Assignment 1

One-dimensional Compressible Flow with Heat Addition and Friction





Introduction




In this exercise, you will investigate one-dimensional flows using the 1D solver available in CFLOW. In total five problems should be solved of which two deals with 1D flow with heat addition and three deals with 1D flow with friction.



OBS Read chapters 1-3 in the course book before starting with the exercise!

When you have done the assignment, you should write a short report and hand in for assessment of this course element (instructions at the bottom of this page).


The following tasks should be solved both analytically and numerically. Note that in order to be able to apply the correct boundary conditions in the numerical simulations, you will need to solve the problems analytically first!





Task 1 - 1D flow with heat addition


Task 1a - subsonic flow with heat addition

Heat is added to an air flow through a 0.3 m diameter pipe. The inlet Mach number is \(M_1\)=0.2 and at the inlet plane the air temperature is \(T_1\)=293.0 K and the pressure is \(P_1\)=1.0 bar (1.e5 Pa). Set up the CFLOW Q1D solver for heat addition simulation with a heat addition corresponding to 90% of the heat needed to get thermal choking \((q=0.9 q^\ast)\).

Remember to export the solver state to a JSON-file when you are done with the task.




Task 1b - supersonic flow with heat addition

Same as Task 1a but with supersonic inlet flow

Heat is added to an air flow through a 0.3 m diameter pipe. The inlet Mach number is \(M_1\)=2.0 and at the inlet plane the air temperature is \(T_1\)=293.0 K and the pressure is \(P_1\)=1.0 bar (1.e5 Pa). Set up the CFLOW Q1D solver for heat addition simulation with a heat addition corresponding to 90% of the heat needed to get thermal choking \((q=0.9 q^\ast)\).

Remember to export the solver state to a JSON-file when you are done with the task.







Task 2 - 1D flow with friction


Task 2a - subsonic flow with friction

Air flows through a 0.3 m diameter pipe with the average friction factor \(\bar{f}=0.005\). The inlet Mach number is \(M_1\)=0.2 and at the inlet plane the air temperature is \(T_1\)=293.0 K and the pressure is \(P_1\)=1.0 bar (1.e5 Pa). Set up the CFLOW Q1D solver for simulation of flow with friction simulation with a pipe length corresponding to 80% of the length needed to get friction choking \(L=0.8L^\ast\).

Remember to export the solver state to a JSON-file when you are done with the task.




Task 2b - supersonic flow with friction

Same as Task 2a but with supersonic inlet flow

Air flows through a 0.3 m diameter pipe with the average friction factor \(\bar{f}=0.005\). The inlet Mach number is \(M_1\)=2.0 and at the inlet plane the air temperature is \(T_1\)=293.0 K and the pressure is \(P_1\)=1.0 bar (1.e5 Pa). Set up the CFLOW Q1D solver for simulation of flow with friction simulation with a pipe length corresponding to 80% of the length needed to get friction choking \(L=0.8L^\ast\).

Remember to export the solver state to a JSON-file when you are done with the task.




Task 2c - supersonic friction choking

Same as Task 2b but with friction choking

Air flows through a 0.3 m diameter pipe with the average friction factor \(\bar{f}=0.005\). The inlet Mach number is \(M_1\)=2.0 and at the inlet plane the air temperature is \(T_1\)=293.0 K and the pressure is \(P_1\)=1.0 bar (1.e5 Pa). Set up the CFLOW Q1D solver for simulation of flow with friction simulation with a pipe length corresponding to 150% of the length needed to get friction choking \(L=1.5L^\ast\).

Remember to export the solver state to a JSON-file when you are done with the task.







Assignment Report




In order to complete the assignment, a report should be written and handed in for assessment. A suggested report structure is given below.



When done, submit the report along with the exported JSON-files in Canvas