Transonic Flow Regime Research Articles

Aeroacoustic Coupling Effect During the Ascent of Space Transportation Systems

After the failure of maiden flight 157 of Ariane 5 Evolution Cryotechnique type A (ECA), the inquiry board responsible for the investigation reported as one of the probable causes the “non-exhaustive definition of the loads to which the Vulcain 2 engine is subjected during flight.” As a result, many research activities were set up with the objective to isolate the driving mechanisms. Driving mechanisms such as pumping, flapping, or swinging were found to excite oscillations in the base region. Despite this finding, the question of why the pressure fluctuations and base flow excitations are especially pronounced in the subsonic to transonic flow regime remained unclear. This question is addressed in the study at hand. Results from the literature are combined with recent wind-tunnel measurements on the base model of a space transportation system. The measurement data were acquired by means of particle image velocimetry, pressure transducers, and high-speed schlieren imaging. The results suggest that an aeroacoustic coupling takes place between a jet noise generation mechanism called screeching and the near-wake dynamics. Due to the nature of both effects, they are likely to reach a resonating frequency during the ascent. The resonant frequency appears to increase unfavorable fluctuations in the base region, which are held responsible for the amplified unsteady loads. A schematic model concept is proposed, which describes the underlying governing mechanism. It provides an explanation for question why buffeting effects are especially amplified in the high subsonic ambient flow regime.

Dynamics of Shock Waves Interacting With Laminar Separated Transonic Turbine Flow Investigated by High-Speed Schlieren and Surface Hot-Film Sensors

Abstract The results presented in this paper are based on experimental investigations on a generic transonic low pressure turbine profile at high subsonic exit Mach numbers. Here, the flow on the suction side reaches a maximum isentropic Mach number of approximately 1.2 and features a large separation bubble in a transonic flow regime characterized by surface hot-film measurements. The measurements are supplemented by Schlieren images recorded with a high-speed camera at 19.2 kHz. A highly unsteady normal shock wave on the suction side is observable upstream of the trailing edge. It is interacting with laminar separated flow which is rarely documented in literature. The interaction of the normal shock with the boundary layer flow seems to amplifies the ongoing transition process over the separation bubble and the flow reattaches shortly downstream. A statistical analysis of the Schlieren images reveals characteristic low frequencies of the shock wave motions and a pulsation of the separation bubble. Additionally, the statistical information of the time-dependent signal from the surface hot-film sensors demonstrate the instabilities influencing the boundary layer linked to the unsteadiness in the main flow.

Supplemental-frequency harmonic balance: A new approach for modeling aperiodic aerodynamic response

Presented in this work is a novel and easy-to-implement supplemental-frequency harmonic balance (SF-HB) approach to efficiently compute dynamically aperiodic systems, which can be cumbersome to model using the nominal high-dimensional harmonic balance (HDHB) technique. The stability of the time-spectral operator and the SF-HB solver involving multiple excitation frequencies is ensured by introducing a group of supplemental frequencies based on the fact that aperiodic (or almost aperiodic) response would contain all possible frequencies. Together with the excitation (primary) frequencies, the frequency set forms a nearly-harmonic series leading to a small condition number for the Fourier transformation matrices directly impacting the stability of the HDHB solver. In contrast to the similar work reported in the literature where optimal unequally-spaced sub-time levels are determined through a rather complicated procedure, the current approach simply uses equally-spaced sub-time levels spanning a time period that depends on a predicted base frequency. At convergence, the original excitation frequency modes dominate the solution as desired. This new technique is verified for a forced pitching airfoil in the transonic inviscid flow regime subjected to two excitation frequencies. Results of both periodic and aperiodic cases show that with the help of Fourier interpolation, the entire time history of the dynamic response can be obtained through a single run of the SF-HB solver, for which the efficiency and robustness of the traditional HDHB method is preserved.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids

In this paper, we present recent improvements of an Immersed Boundary Method (IBM) for the simulation of turbulent compressible flows on Cartesian grids. The proposed approach enables to remove spurious oscillations at the wall on skin pressure and friction coefficients. Results are compared to a body-fitted approach using the same wall function, showing that the stair-step immersed boundary provides a smooth solution compared to the body-fitted one.The immersed boundary method has been modified to adapt the location of forced and forcing points involved in the immersed boundary reconstruction to the Reynolds number. This method has been validated either for subsonic and transonic flow regimes, through the simulation of the subsonic turbulent flow around a NACA0012 profile and the transonic flow around a RAE2822 profile and the three-dimensional ONERA M6 wing.

Numerical Calibration of Three-Dimensional Printed Five-Hole Probes for the Transonic Flow Regime

Abstract This paper presents a method for a cost- and time-effective calibration procedure for five-hole probes for the transonic flow regime based on additive manufacturing and a numerical calibration routine. The computational setup and calibration routine are described in detail. The calibration procedure is tested on a custom-built L-shaped conical probe of 30 deg half-angle with a flat tip and an outer diameter of 2.4 mm. The probe tip is manufactured in stainless steel using direct metal laser sintering. Numerical calibration is carried out over a Mach number range of 0.2–1.4 and pitch and yaw angles of ±45 deg. The numerical calibration charts are validated with wind tunnel tests across the entire Mach number range and the expected accuracy of the numerical calibration method is quantified. Exemplary results of area traverses up- and downstream of a linear transonic turbine cascade with tip clearance are presented and discussed briefly.

Rp‐adaptation for compressible flows

AbstractWe present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature‐based sensors or error estimators. We demonstrate this proof‐of‐concept using two geometries in transonic and supersonic flow regimes. The method has been implemented in the open‐source spectral/hp element framework Nektar++, and adaptivity is performed by its dedicated high‐order mesh generation tool NekMesh. The results show that the proposed rp‐adaptation methodology is a reasonably cost‐effective way of improving simulation accuracy.

Experimental Investigation of Transonic Buffet Control on a Wing Airfoil Using Tangential Jet Blowing

The results of an experimental investigation of the suppression of shock-induced flow separation and the elimination of transonic buffet in transonic flow regimes using tangential jet blowing onto the upper surface of a supercritical wing airfoil are presented. The experimental investigation is performed in the T-112 wind tunnel of the Central Aerohydrodynamic Institute (TsAGI). The results obtained for the baseline configuration and those with jet blowing are analyzed and compared. They showed that the tangential jet blowing suppresses the shock-induced flow separation, increases the lift, and delays the onset of the buffet.

Formation of a transonic region in a variable-section channel for different stagnation temperatures of the flow

Initiation of operation of a ramjet engine with distributed fuel injection along the combustion chamber is studied numerically. A principally important issue is the presence of a compressed air jet producing a throttling effect and preliminary deceleration of the flow to transonic velocities. The Reynolds-averaged Navier-Stokes equations closed by the SST k-ω turbulence model are solved. Hydrogen is used as a gaseous fuel. Transverse injection of the fuel is considered. A pulsed transonic flow regime is obtained. It is demonstrated that the characteristic scale of vortex regions increases with an increase in the stagnation temperature approximately to 1700 K; consequently, the degree of air-hydrogen mixing is significantly enhanced.

Control of the Formation of a Transonic Region in an Axisymmetric Supersonic Flow with the Use of a Jet and a Near-Wall Energy Supply

The control action of a throttling air jet produced by a gas generator and of the energy sources positioned at the walls of an axisymmetric channel, which models the combustion-chamber unit of a ramjet in which a gas flow is decelerated, on the shock-wave structure of a supersonic gas flow in the channel was investigated for the purpose of formation of a lengthy transonic region in it. A heat energy was supplied to the gas flow in the indicated channel in the pulse-periodic regime, and the pressure in the gas generator was also changed periodically. The range of energies corresponding to a stable transonic flow regime in the channel was determined on the basis of solution of the nonstationary Euler equations in dimensionless variables. For comparison, the combustion of a gaseous fuel inflowing to the channel through a slot in the channel wall upstream of the control air jet was considered. A nonstationary gas flow in the channel was calculated on the basis of the Reynolds-averaged Navier–Stokes equations with the use of the k–ω SST model of turbulence. It is shown that a controllable energy release in the channel, providing the obtaining of a transonic flow regime in it analogous to that obtained on the basis of solution of the Euler equations, can be realized with the use of a control transverse air jet.

Numerical Analysis of Transonic Flow around Cones

A new solver is presented for transonic flow around cone-cylinder, axisymmetric bodies. Ground experiments almost always suffer from uncertainty due to operating in the presence of high levels of facility noise. Besides, experimental measurements of these mechanisms are not available at high-speed flows. Direct Numerical Simulations have made it possible to compute details of the transonic mechanisms but still a significant challenge due to the cost. This study aims to present a new solver to model transonic flows. To assess the new solver, the surface Mach number and the drag coefficient are investigated as the freestream Mach number varies. The results are in excellent agreement with experimental data, indicating the new model is capable of accurately predicting the aerodynamics coefficients at transonic flow regimes.

Use of computational fluid dynamics to implement an aerodynamic inverse design method based on exact Riemann solution and moving wall boundary

An aerodynamic inverse design method, which is used in compressors, is introduced in this paper. This inverse design method is based on the exact solution of the local Riemann problem on moving blade surfaces. Furthermore, an improved relaxation factor is added to control the induced velocity for reasonable deformation sizes in different cases. The viscous flow analysis and the inverse design are integrated in the computational fluid dynamics software ANSYS Fluent using the dynamic mesh user-defined function, which reduces the time spent on remeshing the computational domain. A compressor cascade is taken to illustrate the effect of this inverse design method. Using the compressor model, the case of a different loading pattern design under a high subsonic flow regime and the case of a loading smooth design under a transonic flow regime have proved the capability of this inverse design method to realize the prescribed pressure loading distribution.

The influence of dual stream jet nozzle internal parts on the three-dimensional flow structure in a supersonic jet

The work is devoted to the experimental study of a high-speed jet exhausting from a model dual stream jet nozzle, performed using non-contact (shadow visualization) and probe (total-pressure pneumatic receiver) methods for measuring gasdynamic quantities. Azimuthal non-uniformity of the pressure distribution, whose value in the external duct is much higher than that in the internal duct, is revealed. The cause for the formation of the spatial flow structure is related to the supporting pylons inside the nozzle contour and to the occurrence of a transonic flow regime in the external duct.

Steady transonic dense gas flow past two‐dimensional compression/expansion ramps revisited

AbstractSupersonic flow past compression/expansion ramps represents a canonical problem in fluid dynamics which has been studied extensively in the past assuming perfect gas behaviour. More recently real gas effects on such flows have received increasing attention as part of efforts, among others, to increase the efficiency of Organic Rankine Cycles for decentralized power plants. Of special interest in this connection are dense gases of Bethe–Zel'dovich–Thompson fluids which have the distinguishing property that the so called fundamental derivative of gasdynamics Γ takes on negative values in the general neighbourhood of the thermodynamic critical point. Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| ≪ 1, , Kluwick and Cox [1], [2]. These studies have revealed a number of new phenomena and a non‐uniqueness of solutions exceeding that known from the theory of perfect gases.Here we extend the analysis to cover flows where the unperturbed state in the p, 1/ρ plane is in the vicinity of the point on the transition line where Γ and Λ vanish simultaneously. Such flows have |Γ0| ≪ 1, |Λ0| ≪ 1, and are of considerable practical interest as isentropes that can be realized experimentally at present just barely enter the negative Γ region. Again an increased wealth of possible solutions is observed.

Allowance for Gas Compressibility in the γ-Model of the Laminar–Turbulent Transition

The formulation and applicability range of the $$\gamma $$ -model of laminar–turbulent transition are analyzed. Its implementation in the EWT-TsAGI application package and verification results for the problem of computing a transitional boundary layer on a plate are described. The cases of zero and adverse pressure gradients are considered. A modification of the $$\gamma $$ -model that takes into account the effect of compressibility on the laminar–turbulent transition location is proposed. Two problems are considered to calibrate and test the correction term: the flow over the LV6 laminar-flow airfoil and the flow over the nacelle of a bypass turbojet engine. It is shown that, with the used of the proposed correction, the laminar–turbulent transition location can be correctly predicted in transonic flow regimes.

Upgrade and development of elastic surface inverse design method for axial compressor cascade with sharp-edged blades

The aim of an inverse design method is to calculate the geometry corresponding to a target pressure distribution along the walls. Elastic Surface Algorithm (ESA), as one of the newest residual-corrective inverse design method, was proposed for external flows in 2014. In this method, the airfoil walls were considered as a flexible elastic beam that deforms due to the difference between the target and current pressure distribution at each shape modification step. Nevertheless, the previous version of ESA is subjected to oscillation, instability, and divergence for a cascade of sharp-edged blades due to the steep pressure gradient at the leading edge. This study upgrades the ESA for the shape design of sharp-edged blades with steep gradients of pressure near the stagnation point. The basis of this upgrade was to use the deflection curve of Timoshenko beam which is continuous and differentiable at all the nodes. The upgraded ESA against the original ESA used only the physical characteristics of Timoshenko beam instead of applying a geometric filtration for the removal of fractures in the intermediate profiles at large deformations. To increase the beam deformation at each shape modification, the upgraded ESA removed the constraint of node displacement along the spine direction, which is normal to the chord line, so that the nodes of Timoshenko beam could freely move based on the large deformation equations. In addition, the optimal values of elastic modulus, thickness, and width of the beam were obtained to increase the convergence rate of the ESA. The upgraded ESA was finally verified for a DCA blade cascade in subsonic and transonic flow regimes under different angles of attack and different initially-guessed geometries. The results showed the upgraded ESA to be a robust, flexible, and fast-converging inverse design method for sharp-edged blades with steep pressure gradients.

Turbulent Triggers and the Model Quality Influence on Aerodynamic Characteristics of the Laminar Aerofoil in Transonic Flow Regime

Abstract The test with a roughness application on the laminar aerofoil has been conducted in the N-3 trisonic wind tunnel of the Institute of Aviation in Warsaw. The main goal of tests was to investigate the influence of the boundary layer transition triggers on a laminar profile aerodynamic characteristic. For baseline configuration, the natural transition was applied. As a local roughness on the upper model surface, the carborundum strips with different heights were applied. These were positioned on the upper model surface in the front of the shock position occurrence. The Mach number during test was equal Ma = 0.7 and Reynolds number was about 2.85·106. Tests have been conducted for different model incidence in range 0°-7°. Current article refers partially to the previous study, where aerofoil model with lower quality of surface had been tested. Investigation results from previous work indicated that some of transition positions improved an aerodynamic characteristic by reducing the drag coefficient value and decreasing shock wave unsteadiness in the transonic regime. However, current article indicates that beneficial effects in respect to the baseline configuration are also strictly dependent on the model quality and turbulent triggers size. Improved surface quality of the laminar aerofoil model affected on aerodynamic characteristics with and without turbulent triggers. Resultant aerodynamic coefficients of all tested cases i.e. drag, lift and lift to drag ratio were compared.

Determination of the laminar-turbulent transition location in numerical simulations of subsonic and transonic flows past a flat plate

The study is aimed at determining the position of the laminar-turbulent transition in subsonic and transonic two-dimensional boundary layers with the use of a novel software package LOTRAN 2.0 developed by the authors. The package is based on the eN-method and employs numerical data of numerical simulations of the laminar flow performed by standard gas-dynamic software systems based on the Reynolds-averaged Navier-Stokes equations. As an example, the flow past a flat plate is considered. The good agreement of the computed and experimental data on the laminar-turbulent transition location is demonstrated. New data on the laminar-turbulent transition in the boundary layer on a flat plate for transonic flow regimes are obtained.

Aeroelastic Modeling of the AGARD 445.6 Wing Using the Harmonic-Balance-Based One-Shot Method

The harmonic-balance-based one-shot method is developed for modeling the aeroelastic response of three-dimensional configurations such as aircraft wings in transonic flow regimes. This approach computes both of the fluid and structure fields by integrating respective harmonic-balance forms of governing equations in pseudotime, and variables of both fields are converged simultaneously in one shot. Several significant advantages of this code-coupling approach are observed. First, the computational cost is nearly independent of the number of structural modes retained in the analysis, which offers substantial computational efficiency over traditional aeroelastic solution techniques. Second, the solution of the two fields needs not be time synchronized, unlike what is required in traditional dual-time-stepping time-accurate approaches. This allows two solvers to use respective optimal physical time steps (different number of harmonics), different (optimal) pseudotime steps, as well as different integration techniques (explicit or implicit) to achieve the fastest convergence rates. The two operational modes of the one-shot method, which requires either the reduced velocity or the vibration amplitude as the main input, are discussed in detail. Numerical results of the AGARD 445.6 wing model show that the one-shot method can very rapidly predict the flutter boundary as well as the limit-cycle-oscillation response, offering a promising new technique to solve dynamic aeroelasticity problems.

Accurate 2-D Modelling of Transonic Compressor Cascade Aerodynamics

Modern aeronautic fans are characterised by a transonic flow regime near the blade tip. Transonic cascades enable higher pressure ratios by a complex system of shockwaves arising across the blade passage, which has to be correctly reproduced in order to predict the performance and the operative range. In this paper, we present an accurate two-dimensional numerical modelling of the ARL-SL19 transonic compressor cascade. A large series of data from experimental tests in supersonic wind tunnel facilities has been used to validate a computational fluid dynamic model, in which the choice of turbulence closure resulted critical for an accurate reproduction of shockwave-boundary layer interaction. The model has been subsequently employed to carry out a parametric study in order to assess the influence of main flow variables (inlet Mach number, static pressure ratio) and geometric parameters (solidity) on the shockwave pattern and exit status. The main objectives of the present work are to perform a parametric study for investigating the effects of the abovementioned variables on the cascade performance, in terms of total-pressure loss coefficient, and on the shockwave pattern and to provide a quite large series of data useful for a preliminary design of a transonic compressor rotor section. After deriving the relation between inlet and exit quantities, peculiar to transonic compressors, exit Mach number, mean exit flow angle and total-pressure loss coefficient have been examined for a variety of boundary conditions and parametrically linked to inlet variables. Flow visualisation has been used to describe the shock-wave pattern as a function of the static pressure ratio. Finally, the influence of cascade solidity has been examined, showing a potential reduction of total-pressure loss coefficient by employing a higher solidity, due to a significant modification of shockwave system across the cascade.

Wall Temperature and Suction Control of Linear Modes in Compressible Corner Flow

Linear stability behavior of self-similar streamwise corner flows is investigated under the influence of constant wall temperatures and suction rates perpendicular to each wall. For three Mach numbers, 0.1, 0.95, and 1.5, representing subsonic, transonic, and supersonic flow regimes, modes that propagate in the streamwise direction, i.e., with a wave number at the lateral boundaries, are studied first. Then, the influence of and on the stability of oblique modes with is investigated for the transonic flow. It is shown that the effect on the leading viscous mode with is the same for cooling and suction in the case of small variations in temperature and suction relative to the reference flow without control. However, the increase in stability of the inviscid corner modes depends on both the control method and the Mach number. The stability of oblique viscous modes increases as well and it is shown that at the critical point is independent of the wall temperature and the suction rate. In addition, a maximum spanwise wave number is observed for which the most critical viscous mode is still amplified.