Analysis of Pulsating Flows in Infinite and Finite Conical Nozzles

1969 ◽  
Vol 36 (2) ◽  
pp. 159-170 ◽  
Author(s):  
T. Chiang ◽  
F. C. Hsing ◽  
C. H. T. Pan ◽  
H. G. Elrod
Keyword(s):  
Mach Number ◽  
Dynamic Characteristics ◽  
Mass Flux ◽  
Nozzle Exit ◽  
Nozzle Geometry ◽  
Additional Parameter ◽  
Conical Nozzle ◽  
High Frequencies ◽  
Exit Mach Number ◽  
Flux Response

The pulsating flows in both infinite and finite conical nozzles were analyzed theoretically. Sinusoidal pressure disturbances were impressed at the nozzle exit for the infinite nozzle and at either the inlet or at the exit for the case of a finite nozzle. The results have been calculated in terms of mass-flux response. The parameters involved are the Mach number and the modified Strouhal number; the inlet and exit radii ratio enters as an additional parameter for a finite nozzle. The results for an infinite conical nozzle indicate that, when the frequency is low, the quasistatic relationship between the pressure and mass-flux fluctuations holds; the same was reported in reference [1]. But, as the frequency increases, the dynamic characteristics of the pulsating flow become important. And, at high frequencies, the mass-flux response is less than the quasistatic value by an amount depending on the Mach number. For a finite conical nozzle the quasistatic condition is still valid if the frequency is low. However, at higher frequencies, the dynamic behavior becomes critically dependent on the frequency expressed in terms of w, for a given nozzle geometry and exit Mach number.

Development of a Supersonic Ejector for Capturing Very Low-Pressure Vent Gases and Re-Injection Into a High-Pressure Gas Stream

2006 ◽  
Author(s):  
K. K. Botros ◽  
J. Geerligs ◽  
H. Imran ◽  
W. Thompson
Keyword(s):  
Mach Number ◽  
Optimum Design ◽  
Nozzle Exit ◽  
Pressure Ratio ◽  
Supersonic Nozzle ◽  
Low Pressure ◽  
Fuel Gas ◽  
Dry Gas Seal ◽  
Supersonic Ejector ◽  
Exit Mach Number

The purpose of the ejector device is to capture the gas leakage from a dry-gas seal at low pressure, and re-inject it into the fuel gas line to the gas generator (without the use of compressors or rotating elements), hence providing a means to utilize the gas that would otherwise be vented to atmosphere. Implementation of this device will also have the benefit of reducing greenhouse gas emissions to the atmosphere. The primary challenge to achieve the above goal lies in the fact that the leakage gas pressure is in the range of 70–340 kPag, while the minimum pressure required upstream of the fuel gas regulator is in the range of 2400–3300 kPag. The device consists of a two-stage supersonic ejector. The first stage is highly supersonic (nozzle exit Mach number ≃ 2.54), while the second stage is moderately supersonic (nozzle exit Mach number ≃ 1.72). Several tests where conducted on various configurations of the two stages on natural gas in order to arrive at the optimum design and operating parameters. The optimum design gave an expansion pressure ratio (motive/suction) of the order of 14.0 and compression pressure ratio (discharge/suction) of around 8.1. These ratios would meet the requirement of the minimum suction and discharge pressure mentioned above. This paper presents the optimum configuration arrived at after several iterations of different geometries of the supersonic nozzles, particularly for the first stage ejector, and presents the performance test results of the integrated system. The results indicate that the device would meet the requirements of capturing the low pressure, low flow dry gas seal leakage and re-inject it into the fuel gas stream with an overall ejector efficiency (based on thermodynamic availability) of 80%.

The Axisymmetric Impingement of Supersonic Air Jets on Cones

1980 ◽  
Vol 31 (1) ◽  
pp. 26-41 ◽  
Author(s):  
I.K. Jennions ◽  
B.L. Hunt
Keyword(s):  
Experimental Investigation ◽  
Mach Number ◽  
Pressure Distribution ◽  
Surface Pressure ◽  
Nozzle Exit ◽  
Ambient Pressure ◽  
Free Jet ◽  
Air Jets ◽  
Surface Pressure Distribution ◽  
Exit Mach Number

SummaryThis paper reports an experimental investigation into the impingement of three jets from a convergent, conically divergent nozzle on to three cones of apex angles 120°, 90° and 60°. The exit Mach number of the nozzle was 2.2 and the jets were produced by operating with ratios of nozzle lip pressure to ambient pressure of 1, 1.2 and 2. The cones were arranged symmetrically in the jets at nozzle to apex distances of 0, 1 and 2 times the nozzle exit diameter. Surface pressures and shadowgraph pictures are presented. The most striking feature of the flows is the shock pattern produced by the interaction between the cone shock and the jet shock. This pattern can take a wide variety of forms depending on the structure of the free jet and strongly influences the form of the surface pressure distribution. For the most part, the flows can be explained on the basis of inviscid behaviour.

Numerical Modeling of Heat Transfer and Pressure Losses for Uncooled Gas Turbine Blade Tip: Effect of Tip Clearance and Tip Geometry

2007 ◽  
Author(s):  
Lamyaa A. El-Gabry
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Gas Turbine ◽  
Computational Study ◽  
Numerical Models ◽  
Pressure Ratio ◽  
Tip Clearance ◽  
Pressure Losses ◽  
Blade Tip ◽  
Exit Mach Number

A computational study has been performed to predict the heat transfer distribution on the blade tip surface for a representative gas turbine first stage blade. CFD predictions of blade tip heat transfer are compared to test measurements taken in a linear cascade, when available. The blade geometry has an inlet Mach number of 0.3 and an exit Mach number of 0.75, pressure ratio of 1.5, exit Reynolds number based on axial chord of 2.57×106, and total turning of 110 deg. Three blade tip configurations were considered; they are flat tip, a full perimeter squealer, and an offset squealer where the rim is offset to the interior of the tip perimeter. These three tip geometries were modeled at three tip clearances of 1.25, 2.0, and 2.75% of blade span. The tip heat transfer results of the numerical models agree fairly well with the data and are comparable to other CFD predictions in the open literature.

scholarly journals Aerodynamic Losses in Turbines with and without Film Cooling, as Influenced by Mainstream Turbulence, Surface Roughness, Airfoil Shape, and Mach Number

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Phil Ligrani
Keyword(s):  
Surface Roughness ◽  
Mach Number ◽  
Film Cooling ◽  
Total Pressure ◽  
High Speed ◽  
Density Ratio ◽  
Aerodynamic Loss ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Exit Mach Number

The influences of a variety of different physical phenomena are described as they affect the aerodynamic performance of turbine airfoils in compressible, high-speed flows with either subsonic or transonic Mach number distributions. The presented experimental and numerically predicted results are from a series of investigations which have taken place over the past 32 years. Considered are (i) symmetric airfoils with no film cooling, (ii) symmetric airfoils with film cooling, (iii) cambered vanes with no film cooling, and (iv) cambered vanes with film cooling. When no film cooling is employed on the symmetric airfoils and cambered vanes, experimentally measured and numerically predicted variations of freestream turbulence intensity, surface roughness, exit Mach number, and airfoil camber are considered as they influence local and integrated total pressure losses, deficits of local kinetic energy, Mach number deficits, area-averaged loss coefficients, mass-averaged total pressure loss coefficients, omega loss coefficients, second law loss parameters, and distributions of integrated aerodynamic loss. Similar quantities are measured, and similar parameters are considered when film-cooling is employed on airfoil suction surfaces, along with film cooling density ratio, blowing ratio, Mach number ratio, hole orientation, hole shape, and number of rows of holes.

Investigation of the 3D Unsteady Rotor Pressure Field in a HP Turbine Stage

2002 ◽  
Author(s):  
E. Valenti ◽  
J. Halama ◽  
R. De´nos ◽  
T. Arts
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Field ◽  
Pressure Ratio ◽  
Turbine Stage ◽  
Time Resolved ◽  
Mach Number Distribution ◽  
Rotor Surface ◽  
Exit Mach Number ◽  
Unsteady Pressure Measurements

This paper presents steady and unsteady pressure measurements at three span locations (15, 50 and 85%) on the rotor surface of a transonic turbine stage. The data are compared with the results of a 3D unsteady Euler stage calculation. The overall agreement between the measurements and the prediction is satisfactory. The effects of pressure ratio and Reynolds number are discussed. The rotor time-averaged Mach number distribution is very sensitive to the pressure ratio of the stage since the incidence of the flow changes as well as the rotor exit Mach number. The time-resolved pressure field is dominated by the vane trailing edge shock waves. The incidence and intensity of the shock strongly varies from hub to tip due to the radial equilibrium of the flow at the vane exit. The decrease of the pressure ratio attenuates significantly the amplitude of the fluctuations. An increase of the pressure ratio has less significant effect since the change in the vane exit Mach number is small. The effect of the Reynolds number is weak for both the time-averaged and the time-resolved rotor static pressure at mid-span, while it causes an increase of the pressure amplitudes at the two other spans.

Loss Generation in Transonic Turbine Blading

2017 ◽  
Author(s):  
Penghao Duan ◽  
Choon S. Tan ◽  
Andrew Scribner ◽  
Anthony Malandra
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mach Number ◽  
High Speed ◽  
Turbine Blades ◽  
Surface Boundary ◽  
Loss Model ◽  
Exit Mach Number ◽  
Loss Characteristic ◽  
Shock Loss

The measured loss characteristic in a high-speed cascade tunnel of two turbine blades of different designs showed distinctly different trend with exit Mach number ranging from 0.8 to 1.4. Assessments using steady RANS computation of the flow in the two turbine blades, complemented with control volume analyses and loss modelling, elucidate why the measured loss characteristic looks the way it is. The loss model categorizes the total loss in terms of boundary layer loss, trailing edge loss and shock loss; it yields results in good agreement with the experimental data as well as steady RANS computed results. Thus RANS is an adequate tool for determining the loss variations with exit isentropic Mach number and the loss model serves as an effective tool to interpret both the computational and experimental data. The measured loss plateau in Blade 1 for exit Mach number of 1 to 1.4 is due to a balance between a decrease of blade surface boundary layer loss and an increase in the attendant shock loss with Mach number; this plateau is absent in Blade 2 due to a greater rate in shock loss increase than the corresponding decrease in boundary layer loss. For exit Mach number from 0.85 to 1, the higher loss associated with shock system in Blade 1 is due to the larger divergent angle downstream of the throat than that in Blade 2. However when exit Mach number is between 1.00 and 1.30, Blade 2 has higher shock loss. For exit Mach number above around 1.4, the shock loss for the two blades is similar as the flow downstream of the throat is completely supersonic. In the transonic to supersonic flow regime, the turbine design can be tailored to yield a shock pattern the loss of which can be mitigated in near equal amount of that from the boundary layer with increasing exit Mach number, hence yielding a loss plateau in transonic-supersonic regime.

scholarly journals Effects of Tip Clearance Gap and Exit Mach Number on Turbine Blade Tip and Near-Tip Heat Transfer

2013 ◽  
Author(s):  
K. Anto ◽  
S. Xue ◽  
W. F. Ng ◽  
L. J. Zhang ◽  
H. K. Moon
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Turbine Blade ◽  
Leading Edge ◽  
Suction Side ◽  
Tip Clearance ◽  
Pressure Side ◽  
Engine Blade ◽  
Blade Tip ◽  
Exit Mach Number

This study focuses on local heat transfer characteristics on the tip and near-tip regions of a turbine blade with a flat tip, tested under transonic conditions in a stationary, 2-D linear cascade with high freestream turbulence. The experiments were conducted at the Virginia Tech transonic blow-down wind tunnel facility. The effects of tip clearance and exit Mach number on heat transfer distribution were investigated on the tip surface using a transient infrared thermography technique. In addition, thin film gages were used to study similar effects in heat transfer on the near-tip regions at 94% height based on engine blade span of the pressure and suction sides. Surface oil flow visualizations on the blade tip region were carried-out to shed some light on the leakage flow structure. Experiments were performed at three exit Mach numbers of 0.7, 0.85, and 1.05 for two different tip clearances of 0.9% and 1.8% based on turbine blade span. The exit Mach numbers tested correspond to exit Reynolds numbers of 7.6 × 105, 9.0 × 105, and 1.1 × 106 based on blade true chord. The tests were performed with a high freestream turbulence intensity of 12% at the cascade inlet. Results at 0.85 exit Mach showed that an increase in the tip gap clearance from 0.9% to 1.8% translates into a 3% increase in the average heat transfer coefficients on the blade tip surface. At 0.9% tip clearance, an increase in exit Mach number from 0.85 to 1.05 led to a 39% increase in average heat transfer on the tip. High heat transfer was observed on the blade tip surface near the leading edge, and an increase in the tip clearance gap and exit Mach number augmented this near-leading edge tip heat transfer. At 94% of engine blade height on the suction side near the tip, a peak in heat transfer was observed in all test cases at s/C = 0.66, due to the onset of a downstream leakage vortex, originating from the pressure side. An increase in both the tip gap and exit Mach number resulted in an increase, followed by a decrease in the near-tip suction side heat transfer. On the near-tip pressure side, a slight increase in heat transfer was observed with increased tip gap and exit Mach number. In general, the suction side heat transfer is greater than the pressure side heat transfer, as a result of the suction side leakage vortices.

Effects of Shock Wave Development on Secondary Flow Behavior in Linear Turbine Cascade at Transonic Condition

2020 ◽  
Author(s):  
Hoshio Tsujita ◽  
Masanao Kaneko
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Secondary Flow ◽  
Turbine Blade ◽  
Gas Turbines ◽  
Flow Behavior ◽  
Turbine Cascade ◽  
Blade Loading ◽  
Passage Vortex ◽  
Exit Mach Number

Abstract Gas turbines widely applied to power generation and aerospace propulsion systems are continuously enhanced in efficiency for the reduction of environmental load. The energy recovery efficiency from working fluid in a turbine component constituting gas turbines can be enhanced by the increase of turbine blade loading. However, the increase of turbine blade loading inevitably intensifies the secondary flows, and consequently increases the associated loss generation. The development of the passage vortex is strongly influenced by the pitchwise pressure gradient on the endwall in the cascade passage. In addition, a practical high pressure turbine stage is generally driven under transonic flow conditions where the shock wave strongly influences the pressure distribution on the endwall. Therefore, it becomes very important to clarify the effects of the shock wave formation on the secondary flow behavior in order to increase the turbine blade loading without the deterioration of efficiency. In this study, the two-dimensional and the three-dimensional transonic flows in the HS1A linear turbine cascade at the design incidence angle were analyzed numerically by using the commercial CFD code with the assumption of steady compressible flow. The isentropic exit Mach number was varied from the subsonic to the supersonic conditions in order to examine the effects of development of shock wave caused by the increase of exit Mach number on the secondary flow behavior. The increase of exit Mach number induced the shock across the passage and increased its obliqueness. The increase of obliqueness reduced the cross flow on the endwall by moving the local minimum point of static pressure along the suction surface toward the trailing edge. As a consequence, the increase of exit Mach number attenuated the passage vortex.

Nozzle Geometry Effect on Twin Jet Flow Characteristics

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Muthuram A ◽  
Thanigaiarasu S ◽  
Rakesh Divvela ◽  
Rathakrishnan Ethirajan
Keyword(s):  
Mach Number ◽  
Flow Characteristics ◽  
Nozzle Geometry ◽  
Ambient Atmosphere ◽  
Free Jets ◽  
Twin Jets ◽  
Equivalent Area ◽  
Nozzle Configuration ◽  
Jet Nozzle ◽  
Nozzle Geometries

AbstractEffect of nozzle geometries on the propagation of twin jet issuing from nozzles with circle-circle, circle-ellipse, circle-triangle, circle-square, circle-hexagon and circle-star geometrical combinations was investigated for Mach numbers 0.2, 0.4, 0.6 and 0.8. In all the cases, both jets in the twin jet had the same Mach number. All the twin jets of this study are free jets, discharged into stagnant ambient atmosphere. The result of the twin jets issuing from circle-circle nozzle is kept as the reference in this study. For all the twin jet nozzles, the inter nozzle spacing; the distance between the nozzle axes (S) was 20 mm and all the nozzles had an equivalent area of 78.5 mm2. Thus for all the cases of the present study, S/D ratio is 2. The results show that the mixing of the combined jet, after the merging point is strongly influenced by the combined effect of the nozzle geometry and jet Mach number. Among the six different twin jet nozzle configuration studied, circle-square combination is found to be the most superior mixing promoter.

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