Compressor Face Boundary Condition Research Articles

Inlet/Compressor System Response to Short-Duration Acoustic Disturbances

Recent studies have shown that computations of unsteady high-speed inlet flows produce results that strongly depend on the compressor-face boundary condition. Traditionally applied boundary conditions have no experimentalverification, which leads to uncertainty and significant risks in development programs. Experimental information is offered that can serve as a basis for constructing realistic boundary conditions. Short-duration transients were investigated in a constant-area circular inlet attached to an operating high-speed, single-stage, axial flow compressor. The transients were initiated by the generation of short-duration acoustic pulses within the inlet, using an exploding wire method. Pulse duration was typically 2 ms, with a peak amplitude of 3% of the mean inlet static pressure measured at the compressor face. Fast-response wall-mounted pressure transducers were used to detect the incident, reflected, and transmitted pulses. Data were obtained for axial compressor-face Mach numbers from 0.15 to 0.45. Frequency-domain analysis was used to extract dimensionless transfer functions that may be viewed as frequency-resolved reflection and transmission coefficients. The information is appropriate for the characterization of the compressor face for computational purposes. None of the customary boundary conditions predict the data obtained in this study, highlighting the need to revise conventional methods of imposing outflow boundary conditions.

Acoustic-Wave/Blade-Row Interactions Establish Boundary Conditions for Unsteady Inlet Flows

T HE computation of unsteady  ows in high-speed airbreathing inlets requires a compressor-faceboundarycondition (CFBC). The physical basis for the analytical or numerical formulation of a realistic CFBC is the acoustic re ection coefŽ cient of the operating compressor. In Ref. 1 an approximate, one-dimensionalmethod is offered to calculate this information for a single blade-row compressor, when the total approach velocity (vector sum of axial and tangentialcomponents, relative to the rotor blades) is subsonic.The present Note extends the calculation to the practically important case where the total approach velocity is supersonic and the axial component is subsonic. (In this Note, the term “supersonic” refers to this limited range.)The background,motivation,physicalmodel, method of analysis, and nomenclature described in Ref. 1 apply to thisNote without change and are not repeatedhere. Familiaritywith Ref. 1 is essential to the understandingof this Note. In supersonic cascade  ows expansion and compression waves can propagate upstream and can modify the approach  ow, which makes them considerablydifferent from subsonic cases. It has been well established that a steady, uniform, supersonic ow upstream of an inŽ nite, linear cascade of blades can exist only for a unique incidence angle. The existence of such an incidence implies that an upstreammoving acoustic disturbance (which might be initiated by a downstream-movingdisturbancearrivingto thebladerow) cancels the initial disturbance,restoring the undisturbedupstream  ow. The unique incidence angle can be determined in the knowledge of the blade geometry and the upstream Mach number (methods given in Ref. 2). The unique incidence angle is generally small, several degrees only. In the following,the exitMach number is assumed to be subsonic, which is a practically common situation. This assumption also deŽ nes a unique steady  ow when using the simplemean  owmethod of Ref. 1. The choice of subsonic out ow implies the presence of shocks (and, hence, a total pressure loss) in the blade passage. The effect of total pressure losses on the re ection coefŽ cient is demonstrably small and a reasonableestimate is sufŽ cient. Shock lossmay be estimated as that associatedwith a normal shock at the upstream Mach numberMu . The estimationof viscous lossesmay be made on the basisof empiricalinformationvalid for similar bladegeometries. The analysis deals with a transient initiated by the arrival of an acoustic step change to the blade row, the goal being the prediction of the magnitude of the re ected wave, which is also a step change. The equations used in the present analysis are the same as those of Ref. 1, with one exception. In the subsonic case, it was assumed that the direction of the exit  ow, after completion of the transient, is the same as the direction of the undisturbed exit  ow [Eq. (25)

Experiment to Support the Formulation and Validation of Compressor-Face Boundary Conditions

The reliability of unsteady inlet e ow computations may be seriously degraded by the lack of experimentally validated compressor-face (outeow) boundary conditions. The commonly imposed oute ow conditions require a e ow variableto beconstant (pressure, velocity, Mach number,etc. )at theoute owboundary, butthereis littleif any documented evidenceto support theseassumptions, norarethey likely to actually occurduring a rapid transient of arealinlet/enginesystem.Measurementsarepresentedofacousticree ectioncoefe cientsforanoperatingmultistage compressor, a quantity appropriate for the characterization of the compressor face for computational purposes. The experiment used an impulse method, in which short-duration, large-amplitude acoustic pulses (1 ms, with a peak value of nearly 4% of the mean static pressure, respectively ) were generated in a constant-area, annular inlet. The pulse and its ree ection from the compressor face were tracked by fast-response pressure transducers. Frequency-domain analysis of the data yields transfer functions that may be thought of as frequency-resolved ree ection coefe cients. None of the currently availablecompressor-face boundary conditions accurately predict the data obtained in this study, indicating that current practices concerning oute ow boundary conditions are in need of revision.

Implementation of a Compressor Face Boundary Condition Based on Small Disturbances

A compressor-face boundary condition that models the unsteady interactions of acoustic and convective velocity disturbances with a compressor has been implemented into a three-dimensional computational fluid dynamics code. Locally one-dimensional characteristics along with a small-disturbance model are used to compute the acoustic response as a function of the local stagger angle and the strength and direction of the disturbance. Simulations of the inviscid flow in a straight duct, a duct coupled to a compressor, and a supersonic inlet demonstrate the behavior of the boundary condition in relation to existing boundary conditions. Comparisons with experimental data show a large improvement in accuracy over existing boundary conditions in the ability to predict the reflected disturbance from the interaction of an acoustic disturbance with a compressor.

Response of a Two-Dimensional Cascade

Time-accurate Euler simulations of the ow through two-dimensional cascades were used to provide data on the response of the ow entering a compressor to an upstream disturbance. These data were then used to evaluate several compressor face boundary condition hypotheses intended for supersonic inlet stability simulations. An accurate out ow boundary condition for time-accurate Euler/Navier± Stokes simulations of inlet ows is needed to determine the stability margin of an inlet that encounters an atmospheric disturbance. The boundary condition must provide an approximation of the response from the compressor when a disturbance from upstream passes through the inlet and into the compressor face. In the cascade analysis, the blade stagger angle, solidity, shape, and loading; axial Mach number; and disturbance strength were each varied through a representative range. It was found that the response of a cascade to an acoustic disturbance is almost nonre ective for blade geometry parameters characteristic of the compressor hub region and almost at a constant velocity condition for blade geometry parameters characteristic of the blade tip region. A convective (temperature) disturbance was also examined and was found to pass through a cascade without generating an upstream disturbance. Screen, constant Mach number, and constant velocity out ow boundary conditions were evaluated as possible compressor face boundary conditions. It is concluded that the constant velocity boundary condition is preferable to either the screen or the constant Mach number boundary conditions for inlet stability simulations.

Response of a two-dimensional cascade to an upstream disturbance

Time-accurate Euler simulations of the flow through two-dimensional cascades were used to provide data on the response of the flow entering a compressor to an upstream disturbance. These data were then used to evaluate several compressor face boundary condition hypotheses intended for supersonic inlet stability simulations. An accurate outflow boundary condition for time-accurate Euler/Navier-Stokes simulations of inlet flows is needed to determine the stability margin of an inlet that encounters an atmospheric disturbance. The boundary condition must provide an approximation of the response from the compressor when a disturbance from upstream passes through the inlet and into the compressor face. In the cascade analysis, the blade stagger angle, solidity, shape, and loading; axial Mach number; and disturbance strength were each varied through a representative range. It was found that the response of a cascade to an acoustic disturbance is almost nonreflective for blade geometry parameters characteristic of the compressor hub region and almost at a constant velocity condition for blade geometry parameters characteristic of the blade tip region.

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.

Boundary conditions for unsteady supersonic inlet analyses

New bleed and compressor face boundary conditions have been developed to improve the accuracy of unsteady supersonic inlet calculations. The new bleed boundary condition relates changes in the bleed hole discharge coefficient to changes in the local flow conditions; the local bleed flow rate can more than double as a shock moves forward over a bleed band in response to inlet flow disturbances. The stability margin of the inlet is strongly dependent on the throat bleed configuration since the locally rapid increase in bleed flow has a strong effect on the motion of the normal shock. The new compressor face boundary condition accounts for changes in the unsteady flow conditions at the compressor face by specifying the compressor face corrected mass flow or Mach number either as a constant or as a linear function of the stagnation conditions. The effects of inlet flow disturbances on the flow at the compressor face are represented more realistically with this new boundary condition than with traditional fixed static pressure or mass flow conditions. Euler calculations of the dynamic response of an inlet flow to a flow disturbance at the compressor face with 20- and 90-deg throat bleed hole angles are reported. These results indicate that an extra margin of stability for the inlet is obtained with 90-deg bleed holes because the increase in bleed flow rate as the shock moves forward over a bleed band is much larger for 90-deg holes than for 20-deg holes.