SUPERSONIC FLOW PAST A
CONE
SUPERSONIC FLOW PAST A CONE
During our discussion in Prandtl-Meyer flow, we found
that all stream properties are uniform on straight lines
in the physical plane. For axi-symmetric flow, it is
found again that all stream propert

COMPUTATIONAL FLUID
DYNAMICS
INTRODUCTION TO CFD
What is it CFD?
The physical aspects of any fluid flow are governed by
the following three fundamental principles:
(1) mass is conserved;
(2) F=ma (Newtons second law); and
(3) energy is conserved.
These fu

MINISTRY OF SUPPLY
AERONAUTICAL
RESEARCH COUNCIL
CURRENT
A Note
PAPERS
on Shock Tubes
BY
D. W. Holder, BSc., D.I.C.,
of the Aerodynamics
LONDON
Dwslon,
N.P.L.
HER MAJESTYS STATIONERY
7953
THREE SHILLINGS
NET
OFFICE
A Note on Shook Tubea
- By De W. Holder,

FLOW WITH HEAT ADDITION OR
REMOVAL
ONE DIMENSIONAL FLOW IN A CONSTANT AREA DUCT WITH
ADDITION OR REMOVAL HEAT (NEGLECTING VISCOSITY)
For constant area duct continuity becomes
dv/v + d/ =0 (1)
Momentum eq is
dP + vdv =0 (2)
And energy eq is
dQ=m[ cp(T+dT)

FINAL
PRESENTATION
SHOCK TUBE
ANALYSIS
Presented By :Zulbab Rasheed
Sahi
Presented To :Dr.Khalid Perviz
Department: Aeronautics &Astronautics
Institute Of Space Technology, Islamabad
Date : 20- May-2016
INTRODUCTION
The experimental study of nonequilibriu

ADIABATIC FLOW IN A DUCT
WITH FRICTION (FANNO FLOW)
FLOW IN A CONSTANT AREA DUCT
Compressible adiabatic flow in a constant area duct
with frictional effects, is known as, Fannoflow.
Consider a momentum balance for small portion of
the duct.
p, v
v +dv, p

SUPERSONIC FLOW PAST A
CONE
SUPERSONIC FLOW PAST A CONE
During our discussion in Prandtl-Meyer flow, we found that all stream
properties are uniform on straight lines in the physical plane.
For ax symmetric flow, it is found again that all stream properti

EXPANSION WAVES (PRANDTL
MEYER FLOW)
FLOW ON CONVEX CORNER
To determine the type of waves occur at the
convex corner in supersonic flow, let us
assume that these waves are oblique shock
waves.
M >1
L
N V
1
1
1
2
N2
L2
Now analyzing the flow we see that L1

SUPERSONIC FLOW PAST WINGS
OF FINITE SPAN
SUPERSONIC FLOW PAST WINGS OF FINITE
SPAN
Supersonic flow around a finite supersonic wings is
treated as three-dimensional supersonic flow.
Because of the rule that in supersonic flow a
disturbance is felt only wi

8086 instructions
Page 1 of 53
Complete 8086 instruction set
Quick reference:
AAA
AAD
AAM
AAS
ADC
ADD
AND
CALL
CBW
CLC
CLD
CLI
CMC
CMP
CMPSB
CMPSW
CWD
DAA
DAS
DEC
DIV
HLT
IDIV
IMUL
IN
INC
INT
INTO
IRET
JA
JAE
JB
JBE
JC
JCXZ
JE
JG
JGE
JL
JLE
JMP
JNA
JNAE
J

VARIABLE AREA FLOW
EFFECTS OF AREA CHANGES ON FLOW
Continuity
AV=constant
A
V
A+dA
V + dV
Then
AV= ( + d)( A + dA )(V + dV)
Since dP,d, dV and dA are all small, this equation becomes
1st order accuracy then above equation can be written as
Avd + VdA + Ad

FLOW IN TWO AND THREE
DIMENSIONS
FLOW IN TWO AND THREE DIMENSIONS
The analysis previously given for onedimensional flow are exactly correct only for
the flow through an infinitesimal stream tube.
For all real problems the assumption of onedimensionality f

Fanno Flow
Gas
Dynamics
1
Simple frictional flow ( Fanno Flow )
Adiabatic frictional flow in a constant-area duct
* The Flow of a compressible fluid in a duct is
Always accompanied by :-
Variation in the cross sectional area of the duct
Heat t

NORMAL SHOCK ANALYSIS
Normal shock process is an adiabatic and
irreversible process, therefore stagnation
temperature remains constant while stagnation
pressure decreases across the normal shock.
Continuity across the shock is
1V1= 2V2
(1)
Momentum equati

COMPRESSIBLE FLOW
All liquids are incompressible
Gases flowing with Mach No less than 0.3 are
also considered as Incompressible flow.
Gases flow in the range of Mach no 0.3 to0.99
is considered as subsonic compressible flow.
Gases flow with Mach No ab

OBLIQUE SHOCK WAVE
The process of oblique shock is adiabatic and
irreversible i.e stagnation temperature
remains constant across the oblique shock
while stagnation pressure deceases across the
shock. The oblique shock relations can be
deduced from normal

ADIABATIC FLOW IN A DUCT
WITH FRICTION (FANNO FLOW)
FLOW IN A CONSTANT AREA DUCT
Compressible adiabatic flow in a constant area duct
with frictional effects, is known as, Fannoflow.
Consider a momentum balance for small portion of
the duct.
p, v
v +dv, p

EXPANSION WAVES (PRANDTL
MEYER FLOW)
FLOW ON CONVEX CORNER
To determine the type of waves occur at the
convex corner in supersonic flow, let us
assume that these waves are oblique shock
waves.
M >1
L
N V
1
1
1
2
N2
L2
Now analyzing the flow we see that L1