Simulation of the Transient Response of a Helicopter Turboshaft Engine to Hot-Gas Ingestion

2008 ◽  
Author(s):  
Gu¨lru Koc¸er ◽  
Og˘uz Uzol ◽  
I˙lkay Yavrucuk
Keyword(s):  
Transient Response ◽  
Algebraic Equations ◽  
Gas Generator ◽  
Simulation Code ◽  
Exhaust Gases ◽  
Transient Behaviour ◽  
Hot Gas ◽  
Speed Governor ◽  
Linear Algebraic Equations ◽  
Turboshaft Engine

Hot-Gas Ingestion (HGI) to the engines can potentially occur when a rotorcraft or a VTOL/STOVL fixed-wing aircraft is operating in close proximity to the ground. Especially for helicopters, due to the rotor downwash hot exhaust gases get recirculated into the engine inlet. Similar conditions may also occur due to the ingestion of hot exhaust gases from rocket launchers or gun fire. In this study, we present the results of a simulation of the transient response of a helicopter turboshaft engine to HGI. Specifically for this study we will present the results for the T800-LHT-800 turboshaft engine. The simulations are performed using an in-house generic simulation code based on an aerothermal model, which consists of the governing equations representing the aero-thermodynamic process of each engine component. The algorithm is composed of a set of differential equations and a set of non-linear algebraic equations which are solved numerically in a sequence. A simple proportional control algorithm is also incorporated into the simulation code, which acts as a simple speed governor. Simulation results show that the code has the potential to correctly capture the transient behaviour of a turboshaft engine under various HGI conditions, such as the reduction in the gas generator speed and the power levels as well as the decrease in the compressor surge margin. The code can also be used for developing engine control algorithms as well as health monitoring systems.

Transient Response of Distributed Parameter Systems

1997 ◽  
Author(s):  
Jianping Zhou ◽  
Zhigang Feng
Keyword(s):  
Differential Equations ◽  
Transient Response ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
One Dimensional ◽  
Linear Algebraic Equations ◽  
Global Equilibrium ◽  
Distributed Transfer Function

Abstract A semi-analytic method is presented for the analysis of transient response of distributed parameter systems which are consist of one dimensional subsystems. The system is first divided into one dimensional sub-systems. Within each subsystem, replacing differentials on time t by finite difference, the governing partial differential equations are reduced to difference-differential equations. The solution of derived ordinary differential equations is obtained in an exact and closed form by distributed transfer function method and represented in nodal displacement parameters. Assemling global equilibrium equations at each nodes according to displacement continuity and force equilibrium requirements gives simutaneous linear algebraic equations. Numerical results are illustrated and compared with that of finite element method.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

Interaction of Wheelspace Coolant and Main Flow in a New Aeroderivative LPT

2006 ◽  
Author(s):  
Francesco Montomoli ◽  
Michela Massini ◽  
Nicola Maceli ◽  
Massimiliano Cirri ◽  
Luca Lombardi ◽  
...  
Keyword(s):  
Flux Distribution ◽  
Low Pressure ◽  
Main Flow ◽  
Space Region ◽  
Heat Flux Distribution ◽  
Gas Generator ◽  
Component Reliability ◽  
Accuracy Requirement ◽  
Low Pressure Turbine ◽  
Hot Gas

Increased computational capabilities make available for the aero/thermal designers new powerful tools to include more geometrical details, improving the accuracy of the simulations, and reducing design costs and time. In the present work, a low-pressure turbine was analyzed, modeling the rotor-stator including the wheel space region. Attention was focused on the interaction between the coolant and the main flow in order to obtain a more detailed understanding of the behavior of the angel wings, to evaluate the wall heat flux distribution, and to prevent hot gas ingestion. Issues of component reliability related to thermal stress require accurate modeling of the turbulence and unsteadiness of the flow field. To satisfy this accuracy requirement, a full 3D URANS simulation was carried out. A reduced count ratio technique was applied in order to decrease numerical simulation costs. The study was carried out to investigate a new two-stage Low Pressure Turbine from GE Infrastructure Oil&Gas to be coupled to a new aeroderivative gas generator, the LM2500+G4, developed by GE Infrastructure, Aviation.

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