Pamraat Parmar

Paddled wheels in partially immersed configurations are one of the most common propulsion devices for small and/or low speed amphibious vehicles. The wake features of this wheels significantly impact their performance. Higher RPM leads to higher propulsive forces, however, for certain flow regimes, the rate of increment shows a drastic drop and increasing RPM may not be advantegeous.

Github Link: https://github.com/pamraat/port-paddle
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

The case is solved by assuming the wheel constructed of closely placed particles with immersed boundary conditions. From experiments, it is known after certain ratio (V*) of wheel tip to the water flow velocity, a minor increase in lift force requires significant increase in wheel speed. It is noticed that this happens after occurrence of a splash called Bow Splash ahead of wheel. Experiments show (figure below) that the bow splash occurs when a nondimensional number called Froude number (Fr) is greater than 0.85 and the V* less than 0.43. This study is aimed at simulating wakes of multiple cases around the transition region to bow splash using NGA2.

Multiple cases were simulated for comparison with the experiments, however, two cases are shown here. The following figure shows Fr=0.768 and V*=0.329.

The following figure shows Fr=1.92 and V*=1.644. Experiments noticed the bow shock and the same was predicted by NGA2.

Currently, high thrust rocket engines use pressure driven injectors due to degree of atomization required in combustion chamber. High thrust engines require very high chamber pressures upto the range of 250 bars. This leads to having pumping pressures of as high as ≈800 bars, which makes the plumbing systems extremely complicated. The pressure driven injectors utilize pressure energy to atomize, whereas, here, a system is proposed which uses rotational kinetic energy to produce turbulence. The advantage of such a system is that it is easier to produce very high rotational speeds than handling ultra-high pressures across the system.

Github Link: https://github.com/pamraat/port-rta
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

Conventional rotary atomizers in the sense that they rotate at very high speeds fluid undergo Rayleigh-Taylor instability in radial direction, and leaving a jet of fluid in radial direction. These jets undergo Rayleigh-Plateau instability to result in droplet breakup and result in atomized fluid. Here, it is proposed to induce significant turbulence before the fluid streak is formed due to Rayleigh-Taylor instability, thereby causing better atomization at much lower rotational speeds. This study is aimed at simulating Rayleigh-Taylor instability with inherent turbulence and thereby studying the performance of such atomizers.
The video above shows the Rayleigh-Taylor atomizer simulated for a particular set of inputs. The rotational velocity is not enough to creat Rayleigh-Plateau instability. Following are the experimental observations of different ratios of rotational speeds to flow rate.

This project was developed to demonstrate the real engine operation. The numbers used here are inspired by General Electric GE4 single-spool turbojet engine which was designed in late 1960s to power Boeing 2707 supersonic transport. The engine had afterburning capabilities and produced thrust of 220 kN (50,000 lbf) without afterburner and 290 kN (65,000 lbf). This project is a thermodynamic analysis based on aerothermodynamically generated turbomachinery maps. The results are of the similar order as GE4, but not exactly same as we do not have compressor and turbine maps generated through rig testing. The maps used here are generated using Blade Element Theory, which is an analytical approximation of compressor performance.

Github Link: https://github.com/pamraat/port-turbomachinery
Notes: To operate this code, you'll need a valid MATLAB license.

The following figure shows the flowchart of the solver.

The following figures show compressor and turbine map resulting from the solver. The black line describes the operating point of GE4 in cruise.

The study is about analyzing the aerodynamic effects of oscillations of a wing. A computer code is developed for simulating inviscid unsteady flow over thin wing using Vortex Lattice Method.

Github Link: https://github.com/pamraat/port-VLM
Notes: To operate this code, you'll need a valid MATLAB license.

wing planform is divided into panels. The leading segment of the vortex ring is placed on the panel's quarter chord line and the collocation point is at the center of the three-quarter chord line. The normal vector n is defined at this point, too, which falls at the center of the vortex ring. From the numerical point of view these vortex ring elements are stored in rectangular patches (arrays) with i, j indexing as shown by figure above The velocity at any point can be found out by superposition of induced velocity due to each j vortex ring
The result of this code on solving flow over wing is shown below. As can be noticed the starting vortex is causing the wake fold-up.

The lift prediction match the experimentally results very well, as shown in the following figure.

The study was done to gauge capabilities of NGA2 in handling the particle collisions among themselves and with the wall. Two particle diameters were defined, d1=0.01 𝑚, and d2=0.005 m. Particles were assigned the diameters alternately, and due to random positioning of all particles, a system of homogenously distributed particles throughout the space was obtained. Gravity in -Y was applied and simulation was ran so that particle bed can be formed.

Github Link: https://github.com/pamraat/port-partbed
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

For shaking, gravity flipping model is adopted. The gravity is inverted to +Y for time equal to value of parameter flipTime. The gravity is in +Y direction from t = 0 s, to t = flipTime. The gravity is flipped back to -Y direction at t = flipTime, and the duration is set such that the net displacement of particles is 0. However, the velocity of particle at the end of &Deltat is not 0. Thus, by the time particles are near the bottom wall, the particles have a velocity, which makes them bounce on the wall hard. This sets particles to motion in +Y despite gravity being -Y. In the simulation, time to flip gravity from +Y to -Y is set to 3xflipTime, so that particles have flipTime time to levitate while gravity pointing downwards, thus creating real scenario which cause granular convection. The plots for mean y position of both types of particles is shown in figure below.

there is large grouping of small particles on the top, while in rest of the locations small particles exist in smaller groups. The reasoning behind large grouping on top is assumed that small particles being lighter, are propelled much higher compared to large particles after impact on the lower wall, and when the flipping is turned off, all the levitating small particles settle later than large particles, thereby forming a large group on the top. This indicates that horizontal shaking of the particles might be a better choice, however NGA2 requires significant functionality addition to be able to that.

the Stokes number Stp of a particle p is critical in understanding how much a particle is affected by the changes in the carrier flow field. At low values of the Stokes number (i.e., the particle response time scale is short compared to the time scale over which the fluid changes), particles act as “tracers”, closely following the fluid pathlines. At high Stokes number (i.e., the particle response time scale is large compared to the flow time scale), particles act as “cannonballs” that are barely affected by the surrounding flow field. Moreover, it have been knownfor over two decades that resonance between the particles and the flow field can happen if the time scales become comparable, i.e., Stokes number ≈ 1, leading to a phenomenon called “preferential concentration”.

Github Link: https://github.com/pamraat/port-hit
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

Three cases were studied here. First case was with St = 0.57, simulation video shown above.

Second case was with St = 1.33, simulation video shown above.

Third case was with St = 8.1, simulation video shown above.
The comparison of each case with experiment is showed in the following three figure.

The effect of clustering is very prevalent in case I, slightly less in case II, almost nonexistent in case III, from experiment. These findings are correctly simulated by NGA2, as can be seen in the figures above. In simulations, due to dissipative nature of turbulence, the eddies die exponentially, which require us to add forcing term. This forcing term has to be tuned to match the turbulence of experiments which may rarely be exact.

The Stokes number Stp of a particle p is critical in understanding how much a particle is affected by the changes in the carrier flow field. At low values of the Stokes number (i.e., the particle response time scale is short compared to the time scale over which the fluid changes), particles act as “tracers”, closely following the fluid pathlines. At high Stokes number (i.e., the particle response time scale is large compared to the flow time scale), particles act as “cannonballs” that are barely affected by the surrounding flow field. Moreover, it have been knownfor over two decades that resonance between the particles and the flow field can happen if the time scales become comparable, i.e., Stokes number ≈ 1, leading to a phenomenon called “preferential concentration”.

Github Link: https://github.com/pamraat/port-martian
Notes: To operate this code, you'll a valid MATLAB license.

The code is capable to handle the following species:

The code uses NASA CEA to and equilibrium solution as well as to initiate the non-equilibrium solution. Thus, the kind of inputs has to be in realm of CEA. Though it covers most varieties of problems, it fails to cover equilibrium solution of pre-ionized air, i.e. we cannot input the ionized (or electron) species, but it does provide ionized species in output. Because of this limitation, the outputs of any previous run that has to be used in new run cannot be used.
Following picture shows pressure variation in a MOC based bell shape nozzle in martian atmosphere with inlet pressure being 52.5 bars and flow being viscous, non-equilibrium and reactive with ionization.

This is a 2nd order central differencing explicit solver for Vorticity Transport Equation (VTE). Upwind scheme is used for convection and artificial diffusion is provided.

Github Link: https://github.com/pamraat/port-cylinder
Notes: To operate this code, you'll a valid MATLAB license.

The following video shows the output of a viscid flow across a cylinder.

For the same case, following video shows vorticity evolution during the process.

This is a case study to gauge accuracy of NGA2 predictions on rising gas bubbles in a liquid. Because of their importance in a wide range of chemical transformation processes, rising bubbles have been extensively studied. Of particular interest is their terminal velocity (i.e., how fast a bubble rises once a steady-state is reached), their shape (how deformed/spherical is the bubble at steady-state), and their dynamics (how long does it take for the bubble to reach steady-state, does a steady solution even exist or does the bubble oscillate?)

Github Link: https://github.com/pamraat/port-bubble
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

Following figures show the comparison of simulation results and the experimental results from Bhaga and Weber. The Morton number (Mo) is attempted to be kept similar while Eötvos number (Eö) is always 116 in simulation. The shape of bubble is always less spherical (flatter) than expected. This may be because of the inverse viscosity averaging model, which undermines the viscosity in interface region, and thus reduces the Mo. Due to reduce Mo, the bubble may be appearing flatter than in real.

This is a case study to gauge accuracy of NGA2 predictions on Rayleigh-Taylor Instability. The Rayleigh-Taylor instability is a fundamental process by which a heavy layer of fluid on top of a light layer of fluid destabilizes under gravity, leading to rapid collapse of the layers and the formation of a heavy jet moving downward surrounded by light “bubbles” moving upward. Ofparticular interest is the relation between the lengthscale over which the layer is initially perturbed, and the corresponding growth rate of the instability.

Github Link: https://github.com/pamraat/port-mprt
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

For the given configuration, critical wavenumber corresponds to the wavelength of 17 mm. Following is the videos of wavelength of 14 mm. As expected, it is stable, and the instability causes oscillations about the mean surface.

Following is the videos of wavelength of 17 mm. As expected, it is neutrally stable. The disturbance does not grow.

Following is the videos of wavelength of 20 mm. As expected, it is unstable. The disturbance grows. exponentially.

The comparison of growth rate prediction of NGA2 and the theoretical prediction is shown below. As can be seen, the growth rate is matching very closely to the inviscid exact equation. However, the deviation can be seen towards the lower k (which corresponds to higher domain size in x-direction). Since the number of elements are kept same in x-direction, the elements are skewed for lower wavenumbers, which might be the source of deviation since NGA2 gives best result for such simulations when the cels are almost cubic.

A nonlinear dynamic analysis is conducted on a hydraulic valve. The valve being analyzed is shown in the figure below.

Valve is governed by the 3rd order nonlinear ordinary differential equation. Valve position (X) normalized by maximum valve opening distance is used as the independent variable. Depending on the initial set position of the valve, the response of valve varied. It was observed, that for all X < 2, the response was stable, as shown the next figure. The figure after that represent the phase portrait of the system.

For X > 2, the response was oscillating motion of the valve piston, and the phase portrait was converging to a limit cycle, as can be seen in next two figures.

Next, a factor of leak in the valve is introduced, and the system responds with chaotic behavior.

The algorithm written includes Roulette Wheel Selection for crossover and Muhlenbein's Method for mutation. The optimum values of parameters were obtained by observing trend of convergence. Elitisim was later added and convergence time reduce to about 1/8th.

Github Link: https://github.com/pamraat/port-gas
Notes: To operate this code, you'll need to install NGA2 and operate on 'develop' git branch, which can be downloaded from here.

The optimized parameters are as follows:

1. Population number=20
2. Crossover probability=0.8
3. Mutation Probability=0.05
4. Crossover weight=0.3

Following is the performance without elitism.

Following is the performace with elitism. Notice that the actual convergence is very fast, and at least one particle remains at the global optima despite other particles being thrown away due to mutation.