**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1220

# Search results for: Unsteady gas equation

##### 1220 Lagrangian Method for Solving Unsteady Gas Equation

**Authors:**
Amir Taghavi,
kourosh Parand,
Hosein Fani

**Abstract:**

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

**Keywords:**
Unsteady gas equation,
Generalized Laguerre functions,
Lagrangian method,
Nonlinear ODE.

##### 1219 Investigation on Unsteady Flow of a Turbine Stage with Negative Bowed Stator

**Authors:**
Keke Gao,
Tao Lin,
Yonghui Xie,
Di Zhang

**Abstract:**

Complicated unsteady flow in axial turbines produces high-frequency unsteady aerodynamic exciting force, which threatens the safe operation of turbines. This paper illustrates how negative-bowed stator reduces the rotor unsteady aerodynamic exciting force by unsteady flow field. With the support of three-dimensional viscous compressible Navier-Stokes equation, the single axial turbines with 0, -10 and -20 degree bowed stator are comparably investigated, aiming to identify the flow field structure difference caused by various negative-bowed degrees. The results show that negative-bowed stator strengthens the turbulence kinetic energy, which is further strengthened with the increase of negative-bowed degree. Meanwhile, the flow phenomenon including stator wakes and passage vortex is shown. In addition, the interaction of upstream negative-bowed wakes contributes to the reduction of unsteady blade load fluctuation. Furthermore, the aerodynamic exciting force decreases with the increasing negative bowed degree, while the efficiency is correspondingly reduced. This paper provides the reference for the alleviation of the harmful impact caused by unsteady interaction with the method of wake control.

**Keywords:**
Unsteady flow,
axial turbine,
wake,
aerodynamic force,
loss.

##### 1218 CFD of Oscillating Airfoil Pitch Cycle by using PISO Algorithm

**Authors:**
Muhammad Amjad Sohail,
Rizwan Ullah

**Abstract:**

**Keywords:**
Angle of attack,
Centre of pressure,
subsonic flow,
pitching moment coefficient,
turbulence mode

##### 1217 Analytical solution of Gas Flow Through a Micro-Nano Porous Media by Homotopy Perturbation method

**Authors:**
Jamal Amani Rad,
Kourosh Parand

**Abstract:**

**Keywords:**
Unsteady gas equation,
Homotopy perturbation method(HPM),
Porous medium,
Nonlinear ODE

##### 1216 Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation

**Abstract:**

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

**Keywords:**
Navier-Stokes,
'Non-linear grid system',
Splitting method.

##### 1215 Unsteady Temperature Distribution in a Finite Functionally Graded Cylinder

**Authors:**
A. Amiri Delouei

**Abstract:**

In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

**Keywords:**
Functionally graded materials,
unsteady heat conduction,
cylinder,
Temperature distribution.

##### 1214 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 1213 Unsteady Boundary Layer Flow over a Stretching Sheet in a Micropolar Fluid

**Authors:**
Roslinda Nazar,
Anuar Ishak,
Ioan Pop

**Abstract:**

**Keywords:**
Boundary layer,
micropolar fluid,
stretching surface,
unsteady flow.

##### 1212 Unsteady Flow and Heat Transfer of Nanofluid from Circular Tube in Cross-Flow

**Authors:**
H. Bayat,
M. Majidi,
M. Bolhasani,
A. Karbalaie Alilou,
A. Mirabdolah Lavasani

**Abstract:**

Unsteady flow and heat transfer from a circular cylinder in cross-flow is studied numerically. The governing equations are solved by using finite volume method. Reynolds number varies in range of 50 to 200; in this range flow is considered to be laminar and unsteady. Al2O3 nanoparticle with volume fraction in range of 5% to 20% is added to pure water. Effects of adding nanoparticle to pure water on lift and drag coefficient and Nusselt number is presented. Addition of Al2O3 has inconsiderable effect on the value of drags and lift coefficient. However, it has significant effect on heat transfer; results show that heat transfer of Al2O3 nanofluid is about 9% to 36% higher than pure water.

**Keywords:**
Nanofluid,
heat transfer,
unsteady flow,
forced
convection,
cross-flow.

##### 1211 The Application of HLLC Numerical Solver to the Reduced Multiphase Model

**Authors:**
Fatma Ghangir,
Andrzej F. Nowakowski,
Franck C. G. A. Nicolleau,
Thomas M. Michelitsch

**Abstract:**

The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

**Keywords:**
Multiphase flow,
gas-liquid flow,
Godunov schems,
Riemann solvers,
HLL scheme,
HLLC scheme.

##### 1210 Numerical Flow Simulation around HSP Propeller in Open Water and behind a Vessel Wake Using RANS CFD Code

**Authors:**
Kadda Boumediene,
Mohamed Bouzit

**Abstract:**

The prediction of the flow around marine propellers and vessel hulls propeller interaction is one of the challenges of Computational fluid dynamics (CFD). The CFD has emerged as a potential tool in recent years and has promising applications. The objective of the current study is to predict the hydrodynamic performances of HSP marine propeller in open water and behind a vessel. The unsteady 3-D flow was modeled numerically along with respectively the K-ω standard and K-ω SST turbulence models for steady and unsteady cases. The hydrodynamic performances such us a torque and thrust coefficients and efficiency show good agreement with the experiment results.

**Keywords:**
Seiun Maru propeller,
steady,
unsteady,
CFD,
HSP.

##### 1209 Study of Explicit Finite Difference Method in One Dimensional System

**Authors:**
Azizollah Khormali,
Seyyed Shahab Tabatabaee Moradi,
Dmitry Petrakov

**Abstract:**

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

**Keywords:**
Explicit solution,
Numerical simulation,
Petroleum reservoir,
Pressure distribution.

##### 1208 Unsteady Stagnation-Point Flow towards a Shrinking Sheet with Radiation Effect

**Authors:**
F. M. Ali,
R. Nazar,
N. M. Arifin,
I. Pop

**Abstract:**

In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

**Keywords:**
Heat transfer,
Radiation effect,
Shrinking sheet Unsteady flow.

##### 1207 Heat Transfer Characteristics on Blade Tip with Unsteady Wake

**Authors:**
Minho Bang,
Seok Min Choi,
Jun Su Park,
Hokyu Moon,
Hyung Hee Cho

**Abstract:**

Present study investigates the effect of unsteady wakes on heat transfer in blade tip. Heat/mass transfer was measured in blade tip region depending on a variety of strouhal number by naphthalene sublimation technique. Naphthalene sublimation technique measures heat transfer using a heat/mass transfer analogy. Experiments are performed in linear cascade which is composed of five turbine blades and rotating rods. Strouhal number of inlet flow are changed ranging from 0 to 0.22. Reynolds number is 100,000 based on 11.4 m/s of outlet flow and axial chord length. Three different squealer tip geometries such as base squealer tip, vertical rib squealer tip, and camber line squealer tip are used to study how unsteady wakes affect heat transfer on a blade tip. Depending on squealer tip geometry, different flow patterns occur on a blade tip. Also, unsteady wakes cause reduced tip leakage flow and turbulent flow. As a result, as strouhal number increases, heat/mass transfer coefficients decrease due to the reduced leakage flow. As strouhal number increases, heat/ mass transfer coefficients on a blade tip increase in vertical rib squealer tip.

**Keywords:**
Gas turbine,
blade tip,
heat transfer,
unsteady wakes.

##### 1206 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1205 Unsteady 3D Post-Stall Aerodynamics Accounting for Effective Loss in Camber Due to Flow Separation

**Authors:**
Aritras Roy,
Rinku Mukherjee

**Abstract:**

**Keywords:**
Post-stall,
unsteady,
wing,
aerodynamics.

##### 1204 Unsteadiness Effects on Variable Thrust Nozzle Performance

**Authors:**
A. M. Tahsini,
S. T. Mousavi

**Abstract:**

The purpose of this paper is to elucidate the flow unsteady behavior for moving plug in convergent-divergent variable thrust nozzle. Compressible axisymmetric Navier-Stokes equations are used to study this physical phenomenon. Different velocities are set for plug to investigate the effect of plug movement on flow unsteadiness. Variation of mass flow rate and thrust are compared under two conditions: First, the plug is placed at different positions and flow is simulated to reach the steady state (quasi steady simulation) and second, the plug is moved with assigned velocity and flow simulation is coupled with plug movement (unsteady simulation). If plug speed is high enough and its movement time scale is at the same order of the flow time scale, variation of the mass flow rate and thrust level versus plug position demonstrate a vital discrepancy under the quasi steady and unsteady conditions. This phenomenon should be considered especially from response time viewpoints in thrusters design.

**Keywords:**
Nozzle,
Numerical study,
Unsteady,
Variable thrust.

##### 1203 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.

##### 1202 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 1201 Unsteady Flow between Two Concentric Rotating Spheres along with Uniform Transpiration

**Authors:**
O. Mahian,
A. B. Rahimi,
A. Kianifar,
A. Jabari Moghadam

**Abstract:**

**Keywords:**
Concentric spheres,
numerical study,
suction andblowing,
unsteady flow,
viscous torque.

##### 1200 Interaction between Unsteady Supersonic Jet and Vortex Rings

**Authors:**
Kazumasa Kitazono,
Hiroshi Fukuoka,
Nao Kuniyoshi,
Minoru Yaga,
Eri Ueno,
Naoaki Fukuda,
Toshio Takiya

**Abstract:**

**Keywords:**
Computational fluid dynamics,
shock wave,
unsteady jet,
vortex ring.

##### 1199 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 1198 Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation

**Authors:**
Raoudha Chaabane,
Faouzi Askri,
Sassi Ben Nasrallah

**Abstract:**

**Keywords:**
heat generation,
cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

##### 1197 Unsteady Water Boundary Layer Flow with Non-Uniform Mass Transfer

**Authors:**
G. Revathi,
P. Saikrishnan

**Abstract:**

**Keywords:**
Boundary layer,
heat transfer,
non-similar solution,
non-uniform mass,
unsteady flow.

##### 1196 Effect of Amplitude and Mean Angle of Attack on Wake of an Oscillating Airfoil

**Authors:**
Sadeghi H.,
Mani M.,
Ardakani M. A.

**Abstract:**

**Keywords:**
Unsteady wake,
amplitude,
mean angle,
EPPLER
361 airfoil.

##### 1195 Unsteady Heat and Mass Transfer in MHD Flow of Nanofluids over Stretching Sheet with a Non-Uniform Heat Source/Sink

**Authors:**
Bandaris Shankar,
Yohannes Yirga

**Abstract:**

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

**Keywords:**
Manetohydrodynamics,
nanofluid,
non-uniform heat source/sink,
unsteady.

##### 1194 Unsteady Laminar Boundary Layer Forced Flow in the Region of the Stagnation Point on a Stretching Flat Sheet

**Authors:**
A. T. Eswara

**Abstract:**

**Keywords:**
Forced flow,
Keller-box method,
Stagnation point,
Stretching flat sheet,
Unsteady laminar boundary layer,
Velocity ratio parameter.

##### 1193 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

**Keywords:**
KdV equation,
Asymptotic Degeneracy,
Solitons,
Inverse Scattering

##### 1192 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method

**Authors:**
Said Laachir,
Aziz Laaribi

**Abstract:**

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

**Keywords:**
Helmholtz equation,
Nikiforov-Uvarov method,
exact solutions,
eigenfunctions.

##### 1191 A Fast, Portable Computational Framework for Aerodynamic Simulations

**Authors:**
Mehdi Ghommem,
Daniel Garcia,
Nathan Collier,
Victor Calo

**Abstract:**

**Keywords:**
Unsteady aerodynamics,
numerical simulations,
mixed-language approach,
potential flow.