A generalized thermal wind equation and some non-separable exact solutions of the flow equations for three-dimensional spherical atmospheres

2008 ◽  
Vol 134 (636) ◽  
pp. 1931-1939 ◽  
Author(s):  
A. A. White ◽  
A. Staniforth
Keyword(s):  
Exact Solutions ◽  
Three Dimensional ◽  
Flow Equations ◽  
Thermal Wind

A Three-Dimensional Viscous Transonic Inverse Design Method

2000 ◽  
Author(s):  
W. T. Tiow ◽  
M. Zangeneh
Keyword(s):  
Design Method ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Flow Equations ◽  
Flow Solution ◽  
Turbomachinery Blades ◽  
A Cell ◽  
Inverse Design Method ◽  
Euler Solver

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.

Internal-inertia waves in a fluid of variable depth

1973 ◽  
Vol 73 (1) ◽  
pp. 205-213 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Exact Solutions ◽  
Surface Waves ◽  
Internal Waves ◽  
Vertical Velocity ◽  
General Problem ◽  
Three Dimensional ◽  
Variable Depth ◽  
Internal Inertia ◽  
Perturbation Pressure ◽  
Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

scholarly journals Computation of Three-Dimensional, Rotational Flow Through Turbomachinery Blade Rows for Improved Aerodynamic Design Studies

1986 ◽  
Author(s):  
S. V. Subramanian ◽  
R. Bozzola ◽  
Louis A. Povinelli
Keyword(s):  
Three Dimensional ◽  
Maximum Flow ◽  
Cost Effective ◽  
Computer Code ◽  
Integration Scheme ◽  
Aerodynamic Design ◽  
Design Studies ◽  
Flow Equations ◽  
Transonic Compressor ◽  
Numerical Predictions

The performance of a three dimensional computer code developed for predicting the flowfield in stationary and rotating turbomachinery blade rows is described in this study. The four stage Runge-Kutta numerical integration scheme is used for solving the governing flow equations and yields solution to the full, three dimensional, unsteady Euler equations in cylindrical coordinates. This method is fully explicit and uses the finite volume, time marching procedure. In order to demonstrate the accuracy and efficiency of the code, steady solutions were obtained for several cascade geometries under widely varying flow conditions. Computed flowfield results are presented for a fully subsonic turbine stator and a low aspect ratio, transonic compressor rotor blade under maximum flow and peak efficiency design conditions. Comparisons with Laser Anemometer measurements and other numerical predictions are also provided to illustrate that the present method predicts important flow features with good accuracy and can be used for cost effective aerodynamic design studies.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

scholarly journals Three-dimensional dilatonic gravity's rainbow: Exact solutions

2016 ◽  
Vol 2016 (10) ◽  
pp. 103A02 ◽  
Author(s):  
Seyed Hossein Hendi ◽  
Behzad Eslam Panah ◽  
Shahram Panahiyan
Keyword(s):  
Exact Solutions ◽  
Three Dimensional ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow
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