Periodic Transonic Flow Research Articles

A cubic-spline-based time collocation method applied to simulate periodic transonic flows

A cubic-spline-based time collocation method is used to solve periodic transonic flows for aeroelastic analysis. The time periodical flow variables are first approximated by cubic splines, and then the time-derivative terms are represented by a source term, which couples the flow solutions at all the sampled time instants. Simulation of two transonic external unsteady flows, including the oscillating NACA 0012 aerofoil and pitching rectangular supercritical wing, were carried out. The cubic-spline-based time collocation method with relatively small number of time instants sampled demonstrate high accuracy, whilst it is several times faster than the conventional time-marching method. The effect of different basis function used in the time collocation methods are also studied by comparing the results to that of the state-of-the-art time spectral method. This method was also validated against aeroelastic experimental data of the vibrating STCF 11 turbine blades. Only single passage computational mesh is involved by adopting the phase-lag periodic conditions. Good accuracy of the proposed time collocation method is also achieved and about one order of speed-up is obtained as compared with time-marching simulation.

Comparative analysis of computational methods for periodic transonic flows at low and high frequencies

This paper presents a comparative analysis via simulation of time-periodic unsteady inviscid flow at low and high frequencies using Time Spectral Method (TSM) and comparing it with the traditional methods such as BDF and Explicit Structured Adaptive Grid Method. The TSM uses a Fourier representation in time. Mathematical tools used here are discrete Fourier transformations. The TSM has been proposed for the fast and efficient computation of periodic unsteady flows. This method has been evaluated and has been validated with NACA pitching airfoils that are widely used and prevalent 2D external aerodynamics test cases. To validate the results presented by the TSM are compared with experimental data and two the other methods. It shows a significant reduction in the computational expense compared to the conventional time-accurate methods, due to taking advantage of the periodic nature of flow by Fourier representation for temporal discretization that has a high accuracy. Also it has shown that TSM can be applied accurately for ample rang of variations of frequency (NACA 64A010 (CT6)) and variations in angle of attacks (NACA 0012 (CT1)).

Comparative analysis of computational methods for periodic transonic flows at low and high frequencies

Comparative analysis of computational methods for periodic transonic flows at low and high frequencies

Periodic transonic flow and control

AbstractThe current understanding of periodic transonic flow is reviewed briefly. The effects of boundary-layer transition, non-adiabatic wall conditions and modifications to the aerofoil surface geometry at the shock interactions on periodic transonic flow are discussed. Through the methods presented, it is proposed that the frequency of periodic motion can be predicted with reasonable accuracy, but there are limitations on the prediction of buffet boundaries associated with periodic transonic flows. Several methods have been proposed by which the periodic motion may be virtually eliminated, most relevantly by altering the position of transition fix, contouring the aerofoils surface or adding a porous surface and a cavity in the region of shock interaction. In addition, it has been shown that heat transfer can have a significant effect on buffet.

Effect of heat transfer on periodic transonic flows

AbstractThe effects of the model surface to free stream adiabatic temperature ratio (Tw/Tad) on periodic transonic flow over a 14% thick biconvex aerofoil are evaluated using a computational fluid dynamic approach. The analysis is based on the thin layer Navier Stokes equations with Baldwin-Lomax turbulence model. The results of computations showed that on biconves aerofoils there is a large effect of heat transfer on instantaneous pressure distributions and periodic buffet excitation level confirming some of the available experimental data. The effects observed have an implication in wind tunnel measurement of buffet associated periodic transonic flows.

Studies on alleviation of buffet in periodic transonic flow

Studies on alleviation of buffet in periodic transonic flow

On periodic transonic flows of a viscous gas

On periodic transonic flows of a viscous gas

Periodic transonic flow without and with condensation in a 2-D plane channel

Steady 2-D adiabatic viscous flow and diabatic inviscid flow with energy supply by homogeneous condensation in a channel with a wavy wall have been numerically simulated. The methods used are an analytical-numerical combination procedure for the shock/boundary layer interaction and a diabatic finite volume method to solve the time dependent Euler equations, being linked with the classical nucleation theory and a droplet growth law. The influences of viscous effects and heat addition on the flow field with more than one local supersonic region as well as the choking state have been investigated. The aim is to achieve an adiabatic periodic flow field with imbedded shock waves and a diabatic periodical one including condensation and evaporation phenomena. In the case of adiabatic flow the calculated velocity distribution is compared with experimental and analytical results.

Effect of model cooling on periodic transonic flow

Experimental investigations were conducted in a small transonic intermittent tunnel on 14 and 18% thick biconvex airfoils to study the effect of model temperature on periodic transonic flows. The Reynolds number based on the model chord was in the range 0.7-0.9 x 106. Tests were conducted in the Mach number range of 0.7-0.85, and the model-to-tunnel stagnation temperature ratio range of 0.6-1.0. The models were cooled in liquid nitrogen to the required temperature before a run. The measurements included model surface mean pressure and temperatures and tunnel side wall dynamic pressures. The results showed a large effect of model temperature on mean pressure distribution and periodic buffet excitation levels. The effects observed are thought to correspond with what would happen to adiabatic flows at greatly increased Reynolds numbers. Nomenclature Cp = pressure coefficient Cpte = pressure coefficient measured at x/c =0.95 c = model chord length, mm / = frequency, Hz M = freestream Mach number MI = Mach number just upstream of the shock n = nondimensional frequency parameter, 2irfc/u p = rms pressure fluctuations, N/M2 q = kinetic pressure, N/M2 Re = Reynolds number based on model chord TW, Tad = wall and adiabatic recovery temperature, K / = times, s u - freestream velocity, m/s x,y = coordinates from the leading edge of model 5 = boundary-layer thickness

Periodic Transonic Flow with Heat Addition: New Results

Abstract Further experiments on cyclic, unsteady, transonic flow with heat addition are described. The heat addition is produced by condensation by homogeneous nucleation of water vapor or ethanol in the throat region of a Laval nozzle. Different carrier gases are used and frequencies of pressure fluctuations up to 22 kHz are found. Terms in a dimensional analysis that had previously not been investigated were studied. The new terms included different Damkohler parameters and the ratio of the specific heats. Under certain conditions condensation at M<I was observed. A qualitative description of the process and estimates of the frequency yielded satisfactory results.

Numerical Solution of Periodic Transonic Flow through a Fan Stage

A numerical method of solution of the inviscid, compressible, two-dimensional, unsteady flow on a blade-toblade stream surface through a stage (rotor and stator), or a single blade row, of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages, which asymptotically achieves the correct phase between all passages of a stage. A shock-capturin g finitedifference method is employed in the interior of the passage, and a method-of-characteristiics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries, and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges which are assumed to be sharp. Results are presented for a transonic fan stage. The rotor tip section solution is compared with an experimental pressure contour map. The subcritical stator solution is compared with results from a stream function method. Finally, the periodic solution for the stage, which has 44 rotor blades and 46 stator blades, is discussed.