CN104615580A - Fast predicting method for peak value electron concentration of returner flow field - Google Patents

Abstract

The invention provides a fast predicting method for the peak value electron concentration of a returner flow field. According to the method, an air flow total enthalpy is determined according to the incoming flow condition, and shock wave rear gas pressure is determined according to an isentropy relation; the gas static temperature and the component concentration of a stationary point position are solved; the pressure, the gas static temperature and the component concentration are solved to obtain the peak value electron concentration of the stationary point position; an euler equation is solved to obtain pressure distribution of the surface of a returner; the peak value electron concentration of the stationary point position and the pressure of the surface of the returner are solved to obtain the peak value electron concentration of the returner flow field. Compared with the prior art, on the premise of ensuring the result precision, the calculation cost is greatly reduced, the calculation efficiency is improved by ten times, and reliability is greatly improved.

Description

A kind of returner flow field peak electron density method for quick predicting

Technical field

The present invention relates to a kind of returner flow field peak electron density method for quick predicting, belong to hypersonic pneumatic physical technical field.

Background technology

Aircraft with hypersonic in the flight course of endoatmosphere, produce detached shock wave, kinetic transformation is interior energy, because temperature raises, causing aerochemistry to react or dissociation, ionization and surfacing ablation, around aircraft, form " plasma sheath ", greatly weakening causing the ability of aircraft reception or electromagnetic signals, even there will be communication signal time serious to interrupt, thus have influence on the normal flight of aircraft and the normal work of guidance system.Fully realizing the plasma regularity of distribution around aircraft, is the prerequisite of correct Prediction communication signal attenuation characteristic, has very important realistic meaning.

Current method of carrying out flow field electron density prediction is mainly carried out Flow Field Calculation by numerical simulation means and is completed, and needs to solve to describe the full N-S equation of polycomponent that returner reenters flowing.The method can provide returner and stream whole flow field electron density distribution everywhere, is a kind of method of meticulous depiction.But the multicomponent chemical reactive flowfield that existing various method for numerical simulation carries out Hypersonic reentry process solves larger the assessing the cost and time cost of needs consumption, often needs time a couple of days could obtain electron density Flow Field Distribution data.Research and analyse discovery, aerial signal communicating interrupt is analyzed, plasma circular frequency is the important parameter affecting signal interruption, if can provide flow field peak value circular frequency, even without whole flow field along number of passes according to also interrupting carrying out express-analysis and judgement to signal of communication.Rely on experimental analysis and numerical prediction for plasma prediction is main both at home and abroad, also there is no a kind of fast method carrying out peak electron density prediction.

Summary of the invention

Technology of the present invention is dealt with problems and is: for the deficiencies in the prior art, provides a kind of returner flow field peak electron density method for quick predicting, solves the problem that returner signal of communication interrupts express-analysis.

Technical solution of the present invention is:

A kind of returner flow field peak electron density method for quick predicting, comprises the following steps:

(1) according to inlet flow conditions determination air-flow total enthalpy h _s, and according to gaseous tension p after isentropic relation formula determination shock wave _s; Described inlet flow conditions comprises free stream Mach number M _∞, static temperature T _∞, static pressure p _∞;

(2) position, stationary point gas static temperature T, concentration of component c is solved _j;

(3) by pressure p _s, gas static temperature T, concentration of component c _j, solve and obtain position, stationary point peak electron density Ne _s;

(4) solve Eulerian equation and obtain returner surface pressure distribution p;

(5) by region, stationary point peak electron density Ne _s, returner surface pressing p solves and obtains returner flow field peak electron density.

Gas temperature T in step (2), concentration of component c _jdetermination mode as follows:

(2a) given initial gas static temperature and number of components density, solves following equation and obtains π _iwith Δ lnn:

$\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j\mathrm{\Δ}\ln n+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{\left(H_T^0\right)}_j/\mathrm{RT})\mathrm{\Δ}\ln T=(b_k^0-b_k)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{g}_j/\mathrm{RT}$

$\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_i+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j-n)\mathrm{\Δ}\ln n+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{H}_{\mathrm{Tj}}^0/\mathrm{RT})\mathrm{\Δ}\ln T=n-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{g}_j/\mathrm{RT}$

Wherein, n _jfor the number density of component j, g _jfor the free energy of component j, a _kj, a _ijbe respectively the related coefficient of component j about element k and i, bk be in every kg gas potpourri element k kilogram-molal quantity, for gas composition j is at the enthalpy of standard temperature (T=298.15K), π _ifor the number of element i takes advantage of the factor; L represents total number of element; M represents the sum of gas composition; N represents the number density summation of gas; R represents gas law constant, gets 8314J/kg-K;

(2b) by the π obtained in step (2a) _iwith Δ lnn, solve number of components density n _jwith concentration of component c _j, and then utilize concentration of component c _jwith enthalpy of the gases h _sreverse obtains current gas static temperature T:

$\mathrm{\Δ}\ln n_j=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{\mathrm{\π}}_i+\mathrm{\Δ}\ln n+{\left(H_T^0\right)}_j\mathrm{\Δ}\ln T/\mathrm{RT}-g_j/\mathrm{RT}$

$c_j=n_j{M}_j/\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{m}_j$

Wherein, m _jfor the molecular mass of component j;

(2c) formula in the current gas static temperature utilizing step (2b) to solve and number of components density and step (2a), solves the π at lower a moment _iwith Δ lnn, recycling π _isolve gas static temperature and the number of components density at lower a moment with Δ lnn, row iteration of going forward side by side calculates; Iterative computation meets arbitrary condition below and all will terminate:

(2c1) gas temperature that goes out of iterative computation and number of components density are less than 1% relative to the value change of last iterative;

(2c2) iterations reaches restriction iterative steps, and general restriction iterative steps is 20.

In step (3) by pressure p _s, gas static temperature T and concentration of component c _jobtain position, stationary point peak electron density Ne _sdetermination mode as follows:

Wherein, Π is Avogadro constant number; c _qfor c _ja subset; M _qit is the molecular weight of q component; M _jfor the molecular weight of a jth component; R is gas law constant.

Returner flow field peak electron density in step (5) to solve mode as follows:

Ne＝Ne _s·(p/p _s)。

The present invention's advantage compared with prior art:

(1) current carry out returner reenter communicating interrupt analyze time, need to obtain returner whole flow field electron density distribution by solving multicomponent chemical reaction Navier-Stokes equation, and this method moves the feature (position, stationary point peak electron density, stagnation pressure and wall pressure) close to equiulbrium flow by the large underflow of analysis returner, analyze and obtain region, stationary point peak electron density, and then provide whole flow field peak electron density, carry out returner and reenter communicating interrupt analysis.Compared to prior art, the present invention is under the prerequisite ensureing computational accuracy, and assess the cost and greatly reduce, counting yield improves 10 times, and reliability strengthens greatly.

Accompanying drawing illustrates:

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is computation model schematic diagram of the present invention;

Fig. 3 is that the present invention simulates the distribution of gained plasma;

Fig. 4 is method for quick predicting gained peak electron density of the present invention distribution;

Fig. 5 is that the present invention and prior art gained peak electron density contrast.

Embodiment

Below in conjunction with accompanying drawing, principle of work of the present invention and the course of work are further explained and are illustrated.

As shown in Figure 1, a kind of returner flow field of the present invention peak electron density method for quick predicting, comprises the following steps:

(1) according to inlet flow conditions determination air-flow total enthalpy h _s, and according to gaseous tension p after isentropic relation formula determination shock wave _s; Described inlet flow conditions comprises free stream Mach number M _∞, static temperature T _∞, static pressure p _∞;

Air-flow total enthalpy is determined by following formula:

$h_s=\mathrm{Cp}\·T_{\∞}+\frac{1}{2}{U}_{\∞}^2$

Wherein, C _prepresent gas specific heat at constant pressure; U _∞represent speed of incoming flow; T _∞represent static temperature.

Gaseous tension p after shock wave _sdetermination mode as follows:

$p_s=p_{01}\×{(\frac{2\mathrm{\γ}}{\mathrm{\γ}+1}{M}_{\∞}^2-\frac{\mathrm{\γ}-1}{\mathrm{\γ}+1})}^{-\frac{1}{\mathrm{\γ}-1}}\×{\left[\frac{(\mathrm{\γ}+1)M_{\∞}^2}{(\mathrm{\γ}-1)M_{\∞}^2+2}\right]}^{\frac{\mathrm{\γ}}{\mathrm{\γ}-1}}$

Wherein, p ₀₁represent shock wave front gaseous tension, γ is specific heats of gases ratios; M _∞represent free stream Mach number; p _∞represent static pressure.

(2) position, stationary point gas static temperature T, concentration of component c is solved _j;

Gas temperature T, concentration of component c _jdetermination mode as follows:

(2a) given initial gas static temperature and number of components density, solves following equation and obtains π _iwith Δ lnn:

$\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j\mathrm{\Δ}\ln n+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{\left(H_T^0\right)}_j/\mathrm{RT})\mathrm{\Δ}\ln T=(b_k^0-b_k)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{g}_j/\mathrm{RT}$

$\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_i+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j-n)\mathrm{\Δ}\ln n+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{H}_{\mathrm{Tj}}^0/\mathrm{RT})\mathrm{\Δ}\ln T=n-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{g}_j/\mathrm{RT}$ Wherein, n _jfor the number density of component j, g _jfor the free energy of component j, a _kj, a _ijbe respectively the related coefficient of component j about element k and i, b _kfor element k in every kg gas potpourri kilogram-molal quantity, for gas composition j is at the enthalpy of standard temperature (T=298.15K), π _ifor the number of element i takes advantage of the factor; L represents total number of element; M represents the sum of gas composition; N represents the number density summation of gas; R represents gas law constant, gets 8314G/kg.k;

(2b) by the π obtained in step (2a) _iwith Δ lnn, solve number of components density n _jwith concentration of component c _j, and then utilize concentration of component c _jwith enthalpy of the gases h _sreverse obtains current gas static temperature T:

$\mathrm{\Δ}\ln n_j=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{\mathrm{\π}}_i+\mathrm{\Δ}\ln n+{\left(H_T^0\right)}_j\mathrm{\Δ}\ln T/\mathrm{RT}-g_j/\mathrm{RT}$

$c_j=n_j{M}_j/\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{m}_j$

Wherein, m _jfor the molecular mass of component j;

(2c) formula in the current gas static temperature utilizing step (2b) to solve and number of components density and step (2a), solves the π at lower a moment _iwith Δ lnn, recycling π _isolve gas static temperature and the number of components density at lower a moment with Δ lnn, row iteration of going forward side by side calculates; Iterative computation meets arbitrary condition below and all will terminate:

(2c1) gas temperature that goes out of iterative computation and number of components density are less than 1% relative to the value change of last iterative;

(2c2) iterations reaches restriction iterative steps, and general restriction iterative steps is 20.

(3) by pressure p _s, gas static temperature T, concentration of component c _j, solve and obtain position, stationary point peak electron density Ne _s;

By pressure p _s, gas static temperature T and concentration of component c _jobtain position, stationary point peak electron density Ne _sdetermination mode as follows:

Wherein, Π is Avogadro constant number; c _qfor c _ja subset; M _qit is the molecular weight of q component; M _jfor the molecular weight of a jth component; R is gas law constant.

(4) solve Eulerian equation and obtain returner surface pressure distribution p;

(5) by region, stationary point peak electron density Ne _s, returner surface pressing p solves and obtains returner flow field peak electron density.

Returner flow field peak electron density in step (5) to solve mode as follows:

Ne＝Ne _s·(p/p _s)。

Below in conjunction with specific embodiment, the present invention is further explained:

The present invention is directed to returner to reenter profile and be analyzed.Returner has back taper solid of revolution profile blunt nosed greatly, and diameter of the large end is about 1.24m, total length 1.252m, as shown in Figure 2.Quick calculation method under comparative analysis 2 inlet flow conditions and method for numerical simulation gained peak electron density.Be height H=85km, Ma=26. and height H=55km, Ma=16 respectively, these two states are positioned at the initial stage of reentering and reenter latter stage, are the important references trajectory points judging communicating interrupt.

Fig. 3 gives numerical simulation gained two state flow field electron density distribution (left figure: height H=85km right figure: height H=55km).Can see for returner profile, its ambient electron Density Distribution has typical feature: the strong constricted zone in the large end is the most concentrated area of electron density, and windward side electron density is higher than lee face, and lee face still exists the electron density of larger amt.

Fig. 4 under providing 2 states around method for quick predicting gained aircraft of the present invention peak electron density distribution (left figure: height H=85km right figure: height H=55km).

Fig. 5 provides method for quick predicting of the present invention and method for numerical simulation gained windward side and lee face peak electron density and contrasts.Can see that method for quick predicting gained peak electron density of the present invention and method for numerical simulation gained meet better, method for quick predicting in position, the large end a little less than numerical simulation result, difference is within 50%, all numerical simulation result is greater than in other positions, maximum difference is within 3-5 times, be no more than half order of magnitude, meet design requirement.For crossing shoulder expansion area, cause wall pressure to reduce fast owing to crossing shoulder gas expansion, method for quick predicting gained electron density distribution of the present invention is lower than virtual condition herein.

Table 1 provides the institute's spended time contrast in two states of two kinds of distinct methods.

Table 1 two kinds of method contrasts consuming time (d: sky h: hour)

	H＝85km	H＝55km
			Method for numerical simulation	12d6h	10d6h
The present invention	1d	1d

Comprehensive above comparative analysis can obtain drawing a conclusion: method for quick predicting of the present invention can provide peak electron density distribution around returner faster, and gained electron density distribution differ with numerical simulation result meet design needs, can for signal of communication interruption initial analysis data supporting is provided.

The unexposed technology of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (3)

1. a returner flow field peak electron density method for quick predicting, is characterized in that comprising the following steps:

(1) according to inlet flow conditions determination air-flow total enthalpy h _s, and according to gaseous tension p after isentropic relation formula determination shock wave _s; Described inlet flow conditions comprises free stream Mach number M _∞, static temperature T _∞, static pressure p _∞;

(2) position, stationary point gas static temperature T, concentration of component c is solved _j;

(3) by pressure p _s, gas static temperature T, concentration of component c _j, solve and obtain position, stationary point peak electron density Ne _s;

(4) solve Eulerian equation and obtain returner surface pressure distribution p;

(5) by region, stationary point peak electron density Ne _s, returner surface pressing p solves and obtains returner flow field peak electron density.

2. a kind of returner flow field according to claim 1 peak electron density method for quick predicting, is characterized in that: the gas temperature T in described step (2), concentration of component c _jdetermination mode as follows:

(2a) given initial gas static temperature and number of components density, solves following equation and obtains π _iwith Δ ln n:

$\begin{array}{c}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_j+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j\mathrm{\Δ}\ln n+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{\left(H_T^0\right)}_j/\mathrm{RT})\mathrm{\Δ}\ln T=(b_k^0-b_k)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{kj}}{n}_j{g}_j/\mathrm{RT}\\ \underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{n}_j{\mathrm{\π}}_i+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j-n)\mathrm{\Δl\; n}+(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{H}_{\mathrm{Tj}}^0/\mathrm{RT})\mathrm{\Δ}\ln T=n-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{g}_j/\mathrm{RT}\end{array}$

Wherein, n _jfor the number density of component j, g _jfor the free energy of component j, a _kj, a _ijbe respectively the related coefficient of component j about element k and i, b _kfor element k in every kg gas potpourri kilogram-molal quantity, for gas composition j is at the enthalpy of standard temperature, π _ifor the number of element i takes advantage of the factor; L represents total number of element; M represents the sum of gas composition; N represents the number density summation of gas; R represents gas law constant, gets 8314J/kg-K;

(2b) by the π obtained in step (2a) _iwith Δ ln n, solve number of components density n _jwith concentration of component c _j, and then utilize concentration of component c _jwith enthalpy of the gases h _sreverse obtains current gas static temperature T:

$\mathrm{\Δ}\ln n_j=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{\mathrm{\π}}_i+\mathrm{\Δ}\ln n+{\left(H_T^0\right)}_j\mathrm{\Δ}\ln T/\mathrm{RT}-g_j/\mathrm{RT}$

$c_j=n_j{M}_j/\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{n}_j{m}_j$

Wherein, m _jfor the molecular mass of component j;

(2c) formula in the current gas static temperature utilizing step (2b) to solve and number of components density and step (2a), solves the π at lower a moment _iwith Δ ln n, recycling π _isolve gas static temperature and the number of components density at lower a moment with Δ ln n, row iteration of going forward side by side calculates; Iterative computation meets arbitrary condition below and all will terminate:

(2c1) gas temperature that goes out of iterative computation and number of components density are less than 1% relative to the value change of last iterative;

(2c2) iterations reaches restriction iterative steps, and general restriction iterative steps is 20.

3. a kind of returner flow field according to claim 1 peak electron density method for quick predicting, is characterized in that: the returner flow field peak electron density in described step (5) to solve mode as follows:

Ne＝Ne _s·(p/p _s)。