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High-resolution time-resolved experiments on mixing and entrainment of buoyant jets in stratified environments

Fluid jets interacting with a stratified layer play an important role in the safety of several reactor designs. In the containment of nuclear power plants, fluid jets dominate the transport and mixing of gaseous species and consequent hydrogen distribution in case of a severe accident. The mixing phenomena in the containment are driven by buoyant high-momentum injections (jets) and low momentum injection plumes. Mixing near the postulated break is initially dominated by high flow velocities. Plumes with moderate flow velocities are instead relevant in the break compartment during the long-term pressurization phase, or in any of the apertures between two connected compartments if the mass flows are sufficiently high and the density differences between efflux and ambient are sufficiently low. Phenomena of interest include free plumes (as produced by the efflux from the break compartment in a larger room or directly from a break flow), wall plumes (such those produced by low mass flows through inter-compartment apertures), and propagating stratification fronts in the ambient (for any stably stratified conditions). These phenomena have been highly ranked about nuclear reactor design, especially regarding of safety protocols. During a Pressurized Thermal Shock (PTS) scenario, the interaction between the cold ECCS injection plume and the stratified fluid present in the cold (or hot) leg is important in order to determine the temperature at the time-dependent temperature at the inlet of the reactor pressure vessel (RPV) and the potential to cause a thermal shock on the RPV wall. In sodium-cooled fast reactors (SFRs), core channels are typically hydro-dynamically isolated so that there exists a considerable temperature variation at the exit of adjacent fuel assemblies. All the above phenomena are characterized by the interaction of buoyant jets with the stratified flow. In stratified layers baroclinic forces create significant redistribution of turbulent kinetic energy and scales, which leads to anisotropy. This important physical phenomenon is highly three dimensional and is challenging to capture even with high-fidelity CFD simulations, due in part to lack of sufficiently resolved validation data. Furthermore, the experimental data available in the open literature do not feature the level of fidelity needed for an extensive validation of turbulence models in lower order CFD. To shed new lights into the crucial phenomena object of the present research project, it was proposed to conduct coordinated experiments and simulations at the University of Michigan and the George Washington University. The project has resulted in an experimental database of high-resolution time-resolved measurements of jets in uniform and stratified environments. The novel experimental data will be used to validate computational fluid dynamic (CFD) codes, including both Large Eddy Simulations (LES) and unsteady Reynolds-averaged Navier-Stokes equations (URANS) methodologies. In the Experimental and Multiphase flow (ECMF) laboratory at Univerisity of Michigan, we built two experimental facilities to investigate also the effect of scaling. The first facility, DESTROJER (DEnsity Stratified Turbulent ROund free Jet ExpeRiment), featuring a contoured jet nozzle with a diameter of D=12.7mm and a 1m×1m×1m cubic tank, which is made of acrylic glass for optical access. The ratio between the tank width and the nozzle diameter is equal to 78, which ensures that there is no direct interaction between the jet and the side walls. A second, modular experimental facility, features three different tank sizes of size 10×10×30, 20×20×30, 30×30×30 cm3 respectively (all tanks have the same height of 30 cm), and a jet diameter of 2mm. For the modular facility, tank-to-nozzle ratio of 50, 100, and 150 are obtained respectively. Experiments with different-density jet impactions and sharp interface with a density difference of 3.16% In the Laboratory at George Washington University, complementary experiments have been carried out at a facility featuring the same dimensions as DESTROYER. Experiments with different jet diameters have been carried out as well. High-resolution time-resolved measurements have been performed at all facilities using high-speed particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). In this way, simultaneous measurements of velocity and density fields have been carried out. At the University of Michigan, wire-mesh sensors have been designed and built to gather high-resolution, time-dependent data of the stratified front in the tank. These measurements are important to provide accurate initial conditions for the CFD simulations. An important outcome of the project has been the development of novel techniques to achieve refractive index matching (RIM) of acqueous solutions with high density differences. RIM is crucial if optical techniques such as PIV are used to measure velocity fields. Previous to this project, experiments up to 3% density difference had been reported in the literature. With the methodology developed in this project, we have been able to push the envelop to density differences up to 9%. The experiments have been used to validate Reynolds Averaged Navier-Stokes (RANS) turbulence models and Large Eddy Simulations (LES) models. Both NEK5000 and the commercial CFD code STAR-CCM+ have been used. The experimental data will be made available to the community through the NE-KAMS databasehave been successfully conducted in the scaled facility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Jetting Response in Architected Structures

Architected structures are gaining prominence for structural applications as the additive manufacturing technologies that can enable such materials mature. With the expanded design space, such mesoscopic structures occupy the middle ground between random foams and bulk materials. Studies into the deformation response of such structures are limited, particularly under dynamic compression. Early studies indicate the presence of an elastic precursor wave running ahead of the compaction wave. Additional studies also have shown that jetting is known to occur under shock loading conditions due to the presence of geometric perturbations introduced in the long-range periodic structures. Given that starting point, the motivation for this research was to understand the origin of the observed jetting and extend our understanding of how this comes about across a broad spectrum of lattice types, material compositions, length scales, and dynamic loading conditions. The jetting behavior due to lattice structures was studied through a series of dynamic compression plate impact experiments with in-situ x-ray imaging. This work was enabled by the NNSA-funded Dynamic Compression Sector at the Advanced Photon Source, which is housed at Argonne National Laboratory. Prior studies, and also evident in this work, have shown that deformation mechanisms in architected structures are difficult to study using our traditional diagnostics, and the role of in situ observations in this regard cannot be overstated. The role of the impact conditions, the lattice spacing, the lattice architecture, and the lattice base material was explored in the context of promoting or suppressing jet formation. A transition from latticeled to impactor-led jetting is observed above a certain impact threshold. Complementary direct numerical simulations (DNS) were also performed to compare with the experiments, study the underlying stress state giving rise to jetting, and provide insight for conditions not studied experimentally. Such simulations suggest certain trends for promoting or suppressing jetting akin to traditional Richtmyer-Meshkov instability studies. We present a geometric argument to explain the competitive process leading to lattice and/or impactor jetting which incorporates base material properties, the periodicity of the lattice, and basic tunable length scales of the lattice. Our results are consistent with previous observations on such lattices. Expanding on that work, the emergence of a transition of the jet material composition must depends solely on the base material properties and the geometric arrangement of the lattice structure. The fact that we have obtained reasonable qualitative and quantitative agreement regarding the jet formation and propagation behavior leads us to trust the underlying materials models. We can speculate that this and potentially other emergent phenomena might also be possible from a unique combination of base material properties and geometric arrangement of lattice structures. While the transition from polymer-led to flyer-led jetting might seem counterintuitive at first, it is a natural extension of the impact conditions and the arrangement of the materials. Better understanding of how the base material properties are coupled to the lattice structure to give rise to such phenomena will likely improve design for such structures under dynamic compression conditions. As such, the direct numerical simulations provide a pathway to design of architectures in future applications.

36 MATERIALS SCIENCE↗

Evolution of global relativistic jets: Collimations and expansion with kKHI and the Weibel instability

In the study of relativistic jets one of the key open questions is their interaction with the environment. Here we study the initial evolution of both electron–proton (e{sup --}−p{sup +}) and electron–positron (e{sup ±}) relativistic jets, focusing on their lateral interaction with ambient plasma. We follow the evolution of toroidal magnetic fields generated by both the kinetic Kelvin–Helmholtz and Mushroom instabilities. For an e{sup --}−p{sup +} jet, the induced magnetic field collimates the jet and electrons are perpendicularly accelerated. As the instabilities saturate and subsequently weaken, the magnetic polarity switches from clockwise to counterclockwise in the middle of the jet. For an e{sup ±} jet, we find strong mixing of electrons and positrons with the ambient plasma, resulting in the creation of a bow shock. The merging of current filaments generates density inhomogeneities that initiate a forward shock. Strong jet–ambient plasma mixing prevents a full development of the jet (on the scale studied), revealing evidence for both jet collimation and particle acceleration in the forming bow shock. Differences in the magnetic field structure generated by e{sup --}−p{sup +} and e{sup ±} jets may contribute to the polarization properties of the observed emission in AGN jets and gamma-ray bursts.

79 ASTRONOMY AND ASTROPHYSICS↗

Baryon loading efficiency and particle acceleration efficiency of relativistic jets: cases for low luminosity BL Lacs

Relativistic jets launched by supermassive black holes, so-called active galactic nuclei (AGNs), are known as the most energetic particle accelerators in the universe. However, the baryon loading efficiency onto the jets from the accretion flows and their particle acceleration efficiencies have been veiled in mystery. With the latest data sets, we perform multi-wavelength spectral analysis of quiescent spectra of 13 TeV gamma-ray detected high-frequency-peaked BL Lacs (HBLs) following one-zone static synchrotron self-Compton (SSC) model. We determine the minimum, cooling break, and maximum electron Lorentz factors following the diffusive shock acceleration (DSA) theory. We find that HBLs have P{sub B}/P{sub e}∼6.3×10{sup −3} and the radiative efficiency ϵ{sub rad,jet}∼6.7×10{sup −4}, where P {sub B} and P {sub e} is the Poynting and electron power, respectively. By assuming 10 leptons per one proton, the jet power relates to the black hole mass as P{sub jet}/L{sub Edd}∼0.18, where P{sub jet} and L{sub Edd} is the jet power and the Eddington luminosity, respectively. Under our model assumptions, we further find that HBLs have a jet production efficiency of η{sub jet}∼1.5 and a mass loading efficiency of ξ{sub jet}≳5×10{sup −2}. We also investigate the particle acceleration efficiency in the blazar zone by including the most recent Swift/BAT data. Our samples ubiquitously have particle acceleration efficiencies of η{sub g}∼10{sup 4.5}, which is inefficient to accelerate particles up to the ultra-high-energy-cosmic-ray (UHECR) regime. This implies that the UHECR acceleration sites should not be the blazar zones of quiescent low power AGN jets, if one assumes the one-zone SSC model based on the DSA theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Experiments on confined turbulent jets in cross flow.

Results are reported of experiments on the effects of an opposite wall on the characteristics of turbulent jets injected into a cross flow, for unheated and heated jets. Longitudinal and transverse distributions of velocity and temperature are presented for single and multiple circular jets, and trajectories are presented for two-domensional jets. The opposite wall has relatively little effect on a single jet unless the ratio of jet to cross flow momentum flux is large enough for the jet to impinge on the opposite wall. For a row of jets aligned perpendicularly to the cross flow, the opposite wall exerts progressively larger influence as the spacing between jets decreases. Much of the effect of jet and wall proximity can be understood by considering the interaction of the vortex flow which is the major feature of the structure of a single jet in a cross flow. Smoke photographs are shown to elucidate some of the interaction patterns.

Kamotani, Y.↗

Experiments on confined turbulent jets in cross flow

Results are reported of experiments on the effects of an opposite wall on the characteristics of turbulent jets injected into a cross flow, for unheated and heated jets. Longitudinal and transverse distributions of velocity and temperature are presented for single and multiple circular jets, and trajectories are presented for two-dimensional jets. The opposite wall has relatively little effect on a single jet unless the ratio of jet to cross flow momentum flux is large enough for the jet to impinge on the opposite wall. For a row of jets aligned perpendicularly to the cross flow, the opposite wall exerts progressively larger influence as the spacing between jets decreases. Much of the effect of jet and wall proximity can be understood by considering the interaction of the vortex flow which is the major feature of the structure of a single jet in a cross flow. Smoke photographs are shown to elucidate some of the interaction patterns.

Kamotani, Y.↗

Theoretical aerodynamics of upper-surface-blowing jet-wing interaction

A linear, inviscid subsonic compressible flow theory is formulated to treat the aerodynamic interaction between the wing and an inviscid upper-surface-blowing (USB) thick jet with Mach number nonuniformity. The predicted results show reasonably good agreement with some available lift and induced-drag data. It was also shown that the thin-jet-flap theory is inadequate for the USB configurations with thick jet. Additional theoretical results show that the lift and induced drag were reduced by increasing jet temperature and increased by increasing jet Mach number. Reducing jet aspect ratio, while holding jet area constant, caused reductions in lift, induced drag, and pitching moment at a given angle of attack but with a minimal change in the curve of lift coefficient against induced-drag coefficient. The jet-deflection effect was shown to be beneficial to cruise performance. The aerodynamic center was shifted forward by adding power or jet-deflection angle. Moving the jet away from the wing surface resulted in rapid changes in lift and induced drag. Reducing the wing span of a rectangular wing by half decreased the jet-circulation lift by only 24 percent at a thrust coefficient of 2.

Lan, C. E.↗

An experimental study of sound radiation from a subsonic jet in simulated motion

A free-jet anechoic facility is used for quantitative determination of the effect of motion on the pure jet mixing noise from subsonic jets. The farfield measurements obtained outside the free jet are subjected to amplitude and angle corrections due to free-jet shear layer refraction; in addition, corrections are made to account for the distributed nature of the jet noise source as a function of frequency. The corrected results, which provide the changes in the jet mixing noise as a result of simulated jet motion, are presented for a range of jet velocities with a fixed free-jet velocity. Comparisons are made between the findings obtained and those related to other simulation and flight measurements. The results indicate that the effect of motion is to reduce jet mixing noise at all angles of measurement, and the reduction is broadband with the largest magnitude occurring around the spectral peak.

Yu, J. C.↗

A correlation method to predict the surface pressure distribution of an infinite plate or a body of revolution from which a jet is issuing

A correlation method to predict pressures induced on an infinite plate by a jet exhausting normal to the plate into a subsonic free stream was extended to jets exhausting at angles to the plate and to jets exhausting normal to the surface of a body revolution. The complete method consisted of an analytical method which models the blockage and entrainment properties of the jet and an empirical correlation which accounts for viscous effects. For the flat plate case, the method was applicable to jet velocity ratios up to ten, jet inclination angles up to 45 deg from the normal, and radial distances up to five diameters from the jet. For the body of revolution case, the method was applicable to a body at zero degrees angle of attack, jet velocity ratios 1.96 and 3.43, circumferential angles around the body up to 25 deg from the jet, axial distances up to seven diameters from the jet, and jet-to-body diameter ratios less than 0.1.

Perkins, S. C., Jr.↗

Measurement of acoustic shielding by a turbulent jet

The acoustic shielding properties of a turbulent jet have been investigated experimentally. The experimental arrangement consisted of an acoustic point source and a turbulent shielding jet. The source and jet parameters investigated include the source frequency, source spectrum, jet velocity, jet medium and the lateral and longitudinal source positions with respect to the shielding jet. It is found that the acoustic shielding of jet flow is power conserving and the acoustic refraction, diffraction and reflection are the main mechanisms controlling the measured noise field. The balance between refraction and diffraction gives rise to a saturation of shielding with frequency in the shadow zone of the source. Comparison with predicted shielding from an idealized cylindrical non-decaying jet model indicates that the spreading and decay of the jet flow are important. Comparisons between the present data trends and those reported for jet-by-jet shielding suggest that the major effects observed in the latter are acoustical.

Yu, J. C.↗

Flow visualization study of the effect of injection hole geometry on an inclined jet in crossflow

A flow visualization was studied by using neutrally buoyant, helium-filled soap bubbles, to determine the effect of injection hole geometry on the trajectory of an air jet in a crossflow and to investigate the mechanisms involved in jet deflection. Experimental variables were the blowing rate, and the injection hole geometry cusp facing upstream (CUS), cusp facing downstream (CDS), round, swirl passage, and oblong. It is indicated that jet deflection is governed by both the pressure drag forces and the entrainment of free-stream fluid into the jet flow. For injection hole geometries with similar cross-sectional areas and similar mass flow rates, the jet configuration with the larger aspect ratio experienced a greater deflection. Entrainment arises from lateral shearing forces on the sides of the jet, which set up a dual vortex motion within the jet and thereby cause some of the main-stream fluid momentum to be swept into the jet flow. This additional momentum forces the jet nearer the surface. Of the jet configurations, the oblong, CDS, and CUS configutations exhibited the largest deflections. The results correlate well with film cooling effectiveness data, which suggests a need to determine the jet exit configuration of optimum aspect ratio to provide maximum film cooling effectiveness.

Simon, F. F.↗

Flow visualization study of the effect of injection hole geometry on an inclined jet in crossflow

A flow visualization was studied by using neutrally buoyant, helium-filled soap bubbles, to determine the effect of injection hole geometry on the trajectory of an air jet in a crossflow and to investigate the mechanisms involved in jet deflection. Experimental variables were the blowing rate, and the injection hole geometry cusp facing upstream (CUS), cusp facing downstream (CDS), round, swirl passage, and oblong. It is indicated that jet deflection is governed by both the pressure drag forces and the entrainment of free-stream fluid into the jet flow. For injection hole geometries with similar cross-sectional areas and similar mass flow rates, the jet configuration with the larger aspect ratio experienced a greater deflection. Entrainment arises from lateral shearing forces on the sides of the jet, which set up a dual vortex motion within the jet and thereby cause some of the main-stream fluid momentum to be swept into the jet flow. This additional momentum forces the jet nearer the surface. Of the jet configurations, the oblong, CDS, and CUS configurations exhibited the largest deflections. The results correlate well with film cooling effectiveness data, which suggests a need to determine the jet exit configuration of optimum aspect ratio to provide maximum film cooling effectiveness.

Simon, Frederick F.↗

The Near Noise Field of Static Jets and Some Model Studies of Devices for Noise Reduction

An experimental study is presented of the pressure fluctuations near jet exhaust streams made during unchoked operation of a turbojet engine and a 1-inch-diameter high-temperature model jet and during choked operation of various sizes of model jets with unheated air. The tests for unchoked operation indicate a random spectrum of rather narrow band width which varies in frequency content with axial position along the jet. Pressure surveys from the model tests along lines parallel to the 15 degree jet boundary indicate that the station of greatest pressure fluctuations is determined by the jet velocity and the radial distance, with a tendency of the maximum to shift downstream as either parameter is increased. From model tests the magnitude of the fluctuations appears to increase as about the second power of jet velocity at points just outside the jet boundary and as increasingly higher powers of jet velocity as distance from the boundary is increased. A laboratory method of noise reduction with model jets was found to produce large decreases in the magnitude of the lower-frequency components of the spectra and thereby also to reduce the total radiated energy. Choked operation of model jets with unheated air indicates the appearance of a discrete-frequency component of very large magnitude. Shadowgraph records of the flow show that this condition is associated with the appearance of flow formations suggestive of partly formed toroidal vortices in the vicinity of the shocks. Elimination of these formations is found to eliminate the discrete component and thereby to reduce the overall noise level.

Lassiter, Leslie W↗

Response of multi-panel assembly to noise from a jet in forward motion

A model of the interaction of the noise from a spreading subsonic jet with a 4 panel assembly is studied numerically in two dimensions. The effect of forward motion of the jet is accounted for by considering a uniform flow field superimposed on a mean jet exit profile. The jet is initially excited by a pulse-like source inserted into the flow field. The pulse triggers instabilities associated with the inviscid instability of the jet shear layer. These instabilities generate sound which in turn serves to excite the panels. We compare the sound from the jet, the responses of the panels and the resulting acoustic radiation for the static jet and the jet in forward motion. The far field acoustic radiation, the panel response and sound radiated from the panels are all computed and compared to computations of a static jet. The results demonstrate that for a jet in forward motion there is a reduction in sound in downstream directions and an increase in sound in upstream directions in agreement with experiments. Furthermore, the panel response and radiation for a jet in forward motion exhibits a downstream attenuation as compared with the static case.

Bayliss, A.↗

Flow Coupling Effects in Jet-in-Crossflow Flowfields

The combustor designer is typically required to design liner orifices that effectively mix air jets with crossflow effluent. CFD combustor analysis is typically used in the design process; however the jets are usually assumed to enter the combustor with a uniform velocity and turbulence profile. The jet-mainstream flow coupling is usually neglected because of the computational expense. This CFD study was performed to understand the effect of jet-mainstream flow coupling, and to assess the accuracy of jet boundary conditions that are commonly used in combustor internal calculations. A case representative of a plenum-fed quick-mix section of a Rich Burn/Quick Mix/Lean Burn combustor (i.e. a jet-mainstream mass-flow ratio of about 3 and a jet-mainstream momentum-flux ratio of about 30) was investigated. This case showed that the jet velocity entering the combustor was very non-uniform, with a low normal velocity at the leading edge of the orifice and a high normal velocity at the trailing edge of the orifice. Three different combustor-only cases were analyzed with uniform inlet jet profile. None of the cases matched the plenum-fed calculations. To assess liner thickness effects, a thin-walled case was also analyzed. The CFD analysis showed the thin-walled jets had more penetration than the thick-walled jets.

Bain, D. B.↗

Ejector Noise Suppression with Auxiliary Jet Injection

An experimental program to reduce aircraft jet turbulence noise investigated the interaction of small auxiliary jets with a larger main jet. Significant reductions in the far field jet noise were obtained over a range of auxiliary jet pressures and flow rates when used in conjunction with an acoustically lined ejector. While the concept is similar to that of conventional ejector suppressors that use mechanical mixing devices, the present approach should improve thrust and lead to lower weight and less complex noise suppression systems since no hardware needs to be located in the main jet flow. A variety of auxiliary jet and ejector configurations and operating conditions were studied. The best conditions tested produced peak to peak noise reductions ranging from 11 to 16 dB, depending on measurement angle, for auxiliary jet mass flows that were 6.6% of the main jet flow with ejectors that were 8 times the main jet diameter in length. Much larger reductions in noise were found at the original peak frequencies of the unsuppressed jet over a range of far field measurement angles.

Berman, Charles H.↗

The Stability of Radiatively Cooling Jets I. Linear Analysis

The results of a spatial stability analysis of a two-dimensional slab jet, in which optically thin radiative cooling is dynamically important, are presented. We study both magnetized and unmagnetized jets at external Mach numbers of 5 and 20. We model the cooling rate by using two different cooling curves: one appropriate to interstellar gas, and the other to photoionized gas of reduced metallicity. Thus, our results will be applicable to both protostellar (Herbig-Haro) jets and optical jets from active galactic nuclei. We present analytical solutions to the dispersion relations in useful limits and solve the dispersion relations numerically over a broad range of perturbation frequencies. We find that the growth rates and wavelengths of the unstable Kelvin-Helmholtz (K-H) modes are significantly different from the adiabatic limit, and that the form of the cooling function strongly affects the results. In particular, if the cooling curve is a steep function of temperature in the neighborhood of the equilibrium state, then the growth of K-H modes is reduced relative to the adiabatic jet. On the other hand, if the cooling curve is a shallow function of temperature, then the growth of K-H modes can be enhanced relative to the adiabatic jet by the increase in cooling relative to heating in overdense regions. Inclusion of a dynamically important magnetic field does not strongly modify the important differences between an adiabatic jet and a cooling jet, provided the jet is highly supermagnetosonic and not magnetic pressure-dominated. In the latter case, the unstable modes behave more like the transmagnetosonic magnetic pressure-dominated adiabatic limit. We also plot fluid displacement surfaces associated with the various waves in a cooling jet in order to predict the structures that might arise in the nonlinear regime. This analysis predicts that low-frequency surface waves and the lowest order body modes will be the most effective at producing observable features in the jet.

Hardee, Philip E.↗

Determining the Composition of the Vela Pulsar's Jet

The pulsar jet is significant in explaining how the Vela pulsar's rotational energy is transported outward to the rest of the SNR, since direct radiation from the pulsar only accounts for a small percentage of the total power. Our previous ROSAT observations presented the first evidence that the pulsar is driving a narrow, collimated, and remarkably symmetrical jet into the SNR (Markwardt, C. and Oegelman, H., 1995, Nature, 375, p. 40) which we interpret to be from a 'cocoon' of hot gas surrounding the jet itself. We obtained an ASCA exposure of the jet in order to determine whether the spectrum is thermal or power-law continuum. The jet cocoon is detected with ASCA at approximately 2-3 x 10(exp -3) ct/s. The X-ray spectrum of the jet is remarkably similar to the surrounding supernova remnant spectrum and extends to X-ray energies of at least 7 keV, with a total flux of approximately 2 x 10(exp -13) erg/s sq cm sq arcmin. The only strong emission line is from He-like Neon at approx. 0.9 keV; otherwise the spectrum is quite smooth. The spectrum cannot be fit by any one standard plasma emission model, so we used models with two-components. The lower energy component is thermal and has a temperature of 0.29 +/- 0.03 keV; the higher energy portion can either be fit by a thermal component of temperature approx. 4 keV or a power law with photon index approx. 2.0. If the observed spectrum is of a 'traditional' jet cocoon, then we estimate the speed of the jet to be at least 800 km/s, depending on the angle of inclination of the jet axis to our line of sight. The mechanical power driving the jet is greater than or equal to 10(exp 36) erg/s which is comparable to the pulsar's spin-down luminosity of 7 x 10(exp 36) erg/s. and the mass flow rate at the head is greater than or equal to 10(exp -6) solar radius/yr. We conclude that the jet must be entraining material all along its length in order to generate such a large mass flow rate.

Ogelman, Hakki↗