Constant Area Duct Research Articles

On Cooled Anodes in Contact with a Laminar Arc-Heated Flow

This paper is concerned with the physics and operating characteristics of cooled anodes In contact with an arc-heated laminar plasma flow in a constant area duct. Various modes of anode behavior are identified and described. Some Influences of gas type, flow rate, arc current, anode material and geometry are demonstrated. A theory is developed to explain the low-current mode of the anode characteristic. It is shown that the local current density on the anode surface is related approximately to the surface's local bias relative to its electrically floating voltage. Anode current distribution data is presented; the distribution is shown to be unstable above a transition bias volt,. age, with the current concentrating intensely on the edge of the anode toward the cathode. Neighboring points on the duct wall are shown to be electrically independent. This fact greatly simplifies an interpretation of anode phenomena. The information presented makes a fairly complete picture of the physical behavior of finite-length, cooled anodes in contact with fully-developed laminar plasma-arc flows.

Entropy Changes in Nonequilibrium Flows

The entropy increases arising from chemical nonequilibrium in inviscid flows are investigated by the use of an analytical model. After the validity of the model is examined, the irreversibilities in nonequilibrium expansions are studied. The basic approach to the problem is an analytical study of limiting behavior of the entropy integral followed by numerical evaluation of this integral over finite limits. Small perturbation analyses are employed for investigating near-equilibrium and near-frozen flow in order to justify truncation of the entropy integral for some cases. The conditions necessary for the existence of freezing and for the existence of entropy bounds are established for large expansions. The results of exact numerical solutions for nonequilibrium nozzle flows are compared with those from isothermal approximations for upper bounds on entropy increments. Irreversibilities are also evaluated for relaxation flows in a constant-area duct, a shock-wave reaction zone, and a venturi for a previously frozen flow. It is observed that the entropy rise in the freezing process is practically negligible compared with the total entropy for a wide range of conditions characterizing flows of technical interest. The constant-area relaxation and venturi relaxation flows also show small entropy rises. The shock wave and its accompanying relaxation zone lead to substantial irreversibilities. The entropy rise in the expansion cases is small permitting constant entropy approximations which may be utilized in numerical computation.

Observations on distorted turbulent wakes

The question considered here is whether turbulent wakes can undergo a simple self-preserving development when convected through a duct of varying crosssection. A flow is described as self-preserving if the distributions of its mean-value properties at successive sections have the same basic shape, differing only in magnitude and lateral extent. In such flows the scales of the mean velocity variation and turbulence have been found to be proportional.The wakes studied are concentrated near a plane of symmetry through a duct of changing rectangular section but constant area; the portion of the wake near the other plane of symmetry is considered. Measurements in the flows behind three circular cylinders reveal a lack of universality of the scales associated with self-preserving solutions of the momentum equation. The wakes of the smaller cylinders adopt the predicted form, but that of the largest does not. As it moves through the channel, this wake is compressed less rapidly by the imposed lateral strain than is predicted.Interest is then concentrated on the equation governing the kinetic energy of the turbulence and in particular on the relative size of its two production terms, that representing the action of the mean wake shear and that representing the effect of the distortion applied by the duct. It is found that self-preserving wakes can form only in a few kinds of distorting convecting flow. In the experimental duct, which has exponentially varying walls, one of these is set up. Attention is concentrated on this case. A stability analysis (based on the criterion that a stable wake is one in which the total turbulence production decreases as a result of more rapid wake expansion) suggests that, when production by wake shear is greater than that by distortion, a stable self-preserving development is possible in which the turbulence scale and the velocity defect scale remain proportional. But in the alternative, distortion-dominated, case the velocity defect decreases continually relatively to the turbulence.The experimental results are in accord with these predictions. The transition from shear-dominated to distortion-dominated wakes appears to take place when the production terms are about equal. The failure of the one experimental wake to adopt a simple self-preserving form can be attributed to the relatively slight organization of its turbulence when distortion is begun.

Electromagnetic Acceleration of a Shock Wave in a Constant-Area Duct

When a rapid current discharge occurs in a gas between two electrodes, a current sheet forms which accelerates into the gas and produces a shock wave, much as a piston in conventional gas dynamics. Due to the high velocities which it reaches, the shock wave ionizes the gas, and a plasma is formed in the region between the current carrying contact front and the shock wave. Nonsteady electromagnetic acceleration of a one-dimensional shock wave has been studied for the case of an arbitrary but constant specific-heat ratio of the plasma. Approximate closed-form solutions for the velocity of the contact surface and shock wave have been obtained, illustrating both the weak dependence of the contact front velocity on γ, and the relation between the fluid mechanical and ``snowplow'' models of the shock acceleration. It has also been shown, for the case under consideration, that the contact surface and shock positions are initially parabolic, and finally hyperbolic functions of time, and that the pressure may be approximated by a linear function of the Lagrangian variable.

Effect of Boundary-Layer Growth in a Shock Tube on Shock Reflection from a Closed End

The pressure behind a shock wave propagating in a constant-area duct increases slightly with time as a result of the growing boundary layer. This rise is considerably magnified by the shock reflection from the closed end of the duct. Analysis of the local interaction of the reflected shock with the boundary layer yields information on the shock configuration, but the combined effects of the waves produced by the growing boundary layer along the entire shock tube must be considered to obtain the state of the gas behind the reflected shock. The theory of the flow field behind the incident shock is modified to allow for effects in addition to boundary-layer growth which cause deviations from an ideal shock-tube flow. Experimental observations of the pressure rise behind the reflected shock, obtained for shock pressure ratios up to about 4.5 are in satisfactory agreement with the computed results, and estimates for stronger shock waves are presented.

Mixing of Compressible Fluids

The problem of the mixing of two streams of the same compressible fluid in a constant-area duct is solved by applying certain dimensionless parameters first used by Kiselev. The extension to dissimilar fluids or to more than two streams is straightforward. Although the analysis is unrestricted, detailed results are given only for the case where one stream is sonic or supersonic and the other sonic or subsonic at the origin of mixing. For this case, the second law of thermodynamics indicates that, of the two solutions of the conservation equations, the subsonic one is always permitted while some of the supersonic solutions are thermodynamically impossible. Upon examination of experimental data, it is further concluded that of the admissible supersonic solutions, only one may be expected to occur. The establishment of this supersonic solution with its relatively high stagnation pressure leads to the conclusion that when the initial temperatures are sufficiently different, there exist thermodynamically possible solutions with a stagnation pressure higher than that of either of the two initial streams.

Partition of Energy in a Pulsed Plasma Accelerator

It is pointed out that in a plasma behind a magnetically driven strong shock generated in a pulsed type accelerator, the internal energy will equal the kinetic energy only for a specific case. It is shown that the kinetic energy exceeds the thermal energy when the shock overtakes a uniformly moving fluid. In nonsteady flow in a constant area duct further conversion of thermal to kinetic energy is achieved when the strong shock is permitted to collide head-on with a complete rarefaction wave. (B.O.G.)

The Aerothermopressor—A Device for Improving the Performance of a Gas-Turbine Power Plant

Abstract Theoretical and experimental investigations of a novel gas-dynamics device having no moving parts yet performing the function of a compressor, are described. This device, called the “Aerothermopressor,” exploits the possibility of raising the total pressure of a high-speed gas stream through cooling of the gas. When placed at the exhaust of a gas turbine, the Aerothermopressor will reduce the exhaust pressure, thereby improving both fuel economy and power capacity per unit of air flow. Basic elements of the apparatus comprise a nozzle which accelerates hot gas into an evaporation section; a water-injection system which delivers finely atomized water into the high-speed stream; an evaporation section in which the gas is cooled and most of the water evaporated; and, finally, a diffuser in which the gas stream is decelerated and the static pressure increased. Although the Aerothermopressor is simple in structural arrangement, the physical processes occurring within it are exceedingly complex in their details. The simultaneous effects on the gas stream of droplet drag, evaporative cooling, area variation, and wall friction lead to many regimes of operation, including the hitherto unknown passage from subsonic to supersonic speeds in a constant-area duct. Theoretical calculations of a one-dimensional nature, involving for the gas stream the equations of continuity, momentum, and energy, and for the liquid-droplet cloud the equations of motion, heat transfer, and mass transfer, have been carried out on a high-speed, electronic digital computer. The theory reproduces all the behavior patterns of experimental units and is in generally good quantitative agreement with the experimental data. The results of experiments on a small-scale, constant-area unit of 2.13 in. diam are presented and compared with theoretical calculations. The experiments and theory both show that a net stagnation rise is possible only with gas flows greater than about 2 lb/sec; below this value the detrimental effects of wall friction completely absorb the gains due to cooling. In the range of 25 lb/sec a net stagnation pressure rise of about 10 per cent seems assured, while 20 per cent seems possible. Early tests on a recently completed medium-scale unit of 25 lb/sec capacity have already demonstrated a net overall rise in stagnation pressure.

Flow Changes in Gases in which Mass and Impulse are Conserved

SummaryThis note discusses changes in the state of a gas flowing in a duct of constant area. In the past, changes, such as normal shock waves, combustion and other phenomena, which are defined by the equations of energy, conservation of momentum and mass flow, have each been treated on their merits. In this note a method is developed whereby all phenomena governed by these three equations can be solved by a single general method. The method rests on the derivation of a parameter which is unaltered in value by the change, in all cases where the total temperature is constant. A shock wave is an example of such a discontinuity. In problems of heat addition or extraction, the parameter changes its value only because of the change in total temperature. The change in total temperature may be calculated from the known quantity of heat added or extracted.The parameters derived are useful in showing how problems of this type should be attacked analytically. With oblique waves it is easy to derive a relation between the normal velocities before and after the wave, and it is probable that this relationship has not been published before.

A study of free flames in turbulent streams

Although there is considerable information in the literature on studies of the inflammability of mixturcs of gaseous fucls and air (1, 2, 3) very little data are available on ignitibility under flow conditions in a constant area duct at pressures less than one atmosphere. Since there is so much yet to be known about combustion, the fact that this regime has not been thoroughly explored is understandable for a number of reasons, some having to do with the mechanical structure of the apparatus and others with the fluid dynamics of the flow stream. Although visual observation of the continuous inflammation events of a stream flowing through a duct is desirable, combustion imposes a iarge heat load on the system, making it difficult to use transparent materials of construction. This problem is not insurmoutable, however, and much work has been carried out using observation portholes and even fused quartz test sections. Another problem, that of the acceleration of flow by combustion in a constant area duct to a velocity such that choking is encountered (4) places a limit on the inlet conditions or necessitates the use of special ducts not of constant cross section. Adding the requirement that the exhaust products must be continuously removed, which after the combustion process are of considerably increased volume and temperature compared to their standard state, provides another obstacle to inexpensive and simple design. The continuous flow, low pressure, ducted, combustion field has therefore been somewhat neglected even though the mode of combustion is akin to ramjets, rockets and gas turbines.

Mixing of Any Number of Streams in a Duct of Constant Cross-Sectional Area

Mixing of Any Number of Streams in a Duct of Constant Cross-Sectional Area