The Thermodynamics of a Jet Engine Elliot TomsMechanical Engineering with RenewablesUniversity of Dundee Abstract” Jet engines (turbo Jet engines and Ramturbo jets) are complex machines that use compressed air and fuel to create thrust and enable flight for high powered passenger and military aircraft. Introduction Thermodynamic textbooks  will usually describe the Carnot cycle and other closed systems such as the Rankine, Brayton and Diesel cycles. Normally using a reversable transformation to calculate the peak performance in an ideal circumstance. The generic jet engine can be described as an assembly of multiple different machines that use fluids (I.
e. jet fuel) that will exchange the thermal energy with its surroundings. The purpose of this essay is to take a jet engine and show how the laws of thermodynamics apply to one of the 20th centuries most important technological advancements. The main components of the engine such as the compressor (and its compression ratio), the turbine and the creation of materials that need to with stand the extremely high pressures and temperatures associated with the burning of fuels.
Such as the Pratt and Whitney J58 (turboramjet) and its unique compressor bleed and bypass system to allow for higher thrust at speeds beyond MACH 2. These developments will also show how the parts are affected by the imposition of the constraints of the second law of thermodynamics. First, basic concepts of thermal efciencies, thrust and of overall propulsive force. That will help to measure the performance of a jet engine. Second, the thermal efficiencies related to the engine.Jet engine performanceAn aircraft, in order to fly must produce thrust. This in modern aircraft is done in one of two ways. Either but an internal combustion engine and a propeller which creates thrust or by the use of mixing air and fuel in a chamber and burning it thus creating high temperature exhaust gasses which when combined with a nozzle will product thrust. This thrust is equal to the difference in inlet v_i and the exhaust v_e velocities multiplied by the mass of airflow m. F=m(v_e-v_i)  (1)The engines performance is defined by reduced thrust F_r. This is where m describes the size of the engine and its weight. The speed of sound v_s and the force F as shown above. F_r=F/(mv_s )  (2)These then lead to the overall efficiency · which is defined the Force (F) multiplied by the intake velocity –(v—_s) divided by the mass (m) multiplied by the thermal energy per unit mass absorbed by air (q). ·=(Fv_i)/mq (3)v_i T_i v_e T_eThe equation of propulsive efficiency ·_p is the ratio of propulsive power to the rate of the production of kinetic energy. ·_p=(Fv_i)/(m”e_c ) (4)Where –”e—_c is the change in kinetic energy. ”e_c=1/2(v_e^2-v_i^2) (5)the jet engine process At 0 we start in free stream conditions. During flight the inlet allows for air to fill the engine passing through a diffuser. As the air passes through the diffuser the pressure increases as it decelerates slightly at point 2. From the diffuser the air then moves the compressor where the air is compressed at point 3. This air is then mixed with fuel in the combustion chamber. This mix of air and fuel is then burned at a constant pressure from points 3 to 4. The resulting high pressure and high temperature results in the expansion of gasses as it passes into the turbine. This produces enough power to drive the compressor. The gasses then expand to the ambient pressure in the nozzle and leave the engine at high velocity. This results in thrust that pushes the aircraft forward this then brings the flow back to free stream pressure from point 5 to point 8 this is done isentropically . This results in thrust that pushes the aircraft forward. It is normally assumed that the work done by the turbine is equal to the compressor work. All the process in the diffuser, compressor, turbine and nozzle are isentropic. the compressor and, ideally, the temperature change is the same. Figure 2: Ideal Brayton Cycle of a Jet engineIn order to analyze a jet engine, the same equation will be applied to the diffuser, compressor and the nozzle. q-w=€h-€e_c (6)h is the difference between the intake and the exit specific enthalpies, €e_c is still the difference in the kinetic energy per unit mass. In this equation w is the work per unit of mass performed by air. If the previous equation is applied and an assumption is made that the air is at a constant pressure at a specific heat (c_p), the increase in kinetic energy can be shown by €e_c-1/2(C_e^2-C_i^2)=q-€h=q-c_p (T_e-T_i) (7)This means that in the combustion chamber all of the thermal energy is given to the system in order to increase the kinetic energy of the air, resulting in higher thrust. The second law of thermodynamics states that converting all of the thermal energy into work is impossible. Only can the max production of work be obtained if all the processes are reversible. Efficiency Efficiency of a jet engine comes from many varying factors. The efficiency at low velocities, the engine must incorporate a compressor before the combustion chamber (see fig1). The work used to operate the compressor is generated by the turbine which is downstream. If we apply q-w=€h-€e_c to the compressor and the turbine and if energy losses are neglected, the work done on the rotating shafts is related to the temperature differences up and down from the compressor and turbine. w=c_p (T_4-T_3 )=-c_p (T_2-T_1) (8) Where T_1 is the temperature before the compressor and T_2is the temperature after, T_3is the temperature before the turbine and therefore T_4is the temperature after. Because the transformation undergone by air in the compressor and the turbine are adiabatic and reversible, we have,T_4=T_3 –(P_4/P_3 )—^(((1-і))/і), T_1=T_2 –(P_2/P_1 )—^(((1-і))/і) (9)the compression ratio r=P_2/P_1 depends on the type of the compressor the engine uses. Figure 3: Simple diagram of a jet engine with turbine and compressorCompression ratios (r) of a jet engine are the most important part of creating an efficient engine even though the engine is made of five main parts, the final thermal efficiency which is calculated by ·^th=–€e—_c/q=1-a/(1+µ) (10)Where µ is a dimensionless parameter given by. µ=(v_i^2)/(2c_p T_i ) (11)If r = 1 then the thermal efficiency of the jet engine would be very low as there is no compression and would then end with an efficiency rating close to that of a simple ramjet. Modern airliners such as the Boeing 747 Max 8 use a compression rating of r=30.5 the Airbus A30 has an r=40. As these are non-supersonic aircraft and have to adhere to regulations. If the aircraft were to operate at supersonic speeds the r would be lower such as with Concorde which r=15. This is due to the velocity of the air at cruising speed. The second process of efficiency is directly related to the Mach number. Each engine has to be specifically designed to be as efficient as possible when at cruising speed as this is where the most fuel is used. The results for the thermal efciency indicate the behavior of jet engines. Thermal efciency is a simple function of the velocity of the aircraft and the compression ratio of the compressor only. The thermal efciency remains the same regardless of the amount of thermal energy is used. According to these results, if the need to travel faster is there, more fuel (to increase the thermal energy). However, the temperature inside the jet engine will rise with the increase speed therefore the risk of failure of the turbine and compressor blades increase due to the temperature increase. Apart from the compression ratio (r), temperature at the inlet of the turbine T_3 which is the highest temperature reached by the air whilst it is inside the engine, is the second most important factor of the jet engine that needs to be considered. By using rst law of thermodynamics this temperature can be related to the amount of energy that is absorbed,T_q=q/(c_p T_i )=T_3/T_i -(1+µ)/a (12)T_q is another variable that needs to be introduced. Using µ the efficiency of propulsion can be related to ·^thand T_q.