Axial Mach Number Research Articles

Similarity Solution for Magnetogasdynamic Shock Waves in a Weakly Conducting Perfect Gas by Using the Lie Group Invariance Method

Under axial and azimuthal magnetic inductions, the similarity solutions for a cylindrical shock wave in a weakly conducting ideal gas are determined using the Lie group invariance method. The axial and azimuthal magnetic inductions and density are presumed to vary in an ambient medium. This study determines the form of expression for axial and azimuthal magnetic inductions in the ambient medium. The ambient density is considered to be varying according to the power law of the shock radius. The weakly conducting medium causes inadequate magnetic freezing. We have numerically solved the system of ordinary differential equations that resulted from applying the Lie group invariance method to the system of partial differential equations. The impact of the variation in the ambient density exponent, the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers on the shock strength and the flow variables behind the shock front is discussed. It is found that the shock strength decreases with an increase in the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers.

The acoustic impedance of three-dimensional turbines

Thermoacoustic stability assessment of gas turbine combustors requires an acoustic impedance boundary condition for the downstream turbomachinery. Actuator disk type analytical methods offer rapid predictions of acoustic impedance in an iterative design process; previous studies show that this class of models works well for cascades consistent with a two-dimensional assumption. Real turbines, however, are three-dimensional with multiple stages, coolant flows, and leakage flows. The first part of this paper validates a cambered semi-actuator disk model for the acoustic impedance of a realistic multi-stage turbine using non-linear time-marching computations: the two methods agree to within 9% for incident pressure waves and 14% for incident entropy waves. Simulations of the multi-stage turbine with different inlet conditions confirm that, to a close approximation, inlet corrected flow and hence Mach numbers and acoustic impedance are constant during off-design operation. The second part of the paper then applies both analytical and computational approaches to families of parametrically generated turbine stages to quantify three-dimensional design effects. The results show that the influence of hub-to-tip ratio on acoustic impedance is weak, and the two-dimensional analytical model is accurate even for high aspect ratio stages. Front-loaded camber lines increase axial Mach number within blade passages, raising acoustic impedance by up to 51% compared to a datum quadratic camber line. Varying the stator–rotor axial gap changes the relative phase of reflections from vanes and blades, causing the total impedance to either increase or decrease, at different frequencies, by up to 11%. The cambered semi-actuator disk method consistently captures the correct trends, showing that the physical basis of the model is sufficient to produce a broadly applicable design tool for rapid assessment of turbine impedance boundary conditions.

Preliminary Optimization of Multi-Stage Axial-Flow Industrial Process Compressors Using Aero-Engine Compressor Design Strategy

Aero-engine core compressor preliminary design strategy has been successfully applied to the advanced design of gas turbines compressors. However, few researchers have addressed the application of the aero-engine core compressor preliminary design strategy in the preliminary optimal design of industrial process compressors. Here we embedded the aero-engine core compressor preliminary design strategy into a preliminary optimal design method, in which six types of design parameters widely used to define the aero-engine compressor configuration, i.e., aspect ratio, solidity, reaction, rotation speed, outlet axial Mach number, and inlet radius ratio, were used as the design variables. The 4-stage, 5-stage, 6-stage, and 7-stage compressor configuration with the same overall design requirements for a large-scale air separation main compressor were preliminarily optimized by the developed method, in which the 4-stage design has a stage pressure rise level of current aero-engine core compressors, whereas the 7-stage design has that of current industrial process compressors. The optimized compressor configurations were then refined with the throughflow-based detailed design method and finally verified with computational fluid dynamic simulations. It is found that the developed method can optimize design efficiency and accurately predict aerodynamic performance of compressors in a few minutes. Several design guidelines for the advanced industrial process compressors were also identified. This work is of significance in extending aero-engine core compressor design strategy to the design of advanced industrial process compressors.

A preliminary study on static pressure probe mobile measurement method for flow field in transonic wind tunnel

The axial Mach number distribution of the core flow for model in a transonic wind tunnel is an important index to evaluate the performance of the flow field, which is usually measured by the centerline probe. In order to simulate the incoming flow characteristics without interference, the probe will extend from the support section to the shrinkage section, so the probe usually must has longer inches, more static pressure measuring points and smaller blockage requirements. In order to study the influence of the points of the centerline probe on the uniformity distribution of flow field, a new static pressure probe is designed, which is smaller and shorter than the centerline probe. On the basis of the stability of the flow field, the Mach number distribution of the flow field measured by the static pressure probe which is driven by the moving measuring mechanism. The characteristics of the measured values are studied by wind tunnel test. The results show that: when Ma ≤ 0.95, the overall distribution and value of Mach number obtained by the static pressure probe is basically the same as those obtained by the centerline probe, but some flow field details, which mainly shows that Mach number of the static pressure probe has smaller fluctuation, higher accuracy and better uniformity index.

Experimental assessment of the rotor outlet flow in a twin-entry radial turbine by means of Laser Doppler Anemometry

The current paper presents the validation of some hypotheses used for developing a one-dimensional twin-entry turbine model with experimental measurements. A Laser Doppler Anemometry (LDA) technique has been used for measuring the axial Mach number and for counting the number of particles downstream of the rotor outlet. These measurements have been done for different mass flow ratio (MFR) and reduced turbocharger speed conditions. The flow coming from each turbine entry does not fully mix with the other within the rotor since, downstream of the rotor, they can still be differentiated. Thus, the hypothesis of studying twin-entry turbines as two separated single-entry turbines in one-dimensional models is corroborated. Moreover, the rotor outlet area corresponding to each flow branch has linear trends with the MFR value. Therefore, the rotor outlet effective area used for one-dimensional models should vary linearly with the MFR value.

Modelling Turbine Acoustic Impedance

We quantify the sensitivity of turbine acoustic impedance to aerodynamic design parameters. Impedance boundary conditions are an influential yet uncertain parameter in predicting the thermoacoustic stability of gas turbine combustors. We extend the semi-actuator disk model to cambered blades, using non-linear time-domain computations of turbine vane and stage cascades with acoustic forcing for validation data. Discretising cambered aerofoils into multiple disks improves reflection coefficient predictions, reducing error by up to an order of magnitude compared to a flat plate assumption. A parametric study of turbine stage designs using the analytical model shows acoustic impedance is a weak function of degree of reaction and polytropic efficiency. The design parameter with the strongest influence is flow coefficient, followed by axial velocity ratio and Mach number. We provide the combustion engineer with improved tools to predict impedance boundary conditions, and suggest thermoacoustic stability is most likely to be compromised by change in turbine flow coefficient.

Measurementimprovement of flow quality of slotted test section in transonic wind tunnel

Experimental studies were carried out in the 0.6 m×0.6 m continuous transonic wind tunnel of CARDC in order to investigate the flow characteristics of the slotted test section. Experimental results show that the root-mean-square deviation of axial Mach number in the model area is above 0.01 when the test section Mach number is above 1.0.Numerical simulation under the same conditions to investigate the flow characteristics of the slotted section, together with the experimental studies indicate tow phenomena may directly cause the Mach number fluctuation. Firstly, a straight section was installed to connect the nozzle and the test section in the wind tunnel. Weak shock waves due to the curvature discontinuity at the joint of the test section and the straight section contribute to Mach number fluctuation. Secondly, the open-area ratio of both the upper and lower wall of test section, each with 8 slots, is of 10%. The larger porosity leads to stronger expansion waves in the acceleration zone located at the inlet of the test section. The flow was over accelerated because of the stronger expansion wave and thus fluctuate the flow field severely. Two measures were taken to improve the flow quality of the slotted test section based on the above-mentioned analysis: ①Flexible plate instead of solid straight plate was installed to bridge nozzle and test section to eliminate the curvature discontinuity; ②Decreasing the open-area ratio of the upper and lower test section wall to 6% and the number of slots to 6. Numerical and experimental results show that the Mach number fluctuation in the model area was suppressed to a satisfactory degree.

Analytical solutions of acoustic field in annular combustion chambers with non-uniform cross-sectional surface area and mean flow

Low-order acoustic network models, treating the complex combustor geometry as a network of simple geometry elements, are typically used to analyse circumferential combustion instabilities in annular combustion chambers. These elements are typically assumed to have uniform cross-sectional surface area and average radius so that the analytical solutions of the acoustic field within them can be directly obtained. However, this may lead to errors in the combustion instability analyses. The present work derives the analytical solutions of the acoustic field in annular combustion chambers with both varying cross-sectional surface area and average radius sustaining a mean flow. A wave equation for the pressure perturbation is firstly derived based on very few assumptions. Analytical solutions of the acoustic field are then derived based on a modified WKB approximation. These solutions are then validated by comparing them to results by numerically resolving the linearised Euler equations. Results show that accurate predictions can always be obtained for a smooth change of the cross-sectional surface area and small-to-moderate subsonic axial Mach numbers as long as the frequency is larger than a certain value.

Pitot probe response for pulsed supersonic gas flow characterization in beam profile monitor.

For beam profile measurement of high-intensity proton beams in the low-energy high-intensity proton accelerator at Bhabha Atomic Research Centre, a recent noninvasive technique based on gas sheets will be explored. The gas sheet for this instrument needs to be characterized for calibration and fine tuning of the sheet properties to provide better profile measurements. Pulsed sheet generators for similar applications have been characterized using movable vacuum chambers with a small slit and a gauge mounted inside. Pitot probes are more compact instruments and have been used to measure gas jet profiles in molecular beam applications where the jet was not pulsed. The performance of Pitot probes in the measurement of pulsed supersonic gas flow in vacuum was, therefore, investigated in this work. A test system was developed to generate a pulsed supersonic gas jet in vacuum, and a Pitot probe was inserted into the flow at various axial locations with respect to the nozzle. Measurements taken along the nozzle axis using this probe, as well as the axial Mach number and impact pressure computed using computational fluid dynamics and direct simulation Monte Carlo algorithms, were compared with fitting formulas. Schlieren images of the jet with and without the Pitot tube were also taken under different vacuum conditions.

On determining the vortex core center in wing wake at M = 2

The paper presents the processing of the results of numerical simulation of the vortex flow in the wing wake, the purpose of which is to search for the vortex core center. It is based on the results of numerical simulation of the vortex flow in the wake behind of the rectangular wing, performed at the Keldysh Institute of Applied Mathematics RAS. The center of the vortex core was determined in several ways: by the minima of the total and static pressure, the axial Mach number, mass flow rate, the maximum of axial vorticity, and as the center of mass of the axial vorticity distribution. A comparison of the results of determining the position of the vortex core center showed good quantitative agreement. As a result dependencies of vortex core center coordinates on longitudinal coordinate were obtained.

Modal cut-on ratio in ducts with realistic flow profiles and its application to acoustic mode detection

This paper considers the modal cut-on ratio and its use in acoustic mode detection in ducts for a radially varying flow with swirl. These concepts have previously only been considered for the idealised case of uniform axial mean flow and no swirl, and thus in this paper they are generalised and extended to account for radial variations in axial and swirl Mach numbers. The cut-on ratio is shown to no longer satisfy a simple relation with the axial wavenumber, showing that while the cut-on ratio in arbitrary flow is defined its usefulness significantly decreases. Mode distribution functions are also investigated for radially varying flows, both in terms of cut-on ratio and axial wavenumber. In view of the deficiencies of the cut-on ratio highlighted in the paper a recent method for mode detection in ducts that uses just two microphones is generalised to deduce the mode amplitudes in radially varying flows, based on modal axial wavenumber rather than cut-on ratio. This method is shown to perform better than the existing method in radially varying and/or swirling flow in simple test configurations with an idealised source distribution.

Vortex breakdown of compressible subsonic swirling flows in a finite-length straight circular pipe

A global analysis of steady states of inviscid compressible subsonic swirling flows in a finite-length straight circular pipe is developed. A nonlinear partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. The equation reflects the complicated thermo–physical interactions in the flows. Several types of solutions of the resulting nonlinear ordinary differential equation for the columnar case together with a flow force condition describe the outlet state of the flow in the pipe. These solutions are used to form the bifurcation diagram of steady compressible flows with swirl as the inlet swirl level is increased at a fixed inlet Mach number. The approach is applied to two profiles of inlet flows, solid-body rotation and the Lamb–Oseen vortex, both with a uniform axial velocity and temperature. The computed results provide for each inlet flow profile theoretical predictions of the critical swirl levels for the appearance of vortex breakdown states as a function of the inlet Mach number, suggesting that the results are robust for a variety of inlet swirling flows. The analysis sheds light on the dynamics of compressible flows with swirl and vortex breakdown, and shows the delay in the appearance of breakdown with increase of the inlet axial flow Mach number in the subsonic range of operation. The present theory is limited to axisymmetric dynamics of swirling flows in pipes where the wall boundary layer is thin and attached and does not interact with the flow in the bulk.

Design and analysis of pioneering high supersonic axial turbines

The trend towards ultra compact thermal power generation, is constrained by the unavailability of fluid-machinery adequate for supersonic flow conditions. Conventional turbine designs exhibit unacceptable performances related to large aerodynamic losses and a narrow operation range. This paper provides for the first time in the open literature the design procedure, and subsequent analysis of the turbine performance of a turbine adequate for supersonic axial pulsating flows, as those encountered in innovative combustors. The design approach considers the most adverse condition, a steady inlet axial Mach number equal to 3.5. The possible turbine families were classified by the velocity triangles and discussed. A fundamental issue in supersonic passages is to ensure the normal shock at the start of the engine is swallowed through the turbine passages, namely the turbine passage is started. To ensure self-starting capability the turning is restricted to lower values than in the conventional subsonic turbines. The design procedure was based on the method of characteristics, converting the inlet uniform flow into a vortex flow field, such that the adequate deflection is inflicted to the supersonic flow. The performance of the supersonic passage was first assessed and then compared to conventional designs. The present design procedure and analysis of unconventional supersonic turbines provides guidelines for the design and optimization of efficient high supersonic passages, suitable to future tightly packed fluid machinery.

The Influence of the Total Pressure Profile on the Performance of Axial Gas Turbine Diffusers

Large industrial gas turbines for combined heat and power generation normally have axial diffusers leading to the heat recovery steam generator. The diffusers operate with high inlet axial Mach number (0.6) and with a nonuniform inlet total pressure profile from the turbine. Tests have been carried out on a generic highly loaded axial diffuser in a scaled axial diffuser test rig, with different inlet total pressure profiles including those that might be met in practice. The results show that the inlet total pressure profile has a strong effect on the position of flow separation, whereby a hub-strong profile tends to separate at the casing and the tip-strong profile on the hub. Steady computational fluid dynamics (CFD) simulations using the shear stress transport (SST) turbulence model have been carried out based on extensive studies of the best way to model the inlet boundary conditions. These simulations provide good agreement with the prediction of separation in the diffuser but the separated regions often persist too long so that, in this highly loaded case with flow separation, the calculated diffuser pressure recovery can be in error by up to 30%.

Swirling Airflow Through a Nozzle: Choking Criteria

Since the mass flow rate through nozzle is primarily a function of throat density and axial Mach number, the reductioninthelatterwithswirlexplainstheobservedreductioninmass flowatmatchedreservoirpressure.Greater pressures, on the other hand, result in higher throat densities, which compensates for the reduced axial Mach number,andthemass flowratecanbekeptconstantatitsnonswirlingvalue.Itwasalsofoundthatthedistributionof subsonicMachnumber(andnotanyofitscomponents)inaswirling flowissolelydependentoncross-sectionalarea, similar to nonswirling flows; i.e., nonswirling and swirling flows have the same subsonic Mach number profile. In terms of thrust and specific impulse, the application of swirl at matched nozzle reservoir pressure results in the expected reductions in discharge coefficient, thrust, and specific impulse. At matched mass flow, however, the application of swirl results in the enhancement of both thrust and specific impulse. This is attributed to the considerable degree of underexpansion associated with the swirling flow as a result of the higher nozzle reservoir pressure with swirl.

The importance of sensitive parameters effect on the combustion in a high velocity oxygen-fuel spray system

In this study computational fluid dynamics (CFD) model has been developed to predict gas dynamic behavior in a High Velocity Oxygen-Fuel (HVOF) thermal spray gun in which premixed oxygen and propane are burnt in a combustion chamber linked to a parallel-sided nozzle. The CFD analysis is applied to investigate axisymmetric, steady-state, turbulent, compressible, chemically reacting, subsonic and supersonic flow inside and outside the gun. The gas velocity, temperature, pressure and Mach number distributions are presented for various locations inside and outside the gun. The calculated results show that the most sensitive parameters affecting the process are fuel-to-oxygen gas ratio and total gas flow rate. Gas dynamic behavior along the centerline of the gun depends on both total gas flow rate and fuel-to-oxygen gas ratio. The numerical simulations show that the axial gas velocity and Mach number distribution depend on both flow rate and ratio; the highest velocity is achieved at the higher flow rate and most fuel-rich ratio. In addition, the results reported in this paper illustrate that the numerical simulation can be one of the most powerful and beneficial tools for the HVOF system design, optimization and performance analysis.

Numerical Three-Dimensional Pressure Patterns in a Recess of a Turbulent and Compressible Hybrid Journal Bearing

The present work investigates the flow in the feeding recess of a hybrid journal bearing. Numerical integration of the complete Navier-Stokes equations was performed with an appropriate turbulence model. Of primary concern is the pressure field on the rotating journal surface that is commonly known as the recess pressure pattern. The goal of the work is to determine the influences of fluid compressibility, operating conditions and recess geometry. Reference parameters selected for this study comprise feeding Reynolds number Rea of 2.105, sliding Reynolds number Rec of 5.103 and recess depth over film thickness ratio e/H of 2.2. Compressibility was considered first. Three values of the axial exit Mach number were selected for computation, namely 0.2, 0.45, and 0.7. As no significant variation was found, the Mach number was fixed at 0.45 in subsequent studies concerning other parameters: Feeding Reynolds number, Rea 2.104,2.105,4.105 Recess depth, e/H 0, 2.2, 8 Feedhole axis inclination 90°, 135°, 165° Feedhole location (Figs. 1(a) and 13) centered, downstream offset. As each parameter is varied, wire mesh plot of pressure and its sectional profiles are examined and effects of varying various parameters are discussed in reference to flow processes as they may affect the support characteristics of the hybrid journal bearing.

Three-dimensional flow in a cylinder with sidewall mass addition

Three-dimensional, time-dependent, nonlinear flow dynamics within a cylinder with sidewall mass injection are investigated. A nonaxisymmetric transient injection velocity, prescribed along the sidewall boundary of a long, narrow, half-open cylinder, induces a low Mach number, high Reynolds number flow. The injection drives nearly planar axial acoustic disturbances, which interact with the injected fluid to produce the azimuthal component of vorticity on the sidewall in an inviscid manner. A smaller, but important azimuthally dependent transient disturbance, driven by the nonaxisymmetric injection disturbance leads to the axial component of vorticity on the cylinder sidewall. Both components of vorticity are shown to convect toward the center of the cylinder, diffuse radially, and convect downstream. Other results show that the axial component of vorticity produced along the sidewall is largest near the maximum of a mass source distribution in the azimuthal dimension. The amplitude of the axial vorticity component decreases significantly away from the injection surface and at other azimuthal locations. The analysis of these flow processes is based on the full three-dimensional Navier–Stokes equations. A formal multiple-scale asymptotic analysis, based on the behavior of the axial Mach number M→0, is used to derive reduced equations. It is shown that the primary rotational flow response is described by a nonlinear, convection-diffusion equation.

Inlet/Compressor System Response to Short-Duration Acoustic Disturbances

Recent studies have shown that computations of unsteady high-speed inlet flows produce results that strongly depend on the compressor-face boundary condition. Traditionally applied boundary conditions have no experimentalverification, which leads to uncertainty and significant risks in development programs. Experimental information is offered that can serve as a basis for constructing realistic boundary conditions. Short-duration transients were investigated in a constant-area circular inlet attached to an operating high-speed, single-stage, axial flow compressor. The transients were initiated by the generation of short-duration acoustic pulses within the inlet, using an exploding wire method. Pulse duration was typically 2 ms, with a peak amplitude of 3% of the mean inlet static pressure measured at the compressor face. Fast-response wall-mounted pressure transducers were used to detect the incident, reflected, and transmitted pulses. Data were obtained for axial compressor-face Mach numbers from 0.15 to 0.45. Frequency-domain analysis was used to extract dimensionless transfer functions that may be viewed as frequency-resolved reflection and transmission coefficients. The information is appropriate for the characterization of the compressor face for computational purposes. None of the customary boundary conditions predict the data obtained in this study, highlighting the need to revise conventional methods of imposing outflow boundary conditions.

Measurements of leading-edge vortices on a 75° delta planform wing at M = 2.5

AbstractAn experimental study of the supersonic vortices from a 75° swept-back delta wing has been carried out in a Mach 2.49 stream. Five-hole conical probe surveys were conducted at the trailing edge of the planform for 7° and 12° angles-of-attack. The main objective was to determine the Mach number and pressure distributions in the primary vortex. A novel approach of utilising a computational flow solver was used to generate the calibration data for the five-hole probe over a range of Mach numbers and pitch angles. Measurements indicate significant static and total pressure deficits in the vortex core. Both the magnitude and the spatial scale of these deficits increase with the higher incidence angle. The swirl profiles have supersonic peak magnitudes and resemble the low speed Lamb-Oseen vortex. Similar to the case of supersonic wing tip vortices, and contrary to the experimental results from transonic and low speed leading-edge vortices, the axial Mach number distribution in the vortex core is found to have strong wake-like profile.