Introduction

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Introduction

Terminology Station herein will refere the the position withing the engine, absolute. Poistion will refer to the loation relative to the state, e.g. 2 is after the rotor.

Variables

Environmental factors

γ.2 1.4 :

c.p2 1005 J kg K * / * :

λ.c 0.85 :

g.c 1 :

Rbar 287 J kg K * / * :

Target Coefficients

π.LPF 1.4 :

BPR 4.666 :

mdot.a23 2.0 kg s / * :

RPS 250 :

α.inlet 0 deg * :

φ 0.6 :

HTratio 0.55 :

ψ.init 0.44 :

Initial Measuements

T0.inlet 288.15 K * :

P0.inlet 101325 Pa * :

Units

radps 2 π * s / :

Independent Functions

V,T0 MACH 2 γ.2 1 - / T0 T0 V 2^2 c.p2 * / - / (1 - (* sqrt :

M MFP g.c γ.2 Rbar / * sqrt M * 1 γ.2 1 - 2 / (M 2^* + (γ.2 1 + 21 γ.2 - (* /^* :

x 5 m s / * :

y 5 K * :

x,y MACH #

mdot,T0,P0,M A mdot T0 sqrt * P0 M MFP * 0 deg * cos * / :

Initial Calculations

ω RPS radps * : 1570.7963 Hz *

HPC Temp Ratio T03/T023 (Cumpsty) Note: after the fact, I think this should be the LFP increases

τ.LPF π.LPF γ.2 1 - γ.2 λ.c * /^: 1.1197

P0.3 P0.inlet π.LPF * : 1.4186 105^* Pa *

T0.3 T0.inlet τ.LPF * : 322.6542 K *

ΔT0.LPF T0.3 T0.inlet - : 34.5042 K *

ΔP0.LPF P0.3 P0.inlet - : 40530 Pa *

mdot.a2 mdot.a23 BPR * : 9.332 kg s / *

HPC work (NASA, Hall & Dixon)

W.f T0.inlet c.p2 * λ.c / π.LPF γ.2 1 - γ.2 /^1 - (* : J 34378.7126 1 kg / *

Approx Max Spin Rate

C.2max γ.2 1 - (g.c * c.p2 * T0.inlet * 1 γ.2 1 - 2 / (+ / sqrt : 310.6932 m s / *

C.amax C.2max α.inlet cos * : 310.6932 m s / *

U.mmax C.amax φ / : 517.822 m s / *

MaxRev U.mmax radps 0.08 * m * / : 1030.1741

Environment, Inlet by convergence

Δlimit 0.1 m s / * :

C.atemp 40 m s / * :

V.2inlet 0 :

M.2IGV 0 :

T.2IGV 0 :

P.2IGV 0 :

ρ.2IGV 0 :

MFP.M2IGV 0 :

A.2IGV 0 :

r.t 0 :

r.h 0 :

r.m 0 :

U.m 0 :

C.a 0 :

Δconv 1 :

i 0 :

i 50 < V.2inlet C.atemp α.inlet cos / : M.2IGV 2 γ.2 1 - / T0.inlet T0.inlet V.2inlet 2^2 c.p2 * / - / (1 - (* sqrt : T.2IGV T0.inlet 1 γ.2 1 - 2 / (M.2IGV 2^* + / : P.2IGV P0.inlet T.2IGV T0.inlet / (γ.2 γ.2 1 - /^* : ρ.2IGV P.2IGV Rbar T.2IGV * / : MFP.M2IGV M.2IGV MFP : A.2IGV mdot.a2 T0.inlet sqrt * P0.inlet MFP.M2IGV * α.inlet cos * / : r.t A.2IGV π 1 HTratio 2^- (* / sqrt : r.h r.t HTratio * : r.m r.t r.h - 2 / r.h + : U.m r.m ω * : C.a φ U.m * : Δconv C.a C.atemp - : C.a trace i trace C.atemp trace Δconv trace Δconv abs Δlimit < break i i 1 + : C.atemp C.atemp Δconv 2 / + : 21 line if 181 line while

C.a 125.7114 m s / *

U.m 209.519 m s / *

r.m 0.1334 m *

IGV Annulus and height

MFP (Mattingly "Aircraft Engine Design" 1.9.3 p.9) mdot = pAV A=mdot/pV

x C.a :

y T0.inlet :

M.0 x,y MACH : #

MFP.M0 M.0 MFP : #

# MFP.2

*********************all function definitions stopped here due to trainwreck*****

A.0 P0,M.0 A :

h.IGV A.0 2 π r.m * - / : #

C.1inlet C.a α.inlet cos / : 125.7114 m s / *

Stage Count and final Dimensionless Factors

Required stages n = dt * cp /Cw*U^2

n.cnt ΔT0.LPF c.p2 * ψ.init U.m 2^* / : 1.7953

n.cnt n.cnt 0 round : 2

ψ.m ΔT0.LPF c.p2 * n.cnt / U.m 2^/ : 0.395

R.m α.inlet tan φ * ψ.m 2 / + 1 - (1 - (* : 0.8025

ψ.opt 2 φ 2^12 / + R.m R.m 1 - (* + sqrt * : 1.6751

ψ.opt_res 4 φ 2^* 1 + sqrt : 1.562

Sensible design limits between

ψ.opt_exp 0.185 4 φ 2^* 2 + sqrt * : 0.3431

ψ.max 0.32 0.2 φ * (+ : 0.44

Velocity Triangles, Dimensionless

Relative Velocities

Rotor Inflow Velocity Relative W1/U = SQRT{Fc^2+ (R + (Wc/2) )^2 }

W.1m U.m φ 2^R.m ψ.m 2 / + (2^+ sqrt * : 244.3391 m s / *

Rotor Outflow Velocity Relative W2/U = SQRT{Fc^2+ (R - (Wc/2) )^2 }

W.2m U.m φ 2^R.m ψ.m 2 / - (2^+ sqrt * : 178.53 m s / *

Rotor Entry and Stage Exit Velocity C1/U = SQRT{Fc^2+ (1 - R - (Wc/2) )^2 }

C.3m U.m φ 2^1 R.m - ψ.m 2 / - (2^+ sqrt * : 125.7114 m s / *

Stator Inflow Velocity C2/U = SQRT{Fc^2+ (1 - R + (Wc/2) )^2 }

C.2m U.m φ 2^1 R.m - ψ.m 2 / + (2^+ sqrt * : 150.5039 m s / *

Tangential Flow Velocities C01/U=1-R-0.5*Wc

C0.3m U.m 1 R.m - ψ.m 2 / - (* : 0

C02/U=1-R+0.5*Wc

C0.2m U.m 1 R.m - ψ.m 2 / + (* : 82.7531 m s / *

W01/U=R+0.5*Wc

W0.1m U.m R.m ψ.m 2 / + (* : 209.519 m s / *

W02/U=R-0.5*Wc

W0.2m U.m R.m ψ.m 2 / - (* : 126.7659 m s / *

Median Blade and Flow angles - Post Itt inlet calcs a1 = atan( (1/Fc) * (1-R-0.5 * Wc) ) a2 = atan( (1/Fc) * (1-R+0.5 * Wc) )

α.3m 1 φ / 1 R.m - ψ.m 2 / - (* atan : deg 0

α.2m 1 φ / 1 R.m - ψ.m 2 / + (* atan : deg 33.356

β.1m 1 φ / R.m ψ.m 2 / + (* atan : deg 59.0362

β.2m 1 φ / R.m ψ.m 2 / - (* atan : deg 45.2393

V.2inlet C.atemp α.inlet cos / : 125.7892 m s / *

M.2IGV 2 γ.2 1 - / T0.inlet T0.inlet V.2inlet 2^2 c.p2 * / - / (1 - (* sqrt : 0.3747

T.2IGV T0.inlet 1 γ.2 1 - 2 / (M.2IGV 2^* + / : 280.2779 K *

P.2IGV P0.inlet T.2IGV T0.inlet / (γ.2 γ.2 1 - /^* : 91962.8523 Pa *

ρ.2IGV P.2IGV Rbar T.2IGV * / : 1.1433 kg m 3^/ *

MFP.M2IGV M.2IGV MFP : 0.0241 K 12 /^s * m / *

A.2IGV mdot.a2 T0.inlet sqrt * P0.inlet MFP.M2IGV * α.inlet cos * / : 0.0649 m 2^*

r.t A.2IGV π 1 HTratio 2^- (* / sqrt : 0.1721 m *

r.h r.t HTratio * : 0.0947 m *

r.m r.t r.h - 2 / r.h + : 0.1334 m *

U.m r.m ω * : 209.519 m s / *

C.a φ U.m * : 125.7114 m s / *