set.seed(123)

x <- function(){
return( data.frame( matrix(rnorm(10, 1, .5), ncol=2) ) )
}

set.seed(123)

x_improved <- function(sim_nr){
  df <- data.frame( matrix(rnorm(10, 1, .5), ncol=2) )  # simulate data
  sim_nr <- rep(sim_nr, length(df[,1])).                # add reference number
  df <- cbind(df, sim_nr)                               # bind columns
  return(df)
}

list_dataframes <- lapply(c(1,2,3), x_improved)         # create list of dataframes

df <- do.call("rbind", list_dataframes)                 # convert list to dataframe

> df
          X1        X2 sim_nr
1  0.4660881 0.1566533      1
2  0.8910125 1.4188935      1
3  0.4869978 1.0766866      1
4  0.6355544 0.4309315      1
5  0.6874804 1.6269075      1
6  1.2132321 1.3443201      2
7  0.8524643 1.2769588      2
8  1.4475628 0.9690441      2
9  1.4390667 0.8470187      2
10 1.4107905 0.8097645      2
11 0.6526465 0.4384457      3
12 0.8960414 0.7985576      3
13 0.3673018 0.7666723      3
14 2.0844780 1.3899826      3
15 1.6039810 0.9583155      3