Parametric (On-Design) Cycle Analysis for a Separate-Exhaust Turbofan Engine With Interstage Turbine Burner

5.2 Program Outline The program mainly comprises seven types of sheets, namely CoverPage , Instructions , Input , plot sheets, data sheets, Singlept and Station . Meanwhile, the main code structure is shown in figure B.1 in appendix B.

5.2.1 CoverPage .—The CoverPage sheet contains the information of authors of this program. Any questions regarding the program can be addressed to us through email or by phone.

5.2.2 Instructions .—First time users are strongly recommended to read this sheet before running the program. Since there are always possibilities of getting error computations such as division by zero, square root of a negative quantity, or over floating and under floating number, the program is written such that it will not crash if those errors are encountered during the computation. It will instead tell the user where the computation encounters those errors. In this sheet, you will find details of how to run the program and how to fix a problem if something goes wrong.

This sheet also explains several assumptions made in the equations so that the users aware of some cases in the equations that have been idealized to simplify the problems.

5.2.3 Input .—This sheet is where most of the inputs are specified. The program will check input values in this sheet to make sure that all the inputs are specified. It will tell the users if there are inputs that have not been specified.

There are four Combo Box in the Input sheet ( Combo Box is a list box that displays a list of values and lets the users select one of the value in the list), namely ITB , Unit , Fuel Burn Model and Choose a Plot , as shown in figure 5.1. You need first to specify the option in these combo boxes, such as ITB , Unit and Fuel Burn Model , before moving on to combo box Choose a Plot .

Combo Box Unit lets you specify the unit system. Currently, the program can handle two unit systems, i.e., British gravitational units ( English ) and International system of units ( SI ).

Combo Box ITB lets you turn ON and OFF the Inter-stage Turbine Burner ( ITB ). This feature provides a flexibility to choose two types of engine and they are engine with ITB-ON and engine with ITB-OFF. With this feature, you will be able to see how the engine performance behaves with ITB-ON and with ITB-OFF.

Combo Box Fuel Burn Model let user choose two models for the computation of the fuel-air-ratio inside the burner, i.e., Constant Specific Heat ( CSH ) model and the Modified Specific Heat ( MSH ) model [3, 4].

Figure 5.1— Input sheet NASA/TM—2005-213658 19 Once all the input values and the options in combo box ITB , Unit , and Fuel Burn Model are specified, you can specify an option in combo box Choose a Plot . This combo box provides several options to choose from, and they are: 1. Vs Compressor Pressure Ratio 2. Vs Flight Condition Mach Number 3. Vs Fan Pressure Ratio 4. Vs ByPass Ratio 5. Vs Main Burner Exit Temperature In each option, it performs multiple calculations at different values of only one corresponding design variable. Once you select one of them, you will be directed to the relevant plot sheet.

5.2.4 plot sheets .—Please refer to section 5.3 Multi-point Calculations for detailed information.

5.2.5 data sheets .—Please refer to section 5.3 Multi-point Calculations for detailed information.

5.2.6 Singlept .—Please refer to section 5.4 Single-point Calculation for detailed information.

5.2.7 Station .—Please refer to section 5.5 Engine Station for detailed information.

5.3 Multiple-Point Calculations The following discussion describes the instructions on how to run the program for each option available in combo box Choose a Plot in Input sheet. Each option shares the similar code structure as shown in figure B.2 in appendix B.

5.3.1 “Vs Compressor Pressure Ratio” .—When this option is chosen, users will be directed to a plot sheet, namely ST_VS_PIc , as shown in figure 5.2. This sheet is used to plot engine performances (e.g., specific thrust or thrust specific fuel consumption ) and other properties (e.g., overall efficiency, nozzle jet velocity ratios, overall efficiency, fuel-air ratio, ITB inlet velocity and temperature rise across ITB ) versus compressor pressure ratio ( π ) with different bypass ratio. In order to execute the code properly, users are c required to follow those circled number 1 through 3 sequentially as shown in figure 5.2.

First of all, user needs to specify the values for three input parameters (i.e., π , π , and M ) as well cL f 0 as the lower and upper bound limit for “ Compressor pressure ratio ” ( π ) and the increment ( ∆π ) (see c c fig. 5.3). For instance, the lower and upper bound limit are 12 and 50, respectively, whereas the increment is 1.

Figure 5.2.—“Vs Compressor Pressure Ratio” plot sheet NASA/TM—2005-213658 20 What follows is to compute the values for HP -compressor pressure ratio ( π ). By clicking the cH ‘ Generate ’ button, a tabular data for the compressor (including π , π , and π ) will be listed as shown cL cH c in figure 5.4. The cyan cell to the right of π indicates the total number of iteration for π . The smaller the c c value for ∆π , the larger the total number of π ; and, therefore, more calculation at different values of π .

c c c Thirdly, users are free to choose the number of bypass ratio ( α ) by selecting options from the pull down menu as shown in figure 5.5. If it is more than 3 bypass ratios, users are required to manually input any number greater than 3 by selecting ‘ User-Defined ’ option.

At this point, users are ready to run the code and generate the plots, simply by clicking ‘ Calculate ’ button. All computed data will be tabulated in seven separate data sheets, namely, DataSTPIc , DataSFPIc , OverallPIc , NVCorePIc , NVFanPIc , VitbPIc , and dTrisePIc .

Users are advised not to modify or change values in any of these data sheets. Clearing data as well as plots can be done by clicking ‘Clear data & plot’ button (see fig. 5.5).

To return to Input sheet for other runs with different design parameters, users simply click on ‘ Input sheet ’ button next to ‘ Calculate ’ button.

Figure 5.3.—Input parameters in “Vs Compressor Pressure Ratio” plot sheet Figure 5.4.—Tabular data for the compressor pressure ratios NASA/TM—2005-213658 21 Figure 5.5.—Pull-down menu for fan bypass ratios ( α ) 5.3.2 “Vs Flight Condition Mach Number” .—When users choose this option, the program hides the plot sheets and data sheets from the previous use and shows a associated plot sheet (i.e., ST_VS_Mo ) and seven associated data sheets (i.e., DataSTMo , DataSFMo , OverallMo , NVCoreMo , NVFanMo , VitbMo , and dTriseMo .) Users will then be directed from Input sheet to ST_VS_Mo sheet in a second. Similarly, this sheet is used to plot engine performances (e.g., specific thrust or thrust specific fuel consumption ) and other properties (e.g., overall efficiency, nozzle jet velocity ratios, overall efficiency, fuel-air ratio, ITB inlet velocity and temperature rise across ITB ) versus flight Mach number ( M ) with different bypass ratio.

Similar to the instructions for compressor pressure ratio, user first needs to specify the values for three input parameters (i.e., π , π , and π ) as well as the range of M and the increment ( ∆ M ).

cL f c 0 0 Secondly, users are free to choose the number of bypass ratio ( α ) by selecting options from the pull down menu. At this point, users are ready to run the code and generate the plots, by simply clicking ‘ Calculate ’ button. All computed data will be tabulated in all seven separate sheets just mentioned above.

5.3.3 “Vs Fan Pressure Ratio” .—Similar to flight Mach number, this option opens a plot sheet (i.e., ST_VS_PIf ) and seven data sheets (i.e., DataSTPIf , DataSFPIf , OverallPIf , NVCorePIf , NVFanPIf , VitbPIf , and dTrisePIf) . It plots engine performances (e.g., specific thrust or thrust specific fuel consumption ) and other variables (e.g., overall efficiency, nozzle jet velocity ratios, overall efficiency, ITB inlet velocity and temperature rise across ITB ) versus fan pressure ratio ( π ) with different bypass f ratio. The instructions to run the program in this sheet are similar to those for ‘flight Condition Mach number’. (See section 5.3.2.)

5.3.4 “Vs ByPass Ratio” .—This option opens a plot sheet (i.e., ST_VS_Alp ) and seven data sheets (i.e., DataSTAlp , DataSFAlp , OverallAlp , NVCoreAlp , NVFanAlp , VitbAlp , and dTriseAlp) . It plots engine performances (e.g., specific thrust or thrust specific fuel consumption ) and other variables (e.g., overall efficiency, nozzle jet velocity ratios, overall efficiency, ITB inlet velocity and temperature rise across ITB ) versus different bypass ratio ( α ) with different fan total pressure ratios. The instructions to run the program in this sheet are analogous to those described above. The only difference is that selection of α is replaced by π .

f 5.3.5 “Vs Main Burner Exit Temperature” .—This option opens a plot sheet (i.e., ST_VS_Tt4 ) and seven data sheets (i.e., DataSTt4 , DataSFTt4 , OverallTt4 , NVCoreTt4 , NVFanTt4 , VitbTt4 , and dTriseTt4) . It plots engine performances (e.g., specific thrust or thrust specific fuel consumption ) and other variables (e.g., overall efficiency, nozzle jet velocity ratios, overall efficiency, ITB inlet velocity and temperature rise across ITB ) versus main burn exit temperature ( T ) with different flight Mach number.

t4 The instructions to run the program in this sheet are similar to those for ‘flight Condition Mach number’.

(See section 5.3.2.)

NASA/TM—2005-213658 22 5.3.5 Summary .—In summary, you need to do the followings to run the program: 1. Go to the Input sheet 2. Specify the Unit system (SI or English) 3. Specify the ITB switch . Is the computation for engine with ITB-ON or for engine with ITB-OFF?

4. Specify the Fuel Burn Model system (CSH or MSH) 5. Enter all the input parameters indicated in green cells (do not modify or change the value indicated in cyan).

6. Specify Choose a Plot . You will be directed to a new sheet depending on the selection.

In sheet ST_VS_PIc (Compressor Pressure Ratio), a. Specify number of bypass ratio ( α ).

b. Specify all input parameters in green cells.

c. Click ‘ Generate ’ to generate high-pressure compressor total pressure ratio.

d. Click ‘ Calculate ’ to compute and plot the results.

e. Repeat the above steps for different input parameters. To return to Input sheet, simply click ‘ Input sheet ’ button.

In sheet ST_VS_Mo (Flight Condition Mach Number), a. Specify number of bypass ratio ( α ).

b. Specify all input parameters in green cells.

c. Click ‘ Calculate ’ .

d. Repeat the above steps for different input parameters. To return to Input sheet, simply click ‘ INPUT sheet ’ button.

In sheet ST_VS_PIf (Fan Pressure Ratio), a. Specify number of bypass ratio ( α ).

b. Specify all input parameters in green cells.

c. Click ‘ Calculate ’ to compute and plot the results.

d. Repeat the above steps for different input parameters. To return to Input sheet, simply click ‘ Input sheet ’ button.

In sheet ST_VS_Alp (ByPass Ratio), a. Specify number of fan total pressure ratio ( π ).

f b. Specify all input parameters in green cells.

c. Click ‘ Calculate ’.

d. Repeat the above steps for different input parameters. To return to Input sheet, simply click ‘ INPUT sheet ’ button.

In sheet ST_VS_Tt4 (Main Burner Exit Temperature), a. Specify number of flight Mach number ( M ).

b. Specify all input parameters in green cells.

c. Click ‘ Calculate ’.

d. Repeat the above steps for different input parameters. To return to Input sheet, simply click ‘ INPUT sheet ’ button.

NASA/TM—2005-213658 23 5.4 Single Point Calculation All instructions described above are termed as the multi-point calculations at different values of only one design parameter (e.g., π , π , M , α , or T ) The computed results show how the performance of a c f 0 t 4 family of engines was determined by engine design choices and flight Mach number.

Once the most promising engine is selected by users (i.e., all engine components are fixed, e.g., π , π , c f altitude, α etc.), single point calculation is then run to get the engine performance at this particular operating conditions. These output data represents the selected engine’s design point condition. In order to predict the engine performance at off-design conditions, these outputs are then used as the reference conditions in an off-design code. This step is important because different reference conditions (i.e., different engines) will give different performance over the whole flight spectrum.

For user’s reference, the flow chart of this computation is shown in figure B.3 in appendix B.

5.4.1 Exporting Reference Engine Data .—For convenience, authors include ' Input/Output files ' feature in this code. The output data from this on-design code can be exported to be a reference engine data file, which is required in off-design calculation. As a result, users do not need to manually re-input the reference conditions in off-design code, which is a time-consuming process.

Users are to follow the step 1 to 13 to generate a reference engine data file: 1. Select Input sheet (as shown in fig. 5.1).

2. Input the engine characteristics in Input sheet.

3. Select SinglePt sheet (as shown in fig. 5.6).

4. Input values of independent variables (i.e., M , α , altitude, π and throttle settings) in green cells.

0 c 5. Click on ‘ Perform calculation ’ button to calculate the selected engine performance at a design point.

6. Both the input values from Input sheet and the solution will be shown in light-blue cells.

7. Click on ‘ Export reference engine data ’ button to export these reference engine data to a text file.

8. Figure 5.7 will appear and request for specifying the path and filename.

9. Users may need to enter a new path if necessary, for example, “ c:\itb\reference.txt ”. The default path and filename is “c :\reference.txt ”. Figure 5.8 appears when one of these situations happens: (i) The specified directory (default drive is ‘c :\ ’) does not exist.

(ii) The file is being used by another program.

10. Check for existing drive path or/and specify another filename. (Restart from step 3 again).

11. All reference data and engine characteristics of a specific design-point engine are successfully exported.

12. Repeat step 1 to 11 for different engines.

NASA/TM—2005-213658 24 Figure 5.6.—On-design single point calculation sheet.

Figure 5.7.—Dialog box for specifying the path and filename where the reference conditions data will be stored.

NASA/TM—2005-213658 25 Figure 5.8.—This dialog box appears when there is an error writing reference conditions data to a specified file.

Figure 5.9.—Engine station data sheet 5.5 Engine Station Data The last sheet in the program is the Station sheet. This sheet displays the engine station flow properties (i.e., temperature and pressure) in forms of a table (see fig. 5.9) and charts (see fig. 5.10) based on the user input Mach number data at certain stations.

Most of the input parameters are from the Input sheet. Additional inputs are also needed, such as those listed in “Inputs” column (i.e., to the left of the engine station data table) and Mach numbers at some engine stations (as shown in fig. 5.9). To click the ‘ Update Station Data ’ button will update the flow properties at each engine station. Please refer to figure B.4 in appendix B for the code structure of this sheet.

NASA/TM—2005-213658 26 (a) Temperature (b) Pressure Figure 5.10.—Examples of pressure and temperature vs engine stations 5.6 Discussions A typical value for local Mach number at the ITB entrance is selected to be 0.3. This value ( M = 0.3) is then used to compute ITB inlet velocity ( v ), on which one of the factors ITB design 4.4 4.4 was based. In fact, each plot sheet will show the change of ITB inlet velocity with the corresponding design parameter, for example, v versus M in ST_VS_Mo sheet.

4.4 0 At ITB-OFF condition, a plot of “ Temperature Rise across ITB ” in each plot sheet (e.g., ST_VS_PIc , ST_VS_Mo , ST_VS_PIf , and ST_VS_Alp ) will be cleared out. It is because the ITB-OFF engine acts as if it is a turbofan engine without any increase across ITB .

5.7 Troubleshooting This program has been debugged several times. Therefore, whenever you encounter computation errors due to either zero division or square root of a negative quantity, you will be notified by a pop up window indicating where the computation problem is. It will tell you on which equation that the computational error is encountered. If you have any comments or bug problems you encounter in the program, you can report them to us for further improvement. Details about the contact number can be found in the CoverPage sheet of the program.

NASA/TM—2005-213658 27 (a) (b) Figure 5.11.—Pop-up windows showing warning or error messages: (a) Equations where the error occurs; (b) The current values of design variables while error is encountered.

5.7.1 Out of Range .—In multiple-point calculation, users may always see these pop-up windows as shown in figures 5.11a and 5.11b. There are two possibilities of having this error or warning messages: (i) The input values are incorrect. For instance, the main burner exit temperature ( T ) may be 4 t too small for an engine to produce enough thrust. Please double check all input values and try again.

(ii) During the multiple-point computation, the design variable may be out of range. It will happen, especially for these design variables such as flight Mach number, fan pressure ratio and bypass ratio. For instance, the specific thrust of an engine is approaching zero as the flight Mach number is 3. If the upper limit of flight Mach number is set to be greater than 3 (e.g., 5), the code will not be able to proceed at Mach number higher than 3 and thus give these warning messages.

5.7.2 Plotting errors .—It is also predicted that the plotting macro can encounter some problems in the future if the users do not fully understand the program. Therefore, authors have set up a way in order to fix the problem. In case the plot starts giving problem, you need to do the followings (this apply to all plot sheets: ST_VS_PIc , ST_VS_Mo , ST_VS_PIf , ST_VS_Alp, and ST_VS_T ): t4 a. Go to the plot sheet (e.g., ST_VS_Mo ) b. Go to cell D5 c. Note that you will not be able to click on that cell because it is lying on the back of the plot chart.

You may want to use arrow button from your keyboard in order to move to cell D5 .

d. In that cell, you will see “SUCCESS”. Change the character to “FAIL”.

e. Clear the series in the chart plot by clicking right mouse button (RMB)on the chart plot.

f. In RMB menu list, choose Source Data g. In ‘Source Data’ windows, pick Series tab and remove all the series.

Users are not expected to understand macro code in the program. However the part that takes care the ® computation can be found in Module1 Sub Itb ( ). To open Microsoft Excel Visual Basic windows, users need to press Alt + F11 . Any modification can be made in subroutine Itb ( ). Do not add new variables into the program!

NASA/TM—2005-213658 28

Appendix A—Macro Visual Basic Code

Sub itb() Dim rc, rb, rt, a0, v0, eta_r, tau_alp_b, tau_alp_itb Dim tau_c, tau_b, tau_itb Dim T19_T0, fc_mc, ff_mf, denu, nume, v19, v9 ' Style = vbYes Style1 = vbYes ' Msg = "Do you want to jump to the next alpha?"

Msg1 = "Division by zero ==> Check zero inputs for gama's (eqn 1,2,3)" Msg2 = "Imaginary sound speed ==> Check negative inputs for gamac, gc or T0 (eqn 4)" Msg3 = "Division by zero ==> gamac cannot = 1 (eqn 7)" Msg4 = "Division by zero ==> Check zero inputs for cpc, T0, ecH, ecL & ef (eqn 10, 11, 12, 13 & 14)" Msg5 = "Division by zero ==> Check zero inputs for tau_r & tau_c (eqn 16)" Msg6 = "Division by zero ==> tau_cH, tau_cL & tau_f cannot =1 (eqn 17, 18, 19)" Msg7 = "Invalid (negative) tau_tH ==> Refer to equation 21" Msg8 = "Imaginary M9 ==> Pt9/P9 < 1 (eqn 31 & 34)" Msg9 = "Imaginary M19 ==> Pt19/P19 < 1 (eqn 36 & 37)" Msg10 = "Division by zero => denominator of 'fb' eqn cannot =0 (eqn 20)" Msg11 = "Division by zero => denominator of 'fitb' eqn cannot =0 (eqn 22)" wdata = 1 fbi = 0 fitbi = 0 'warn = 0 ' 'If gamac = 0# Or gamat = 0# Or gamaitb = 0# Then 'response = MsgBox(Msg1, style, Title) 'Msg1 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha 'response = MsgBox(Msg1, Style, Title) 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) 'GoTo 10 'End If ' 'added on 5/13/04 for controling ITB switch -1 itbinit = 1 If Sheets("Input").ComboBox2.Value = "OFF" Then itbinit = 0 'added on 5/13/04 for controling ITB switch -2 'Constants Call enthalpy(1, T_o, 0, 0, Cpc, gamac) Call enthalpy(1, Tt4, 0, 0, Cpt, gamat) rc = (gamac - 1#) * Cpc / gamac '(1) rt = (gamat - 1#) * Cpt / gamat '(2) ' If gamac < 0# Or rc < 0# Or T_o < 0# Or gc < 0# Then response = MsgBox(Msg2, Style, Title) 'Msg2 = "Occurs at " & "PIc,PIf,Mo,ByPass = " & pi_cH * pi_cL & "," & pi_f & "," & M0 & "," & alpha 'Msg2 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg2, Style, Title) 'warn = 1 'If singlept <> 1 Or last = 0 Then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If a0 = (gamac * rc * T_o * gc) ^ 0.5 '(4) NASA/TM—2005-213658 29 v0 = a0 * M0 '(5) ' If gamac = 1# Then response = MsgBox(Msg3, Style, Title) 'Msg3 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg3, Style, Title) 'warn = 1 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If ' tau_r = (gamac - 1#) * (0.5 * M0 ^ 2) + 1# '(6) pi_r = tau_r ^ (gamac / (gamac - 1)) '(7) ' If M0 <= 1# Then '(8) eta_r = 1# End If If M0 > 1 And M0 <= 5 Then eta_r = 1# - 0.075 * (M0 - 1#) ^ 1.35 End If If M0 > 5 Then eta_r = 800# / (935# + M0 ^ 4) End If pi_d = pi_dmax * eta_r '(9) ' If pi_cL < pi_f Then pi_cL = pi_f pi_cH = pi_c / pi_cL ' If Cpc = 0# Or T_o = 0# Or gamac = 0# Or e_cH = 0# Or e_cL = 0# Or e_f = 0# Then response = MsgBox(Msg4, Style, Title) 'Msg4 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg4, Style, Title) 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) 'warn = 1 GoTo 10 End If tau_alp_b = Cpt * Tt4 / (Cpc * T_o) '(10) tau_cH = pi_cH ^ ((gamac - 1#) / (gamac * e_cH)) '(12) tau_cL = pi_cL ^ ((gamac - 1#) / (gamac * e_cL)) '(13) tau_f = pi_f ^ ((gamac - 1#) / (gamac * e_f)) '(14) tau_c = tau_cH * tau_cL '(15) ' If tau_r = 0# Or tau_c = 0# Then response = MsgBox(Msg5, Style, Title) 'Msg5 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg5, Style, Title) 'warn = 1 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If tau_b = Tt4 / (T_o * tau_r * tau_c) '(16) ' NASA/TM—2005-213658 30 If tau_cH = 1# Or tau_cL = 1# Or tau_f = 1# Then response = MsgBox(Msg6, Style, Title) 'Msg6 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg6, Style, Title) 'warn = 1 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If eta_cH = ((tau_cH ^ e_cH) - 1#) / (tau_cH - 1#) '(17) eta_cL = ((tau_cL ^ e_cL) - 1#) / (tau_cL - 1#) '(18) eta_f = ((tau_f ^ e_f) - 1#) / (tau_f - 1#) '(19) ' 'add MSH on 7/30/04 -1 'Component: MAIN BURNER h_0 = Cpc * T_o temp_fb = eta_b * hPRb / h_0 - tau_alp_b If temp_fb = 0# Then response = MsgBox(Msg10, Style, Title) 'Msg7 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg7, Style, Title) 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) 'warn = 1 GoTo 10 End If 'Fuel model 1: CSH If Sheets("Input").ComboBox4.Value = "CSH" Then fb = (tau_alp_b - tau_r * tau_c) / temp_fb '(20a) Else 'Fuel model 2: MSH loop3 = 0 Tt3 = T_o * tau_r * tau_c 'eqn(20b) Call enthalpy(0, Tt3, 0, h_t3, 0, 0) f_4i = (tau_alp_b - tau_r * tau_c) / temp_fb 'eqn(20c),initial value for f_4i If loop3 > 20 Then GoTo 10 End If Call enthalpy(0, Tt4, f_4i, h_t4, 0, 0) temp_fb = eta_b * hPRb - h_t4 If temp_fb = 0# Then response = MsgBox(Msg10, Style, Title) 'Msg7 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg7, Style, Title) 'If singlept <> 1 Then jump = MsgBox(Msg_jump, Style1, Title) 'warn = 1 GoTo 10 End If fb = (h_t4 - h_t3) / temp_fb 'eqn(20d) If Abs(fb - f_4i) > 0.0001 Then f_4i = fb loop3 = loop3 + 1 GoTo 3 End If NASA/TM—2005-213658 31 End If 'lkh1 - added cp=cp(T,f) and gama=gama(T,f) on 11/15/04 Err_fb = Abs(fbi - fb) If Err_fb > 0.0001 Then fbi = fb Call enthalpy(1, Tt4, fb, 0, Cpt, gamat) GoTo 24 End If 'lkh2 'add MSH on 7/30/04 -2 ' tau_tH = 1# - (tau_cH - 1#) * tau_cL * tau_r / ((1# + fb) * tau_alp_b * effm_tH) '5/11/04 '(21) If tau_tH < 0# Then response = MsgBox(Msg7, Style, Title) 'Msg7 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg7, Style, Title) Cells(22, 4).Select Msg7 = "The Tt4 lower limit (as indicated) is too low to converge, increase Tt4 lower limit and try again!"

response = MsgBox(Msg7, Style, Title) 'warn = 1 GoTo 10 End If If itbinit = 0 Then Tt4p5 = Tt4 * tau_tH Call enthalpy(1, Tt4p5, 0, 0, Cpitb, gamaitb) tau_alp_itb = Cpitb * Tt4p5 / (Cpc * T_o) '(11) fitb = 0# tau_itb = 1# GoTo 5 End If Call enthalpy(1, Tt4p5, 0, 0, Cpitb, gamaitb) tau_alp_itb = Cpitb * Tt4p5 / (Cpc * T_o) If tau_alp_itb <= (tau_alp_b * tau_tH) Then itbinit = 0 Tt4p5 = Tt4 * tau_tH Call enthalpy(1, Tt4p5, 0, 0, Cpitb, gamaitb) fitb = 0# tau_itb = 1# tau_alp_itb = Cpitb * Tt4p5 / (Cpc * T_o) GoTo 5 End If ' If itbinit = 1 Then 'add MSH on 8/1/04 for ITB -1 'Component: INTERSTAGE-TURBINE BURNER temp_fitb = eta_itb * hPRitb / h_0 - tau_alp_itb If temp_fitb = 0# Then response = MsgBox(Msg11, Style, Title) 'Msg7 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg7, Style, Title) 'If singlept <> 1 Then jump = MsgBox(Msg_jump, Style1, Title) NASA/TM—2005-213658 32 'warn = 1 GoTo 10 End If 'Fuel model 1: CSH If Sheets("Input").ComboBox4.Value = "CSH" Then fitb = (tau_alp_itb - tau_alp_b * tau_tH) / (temp_fitb) * (1# + fb) '9/3/04 '(22a) Else 'Fuel model 2: MSH loop4 = 0 Tt4p4 = Tt4 * tau_tH '(22b) Call enthalpy(0, Tt4p4, fb, h_t4p4, 0, 0) f_4p5i = (1# + fb) * (tau_alp_itb - tau_alp_b * tau_tH) / (temp_fitb) '(22c),initial value for f_4p5i If loop4 > 20 Then loop4 = 21 GoTo 10 End If Call enthalpy(0, Tt4p5, f_4p5i, h_t4p5, 0, 0) temp_fitb = eta_itb * hPRitb - h_t4p5 If temp_fitb = 0# Then response = MsgBox(Msg11, Style, Title) 'Msg7 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg7, Style, Title) 'warn = 1 'If singlept <> 1 Then jump = MsgBox(Msg_jump, Style1, Title) GoTo 10 End If fitb = (1# + fb) * (h_t4p5 - h_t4p4) / (temp_fitb) '(22d) If Abs(fb + fitb - f_4p5i) > 0.0001 Then f_4p5i = fb + fitb loop4 = loop4 + 1 GoTo 4 End If End If 'lkh1 - added cp=cp(T,f) and gama=gama(T,f) on 11/15/04 Err_fitb = Abs(fitbi - fitb) If Err_fitb > 0.0001 Then fitbi = fitb Call enthalpy(1, Tt4p5, fitb, 0, Cpitb, gamaitb) GoTo 25 End If 'lkh2 'add MSH on 8/1/04 for ITB -2 tau_itb = Tt4p5 / (T_o * tau_r * tau_c * tau_b * tau_tH) '(24) End If ritb = (gamaitb - 1#) * Cpitb / gamaitb '(3) f = fb + fitb '(23) tau_tL = 1# - (tau_cL - 1# + alpha * (tau_f - 1#)) * tau_r / ((1# + fb + fitb) * tau_alp_itb * effm_tL) '(26) pi_tH = tau_tH ^ (gamat / ((gamat - 1#) * e_tH)) '(27) pi_tL = tau_tL ^ (gamaitb / ((gamaitb - 1#) * e_tL)) '(28) NASA/TM—2005-213658 33 eta_tH = (1# - tau_tH) / (1# - tau_tH ^ (1# / e_tH)) '(29) eta_tL = (1# - tau_tL) / (1# - tau_tL ^ (1# / e_tL)) '(30) ' Pt9_P9 = P0_P9 * pi_r * pi_d * pi_cL * pi_cH * pi_b * pi_tH * pi_itb * pi_tL * pi_n '(31) tempM9 = Pt9_P9 ^ ((gamaitb - 1#) / gamaitb) If tempM9 < 1# Then response = MsgBox(Msg8, Style, Title) 'Msg8 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg8, Style, Title) 'warn = 1 'If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If Tt9_T0 = tau_r * tau_c * tau_b * tau_tH * tau_itb * tau_tL '(32) T9_T0 = Tt9_T0 / Pt9_P9 ^ ((gamaitb - 1#) / gamaitb) '(33) ' M9 = ((tempM9 - 1#) * 2# / (gamaitb - 1#)) ^ 0.5 '(34)'5/5/04 M8 = M9 If M9 >= 1 Then M8 = 1 v9_a0 = M9 * (gamaitb * ritb * T9_T0 / (gamac * rc)) ^ 0.5 '(35) v9 = v9_a0 * a0 v9_v0 = v9 / v0 ' Pt19_P19 = P0_P19 * pi_r * pi_d * pi_f * pi_fn '(36) tempM19 = Pt19_P19 ^ ((gamac - 1#) / gamac) If gamac < 1# Or tempM19 < 1# Then response = MsgBox(Msg9, Style, Title) 'Msg8 = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 'response = MsgBox(Msg9, Style, Title) 'warn = 1 'If singlept <> 1 then jump = MsgBox(Msgsheet, Style1, Title) GoTo 10 End If M19 = ((tempM19 - 1#) * 2# / (gamac - 1#)) ^ 0.5 '(37) M18 = M19 If M19 >= 1 Then M18 = 1 Tt19_T0 = tau_r * tau_f '(38) T19_T0 = Tt19_T0 / Pt19_P19 ^ ((gamac - 1#) / gamac) '(39) v19_a0 = M19 * T19_T0 ^ 0.5 '(40) v19 = v19_a0 * a0 v19_v0 = v19 / v0 ' fc_mc = (1# + f) * v9_a0 - M0 + (1# + f) * (ritb / rc) * (T9_T0 / v9_a0) * (1# - P0_P9) * (1# / gamac) '(41) ff_mf = v19_a0 - M0 + (T19_T0 / v19_a0) * (1# - P0_P19) / gamac '(42) F_mo = (a0 / gc) * (fc_mc + alpha * ff_mf) / (1# + alpha) '(43) ' unitchange = 1# If Sheets("Input").ComboBox1.Value = "SI" Then unitchange = 1000000# Else NASA/TM—2005-213658 34 unitchange = 3600# End If s = f / ((1# + alpha) * F_mo) * unitchange '(44) '(44) If F_mo < 0 Or s < 0 Then wdata = 0 ' 'Efficiencies corenume = (1# + f) * v9 * v9 - v0 * v0 'corrected on 6/16/04 fanume = alpha * (v19 * v19 - v0 * v0) nume = 0.5 / gc * (corenume + fanume) '(45) denu = fb * hPRb * eta_b + fitb * hPRitb * eta_itb '(46) ' eta_thermal = nume / denu * 100# '(47) eta_P = (1# + alpha) * F_mo * v0 / nume * 100# '(48) eta_O = (1# + alpha) * F_mo * v0 / denu * 100# '(49) ' 'Mach = 0.3 at HP turbine exit M4p4 = 0.3 Tt4p4 = tau_r * tau_c * tau_b * tau_tH * T_o T4p4 = Tt4p4 / (1# + 0.5 * (gamat - 1#) * M4p4 * M4p4) v4p4 = M4p4 * (gamat * rt * gc * T4p4) ^ 0.5 dTitb = Tt4p4 * (tau_itb - 1#) GoTo 11 'If warn = 1 Then 'added on 11/30/04 Msg = "Occurs at " & "PIc=" & pi_cH * pi_cL & ", PIf=" & pi_f & ", Mo=" & M0 & ", alpha=" & alpha & ", Tt4=" & Tt4 response = MsgBox(Msg, Style, Title) If last = 1 Then jump = 1 GoTo 11 End If If singlept <> 1 Then jump = MsgBox(Msgsheet, Style1, Title) ' End If End Sub NASA/TM—2005-213658 35

Appendix B — Flowchart of Iterative Solution Scheme in

®

Excel Code

Microsoft

® Figure B.1.—Flow-chart of the main structure for ITB on-design Microsoft Excel code.

NASA/TM—2005-213658 37 Figure B.2.—Flow-chart of the iterative solution scheme for on-design multiple-point calculation.

Remarks : *DLV – Do Loop Variables; **FLV – For Loop Variables.

NASA/TM—2005-213658 38 Figure B.3.—Flow-chart of the solution scheme for ITB on-design single point calculation.

NASA/TM—2005-213658 39 Figure B.4.—Flow-chart of the solution scheme for ITB engine station data computation.

NASA/TM—2005-213658 40 Figure B.5.—Flow-chart of the iterative solution scheme for ITB computation subroutine.

NASA/TM—2005-213658 41

Appendix C—Combustion Fuel Burn Models

C.1 Types of Fuel Burn Models Two models (p. 116 of ref. 4) are being used to calculate the fuel burned in the main burner and the ITB : (1) Constant Specific Heat ( CSH ) model – The air and combustion gases at inlet and exit of each component are modeled as “calorically perfect gases” with constant specific heats. The values of the specific heats are different at inlet and exit of two combustors (main burner and ITB ) (2) Modified Specific Heat ( MSH ) model – All engines properties are calculated using CSH model except the fuel used. In this model, the inlet total temperature ( T and T ) of combustors are calculated t3 t4.4 using CSH model while the exit total temperatures ( T and T ) are directly obtained from the user t4 t4.5 inputs. Nevertheless, the total enthalpies ( h , h , h , and h ) will be calculated directly from the t3 t4 t4.4 t4.5 Variable Specific Heat ( VSH ) model (p. 116 of Ref. 4). Provided h is given, the amount of fuel burned PR is then calculated using eq. (B4) and (B7), respectively. Therefore, the improvement on enthalpy calculation gives better estimates of fuel used.

The following ENTHALPY subroutine is based on pages 105–106 of reference 3 and used in the MSH model to calculate the enthalpy ( h ) at engine stations t3, t4, t4.4, and t4.5.

Subroutine Enthalpy ENTHALPY ( 0,T , f , h,0,0 ) Inputs : T and f Output : h A A A A A A A ⎤ ⎡ 7 6 5 4 3 2 1 8 7 6 5 4 3 2 T T T T T T T T A h h + + + + + + + + = (C.1) ref air 0 ⎥ ⎢ 8 7 6 5 4 3 2 ⎦ ⎣ air A A A A A A A ⎤ ⎡ 7 6 5 4 3 2 1 8 7 6 5 4 3 2 T T T T T T T T A h h + + + + + + + + = (C.2) ref prod 0 ⎥ ⎢ 8 7 6 5 4 3 2 ⎦ ⎣ prod h f h + prod air h = (C.3) mix f + 1 where the constants A , etc. are given in Table C.1 (p.106 of Ref. 3).

Table C.1.—Constants for air and combustion products used in subroutine ENTHALPY( 0, T , f , h, c , γ ).

p Constant Air alone Combustion products of air and (CH fuels 2) n –1 –1 A 2.5020051 × 10 7.3816638 × 10 –5 –5 A –5.1536879 × 10 1.2258630 × 10 –8 –8 A 6.5519486 × 10 –1.3771902 × 10 –12 –12 A –6.7178376 × 10 9.9686793 × 10 –14 –14 A –1.5128259 × 10 –4.2051104 × 10 –18 –18 A 7.6215767 × 10 1.0212913 × 10 –21 –21 A –1.4526770 × 10 –1.3335668 × 10 –25 –25 A 1.0115540 × 10 7.2678710 × 10 –1.7558886 Btu/lbm 30.58153 Btu/lbm h ref NASA/TM—2005-213658 43 The equations needed to calculate the fuel-air ratios of the main burner ( f ) and the ITB ( f ) are b itb listed below for both the CSH and MSH models.

Main burner If CSH model then τ τ − τ cH cL b − λ f = (C.4) b h h τ − η b PR b − λ 0 Else T T τ τ τ = (C.5) cH cL r t 0 3 ENTHALPY 0, , 0, , 0, 0 T h

( )

3 3 t t Set initial value of fuel/air ratio at station 4 = f 4i

3 ENTHALPY ( ) 0, , , , 0, 0 T f h

4 4 4 t i t h h − 3 4 t t f = (C.6) b h h − η 4 t PR b If > − f f 0.0001, then f f = and go to 3; else continue.

i b 4 b i 4 End if Inter-stage Turbine Burner If CSH model then τ τ − τ tH b itb − λ − λ

( ) i f + = 4 1 (C.7)

itb h h τ − η itb PR itb − λ 0 Else T T τ = tH t t 4 4 . 4 ENTHALPY 0, , , , 0, 0 T f h

( )

4.4 4.4 t b t Set initial value of fuel/air ratio at station 4.4 = f 4.5i 4 ENTHALPY 0, , , , 0, 0 T f h

( )

4.5 4.5 4.5 t i t h h − 4 . 4 5 . 4 t t

( )

1 f f + = (C.8) b itb h h − η 5 . 4 t PR itb If > − + f f f 0.0001, then f f f + = and go to 4; else continue.

i itb b 5 . 4 itb b i 5 . 4 End if 0 = f R R = If then , , C C = γ = γ and itb pt pitb t itb t itb NASA/TM—2005-213658 44

References

1. Model Specification for Engines, Aircraft, Turbojet , Military Specification MIL-E-5008B, Department of Defense, January 1959.

2. “Gas Turbine Engine Performance Station Identification and Nomenclature,” Aerospace Recommended Practice (ARP) 755A , SAE, Warrendale, PA, 1974.

3. Mattingly, J.D., “Elements of Gas Turbine Propulsion,” McGraw Hill, Inc. New York, NY 1996.

4. Mattingly, J.D., Heiser, W.H., and Pratt, D.T., Aircraft Engine Design, Second Edition , AIAA Education Series, AIAA, Reston, VA, 2002.

NASA/TM—2005-213658 45 Form Approved

REPORT DOCUMENTATION PAGE

OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 1. AGENCY USE ONLY ( Leave blank) Technical Memorandum July 2005 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Parametric (On-Design) Cycle Analysis for a Separate-Exhaust Turbofan Engine With Interstage Turbine Burner WBS–22–066–10–12 6. AUTHOR(S) K.H. Liew, E. Urip, S.L. Yang, Y.K. Siow, and C.J. Marek 8. PERFORMING ORGANIZATION 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) REPORT NUMBER National Aeronautics and Space Administration John H. Glenn Research Center at Lewis Field E–15148 Cleveland, Ohio 44135 – 3191 10. SPONSORING/MONITORING 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AGENCY REPORT NUMBER National Aeronautics and Space Administration Washington, DC 20546– 0001 NASA TM—2005-213658 11. SUPPLEMENTARY NOTES K.H. Liew, E. Urip, S.L. Yang, and Y.K. Siow, Michigan Technological University, Department of Mechanical Engineering and Engineering Mechanics, 1400 Townsend Drive, Houghton, Michigan 49931–1200; and C.J. Marek, NASA Glenn Research Center. Responsible person, C.J. Marek, organization code RTB, 216–433–3584. This report contains a supplemental ® Microsoft Excel spreadsheet (TM–2005-213658/SUPPL1) available at http://gltrs.grc.nasa.gov.

12b. DISTRIBUTION CODE 12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified - Unlimited Subject Category: 07 Available electronically at http://gltrs.grc.nasa.gov This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

13. ABSTRACT (Maximum 200 words) This study focuses on a parametric (on-design) cycle analysis of a dual-spool, separate-flow turbofan engine with an Interstage Turbine Burner ( ITB ). The ITB considered in this paper is a relatively new concept in modern jet engine propul- sion. The ITB serves as a secondary combustor and is located between the high- and the low-pressure turbine, i.e., the transition duct. The objective of this study is to use design parameters, such as flight Mach number, compressor pressure ratio, fan pressure ratio, fan bypass ratio, and high-pressure turbine inlet temperature to obtain engine performance param- eters, such as specific thrust and thrust specific fuel consumption. Results of this study can provide guidance in identifying the performance characteristics of various engine components, which can then be used to develop, analyze, integrate, and ® optimize the system performance of turbofan engines with an ITB . Visual Basic program, Microsoft Excel macrocode, and ® ® Microsoft Excel neuron code are used to facilitate Microsoft Excel software to plot engine performance versus engine design parameters. This program computes and plots the data sequentially without forcing users to open other types of plotting programs. A user’s manual on how to use the program is also included in this report. Furthermore, this stand-alone program is written in conjunction with an off-design program which is an extension of this study. The computed result of a selected design-point engine will be exported to an engine reference data file that is required in off-design calculation.

14. SUBJECT TERMS 15. NUMBER OF PAGES Turbofan cycles; Interstage turbine burner; ITB 16. PRICE CODE 19. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 17. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF ABSTRACT OF THIS PAGE OF REPORT Unclassified Unclassified Unclassified NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102