Theoretical Solution of High Subsonic Flow Past Two-Dimensional Cascades of Airfoils

1975 ◽  
Vol 97 (3) ◽  
pp. 355-360
Author(s):  
C. Lakomy´
Keyword(s):  
Compressible Flows ◽  
Inviscid Flow ◽  
Computer Time ◽  
Theoretical Solution ◽  
Two Dimensional ◽  
Flow Angle ◽  
Flow Past ◽  
Outlet Flow ◽  
Method Show ◽  
Good Agreement

The paper presents an entirely novel theoretical solution of inviscid flow past two-dimensional cascades of aerofoils at high subsonic velocities. The solution is carried out in the physical plane by the help of transformation equations derived for streamline coordinates. The transformation equations define the dependence between the flow fields in the regions of incompressible and compressible flows past the cascade. Knowing the incompressible flow, one can calculate the velocity distribution on an aerofoil and the outlet flow angle of the cascade in a comparatively simple way. The method makes it possible to determine the critical Mach number of the cascade with ease. The requisite computer time is relatively short. The results obtained by the new method show a very good agreement with those of other authors and with experiments.

Study of Vaneless Diffuser Rotating Stall Based on Two-Dimensional Inviscid Flow Analysis

1996 ◽  
Vol 118 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Yoshinobu Tsujimoto ◽  
Yoshiki Yoshida ◽  
Yasumasa Mori
Keyword(s):  
Propagation Velocity ◽  
Flow Instability ◽  
Present Report ◽  
Inviscid Flow ◽  
Rotating Stall ◽  
Critical Flow ◽  
Two Dimensional ◽  
Vaneless Diffuser ◽  
Flow Angle ◽  
Pressure Disturbance

Rotating stalls in vaneless diffusers are studied from the viewpoint that they are basically two-dimensional inviscid flow instability under the boundary conditions of vanishing velocity disturbance at the diffuser inlet and of vanishing pressure disturbance at the diffuser outlet. The linear analysis in the present report shows that the critical flow angle and the propagation velocity are functions of only the diffuser radius ratio. It is shown that the present analysis can reproduce most of the general characteristics observed in experiments: critical flow angle, propagation velocity, velocity, and pressure disturbance fields. It is shown that the vanishing velocity disturbance at the diffuser inlet is caused by the nature of impellers as a “resistance” and an “inertial resistance,” which is generally strong enough to suppress the velocity disturbance at the diffuser inlet. This explains the general experimental observations that vaneless diffuser rotating stalls are not largely affected by the impeller.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

Application of a Two-Dimensional Supersonic Passage Analysis to the Design of Compressor Rotors

1974 ◽  
Author(s):  
R. G. Hantman ◽  
A. A. Mikolajczak ◽  
F. J. Camarata
Keyword(s):  
Leading Edge ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Compressor Rotor ◽  
Pressure Distributions ◽  
Displacement Thickness ◽  
Blade Section ◽  
Comparison Of The Results ◽  
Rotational Method ◽  
Good Agreement

A description of a two-dimensional supersonic cascade passage analysis and its application to the design of a high hub-to-tip ratio supersonic compressor rotor is presented. The analysis, applicable to the case in which the inviscid flow is everywhere supersonic, includes an entrance region calculation which accounts for blade leading edge bluntness effects, and a passage and wake region calculation. The inviscid part of the analysis is solved using a rotational method of characteristics. The effect of the blade boundary layer displacement thickness is taken into consideration. Comparison of the results of the analysis with supersonic cascade data is made, showing good agreement in overall performance prediction, in blade surface static pressure distributions, and in achievement of the desired shock wave patterns. A comparison of the results of the analysis is made also with the performance of a blade section of a high hub-to-tip ratio supersonic compressor and acceptable agreement obtained.

Acoustic destablilization of vortices

1979 ◽  
Vol 290 (1372) ◽  
pp. 353-371 ◽  
Keyword(s):  
Boundary Condition ◽  
Growth Rate ◽  
Mach Number ◽  
Acoustic Waves ◽  
Polar Angle ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Low Mach Number ◽  
The Stability ◽  
Good Agreement

A line vortex which has uniform vorticity 2Ω 0 in its core is subjected to a small two-dimensional disturbance whose dependence on polar angle is e imθ . The stability is examined according to the equations of compressible, inviscid flow in a homentropic medium. The boundary condition at infinity is that of outgoing acoustic waves, and it is found that this capacity to radiate leads to a slow instability by comparison with the corresponding incompressible vortex which is stable. Numerical eigenvalues are computed as functions of the mode number m and the Mach number M based on the circumferential speed of the vortex. These are compared with an asymptotic analysis for the m = 2 mode at low Mach number in which it is found that the growth rate is (π/ 32) M 4 Ω 0 in good agreement with the numerical results.

scholarly journals Prandtl–Batchelor flow past a flat plate with a forward-facing flap

1984 ◽  
Vol 143 ◽  
pp. 351-365 ◽  
Author(s):  
P. G. Saffman ◽  
S. Tanveer
Keyword(s):  
Flat Plate ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Two Dimensional ◽  
Rear Edge ◽  
Flow Past ◽  
Range Of Values ◽  
Streamline Method

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.

A parametric method for optimal design of two-dimensional cascades

2001 ◽  
Vol 215 (4) ◽  
pp. 465-473 ◽  
Author(s):  
E Benini ◽  
A Toffolo
Keyword(s):  
Fluid Dynamics ◽  
Genetic Algorithm ◽  
Optimal Design ◽  
Large Range ◽  
Parametric Method ◽  
Geometry Optimization ◽  
Axial Flow ◽  
Two Dimensional ◽  
Flow Angle ◽  
Outlet Flow

A parametric method for optimal design of two-dimensional cascades, based on the coupling between a genetic algorithm and a commercial computational fluid dynamics code, is introduced. The results of cascade geometry optimization for a large range of inlet and outlet flow angle pairs are presented. The method is a simple as well as effective tool for the optimal design of cascades for axial flow pumps.

Inviscid compressible flow with shock in two-dimensional slender nozzles

1985 ◽  
Vol 157 ◽  
pp. 265-287 ◽  
Author(s):  
C. Q. Lin ◽  
S. F. Shen
Keyword(s):  
Pressure Gradient ◽  
Compressible Flows ◽  
Flow Region ◽  
Expansion Method ◽  
Inviscid Flow ◽  
Present Theory ◽  
Two Dimensional ◽  
Transverse Pressure ◽  
Leading Term ◽  
Inviscid Compressible Flows

The present theory provides an asymptotic-expansion method for inviscid compressible flows with shock in arbitrary two-dimensional slender nozzles. The flow in front of the shock is assumed to be potential, whereas the flow behind the shock is considered to be rotational owing to the presence of the shock. A parameter that measures the slenderness of the nozzle is used as the expansion quantity. It is found that, except for the region immediately behind the shock, the same coordinate scale can be used for the flows both in front of and further downstream behind the shock. The flows for the regions thus obtained show that all the streamlines are approximately affinely similar to the nozzle wall, and the leading term of the transverse pressure gradient is determined by the local wall shape. For the flow region immediately behind the shock, however, the transverse pressure gradient just behind the shock is determined by the shock conditions rather than by the local wall shape, and a solution is found for that region which transforms the transverse pressure gradient from that determined by the shock conditions to that determined by the local wall shape. The well-known flow singularity at the intersection of the wall and the shock is involved in the solution. Meanwhile, a critical shock location at which the flow has no singularity is derived. A numerical example shows also that the inviscid flow may separate from the wall, owing to the different entropy increase across the shock for different streamlines. The predicted separation point, however, is only of qualitative value, since our theory does not account for reverse flows.

The study of acoustic scattering from a single sound-permeable sphere

2018 ◽  
Vol 13 (4) ◽  
pp. 79-91 ◽  
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Speed Of Sound ◽  
Numerical Technique ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Physical Parameters ◽  
Fast Method ◽  
Scattering Field ◽  
Permeable Sphere ◽  
Test Verification ◽  
Good Agreement

The paper presents a generalized mathematical model and numerical investigation of the problem of acoustic scattering from a single sound-permeable sphere during the passage of two types of waves - spherical from a monopole radiation source and a plane one. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained at the lowest cost of computer time. The calculations are compared with known experimental data and a good agreement is obtained. The formulas for calculating the main characteristic of the scattering field (the total scattering cross section) for a sound-permeable sphere are generalized. The effect on this characteristic of the physical parameters of media outside and inside the sphere, such as the density and speed of sound, is shown. A numerical parametric analysis of the pressure distribution around a single sound-permeable sphere for different values of the wave radius, density, and speed of sound of the outer and inner medium of the sphere is carried out. The obtained results will later be used for test verification calculations for the numerical solution of the generalized problem of acoustic scattering of a set of sound-permeable spheres (coaxial or arbitrarily located in space).

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