Euler Analysis Research Articles

Prediction of supersonic inlet unstart caused by freestream disturbances

The objective of this article is to report progress toward the development of an Euler analysis procedure for predicting the unstart tolerance of supersonic inlets. As an aid to understanding boundary condition issues, a one-dimensional, linear-analysis procedure was developed and used to analyze inlet unstart behavior. Using these results as a guide, an Euler analysis procedure was extended through the addition of a new bleed boundary condition, a new compressor face boundary condition, and an engine demand model for the simulation of unsteady inlet flows caused by freestream flow disturbances. Five unstart conditions were identified with the Euler analysis of the axisymmetric inlet for both 20- and 90-deg throat bleed configurations. Results show that both increases and decreases in temperature or velocity will unstart the inlet, whereas only pressure decreases will unstart the inlet. It was also found that 90-deg throat bleed improves the unstart tolerance relative to 20-deg throat bleed for freestream pressure decreases, temperature increases, and changes in velocity.

An Euler solver for three‐dimensional turbomachinery flows

AbstractA time‐marching finite volume numerical procedure is presented for three‐dimensional Euler analysis of turbomachinery flows. The proposed scheme is applied to the conservative form of the Euler equations written in general curvilinear co‐ordinates. A simple but computationally efficient grid is constructed. Numerical solution results for three 3D turbine cascade flows have been presented and compared with available measurements as well as with another state‐of‐the‐art 3D Euler analysis numerical solution in order to demonstrate the accuracy and computational efficiency of the analysis method. Also, the predicted results are compared with a 3D potential flow solver and comparison is made with the analytical solution. The proposed method is an accurate and reliable technique for solving the compressible flow equations in turbomachinery geometries.

A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery

A computational method for efficiently predicting unsteady transonic flows in two-and three-dimensional cascades is presented. The unsteady flow is modeled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax–Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.

Unsteady Aerodynamics and Gust Response in Compressors and Turbines

A comprehensive series of experiments and analyses was performed on compressor and turbine blading to evaluate the ability of current, practical, engineering/analysis models to predict unsteady aerodynamic loading of modern gas turbine blading. This is part of an ongoing effort to improve methods for preventing blading failure. The experiments were conducted in low-speed research facilities capable of simulating the relevant aerodynamic features of turbomachinery. Unsteady loading on compressor and turbine blading was generated by upstream wakes and, additionally for compressors, by a rotating inlet distortion. Fast-response hot-wire anemometry and pressure transducers embedded in the airfoil surfaces were used to determine the aerodynamic gusts and resulting unsteady pressure responses acting on the airfoils. This is the first time that gust response measurements for turbines have been reported in the literature. Several different analyses were used to predict the unsteady component of the blade loading: (1) a classical flat-plate analysis, (2) a two-dimensional linearized flow analysis with a ‘frozen gust’ model, (3) a two-dimensional linearized flow analysis with a “distorted gust” model, (4) a two-dimensional linearized Euler analysis, and (5) a two-dimensional nonlinear Euler analysis. Also for the first time, a detailed comparison of these analyses methods is made and the importance of properly accounting for both vortical and potential disturbances is demonstrated. The predictions are compared with experiment and their abilities assessed to help guide designers in using these prediction schemes.

Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations

An efficient three-dimensional Euler analysis of unsteady flows in turbomachinery is presented. The unsteady flow is modeled as the sum of a steady or mean flow field plus a harmonically varying small perturbation flow. The linearized Euler equations, which describe the small perturbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A pseudo-time time-marching finite-volume Lax-Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturbation flow quantities. Local time stepping and multiple-grid acceleration techniques are used to speed convergence. For unsteady flow problems involving blade motion, a harmonically deforming computational grid, which conforms to the motion of the vibrating blades, is used to eliminate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluation of the unsteady surface pressure. Results are presented for both linear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.

Unsteady blade pressures on a propfan at takeoff - Euler analysis and flight data

The unsteady blade pressures due to the operation of the propfan at an angle to the direction of the mean flow are obtained by solving the unsteady three dimensional Euler equations. The configurations considered is the eight bladed SR7L propfan at takeoff conditions and the inflow angles considered are 6.3 deg, 8.3 deg, 11.3 deg. The predicted blade pressure waveforms are compared with inflight measurements. At the inboard radial station (r/R = 0.68) the phase of the predicted waveforms show reasonable agreement with the measurements while the amplitudes are over predicted in the leading edge region of the blade. At the outboard radial station (r/R = 0.95), the predicted amplitudes of the waveforms on the pressure surface are in good agreement with flight data for all inflow angles. The measured (installed propfan) waveforms show a relative phase lag compared to the computed (propfan alone) waveforms. The phase lag depends on the axial location of the transducer and the surface of the blade. On the suction surface, in addition to the relative phase lag, the measurements show distortion (widening and steepening) of the waveforms. The extend of distortion increases with increase in inflow angle. This distortion seems to be due to viscous separation effects which depend on the azimuthal location of the blade and the axial location of the transducer.

Results from a conical Euler methodology developed for unsteady vortical flows

We report on the development of a conical Euler analysis method to study unsteady, vortex-dominated flows about rolling delta wings undergoing either pulsed motion, forced harmonic motion, or free-to-roll motion.

Predicted pressure distribution on a prop-fan blade through Euler analysis

Applicability of a numerical code to aerodynamic design of a prop-fan is established by precise agreement of numerical results with experimental data, i.e., not only measured integrated performance indices, such as power coefficient or net efficiency, but also pressure distribution on the blade surface should agree well with computed results. For this purpose, a Euler Code using the Total Variation Diminishing scheme has been developed. Numerical calculations are performed with this scheme for the SR-7L Prop-Fan at the freestream Mach number 0.5 and 0.78. The computed power coefficient, CP = 0.34 at M^ — 0.5 shows good agreement with experimental data. At this computed CP, the computed pressure distributions on the blade surfaces show good agreement with the experimental results. For the O.VSM^ case the computed CP of 0.23 also shows good agreement with the experimental results, and the computed pressure distributions are in general agreement with the experimental data. These results indicate that the present Euler-Code could provide guidance for aerodynamic design of a Prop-Fan of the SR-7L type.

Unsteady Euler analysis of the flowfield of a propfan at an angle ofattack

Unsteady Euler analysis of the flowfield of a propfan at an angle ofattack

Inviscid analysis of a dual mode scramjet inlet

A three-dimensional inviscid flow computation was made on a dual mode scramjet inlet model that had been tested in the wind tunnels. An Euler solver based on a high accuracy total variation diminishing scheme was used to carry out the analysis. The objective was to establish three-dimensional scramjet inlet computational fluid dynamics capability and to evaluate the applicability of Euler solutions for inlet performance calculation. The computations were made for freestream Mach numbers 2 and 5. A postprocessor was developed to calculate the inlet performance. Comparison between computed and available test data showed the Euler analysis was able to predict the trend of the inlet performance and provide insight of the flowfield.

Unsteady blade-surface pressures on a large-scale advanced propeller- Prediction and data

An unsteady 3-D Euler analysis technique is employed to compute the flow field of an advanced propeller operating at an angle of attack. The predicted blade pressure waveforms are compared with wind tunnel data at two Mach numbers, 0.5 and 0.2. The inflow angle is three degrees. For an inflow Mach number of 0.5, the predicted pressure response is in fair agreement with data: the predicted phases of the waveforms are in close agreement with data while the magnitudes are underpredicted. At the low Mach number of 0.2 (takeoff), the numerical solution shows the formation of a leading edge vortex which is in qualitative agreement with measurements. However, the highly nonlinear pressure response measured on the blade suction surface is not captured in the present inviscid analysis.

Inviscid-Viscous Interaction Analysis of Compressor Cascade Performance

An inviscid-viscous interaction technique for the analysis of quasi-three-dimensional turbomachinery cascades has been developed. The inviscid flow is calculated using a time-marching, multiple-grid Euler analysis. An inverse, finite-difference viscous-layer analysis, which includes the wake, is employed so that boundary layer separation can be modeled. This analysis has been used to predict the performance of a transonic compressor cascade over the entire incidence range. The results of the numerical investigation in the form of cascade total pressure loss, exit gas angle, and blade pressure distributions are compared with existing experimental data and Navier–Stokes solutions for this cascade, and show that this inviscid-viscous interaction procedure is able to predict cascade loss and airfoil pressure distributions accurately. Several other aspects of the present interaction analysis are examined, including transition and wake modeling, through comparisons with data.

Large-scale advanced propeller blade pressure distributions - Prediction and data

Two Euler analysis techniques, finite difference and finite volume, are employed to predict the blade surface pressure distributions of a large scale advanced propeller. The predicted pressure distributions are compared with wind tunnel data. Both techniques produced blade pressure distributions which are in fairly good agreement with the data over the range of test Mach numbers of 0.2 to 0.78. However, the numerical simulations fail to predict correctly the measured pressure distributions for the low Mach number, high power case which seem to have a leading edge vortex. A discussion of the compressibility effects is also presented.

Euler analysis of a High-Speed Civil Transport concept at Mach 3

A marching Euler solver, GEM3D, was used to predict the Mach 3 flowfield for the wing and body of a Highspeed Civil Transport (HSCT) concept. The analysis focused on a typical cruise lift coefficient of 0.1 at a = 3 deg. The Euler solution indicated that embedded shocks formed on the upper surface of the inboard wing panel and at the leading edge of the outboard wing panel caused by its supersonic leading-edge condition. According to a simple static-pressure criterion, the embedded wing upper-surface shocks were sufficiently strong to separate a turbulent boundary layer. Comparison of aerodynamic coefficients from the Euler solver with those from linear theory showed that the linear theory estimates of lift and drag were optimistic, which would lead to optimistic estimates of cruise range.

Numerical analysis of Three-dimensional viscous flows around a high-speed propeller.

Three-dimensional viscous flows around a single-rotation high-speed propeller are investigated by solving compressible Navier-Stokes equations. An implicit finite difference code based on a high accuracy TVD scheme with a Baldwin-Lomax model of turbulence has been developed and applied. Computations are successfully carried out at cruise and take-off conditions with particular emphasis on grid resolution effects. The solutions clearly capture a leading edge vortex as well as a shock wave so that physical characteristics of the flow field are made clear. Numerical results are compared with the experimental data. Computed surface flow patterns show good agreement with oil flow visualization results. The present results show that the Navier-Stokes approach is capable of accurately simulating viscous phenomena around the propeller while the Euler analysis cannot, and that the propeller flow field is unexpectedly complicated because of the thin, highly swept blade.

Computational Fluid Dynamic Applications for Jet Propulsion System Integration

The impact of computational fluid dynamics (CFD) methods on the development of advanced aerospace vehicles is growing stronger year by year. Design engineers are now becoming familiar with CFD tools and are developing productive methods and techniques for their applications. This paper presents and discusses applications of CFD methods used at Grumman to design and predict the performance of propulsion system elements such as inlets and nozzles. The paper demonstrates techniques for applying various CFD codes and shows several interesting and unique results. A novel application of a supersonic Euler analysis of an inlet approach flow field, to clarify a wind tunnel-to-flight data conflict, is presented. In another example, calculations and measurements of low-speed inlet performance at angle of attack are compared. This is highlighted by employing a simplistic and low-cost computational model. More complex inlet flow phenomena at high angles of attack, calculated using an approach that combines a panel method with a Navier-Stokes (N-S) code, is also reviewed. The inlet fluid mechanics picture is rounded out by describing an N-S calculation and a comparison with test data of an offset diffuser having massively separated flow on one wall. Finally, the propulsion integration picture is completed by a discussion of the results of nozzle-afterbody calculations, using both a complete aircraft simulation in a N-S code, and a more economical calculation using an equivalent body of revolution technique.

Analysis of Three-Dimensional Turbomachinery Flows on C-Type Grids Using an Implicit Euler Solver

A three-dimensional Euler analysis for turbomachinery flows on a C-type grid is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Euler equations and is derived from the ARC3D code developed by Pulliam at NASA Ames Research Center. Modifications made to convert this code from external flow applications to internal turbomachinery flows are given in detail. These changes include the addition of inflow, outflow, and periodic boundary point calculation procedures. Also presented are the C-grid construction procedures. Finally, results of code experimental verification studies for three-dimensional compressor cascade and rotor flows are presented.

Euler Analysis of the Three-Dimensional Flow Field of a High-Speed Propeller: Boundary Condition Effects

This paper presents the results of an investigation of the effects of far field boundary conditions on the solution of the three-dimensional Euler equations governing the flow field of a high-speed single rotation propeller. The results show that the solutions obtained with the nonreflecting boundary conditions are in good agreement with experimental data. The specification of nonreflecting boundary conditions is effective in reducing the dependence of the solution on the location of the far field boundary. Details of the flow field within the blade passage and the tip vortex are presented. The dependence of the computed power coefficient on the blade setting angle is examined.

Euler analysis of transonic propeller flows

A three-dimensional Euler code, previously developed for high-speed propellers, was rewritten and vectorized for the Cray computer. First-order accurate, implicit integration was combined with approximate factorization, central differences, and constant coefficient dissipation to solve the unsteady, compressible Euler equations in general curvilinear coordinates. Calculations were compared with previous results and measurements. The new code required less memory and was more than two times faster than its predecessor. New boundary conditions produced more accurate results in terms of integrated performance characteristics. The code is a useful tool for examining the fluid dynamics and performance of propellers.

Drill Pipe Buckling in Inclined Holes

Abstract In high-angle wells the force of gravity pulls the drill string against the low side of the hole. This stabilizes the string and allows drill pipe to carry high axial loads without buckling. In addition to this, the small size of typical wellbores limits the deflection of buckled pipe to values that are often acceptable. These two effects make it practical to run drill pipe in compression in certain situations. Introduction In drilling vertical wells it is common oil-industry practice to avoid loading drill pipe so that it would be unstable from a simple column-buckling point of view. Drill pipe is kept stable by making sure that the buoyed weight of the drill collars and heavy-weight pipe exceeds the weight-on-bit to be used. This practice is based on an analysis of drill-string buckling published by Lubinski in 1950. In drilling directional wells it is common practice to use about the same bottom-hole assembly practice to use about the same bottom-hole assembly weight that would be used for a vertical well. Most operators do not add collars as hole angle increases even though they may have several thousand feet of drill pipe in compression in high-angle holes. This practice seems to work fairly well; the high practice seems to work fairly well; the high incidence of drill-string failure that would be expected if compression were really harmful does not occur. This paper is intended to justify and support this practice by showing that drill pipe can tolerate practice by showing that drill pipe can tolerate significant levels of compression in small-diameter high-angle holes because of the support provided by the low side of the hole. The benefit of using drill pipe in compression is that the BHA weight can be kept low in high-angle drilling. This, in turn, helps reduce torque and drag, which are often operational constraints in very deep directional drilling. BUCKLING ANALYSIS This section presents two types of buckling analysis. The first analysis shows that pipe is very resistant to buckling in inclined holes. The second analysis shows that, under some conditions, pipe can buckle without harmful consequences. At pipe can buckle without harmful consequences. At the end of this section these two analyses are combined to give proposed operating guidelines for using drill pipe in compression. Inclined Hole Analysis Paslay and Bogy have analyzed the stability of a circular rod lying on the low side of an inclined circular hole. As is shown in the Appendix, their result may be simplified to yield the following expression for the critical compressive load: (1) This equation should be used to predict the onset of buckling in inclined holes. It replaces the simple Euler column-buckling condition: (2) The Paslay-Bogy analysis predicts a much higher buckling load than would be calculated from the Euler analysis. Consider, for example, 1000 ft of 5-in., 19.5-ppf drill pipe in an 8.5-in. hole at a 45 deg. angle. Equation (1) gives a critical load of 35,000 lb in this case while Eq.(2) gives a critical load of only 29 lb. This illustrates the profound difference between the two types of buckling analysis. The reason that pipe in an inclined hole is so resistant to buckling is that the hole is supporting and constraining the pipe throughout its length.