Freepower Turbines
Following on from our example with 1.41 lb/sec having a 1.44 Pressure Ratio
available in the jetpipe at 918 deg K. Firstly we find the square root of 1.44 so as to
get an equal division of pressure drop across the scroll and within the turbine to
maximise results by minimising losses. Square root 1.44 = 1.2 pressure ratio across
each , now some more maths :-))
Punch 1.2 into your trusty calculator, hit Yx key then 0.248 for 1.046 , divide our 918
deg K by the 1.046 to give 877 deg K, take 877 from 918 to give us a 41 C degs drop
at 100%, multiply by 0.9 to give 37 deg drop at 90% , multiply 37 by 64.4 ( twice
gravity) and by 1400 ( a constant) and by 0.276 ( Cp of hot gases at about our temps)
for 920714 , square rooting this will give 960 our velocity in ft/sec of the gases going
into the turbine at 881 deg K (918 minus 35), with density of, 881 x 96 (constant) div
by 1.2 ( PR) div by 14.7 div by 144 to give 33.3 cu ft/lb ,so 33.3 multiplied by
1.41lbs/sec will give 47 cu ft/sec going into the turbine.
Pressure ratio thru turbine is 1.2 again , Yx key ,0.248 =1.046, div into only 881 K
this time gives 842 or a 39 deg drop at 100% so by 0.9 for a 35 deg drop at 90% , a
more realistic figure . 35 by 64.4 by 1400 by 0.276 = 870945 , square rooting gives
933 ft/sec velocity out thru the turbines exducer at a temp of 846 degs Kelvin at a
density of , 846 X 96 div by 14.7 ( atmosp pres ) div by 144 =38.4 cuft/lb , multiply
by our 1.41 lbs/sec to give 54.2 cuft/sec .
As most turbine exducer tip angles are around 30 deg we'll use that angle as the outlet
angle of all the gases across the outlet annulus with the gases travelling at our
calculated 933 ft/sec , to find the axial velocity in the outlet annulus rather than the
933 at 30 degs we multiply the Sine of 30 degrees by the 933 , Sin 30 = 0.5 X
933ft/sec = 466 ft/sec . Now those 54.2 cu ft/sec of exhaust gases have to get thru our
unknown area of turbine exducer annulus at an axial velocity of 466 ft/sec ,we simply
divide our 54.2 by 466 to give us 0.116 sq ft , X 144 to give us 16.75 sq inches , add
on maybe 1.25 sq ins for the hub for a round figure of 18 sq inches for the whole
turbine outlet area ,18 div by Pi ( 3.14) will give us 5.73, square root this for our
required radius of 2.393, X 2 = 4.787 inches for the diameter of our freepower
turbines exducer.
Inlet conditions to the turbine will depend on the turbine tip height as well as its dia ,
and can be influenced by the scrolls A/R or by inlet guide vane angles to give the
correct flow rates for the mass flow and density thru any area. This example could
produce approx 55 HP at 40,000 rpm , but would require a redux box with a ratio of
anything from 3 to 6 :1 for kart use , or the freepower could make near 30 HP if run
with a direct chain drive at around 15,000rpm of the turbine , but care would need to
be taken not to overspeed the chain drive as the turbine is capable of spinning way
past the chains destruction point , all the while making more power as the rpm
increased.
If one wished to construct their own axial freepower stage for this example, firstly
they need to find a solid section of heavy walled tubing for the burst shield/ NGV
housing . For this purpose, let's settle on using a short section of '6 inch' Schedule 40
316 stainless (OD ~168.40mm, ID ~ 154.18mm, giving a ~7.11mm wall thickness) as
the "outer body/containment ring" for a DIY axial turbine. This ideally would
require/produce a turbine of 153.18 mm OD (1mm diametrical clearance or 0.5mm
radial clearance ). Pipe construction may not be perfectly round, so for 'safety' we
could go a bit smaller, say a round figure of 6" ( 152.4mm ) giving us a 1.78mm
diametrical clearance or 0.89mm radial clearance.
For simplicity lets assume a 6 inch OD annulus for the Nozzle Guide Vanes (NGVs )
and turbine to run in at 15,000 rpm, also a 30 degree NGV angle. 'Left" or "Right"
hand directional orientation of the NGV "tail" and turbine blade "tail" will depend on
rotational requirements in the transmission so that the road wheel/s turn in the
correct direction.
Sine of 30 degrees is 0.5 and as we have 960 ft/sec velocity issuing from the NGVs ,
their "axial velocity" will be only, 960 X 0.5 =480 ft/sec , and with a density of 33.3
cuft/lb , that’s 47 cu ft /sec going thru the annulus in an axial direction at 480 ft/sec,
this will require 0.0979 sq ft or ~14.1 sq inches , we need to add on at least a couple
more square inches for the NGV blade thickness and boundary layers etc ,so lets settle
on ~17 sq inches .
This would require NGV blades of 1.125 inches in height if using a 30 degree angle
This will produce a gas approach angle of 45 degrees to the moving turbine blade
doing 15,000rpm , this is the inlet angle for the turbine blade.
Because the gases exiting the turbine will be travelling slower and at a reduced
density to those exiting the NGVs , either the turbine exit angle needs to be greater or
the blade length increased so as to produce a larger flow area for the gases.
Lets make the turbine blades 1.25 inches long , only an eighth of an inch longer , but
it'll make all the difference :-))
With 1.25 inch long blades, the mean blade diameter will be , 6 minus 1.25 = 4.75
inches , this will give us a mean blade velocity of 310 ft/sec at 15,000rpm (415 ft/sec
if one wanted to push the rpm to 20,000, about the upper limit of karting
sprocket/racing chain ).
The annulus area is now 6 "OD and 3.5 "ID for 18.6 sq ins or 0.129 sq ft , with some
54.2 cu ft/sec going thru it at an axial velocity of ~420 ft/sec . With allowances made
for blade thickness , an exducer blade angle of 30 degrees can be used on the
freepower , just to keep things simple.
At 15,000 rpm, the velocity triangles , using the angles and gas velocities above ,
produce ~1300 ft of gas deflection, along with our 310ft/sec mean blade velocity and
1.4 lbs/sec mass flow , when divided by gravity at 32.2 and 550 ft lbs/hp, produce a
figure of 31.8 bhp (1300 X 310 X 1.4 div 32.2 div 550 ).
At 20,000 rpm with ~1200 ft of deflection and 415 ft/sec blade speed its 39.3 bhp.
If the DIY turbine was strong enough and its output was put thru a gearbox prior to
the final chain drive , then .....
At 30,000 rpm with ~1,000 ft of deflection and 620 ft/sec blade velocity it'd be 49
bhp.
And at 40,000 rpm (the maximum rpm befor power starts to drop off) and with ~800
ft of deflection and 830 ft/sec blade velocity the horsepower would be 52.5 bhp.
With a little larger axial annulus for the stage and with shallower angles for the NGV
and exducer , there could be some small gain in horsepower outputs , maybe ~10%
max .
It would be possible to modify this "6 inch" freepower stage to suit a DIY engine with
a smaller mass flow by tightening up the NGV and exducer angles to ~25 degrees
rather than the 30 degrees in the example or simply to shorten the height of NGV and
length of turbine blade by roughly the percentage difference of the mass flows .
Considering the huge range of possible outputs from similar mass flowing DIY gas
producers due to differing construction and running parameters , one really needs to
check the mass flow and thermodynamic outputs of their gas producer when in "pure
jet" form, prior to starting work on construction of a freepower turbine stage .
If an upper limit of 15,000 rpm is used for the homemade turbine and along with max
temps of 600 deg C , there shouldn't be problems constructing the turbine disc from
high tensile steel with turbine blades cut from segments of stainless tubing (possibly
1-1.25inch dia tubing with 2-3 mm wall thickness ) and welded to the disc . Ordinary
ball races in the 16-20mm ID range will happily cope with the rpm especially if
supplied with occassional drips of bleed oil and some bleed air for cooling , with this
oil/air mix going thru both freepower shaft bearings before exiting against the
freepower disc and then out the exhaust .With reasonable constructional care, the
balance of the finished turbine should be good enough for these "low" 15,000 rpm .