Air-Jet Ejectors

85 Pages·2.322 MB·English

by  Wu, Wen

AIR-JET EJECTORS
THESIS
Submitted in partial fulfillm ent
of the requirement for the
degree of
MASTER OF MECHANICAL ENGINEERING
at the
POLYTECHNIC INSTITUTE OF BROOKLYN
by
Wen Wu
September 1951
Approved :
Depart;aept anc
Thesis Advise]
(cid:3)
(cid:3)
(cid:3)
(cid:3)
ProQuest Number:27591466
(cid:3)
(cid:3)
(cid:3)
(cid:3)
All rights reserved
(cid:3)
INFORMATION TO ALL USERS
Thequality of this reproduction is dependent upon the qualityof the copy submitted.
(cid:3)
In the unlikely event that the authordid not send a complete manuscript
and there are missing pages,these will be noted. Also, if material had to be removed,
a notewill indicate the deletion.
(cid:3)
(cid:3)
(cid:3)
(cid:3)
(cid:3)
ProQuest 27591466
(cid:3)
Published by ProQuest LLC ( 2019). Copyrightof the Dissertation is held by the Author.
(cid:3)
(cid:3)
All rights reserved.
This work is protected against unauthorized copying under Title 17, United States Code
Microform Edition © ProQuest LLC.
(cid:3)
(cid:3)
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
ACKNOWLEDGEMENT
The author takes this opportunity to express
his deep appreciation to professor E. L. Midgette,
Head of the Department of Mechanical Engineering
of the In stitu te, for his invaluable advice to
this work.
SUMMARY
The general performance of the a ir-je t ejector is
firs t analyzed for the flow in the constant pressure
mixing section, the constant area mixing section and
the diffuser. Then the criterion for the minimum value
of the driving stream and the charateristic equations
of the ejectors are formulated. A numerical example is
given to illu strate the procedure of the design of the
a ir-je t ejector*
TABLE OF CONTENTS
I. Nomenclature Page 1
II. Introduction 4
III. Methods Of Analysis 7
(1) The Driving Stream 7
(z) The Entrained Stream 8
(5) The Constant Pressure Mixing 9
(4) The Constant Area Mixing 25
(5) Diffuser 57
(6) Minimum Value Of The Driving Stream 44
IV. Example Of Design 53
V. Appendix A-1
VI. Bibliography A-18
I. NOMENCLATURE
z
A : cross sectional area .... ft.
c local sound velocity of air . . . . ft/sec.
c : constant pressure specific heat od air = 0.24 .. BTU/lb-E.
D : diameter . ... ft.
F : frictional force between air stream and solid wall .. lb.
f : coefficient of the frictional force between air
stream and solid wall ... dimensionless
mass flow rate of air stream . ... lb/sec.
gravitional constant = 32.2 ... ft/sec.
enthalpy of air stream ... BTU/lb.
mechanical equivalent constant = 776 .. ft-lb/BTU.
specific heat ratio of air = 1.4 ... dimensionless
length . . .. ft.
Mach number of air stream ... dimensionless
dragging force between the driving stream
and the entrained stream .... lb.
p : static pressure of the air stream .... lb/ft.ab s.
R : gas constant of air = 53*35 ft-lb/lb-R .
: area ratio between the constant area mixing section
and the primary nozzle throat = dimensionless
^ it
r^ i temperature ratio between the entrained stream
m
and the driving stream = dimensionless
Tpi ; pressure ratio between the entrained stream
and the driving stream = ... dimensionless
^i
Tpg : pressure ratio between thee ntrained stream
and the exit stream = -^o- ... dimensionless
Pe
T : absolute temperature of air stream ••• (‘^F abs.)
V ; mean air stream velocity ... ft/sec.
X : coefficient of the dragging force between the
driving stream and the entrained stream ... dimensionless
/U : viscosity of air ... Ib/ft-sec.
p i density of air stream ... Ih /tt .
00 : mass flow ratio = ■ ... dimensionless
Gq
Subscriptions:
a, b; d; e : sections corresponding to figure 1.
c : the complete mixing section
1 : the driving stream
n : section where the normal shock occurs
0 ; the entrained stream
t : throat section of the primary nozzle
?
e
Cl.
Cl
4
II. INTRODUCTION
Up to the present time, the available literature regarding
the design of the a ir-je t ejectors are few. The problem lies in
the lacking of understanding of the mixing mechanism of two fluid
1 2
streams. Some analytical methods * have been proposed in design­
ing the a ir-je t ejectors. Their efforts however confined mainly
in the following two ways; (1) To simplify the entire mixing pro­
cess either as a constant pressure mixing or as a constant area
mixing. (2) To determine only the cross sectional area of the eje­
ctors and leave the length of the ejectors to be determined experi­
mentally. It is therefore the purpose oft his paper tof ormulate
an approximate method to determine both the cross sectional area
and the length of the ejectors by considering both the constant
pressure and the constant area mixing at the same time. The fo ll­
owing assumptions are being made in this analysis:
(1) The air-flow is one dimensional. The velocity of the air
stream, either the driving or the entrained, assumes a single value
at each section and varies along the flow-wise direction. There
is no transverse flow across each section.
(2) The flow is adiabatic. No heat is being transferred bet­
ween the ejector and the surroundings.
(^) The air is a perfect gas.
(4) The flow is.a steady one.
1,2 - Superscript numbers refer to Bibliography at the end of
the paper.
The function of the a ir-je t ejectors works as a compressing
apparatus. However, i t differs from the conventional compressing
equipment, which uses a moving solid part, ( either a reciproca­
ting piston or a rotating im peller,) to compress the fluid from
the low pressure region to the high pressure region. The ejector
uses the fluid its e lf as the compressing medium. The driving st­
ream transfers its high velocity kinetic energy to the low velo­
city entrained stream during both the constant pressure mixing
and the constant area mixing periods. The entrained stream, after
receiving the energy, moves from the low pressure chest to the
high pressure exhaust region. Since the driving stream and the
entrained stream are the same fluid - air, in this case - they
w ill possess the same properties when the mixing is completed;
which is assumed to occur at the end of the constant area mixing
section. In other words, the energy transfer from the driving
stream to the entrained stream w ill cease at the end of the con­
stant area section. After the mixing is completed, the problem
becomes how to convert the high velocity low pressure stream to
a low velocity high pressure stream. Since the diffuser is the
best known apparatus to convert the velocity energy to the pot­
ential energy, i.e . the pressure; therefore, the diffuser is used
after the constant area section.
Usually the stream is at a supersonic velocity when the mix­
ing is completed. But the stream coming out of the diffuser is
usually at a very low velocity. Thus the stream will reduce its