CN114912227B - Non-steady-state similarity method for centripetal turbine - Google Patents
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Abstract
The invention provides a method for unsteady state similarity of a centripetal turbine, which combines the existing steady state similarity criterion and important unsteady state characteristics of the centripetal turbine to establish a time-varying similarity criterion number suitable for the unsteady state process of the turbine, wherein the time-varying similarity criterion number comprises a time-varying expansion ratio and a time-varying specific rotation speed; and determining a time scale under experimental conditions and a change rule of the input aerodynamic thermal conditions according to the consistency of the time-varying similarity criteria under dimensionless conditions, wherein the change rule comprises total inlet pressure, total inlet temperature, back pressure at an outlet and rotating speed. By adopting the method, the actual unsteady state process of the centripetal turbine can be better and accurately and effectively reflected by the unsteady state experiment, and the experiment cost is reduced.
Description
Technical Field
The invention provides a non-steady-state similarity method for a centripetal turbine, and belongs to the technical field of turbines.
Background
Turbines are an essential and important core component in engines, whose aerodynamic performance can significantly affect the operating state of the engine as well as the energy conversion efficiency. Turbines can be classified into axial flow turbines and centripetal turbines according to the intake mode. The centripetal turbine has the characteristics of simple structure, wider operation range and the like, and is widely applied to the fields of aerospace, vehicles, ships and the like.
Typically, the analysis and design system of the aerodynamic performance of the centripetal turbine is based on a steady state (steady state) operation, but the full operating envelope of the turbine also includes a special operating state that may deviate significantly from an unsteady state process, typically during start-up, braking, etc. For the related research of the transient characteristics of the turbine in the unstable state process, the state is still at the starting stage in China at present, foreign published documents are relatively few, and related experiments for the typical unstable state process of the centripetal turbine are needed to be carried out so as to fully and comprehensively grasp the performance of the turbine in the unstable state process.
In the related art, the empire university [1] has developed an unsteady turbine experiment of a turbocharger to study the effect of time-varying incoming flow conditions on the unsteady aerodynamic performance of the turbine. These experiments were performed at a pulsed air turbine laboratory bench, i.e. by adjusting the pulsing means to ensure the required non-steady state turbine inflow conditions. However, the similarity criteria adopted by the students of empire universities are based on steady state methods, and do not take into account similar scaling problems on the time scale, which results in significant differences in unsteady characteristics, particularly hysteresis effects, under high and low temperature conditions.
Related researches of China North engine institute [2] indicate that when parameters such as incoming flow temperature/pressure and the like are changed in a sinusoidal periodicity, a corresponding relation of time scales under different working environments can be established by combining St numbers (Strhouhal Number). The criterion number reflects the period time length of parameter change and the propagation velocity of working medium, and is defined as the ratio of the time sequence change frequency of pressure to the rotating speed. However, the typical radial inflow turbine unsteady process may not have a definite periodicity, nor is this similar method in terms of St numbers applicable.
At present, research on unsteady state similarity is still in a just-started stage, and a theory and a result which can be referred are difficult to find, so that the research is just a pain point for developing a turbine unsteady state experiment, and a similar method suitable for refining engineering is needed.
Disclosure of Invention
The invention aims to provide a method for similarity of unsteady performance of a centripetal turbine, which is used for guiding performance experiments of the centripetal turbine under laboratory conditions.
The technical means of the invention: combining the existing steady-state similarity criterion and important unsteady-state characteristics of the centripetal turbine, and establishing a time-varying similarity criterion number suitable for the unsteady-state process of the turbine, wherein the time-varying similarity criterion number comprises a time-varying expansion ratio and a time-varying specific rotating speed; and determining the time scale and the time-varying input aerodynamic thermodynamic conditions under the experimental conditions, wherein the time scale and the time-varying input aerodynamic thermodynamic conditions comprise total inlet pressure, total inlet temperature, outlet back pressure and rotating speed according to the consistency of the time-varying similarity criteria under the dimensionless conditions.
Parameters that affect turbine flow field flow and performance under steady state conditions under compressible, adiabatic, and neglecting the effects of gravity on the aerodynamic performance of a core turbine include:
Mechanical parameters: stage average diameter D, rotor speed n
Physical parameters of the fluid: gas constant R, dynamic viscosity coefficient mu, specific heat ratio gamma
State parameters of the flow: inlet total temperature T 1t, inlet total pressure p 1t, flow G, turbine outlet total pressure p 2t
Turbine characteristic parameters: efficiency eta, power P
The functional relation of the physical quantity is as follows:
η,P,G＝f(D,n,R,μ,γ,T1t,p1t,p2t)
in combination with the dimensional analysis method, the 11 physical quantities include 4 basic physical quantities in total, and a relational expression can be established with respect to the remaining 7 dimensionless criterion numbers:
the 7 dimensionless numbers of criteria include 3 dependent variables and 4 independent variables:
dependent variables: 1. efficiency eta 2 reduced power 3. Reduced flow/>
Independent variable:
1. Expansion ratio 2. Specific rotation speed/>
3. Specific heat ratio gamma 4 Reynolds number
Wherein, P ad is isentropic work, and the definition formula is as follows:
For non-steady state processes of a centripetal turbine, each aerodynamic thermal parameter may change over time, for any time-varying aerodynamic thermal parameter (including dimensionless numbers of criteria consisting of time-varying aerodynamic thermal parameters) Can be regarded as a function of the dimensionless time t *, i.e./>That is, the relation of the 7 criterion numbers can be written as:
In an actual experiment, a significant temperature difference may exist between high and low temperature working conditions (an actual working condition and an experimental working condition), so that consistency of the specific heat ratio similarity criterion under the whole unsteady non-dimensional time scale cannot be ensured, and the existing similarity criterion can be corrected by combining the specific heat ratio; in the range of the self-mode region of the turbine (Re >2× 5), the influence of the time sequence change of the Reynolds number Re on the turbine efficiency can be ignored to a certain extent.
After the simplification, the similarity relation is converted into:
The above-mentioned bold variables are all non-steady state time sequence variation functions with respect to dimensionless t *. In order to ensure the completeness of the method, a relational expression of the physical time reference t ref among different working conditions is further provided to complete dimension reduction.
The corresponding relation of the physical time reference t ref between the high-temperature working condition (subscript act) and the low-temperature working condition (subscript exp) is as follows:
on the other hand, considering the physical relationship between the references, the time reference t ref can be written as a relational expression about the composition of other references, namely, written as:
Wherein u ref represents a speed reference, L ref represents a length reference (any corresponding geometric dimension of two working conditions can be selected), gamma ref represents a specific heat reference, and T ref represents a temperature reference; k u represents a speed coefficient, k L represents a length coefficient, and the specific values of the two coefficients depend on the specific selection mode of the reference physical quantity; according to the similarity, the speed coefficient and the length coefficient between the high temperature working condition and the low temperature working condition which are similar to each other are consistent with the corresponding Mach number Ma.
As can be seen from the above relation, the physical time reference T ref can be expressed as a relation of the specific heat reference γ ref and the temperature reference T ref; according to the above assumption, if the difference of the reference specific heat between the high and low temperature conditions is negligible, the temperature reference T ref (the total inlet temperature usually selected as the non-steady state starting time in engineering) can directly represent the relation of the physical time reference T ref between different conditions.
To sum up, aiming at the unsteady-state similarity problem of the centripetal turbine, a similarity criterion under a dimensionless time scale is provided:
1. Expansion ratio 2. Specific rotation speed/>
Wherein, t represents time, plus a marked asterisk t * represents dimensionless time, p 1t is total pressure of the turbine inlet, and p 2t is total pressure of the turbine outlet; n represents the rotational speed at which the motor is rotated,Representing flow, P ad representing turbine isentropic work;
according to the total inlet temperature and total pressure, the total outlet pressure (or outlet back pressure) and the time sequence change rule of the rotating speed of the process A (such as a practical process) to be obtained and the total inlet temperature and total outlet pressure (or outlet back pressure) of the starting point of the process B (such as a practical process), all input parameters under the condition of the process B can be obtained by using the similar method, wherein the specific method is as follows:
Firstly, any corresponding time of the unsteady state processes A and B is selected as a starting time, and the total inlet temperature and the total outlet pressure (or outlet back pressure) at the time are regarded as a temperature reference quantity T ref and a pressure reference quantity p ref;
Step two, according to the temperature reference quantity T ref of the processes A and B, determining the corresponding relation of the time reference quantity T ref, so as to determine the time span of the processes A and B;
Where u ref represents a speed reference, L ref represents a length reference, γ ref represents a specific heat reference, and T ref represents a temperature reference; k u denotes a velocity coefficient, and k L denotes a length coefficient;
Thirdly, determining a time sequence change rule of the inlet total temperature and the outlet total pressure (or outlet back pressure) of the process B according to the consistency of the dimensionless inlet total temperature and the outlet total pressure (or outlet back pressure) in the process and the time sequence change of the inlet total temperature and the outlet total pressure (or outlet back pressure) of the process A;
(T1t(t*)/Tref)A＝(T1t(t*)/Tref)B
(p2t(t*)/pref)A＝(p2t(t*)/pref)B
or (p) 2(t*)/pref)A＝(p2(t*)/pref)B
And fourthly, determining the total inlet pressure of the process B and the time sequence change rule of the rotating speed according to the expansion ratio and the similarity criterion of the specific rotating speed, thereby obtaining all required input parameters.
The invention has the beneficial effects that: the unsteady state experiment can accurately and effectively reflect the actual turbine unsteady state process, and the experiment cost is reduced.
Drawings
FIG. 1 is a graph showing a comparison of a low temperature operating mode parameter curve and a high temperature operating mode parameter curve obtained by two similar modeling methods according to the embodiment;
FIG. 2a is a graph showing the maximum deviation of the example using a similar approach between unsteady and steady-state;
FIG. 2b is a graph comparing average deviations of the example using a method similar to that of the unsteady state and the steady state.
Detailed Description
In order to verify the unsteady state similar method, taking a typical unsteady state process of a certain turbine as an example, a commercial numerical simulation software ANSYS CFX is utilized to solve URANS equation sets, and the similarity precision of different similar methods is analyzed.
In the numerical simulation calculation, the turbulence model adopts an SST k-omega model, the space dispersion adopts a second-order windward format, and the time dispersion adopts a second-order Euler post-difference format. In the unsteady state numerical simulation process, the given inlet total temperature, inlet total pressure and rotating speed show periodic variation along with time, so that the average result of the corresponding phases of a plurality of periods can be conveniently obtained to improve the similar precision. The average value of the periodic variation of each parameter is consistent with the parameter of the design point, so that the working range of the turbine in the whole process is basically positioned in the actual working envelope of the turbine.
The time-varying boundary strip parameters corresponding to the low-temperature working conditions are obtained by adopting the similar method and the original steady-state similar method respectively. Based on the method, the high-temperature unsteady state process, the low-temperature unsteady state process obtained by modeling by adopting the similar method and the unsteady state numerical simulation of the low-temperature unsteady state process obtained by modeling by adopting the original similar method based on the steady state are completed, and the similar precision of the two methods is analyzed by comparing the parameter curves of the three unsteady state processes.
The comparison of the low temperature operating mode parameter curve and the high temperature operating mode parameter curve obtained by adopting the two similar modeling methods is shown in figure 1. Therefore, the fitting degree of the low-temperature working condition reduced power curve and the high-temperature working condition curve obtained by the unsteady state similar method is far higher than that of the steady state method, and the accuracy of the unsteady state similar method is proved.
In order to more intuitively compare the similarity accuracy of two similar methods, a definition of the maximum difference and the average difference between the shaft powers of the high and low temperature working conditions is given below.
Maximum deviation:
average deviation:
And adjusting the variation rule of the inlet parameters in the unsteady state process, completing similar calculation by the method, and comparing the difference of the folded power. Fig. 2a and 2b show the maximum deviation and the average deviation of the non-steady state and steady state similar method, and it can be seen that the similarity accuracy of the similar method is significantly improved compared with the original method, which proves the advantages of the similar method.
By adopting the similar method, the similar precision of the unsteady state process can be effectively ensured, the unsteady state performance of the turbine under the actual working condition and the deviation degree of the unsteady state process relative to the steady state can be accurately simulated through the centripetal turbine unsteady state experiment under the laboratory condition, and the experiment cost of the turbine unsteady state is greatly reduced.
The method can be widely applied to typical unsteady processes of various centripetal turbines, and the similarity criteria directly relate to the aerodynamic performance of the turbines in form, have definite physical meaning and have stronger engineering value.
When the unsteady state process involved is a process in which the time-varying solution condition is periodically changed or is regarded as a steady state process approximately, the method can also be degenerated into a periodic or steady state similar method, in other words, the periodic/steady state similar method is a special form of the unsteady state similar method.
Claims (1)
1. A method for unsteady state similarity of a centripetal turbine, which is characterized by comprising the following steps of: combining the existing steady-state similarity criterion and important unsteady-state characteristics of the centripetal turbine, and establishing a time-varying similarity criterion number suitable for the unsteady-state process of the turbine, wherein the time-varying similarity criterion number comprises a time-varying expansion ratio and a time-varying specific rotating speed; according to the consistency of time-varying similarity criteria under dimensionless conditions, determining time scales under experimental conditions and time-varying input aerodynamic thermal conditions, wherein the time-varying input aerodynamic thermal conditions comprise total inlet pressure, total inlet temperature, outlet back pressure and rotating speed;
The method specifically comprises the following steps:
The similarity criterion under the dimensionless time scale is proposed:
(1) Expansion ratio (2) Specific rotation speed/>
Wherein, t represents time, plus a marked asterisk t * represents dimensionless time, p 1t is total pressure of the turbine inlet, and p 2t is total pressure of the turbine outlet; n represents the rotational speed at which the motor is rotated,Representing flow, P ad representing turbine isentropic work;
According to the total inlet temperature and total pressure, total outlet pressure or outlet back pressure of an unstable state process A to be obtained and the time sequence change rule of the rotating speed, and the total inlet temperature and total outlet pressure or outlet back pressure of the starting point of the unstable state process B, an unstable state similar method is used, and all input parameters under the condition of the process B to be solved can be obtained, wherein the method specifically comprises the following steps:
Firstly, selecting any corresponding time of the unsteady state processes A and B as a starting time, wherein the total inlet temperature and the total outlet pressure or the outlet back pressure at the time are regarded as a temperature reference T ref and a pressure reference p ref;
Step two, according to the temperature reference quantity T ref of the non-steady-state processes A and B, determining the corresponding relation of the time reference quantity T ref, thereby determining the time span of the whole process;
Where u ref represents a speed reference, L ref represents a length reference, and T ref represents a temperature reference; k u denotes a velocity coefficient, and k L denotes a length coefficient;
thirdly, determining a time sequence change rule of the inlet total temperature and the outlet total pressure/back pressure in the process B according to the time sequence change of the inlet total temperature and the outlet total pressure or the outlet back pressure in the process A according to the consistency of the dimensionless inlet total temperature and the outlet total pressure or the outlet back pressure in the unsteady state process;
(T1t(t*)/Tref)A＝(T1t(t*)/Tref)B
(p2t(t*)/pref)A＝(p2t(t*)/pref)B
or (p) 2(t*)/pref)A＝(p2(t*)/pref)B
Step four, determining the total inlet pressure of the process B and the time sequence change rule of the rotating speed according to the similarity criteria of the expansion ratio and the specific rotating speed in the unsteady state process, so as to obtain all required input parameters;
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| CN113065206A (en) * | 2021-03-24 | 2021-07-02 | 北京航空航天大学 | Transition state control method and device, electronic equipment and storage medium |
| CN113962026A (en) * | 2021-10-26 | 2022-01-21 | 北京航空航天大学 | Method and device for simulating transition state performance of aviation gas turbine |
| CN113962027A (en) * | 2021-10-26 | 2022-01-21 | 北京航空航天大学 | Method and device for determining turbine similarity test conditions and storage medium |
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| DE102005017400A1 (en) * | 2005-04-15 | 2006-10-19 | Mtu Aero Engines Gmbh | Method for specifying turbine entry temperature of gas turbine in unsteady conditions involves determining by combination of turbine entry temperature in stationary mode and correction term |
| CN113065206A (en) * | 2021-03-24 | 2021-07-02 | 北京航空航天大学 | Transition state control method and device, electronic equipment and storage medium |
| CN113962026A (en) * | 2021-10-26 | 2022-01-21 | 北京航空航天大学 | Method and device for simulating transition state performance of aviation gas turbine |
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