Effective Date: 15 June 98
Editor's Note: This propulsion section is still under graphics (equations) update.
Background
The accurate calculation of inflight thrust on the generic high bypass engine is required to adequately determine the drag and performance characteristics of the airplane. Due to the high inlet mass flow rates, and the associated high thrust produced by the generic high bypass engine, the method of computing inflight thrust becomes more critical. The method of calculating thrust consists basically of measuring certain internal engine parameters and the core engine and fan (bypass) discharge temperatures and pressures from rakes and pick-ups installed by engine manufacture. From these measured data, mass flow rates and gross thrust parameters are calculated. Net thrust is computed by applying the appropriate coefficients to the ideal gross thrust and then subtracting the ram drag term.
The nozzle coefficients used in the calculation of thrust are derived from test results from model testing and full scale testing in the engine manufacture altitude chamber and test cells. The derivation of these coefficients is discussed in section on DERIVATIONs.
Engine Performance - Fuel Flow
Fuel flow will be measured and evaluated both as a volumetric flow and as a mass flow. Traditionally fuel flow is normalized in the form:
However, it is possible that a Theta exponent other than 0.5 may be applicable on the high bypass. If this is the case, test data will verify the final exponent.
Mass Fuel Flow
Fuel flow will be measured and evaluated using a mass-type fuel flow meter which measures the change in angular momentum of the fuel passing through the meter and is independent of the fuel density (temperature).
A comparison will be made between the fuel flow calculated by the mass and the volumetric system. However, the volumetric flow rate will be considered primary because past experience indicates better accuracy and repeatibility with volumetric rate measurement.
Volumetric Fuel Flow
Ideally, the mass fuel flow is calculated from the measured volumetric flow as follows:
Since fuel density (Rho) cannot be measured in flight for each test point, the test point fuel temperature, the preflight density and temperature, and a knowledge of the change in density per change in temperature can be used to calculate the test fuel density as follows:
However, it is more convenient to correct the preflight sample data to 15.5 Deg C (60 Deg F) because the hydrometers are calibrated at 15.5 Deg C (60 Deg F). Combining equations (1) and (2), and subscripting for data corrected to 15.5 Deg C,
Equation (3) is used to calculate the mass fuel flow from the measured volumetric data. The density (Rho15.5) is obtained by converting the preflight sample specific gravity reading to the equivalent density at 15.5 Deg C., (See section on DERIVATIONs). The change in density per change in temperature (dRho/dT) is obtained from a curve similar to that shown in Figure 1, which is based on previous laboratory analysis of fuel samples. This is discussed in more detail in the section on DERIVATIONs.
Fuel Flow Evaluation
Using fuel flow data obtained during testing, the following set of generalized plots will be evaluated for bleed off:
A typical correction factor plot is shown; however, analysis of the data may indicate that the correction factors are not required.
Engine Performance - Bleed Data
Compressor bleed air is obtained from the intermediate (IP) and high pressure (HP) compressor, and routed to the appropriate bleed supply ducts. For most of the flight regime (take-off, climb, and cruise conditions) the supply source is IP air. For other conditions, idle descent, it is necessary to use HP air either solely or partially in which case the IP air is boosted by feeding the HP air through the nozzle of a mixing ejector. HP air is also used to boost the temperature of the IP air to a minimum of 450 Deg F for example whenever wing anti-icing is required.
Bleed Flow Calculation
From ideal gas flow, the IP bleed flow rate for each engine is calculated as follows:
The bleed flow rate is,
The specific heat ratio from Figure 3.
The HP bleed flow (WHP) is calculated in the same manner using HP bleed measurements.
Bleed Data Evaluation
Analysis of the compressor bleed data, from the propulsion analysis standpoint, consists primarily of
(1) determining bleed effects on engine performance parameters,
(2) generalizing bleed parameters for use in the expansion program, and
(3) normalizing bleed flow, as a function of EPR and altitude for example, for a given bleed configuration.
To determine the effects of bleed on engine performance comparison of various engine parameters with and without bleed will be accomplished. The bleed effects will be normalized with respect to percentage bleed flow and analyzed as a plot of the following form, for example,
where:
# WF = change in normalized fuel flow per % WBLD percent bleed constant EPR lb/%.
The percent bleed is the ratio of the calculated bleed flow to the calculated core engine airflow.
Bleed flow rates will be evaluated by normalizing measured bleed flows as a function of the EPR and altitude for a given configuration. An example of this type plot is shown below. It is possible, however, correction factors for other variables (such as Mach No.) may be required.
Engine Performance - Nozzle Expansion
The geometric nozzle areas (fan and core exit) at a given temperature are calculated by the following equation:
In the above equation, AC and AH are furnished by Engine manfacture. The cold nozzle area (AC) will be measured, while Alpha is a function of this nozzle material. The derivation of Equation 5 is discussed later.
Engine Performance - Thrust
The thrust method used for the airplane/high bypass performance evaluation employs nozzle internal rake temperatures and pressures to calculate gross thrust and nozzle airflow. In general, this method uses nozzle total pressure divided by ambient pressure (PT/PAM) to evaluate both the airflow and the gross thrust produced by the engine. The classical method of calculating net thrust on low bypass engines is to determine gross thrust from nozzle measurements and ram drag (airflow) from fan speed. Since the method selected for the airplane/high bypass uses the nozzle airflow to determine nozzle gross thrust, the accuracy of net thrust (gross thrust minus ram drag) is greatly increased.
Airflow
The cooling airflow for the nacelle ventilation, IDG oil cooler, and the air cooled oil cooler (ACOC), is extracted from fan (bypass) air and must be accounted for in the evaluation of total airflow.
The Zone 2 and 3 ventilation air flows are computed as follows:
When the ventilation analysis has been completed (Section 9.0), Zone 2 and Zone 3 flow rates will then be calculated from these curves, derived from flight test data.
The IDG oil cooler airflow (WIDG), the ACOC airflow (WACOC), and an additional term WL which accounts for fan airflow leakage are based on results of Engine manfacture testing. The calculated fan bleed therefore is the sum of the above bleed flows,
The ideal bypass airflow is computed as follows:
(Note that for a rigorous analysis the specific heat ratio should be a function of the static temperature; however, the error introduced by using the total temperature is considered to be insignificant.)
The bypass nozzle airflow is:
The fan exit airflow (W25) is the bypass nozzle airflow plus the fan bleed. Stated mathematically:
The core engine exit gas flow (WE) is calculated in the same manner as the bypass airflow calculation using PT8/PAM, WE' CDE' CDRE' and AE.
The core engine inlet airflow is equal to the exit flow plus the compressor bleed flow, less the addition of fuel flow. In equation form, this is expressed as
The fan compressor or total airflow inlet is equal to the core engine inlet flow plus the fan exit airflow,
The total inlet airflow is used in conjunction with the inlet
analysis , as well as the ram drag portion of
the thrust calculations. The normalized total inlet airflow 
will be evaluated in one or more of the following
forms:
In the above evaluations, corrections due to altitude or Reynolds Number Index may be required.
Gross Thrust
The calculation of fan and core gross thrust consists of determining the gross thrust parameter, calculating the ideal gross thrust, and applying the coefficient to obtain the actual gross thrust. The fan gross thrust parameter is a function of the fan nozzle expansion ratio and the specific heat. The derivation is discussed later,
The ideal fan gross thrust is,
Next, the fan velocity coefficient (CVB), is used to calculate the actual fan gross thrust as follows
The core engine gross thrust (FLzE) is calculated in the same manner as the fan thrust using PT8/PAM. CVE' and AE.
The total gross thrust is the sum of the fan and core gross thrust,
Drag
The ram drag, or inlet momentum, is calculated as follows:
The above form of the inlet momentum equation is simplified into the following form:
Two additional drag terms have been defined, jet effects and spillage drag. These two drag terms are not accounted for in the calculation of net thrust because the reduction and expansion process will use the same calculation procedure and these drag terms cancel out.
The spillage drag increment (FSD) accounts for inlet spillage at low mass flow ratios. The spillage drag is a function of Mach number and mass flow ratio. The spillage drag is determined from data from wind tunnel tests of a full span model with flow- through nacelles. Typical spillage drag is shown in Figure 3.
The remaining drag term is termed jet effects. This thrust increment accounts for the interaction of the pylon or aft fuselage and the engine flow field. The effect of the airplane flow field on engine thrust has been measured in the wind tunnel on a model. Typical jet effects (FJET) are shown in Figure 4. for the center engine installation. It should be noted that jet effects are additive, since jet effects reduce form drag.
Net Thrust
At this point in the calculations, all the terms required to compute the net thrust have been defined. Propulsion net thrust may be computed as the gross thrust less the ram air drag as follows
The net thrust calculated in Equation 19 will be used to (1) establish the relationship between net thrust and (cockpit) engine pressure ratio (EPR), and (2) evaluate the performance of the airplane by using this thrust value in conjunction with aerodynamic analysis (Reference 2).
Windmilling Drag
The estimated windmilling drag for a pod and center engine installation is shown in Figure 5. This drag will be used in determining engine-out performance analysis. This data has been derived from information supplied by engine manfacture, plus the results of model tests.
Theoretically, the methods previously discussed to calculate net propulsive thrust should reproduce windmilling thrust (drag) for an inoperative engine. An attempt will be made to calculate windmilling drag by these methods, however, the instrumentation limitations at low pressure and temperatures may negate this procedure.
Reverse Thrust
In the reverse thrust mode the hot stream spoilers deploy and the core engine exit flow is diverted 90 degrees so as to produce no thrust in the longitudinal direction. Therefore, FgE = 0 in the reverse mode.
The fan airflow and gross thrust are calculated the same way as in the forward mode, except that the flow and velocity coefficient are modified to account for the flow exiting through the reverser cascades. In addition. the fan airflow (WB) is now calculated as a function of PT25P and TT25 instead of PTB and TTB, since the latter two measurements are located aft of the reverser blocker doors. PT25P is a measured value and TT25 is determined from the curve shown in Figure 6. The net thrust in reverse is then calculated as follows:
The axial component of the fan reverse thrust is,
For the present, the reverser effectiveness is assumed to be a constant value (.513), however, test results may indicate that effectiveness is a function of fan pressure ratio or fan rotor speed.
The base drag (FDR) in reverse, acting on the deployed spoiler and reverser doors, is obtained from Figure 7.
The net thrust in reverse is,
Engine Performance - Installed Data
The basic installed data will consist of curves of engine performance parameters in the bleed-off configuration. Data for these curves will be obtained from static engine calibrations and from the bleed- off portion of inflight testing.
The resultant curves will be used to define the basic installed gas generator characteristics. In addition, these curves will be used as input to the data expansion program as discussed later.
The basic installed engine data will be evaluated primarily in terms of engine pressure ratio (EPR) and Mach No. As an alternative, corrected fan speed, (Nl/(SQRT (Theta)t2) may be used in lieu of EPR. Listed below are the various normalized parameters which will be evaluated.
Thrust Setting Curves
Data for the construction of the generic high bypass thrust setting curves are furnished by engine manfacture. These curves are based on ratings for an uninstalled engine with estimated installation effects applied. The uninstalled ratings are derived such that the engine meets or exceeds specification thrust requirements. The final thrust setting curves will account for installation effects based on data obtained during the test program.
The thrust setting curves will include take-off, maximum continuous thrust (MCT) and maximum cruise thrust (MCRT) ratings. Typical thrust setting curves are shown in Figure 2b. Figures 1 through 72. It is anticipated that back-up thrust setting curves will be derived using fan speed (Nl) as the thrust setting parameter in lieu of EPR.
Data Expansion
The data expansion will be based upon generalized inputs derived from curves from flight test data as described in Section xxx5.0. These data include engine inlet and exit pressures and temperatures, bleed flow pressures and temperatures, fuel flow and rotor speeds. The format for the flight test data will be chosen on the basis of minimum effect of flight speed, altitude and ambient temperature conditions.
It is expected that the calculation method for expanded data thrust will be identical to that used for flight test data reduction. Basic flight test data correlations will be developed with no bleed flow conditions; then these are corrected by supplementary flight test data to the specific bleed condition.
Several bleed configurations will be developed for data expansion; these include normal bleed operation as well as wing anti-icing, engine anti-icing and conditions with one or two engines inoperative.
All appropriate limitations (physical as well as engine ratings), will be used in the expansion process.
The procedure for data expansion consists basically of
(1) defining conditions (Mach, altitude, engine power, etc.);
(2) obtaining necessary parameters (temperatures pressures, etc.) from curves based on Flight Test results;
(3) calculating thrust and the required expansion parameters, correcting for bleed and the appropriate limitations where necessary.
This is shown schematically in the flow chart on Figure 2b. .
Short Form Thrust
A short form of thrust look-up chart will be developed which will require the definition of only three quantities to determine thrust (Mach No., Altitude, and (EPR). The charts to be developed are discussed below.
Basic Thrust Chart
A thrust chart as shown below will be developed for the normal bleed configuration.
This basic thrust curve may require an altitude correction, and possibly an incremental correction for the center engine to account for PT2 probe recovery. The data to generate this curve will be developed from the data expansion program.
Flight Idle Map
A flight idle map will be developed from test data in one or both of the following forms:
Thrust During Take-Off
Thrust will be calculated continuously during take-off to determine the thrust lapse rate. An accurate ground speed will be determined using an airfield space positioning system in conjunction with weather station data. The following curve will be developed to confirm the theoretical thrust lapse rate:
Reverse Thrust
Reverse thrust data will be obtained at various power settings during landing in order to develop a reverse thrust curve as shown below. The airfield space positioning system and weather station data will be used to determine an accurate ground speed and temperature. The calculation procedure for reverse thrust is discussed later.
INLET ANALYSIS
Engine inlet performance characteristics, including inlet recovery and distortion, will be evaluated on one wing pod engine and on the center engine installation.
Instrumentation
Each inlet instrumentation installation consists of an inlet rake employing ten equally spaced spokes, each having eight total pressure probes. The probes are located radially such that they are equally split between the bypass and gas generator flows with approximately equal area weighting within each stream. Inlet total temperature is measured from temperature probes on every other rake spoke.
Recovery
Inlet total pressure recovery is the average total pressure level (#1#2) at the engine inlet face relative to the freestream total pressure (PTO).
The inlet total pressure can be computed as the sum of the area weighted average pressure at the bypass inlet and the gas generator inlet. This allows separate analysis of the bypass and gas generator recovery.
The bypass inlet recovery is
# (PT2BX FBX)/(PTO) #B = (PT2B/PTO) = FBB (8.1)
where,
#B = Bypass inlet recovery
PT2B = Average area weighted bypass inlet pressure
PTO = Freestream total pressure = (PAM + qC)
PT2BX = Measured bypass total pressure at rake probe location X
FBX = Area weighing factor for rake probe location X
FBB = Bypass area weighing factor
A similar equation is used to determine the gas generator inlet recovery (###G).
The overall average inlet pressure is computed by
(###FB- + ##;#FBC#)
# = PT2/PTO = # FBB + # FBGG (xxxx8-2)
The inlet recovery will be evaluated from data acquired under steady state conditions and presented as a function of airflow and Mach No. as shown below.
The inlet airflow (Wo###f2/##T2), is obtained from an airflow map derived from test data.
An additional analysis of inlet recovery consists of evaluating each total pressure probe reading in terms of its angular and radial location for a given condition, as shown below,
The above plot provides analysis of total pressure readings in terms of the probe locations, (ideally, the total pressure readings should be symmetrical with respect to angular rake location). In addition, the recovery at the inlet pressure probe (PT2P) for EPR will be evaluated for both wing pod and center engine installation. It wi11 be presented as a function of airflow and Mach No. similar to the previously described presentation for inlet recovery.
Engine Performance - Distortion
Since the inlet total pressure distortion level provides a relative indication of fan blade stress levels, the distortion is of prime importance to both engine manufacture and airframe manufacture. Based on theoretical studies and past compressor and engine development experience, distortion parameters (defined below), have been developed by Engine manufacture which define the relative severity of various levels and patterns of inlet total pressure distortion.
The engine manufacture should have set a distortion limit of 0 to -1 (zero to minus one) for distortion parameter DMIN while typical DC60 limit characteristics are shown on Figure xxxx8-1 for both the gas generator and bypass airflows. The distortion parameters are calculated as follows:
DC60 = ((PMIN)60 - ##)/qc (8xxxx-3)
DMIN = (PMIN - ##)/qc (xxxx8-4)
where,
DC60 = Normalized circumferential distortion over any 60 degree sector of the appropriate area of the compressor face.
DMIN = Distortion based on minimum pressure at any point (as opposed to a 60 degree sector)
(PMI!#)60 = Minimum mean value of total pressure over any 60 degree sector
PMIN = Minimum mean value of total pressure at any point
PT = Area weighted average total pressure
q#= Dynamic head at the compressor face
In addition, a more conventional distortion parameter, DLAC, is calculated by the following equation
DLAC = (P#### - PMIN)/##2 (8xxxx-5)
Inlet distortion will be evaluated during steady state conditions, as well as stalls, sideslips, and cross-wind. Analysis will consist of plotting distortion versus the appropriate values of corrected airflow and Mach No., angle of attack, yaw angle, or cross-wind. These data will then be examined to insure the distortion limits will not be exceeded.
The airframe manufacture has devised an additional analytical tool for inlet analysis, and this is shown in Figure xxx8-2 . This is a specialized total pressure distribution plot. This computer made plot provides a graphical means of analyzing areas with adverse inlet recovery.
Engine Performance - Nozzle Areas
Both fan and core nozzle exit plane minimum flow areas will be measured by engine manufacture on each instrumented engine and supplied to airframe manufacture. The measured areas are used in calculation of nozzle airflow.
The measurement of core nozzle exit plane is relatively straightforward since there are no physical obstructions at the measuring station. Six diameters will be measured approximately 30 degrees apart. The average diameter will be used to calculate the area as shown below.
Area = AE = %\ (D)2/4 ( -l)
D = (%Dn)/n
The calculation of the fan nozzle exit plane area is complicated by the presence of the pylon splitter at the measuring station.
Referring to Figure -l, the fan nozzle area consists of an annular area less the pylon splitter area.
The average fan radial segment is,
RF = (%#RFn)/n ( -2)
where n = 11 (every 30 Deg except O Deg)
COS % = OF/RC ( -3)
OD = OF + FD = OF + EA ( -4)
Combining Equations ( -3) and ( -4),
OD = RC COS % + EA ( -5)
RO = RF + RC ( -6)
From the right triangle AOD,
(R0)2 = (OD)2 + (AC/2)2 ( -7)
Substituting Equation ( -5) into ( -7),
(R0)2 = (RC COS % + EA)2 + (AC/2)2 ( -8)
EF = AC/2 ( -9)
0 = SIN-l EF/RC = SIN-l AC/2RC ( -lO)
Substituting Equation ( -6) into ( -8),
(RF)2 + (RC)2 + 2(RF)(RC) - (RC COS % + EA)2 - (AC/2)2 =0 ( -ll)
Substituting Equation ( -lO) into ( -ll),
(RF)2 + (RC)2 + 2(RF)(RC) - [RC COS (SIN-l (AC/2RC)+ EA]2 - (AC/2)2 = 0 ( -12)
In equation (-12), RF, AC, and EA are measured quantities. The one unknown is RC.
To calculate the area of the pylon splitter (Ap),
EH = %RC ( -13)
The core circumference (CE) is,
CE = 2 EH + CEM = 2%RC + CEM ( -14)
where CEM is measured.
As shown in Figure l, the pylon area is,
AP = ACGE + A3 - A4 - Al - A2 ( -15)
Areas Al and A2 are measured on the engine using a template, and a planimeter to calculate the area.
Using the standard equations for the area of a segment of a sector:
A3 = (R0)2 (2c%#- SIN 2%,%) ( -16)
A4 = (RC)2 (2% - SIN 2%) ( -17)
From Figure -l,
ACGE = (AC) (EA + CG) 1/2 ( -18)
Each of the terms of the right hand side are measured quantities. The angles c%-and % are,
<%# = SIN-l AC/2RO ( -19)
% = SIN-l AC/2RC ( -20)
Substituting Equations ( -16), ( -17), and ( -18) into Equation ( -15), the pylon area becomes
AP = (AC) (EA + CG)% + (R0)2 (2%=% - SIN2c%- ) - (RC)2 (2 % - SIN 2 0) - Al - A2 ( -21)
In the above equation,
AC, EA, CG, Al, A2 Measured quantities
%# && Equations ( -19) ( - 20)
RC Equation ( -12)
RO Equation ( -6)
Finally, the fan nozzle exit plane area is
AB = -%#(R02 - RC2) - AP
where AP is from Equation ( -21), RO from ( -6) and RC from ( -12).
Engine Performance - Fuel Sample Analysis
Fuel Sample Analysis Propulsion performance testing will be conducted using Jet-A commercial specification aviation turbine fuel. Analysis of this fuel, from the performance standpoint, consists of determining the heating value, and the specific gravity- temperature relationship. During the engine performance phase of the testing, fuel samples will be taken and analyzed approximately every flight. The lower heating value (LHV) of the fuel sample will be determined using a Bomb Calorimeter using the 1969 ASTM Test Method D240-672. This analysis may be accomplished by an independent testing laboratory.
Fuel samples will be analyzed periodically to obtain statistical information on the specific gravity-temperature relationship, which is required to calculate fuel flow. The specific gravity- temperature relationship is determined by measuring the specific gravity of the fuel, using a Psycnometer, at various fuel temperatures. The results of each sample analysis are plotted as shown in Figure 1. This information can be converted to the change in density per change in temperature (dRho/dT) using the constants to convert specific gravity to density.
Prior to each performance test flight, the specific gravity and fuel temperature will be obtained from a fuel sample from the airplane. A hydrometer calibrated to 60 Deg F will be used, and the specific gravity reading will be corrected to 60 Deg F using the standard tables. This data point should fall on the specific gravity-temperature line generated from analysis of previous fuel samples. If this data point does not fall on the line (due to a new fuel batch, for example) or if there is more than one slope, the slope adjacent to the preflight sample will be used in computing fuel flow for that test.
Engine Performance - Thrust Coefficient
The method used to compute the in-flight thrust of the generic high bypass engine is a conventional nozzle thrust calculation procedure. As such it requires the use of nozzle flow coefficients for airflow determination, and nozzle velocity coefficients for thrust determination. The definitions of these coefficients are conventional; i.e.,
CT = Cv x CD where:
CD = W act W ideal
CV = W act V ideal C-D
The values of these coefficients have been derived from full scale engine tests with engines having the production engine nozzle system. To obtain the necessary data, engines have been run on both sea level and altitude engine test stands.
The sea level beds generally used are those located at the engine manufacture facilities. The altitude facility generally used is a government developed test facility. The coefficients being employed for thrust determination were developed from data obtained on a test engine which may be from an early batch of standard of high bypass engines having an exhaust system representative of those on production engines.
As noted in Section xxx4, the thrust calculation uses an internal total to free stream static pressure ratio to compute the ideal airflow. A CD is applied to the ideal value to obtain the actual airflow which is then used to obtain in-flight gross thrust as shown below.
Note: This equation combines equations -13, -14, -15 and -16.
The value of # Fg, used in the above equation, is obtained from the NGTE force accounting equation shown below:
The velocity coefficient of the fan nozzle is determined by taking the #Fg term from equation -2 and substituting it into equation -l. The latter equation is then solved for CVB using the following inputs:
o WE calculated from the choked turbine nozzle guide vane area and known pressure and temperature.
o WB calculated from measured W2 and the solution of equations 72-8, 72-10, 72-11 and 72-12.
o TTB and TT8 as measured.
o FgB and FgE as determined by equation 72-13.
-Wa # TTB i WE ./TT8 i
o CVE set at .998 which is the value recommended by Engine manufacture.
All the CVB data thus computed is then fit by root-sum-square methods to a single valued curve of CVB versus PTB/PAM.
The flow coefficients of the fan and primary nozzles are used to obtain the temperature-corrected flow terms WB # TTB and ###TT8 equation -2. When divided respectively by the terms PTB AB and PT8 AE appropriate to the data point, the "actual" flow parameter required to determine the flow coefficients CAB and CAE are obtained. The thrust calculation uses the conventional expansion ratio, PT/PAM, to define the "ideal" flow parameter, and thereby, the flow coefficient. Since PAM exists only in the expanded exhaust stream and not uniquely at the nozzle plane, external influences will affect nozzle plane pressure and, therefore, the flow coefficient. As an example, fan nozzle flow coefficient is affected by engine position, aircraft angle-of- attack, and flight Mach number.
The core engine nozzle flow coefficient is influenced by these same variables plus the fan efflux. The NGTE full-scale engine data in this case are only used to define the flow coefficients in a quiescent environment (M = 0). Scale model test results used to define the correction to the airflow reflect external effects. This correction is defined as a flow coefficient ratio; i.e.,
CD (in A/C flow) CDR = CD (in quiescent air)
Figures -l and -2 present the values of CDR to use in calculating nozzle airflows. The values have been derived from test results obtained on two 1/20 scale models; one a semi-span aircraft model equipped with a Tech Development powered nacelle and the other an empennage model with blown nozzles. The CDR was derived by taking the ratio of measured airflow to calibrated airflow in the quiescent envirorment. Where direct airflow measurements were not available in the aircraft environment, e.g., fan flow on the powered nacelle, an airflow calibration using internal nozzle static pressures was used to obtain CDR. A flow diagram showing how the various flow coefficient data interface with the thrust validation procedure is presented in Figure -3.
Engine Performance - Derivation
The ideal gas flow parameter is calculated from the following equation,
Equation .1-l can be found in any Gas Dynamics textbook, (The K term is for units conversion).
Nozzle Areas
If the metal is heated, the hot area is
The incremental change in radius is the product of the radius, coefficient of linear expansion, and the temperature change.
From equation ( -3) and ( -4)
The coefficient of expansion,#,#, is of the order 2 x 10-5 per oC; therefore, (c#)2 is negligible and equation ( -7) reduces to:
Similarly, for the inner radius, r2'
Substituting ( -8) and ( -9) into equation ( -3),
Using the equation ( -2) and ( -lO), the hot area is
Gross Thrust Parameter
The ideal gross thrust can be computed as the total momentum plus the force acting at the exit,
F = WV + (PS - g ( -12)
Bernoulli's equation for compressible flow is,
## P + V2 = Constant##-1 ## 2 ( -13)
Writing equation ( -13) between ambient and a stagnation point,
=0 ## ( -14)
PAM V2 PT + 2 = ##-1 +/2 #T
For a perfect gas,
)AM PAM_ '# ( -15)
Multiplying Equation ( -14) by # AM,
V2 AM PAM + 2 .AM = #.-1 PT ( -16)
Substituting Equation ( -15) into ( -16),
#.-1 PAM + 2 .AM = ##-1 PT\_P# ( -17)
Using the gas law relationship #> = P/gRT in the above equation,
V2PAM PAM \ ##.##-1 PAM +2gRTAM = ##-1 PT# PT / ( -18)
Solving Equation ( -18) for V2,
PT /PAM)V2 = 2## (gRT) ___, ( -19)
Substituting
TAM = ##&&
into equation ( -19), and solving for V,
V = #$% (gR) TT 1 - ( -20)
Substituting Equation ( -20) into Equation ( -12), assuming complete expansion at the exit (PS = PAM), the gross thrust parameters is,
### = F PAM 1 - 2.443 ( -21)
Ram Drag
The Ram Drag is numerically equal to the inlet momentum, or the product of the inlet airflow and the free stream velocity.
FRD = g ( -22)
Multiplying top and bottom of equation ( -22) by ###gRT ,
FRD = W2 g # ##gRT ( -23)
Using definition of Mach No.,
# #-gRT FRD = W2 M g ( -24)
Substituting in consistant units in ( -24) as follows,
# = 1.4
g = 32.174 ft./ sec.2
R = 53.35(1.8) ft.-lbm/lbf oK
T = Deg K
#AM = T/288.16
FRD = 372.7 W2 M##AM ( -25)