End of the combustion temperature.

To facilitate the derivation of the equation, from which it will be possible to determine the temperature of the current T_z point z conditional end of the combustion, we spend some simplification of the indicator chart in the part, which displays the burning process. FIG. 9 given indicator diagrmma speed diesel engine.

 

Figure 9

Permissible simplification is estimated that in the beginning of the combustion TDC, assume that the combustion process is carried out on the mixed cycle, first the line v = const, then p = const. Therefore, instead of the diagram shown in FIG. 9, the shaded area, we consider the simplified chart racz^l zbb^l. The temperature of the end of the combustion Tz, we call the temperature at the point z.

All calculations were performed for 1 kg of fuel. Let Q_n lower calorific value of the fuel. Up to a point z reaches not all the heat the fuel, of the fuel is not yet time to burn and will burn out on the extension line of the heat during combustion enters the cooling system; part of the heat will be spent on the dissociation process, as due to the high temperature and pressure, some of the molecules of the combustion products will disintegrate. This shortfall is characterized by heat "heat emission coefficient" x. Therefore, the calculation does not take all the fuel calorific value, but only a portion equal to Q_н. For diesel engines, which are due to imperfect mixing phenomenon of burnout manifests itself more strongly as compared with gasoline engines and combustion itself takes place over a long period of time, the ratio is from 0.7 to 0.8; for gasoline = 0,85-0,95. By the time of the start of combustion (indicator diagram point) in the cylinder are residual from the previous cycle gas in the amount of Mr moles of the fresh charge in the number of moles of M1. These gases are heated to a temperature Tc, contain a quantity of heat equal to the number of moles per mole and the specific heat at a temperature that is

M _t (m c _v )_{T c} T _c + M _l (m c _v ^l )_{T c} T _c ,

where (m c _v )_{T c} и (m c _v ^l )_{T c} - average molar heat capacity at constant volume for a fresh charge of the combustion products at a temperature T_c. thus, before we have a number of combustion heat which is: Q_н + M _t (m c _v )_{T c} T _c + M _l (m c _v ^l )_{T c} T _c ,

After combustion in our diagrams point z of the gases in the cylinder is equal to the number M _t of the residual gases and the number of moles of M ₂ combustion. These gases are heated to a temperature T_z and contain equal amounts of heat.

(M _t + M ₂) (m c _v )_{T z} T _z

where (m c _v )_{T z} - average specific heat of combustion gases at a temperature T _z

The high-speed engines during the combustion gases expand (from point to point z¹ z indicator diagram), making mechanical work. In this work done by the gas consumed quantity of heat equal to.

A – L _z¹_{- z}

A – thermal equivalent of mechanical work equal kcal / kg;

L _z¹_{- z} - kgm, work prior expansion of the gases from the point z¹ to point z Assuming that the amount of heat in latent (calorific value of fuel), and physical condition (hot gas) until equal to the total heat of combustion (heat gases and the heat turned into pre-expansion operation) after combustion, combustion, we can write equation: Q_н + M _t (m c _v )_{T c} T _c + M _l (m c _v ^l )_{T c} T _c = A – L _z¹_{- z} +(M _t + M ₂) (m c _v )_{T z} T _z (32)

Work prior expansion of gases L _z¹_{- z} It is equal to the square z¹zl k

The indicator diagram. Area z¹zl k = zmol – z¹ mok; therefore, work L _z¹_{- z} = p _z V _z - p_с V _c кгм.

Designating = l, will have;

L _z¹_{- z} = p _z V _z - l p_с V _c.

From the characteristic equation, we have:

p _z V _z =(M _t + M ₂) 848,5 T _z

p_с V _c = (M _t + M₁)848,5 T _c.

hence

L _z¹_{- z} =848,5[ (M _t + M ₂) T _z – l (M _t +M _l ) T _c],

A – L _z¹_{- z} = 1,985[(M _t + M ₂) T _z – l (M _t +M _l ) T _c], (33)

where 1,985 = kcal / mole degree - there are the work of expansion of one mole of gas when it is heated to 10 ° C, expressed in kilocalories. Substituting (33) into the equation (32) and transferring all terms containing the factor T _{z ,} the right side of the equation, we have: Q_н + M _t (m c _v )_{T c} T _c + M _l (m c _v ^l )_{T c} T _c +1,985l (M _t + M₁) T _c = [(M _t + M ₂) (1,985+ m c _v )_{T z} ] T _z

Given that the number of moles of residual gases M_t is a few percent of the number of moles of M l fresh charge and molar heat capacity (m c_v) combustion products is not much different from the mole of a fresh charge of the specific heat, can without great error in the left side of the equation to consider the heat capacity of the same, and then we get: Q_н +(M _t + M _l)[ (m c _v ^l )_{T c} T _c +1,985l] T _c = (M _t + M ₂) (m c _p )_{T z} ] T _z

wherein the molar specific heat at constant pressure

(m c _p)= 1,985 +(m c _v).

Деля обе части уравнения на (M _t + M₁), получим:

+ (1,985l + (m c _v ^l )_{T c} T _c = (m c _p )_{T z} T _z,

Or

+ (1,985l + (m c _v ^l )_{T c} T _c = m (m c _p )_{T z} T _z,

 

where g = - residual gas ratio;

m = - the actual rate of molecular change.

For diesel engines the number of moles of the fresh charge М ₁ = a L ₀ therefore have the final form of the equation:

+ (1,985l + (m c _v ^l )_{T c} T _c = m (m c _p )_{T z} T _z, (35)

For high-speed diesels end of the combustion pressure p _z it depends on the method of mixing. With direct injection p _z = 80 85 ата, the vortex p _z = 50 60 ата, at the pre - p _z = 40 50 ата, knowing the p _z easy to set the value l = . Knowing the values of molar heat capacities (m c _v ^l )_{T c} and the fresh charge (m c _p )T _z combustion products from the equation (35 )

It determines the temperature of the T _z end of the combustion (at z indicator diagram). The situation in the indicator diagram of z the end of the theoretical combustion is defined by two coordinates P _z V _z , ratio

It is the degree of pre-expansion, and is denoted r,

r = .

To determine the value p take the characteristic equation for the moment of the end of the compression. Corresponds to the point with the indicator diagram, and for the moment the end of the burning - for point z.

p _z V _z = (M ₂+ M _t)848,5 T _z

p _с V _с = (M ₁+ M _t)848,5 T _с

dividing the first equation by the second, we have:

l r = m ; (36)

r = (37)

hence V _z = V _с

For thermal calculation gasoline engines or gas engine combustion equation (35) may be somewhat simplified.

r size for these engines is one, because these engines operate on the Otto principle, so l = m ; (38)

Substituting (38) into the equation (34) we have;

+ 1,985m T _c + (m c _v ^l )_{T c} T _c = m (m c _p )_{T z} T _z,

 

Moving the second term of the left side of his right-hand side, we get:

+ (m c _v ^l )_{T c} T _c = m [(m c _p )_{T z} -1,985] T _z,

as

(m c _p )- 1.985=(m c _v).

the + (m c _v ^l )_{T c} T _c = m (m c _p )_{T z} T _z, (39)

When calculating the carburettor engine should be noted that the charge contained in the fresh air and fuel vapor, so the number of moles of the fresh charge M ₁= a L₀ + , где - number of moles of vapor 1 kg fuel. The amount of the molecular weight m to the carburettor fuel is 100 - 104.

t is also necessary to take into account that the calculation of the carburettor engine at maximum power mode, the excess air ratio a 1(a = 0,9), and the need to provide for the shortage of heat according to the equation (31):

DQ =28700(1- a) L₀ ккал /кг,

For this case, the calculation of the carburettor engine, equation (39) takes the form:

+ (m c _v ^l )_{T c} T _c = m (m c _p )_{T z} T _z, (40)

Temperature T _z, As seen above indicated, carburettor engines reaches values up to 2700⁰ abc, in high-speed diesel engines, which depending on α carburetion of from 1,2 to 1,5 T z, will be relatively low, reaching a value of up to 2300⁰ abc.