluid through channels of various cross-sections is considered with reference to models of radio galaxies. Soliton-like solutions are found and their topologies are discussed. The calculations show that these solutions are unstable. It is suggested that under realistic astrophysical conditions the growth rate of the instabilities is so slow that soliton-type blobs may persist for a significant time.
Lerche, I.↗
A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow
An analysis of the oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is presented. The study is similar to that of Hersh and Rogers but with the addition of the grazing flow. Starting from the momentum and continuity equations, a considerably simplified system of partial differential equations is developed with the assumption that the flow can be described by an oscillatory motion superimposed upon the known steady flow. The equations are seen to be linear in the region where the grazing flow effects are dominant, and a solution and the resulting orifice impedance are presented for this region. The nonlinearity appears to be unimportant for the usual conditions found in aircraft noise suppressors. Some preliminary conclusions of the study are that orifice resistance is directly proportional to grazing flow velocity (known previously from experimental data) and that the orifice inductive (mass reactance) end correction is not a function of grazing flow. This latter conclusion is contrary to the widely held notion that grazing flow removes the effect of the orifice inductive end correction. This conclusion also implies that the experimentally observed total inductance reduction with grazing flow might be in the flow within the orifice rather than in the end correction.
Rice, E. J.↗
The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow
We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.
Hewitt, R. E.↗
Feasibility study: Atmospheric general circulation experiment, volume 1
The atmospheric general circulation experiment (AGCE) uses a rotating fluid flow cell assembly. The key technical areas affecting the feasibility of the design and operation of the AGCE are investigated. The areas investigated include materials for the flow cell assembly, thermal design, high voltage power supply design, effective retrieval and handling of experiment data and apparatus configuration. Several materials, DMSO and m-tolunitrile, were selected as candidate fluids for the flow cell principally for their high dielectric constant which permits the high voltage power supply design to be held to 15 kV and still simulate terrestrial gravity. Achievement of a low dissipation factor in the fluid to minimize internal heating from the applied electrical field depends strongly on purification and handling procedures. The use of sapphire as the outer hemisphere for the flow cell provides excellent viewing conditions without a significant impact on attaining the desired thermal gradients. Birefringent effects from sapphire can be held to acceptably low limits. Visualization of flow fluid is achieved through the motion of a dot matrix formed by photochromic dyes. Two dyes found compatible with the candidate fluids are spiropyran and triarylmethane. The observation of the dot motion is accomplished using a flying spot scanner.
Homsey, R. J.↗
Development of an Additive Manufactured Cryogenic TVS Augmented Injector
Cryogenic fluid transfer is critical in ground and space systems. Transfer typically requires venting a receiver vessel during the chill and fill process to maintain a pressure favorable to fluid flow. Venting in space is problematic due to low-gravity where fluid position is indeterminate; possibly allowing fluid to flow out the vent. To control receiver tank venting the vented chill/no-vent fill methodology is attractive. An additively manufactured Injector coupled with a Thermodynamic Venting System (TVS) augmentation can enable the vented chill/no-vent fill approach with simplified operations. The TVS augmented injector includes an internal heat exchanger, fluid injector spray head, and external surface condensation heat exchange; combined with integrated flow paths in one part. Operations using the injector allow the tank vent to be closed very early in the transfer and not reopened. The TVS circuit eliminates the potential for stalled fill by maintaining cooling flow on the injector and condenser elements, reducing tank pressure. The injector can also be employed for long-term cryo fluid storage as a means of controlling tank pressure if integrated with a recirculation pump. A cryo-cooler can be used in place of/or augmenting the TVS flow circuit for a zero loss pressure control system. The Injector was developed using the principles of design for additive manufacture and printed as one part, resulting in part count reduction, improved reproducibility, shorter lead times, and reduced cost. The TVS augmented injector is compact and highly adaptable simplifying its integration. A key benefit is that this methodology enables simplified operations in reaching 100% fill conditions.
Omar Mireles↗
Capillary Corner Flows With Partial and Nonwetting Fluids
Capillary flow in containers or conduits with interior corners are common place in nature and industry. The majority of investigations addressing such flows solve the problem numerically in terms of a friction factor for flows along corners with contact angles below the Concus-Finn critical wetting condition for the particular conduit geometry of interest. This research effort provides missing numerical data for the flow resistance function F(sub i) for partially and nonwetting systems above the Concus-Finn condition. In such cases the fluid spontaneously de-wets the interior corner and often retracts into corner-bound drops. A banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales x(sub s) and y(sub s) to nondimensionalize the problem. The optimal scaling is found to be identical to the wetting scaling, namely x(sub s) = H and y(sub s) = Htan (alpha), where H is the height from the corner to the free surface and a is the corner half-angle. Employing this scaling produces a relatively weakly varying flow resistance F(sub i) and for subsequent analyses is treated as a constant. Example solutions to steady and transient flow problems are provided that illustrate applications of this result.
Bolleddula, D. A.↗
Thermocapillary Flow and Aggregation of Bubbles on a Solid Wall
During the electrolytic evolution of oxygen bubbles forming on a vertically oriented transparent tin oxide electrode, bubbles were found to be mutually attractive. The mechanism of the aggregation had never been explained satisfactorily until Guelcher et al. attributed it to thermocapillary flow. The gradient of surface tension of the liquid at the bubble's surface, which was established because of reaction heat and ohmic heat loss at the electrode wall, drives flow of the liquid adjacent to each bubble; the bubble "pumps" fluid along its surface away from the wall. Fluid flows toward the bubble to conserve mass and entrains nearby bubbles in the flow pattern. The same logic would apply when two bubbles of equal size are adjacent to each other on a warm wall. Each bubble drives thermocapillary flow and hence entrains the other in its flow pattern, which drives the aggregation. Our objective here is to perform experiments where the temperature gradient at the wall is well known and controlled. The theory can be quantitatively tested by studying aggregation of bubble pairs of equal size, and by varying system parameters such as temperature gradient, bubble size and fluid viscosity. The results are then compared with the theory in a quantitatively rigorous manner. We demonstrate that the theory without adjustable parameters is capable of quantitatively modeling the rate of aggregation of two bubbles. The equations governing the thermocapillary flow around a single stationary bubble on a heated or cooled wall in a semi-infinite domain were solved. Both Reynolds number and Marangoni number were much less than unity. The critical result is that liquid in the vicinity of a warm wall flows toward a stationary collector bubble. Consequently the thermocapillary flow around the stationary bubble entrains another bubble toward itself. The bubbles undergo hindered translation parallel to the wall with velocity U while the fluid flow field is described with u. Two velocities were equated by using a wall hindrance parameter q: U = qu [1] which shows the velocity of bubble is proportional to the entraining velocity. The hindrance parameter q can experimentally be measured independently. q can also be calculated by solving the equations of motion for a bubble translating parallel to a solid wall. The experimental cell is cylindrical with an ID of 10 cm and consists of a 1 cm deep main cell filled with silicone oil and flanked by two thermal reservoirs. The upper thermal reservoir was heated and the lower thermal reservoir was cooled so that the bubbles aggregate. Two types of silicone oil (eta = 0.02 and 0.50 Pa s) were used. Two equal sized air bubbles were injected into the cell with a syringe. The center-to-center distance of bubbles was observed through a microscope. Bubble radius ranged from 0.40 mm to 0.65 mm and the temperature gradients along with the cell ranged from 1400 to 5000 K/m. The bubbles aggregated when heat flows from the wall to the fluid. The velocities of bubbles were in the range of 1 - 10 microns/s. The separation r decreased more quickly when the temperature gradient was higher, bubble size was larger, and the oil viscosity was lower. r decreased more rapidly as the bubbles approached each other. Dimensionless time was arbitrarily set to be zero when the dimensionless center-to-center distance between the bubbles was 4. All the bubble trajectories fall onto one line, especially in the range of dimensionless distance from 4 to 3. This means the relative movement of the bubble pair is proportional to the temperature gradient and bubble size and it is inversely proportional to the viscosity of the oil. This result strongly suggests that the thermocapillary flow-based aggregation mechanism is correct. A value of q can be estimated by fitting the scaled data to Eq. [1]. A best fit value of q was obtained as q = 0.26 with a standard deviation of 0.03. Independent experimental results for q for a 0.5 mm radius bubble, give values of q in the range 0.11 to 0.23. The value of q obtained from solving the equations of motion reveals q has values in the range 0.23 - 0.30. Since the full scale of possible values of q is zero to one, the maximum deviation of independently determined values of q from the best fit value was 15% of this full scale. Thus reasonable quantitative agreement between theory and experiment has been obtained.
Kasumi, Hiroki↗