Adiabatic stagnation

The temperature T0 corresponding to zero velocity is known as the adiabatic stagnation temperature it is the temperature that the flowing gas would attain if it were brought to rest adiabatically without doing any shaft work. It is sometimes called the total temperature. The temperature difference is small for air flowing at a speed of 100 m/s, T0 - T = 5 K. 

Total Pressure is the pressure that would occur if the fluid were brought to rest in a reversible adiabatic process. Many texts and engineers use the words total and stagnation to describe the flow characteristics interchangeably. To be accurate, the stagnation pressure is the pressure that would occur if the fluid were brought to rest adia-baticaUy or diabatically. 

Total temperature is the temperature that would occur when the fluid is brought to rest in a reversible adiabatic manner. Just like its co mie p2L totalpressure, total eMd stagnation temperatures are used interchangeably by many test engineers. 

Two-dimensional compressible momentum and energy equations were solved by Asako and Toriyama (2005) to obtain the heat transfer characteristics of gaseous flows in parallel-plate micro-channels. The problem is modeled as a parallel-plate channel, as shown in Fig. 4.19, with a chamber at the stagnation temperature Tstg and the stagnation pressure T stg attached to its upstream section. The flow is assumed to be steady, two-dimensional, and laminar. The fluid is assumed to be an ideal gas. The computations were performed to obtain the adiabatic wall temperature and also to obtain the total temperature of channels with the isothermal walls. The governing equations can be expressed as... 

A homogeneous flow basis must be used when thermodynamic equilibrium is assumed. For furtl er simplification it is assumed there will be no reaction occurring in the pipeline. The vapor and liquid contents of the reactor are assumed to be a homogeneous mass as they enter the vent line. The model assumes adiabatic conditions in the vent line and maintains constant stagnation enthalpy for the energy balance. 

Equation (4.4), which connects the known variables, unbumed gas pressure, temperature, and density, is not an independent equation. In the coordinate system chosen, //, is (lie velocity fed into the wave and u2 is the velocity coming out of the wave. In the laboratory coordinate system, the velocity ahead of the wave is zero, the wave velocity is uh and (u — u2) is the velocity of the burned gases with respect to the tube. The unknowns in the system are U, u2, P2, T2, and p2. The chemical energy release is q, and the stagnation adiabatic combustion temperature is T, for n-> = 0. The symbols follow the normal convention. 

After the bifurcation behavior is examined, the role of flame-wall thermal interactions in NOj is studied. First, adiabatic operation is considered. Next, the roles of wall quenching and heat exchange in emissions are discussed. Two parameters are studied the inlet fuel composition and the hydrod3mamic strain rate. Results for the stagnation microreactor are contrasted with the PSR to understand the difference between laminar and turbulent flows. 

The adiabatic surface temperature (for stagnation flow) and the adiabatic PSR temperature are shown in Fig. 26.4a as a function of the inlet fuel composition. The residence time in the PSR is simply taken as the inverse of the hydrodynamic strain rate. In both cases, the adiabatic temperature exhibits a maximum near the stoichiometric composition. The limits of the adiabatic operation are 8% and 70% inlet H2 in air for the stagnation reactor. For a PSR, the corresponding limits are 12% and 77% inlet H2 in air. Beyond these compositions, the heat generated from the chemical reactions is not sufficient to sustain combustion. 

Figure 26.4 Surface temperature and surface fuel mole fraction (a), and NO (6) as functions of inlet composition, along the adiabatic curve, for the stagnation reactor (solid curves) and the PSR (dashed curves). The fuel-lean and fuel-rich regions are indicated. The conditions are pressure of 1 atm, inlet temperature of 25 °C, a strain rate of 1000 s (stagnation reactor), and a residence time of 1 ms (PSR)...

Figure 26.5 Surface mole fractions of fuel and NO as functions of stagnation surface (solid curves) and PSR temper-atirre (dashed curves), for 28% inlet H2 in air (a) and 12% inlet H2 in air (b). The maximum temperature indicates adiabatic operation. The conditions are the same as in Fig. 26.4...

To solve a particular problem, we must also specify the process. For example, reversible adiabatic flow through a nozzle yields the following familiar expressions relating the properties at some point in the flow to the Mach number and the stagnation properties, i.e., the properties where the velocity is zero ... 

A wind tunnel is to be constructed to produce flow conditions of Mach 2.8 at Ix = -40°C and p = 0.05 atm. What is the stagnation temperature for these conditions What would be the adiabatic wall temperature for the laminar and turbulent portions of a boundary layer on a flat plate If a flat plate were installed... 

The solution to this equation is first obtained for the case of an adiabatic plate. By introducing a new dimensionless temperature profile in terms of the stagnation temperature T0,... 

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