A Note on the Critical Pressure Ratio Across a Fluid Meter

1973 ◽  
Vol 95 (3) ◽  
pp. 337-341
Author(s):  
R. P. Benedict ◽  
R. D. Schulte
Keyword(s):  
Critical Pressure ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Numerical Studies

The concept of critical static pressure ratio across a fluid meter is first discussed. Various formulations for critical pressure ratios are then developed and solutions are tabulated for convenience. Conclusions, based on graphical and numerical studies, are drawn as to which critical pressure ratios apply in the various supercritical formulations.

Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
W. F. Fuls
Keyword(s):  
Finite Number ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Axial Flow ◽  
Nozzle Flow ◽  
Flow Equations ◽  
Numerical Studies ◽  
Multistage Turbine ◽  
Definition Of ◽  
Stage Analysis

This paper studies the origin and applicability of the traditional Stodola ellipse law and demonstrates its deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition of a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law (EL), especially for turbines with a low number of stages. It does, however, require knowledge of the choking behavior of the turbine, as well as an appropriate pressure ratio exponent. Through numerical studies and careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multistage turbine, taking nozzle and blade efficiency into account. Correlations are also presented to obtain an appropriate pressure ratio exponent to use in the semi-ellipse law. A methodology is proposed through which the necessary semi-ellipse law terms can be calculated using only design base conditions and estimates of efficiencies. This was successfully validated on a steam turbine. The semi-ellipse law is believed to be the most accurate way of modeling an axial-flow multistage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.

scholarly journals A new method for calculating the sonic conductance of airflow through a short-tube orifice

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401668726 ◽  
Author(s):  
Fan Yang ◽  
Gangyan Li ◽  
Dawei Hu ◽  
Toshiharu Kagawa
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Momentum Equation ◽  
Diameter Ratio ◽  
Test Method ◽  
Theoretical Formula ◽  
Engineering Applications ◽  
Short Tube ◽  
Length To Diameter Ratio

In this study, we proposed a method for calculating the sonic conductance of a short-tube orifice. First, we derived a formula for calculating the sonic conductance based on a continuity equation, a momentum equation and the definition of flow-rate characteristics. The flow-rate characteristics of different orifices were then measured using the upstream constant-pressure test method in ISO 6358. Based on these test data, the theoretical formula was simplified using the least squares fitting method, the accuracy of which was verified experimentally. Finally, the effects of the diameter ratio, the length-to-diameter ratio and the critical pressure ratio were analysed with reference to engineering applications, and a simplified formula was derived. We conclude that the influence of the diameter ratio is greater than that of the length-to-diameter ratio. When the length-to-diameter ratio is <5, its effect can be neglected. The critical pressure ratio has little effect on the sonic conductance of a short-tube orifice, and it can be set to 0.5 when calculating the sonic conductance in engineering applications. The formula proposed in this study is highly accurate with a mean error of <3%.

Numerical Studies of Novel Aero Engine Secondary Combustors for Low-NOx Emissions

2020 ◽  
Author(s):  
Andrew Rolt ◽  
Victor Martínez Bueno ◽  
Mirko Romanelli ◽  
Xiaoxiao Sun ◽  
Pierre Gauthier ◽  
...  
Keyword(s):  
Thermal Efficiency ◽  
Pressure Ratio ◽  
Flow Region ◽  
Nox Emissions ◽  
Low Oxygen ◽  
Engine Operation ◽  
Horizon 2020 ◽  
Novel Technologies ◽  
Numerical Studies ◽  
Aero Engine

Abstract Gas turbine thermal efficiency and fuel burn are very dependent on turbine entry temperature and overall pressure ratio (OPR). Unfortunately, increases in these two parameters compromise other key aspects of engine operation and tend to increase emissions of nitrogen oxides (NOx). The European Horizon 2020 ULTIMATE project researched advanced-cycle aero engines with synergistic combinations of novel technologies to increase thermal efficiency without increasing emissions. One candidate technology was the addition of secondary combustion to increase the mean temperature of heat addition to improve thermal efficiency while limiting the primary combustor flame temperatures and NOx formation. However, an overall reduction in NOx also requires the secondary combustor to be a low-NOx design. This paper describes numerical studies carried out on novel aero engine secondary combustor concepts developed in two MSc-thesis research projects. The studies have explored the potential of oxy-poor-flame combustion concepts. These annular combustor designs featured two distinct regions: (i) the vortex zone, which promotes recirculation of combustion products, a prerequisite for low-oxygen combustion, and (ii) a through-flow region where part of the incoming flow bypasses the vortex before the flows mix again. These studies have demonstrated the advantages and some limitations of the proposed designs and emissions assessments in comparison with previous secondary combustor studies. They suggest very low NOx is achievable with oxy-poor combustion, but will be more difficult if the incoming oxygen levels are above 10%. More-accurate assessments will require LES modelling and inclusion of the primary combustor in the simulations. However, if the low overall NOx emissions would include relatively higher levels of nitrous oxide (N2O) then this might raise concerns with respect to global warming.

An Investigation of Flow Characteristics and Parameter Effects for a New Concept of Hybrid SVC Nozzle

2018 ◽  
Author(s):  
F. Song ◽  
J. W. Shi ◽  
L. Zhou ◽  
Z. X. Wang ◽  
X. B. Zhang
Keyword(s):  
Static Pressure ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Exhaust System ◽  
Aircraft Engine ◽  
Thrust Coefficient ◽  
Thrust Vectoring ◽  
Static Pressure Distribution ◽  
Thrust Vector ◽  
Vector Angle

Lighter weight, simpler structure, higher vectoring efficiency and faster vector response are recent trends in development of aircraft engine exhaust system. To meet these new challenges, a concept of hybrid SVC nozzle was proposed in this work to achieve thrust vectoring by adopting a rotatable valve and by introducing a secondary flow injection. In this paper, we numerically investigated the flow mechanism of the hybrid SVC nozzle. Nozzle performance (e.g. the thrust vector angle and the thrust coefficient) was studied with consideration of the influence of aerodynamic and geometric parameters, such as the nozzle pressure ratio (NPR), the secondary pressure ratio (SPR) and the deflection angle of the rotatable valve (θ). The numerical results indicate that the introductions of the rotatable valve and the secondary injection induce an asymmetrically distributed static pressure to nozzle internal walls. Such static pressure distribution generates a side force on the primary flow, thereby achieving thrust vectoring. Both the thrust vector angle and vectoring efficiency can be enhanced by reducing NPR or by increasing θ. A maximum vector angle of 16.7 ° is attained while NPR is 3 and the corresponding vectoring efficiency is 6.33 °/%. The vector angle first increases and then decreases along with the elevation of SPR, and there exists an optimum value of SPR for maximum thrust vector angle. The effects of θ and SPR on the thrust coefficient were found to be insignificant. The rotatable valve can be utilized to improve vectoring efficiency and to control the vector angle as expected.

Performance of Strongly Bowed Stators in a Four-Stage High-Speed Compressor

2004 ◽  
Vol 126 (3) ◽  
pp. 333-338 ◽  
Author(s):  
Axel Fischer ◽  
Walter Riess ◽  
Joerg R. Seume
Keyword(s):  
Mass Flow ◽  
High Speed ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Pressure Rise ◽  
Maximum Pressure ◽  
Controlled Diffusion ◽  
Stage 4 ◽  
The University

The FVV sponsored project “Bow Blading” (cf. acknowledgments) at the Turbomachinery Laboratory of the University of Hannover addresses the effect of strongly bowed stator vanes on the flow field in a four-stage high-speed axial compressor with controlled diffusion airfoil (CDA) blading. The compressor is equipped with more strongly bowed vanes than have previously been reported in the literature. The performance map of the present compressor is being investigated experimentally and numerically. The results show that the pressure ratio and the efficiency at the design point and at the choke limit are reduced by the increase in friction losses on the surface of the bowed vanes, whose surface area is greater than that of the reference (CDA) vanes. The mass flow at the choke limit decreases for the same reason. Because of the change in the radial distribution of axial velocity, pressure rise shifts from stage 3 to stage 4 between the choke limit and maximum pressure ratio. Beyond the point of maximum pressure ratio, this effect is not distinguishable from the reduction of separation by the bow of the vanes. Experimental results show that in cases of high aerodynamic loading, i.e., between maximum pressure ratio and the stall limit, separation is reduced in the bowed stator vanes so that the stagnation pressure ratio and efficiency are increased by the change to bowed stators. It is shown that the reduction of separation with bowed vanes leads to a increase of static pressure rise towards lower mass flow so that the present bow bladed compressor achieves higher static pressure ratios at the stall limit.

Some Studies on Low Solidity Vaned Diffusers of a Centrifugal Compressor Stage

2005 ◽  
Author(s):  
T. Ch. Siva Reddy ◽  
G. V. Ramana Murty ◽  
Prasad Mukkavilli ◽  
D. N. Reddy
Keyword(s):  
Centrifugal Compressor ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Pressure Recovery ◽  
Compressor Stage ◽  
Recovery Coefficient ◽  
Vaned Diffuser ◽  
Flow Angle ◽  
Centrifugal Compressor Stage ◽  
Pressure Recovery Coefficient

Numerical simulation of impeller and low solidity vaned diffuser (LSD) of a centrifugal compressor stage is performed individually using CFX- BladeGen and BladeGenPlus codes. The tip mach number for the chosen study was 0.35. The same configuration was used for experimental investigation for a comparative study. The LSD vane is formed using standard NACA profile with marginal modification at trailing edge. The performance parameters obtained form numerical studies at the exit of impeller and the diffuser have been compared with the corresponding experimental data. These parameters are pressure ratio, polytropic efficiency and flow angle at the impeller exit where as the parameters those have been compared at the exit of diffuser are the static pressure recovery coefficient and the exit flow angle. In addition, the numerical prediction of the blade loading in terms of blade surface pressure distribution on LSD vane has been compared with the corresponding experimental results. Static pressure recovery coefficient and flow angle at diffuser exit is seen to match closely at higher flows. The difference at lower flows could be due to the effect of interaction between impeller and diffuser combinations, as the numerical analysis was done separately for impeller and diffuser and the effect of impeller diffuser interaction was not considered.

Effect of Non-Condensible Gas on the Subcooled Water Critical Flow in a Safety Valve

2002 ◽  
Author(s):  
Se Won Kim ◽  
Sang Kyoon Lee ◽  
Hee Cheon No
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Safety Valve ◽  
Pressure Ratio ◽  
Water Flow Rate ◽  
Critical Flow ◽  
Inlet Temperature ◽  
Nitrogen Gas ◽  
Critical Flow Rate ◽  
Subcooled Water

The effect of non-condensable gas on the subcooled water critical flow in a safety valve is investigated experimentally at various subcoolings with 3 different disk lifts. To evaluate its effect on the critical pressure ratio and critical flow rate, three parameters are considered: the ratios of outlet pressure to inlet pressure, the subcooling to inlet temperature, and the gas volumetric flow to water volumetric flow are 0.15–0.23, 0.07–0.12, and 0–0.8, respectively. It turns out that the critical pressure ratio is mainly dependent on the subcooling, and its dependency on the gas fraction and the pressure drop is relatively small. When the ratio of nitrogen gas volumetric flow to water volumetric flow becomes lower than 20%, the subcooled water critical flow rate is decreased about 10% compare to the water flow rate of without non-condensable gas. However, it maintains a constant value after the ratio of gas volumetric flow to water volumetric flow becomes higher than 20%. The subcooled water critical flow correlation, which considers subcooling, disc lift, backpressure, and non-condensable gas, shows good agreement with the total present experimental data with the root mean square error 8.17%.

scholarly journals Interpreting Aerodynamics of a Transonic Impeller from Static Pressure Measurements

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Fangyuan Lou ◽  
John Charles Fabian ◽  
Nicole Leanne Key
Keyword(s):  
Flow Field ◽  
High Speed ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Leading Edge ◽  
Pressure Measurements ◽  
High Loss ◽  
Supersonic Inlet ◽  
Mach Numbers ◽  
Inlet Conditions

This paper investigates the aerodynamics of a transonic impeller using static pressure measurements. The impeller is a high-speed, high-pressure-ratio wheel used in small gas turbine engines. The experiment was conducted on the single stage centrifugal compressor facility in the compressor research laboratory at Purdue University. Data were acquired from choke to near-surge at four different corrected speeds (Nc) from 80% to 100% design speed, which covers both subsonic and supersonic inlet conditions. Details of the impeller flow field are discussed using data acquired from both steady and time-resolved static pressure measurements along the impeller shroud. The flow field is compared at different loading conditions, from subsonic to supersonic inlet conditions. The impeller performance was strongly dependent on the inducer, where the majority of relative diffusion occurs. The inducer diffuses flow more efficiently for inlet tip relative Mach numbers close to unity, and the performance diminishes at other Mach numbers. Shock waves emerging upstream of the impeller leading edge were observed from 90% to 100% corrected speed, and they move towards the impeller trailing edge as the inlet tip relative Mach number increases. There is no shock wave present in the inducer at 80% corrected speed. However, a high-loss region near the inducer throat was observed at 80% corrected speed resulting in a lower impeller efficiency at subsonic inlet conditions.

A Correction to the Barotropic Model of Gaseous Cavitation in Choked Converging-Diverging Nozzle Flows

2020 ◽  
Author(s):  
Michael Waldrop ◽  
Flint Thomas
Keyword(s):  
Static Pressure ◽  
Pressure Ratio ◽  
Normal Shock ◽  
Inlet Pressure ◽  
Maximum Pressure ◽  
Prediction Errors ◽  
Cavitation Model ◽  
Static Pressure Distribution ◽  
Shock Solution ◽  
Nozzle Inlet

Abstract The Barotropic Cavitation Model describes the behavior of a homogeneous mixture of liquid and gas bubbles (gaseous cavitation) as it traverses a converging-diverging (CD) nozzle. Its normal shock formulation makes reliable and accurate predictions of streamwise static pressure distribution from the nozzle inlet to just downstream of the throat and in the diverging section as the flow approaches the nozzle outlet. It fails in the intermediate portion of the divergence with maximum pressure prediction errors (as a fraction of nozzle inlet pressure) roughly equivalent to the back pressure ratio (as high as 0.46). A correction to the streamwise static pressure distributions predicted by the normal shock solution of the Barotropic Cavitation Model is proposed, applied and compared to experiments with aerated and non-aerated cavitation in several fluids. When used to simulate aerated cavitation of dodecane in a CD nozzle it predicts the location of first disagreement between the normal shock solution and experimental static pressure measurements within 4% of nozzle length. A polynomial curve fit between this predicted point (xcorr) and the normal shock location (xshock) then reduces maximum prediction error for static pressure in the correction region to no more than 0.11 (as a fraction of inlet pressure) for the aerated dodecane cases examined. For non-aerated gaseous cavitation in dodecane, water or JP8 jet fuel this error ratio does not exceed 0.13 and typical values are less than 0.07.

Using Optimization in Industrial Multi-Point Radial Compressor Design: Map Correction

2019 ◽  
Author(s):  
Edward P. Childs ◽  
Dimitri Deserranno ◽  
Akshay Bagi
Keyword(s):  
Mass Flow ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Base Case ◽  
Design Specification ◽  
Radial Compressor ◽  
Surrogate Based Optimization ◽  
Compressor Design ◽  
Mass Flow Rates ◽  
Operating Points

Abstract The application of Surrogate-Based Optimization (SBO) to the industrial design process for a radial compressor with two operating points is described. The design specification includes two operating points at mass flow rates differing by a factor of three, and efficiency and pressure ratio targets for each point. The base case, while roughly sized from 1D analysis, fails to achieve the pressure ratio targets. In this paper, the optimization focusses on correcting the two speed-line map of total to static pressure ratio vs. mass flow rate. “Smart parameterization”, combining independent and dependent geometric parameters, and yielding reasonable geometries for most input combinations, coupled with efficient SBO, with separate models for response surface modeling and failure prediction, yields a design achieving the targets in just 57 CFD runs. FINE/Turbo [1] is used as the CFD analysis code and FINE/Design3D [2] and MINAMO [3] as the multi-objective optimizer.

Sign in / Sign up

Export Citation Format

Share Document