The flow duration was approximately 4 seconds when the nitrous oxide was discharged from its tank at 750psi into the open air. Given the effective tank volume of about 1000 cm^3 and nitrous density of 1.228 g/cm^3 the flow rate was approximately 300 g/sec. Since the flow rate is proportional to the square root of the pressure drop, an operating pressure of 500psi inside the motor would produce:
Oxidizer Mass Flow Rate ~ 175 g/sec
Flow Duration ~ 7 sec
The initial core diameter of the fuel grain is approximately 1cm to begin and 3cm at the end. Averaging of the cross-sectional area using integration yields
Avg Port Area = .0003404 meters^2
Avg Port Radius = 1.04 cm
Provided with the oxidizer mass flow rate and average port area, the expected average oxidizer mass flux is found
Gox ~ 510 Kg/M^2
Given the regression equation for HTPB given by Chiaverini et al. 2001, regression rate can be found if HTPB were used as the fuel.dr/dt HTPB = .049 * Gox^0.61
dr/dt HTPB ~ 2.19 mm/sec
The fuel grain length is approximately 35 cm and the density is about 1g/cm yielding
Fuel Mass Flow Rate ~ 50 g/sec
O/F HTPB ~ 3.45
Provided with the regression rate equation for a polymer/paraffin combination of 50% given by Tsong-Sheng Lee et al. "Combustion Characteristics of a Paraffin-Based Fuel Hybrid Rocket"
dr/dt 50%Paraffin = .026 * Gox^0.8076
dr/dt 50%Paraffin ~ 4.00 mm/sec
Fuel Mass Flow Rate ~ 90 g/sec
O/F 50%Paraffin ~ 1.90
is there a method to your madness with your nozzle design?? or are you just trying to get the nitrous out fast
ReplyDeleteThanks for your comment JC, sorry I've been too busy writing the final papers to update the blog! Anyway, the injector nozzle does play a role in the internal ballistics of most hybrid rocket motors. By varying the injector geometry, the oxidizer flow field entering the fuel port may be varied greatly, influencing the formation and structure of the flame sheet and boundary layer. All known regression behavior is directly tied to the thermal and kinetic interactions between these formations and the fuel surface. For example, swirling injectors have demonstrated the greatest gains in burn rate. These injectors force the oxidizer flow closer to the fuel surface, compressing the boundary layer and bringing the flame sheet closer to the fuel surface. Moreover, the induced turbulence in the flow causes increased mixing and combustion efficiency. Obviously, the effects of the injector diminish with increasing port length as turbulence dissipates the initial flow kinetic energy.
ReplyDeleteAnyway, I decided to use a basic circular injector orifice due to simplicity over the injector shown here. Flow rate itself is governed by the pressure drop across the injector, injector area, and a dimensionless discharge coefficient associated with losses particular to the geometry of the orifice itself. Oxidizer mass injection in practical hybrid rockets is aimed at sustaining an oxidizer to fuel ratio optimal for combustion. In experimental motors such as this, the mass injection need not be optimal due to the existence of correction factors to the derived regression model.
-Sam