Calculation of Cascade Profiles From the Velocity Distribution

1974 ◽  
Vol 96 (4) ◽  
pp. 407-412 ◽  
Author(s):  
C. Lecomte
Keyword(s):  
Mach Number ◽  
Velocity Distribution ◽  
Subsonic Flow ◽  
A Priori ◽  
External Flow ◽  
Analytical Function ◽  
Graphic Display ◽  
Analytical Functions ◽  
Number Distribution ◽  
Mach Number Distribution

The method using the properties of analytical functions is applied to a plane, steady, inviscid, everywhere subsonic flow. From data fixed a priori concerning the external flow and some details of the profile, the hodograph is obtained as an analytical function whose real part is known on a contour. The set of imposed conditions being in general superabundant, the proposed Mach number distribution is corrected by means of a function whose form is fixed a priori, or rejected altogether. The problem is treated on a graphic display console connected with a computer, which provides also the profile corresponding to the calculated hodograph.

Mach number distribution over the axis of supersonic underexpanded jets

1968 ◽  
Vol 15 (6) ◽  
pp. 1153-1157 ◽  
Author(s):  
Yu. P. Finat'ev ◽  
L. A. Shcherbakov ◽  
N. M. Gorskaya
Keyword(s):  
Mach Number ◽  
Underexpanded Jets ◽  
Number Distribution ◽  
Mach Number Distribution

Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

1992 ◽  
Vol 114 (3) ◽  
pp. 553-560 ◽  
Author(s):  
O. Le´onard ◽  
R. A. Van den Braembussche
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Pressure Distribution ◽  
Velocity Component ◽  
Design Method ◽  
Normal Velocity ◽  
Flow Solver ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Transonic Cascade

A iterative procedure for blade design, using a time marching procedure to solve the unsteady Euler equations in the blade-to-blade plane, is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a nonzero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.

Investigation of the Influence of Trailing Edge Shock Waves on Film Cooling Performance of Gas Turbine Airfoils

2007 ◽  
Author(s):  
M. Ochs ◽  
A. Schulz ◽  
H.-J. Bauer
Keyword(s):  
Mach Number ◽  
Shock Waves ◽  
Film Cooling ◽  
Suction Side ◽  
Test Rig ◽  
Local Cooling ◽  
Trailing Edge ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Turbine Airfoils

Transonic turbine stage flows are strongly influenced by shock waves. The oblique trailing edge shock generated at the pressure side impinges on the suction side of the neighboring airfoil leading to a significant alteration of the Mach number distribution. On film cooled turbine airfoils this shock interacts with the local cooling film. The present study deals with the investigation of this kind of shock wave – film cooling interaction. Experiments are conducted in a high pressure high temperature transonic test rig which allows setting engine realistic Reynolds numbers and Mach numbers, as well as temperature and density ratios. The generic test rig simulates a transonic region of an airfoil passage with the advantage of accessibility for optical measurement techniques. Coolant is ejected from a row of 5 cylindrical and 5 fanshaped holes at different locations relative to the position of shock impingement. Blowing ratios are varied within a range of 0.25<M<1.5. A simulated suction side Mach number distribution is generated with a Mach number Mam = 1.45 upstream and Mam = 1.14 downstream of the shock. Experimental data presented comprise spatially resolved and laterally averaged film cooling effectiveness and heat transfer coefficients within the vicinity of the interaction zone.

Investigation of Wall Effect on Flow Characteristics in Supersonic Rarefied Gas Flow Past a Confined Square Cylinder Using the DSMC Method

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Blockage Ratio ◽  
Parallel Plates ◽  
Square Cylinder ◽  
Rarefied Gas Flow ◽  
Number Distribution ◽  
Mach Number Distribution

In the present study, the effect of wall in supersonic rarefied gas flow past a square cylinder is numerically studied. Therefore, a supersonic rarefied gas flow over a square cylinder is simulated first. Then, the simulations are repeated for a square cylinder confined between two parallel plates. In both cases, the Mach number distribution in the flow field of supersonic rarefied gas over the square cylinder is obtained using the direct simulation Monte Carlo method. Close inspection of contour lines of Mach number over the square cylinder shows that a discontinuity in the flow field occurs across the shock wave at the slip regime while there is no discontinuity at the transition flow regime. In the present paper, the effect of blockage ratio (defined as the distance between two parallel plates divided by the cylinder length) on the Mach number distribution in the flow field of supersonic rarefied gas over the square cylinder is also studied. Meanwhile, the obtained results from both mentioned cases are compared to each other. It is found that the deviation of two sets of data diminishes gradually as the blockage ratio increases.

Steady VGJ Flow Control on a Highly Loaded Transonic LPT Cascade: Effects of Compressibility and Roughness

2014 ◽  
Author(s):  
Chiara Bernardini ◽  
Stuart I. Benton ◽  
John D. Lee ◽  
Jeffrey P. Bons ◽  
Jen-Ping Chen ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Mach Number ◽  
Flow Control ◽  
High Speed ◽  
Operating Conditions ◽  
Control Performance ◽  
Blowing Ratio ◽  
Number Distribution ◽  
Turbulent Separation ◽  
Mach Number Distribution

A new high-speed linear cascade has been developed for low-pressure turbine (LPT) studies at The Ohio State University. A compressible LPT profile is tested in the facility and its baseline performance at different operating conditions is assessed by means of isentropic Mach number distribution and wake total pressure losses. Active flow control is implemented through a spanwise row of vortex-generator jets (VGJs) located at 60% chord on the suction surface. The purpose of the study is to document the effectiveness of VGJ flow control in high-speed compressible flow. The effect on shock-induced separation is assessed by Mach number distribution, wake loss surveys and shadowgraph. Pressure Sensitive Paint is applied to understand the three dimensional flow and shock pattern developing from the interaction of the skewed jets and the main flow. Data show that with increasing blowing ratio the losses are first decreased due to separation reduction, but losses connected to compressibility effects become stronger due to increased passage shock strength and jet orifice choking; therefore the optimum blowing ratio is a tradeoff between these counteracting effects. The effect of added surface roughness on the uncontrolled flow and on flow control behavior is also investigated. At lower Mach number turbulent separation develops on the rough surface and a different flow control performance is observed. Steady VGJs appear to have control authority even on a turbulent separation but higher blowing ratios are required compared to incompressible flow experiments reported elsewhere. Overall, the results show a high sensitivity of steady VGJs control performance and optimum blowing ratio to compressibility and surface roughness.

scholarly journals A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1991 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three–dimensional aerothermodynamic design problem with some type of the Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachinery the three–dimensional coordinates of the blade is attained through the stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

1991 ◽  
Author(s):  
O. Léonard ◽  
R. A. Van Den Braembussche
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Pressure Distribution ◽  
Velocity Component ◽  
Design Method ◽  
Normal Velocity ◽  
Flow Solver ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Transonic Cascade

An iterative procedure for blade design, using a Time Marching procedure to solve the unsteady Euler equations in the blade-to-blade plane is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a non-zero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.

A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1992 ◽  
Vol 114 (3) ◽  
pp. 548-552 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three-dimensional aerothermodynamic design problem with some type of Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachine, the three-dimensional coordinates of the blade are attained through stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem, the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

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