Diffuser Analysis

Diffuser

 

Introduction


This section provides an isentropic diffuser analysis when the working fluid is air. 
 

Analysis 
 

In the presented diffuser analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value.  Ideal gas state equation is valid -- pv = RT. 
 

Air enters a diffuser at point 1 and it exits the diffuser at point 2.  Working fluid inlet velocity gets reduced to zero resulting in the stagnation temperature and pressure inrease.  Isentropic process is considered with no entropy change. 


Figure 1 contains a diffuser schematic layout. 

Figure 1 - Diffuser Schematic Layout


Figure 2 presents a diffuser temperature vs entropy diagram. 

Figure 2 - Diffuser Temperature vs Entropy Diagram 
 

Figure 3 presents diffuser performance -- stagnation over static temperature and pressure ratio values as a function of the Mach Number.  Only subsonic diffuser operation is considered.  It should be noted that air enters the diffuser at the static conditions of 298 [K] and 1 [atm] of absolute pressure. 

Figure 3 - Diffuser Performance 
 

One can notice that diffuser stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. 
 

Assumptions 
 

Working fluid is air. There is no friction and heat transfer. Isentropic process -- there is no entropy change.  Ideal gas state equation is valid -- pv = RT.  Air behaves as a perfect gas -- specific heat has a constant value. 
 

Governing Equations 
 

Tt/T = (1 + M^2(k - 1)/2)
p
t/p = (1 + M^2(k - 1)/2)^
ϰ/(ϰ-1)
T
t/T = (pt/p)^(
ϰ-1)/ϰ 
T
t = T + v^2/(2cp)
v
s = (
ϰRT)^1/2
M = v/v
s

ϰ = cp/cv
cp - cv = R
pv = RT

 

Input Data 
 

T1 = 298 [K] 
p
1 = 1 [atm] 
R = 0.2867 [kJ/kg*K] 
c
p = 1.004 [kJ/kg*K] 

ϰ = 1.4 [/]

M = 0.29, 0.58 and 0.95 [/]
 

Results 
 

Diffuser Performance vs Inlet Mach Number
Diffuser Inlet Static Temperature = 298 [K] and Presuure = 1 [atm]

Inlet Mach
Number

[/]

0.29

0.58

0.95

Stagnation/Static
Temperature Ratio

[/]

1.017

1.067

1.182

Stagnation/Static
Pressure Ratio

[/]

1.06

1.25

1.80

Conclusions 

Diffuser stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. 
 

References 
 

JANAF Thermochemical Data - Tables, 1970 

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