Nozzle Boundary Layer Research Articles

Starting flow through nozzles with temporally variable exit diameter

Starting flow through a nozzle or orifice typically results in the transient formation of a leading vortex ring and trailing jet. Experiments are conducted to investigate the dynamics of this process in the case of a temporally variable nozzle exit diameter, with the aim of understanding these flows as they occur in Nature and emerging technologies. By kinematically decoupling the source flow from the nozzle motion, comparison across several classes of exit diameter temporal variation is facilitated. Kinematic models of the starting flows are used to accurately predict the fluid circulation produced by the vortex generators, and to emphasize the special role of the nozzle boundary layer in dictating the nature of the global flow patterns. A dimensionless temporal parameter is derived in order to track the vortex formation process for the various classes of nozzle motion. Dynamics of vortex ring disconnection from the source flow are studied in this new dimensionless framework. We show that temporally increasing the nozzle exit diameter as the starting flow develops results in higher-energy vortex ring structures with peak vorticity located further from the axis of symmetry relative to a static nozzle case. In addition, the normalized energy supplied by the vortex generator is increased in this process. We do not observe a delay in the onset of vortex ring disconnection from the trailing jet, as predicted by previous numerical simulations. In contrast, growth of the leading vortex ring is substantially augmented by temporally decreasing the nozzle exit diameter during fluid ejection, as noted in a previous experiment. Normalized vortex ring circulation is increased 35% in these cases, and the normalized energy of the generated vortex rings is equivalent to that of Hill's spherical vortex. These observed effects are explained by considering the measured vorticity distribution and energy of the starting flows. Strategies are suggested to exploit the discovered dynamics for various pulsed-jet applications.

Simulation Strategy of Turbulent Internal Flow in Solid Rocket Motor

A strategy for the simulation of turbulent internal flows in a solid rocket motor (SRM) is described. Sources of turbulence inside an SRM are identified and their dominance relative to each other is characterized to set a priority in the modeling effort. This complex problem is simplified by subdividing it into problem components allowing for a more detailed study of each component. Problems of interest in which investigations have been pursued are compressible periodic rockets, spatial transition in a laboratory-scale rocket, and effect of inhibitors and large-eddy simulation (LES) wall-layer modeling (WLM) for the nozzle boundary layer. Grid sensitivity is observed in the application of dynamic LES to a transitional flow in an SRM. Inhibitors at the segment juctions act as a trip in the transition to turbulence and play a more dominant role compared to the injection of turbulence from the propellant surface. Detached-eddy simulation provides relatively accurate wall gradient properties and is more generally applicable than WLM. This hybrid method, however, requires some degree of implicitness in the time discretization to be efficient.

Throat Heating Effect on Critical Roughness and Nozzle Wall Boundary-Layer Stability

The effect of wall heating in the throat region on the e ow quality in a Mach 3.5 and a Mach 2.4 axisymmetric nozzle is investigated. Because of the boundary-layer thickening effect, the critical roughness height to trigger laminar‐turbulent transition is larger in the heated cases. Therefore, for a given surface e nish, the adverse effect of roughness on transition can be minimized by sufe cient wall heating. However, the combined effect of heating and pressure gradients is to introduce an overshoot in the streamwise velocity proe le, as earlier predicted by Cohen and Reshotko. Associated with this overshoot is a new generalized ine ection point near the edge of the boundary layer, and, as a consequence, the nozzle wall boundary layer supports high-frequency two-dimensional inviscid disturbances. N-factor results indicate that, with excessive throat heating, these disturbances could cause prematuretransitiondownstream ofthethroatand,hence, jeopardizethequiet performance.Therefore, favorable (on critical roughness height ) and adverse (on boundary-layer instability ) effects of heating have to be carefully evaluated. Mean e ows are computed by using both a boundary-layer code and a Navier ‐Stokes solver, the critical roughnessheights are calculated based on an empirical formula, and the destabilizing effect of heating is evaluated by using compressible linear stability theory. The critical roughness heights are established for the two nozzles for given heating strips.

Effect of boundary layer swirl on supersonic jet instabilities and thrust

This paper reports the effects of nozzle exit boundary layer swirl on the instability modes of underexpanded supersonic jets emerging from plane rectangular nozzles. The effects of boundary layer swirl at the nozzle exit on thrust and mixing of supersonic rectangular jets are also considered. The previous study was performed with a 30° boundary layer swirl (S=0.41) in a plane rectangular nozzle exit. At this study, a 45° boundary layer swirl (S=1.0) is applied in a plane rectangular nozzle exit. A three-dimensional unsteady compressible Reynolds-Averaged Navier-Stokes code with Baldwin-Lomax and Chien’sk-e two-equation turbulence models was used for numerical simulation. A shock adaptive grid system was applied to enhance shock resolution. The nozzle aspect ratio used in this study was 5.0, and the fully-expanded jet Mach number was 1.526. The “flapping” and “pumping” oscillations were observed in the jet’s small dimension at frequencies of about 3,900Hz and 7,800Hz, respectively. In the jefs large dimension, “spanwise” oscillations at the same frequency as the small dimension’s “flapping“ oscillations were captured. As reported before with a 30° nozzle exit boundary layer swirl, the induction of 45° swirl to the nozzle exit boundary layer also strongly enhances jet mixing with the reduction of thrust by 10%.

Effect of Wall on Impulse of Solid Propellant Driven Millimeter-Scale Thrusters

An analytic model is presented for evaluating the decrement in impulse due to wall effects in millimeter-scale solid propellant driven thrusters. The model assumes a thin flame sheet moving with constant velocity along the thruster axis. Both frontend ignition (FEI) and backend ignition (BEI) are considered. The decrement in impulse due to plenum heat loss and the nozzle wall boundary layer is evaluated as a function of thruster geometric scale r and a flame speed parameter V f =t p /t s , where t s and t p are characteristic times for steady-state flame propagation and for pulsed flow operation, respectively. For the case of deflagration waves (V f <<1), the plenum heat loss in BEI devices and the nozzle boundary layer loss in FEI devices vary as (rV f ) -1/2 . Thus, relatively large flame speeds are needed in millimeter-scale thrusters to avoid significant impulse loss. In a numerical example, three out of six prospective high flame speed propellants had losses of about 10% or less. Hence, millimeter-scale thrusters appear viable with regard to wall loss. However, experimental confirmation of fabrication techniques, ignition techniques, and propellant performance is needed.

Influence of disturbances generated by the nozzle boundary layer on the heat exchange on the cylindrical nose of a body in a hypersonic flow

The heat transfer to a cylindrical surface whose generators are perpendicular to the freestream direction is investigated. Experiments were carried out in a short-duration wind tunnel at Mach numbers M=6 and 16. At M=6, the Reynolds number based on the cylinder diameter was varied on the range from 2.2·104 to 0.95·106 for the purpose of studying the effect of acoustic disturbances generated by the nozzle boundary layer on the heat exchange.

Numerical Study of Shear-Induced Heating in High-Speed Nozzle Flow of Liquid Monopropellant

A numerical study is performed which focuses on peak temperatures experienced by a liquid monopropellant during high-speed injection in a small-diameter nozzle. Attention is focused on short-duration injection during which the nozzle wall boundary layer is predominantly laminar. An unsteady ID analysis of the temperature distribution associated with sudden fluid acceleration over a flat insulated boundary is first conducted. Expressions are provided which relate the normalized peak wall temperature to the prevailing Eckert and Prandtl numbers. Results reveal a quadratic dependence of the normalized wall temperature on impulse velocity, and a nonlinear variation with Prandtl number. Next, simulation of high-speed flow in an axisymmetric nozzle is performed. The numerical schemes are based on finite-difference discretization of a vorticity-based formulation of the mass, momentum, and energy conservation equations. Implementation of the numerical schemes to flow of LP 1846 in a 4 mm diameter nozzle indicates that preignition is likely to occur for velocities higher than 200 m/s. The effects of wall heat transfer and temperature-dependent properties are also discussed.

Stabilization of a nozzle boundary layer by local surface heating

On the basis of earlier experiments demonstrating that boundary-layer transition in a supersonic nozzle can be moved upstream by local surface cooling, transition delay was sought by locally heating the nozzle surface. This experiment was done in a two-dimensional Mach 3 DeLaval nozzle that had provisions for heating the nozzle surface at the nozzle throat by two different methods. During the tests the surface temperature was increased up to a maximum of about 12% of the stagnation temperature above adiabatic, and the nozzle boundary layer was probed with steady-state and dynamic pitot probes. Without heating, the test conditions were chosen so that the boundary layer downstream of the throat became turbulent by the growth and bursting of a low-frequency instability. With increasing surface temperatures the instability downstream of the throat decreased greatly in amplitude, as did the magnitude of the bursts and their frequency of occurrence. This suggests that the surface heating can play an important role in attenuating nozzle boundary-layer instabilities and delaying boundary-layer transition.

Velocity and spanwise vorticity measurements in an excited mixing layer of a plane jet

The mixing layer of a plane jet was subjected to periodic weak excitation at two different frequencies corresponding to shear layer mode (Stθ=0.012) and preferred mode (St D =0.36). The nozzle exit boundary layer was identical for the unexcited and excited flows. Measurements of mean velocity, longitudinal and lateral velocity fluctuations, Reynolds shear stress and spanwise component of fluctuating vorticity were made over a longitudinal distance x/D of 6 for both the unexcited and the excited flows. Even weak excitation was observed to influence the development of the mixing layer. Under shear layer mode of excitation, the width of the layer and longitudinal turbulence level decrease compared to the naturally developing (unexcited) flow whereas preferred mode of excitation results in increase in the width and turbulence levels. The rms spanwise vorticity showed an increase for shear layer mode of excitation whereas the preferred mode of excitation resulted in a decrease compared to the values in an unexcited flow. Spectra of velocity and vorticity fluctuations exhibited subharmonic peaks, suggesting the possible occurrence of vortex pairing in both unexpected and excited flows. The influence of excitation is found to decrease as x/D increases and is not significant at x/D=6.

Navier-Stokes numerical simulation of supersonic hydrogen-fluorine combustion in CW chemical lasers

Results are presented of numerical simulations of nonpremixed supersonic combustion with an accountof nonequilibrium vibration energy exchange and stimulated radiation in the continuous-wave (CW) HF chemical lasers with different fuel/oxidant mixing devices. The main goal of the study was to obtain better insight into the mechanism of coupling between the processes in the combustion region (laser cavity) and in the supersonic supply system (nozzle array). In order to take into account this effect, which is caused by the upwind influence of the cavity processes on the nozzle array flow, a coupled one-domain approach is used, i.e., a simultaneous Navier-Stokes simulation of both nozzle and cavity flows. The results of the computations clearly show that coupling or, more exactly, the feedback mentioned above, is explained mainly by the fuel and oxidant nozzle flows interaction due to propagation of the pressure disturbances from one nozzle to another through the nozzle array base recirculation zone and subsonic part of the nozzle boundary layers. It causes significant deformation of the mixing zone and flame configuration and turns out to be crucial when the difference between the nozzle exit pressure levels is large. In this case, separation of the nozzle boundary layer may occur, which leads to the ignition of the mixture inside the nozzle array. The results illustrate also the influence of the regime parameters and the design of the nozzle array on the flow wave pattern, flame configuration, structure of the base recirculation zones, and the laser output characteristics.

Three-parameter turbulence model: Numerical investigation of the boundary layer in a nozzle with gas-film wall cooling

One of the principal problems in designing powerful liquid-fuel rocket engines (LRE) is how to protect the nozzle walls from heat fluxes, which in the region of the throat may reach tens of MW/m 2. The investigation of the processes in the nozzle wall zone is a problem of turbulent boundary layer theory under extreme conditions (with respect to temperature, velocity and pressure) in the external flow. The methods of calculating the turbulent boundary layer in a supersonic flow, as they existed in 1978, are reviewed in [1]. In[2] methods of calculating the boundary layer in LRE nozzles are described. Of these the best known among engineers are the methods of Avduevskii [3] and levlev [4]. These are integral methods, i.e., they are based on the use of integral momentum and energy relations closed by the algebraic relations for the friction coefficient, the form parameter and the Stanton number. Differential methods of calculating the supersonic boundary layer are also reviewed in [1]. Study [5] is a concrete example of nozzle boundary layer calculations using the transport equation for the turbulent viscosity. The above-mentioned studies relate to the case of so-called external cooling of the LRE nozzle walls. To reduce the high heat fluxes the walls are film-cooled by feeding the fuel through tangential slits [2]. Integral methods of calculating the film cooling of nozzle walls are reviewed in [6]. Differential models of turbulence have been used for calculating plane wall jets in supersonic [7] and subsonic [81 flows. These calculations were made in order to check the applicability of the models by comparison with experiment. Our aim is to calculate the boundary layer in a LRE nozzle using the three-parameter differential model of turbulence developed in [9] and extended to flow with heat transfer in [10], which has been comprehensively tested over a broad range of problems of flow and heat transfer in boundary layers and channels [11].

Sound radiation by two elliptic vortex rings

The sound generation during the motion of two thin vortex rings which are initially parallel and have the shape of an ellipse is calculated. It is found that the generated sound is not axisymmetric. Contrary to the case of a single ring, which does not show a direction of preferential radiation, one finds that the radiation in the direction ofthe minor axis of the ellipse dominates for not too large initial distances. This is compared with a recent experiment on an elliptic jet where preferential radiation into the direction of the minor axis is found for the laminar nozzle boundary layer.

Investigation on the Theoretical Modeling of a Supersonic Flow CO Chemical Laser

Small signal gain coefficients of a supersonic flow CO chemical laser are calculated using a theoretical model which was developed previously and compared with the corresponding experimental results. It is shown that the model predicts the gain characteristics only qualitatively. The measured small signal gain coefficients are rather small compared with the calculated results. In the present investigation, the theoretical model is improved significantly by modifying the relaxation rate constants and by including the effects of the boundary layers which develop in the optical test section. However, further improvement on the theoretical model is necessary by including the effects of the nozzle boundary layers and shock waves.

Investigation on the theoretical modeling of a supersonic flow CO chemical laser.

Small signal gain coefficients of a supersonic flow CO chemical laser are calculated using a theoretical model which was developed previously and compared with the corresponding experimental results. It is shown that the model predicts the gain characteristics only qualitatively. The measured small signal gain coefficients are considerably small compared with the calculated results. In the present investigation, the theoretical model is improved significantly by modifying the relaxation rate constants and including the effects of the boundary layers which develop in the test section. However, further improvement on the theoretical model is necessary by including the effects of the nozzle boundary layers and shock waves.

Roles of initial condition and vortex pairing in jet noise

This is a study of the effect of initial condition on sound generated by vortex pairing in a low Mach number, cold air jet (0·15 ⩽ M ⩽ 0·35). Data has been taken, both flow velocity fields and sound pressure far fields, in a quality anechoic facility, with careful documentation of the effect of initial condition on the sound field of jets of two different geometries (i.e., circular and elliptic). Explanations are presented for most of the observed effects by applying Möhring's theory of vortex sound to vortex filament models of coherent structures in the jets. The explanations also draw upon experience with coherent structure dynamics. The sound source of interest here is that associated with the pairing of shear layer vortices. The evolution of these vortices is greatly affected by the initial condition as is their resultant sound field. The elliptic jets with laminar boundary layers show azimuthal directivity, namely, sound pressure levels in the minor axis plane were greater than in the major axis plane. This difference decreases as the nozzle boundary layer undergoes natural transition with increasing jet speed. When the nozzle boundary layer is tripped, making it fully turbulent and removing the shear layer mode of pairing, the elliptic jet sound fields become nearly axisymmetric. What appears to be the most acoustically active phase of vortex pairing has been modeled, and the resulting sound field calculated for the circular jet. Supporting evidence is found in the experimental data for the validity of this model. The model explains the connection between the initial condition and the far field sound of jets. Interestingly, a general result of Möhring's theory is that motions of vortex rings (of any arbitrary shape) can produce only axisymmetric sound fields if the rings remain in a plane. This implies that the observed asymmetric directivity of the laminar elliptic jet sound field must be due to non-planar ring motions of the vortical structures. The primary contribution of this paper is to examine quantitatively the role of vortex pairing in the production of jet noise; the results are used to reemphasize that “pairing noise” cannot be dominant in most practical jet sound fields, contrary to claims by other researchers.

Thrust vector control utilizing asymmetric jet nozzles

R interest in thrust vector control with rigidly mounted thrusters has been revived. The results described in this Note are associated with the side-force generated by a supersonic jet with an exit plane which is oblique to the centerline of the exhaust flow. As shown in Fig. 1, depending on whether the flow is overor under-expanded, the direction of the exhaust flow is deflected either toward or away from the normal to the exit plane by an amount related to the pressure imbalance and the projected area of the exit plane in the lateral direction. Therefore, control over the direction and amount of side-force is available by varying the stagnation pressure and exit plane obliquity. Although the present results are associated with a twodimensional configuration, with the exit plane obliquity established by extending one wall of the nozzle, application to an axisymmetric configuration is conceivable. For example, consider a fixed axisymmetric thruster enclosed by a cylindrical housing which is split longitudinally into various sections (see Fig. 1). At the null position, the end of the cylinder coincides with the exit plane of the thruster. As various combinations of cylindrical sections are translated forward of the exit plane, the radially projected area of the exit plane may be oriented toward any azimuthal angle. The amount of projected area and its orientation may also be changed rapidly, which adds another control feature to the thrust vectoring. The focus of the work described in Ref. 2 involved the extent to which viscous effects affected the performance, particularly at over-expanded conditions. A two-dimensional supersonic jet of aspect ratio (height/width) equal to 1.5 was established over the Mach number range 1.0 to 3.0. One wall of the nozzle contour was then extended a specified fraction of the nozzle height to establish an oblique exit plane. Transparent and parallel lateral sidewalls bounded the nozzle and extensions thereof through which the flow angle could be observed. The side force generated was measured with a strain gage balance to an accuracy of ±2% of the reading, based on the scatter in repeated experiments and comparison to the measured flow angle. In order to assess the degree to which viscous effects impede accurate analytical prediction, the amount of asymmetry was limited to maintain the wall extension within the domain established by the Mach wave originating from the opposite nozzle wall at the exit plane. Figures 2-4 depict the forces measured on three nozzles whose exit plane is offset by an amount 1.0, 4/3, and 5/3 times the jet height, respectively. Comparison with predictions of two-dimensional inviscid flow theory is shown also. These results may be converted into force coefficients by dividing the results by the surface area of the wall extension and the exit dynamic pressure. The corresponding plot of the Fig. 3 data is presented in Fig. 5. These results indicate that, even in the simple case established here, nontrivial deviations between inviscid flow theory and experiment are observed, although the general trends predicted by analysis are correct. It is also clear that the vectoring control may extend well into the overexpanded region before the nozzle boundary layers begin to

A procedure for the design of nozzles used for the production of turbulent liquid jets

Where turbulent liquid jets are used for cutting and mining purposes the pressure generated by impact must be maximized. Initial jet behaviour has an important influence on subsequent jet impact pressures at medium range. Nozzle wall boundary layer history has a strong influence on the initial jet, and certain boundary layer features can be linked to poor jet performance. The procedure outlined in this paper was developed to eliminate new nozzle designs or changes in operating conditions on the grounds of badly behaved nozzle boundary flow. The design procedure consists of a potential flow analysis and a boundary layer analysis coupled to empirical correlations for boundary layers in accelerated flows. The procedure is exemplified by application to the design of a nozzle to be used for the specific purpose of mining china clay.

Homogeneous nucleation of sulfur hexafluoride clusters in Laval nozzle molecular beams

The condensation of SF6 in Ar and He carrier gases has been studied in diverging Laval nozzles with throat diameters in the range of 0.1 to 0.2 mm. The clustering is detected using laser scattering, molecular beam intensity measurements, and high energy electron diffraction. Although the nozzles have cooling rates in the 107 °C/sec range, the correction for nucleation lag time results in changes which are less than 15% from the steady state rate theory. For 3% SF6 in Ar the onset may enter the Ar supersaturation region with the attendant possibility for binary nucleation. Even though these expansions are not isentropic, due to nozzle wall boundary layers, they are nevertheless much more effective cluster sources than the ’’isentropic’’ free jet expansions. The onset of condensation is consistent with earlier results for much larger nozzles and agrees with the classical Volmer theory.

A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1

A three-dimensional ‘turbulent spot’ has been induced in the axisymmetric free mixing layer of a 12.7 cm diameter air jet by a spark generated at the nozzle boundary layer upstream of the exit. The spot coherent-structure signature, buried in the large-amplitude random fluctuating signal, has been educed at three downstream stations within the apparent self-preserving region of the mixing layer (i.e. x/D = 1.5, 3.0 and 4.5) at the jet exit speed of 20 ms−1. The eduction has been performed through digital phase averaging of the spot signature from 200 realizations. In order to reduce the effect of the turbulence-induced jitter on the phase average, individual filtered signal arrays were optimally time-aligned through an iterative process of cross-correlation of each realization with the ensemble average. Further signal enhancement was achieved through rejection of realizations requiring excessive time shifts for alignment. The number of iterations required and the fraction of realizations rejected progressively increase with the downstream distance and the radial position.The mixing-layer spot is a large-scale elongated structure spanning the entire width of the layer but does not appear to exhibit a self-similar shape. The dynamics of the mixing-layer spot and its eduction are more complicated than those of the boundary-layer spot. The spot initially moves downstream essentially at a uniform speed across the mixing layer, but further downstream it accelerates on the high-speed side and decelerates on the low-speed side. This paper discusses the data acquisition and processing techniques and the results based on the streamwise velocity signals. Phase average distributions of vorticity, pseudo-streamlines, coherent and background Reynolds stresses and further dynamics of the spot are presented in part 2 (Hussain, Kleis &amp; Sokolov 1980).

Measurements of Flowfield Properties in a Gasdynamic Laser Nozzle Wake

Detailed measurements were made in the nonreacting (cold-flow) wake of a gasdynamic laser (GDL) nozzle array to provide flowfield data with which to evaluate theoretical GDL fluid mechanical models and numerical prediction schemes. Pitot pressure, stagnation temperature, and static pressure measurements were made across the wake and along the wake centerline at twelve streamwise locations and at two nozzle Reynolds numbers. Redundant static pressure measurements were made to identify and correct any probe interference errors caused by the small dimensional wake scales. Pitot measurements across the GDL nozzle boundary layer were included to provide information on the initial conditions to the wake, and hot wires were used to identify the regions of the wake where turbulence exists. Measured wake centerline static pressures were observed to be as much as 40% higher than wake edge static pressures. Turbulent wake centerline data and lateral wake profiles showed good agreement with predictions from an existing linearized similarity theory for turbulent GDL wakes. Measurements in a transitional wake indicated that transition begins near the wake edge and moves toward the wake centerline as Reynolds number is increased. Centerline flow properties observed in the transitional wake could not be predicted by transitional linearized similarity theory.