Analysis of Heat and Compressibility Effects in Internal Flow Systems and High-Speed Tests of a Ram-Jet System Page: 2 of 40
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REPORT NO. 773-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The body used in this investigation was designed to con-
form closely with the duct arrangement assumed in the anal-
ysis given in part I. Heat was added by a specially con-
structed radiator causing negligible blockage of the duct
flow and insignificant friction loss. This manner of adding
heat minimized the fire hazard in the wind tunnel and
eliminated the combustion problem that would have existed
if fuel were burned in the duct. The amount of heat added
(16Q kw max.) produced a thrust equal to about 40 percent
of the drag of the test body at 1=0.75. This rate of heating,
although lower than the rates obtainable by combustion of
fuel, was large enough to permit accurate measurements of
the thrust and other effects of heating to be obtained and
thus to provide the basis for significant comparisons with the
analytical investigation.
SYMBOLS
A area, square feet
a velocity of sound, feet per second
0 mass-flow coefficient (pV) or ( )
CD internal-drag coefficient Q5)
ACD internal-drag-coefficient increment
C, drag coefficient of radiator tube (-
CDr radiator drag coefficient 9qA-
c, specific heat at constant pressure (for air 0.24
Btu/lb/F)
D net drag due to internal flow, pounds r
AD internal-drag increment, pounds
D, drag force due to friction within the radiator tubes,
pounds
D, total drag force acting on the radiator, pounds
d duct diameter, inches
F maximum fuselage cross-section area, square feet
(1.009 for model tested)
g acceleration of gravity (32.2 ft/sec2)
H heat added, Btu per second
h total pressure, pounds per square foot absolute
Ah total-pressure loss, pounds per square foot
J mechanical equivalent of heat (778 ft-lb/Btu)
K. E. kinetic energy, foot-pounds
L over-all length of fuselage, inches
1 distance from nose, inches
I Mach number (v/a)
m mass-flow rate, slugs per second
P pressure coefficient
p static pressure, pounds per square foot absolute
Ap static-pressure decrease, pounds per square foot
Q quantity of flow, cubic feet per second
q dynamic pressure, pounds per square foot 2p)
R gas constant, feet per' oF (for air, 53.3)R radius, inches
T
T
At
Vo
V
x
5'
Eg
p
1+71temperature, F absolute
thrust, pounds
temperature change, F
free-stream velocity, feet per second
velocity within duct, feet per second
distance from leading edge of respective sections,
inches
ratio of specific heats (for air, 1.40)
heat-cycle efficiency (equation (31))
mechanical-efficiency factor (equation (33))
propulsive efficiency (EEM) (equation (32))
density, slugs per cubic foot
diffuser efficiency
compressibility factor
(h-pAMPM A P..
q 440 1600Subscripts:
0 to 5 stations in internal flow system shown in figure 1
c test condition without heat
d value at any station in duct
f friction component
i low speed, incompressible-flow condition
r condition across the radiator or heating device
r within, the radiator at the tube entrances
re within the radiator at the tube exits
t condition within the radiator tubes
A prime after a symbol indicates the condition without
heat but with same mass flow as with heat.
I. ANALYSIS OF INTERNAL FLOW SYSTEMS
CALCULATION OF THE FLOw CHARACTERISTICS AT KEY STATIONS IN
A TYPICAL INTERNAL FLOW SYSTEM
In the design of efficient aircraft, the flow characteristics
(static pressure, density, and velocity) must be computed
at several key stations in each internal flow system. The
objects of such calculations are to determine the state ofTihe
air entering the radiators, the pressures available for cooling,
the flow changes across the heating device, the net drag or
propulsive force due to the internal flow, and the required
sizes of inlet and outlet openings. It will be shown that
under present-day operating conditions compressibility
effects and the secondary effects of heating cannot be neg-
lected in the calculations.
Methods.will be presented for analyzing the internal flow
system that will account for the effects of heating and
compressibility and will yet be simple to use. Elimination
of much of the mathematical work will be effected through
solution of the more cumbersome equations in chart form.
The methods presented are generally applicable to any
internal flow system, either with or without the addition of
heat or mechanical energy (internal blower), and for any
rate of internal flow.
One-dimensional flow and a uniform velocity distribution
across the duct is assumed throughout the analysis.
The theory of the process whereby the heat energy added
to the internal flow is converted into mechanical energy is
described under a subsequent subheading of part I.408
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Becker, John V. & Baals, Donald D. Analysis of Heat and Compressibility Effects in Internal Flow Systems and High-Speed Tests of a Ram-Jet System, report, July 21, 1942; (https://digital.library.unt.edu/ark:/67531/metadc60041/m1/2/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.