CoA. Memoranda: Aero (1964-1968)https://reports.aerade.cranfield.ac.uk/handle/1826.2/43142023-09-30T00:46:51Z2023-09-30T00:46:51ZEffect of engine, tank and propellant specific cost on single stage recoverable booster economicshttps://reports.aerade.cranfield.ac.uk/handle/1826.2/43192022-05-09T10:00:15ZEffect of engine, tank and propellant specific cost on single stage recoverable booster economics
Reusable first stages using hydrogen-oxygen, hydrogen-fluorine
and kerosine-oxygen are compared with non-reusable stages using a solid
in addition to the liquid combinations. The criterion used for comparison
is the minimum specific cost of the "loaded and ready for launch"
stage cost per unit of stage payload mass. A closed form relationship
is used in which the empty stage mass without payload is taken to scale
in part proportional to propellant mass, and in part to mass flow rate.
The stage specific cost is proportional to specific cost of engine (or
nozzle) tank and propellant. In the second part the hydrogen-oxygen
combination is consiaered,in more detail. The sensitivity of the
results to changes in various specific costs including that of refurbishing
are described.
Throughout, the stage velocity increments are compared in the
3000-6000 metres/second range with losses.
Non-equilibrium flow in plane expansion waveshttps://reports.aerade.cranfield.ac.uk/handle/1826.2/43212022-05-09T10:00:15ZNon-equilibrium flow in plane expansion waves
The non-equilibrium supersonic flow of a relaxing or reacting
gas through a plane expansion has been studied from a numerical,,
analytical and experimental point of view.
The flow of an ideal dissociating gas in a two dimensional
expansion has been solved numerically by writing the governing
equations of motion in their characteristic form.
In conflict with linearised theory along the wall, the
numerical solutions do not asymptote to the infinite rate equilibrium
values. To estimate how far the asymptotic state deviates from the
infinite rate equilibrium values, a formal second order solution has
been developed with the aid of transform techniques. An example has
been discussed for a simplified relaxing gas model, and estimates of
the asymptotic state have been obtained. An exact solution over the
whole field was not possible but by treating the parameter
as small, an approximate answer has been found.
To understand in more detail the coupling effects of two
relaxation processes, linearised theory has been extended to cope
with the flow of a gas with more than one relaxing mode. An example
has been discussed far Carbon Dioxide and the effect of possible
coupling between the bending and stretching modes of the molecule
in a plane expansion has been investigated.
The Mach-Zehnder interferometer and Schlieren method have
been used in conjunction with a 2" - diameter shock tube to study the
density and density gradients within, and following a sharp two-dimensional
expansion for shock heated Carbon Dioxide. Measurement
of the density gradient at the leading edge of the expansion by
quantitative Schlieren methods have allowed relaxation times to be
obtained. This method has the advantage that relaxation times can
be obtained for specific values of the density and temperature for
only small departures from an equilibrium state.
Boundary layers with suction or injectionhttps://reports.aerade.cranfield.ac.uk/handle/1826.2/43222022-05-09T10:00:15ZBoundary layers with suction or injection
Approximate integral equations are derived for the
compressible laminar boundary layer with arbitrary pressure
gradient and arbitrary suction or injection velocity through a
porous wall, Reasonable agreement is obtained when particular
solutions to the integral equations are compared with solutions
by previous authors.
Experiments in an incompressible turbulent boundary
layer over a porous surface reveal two laws for the inner and
cuter regions; laws which correlate previous experimental results.
The lams are used to calculate shear distributions and variations
of skin friction with Reynolds number and enable Preston tubes to
be used to estimate skin friction over a porous surface.
The outer region theory is extended to boundary layers
in small pressure gradients and at separation. The only universal
functions required are obtained from zero pressure gradient flow.
No other constants are used to calculate the mean velocity profiles
for boundary layers in small pressure gradients, with suction or
injection and at separation or reattachment. The theory agrees
with the available experimental results for turbulent boundary
layers in energy equilibrium.
Experiments in folly developed pipe flow show haw the
mean flow is altered when there is suction through a porous
section of the pipe. An approximate theory for the inner region
compares reasonably well with the experiments for small suction
velocities.
Optimum structureshttps://reports.aerade.cranfield.ac.uk/handle/1826.2/43202022-05-09T10:00:15ZOptimum structures
The design of the best structure for a given purpose
depends upon the criterion used for optimisation. Structures
may be designed to safely transmit a given system of forces using
the least weight of material.. They may also be designed to have
maximum stiffness of a certain type for a given weight or
alternatively to have the greatest possible fundamental
frequency of vibration. These problems, although in general
distinct from one another, are closely related and much can be
achieved towards maximisation of stiffness and frequency by the
use of minimum weight designs. In fact it can be shown that a
minimum weight framework is the stiffest structure of that weight
for the force system, which it is designed to carry.x
The present report is concerned exclusively with the problem of
the design of structures of minimum weight, which are required
to transmit specified forces. Some attention will be given to
frameworks because, in particular, methods of approximate
numerical analysis are more readily formulated for this type of
structure, but the main emphasis will be placed upon the design
of structures formed from plates of variable thickness reinforced
by direct load carrying members.
See para,l.4