An Analytical Approach for Gas Turbine Parameter Corrections

2008 ◽  
Author(s):  
Vasileios E. Kyritsis ◽  
Pericles Pilidis
Keyword(s):  
Mach Number ◽  
Mass Flow ◽  
Pressure Ratio ◽  
Mathematical Formulation ◽  
Flow Speed ◽  
Correction Factors ◽  
Specific Heats ◽  
Isentropic Exponent ◽  
Scaling Parameters ◽  
Mach Numbers

Turbomachinery component behavior depends on dimensionless parameters, such as inlet and circumferential Mach numbers and the ratio of specific heats. Regarding mass flow and speed, their dimensionless scaling parameters are usually used instead based on Mach number similarity. A given dimensionless aerodynamic operating point is defined by certain values of axial and circumferential Mach numbers. To such a point and for a certain value of isentropic exponent, a given dimensionless enthalpy variation corresponds as the work parameter. When turbo-machinery performance sizes, such as the work parameter and efficiency, are plotted against mass flow and speed to form a characteristic, the absence of the isentropic exponent as an additional dimension causes inaccuracies. The extent of the inaccuracies firstly depends on the scaling groups used for mass low, speed and work, that is whether they include the gas property parameters, such as the isentropic exponent and the gas constant. The aforementioned shows that for rigorous calculations correction factors have to be applied, especially when quasi-dimensionless groups are used and/or pressure ratio is used as the work parameter. Typically, the corrections for mass flow and speed may take the form of multipliers, which consist of ratios of the isentropic exponent and/or the gas constant between the examined condition and the reference one. Alternatively, for the case of mass flow the exponents of temperature and pressure can deviate from their theoretical values of 0.5 and 1.0 respectively. Scope of the current work is the mathematical formulation of such exponents for a variety of scaling groups regarding mass flow, speed and work. The correction factors are a strong function of the operating condition, temperature and gas composition, which fully define gas properties. Among the findings of the current study, evidence is provided that the practically one-to-one relationship considered between dimensionless mass flow and inlet Mach number holds for low Mach number values. This is particularly true, since its sensitivity to variations of the isentropic exponent gets increasingly larger with Mach number. Additionally, for a given dimensionless enthalpy change, the exchange rate of pressure ratio against variations of the isentropic exponent is much more increased for an expansion rather than a compression. The latter justifies the use of dimensionless enthalpy drop in turbine characteristics.

The representation of GT component maps using Mach numbers

2007 ◽  
Vol 111 (1121) ◽  
pp. 453-460
Author(s):  
V. E. Kyritsis ◽  
P. Pilidis ◽  
K. Ramsden
Keyword(s):  
Chemical Composition ◽  
Mach Number ◽  
Mass Flow ◽  
Rotational Speed ◽  
Pressure Ratio ◽  
Working Fluid ◽  
Stagnation Temperature ◽  
Perfect Gas ◽  
Full Account ◽  
Mach Numbers

Abstract Component maps are produced under certain environmental conditions using air as the working fluid during static ground operation. Any changes of the component characteristics when operating under different temperature conditions and/or with different working fluid are partially taken into account, because of the existence of the gas constant and the ratio of the specific heats in the non-dimensional mass flow and rotational speed. This provides a second order correction for the component characteristics, which may be adequate for the initial modeling of engines. However, for rigorous performance calculations correction factors are applied to the non-dimensional mass flow, rotational speed and pressure ratio distributions of a map, when deviations from the reference conditions under which it was extracted, are experienced. In the current study, a different approach is considered in order to eliminate the inaccuracies caused by the varying temperature and chemical composition. It makes direct use of inlet and circumferential Mach numbers based upon stagnation temperature in conjunction with dimensionless enthalpy variation. A sensitivity analysis against gas property variations is conducted to quantify the benefits gained in precision. Generally, the well-known relationships correlating the Mach number with total and static properties are based on the assumption of perfect gas and constant gas properties. Introducing dependency on temperature and/or chemical composition for the caloric properties of the semi-perfect gas, proper mean values are defined and some theoretical corrections are provided for the well-known equations. The mass flow compatibility equation is then based on the ‘corrected’ expression correlating dimensionless mass flow and Mach number and takes full account of gas property variations.

A parametric survey of the first critical Mach number for a fast MHD shock

1984 ◽  
Vol 32 (3) ◽  
pp. 429-441 ◽  
Author(s):  
J. P. Edmiston ◽  
C. F. Kennel
Keyword(s):  
Mach Number ◽  
Flow Speed ◽  
Interplanetary Shocks ◽  
Plasma Parameters ◽  
Energetic Ions ◽  
Critical Mach Number ◽  
Specific Heats ◽  
Solar Wind Parameters ◽  
The One ◽  
Downstream Flow

The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.

Sweep Effects on Fan-Intake Aerodynamics at High Angle of Attack

2021 ◽  
Author(s):  
Ben Mohankumar ◽  
Cesare A. Hall ◽  
Mark J. Wilson
Keyword(s):  
Mach Number ◽  
Pressure Ratio ◽  
Angle Of Attack ◽  
Pressure Rise ◽  
Low Pressure ◽  
Rotating Stall ◽  
High Angle ◽  
High Angle Of Attack ◽  
Mach Numbers ◽  
High Mach

Abstract Sweep in a transonic fan is conventionally used to reduce design point losses by inclining the passage shock relative to the incoming flow. However, future low pressure ratio fans operate to lower Mach numbers meaning the role of sweep at cruise is diminished. Instead, sweep might be repurposed to improve the performance of critical high Mach number off-design conditions such as high angle of attack (AOA). In this paper, we use unsteady computational fluid dynamics to compare two transonic low pressure ratio fans, one radially stacked and one highly swept, coupled to a short intake design, at the high AOA flight condition. The AOA considered is 35°, which is sufficient to separate the intake bottom lip. The midspan of the swept fan was shifted upstream to add positive sweep to the outer span. Based on previous design experience, it was hypothesised the swept fan would reduce transonic losses when operating at high AOA. However, it was found the swept fan increased the rotor loss by 24% relative to the radial fan. Loss was increased through two key mechanisms. i) Rotor choking: flow is redistributed around the intake separation and enters the rotor midspan with high Mach numbers. Sweeping the fan upstream reduced the effective intake length, which increased the inlet relative Mach number and amplified choking losses. ii): Rotor-separation interaction (RSI): the rotor tip experiences low mass flow inside the separation, which increases the pressure rise across the casing to a point where the boundary layer separates. The swept fan diffused the casing streamtube, causing the casing separation to increase in size and persist in the passage for longer. High RSI loss indicated the swept fan was operating closer to the rotating stall point.

Semi-Closed Cycle O2/CO2 Combustion Gas Turbines: Influence of Fluid Properties on the Aerodynamic Performance of the Turbomachinery

2002 ◽  
Author(s):  
S. K. Roberts ◽  
S. A. Sjolander
Keyword(s):  
Mass Flow ◽  
Gas Turbines ◽  
Pressure Ratio ◽  
Working Fluid ◽  
Working Fluids ◽  
Combustion Gas ◽  
Isentropic Flow ◽  
Isentropic Exponent ◽  
Fluid Properties ◽  
Compressor Map

Many gases, including carbon dioxide and argon, have been considered as alternatives to air as working fluids in a number of design studies for closed and semi-closed gas turbine engines. In many of these studies, it has been assumed that if the gas constant R and specific heat ratio (isentropic exponent) γ are included in the speed and flow parameters, the compressor map or turbine characteristic is applicable to other working fluids. However, similarity arguments show that the isentropic exponent itself is a criterion of similarity and that the turbomachinery characteristics, even when appropriately non-dimensionalized, will in principle vary as the γ of the working fluid varies. This paper examines the effect of γ on turbomachinery characteristics, mainly in terms of compressors. The performance of a centrifugal compressor stage was measured using air (γ = 1.4), CO2 (γ = 1.29), and argon (γ = 1.67). For the same values of the non-dimensional speed and mass flow, the pressure ratio, the efficiency, and the choking mass flow were found to be significantly different for the three test gases. The experimental results have been found to be consistent with a CFD analysis of the impeller. Finally, it is shown that the changes in performance can be predicted reasonably well with simple arguments based mainly on one-dimensional isentropic flow. These arguments form the basis for correction procedures that can be used to project compressor characteristics measured for one value of γ to those for a gas with a different value.

Development of Large Intermittent Wind Tunnels

1955 ◽  
Vol 59 (532) ◽  
pp. 259-278 ◽  
Author(s):  
J. Lukasiewicz
Keyword(s):  
Mach Number ◽  
Wind Tunnel ◽  
Mass Flow ◽  
High Speed ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Wind Tunnels ◽  
Number Range ◽  
Pressure Storage ◽  
Vacuum Storage

SummaryTwo types of intermittent wind tunnel drives, the pressure storage drive(with atmospheric exhaust) and the vacuum storage drive (with atmospheric inlet), are examined and found to match well the tunnel pressure ratio-mass flow characteristics over a wide Mach number range (0 to 4). The design of components of intermittent wind tunnel installations, their operation and instrumentation are then considered in some detail. In order to increase the output of intermittent wind tunnels to a level comparable to that of continuously running tunnels, it is proposed to drive the models during each tunnel run through a range of incidence. This technique is at present under development in the National Aeronautical Establishment's High Speed Aerodynamics Laboratory and results so far obtained are discussed. Two tunnels are considered as examples of large intermittent installations: a 4 ft. square pressure-driven tunnel and a 6 ft. square vacuum-driven tunnel. The former is found to be a more compact and economical installation. Relative merits of continuous and intermittent installations are discussed.

Design, Analysis, Fabrication and Test of an Aspirated Fan Stage

2000 ◽  
Author(s):  
Brian J. Schuler ◽  
Jack L. Kerrebrock ◽  
Ali A. Merchant ◽  
Mark Drela ◽  
John Adamczyk
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Mass Flow ◽  
Pressure Ratio ◽  
3D Analysis ◽  
Suction Surface ◽  
Design Speed ◽  
Tip Shroud ◽  
Experimental Stage ◽  
Design Pressure

A fan stage designed by means of a MISES-based quasi-3D approach (Youngren and Drela, 1991), for a pressure ratio of 1.6 at a tip Mach number of 0.7, has been analyzed by viscous 3D CFD, fabricated and tested in the MIT Blowdown Compressor. The design incorporates a rotor tip shroud and boundary layer removal on the suction surfaces of the rotor and stator and at other critical locations. The fully viscous 3D analysis enabled final detailing of the design. In tests, the stage has met its design objectives, producing the design pressure ratio of 1.6 at design speed. The mass flow removed totaled 4.7%, approximately 1.0% through slots on the suction surface of the rotor and stator, and the remainder distributed over the rotor shroud and stator hub. The measured adiabatic efficiency of the rotor for the throughflow was 96% at the design point and that for the stage was 90%. This paper presents the design, the results of the analysis and the experimental stage performance both at design and at some off-design conditions.

scholarly journals Numerical Study of Characteristics of Underexpanded Supersonic Jet

2020 ◽  
Author(s):  
Priyadharshini Murugesan ◽  
Arjun Biju Kumar ◽  
Akhil Teja Kambhampati ◽  
Shashank Pillai ◽  
Girish Chandar Chandrasekar ◽  
...  
Keyword(s):  
Mach Number ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Supersonic Jet ◽  
Working Fluid ◽  
Shock Cell ◽  
Specific Heats ◽  
Supersonic Core Length ◽  
The Mean ◽  
Jet Characteristics

Correlations for the supersonic jet characteristics, the mean shock cell length and the supersonic core length, have been obtained in terms of the jet parameters. The jet parameters considered in this study are the exit diameter of the nozzle (de), the design Mach number (Me), the nozzle pressure ratio (NPR) and the ratio of specific heats of the medium (γ). The parameters were varied as follows: exit diameters, from 0.5 to 25 mm; Mach number from 1 to 3; the NPR from 2.14 to 35. Initially, working fluid used is cold air and then effect of variation of γ is taken into consideration. The computational model has been validated and then used for all the numerical simulations. A quadratic fit for both characteristics has been obtained which is applicable to any supersonic jet. The correlations developed are valid within the respective ranges of the parameters stated above.

scholarly journals Influence of Different Gases on the Design Point of an Industrial Axial Compressor and Deduced Aerodynamical Rematching Methodology

2020 ◽  
Vol 4 ◽  
pp. 238-252
Author(s):  
Henrik Hoffmann ◽  
Lukas Stuhldreier ◽  
Ruben van Rennings ◽  
Peter Jeschke
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Operating Point ◽  
Air Compressor ◽  
Isentropic Exponent ◽  
Compressor Inlet ◽  
Downstream Flow ◽  
Carbon Dioxide Co2

This paper presents a numerical investigation of the effects of compressing various gases, for example, carbon dioxide (CO2) and methane (CH4), on an eight-stage axial air compressor. Several adaptation methods are applied to achieve a similar operating point as for air. Theoretically, the operating point depends on Mach number, flow angles, Reynolds number and isentropic exponent. Numerical results show mismatch effects which arise in the parameters using a non-adapted geometry. A rematching procedure is described, including deduced speed adjustments, in order to achieve Mach number equality at compressor inlet. Only shroud modifications are performed to rematch the flow angles of the air simulation. Although Reynolds and Mach number are kept constant at compressor inlet, an inevitable deviation in downstream flow causes mismatches in efficiency and pressure ratio. Both analytical and numerical methodologies show that the scale of shroud adjustments, as well as the size of mismatch in Mach and Reynolds number, can be correlated to the isentropic gas exponent. In summary, the main impact on gas behavior in an axial air compressor is attributable to the change in isentropic exponent. Derivations of shroud adaptation and analyses of inevitable aerodynamic mismatch are therefore developed depending on the isentropic exponent.

Design and Numerical Simulation of Convergent Divergent Nozzle

2016 ◽  
Vol 852 ◽  
pp. 617-624
Author(s):  
V. Ramji ◽  
Raju Mukesh ◽  
Inamul Hasan
Keyword(s):  
Mach Number ◽  
Computational Analysis ◽  
Turbulence Modeling ◽  
Pressure Ratio ◽  
Minimum Length ◽  
Ansys Fluent ◽  
Exit Pressure ◽  
Constant Height ◽  
Mach Numbers ◽  
Exit Mach Number

This works centers on the design of a De Laval (convergent - Divergent) nozzle to accelerate the flow to supersonic or hypersonic speeds and computational analysis of the same. An initial design of the nozzle is made from the method of characteristics. The coding was done in Matlab to obtain the contour of the divergent section for seven different exit Mach numbers viz. 2.5,3,3.5,4,4.5,5 and 5.5.To quantify variation in the minimum length of the nozzle divergent section with respect to the exit mach number, a throat of constant height (0.005m) and width (0.05m) was chosen for all the design. The area exit required for each mach no varying from 1 to 5.5 was plotted using isentropic relations and was also used to verify the exit area of the nozzle for each of those mach numbers. An estimate of the exit pressure ratio is obtained by using isentropic and normal shock relations. With this exit pressure ratio, a more refined verification is done by computational analysis using ANSYS Fluent software for a contour nozzle with exit Mach number 5.5. The spalart Allmaras and k-epsilon model were used for turbulence modeling.

Supersonic Flow With Variable Specific Heat

1952 ◽  
Vol 19 (1) ◽  
pp. 57-62
Author(s):  
F. P. Durham
Keyword(s):  
Shock Wave ◽  
Specific Heat ◽  
Total Pressure ◽  
Pressure Ratio ◽  
Correction Factors ◽  
One Dimensional ◽  
Specific Heats ◽  
Flow Through ◽  
Total Pressure Ratio ◽  
The Ideal

Abstract Formulas are developed for stagnation conditions and one-dimensional flow through shock waves, including Rankine-Hugoniot values, taking into account the variation of the specific heat of air with temperature by means of the concept of mean specific heats. These formulas are reduced to correction factors that may be applied to the widely used constant specific-heat formulas up to a Mach number of 7. The corrections involved are appreciable in the case of the density change through a shock wave and for the total pressure ratio across a shock wave, as well as for stagnation pressures and temperatures. The limitations imposed by the deviation of a gas at high pressure from the ideal equation of state, relaxation time, and dissociation are discussed.

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