scholarly journals A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Chunhua Sheng
Keyword(s):  
Mach Number ◽  
Current Method ◽  
Viscous Flows ◽  
Original Method ◽  
Superior Performance ◽  
Governing Equations ◽  
Free Stream Mach Number ◽  
Rotating Frames ◽  
Mach Numbers ◽  
Diffusive Fluxes

An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

Influence of Loading Distribution on the Off-Design Performance of High-Pressure Turbine Blades

2006 ◽  
Author(s):  
D. Corriveau ◽  
S. A. Sjolander
Keyword(s):  
High Pressure ◽  
Mach Number ◽  
Turbine Blades ◽  
Operating Conditions ◽  
Design Flow ◽  
Superior Performance ◽  
High Pressure Turbine ◽  
Design Performance ◽  
Mach Numbers ◽  
Exit Mach Number

Linear cascade measurements for the aerodynamic performance of a family of three transonic, high-pressure (HP) turbine blades have been presented previously by the authors. The airfoils were designed for the same inlet and outlet velocity triangles but varied in their loading distributions. The previous papers presented results for the design incidence at various exit Mach numbers, and for off-design incidence at the design exit Mach number of 1.05. Results from the earlier studies indicated that by shifting the loading towards the rear of the airfoil an improvement in the profile loss performance of the order of 20% could be obtained near the design Mach number at design incidence. Measurements performed at off-design incidence, but still at the design Mach number, showed that the superior performance of the aft-loaded blade extended over a range of incidence from about −5.0° to +5.0° relative to the design value. For the current study, additional measurements were performed at off-design Mach numbers from about 0.5 to 1.3 and for incidence values of −10.0°, +5.0° and + 10.0° relative to design. The corresponding Reynolds numbers, based on outlet velocity and true chord, varied from roughly 4 × 105 to 10 × 105. The measurements included midspan losses, blade loading distributions and base pressures. In addition, two-dimensional Navier-Stokes computations of the flow were performed to help in the interpretation of the experimental results. The results show that the superior loss performance of the aft-loaded profile, observed at design Mach number and low values of off-design incidence, does not extend readily to off-design Mach numbers and larger values of incidence. In fact, the measured midspan loss performance for the aft-loaded blade was found to be inferior to, or at best equal to, that of the baseline, mid-loaded airfoil at most combinations of off-design Mach number and incidence. However, based on the observations made at design and off-design flow conditions, it appears that aft-loading can be a viable design philosophy to employ in order to reduce the losses within a blade row provided the rearward deceleration is carefully limited. The loss performance of the front-loaded blade is inferior or at best equal to that of the other two blades for all operating conditions. As such, it appears that there is no advantage to front loading the airfoil for transonic high-pressure turbine blades. The results also provide a significant addition to the data available in the open literature on the off-design performance of transonic HP turbine airfoils.

Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number

2011 ◽  
Vol 672 ◽  
pp. 245-267 ◽  
Author(s):  
L. DUAN ◽  
I. BEEKMAN ◽  
M. P. MARTÍN
Keyword(s):  
Mach Number ◽  
Boundary Layers ◽  
Large Scale ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Thermodynamic Quantities ◽  
Reynolds Analogy ◽  
Number Range ◽  
Free Stream Mach Number ◽  
Mach Numbers

In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scalings with respect to the mean and turbulence behaviours as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers (M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walz's relation, Morkovin's scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure–strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities (p′rms/pw, ρ′rms/ρ, T′rms/T) and turbulence Mach numbers (Mt, M′rms), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.

Influence of Loading Distribution on the Off-Design Performance of High-Pressure Turbine Blades

2006 ◽  
Vol 129 (3) ◽  
pp. 563-571 ◽  
Author(s):  
D. Corriveau ◽  
S. A. Sjolander
Keyword(s):  
High Pressure ◽  
Mach Number ◽  
Turbine Blades ◽  
Reynolds Numbers ◽  
Operating Conditions ◽  
Design Flow ◽  
Superior Performance ◽  
Navier Stokes ◽  
Mach Numbers ◽  
Exit Mach Number

Linear cascade measurements for the aerodynamic performance of a family of three transonic, high-pressure (HP) turbine blades have been presented previously by the authors. The airfoils were designed for the same inlet and outlet velocity triangles but varied in their loading distributions. The previous papers presented results for the design incidence at various exit Mach numbers, and for off-design incidence at the design exit Mach number of 1.05. Results from the earlier studies indicated that by shifting the loading towards the rear of the airfoil an improvement in the profile loss performance of the order of 20% could be obtained near the design Mach number at design incidence. Measurements performed at off-design incidence, but still at the design Mach number, showed that the superior performance of the aft-loaded blade extended over a range of incidence from about −5.0deg to +5.0deg relative to the design value. For the current study, additional measurements were performed at off-design Mach numbers from about 0.5 to 1.3 and for incidence values of −10.0deg, +5.0deg, and +10.0deg relative to design. The corresponding Reynolds numbers, based on outlet velocity and true chord, varied from roughly 4×105 to 10×105. The measurements included midspan losses, blade loading distributions, and base pressures. In addition, two-dimensional Navier–Stokes computations of the flow were performed to help in the interpretation of the experimental results. The results show that the superior loss performance of the aft-loaded profile, observed at design Mach number and low values of off-design incidence, does not extend readily to off-design Mach numbers and larger values of incidence. In fact, the measured midspan loss performance for the aft-loaded blade was found to be inferior to, or at best equal to, that of the baseline, midloaded airfoil at most combinations of off-design Mach number and incidence. However, based on the observations made at design and off-design flow conditions, it appears that aft-loading can be a viable design philosophy to employ in order to reduce the losses within a blade row provided the rearward deceleration is carefully limited. The loss performance of the front-loaded blade is inferior or at best equal to that of the other two blades for all operating conditions.

Heat Transfer in Rotating Serpentine Coolant Passage With Ribbed Walls at Low Mach Numbers

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Shang-Feng Yang ◽  
Je-Chin Han ◽  
Salam Azad ◽  
Ching-Pang Lee
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Transfer Coefficients ◽  
Low Mach Number ◽  
Heat Transfer Coefficients ◽  
Rotation Numbers ◽  
Wide Range ◽  
Mach Numbers

This paper experimentally investigates the effect of rotation on heat transfer in typical turbine blade serpentine coolant passage with ribbed walls at low Mach numbers. To achieve the low Mach number (around 0.01) condition, pressurized Freon R-134a vapor is utilized as the working fluid. The flow in the first passage is radial outward, after the 180 deg tip turn the flow is radial inward to the second passage, and after the 180 deg hub turn the flow is radial outward to the third passage. The effects of rotation on the heat transfer coefficients were investigated at rotation numbers up to 0.6 and Reynolds numbers from 30,000 to 70,000. Heat transfer coefficients were measured using the thermocouples-copper-plate-heater regional average method. Heat transfer results are obtained over a wide range of Reynolds numbers and rotation numbers. An increase in heat transfer rates due to rotation is observed in radially outward passes; a reduction in heat transfer rate is observed in the radially inward pass. Regional heat transfer coefficients are correlated with Reynolds numbers for nonrotation and with rotation numbers for rotating condition, respectively. The results can be useful for understanding real rotor blade coolant passage heat transfer under low Mach number, medium–high Reynolds number, and high rotation number conditions.

Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet

2001 ◽  
Vol 105 (1043) ◽  
pp. 9-16 ◽  
Author(s):  
S. B. Verma ◽  
E. Rathakrishnan
Keyword(s):  
Mach Number ◽  
Fundamental Frequency ◽  
Acoustic Field ◽  
Major Axis ◽  
Shock Structure ◽  
Minor Axis ◽  
Noise Levels ◽  
Underexpanded Jets ◽  
Barrel Shock ◽  
Mach Numbers

Abstract The shock-structure and the related acoustic field of underexpanded jets undergoes significant changes as the Mach number Mj is increased. The present investigation is carried out to study the effect of Mach number on an underexpanded 2:1 elliptic-slot jet. Experimental data are presented for fully expanded Mach numbers ranging from 1.3 to 2.0. It is observed that the ‘cross-over’ point at the end of the first cell at low Mach numbers gets replaced by a normal shock at a highly underexpanded condition resulting in the formation of a ‘barrel’ shock along the minor-axis side with a ‘bulb’ shock formed along the major-axis side. The above change in shock structure is accompanied by a related change in the acoustic field. The amplitude of fundamental frequency along the minor-axis side grows with Mj but falls beyond Mj = 1.75. Along the major-axis side, however, the fundamental frequency does not exist at low Mach numbers. It appears at Mj = 1.75 but then falls at Mj = 2.0. The related azimuthal directivity of overall noise levels (OASPL) shows significant changes with Mj.

Aeroelastic Problems in connection with High-Speed Flight

1956 ◽  
Vol 60 (547) ◽  
pp. 459-475 ◽  
Author(s):  
E. G. Broadbent
Keyword(s):  
Mach Number ◽  
High Speed ◽  
The Other ◽  
Control Surface ◽  
The Past ◽  
Other Hand ◽  
Aerodynamic Derivatives ◽  
Mach Numbers ◽  
The One

SummaryA review is given of developments in the field of aeroelasticity during the past ten years. The effect of steadily increasing Mach number has been two-fold: on the one hand the aerodynamic derivatives have changed, and in some cases brought new problems, and on the other hand the design for higher Mach numbers has led to thinner aerofoils and more slender fuselages for which the required stiffness is more difficult to provide. Both these aspects are discussed, and various methods of attack on the problems are considered. The relative merits of stiffness, damping and massbalance for the prevention of control surface flutter are discussed. A brief mention is made of the recent problems of damage from jet efflux and of the possible aeroelastic effects of kinetic heating.

Measurements of Endwall Flows in Transonic Linear Turbine Cascades: Part II—High Flow Turning

2010 ◽  
Author(s):  
F. Taremi ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Mach Number ◽  
Kinetic Energy ◽  
Flow Visualization ◽  
Flow Separation ◽  
Surface Flow ◽  
Streamwise Vorticity ◽  
Vortical Structures ◽  
Turbine Cascades ◽  
Mach Numbers ◽  
Surface Flow Visualization

An experimental investigation of two low-turning (90°) transonic linear turbine cascades was presented in Part I of the paper. Part II examines two high-turning (112°) turbine cascades. The experimental results include total pressure losses, streamwise vorticity and secondary kinetic energy distributions. The measurements were made using a seven-hole pressure probe downstream of the cascades. In addition to the measurements, surface flow visualization was conducted to assist in the interpretation of the flow physics. The turbine cascades in Part II, referred to as SL1F and SL2F, have the same inlet and outlet design flow angles, but different aerodynamic loading levels: SL2F is more highly loaded than SL1F. The surface flow visualization results show evidence of small flow separation on the suction side of both airfoils. At the design conditions (outlet Mach number ≈ 0.8), SL2F exhibits stronger vortical structures and larger secondary velocities than SL1F. The two cascades, however, produce similar row losses based on the measurements at 40% axial chord lengths downstream of the trailing edge. Additional data were collected at off-design outlet Mach numbers of 0.65 and 0.91. As the Mach number is raised, the cascades become more aft-loaded. The absolute blade loadings increase, but the Zweifel coefficients decrease due to higher outlet dynamic pressures. Both profile and secondary losses decrease at higher Mach numbers; the main vortical structures and the corresponding peak losses migrate towards the endwall, and there are reductions in secondary kinetic energy and exit flow angle variations. The streamwise vorticity distributions show smaller peak vorticities associated with the passage and the counter vortices at higher exit Mach numbers. The corner vortex, on the other hand, becomes more intensified, resulting in reduction of flow overturning near the endwall. The results for SL1F and SL2F are compared and contrasted with the results for the lower turning cascades presented in Part I. The possible effects of suction-surface flow separation on profile and secondary losses are discussed in this context. The current research project is part of a larger study concerning the effects of endwall contouring on secondary losses, which will be presented in the near future.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH
Keyword(s):  
Mach Number ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Heat Release ◽  
Acoustic Field ◽  
Release Rate ◽  
Governing Equations ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acceleration Term

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.

A New Concept of a Two-Dimensional Supersonic Relative Inlet Mach Number Compressor Cascade

2009 ◽  
Author(s):  
Toyotaka Sonoda ◽  
Markus Olhofer ◽  
Toshiyuki Arima ◽  
Bernhard Sendhoff
Keyword(s):  
Mach Number ◽  
Total Pressure ◽  
Optimization Method ◽  
Superior Performance ◽  
Compressor Cascade ◽  
Pressure Loss Coefficient ◽  
Supersonic Inlet ◽  
Flow Mechanisms ◽  
Improved Performance ◽  
Total Pressure Loss Coefficient

In this study, a numerical shape optimization method based on evolutionary algorithms coupled with a verified CFD solver has been applied to the ambitious target of a shock free 2-D supersonic inlet Mach number compressor cascade. The study is based on the DLR-PAV-1.5 supersonic compressor cascade designed by the pre-compression blading concept. The DLR cascade airfoil has been optimized using a verified CFD code. A superior performance of the optimized supersonic cascade with about 24% reduction of the total pressure loss coefficient compared to the original cascade has been realized. The flow mechanisms observable around the blade with improved performance and the resulting design concept are discussed in this paper.

Sign in / Sign up

Export Citation Format

Share Document