Modified Governing Equations for Unsteady Compressible Flow in Ducts

1978 ◽  
Vol 45 (4) ◽  
pp. 723-726 ◽  
Author(s):  
A. Celmin¸sˇ
Keyword(s):  
Compressible Flow ◽  
Power Law ◽  
Unsteady Flows ◽  
Tube Flow ◽  
Axially Symmetric ◽  
Governing Equations ◽  
Flow Equations ◽  
Circular Tubes ◽  
First Order ◽  
General Conservation

Conventional governing equations for unsteady compressible tube flows are reviewed and it is shown that they neglect first-order terms which can have significant magnitudes. The derivation of correct tube flow equations from general conservation laws is demonstrated for the case of axially symmetric straight tubes. The traditionally neglected terms are computed explicitly for unsteady flows with power law profiles through circular tubes.

scholarly journals The effect of core size on the speed of compressible hollow vortex streets

2017 ◽  
Vol 836 ◽  
pp. 797-827 ◽  
Author(s):  
Darren G. Crowdy ◽  
Vikas S. Krishnamurthy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Vortex Core ◽  
Perturbation Expansion ◽  
Core Size ◽  
Flow Equations ◽  
Stable Case ◽  
First Order ◽  
Aspect Ratios ◽  
Vortex Streets

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Mach-number perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai–Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky–Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down.

Rotordynamic Coefficients for Compressible Flow in Tapered Annular Seals

1985 ◽  
Vol 107 (3) ◽  
pp. 318-325 ◽  
Author(s):  
C. C. Nelson
Keyword(s):  
Compressible Flow ◽  
Flow Model ◽  
Space Shuttle ◽  
Governing Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Stiffness And Damping ◽  
Main Engine

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs’ turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes

2021 ◽  
pp. 107754632110004
Author(s):  
Hassan Afshari ◽  
Hossein Amirabadi
Keyword(s):  
Carbon Nanotubes ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Conical Shells ◽  
First Order ◽  
Effective Mechanical Properties ◽  
Comprehensive Study

In this article, a comprehensive study is conducted on the free vibration analysis of rotating truncated conical shells reinforced with functionally graded agglomerated carbon nanotubes The shell is modeled based on the first-order shear deformation theory, and effective mechanical properties are calculated based on the Eshelby–Mori–Tanaka scheme along with the rule of mixture. By considering centrifugal and Coriolis accelerations and initial hoop tension, the set of governing equations is derived using Hamilton’s principle and is solved numerically using the differential quadrature method Convergence and accuracy of the presented model are confirmed and the effects of different parameters on the forward and backward frequencies of the rotating carbon nanotube-reinforced truncated conical shells are investigated.

An Asymptotic, Thermo-Diffusive Ignition Theory of Porous Solid Fuels

1976 ◽  
Vol 98 (2) ◽  
pp. 269-275 ◽  
Author(s):  
Choong Se Kim ◽  
Paul M. Chung
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Porous Solid ◽  
Solid Fuels ◽  
Thermal Ignition ◽  
Mass Balances ◽  
Governing Equations ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Time Space ◽  
Gaseous Oxidant

The governing equations of thermal ignition are analyzed for porous solid fuel, such as coal, of various two-dimensional and axisymmetric geometries by the Laplace asymptotic method. Mass diffusion of the gaseous oxidant through the porous fuel is included. The nonlinear partial differential equations of energy and mass balances in time-space coordinates containing the Arrhenius volumic chemical reaction terms are analyzed. By employing the Laplace asymptotic technique and by invoking a certain limit theorem, the governing equations are reduced to a first order ordinary differential equation governing the fuel surface temperature, which is readily solved numerically. Detailed discussion of the effects of the various governing parameters on ignition is presented. Because of the basically closed-form nature of the solutions obtained, many general and fundamental aspects of the ignition criteria hitherto unknown are found.

scholarly journals BACH FLOWS OF PRODUCT MANIFOLDS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250039 ◽  
Author(s):  
SANJIT DAS ◽  
SAYAN KAR
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Ricci Flow ◽  
Flow Characteristics ◽  
Geometric Flow ◽  
Flow Equations ◽  
First Order ◽  
Bach Tensor ◽  
Point Condition ◽  
Future Work

We investigate various aspects of a geometric flow defined using the Bach tensor. First, using a well-known split of the Bach tensor components for (2, 2) unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like S2 × S2, R2 × S2. In addition, we obtain the fixed-point condition for general (2, 2) manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped 4-manifolds, we reduce the flow equations to a first-order dynamical system, which is solved exactly to find the flow characteristics. We compare our results for Bach flow with those for Ricci flow and discuss the differences qualitatively. Finally, we conclude by mentioning possible directions for future work.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

Mixed State Hamiltonian Element for Plane Transversely Isotropic Magnetoelectroelastic Solids

2013 ◽  
Vol 275-277 ◽  
pp. 1978-1983
Author(s):  
Xiao Chuan Li ◽  
Jin Shuang Zhang
Keyword(s):  
Mixed State ◽  
Hamiltonian Formulation ◽  
Transversely Isotropic ◽  
Laminated Plates ◽  
Governing Equations ◽  
Time Coordinate ◽  
First Order ◽  
Linear Elements ◽  
Propagation Matrix ◽  
Magnetoelectroelastic Solids

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

scholarly journals Black holes, first-order flow equations and geodesics on symmetric spaces

2009 ◽  
Vol 57 (5-7) ◽  
pp. 659-665
Author(s):  
J. Perz ◽  
P. Smyth ◽  
T. Van Riet ◽  
B. Vercnocke
Keyword(s):  
Black Holes ◽  
Symmetric Spaces ◽  
Order Flow ◽  
Flow Equations ◽  
First Order
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