{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Preliminary sizing of a rotor blade\n", "\n", "As previously mentioned we will use the work of Adkins and Liebeck to perform both optimisation and off design analysis. Let us start with the rotor blade optimisation.\n", "\n", "The method has been implemented in Python in the package called `tuduam`, i.e TU Delft Urban Air Mobility. Hence, when creating the input we have to keep in mind the [documentation](https://saullocastro.github.io/tuduam/) on what the functions expect. Feel free to roam around the documentation to see what other functionalities are offered by the package. Keep in mind however that the package is under active development.\n", "\n", "The design is initiated with the specified conditions of power (or thrust), hub and tip radius, rotational rate, freestream velocity, number of blades, and a finite number of stations at which blade geometry is to be determined. Let us define this in the next block\n", "\n", "## Defining the conditions\n", "\n", "Most of the code below does not need explaining, however as previously mentioned we must take into account the [API documentation](https://saullocastro.github.io/tuduam/) . Here it says that the blade parameter must be defined in the `Propeller` data structure. Furthermore, BEM analysis requires airfoil polar at a large range of reynolds numbers. `tuduam` relies on the user to input this data in the form of a path to a directory which contains all the polars. These files should be in the common format outputted by [xfoil](https://web.mit.edu/drela/Public/web/xfoil/). A tutorial on how to create this data has also been made which can be found in the course. Sample data for the NACA 4412 is readily available however in the `tuduam` repository. The NACA 4412 is shown in [Figure 1](#figure1)\n", "\n", "
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\n", "Figure 1: The NACA 4412 airfoil\n", "

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\n", "\n", "The conditions required for the optimisation are loaded into the Python kernel below. Carefully read the comments surrounding the code for more pointers. Note that the repository makes use of data structures in order to limit input size into functions, in this case we have to make use of the `Propeller` data structure." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: tuduam in c:\\users\\damie\\anaconda3\\envs\\tuduam_notebook\\lib\\site-packages (2024.15)\n", "Requirement already satisfied: numpy in c:\\users\\damie\\anaconda3\\envs\\tuduam_notebook\\lib\\site-packages (from tuduam) (1.26.4)\n", "Requirement already satisfied: scipy in c:\\users\\damie\\anaconda3\\envs\\tuduam_notebook\\lib\\site-packages (from tuduam) (1.12.0)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Cloning into 'tuduam'...\n" ] } ], "source": [ "!pip install tuduam\n", "!git clone https://github.com/saullocastro/tuduam.git\n", "# If the following error occurs \"fatal: destination path 'tuduam' already exists and is not an empty directory.\" please continue as your environment is already set up correctly" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
a_snd=335.62572904948746  \n",
       "rho_cr=1.0899402822825992  \n",
       "dyn_vis=1.7736932645281385e-05  \n",
       "prop_class=Propeller(n_blades=6.0, r_prop=0.55, rpm_cruise=1200.0, xi_0=0.1, chord_arr=None, rad_arr=None, \n",
       "pitch_arr=None, tc_ratio=0.12)\n",
       "
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       "       0.5401]),\n",
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power required = 4.05 Kw\n",
       "
\n" ], "text/plain": [ "power required = \u001b[1;36m4.05\u001b[0m Kw\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "# Initialise BEM class\n", "design = prop.BEM(data_path, prop_class, rho_cr, \n", " dyn_vis, v_cruise, n_stations, a_snd, T=thrust_req)\n", "\n", "# Execute the BEM optimisation with initial estimate of 0\n", "res_dict = design.optimise_blade(zeta_init=0)\n", "\n", "# Print the resulting dictionary \n", "rich.print(res_dict)\n", "rich.print(f'power required = {np.round(res_dict[\"pc\"]*rho_cr*(prop_class.rpm_cruise/60)**3*32*prop_class.r_prop**5/1e3,2)} Kw')\n", "\n", "# Plot the resulting blade geometry \n", "plot = prop.PlotBlade(prop_class, coord_path)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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interactive 3D plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Offdesign analysis\n", "\n", "We now have an optimised blade which is stored in the `Propeller` data structure and in the output of the function, i.e `res_dict`. We can do a quick test in order to check this. Run the following cell to see what the data structure now contains. As seen it now contains 3 extra arrays describing the propeller blade.\n", "\n", "We would now like to test whether it can meet a certain off design condition. If you want to know more about a specific step, please refer to the paper which is available on the course site. The general procedure for doing so is as follows:\n", "\n", "1. Specify a freestream velocity, RPM and $\\Delta \\beta$\n", "2. Make in initial estimate on the flow angle using $\\phi = \\frac{\\lambda}{\\xi}$ where $\\xi$ is the nondimensional spanwise location and $\\lambda= \\frac{V_{inf}}{\\omega*R} $\n", "3. Since $\\beta$ is known, compute $\\alpha = \\beta - \\phi$ and the Reynolds number at each station.\n", "4. The airfoil coefficients are then known from the airfoil section data.\n", "5. The new estimate for $\\phi$ can then be computed as in equation 1. Let a and $a`$ be the axial and rotational interference factor, r the local radius and V the freestream velocity. Note that a and $a`$ are clipped to -0.7 and 0.7 respectively. This is required for adequate convergence near the tip (Viterna and Janetzke (1981)). For more details please see Adkins and Liebeck (1984) on the course site.\n", "\n", "$$\n", "\\begin{equation}\n", "\\tag{1}\n", "\\tan \\phi = \\frac{V(1 + a)}{\\Omega r (1 - a`)}\n", "\\end{equation}\n", "$$\n", "6. Steps 1 to 5 are then repeated until convergence is reached.\n", "7. The thrust and torque per unit radius can then be found using:\n", "\n", "$$\n", "\\begin{align}\n", "\\tag{2}\n", "T` & = \\frac{1}{2} \\rho W^2 cB C_y \\\\ \n", "\\tag{3}\n", "Q`/r & = \\frac{1}{2} \\rho W^2 cB C_x \\\\\n", "\\end{align}\n", "$$\n", "\n", "8. Then finally the thrust and power coefficient are defined as folows. Where n is the revolutions per second.\n", "\n", "$$\n", "\\begin{align}\n", "\\tag{4}\n", "C_T & = \\frac{T}{\\rho n^2 D^4} \\\\\n", "\\tag{5}\n", "C_P & = \\frac{P}{\\rho n^3 D^5} \\\\\n", "\\end{align}\n", "$$\n", "\n", "Finally, this can then be integrated. In the source code this is done using a simple trapezoid integration, more specifically the `scipy.integrate.trapezoid` function. \n", "\n", "# Hover example\n", "\n", "Let's do an sample example of a vtol rising vertically to see how this would look like using the `tuduam` repository. The inflow from the freestream is now significantly reduced. The parameter that significantly changes is the freestream velocity, the only significant component left is the induced velocity caused by the rotor. Determining the value of the induced velocity is difficult, engineering judgement is used. [1] mentions an equation to estimate it however it is only reliable for higher flight speeds. Thus in our script we have assumed the freestream velocity to be 10 m/s.\n", "\n", "Furthermore it is important to consider how we should change our pitch control of the rotor. As seen in [Figure 2](#figure2), the resultant relative wind will lay nearly in parrallel to tip-path axis. Therefore if we would keep the same pitch as the one during cruise the blade will most surely stall. The implication in the code being an error that an angle of attack outside of the dataset has been encountered. \n", "\n", "

\n", " \n", "
\n", "

\n", "\n", "Therefore we would like to lower our pitch angle. To increase the thrust for hover we would like to increase our RPM. However keep in mind that our rpm is limited by the onset of shock waves at the tip of the blade. Thus we have to compute the maximum rpm and limit the rpm to that value. We will now analyse the propeller at a singular offdesign conditions. Namely a freestream velocity of 10 m/s, a maximum mach number of 0.7 at the tip and a 39 degree decrease in pitch on the rotor blades. Read and run the code below for the results.\n", "\n", "\n", "## Sources\n", "\n", "[1] Castles, W. Jr., & De Leeuw, J. H. (1954). The normal component of the induced velocity in the vicinity of a lifting rotor and some examples of its application (Report No. 1184). Georgia Institute of Technology.\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
rpm_hvr=4135.43320654644\n",
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{\n",
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       "    'eff': 0.3833096128070276,\n",
       "    'thrust_coeff': 0.5728390932248073,\n",
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       "       0.34950426, 0.34547205, 0.35195982, 0.33585566, 0.32746425,\n",
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       "    'lift_coeff': array([1.19482265, 1.35056012, 1.40478863, 1.1920388 , 1.19503635,\n",
       "       1.19855278, 1.55793305, 1.55460521, 1.58987287, 1.6089598 ,\n",
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The power required for a single rotor is 127.32957449453333 kW\n",
       "
\n" ], "text/plain": [ "The power required for a single rotor is \u001b[1;36m127.32957449453333\u001b[0m kW\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "# Define constants required for analysis\n", "mach_max = 0.7 # Point when shockwave occurs over the airfoil\n", "isa = tud.ISA(0) # Assume sea level\n", "rho = isa.density()\n", "dyn_vis = isa.viscosity_dyn()\n", "a_snd = isa.soundspeed()\n", "\n", "# Operations conditions\n", "vtip_max = mach_max*a_snd\n", "omega_max = vtip_max/prop_class.r_prop\n", "rpm_hvr = omega_max/(2*np.pi)*60 # Vertical speed of the vtol\n", "v_hvr = 10 # Vertical speed of the vtol plus additional \n", "delta_pitch = np.radians(-39)\n", "\n", "rich.print(f\"{rpm_hvr=}\")\n", "\n", "hover_cond = prop.OffDesignAnalysisBEM(data_path, prop_class, v_hvr, rpm_hvr, rho, dyn_vis, a_snd)\n", "res = hover_cond.analyse_propeller(delta_pitch, abs_extrapolation=7)\n", "\n", "power_req = res[\"power_coeff\"]*rho*(rpm_hvr/60)**3*32*prop_class.r_prop**5/1e3\n", "\n", "rich.print(res)\n", "rich.print(f\"The power required for a single rotor is {power_req} kW\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Finding the max thrust of a blade\n", "\n", " Let us now try a range of values for the both the change in pitch and rpm values to see if we can achieve better thrust values. We could opt to use `scipy.optimize` for this purpose however the analysis is prone to failure due to either to high AoA or a non-converging solution. This will complicate the optimisation where we'll have to assign penalization when such an error occurs. Instead we'll use a brute force method since the analysis is swift. We'll create a mesh where x will be the rpm and y the pitch. Then for each coordinate we'll compute the thrust, after which a surface plot can be created. This is implemented below, the cell takes about 30 seconds to run, so some patience is required. \n", "\n", "Feel free to play with the parameters!" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "type": "surface", "x": [ [ 2500, 2625.802554349726, 2751.605108699452, 2877.407663049178, 3003.2102173989047, 3129.0127717486307, 3254.8153260983568, 3380.617880448083, 3506.420434797809, 3632.2229891475354, 3758.0255434972614, 3883.8280978469875, 4009.6306521967135, 4135.43320654644 ], [ 2500, 2625.802554349726, 2751.605108699452, 2877.407663049178, 3003.2102173989047, 3129.0127717486307, 3254.8153260983568, 3380.617880448083, 3506.420434797809, 3632.2229891475354, 3758.0255434972614, 3883.8280978469875, 4009.6306521967135, 4135.43320654644 ], [ 2500, 2625.802554349726, 2751.605108699452, 2877.407663049178, 3003.2102173989047, 3129.0127717486307, 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"title": { "text": "Thrust plot 14 x 14 mesh " } } } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import plotly.graph_objects as go\n", "\n", "n = 14 # Mesh size\n", "\n", "pitch_arr = np.linspace(-20, -50, n)\n", "rpm_arr = np.linspace(2500,rpm_hvr, n)\n", "X,Y = np.meshgrid(rpm_arr,pitch_arr)\n", "Z_thrust = np.zeros(X.shape)\n", "Z_eff = np.zeros(X.shape)\n", "Z_power = np.zeros(X.shape)\n", "\n", "for col, rpm in enumerate(rpm_arr):\n", " hover_cond = prop.OffDesignAnalysisBEM(data_path, prop_class, v_hvr, rpm, rho, dyn_vis, a_snd)\n", "\n", " for row, dpitch in enumerate(np.radians(pitch_arr)):\n", " try:\n", " res = hover_cond.analyse_propeller(dpitch, abs_extrapolation=7)\n", " except ValueError:\n", " continue\n", " except RuntimeError as error:\n", " continue\n", "\n", " power_req = res[\"power_coeff\"]*rho*(rpm_hvr/60)**3*32*prop_class.r_prop**5/1e3\n", "\n", " Z_thrust[row,col] = res[\"thrust\"]\n", " Z_eff[row,col] = res[\"eff\"]*100\n", " Z_power[row,col] = power_req\n", "\n", "\n", "# Create the figure\n", "fig = go.Figure(data=[go.Surface(z=Z_thrust, x=X, y=Y)])\n", "fig.update_layout(\n", " scene=dict(\n", " xaxis_title='RPM',\n", " yaxis_title= 'Delta pitch [deg]',\n", " zaxis_title=f'Thrust [N]'))\n", "\n", "fig.update_layout(\n", " scene_camera=dict(\n", " eye=dict(x=1.8, y=1.8, z=1.8)))\n", "\n", "fig.update_layout(title=f'Thrust plot {n} x {n} mesh ', autosize=True,\n", " margin=dict(l=65, r=50, b=65, t=90))\n", "\n", "# Show the plot\n", "fig.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Iteration of the rotor design.\n", "\n", "So what happens if the maximum thrust we find is not sufficient? Remember when a thrust or power value was specified for which the rotor would be optimized? We can increase this value to increase the maximum thrust value, this however does come at a cost that the blade is less efficient at the cruise setting. With the updated geometry we can then perform the offdesign analysis again to find the newly acquired maximum thrust. This process is then repeated until the engineer is sufficiently happy with the margin on the maximum thrust and the design thrust of the propeller.\n", "\n", "The opportunity is given below to go through this process yourself with the code cell below where all of the relevant code has been appended. The mesh spacing has been increased to decrease computation time, however when nearing to your final design you can decrease the mesh spacing again. The design point is described in the first few lines of code. Sometimes the results are odd with the majority failing or having no solution at all. In this case it is advised to increase the radius of your propeller or change the amount of blades to reduce disk and/or blade loading." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "black" }, "mode": "lines", "showlegend": false, "type": "scatter3d", "x": [ 0.002286861458457408, 0.00288497995903235, 0.0034274452763790094, 0.00434541636138748, 0.005051905350128478, 0.005563608197570488, 0.005852698312099367, 0.005896914420423805, 0.005579384837764407, 0.005236964541781375, 0.004749845969404809, 0.004095767847343397, 0.003224642310691683, 0.0026889038125549173, 0.0020418589479615874, 0.0012222892153605815, 0.000656675436020888, -0.0007381707734202137, -0.0014971027549136415, -0.0017495907690296996, -0.001976300881120403, -0.0020416167618490877, -0.0020345835043810052, -0.001898079986342619, -0.001672531375138981, 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"automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Thrust plot 5 x 5 mesh " } } } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define operatonal parameters\n", "thrust_req = 350\n", "v_cruise = 210/3.6\n", "h_cruise = 1200\n", "isa = tud.ISA(h_cruise) \n", "a_snd = isa.soundspeed() # Speed of sound\n", "rho_cr = isa.density() # Air density\n", "dyn_vis = isa.viscosity_dyn() # Dynamic viscosity\n", "\n", "# Define the specified conditions for the propeller geometry in the data structure\n", "prop_class = tud.Propeller(\n", " n_blades=6, # Number of blades\n", " r_prop=0.525, # propeller radius\n", " rpm_cruise=1200, \n", " tc_ratio=0.12, # Thickness to chord ratio of airfoil\n", " xi_0=0.1 # nondimensional hub radius (r_hub/R)\n", " ) \n", "\n", "#---------------------------- Blade geometry optimization ---------------------------------\n", "# Initiazlie BEM class\n", "design = prop.BEM(data_path, prop_class, rho_cr, \n", " dyn_vis, v_cruise, n_stations, a_snd, T=thrust_req)\n", "\n", "# Execute the BEM optimisation with initial estimate of 0\n", "res_dict = design.optimise_blade(zeta_init=0)\n", "plot = prop.PlotBlade(prop_class, coord_path)\n", "plot.plot_3D_plotly() # Creates an interactive 3D plot\n", "\n", "#------------------- Off design analysis ---------------------------------------------------------\n", "n = 5 # Mesh size\n", "\n", "pitch_arr = np.linspace(-20, -50, n)\n", "rpm_arr = np.linspace(2500,rpm_hvr, n)\n", "X,Y = np.meshgrid(rpm_arr,pitch_arr)\n", "Z_thrust = np.zeros(X.shape)\n", "Z_eff = np.zeros(X.shape)\n", "Z_power = np.zeros(X.shape)\n", "\n", "for col, rpm in enumerate(rpm_arr):\n", " hover_cond = prop.OffDesignAnalysisBEM(data_path, prop_class, v_hvr, rpm, rho, dyn_vis, a_snd)\n", "\n", " for row, dpitch in enumerate(np.radians(pitch_arr)):\n", " try:\n", " res = hover_cond.analyse_propeller(dpitch, abs_extrapolation=7)\n", " except ValueError:\n", " continue\n", " except RuntimeError as error:\n", " continue\n", "\n", " power_req = res[\"power_coeff\"]*rho*(rpm_hvr/60)**3*32*prop_class.r_prop**5/1e3\n", "\n", " Z_thrust[row,col] = res[\"thrust\"]\n", " Z_eff[row,col] = res[\"eff\"]*100\n", " Z_power[row,col] = power_req\n", "\n", "\n", "# Create the figure\n", "fig = go.Figure(data=[go.Surface(z=Z_thrust, x=X, y=Y)])\n", "fig.update_layout(\n", " scene=dict(\n", " xaxis_title='RPM',\n", " yaxis_title= 'Delta pitch [deg]',\n", " zaxis_title=f'Thrust [N]'))\n", "\n", "fig.update_layout(\n", " scene_camera=dict(\n", " eye=dict(x=1.8, y=1.8, z=1.8)))\n", "\n", "fig.update_layout(title=f'Thrust plot {n} x {n} mesh ', autosize=True,\n", " margin=dict(l=65, r=50, b=65, t=90))\n", "\n", "# Show the plot\n", "fig.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "honours", "language": "python", "name": "python3" }, "language_info": { 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