Pressure, mach number and temperature changes through normal shock waves. This program solves the prandtl meyer expansion wave problem by using the maccormacks predictorcorrector technique, as described in the book computational fluid dynamics. Hall published a paper in the aeronautical journal in which he described an rational polynomial function that approximated the inverse prandtlmeyer function with accuracy sucient for most engineering purposes. The physical interpretation of the prandtlmeyer function is that it is the angle through which you must expand a sonic m1 flow to obtain a given mach number. The following matlab project contains the source code and matlab examples used for prandtl meyer expansion wave solver. Envisioned with a wingspan of two feet and weighing less than three pounds, the aircraft would be able to.
The fan consists of an infinite number of mach waves, diverging from a sharp corner. If necessary, use the vertical or horizontal scrollbar in the new window to view more of the material or you can resize the window. The maximum angle through which a sonic m 1 flow can be turned around a convex corner is calculated for m for an ideal gas, it is expressed as follows. Find the mach number and pressure of the flow downstream of the corner. The amount of the increase depends on the incoming mach number and the angle of the expansion. Isentropic expansion calculations this form calculates properties of a supersonic flow through an expansion angle. Expansion happens due to changes in the direction of the flow. M1mach number of stream flow m2mach number of flow after passing through normal shock wave nuprandtlmeyer angle, deg, for expanding flow. Mod01 lec23 oblique shock waves prandtl meyer waves duration. Functions in the toolbox can be used together to solve more complex compressible flow. Previously, we examined 1 supersonic flow over sharp.
In prandtl meyer angle input mode, mach outputs are the same size as the array input or array inputs. Mod01 lec40 introduction to expansion wave and prandtl. The solution technique is to consider that the flow originated at mach 1 where the prandtlmeyer angle. Build nasas prandtl flying wing the aircraft features a new method for determining the shape of the wing with a twist that could lead to an 11percent reduction in drag. Calculates the prandtlmeyer function for supersonic flows. Horizontal velocity field in the prandtl meyer expansion wave simulation done for linkopings course on cfd. Pdf numerical formulation for flow computation in 2d supersonic. Matlab code for the numerical solution of a prandtlmeyer expansion wave flow field. This is a steady, inviscid expansion case commonly used for validation. Prandtlmeyer flow article about prandtlmeyer flow by. Numerical investigation of homogeneous condensation in. Prandtl meyer expansion wave solver in matlab download. Prandtl meyer expansion wave solver in matlab download free. This program solves the prandtlmeyer expansion wave problem by using the maccormacks predictorcorrector technique, as described in the book computational fluid dynamics.
The centered wave, more often called a prandtlmeyer expansion fan, is the counterpart, for convex corner, of. The expansion fan is bounded downstream by another mach wave which makes the angle x2 with respect to the downstream flow, where fi2 arcsinlm2. It is based on method developed by im hall in 1975. Solution difficult to obtain by prandtl stress function 3 1 2 2 max 2 2 2 2 k g b h t k b h t. Each function has an mtype argument that lets you specify the inputs for the flow. Matlab code for the numerical solution of a prandtlmeyer.
The concept may also lead to significantly enhanced controllability that could eliminate the. Just as we saw with shock waves, if we apply conservation of mass and momentum across a single wave, the tangential velocity is unchanged. A supersonic expansion fan, technically known as prandtlmeyer expansion fan, a twodimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. Prandtlmeyer expansion wave solver file exchange matlab.
If youve ever taken a gas dynamics compressible flow course, youve probably spent hours flipping through the tables at the back of the book to find the correct prandtlmeyer pm angle for your mach number, or vice versa. Prandtl meyer 18 ae3450 school of aerospace engineering copyright 2001 by jerry m. Equations translated from t e x by t t m,version 3. Prandtlmeyer tables staff posted on october 20, 2006 prandtlmeyer tables. M is a script file not a function, with an input section, giving as output a number of variables useful for a predesign of a wing. Prandtlm work on the prandtld led to a concept for a mars airplane. The prandtlmeyer angle is the angle change required for a.
The prandtl meyer angle is the angle change required for a mach 1 flow to achieve a given mach number after expansion. You can also download your own copy of the program to run offline by clicking on this button. The value of the prandtlmeyer function is therefore called the prandtlmeyer angle. How do you compute the inverse of the prandtl meyer function. Mod01 lec40 introduction to expansion wave and prandtl meyer flow. But avoid asking for help, clarification, or responding to other answers. In prandtlmeyer angle input mode, mach outputs are the same size as the array input or array inputs. This supersonic expansion is named after ludwig prandtl and his student theodor meyer because they were the first ones to work out a theory for a centered expansion wave. Fluid dynamics projects and source code download fluid.
When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at. Chenzhangzhu 8, but also l1stable with respect to steady small perturbation of both the ramp slope and the incoming steady upstream. Prandtlmeyer angle and mach angle for expanding flows. Calculate flow relations for fanno lines, isentropic, normal shock, prandtlmeyer functions, and rayleigh lines. When possible, these functions assume perfect gas environments. Calculate prandtlmeyer functions for expansion waves matlab. Prandtls lifting line introduction mit opencourseware. Mod01 lec23 oblique shock waves prandtl meyer waves.
Computing the inverse of the prandtlmeyer function. Calculate prandtlmeyer functions for expansion waves. Torsional parameters for rectangular cross sections bh 1 1. This documentation analyzes centerline pressure values at the expansion fan as well as mach contours. The user should note that the scope of this guide is limited to documenting the individual functions and providing instruction in using them to solve simple compressible flow examples. Prandtlmeyer expansion georgia tech fixed wing design. If the preliminary research aerodynamic design to land on mars, or prandtlm aircraft, is successful, it could collect and transmit valuable information back to earth. Thanks for contributing an answer to mathematica stack exchange. The required input is the mach number of the upstream flow and the expansion angle theta. To view the lecture material accompanying this lecture in a new window, please click the button below. The prandtlmeyer function is denoted by the greek letter nu on the. Direct mach number to angle and inverse angle to mach number tables are given on page 91, for a range of mach number from i to 5, for intervals of 0. A twodimensional, supersonic fluid flow in which an initially uniform flow passes a sharp, convex corner in a boundary, resulting in expansion of the fluid explanation of prandtlmeyer flow. Now analyzing the flow we see that l 1 l 2 for oblique shock wave.
Order your copy of public domain computer programs for the aeronautical engineer. Matlab code for the numerical solution of a prandtlmeyer expansion. Expansion waves prandtl meyer flow shock wave mach. User guide for compressible flow toolbox ntrs nasa. The physical interpretation of the prandtl meyer function is that it is the angle through which you must expand a sonic m1 flow to obtain a given mach number. A graphic showing the physics of the prandtlmeyer angle. Invprandtlmeyerv file exchange matlab central mathworks. The value of the prandtl meyer function is therefore called the prandtl meyer angle. Flow on convex corner to determine the type of waves occur at the convex corner in supersonic flow, let us assume that these waves are oblique shock waves. Multiple shock waves are observed in the numerical schlieren image, which are caused by a sequence of quenching by the condensation shock and rebuilding by the prandtlmeyer expansion of the condensation.
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